tag:blogger.com,1999:blog-28238160270803912902024-03-05T07:12:52.084+01:00Miscellaneous Bicycle WisdomBicycle-related stuff that you may not find elsewhere on the netiikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.comBlogger26125tag:blogger.com,1999:blog-2823816027080391290.post-34943152664185534132023-03-23T13:41:00.007+01:002023-03-30T11:55:21.276+02:00Ultralight Mesh Rack<div style="text-align: left;">Plastic meshes obviously become my favorite material for bicycle carriers.</div><div style="text-align: left;"><br />After mesh handlebar bag and mesh under seat bag (see <a href="https://iikmisc.blogspot.com/2018/03/minimalist-eco-under-seat-bicycle-bag.html">here</a>), it's now time for<br />something bigger - a mesh rack. I hope it will be the revolutionary idea how to</div><div style="text-align: left;">carry your bicycle stuff with minimal weight containers. This front rack is made </div><div style="text-align: left;">of a bit sturdier, 1 mm thick mesh. Its dimensions are 40 x 30 cm and is attached</div><div style="text-align: left;">at one end to the front tube or brake cables and at the other end to the old style </div><div style="text-align: left;">Shimano derailleur cables which run outside the handlebar tape. Weight: 15 g. </div><div style="text-align: left;">You just put the bag or small rucksack (up to 15 L) in it. maybe secured by a </div><div style="text-align: left;">piece of string. If you don't have Shimano style cables, attach any kind of cable</div><div style="text-align: left;">to the drops of the handlebar. </div><div style="text-align: left;"><br /></div><div style="text-align: left;">On the other end of the bicycle you might attach something bigger - like a tent - </div><div style="text-align: left;">under the seat and you're good for a RTW trip. I will show this set-up shortly.</div><div class="separator" style="clear: both; text-align: center;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6qErd0ZrPtIoGBotKUl_7yJ2_8dwMt2RU1mSVkz-2NQLQhpEv_JYaeT_ZsTru89QiKE9sak_8gOfOyMZwAWoPy5tNLgZ4WhtUlAOyMFtKAwP_jd2M0FlbnTf-drAdxYWVhYYd2FChzDxkRECaH6y459vDY8ZYSjIZQtsh4RTMxVeTV_JNvfv37Qoy/s4000/IMG_20220527_170817.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="3000" data-original-width="4000" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg6qErd0ZrPtIoGBotKUl_7yJ2_8dwMt2RU1mSVkz-2NQLQhpEv_JYaeT_ZsTru89QiKE9sak_8gOfOyMZwAWoPy5tNLgZ4WhtUlAOyMFtKAwP_jd2M0FlbnTf-drAdxYWVhYYd2FChzDxkRECaH6y459vDY8ZYSjIZQtsh4RTMxVeTV_JNvfv37Qoy/w400-h300/IMG_20220527_170817.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;">Simple mesh rack ...</span></td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt23yrrYbP3abqamEX7013aZPmehkEeiNj7ZICofggJMsiNxZKA1au2VOvGxq7lKHzCMVwHsRtHWt3uijRSDId45nUY_S4wJ_zg--UrL5PofIxPMD6InAC_EyruWVoNJJKjzpySWHbHRkViRimQodNs07Sge79476CGqRVbmHM-K4vgsXK0BqOby3Z/s4000/IMG_20220528_073304.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="3000" data-original-width="4000" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt23yrrYbP3abqamEX7013aZPmehkEeiNj7ZICofggJMsiNxZKA1au2VOvGxq7lKHzCMVwHsRtHWt3uijRSDId45nUY_S4wJ_zg--UrL5PofIxPMD6InAC_EyruWVoNJJKjzpySWHbHRkViRimQodNs07Sge79476CGqRVbmHM-K4vgsXK0BqOby3Z/w400-h300/IMG_20220528_073304.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;"><span style="font-size: medium;">... with a bag in it.</span></td></tr></tbody></table><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8o3fWbZNAmZ3JbjAMX7VjRLBHJrGhdVngcgas3pYzbEco-k1ZtmLaZuKKOUgam5NWe7bhRgC63lyoJLv_ohwYmz0IanScfKHL3kiQV23Bok9_VMlrKDnUcyv5w3mkxcN6rUzOcIXLIMKTPd4u3xK0dp0r7qOTmQLzPfzM4J7FeyHMrA9eIElI_bX5/s4000/IMG_20220527_170735_1.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="3000" data-original-width="4000" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8o3fWbZNAmZ3JbjAMX7VjRLBHJrGhdVngcgas3pYzbEco-k1ZtmLaZuKKOUgam5NWe7bhRgC63lyoJLv_ohwYmz0IanScfKHL3kiQV23Bok9_VMlrKDnUcyv5w3mkxcN6rUzOcIXLIMKTPd4u3xK0dp0r7qOTmQLzPfzM4J7FeyHMrA9eIElI_bX5/w400-h300/IMG_20220527_170735_1.jpg" width="400" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJ350mSepHqDfShT0f7L8QOzv3ditNijVKadMRbnMdHwDt787TPmSUFlQQYBTW4pwAFQEKHIWwS5-Loz5wqHLYR_hlwqkSTjLtqpBur9Z6HVVotBhFV_mVNI4w7y4X24cs_zk7qcggpFO5S3OgaNm-uRoPSUFDJNMK-Il8XmlY-cjvK7a_A3xycOq6/s4000/IMG_20220903_191207.jpg" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="3000" data-original-width="4000" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjJ350mSepHqDfShT0f7L8QOzv3ditNijVKadMRbnMdHwDt787TPmSUFlQQYBTW4pwAFQEKHIWwS5-Loz5wqHLYR_hlwqkSTjLtqpBur9Z6HVVotBhFV_mVNI4w7y4X24cs_zk7qcggpFO5S3OgaNm-uRoPSUFDJNMK-Il8XmlY-cjvK7a_A3xycOq6/w400-h300/IMG_20220903_191207.jpg" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">... and with a 15 litre rucksack.</td></tr></tbody></table><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div style="text-align: left;"><br /></div>iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com1tag:blogger.com,1999:blog-2823816027080391290.post-84824907537392984832020-11-30T08:49:00.002+01:002020-11-30T08:49:56.396+01:00Evolution of screw drivers<div>Some people believe that Darwin's teory of evolution of living organisms is one of the major corner stones of human civilisation. Richard Dawkins went even further and defined a "meme", the generalization of the gene, as the driving force of the evolution of morality in human society. </div><div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhL9X-zoe7IPPLpiZHH6JaJBaqG4sbP6VooKtqAq9NF_pSuvgHe-itN4vyVkmG4o7BcpRO52LdKqBCl3eKNqCUV9NotjPbmHH-DycDIQYgR5JgRxn2nZGm8TF-KoDTPgqvbKuEZzd2GNuM/s800/ScrewDrivers.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="540" data-original-width="800" height="270" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhL9X-zoe7IPPLpiZHH6JaJBaqG4sbP6VooKtqAq9NF_pSuvgHe-itN4vyVkmG4o7BcpRO52LdKqBCl3eKNqCUV9NotjPbmHH-DycDIQYgR5JgRxn2nZGm8TF-KoDTPgqvbKuEZzd2GNuM/w400-h270/ScrewDrivers.JPG" width="400" /></a></div><br /><div><br /></div><div>In this post we go a few steps back and consider the evolution of non-living things - namely screwdrivers. The evolutionary trend is - as should be expected from this blog - towards minimizing weight and size and maximizing simplicity. The first three screw drivers from the top in the picture need no further explanation. The fourth screwdriver is part of a multitool that was destined to be cut along the red line (reducing its weight to 15 g), but luckily it was spared that miserable destiny by the following consideration.</div><div><br /></div><div>The fifth "screw driver" is actually a steel washer with the diameter 25 mm and thickness 1 mm. I filed it at the point A to produce a short flat part (not clearly visible in the picture) which acts as a flat screw driver. To be honest, this flat part is likely not even necessary. It works well with both flat and cross screw heads.</div><div><br /></div><div>The cut in the washer at the point B serves a totaly different purpose: it is used when trueing a bicycle wheel with bladed spokes (Mavic Ksyrium wheels for example) to hold the spoke and prevent it from turning. This cut thus makes this washer-screwdriver a multitool - with 3 g probably the world's lightest bicycle multitool. </div><div><br /></div>iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-18935702694651044132020-06-30T16:14:00.001+02:002021-01-19T09:23:19.309+01:00 Ultralight tripod (for smart phones)<div style="text-align: justify;">
Strictly speaking, tripod should not be a part of an ultralight cyclist's luggage - it's too awkward and heavy and there should always be a way to get away with improvisation. But, as we grow old, we realize that a small compromise is often more comfortable than strict principles. </div>
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So here is my shameless compromise to a tripod for a smart phone. It's made of two clothespins, padded with pieces of cardboard. It weights 12 g. It should be useful when shooting self portrets on a bike or using long exposures. Not to mention that on a cycling tour clothespins can be used for their original purpose, to hang out something to dry or generally to pin something.</div>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieDF3bel2NDM0EyKL2LnbtNRw0MncW4OAL6LQf4PjA8UVqZc7Sc6iEp5tc1tLeSj-y9CaOzjFKTkBGM4vP98oWdLf4MXCqVo7Gm3QslnJugh-e_2fwvifeB9LzQ78ilC994IsnQkR2LPg/s1600/P1010485.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="617" data-original-width="1024" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieDF3bel2NDM0EyKL2LnbtNRw0MncW4OAL6LQf4PjA8UVqZc7Sc6iEp5tc1tLeSj-y9CaOzjFKTkBGM4vP98oWdLf4MXCqVo7Gm3QslnJugh-e_2fwvifeB9LzQ78ilC994IsnQkR2LPg/s400/P1010485.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Clothespin "tripod" (actually a quadruped), front side.</td></tr>
</tbody></table>
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<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkVfRepQ0UghgQ4cf-11EDgDv-omOMgfnTxCHtW4uEgvPAAV0X8NcE4qDiLTkRMzd8gsSJvz4q4FdEeqDIUBtYVwLiOp8IfYXqNnZHH2ckbeNP_dXUQH8nRJ4yaB_xa02s1ngzsFvbxVc/s1600/P1010486.JPG" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="885" data-original-width="1024" height="276" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkVfRepQ0UghgQ4cf-11EDgDv-omOMgfnTxCHtW4uEgvPAAV0X8NcE4qDiLTkRMzd8gsSJvz4q4FdEeqDIUBtYVwLiOp8IfYXqNnZHH2ckbeNP_dXUQH8nRJ4yaB_xa02s1ngzsFvbxVc/s320/P1010486.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Clothespin "tripod" (actually a quadruped), rear side.</td></tr>
</tbody></table>
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<div style="text-align: justify;">The next episode of lightweight tripod is here. I resigned to the clothespins' tripod; it was too awkward to use, not very stable and too heavy (12g). The new version (4g) is here: take a plastic bottle, cut off a 3 cm strip from the middle part of it and cut two slots to hold your smartphone. I think this is the last step in the evolution of tripods and not even genetic manipulation could make it better.</div><div style="text-align: justify;"><br /></div><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4ROoLf6thIvOYvls1s7_KRIeYVYQQtBZT6SK8PxNij-x27-01f81eYv7jg8P8TJvjLAP6qoLmkZRhf-gA4a57a0JBotJwkeUgwC8xrVXeAPvfp5BP1pN_471rwWrI5K4Ap7PQxQzYP3E/s1024/tripod-1.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="735" data-original-width="1024" height="288" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4ROoLf6thIvOYvls1s7_KRIeYVYQQtBZT6SK8PxNij-x27-01f81eYv7jg8P8TJvjLAP6qoLmkZRhf-gA4a57a0JBotJwkeUgwC8xrVXeAPvfp5BP1pN_471rwWrI5K4Ap7PQxQzYP3E/w400-h288/tripod-1.JPG" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Cut a part of plastic bottle</td></tr></tbody></table><br /><div style="text-align: justify;"><br /></div><div style="text-align: justify;"><br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto;"><tbody><tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKfqyRITSYR11UKdO5h_w5z908TyqKy-CVCm2FlCuu7Z7ZCldGul_6Cn44PaS7xQiA-NA1V6ulpyY0n_ckBGPSftAawAXMgLdgtUDfX8wN2qdmL0wTUuRW8v2MJARPD0l-ySd4gzzSH_8/s1024/tripod-2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="683" data-original-width="1024" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjKfqyRITSYR11UKdO5h_w5z908TyqKy-CVCm2FlCuu7Z7ZCldGul_6Cn44PaS7xQiA-NA1V6ulpyY0n_ckBGPSftAawAXMgLdgtUDfX8wN2qdmL0wTUuRW8v2MJARPD0l-ySd4gzzSH_8/w400-h266/tripod-2.JPG" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Make 2 slots in the plastics to hold the phone.</td></tr></tbody></table><br />iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com1tag:blogger.com,1999:blog-2823816027080391290.post-85508063679984373362019-02-14T08:48:00.001+01:002019-05-28T10:57:03.636+02:00The ultimate wheel calculator <br />
<div style="margin: 8.25pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 90%;">The usual, boring, spoke length calculators allow only the same number of
hub holes, rim holes and number </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">of<span style="letter-spacing: -0.8pt;"> </span>spokes.<span style="letter-spacing: -0.2pt;"> </span>What<span style="letter-spacing: -0.75pt;"> </span>a<span style="letter-spacing: -0.75pt;"> </span>waste<span style="letter-spacing: -0.75pt;"> </span>of<span style="letter-spacing: -0.75pt;"> </span>life<span style="letter-spacing: -0.75pt;"> </span>and<span style="letter-spacing: -0.75pt;"> </span>inteligence!<span style="letter-spacing: -0.2pt;"> </span>This<span style="letter-spacing: -0.75pt;"> </span>is<span style="letter-spacing: -0.75pt;"> </span>a<span style="letter-spacing: -0.75pt;"> </span>thing<span style="letter-spacing: -0.8pt;"> </span>of<span style="letter-spacing: -0.75pt;"> </span>the<span style="letter-spacing: -0.75pt;"> </span>past.<span style="letter-spacing: -0.2pt;"> </span>The<span style="letter-spacing: -0.75pt;"> </span>times<span style="letter-spacing: -0.75pt;">
</span>when<span style="letter-spacing: -0.75pt;"> </span>it<span style="letter-spacing: -0.75pt;"> </span>was<span style="letter-spacing: -0.75pt;"> </span>important
</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 90%;">that a <span style="letter-spacing: 0.1pt;">good </span>bicycle
wheel lasts few decades without breaking a spoke are definitely gone. The new
trend is </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">esthetics<span style="letter-spacing: -0.85pt;"> </span>above<span style="letter-spacing: -0.8pt;"> </span>functionality;<span style="letter-spacing: -0.75pt;"> </span>and<span style="letter-spacing: -0.85pt;"> </span>this<span style="letter-spacing: -0.8pt;"> </span>requires<span style="letter-spacing: -0.85pt;">
</span>to<span style="letter-spacing: -0.8pt;"> </span><span style="letter-spacing: 0.1pt;">be</span><span style="letter-spacing: -0.8pt;"> </span>able<span style="letter-spacing: -0.85pt;"> </span>to<span style="letter-spacing: -0.8pt;"> </span>build<span style="letter-spacing: -0.85pt;"> </span>a<span style="letter-spacing: -0.8pt;"> </span>wheel<span style="letter-spacing: -0.8pt;"> </span>with<span style="letter-spacing: -0.85pt;"> </span>any<span style="letter-spacing: -0.8pt;"> </span>kind<span style="letter-spacing: -0.85pt;"> </span>of<span style="letter-spacing: -0.8pt;"> </span>combination<span style="letter-spacing: -0.8pt;"> </span>of holes and spokes. This is where I jump in. What you will get
here is a spoke length calculator (as well as wheel building motivator) for any
number and combination of holes, spokes, cross<span style="letter-spacing: 0.45pt;">
</span>patterns.</span></div>
<br />
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">I’ll give more detail. <span style="letter-spacing: -0.15pt;">Parts </span>of
the wheel are hub, rim and spokes. The hub has <span style="letter-spacing: -0.2pt;">two </span>flanges, left and right, each<span style="letter-spacing: -0.8pt;"> </span>having<span style="letter-spacing: -0.75pt;"> </span>half<span style="letter-spacing: -0.75pt;"> </span>the<span style="letter-spacing: -0.8pt;"> </span>total<span style="letter-spacing: -0.75pt;"> </span>number<span style="letter-spacing: -0.75pt;">
</span>of<span style="letter-spacing: -0.8pt;"> </span>hub<span style="letter-spacing: -0.75pt;"> </span>spoke<span style="letter-spacing: -0.75pt;"> </span>holes.<span style="letter-spacing: -0.2pt;"> </span>This<span style="letter-spacing: -0.75pt;"> </span>also<span style="letter-spacing: -0.8pt;"> </span>defines<span style="letter-spacing: -0.75pt;">
</span>the<span style="letter-spacing: -0.75pt;"> </span>left<span style="letter-spacing: -0.75pt;"> </span>and<span style="letter-spacing: -0.8pt;"> </span>right<span style="letter-spacing: -0.75pt;"> </span>side<span style="letter-spacing: -0.75pt;"> </span>of<span style="letter-spacing: -0.8pt;"> </span>the<span style="letter-spacing: -0.75pt;"> </span>wheel.
The<span style="letter-spacing: -0.7pt;"> </span>holes<span style="letter-spacing: -0.7pt;"> </span>on<span style="letter-spacing: -0.7pt;"> </span>the<span style="letter-spacing: -0.7pt;"> </span>left<span style="letter-spacing: -0.7pt;"> </span>and<span style="letter-spacing: -0.65pt;"> </span>right<span style="letter-spacing: -0.7pt;"> </span>flange<span style="letter-spacing: -0.7pt;"> </span>are<span style="letter-spacing: -0.7pt;"> </span>o</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "Arial Unicode MS"; mso-fareast-font-family: "Arial Unicode MS"; mso-font-width: 95%;">ff</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">set<span style="letter-spacing: -0.65pt;"> </span><span style="letter-spacing: -0.15pt;">by</span><span style="letter-spacing: -0.7pt;"> </span>an<span style="letter-spacing: -0.7pt;"> </span>angle;<span style="letter-spacing: -0.7pt;"> </span>if<span style="letter-spacing: -0.65pt;"> </span>that<span style="letter-spacing: -0.7pt;"> </span>wouldn’t<span style="letter-spacing: -0.7pt;"> </span><span style="letter-spacing: 0.1pt;">be</span><span style="letter-spacing: -0.7pt;"> </span>the<span style="letter-spacing: -0.7pt;"> </span>case,<span style="letter-spacing: -0.65pt;"> </span><span style="letter-spacing: -0.15pt;">we</span><span style="letter-spacing: -0.7pt;"> </span>could<span style="letter-spacing: -0.7pt;"> </span>not<span style="letter-spacing: -0.65pt;"> </span>have </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 90%;">radial
spokes on both sides of the wheel. The spoke holes in the rim, however, are
less obviously divided to left<span style="letter-spacing: -0.15pt;"> </span>and<span style="letter-spacing: -0.1pt;"> </span>right<span style="letter-spacing: -0.15pt;"> </span>and<span style="letter-spacing: -0.15pt;"> </span>it<span style="letter-spacing: -0.1pt;"> </span>is<span style="letter-spacing: -0.15pt;"> </span>important<span style="letter-spacing: -0.15pt;"> </span>not<span style="letter-spacing: -0.15pt;"> </span>to<span style="letter-spacing: -0.1pt;"> </span>confuse<span style="letter-spacing: -0.15pt;">
</span>the<span style="letter-spacing: -0.15pt;"> </span>total<span style="letter-spacing: -0.1pt;"> </span>number<span style="letter-spacing: -0.15pt;">
</span>of<span style="letter-spacing: -0.15pt;"> </span>rim<span style="letter-spacing: -0.15pt;"> </span>holes<span style="letter-spacing: -0.1pt;"> </span>with<span style="letter-spacing: -0.15pt;"> </span>the<span style="letter-spacing: -0.15pt;"> </span>number<span style="letter-spacing: -0.15pt;"> </span>corresponding </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">just<span style="letter-spacing: -0.6pt;"> </span>to<span style="letter-spacing: -0.6pt;"> </span>one<span style="letter-spacing: -0.6pt;"> </span>side<span style="letter-spacing: -0.6pt;"> </span>of<span style="letter-spacing: -0.6pt;"> </span>the<span style="letter-spacing: -0.6pt;"> </span>wheel.<span style="letter-spacing: 0.15pt;"> </span>Further,<span style="letter-spacing: -0.55pt;">
</span>spokes<span style="letter-spacing: -0.6pt;"> </span>might<span style="letter-spacing: -0.6pt;"> </span><span style="letter-spacing: 0.1pt;">be</span><span style="letter-spacing: -0.6pt;"> </span>inclined<span style="letter-spacing: -0.55pt;">
</span>out<span style="letter-spacing: -0.6pt;"> </span>of<span style="letter-spacing: -0.6pt;"> </span>the<span style="letter-spacing: -0.6pt;"> </span>radial<span style="letter-spacing: -0.6pt;"> </span>direction<span style="letter-spacing: -0.6pt;">
</span>for<span style="letter-spacing: -0.6pt;"> </span>some<span style="letter-spacing: -0.55pt;"> </span>angle<span style="letter-spacing: -0.6pt;"> </span>-
</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 90%;">this is usually expressed as a cross-number <span style="letter-spacing: 0.35pt;">C, </span>the number of spokes on one hub flange
that a certain spoke </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">crosses.<span style="letter-spacing: 0.45pt;"> </span>Radial<span style="letter-spacing: -0.3pt;"> </span>spokes<span style="letter-spacing: -0.35pt;"> </span>don’t<span style="letter-spacing: -0.3pt;"> </span>cross<span style="letter-spacing: -0.3pt;"> </span>any<span style="letter-spacing: -0.35pt;"> </span>other<span style="letter-spacing: -0.3pt;"> </span>spoke,<span style="letter-spacing: -0.3pt;"> </span>so<span style="letter-spacing: -0.3pt;"> </span>they<span style="letter-spacing: -0.35pt;"> </span>have<span style="letter-spacing: -0.3pt;"> </span>cross<span style="letter-spacing: -0.3pt;"> </span>number<span style="letter-spacing: -0.3pt;"> </span>C<span style="letter-spacing: -1.05pt;"> </span>=<span style="letter-spacing: -0.7pt;"> </span>0.<span style="letter-spacing: 0.45pt;"> </span>When<span style="letter-spacing: -0.3pt;"> </span>C<span style="letter-spacing: -0.8pt;"> </span>is<span style="letter-spacing: -0.35pt;"> </span>not<span style="letter-spacing: -0.3pt;"> </span>0<span style="letter-spacing: -0.35pt;"> </span><span style="letter-spacing: -0.15pt;">we </span>might<span style="letter-spacing: -0.95pt;"> </span>have<span style="letter-spacing: -0.9pt;"> </span><span style="letter-spacing: -0.2pt;">two</span><span style="letter-spacing: -0.9pt;"> </span>kinds<span style="letter-spacing: -0.9pt;"> </span>of<span style="letter-spacing: -0.9pt;"> </span>spokes<span style="letter-spacing: -0.9pt;"> </span>on<span style="letter-spacing: -0.9pt;"> </span>the<span style="letter-spacing: -0.9pt;"> </span>same<span style="letter-spacing: -0.95pt;"> </span>side<span style="letter-spacing: -0.9pt;"> </span>of<span style="letter-spacing: -0.9pt;"> </span>the<span style="letter-spacing: -0.9pt;"> </span>wheel:<span style="letter-spacing: -0.45pt;">
</span>leading<span style="letter-spacing: -0.9pt;"> </span>spokes<span style="letter-spacing: -0.9pt;"> </span>and<span style="letter-spacing: -0.9pt;"> </span>trailing<span style="letter-spacing: -0.9pt;"> </span>spokes.<span style="letter-spacing: -0.4pt;">
</span>The<span style="letter-spacing: -0.9pt;"> </span>first </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 90%;">ones are inclined clockwise, the others counter-clockwise. And <span style="letter-spacing: -0.15pt;">finaly, </span>you might not want to (or could
not) </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;">use all the holes in the hub <span style="letter-spacing: -0.15pt;">or </span>in
the rim. <span style="letter-spacing: -0.15pt;">We </span>will consider all of
these<span style="letter-spacing: -0.5pt;"> </span>possibilities.</span></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYtGFv7KRUDDC1ddkR9TJ7kNB5LuPx10Msclb7QTZxXtcu3DaJTBcbe4C0D9xUcAFUydPKi0eWuSvGZmUohhBGq6u3R688uSuIGgVReLtsgeQCSuan55eEtL4Gkiex7EpUMVZJmO42uKg/s1600/wheel.bmp" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="459" data-original-width="492" height="298" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYtGFv7KRUDDC1ddkR9TJ7kNB5LuPx10Msclb7QTZxXtcu3DaJTBcbe4C0D9xUcAFUydPKi0eWuSvGZmUohhBGq6u3R688uSuIGgVReLtsgeQCSuan55eEtL4Gkiex7EpUMVZJmO42uKg/s320/wheel.bmp" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-fareast-font-family: "Times New Roman";">Figure 1. Schematical model of a Wheel.</span></td></tr>
</tbody></table>
<div style="line-height: 8.15pt; margin: 5.2pt 0cm 0pt 63.4pt; mso-line-height-rule: exactly; text-align: justify;">
<span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-fareast-font-family: "Times New Roman";"><br /></span></div>
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span style="font-family: "times new roman";">
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 95%;">Figure<span style="letter-spacing: -0.6pt;"> </span>1<span style="letter-spacing: -0.55pt;"> </span>shows<span style="letter-spacing: -0.55pt;"> </span>a<span style="letter-spacing: -0.55pt;"> </span>wheel<span style="letter-spacing: -0.55pt;"> </span>schematicaly.<span style="letter-spacing: 0.2pt;"> </span>Point<span style="letter-spacing: -0.55pt;"> </span>O<span style="letter-spacing: -1.35pt;"> </span>is<span style="letter-spacing: -0.55pt;"> </span>the<span style="letter-spacing: -0.55pt;"> </span>center<span style="letter-spacing: -0.55pt;">
</span>of<span style="letter-spacing: -0.55pt;"> </span>the<span style="letter-spacing: -0.55pt;"> </span>wheel.<span style="letter-spacing: 0.2pt;"> </span>Line<span style="letter-spacing: -0.55pt;"> </span><span style="letter-spacing: 0.4pt;">HR</span><span style="letter-spacing: -1.4pt;"> </span>represents<span style="letter-spacing: -0.55pt;"> </span>a<span style="letter-spacing: -0.55pt;"> </span>radial<span style="letter-spacing: -0.55pt;"> </span>spoke </span><span lang="EN-US" style="font-family: "arial";">that<span style="letter-spacing: -0.65pt;"> </span>goes<span style="letter-spacing: -0.6pt;"> </span>through<span style="letter-spacing: -0.65pt;">
</span>hole<span style="letter-spacing: -0.6pt;"> </span>H<span style="letter-spacing: -1.2pt;"> </span>in<span style="letter-spacing: -0.6pt;"> </span>the<span style="letter-spacing: -0.65pt;"> </span>hub<span style="letter-spacing: -0.6pt;"> </span>and<span style="letter-spacing: -0.65pt;"> </span>hole<span style="letter-spacing: -0.6pt;"> </span>R<span style="letter-spacing: -1.55pt;"> </span>in<span style="letter-spacing: -0.6pt;"> </span>the<span style="letter-spacing: -0.65pt;"> </span>rim<span style="letter-spacing: -0.6pt;"> </span>and<span style="letter-spacing: -0.65pt;"> </span>has<span style="letter-spacing: -0.6pt;"> </span>inclination<span style="letter-spacing: -0.6pt;"> </span>angles<span style="letter-spacing: -0.65pt;">
</span>α<span style="letter-spacing: -1.65pt;"> </span>=<span style="letter-spacing: -0.95pt;"> </span>β<span style="letter-spacing: -1.45pt;"> </span>=<span style="letter-spacing: -0.9pt;"> </span>0<span style="letter-spacing: -0.8pt;"> </span>to<span style="letter-spacing: -0.6pt;"> </span>the<span style="letter-spacing: -0.65pt;"> </span>x
<span style="mso-font-width: 95%;">axis.<span style="letter-spacing: 0.5pt;"> </span>If<span style="letter-spacing: -0.25pt;"> </span>the<span style="letter-spacing: -0.25pt;"> </span>effective<span style="letter-spacing: -0.3pt;"> </span>rim<span style="letter-spacing: -0.25pt;"> </span>radius<span style="letter-spacing: -0.25pt;"> </span>is<span style="letter-spacing: -0.3pt;"> </span>R<i style="mso-bidi-font-style: normal;"><sub>r</sub><span style="letter-spacing: -0.25pt;"> </span></i>=<span style="letter-spacing: -0.55pt;"> </span>OR,<span style="letter-spacing: -0.25pt;"> </span>and<span style="letter-spacing: -0.25pt;"> </span>hub-hole<span style="letter-spacing: -0.25pt;"> </span>radius<span style="letter-spacing: -0.25pt;">
</span>is<span style="letter-spacing: -0.3pt;"> </span>R<i style="mso-bidi-font-style: normal;"><sub>h</sub><span style="letter-spacing: -0.35pt;"> </span></i>=<span style="letter-spacing: -0.6pt;"> </span><span style="letter-spacing: 0.35pt;">OH,</span><span style="letter-spacing: -0.2pt;"> </span>then<span style="letter-spacing: -0.25pt;"> </span>the<span style="letter-spacing: -0.3pt;"> </span>length<span style="letter-spacing: -0.25pt;">
</span>of<span style="letter-spacing: -0.3pt;"> </span>radial<span style="letter-spacing: -0.25pt;"> </span>spoke </span>would<span style="letter-spacing: -0.65pt;"> </span><span style="letter-spacing: 0.1pt;">be</span><span style="letter-spacing: -0.65pt;"> </span>S<sub>0</sub><span style="letter-spacing: -0.9pt;"> </span>=<span style="letter-spacing: -1pt;"> </span>R<i style="mso-bidi-font-style: normal;"><sub>r </sub><span style="letter-spacing: 1.25pt;">- </span></i><span style="letter-spacing: 0.15pt;">R<i style="mso-bidi-font-style: normal;"><sub>h</sub></i>.</span><span style="letter-spacing: -0.05pt;"> </span>Line<span style="letter-spacing: -0.65pt;"> </span>AB<span style="letter-spacing: -1.3pt;"> </span>represents<span style="letter-spacing: -0.65pt;"> </span>non-radial<span style="letter-spacing: -0.65pt;"> </span>spoke.<span style="letter-spacing: -0.05pt;"> </span>It’s<span style="letter-spacing: -0.65pt;"> </span>starting<span style="letter-spacing: -0.65pt;">
</span>inclination<span style="letter-spacing: -0.65pt;"> </span>angle<span style="letter-spacing: -0.65pt;"> </span>is <span style="mso-font-width: 95%;">α and
ending inclination is <span style="letter-spacing: 0.25pt;">β. </span>Note that AB
is a projection of the spoke to the plane <span style="letter-spacing: 0.1pt;">xy.
</span><span style="letter-spacing: -0.15pt;">We </span>have to<span style="letter-spacing: -1pt;"> </span>take into account that spoke has a
component in z direction. If H<i style="mso-bidi-font-style: normal;"><sub>z</sub>
</i>is a dimension from the hub flange to the </span>center of the rim (figure
2), then the spoke length is straightforward to<span style="letter-spacing: 0.75pt;"> </span>calculate:</span></span></span><br />
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span style="font-family: "times new roman";">
</span></div>
<div style="margin: 4.7pt 0cm 0pt;">
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="mso-spacerun: yes;"> </span>L<i style="mso-bidi-font-style: normal;"><sub>AB </sub></i><span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;">2</span><i style="mso-bidi-font-style: normal;"><span style="mso-spacerun: yes;"> </span></i>= (B<i style="mso-bidi-font-style: normal;"><sub>x</sub> </i>− A<i style="mso-bidi-font-style: normal;"><sub>x</sub></i>)<span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;">2 </span>+ (B<i style="mso-bidi-font-style: normal;"><sub>y</sub> </i>− A<i style="mso-bidi-font-style: normal;"><sub>y</sub></i>)<span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;">2 </span>+ H<em><sub><span style="font-size: x-small;">z</span></sub></em><span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;">2 </span>= R<span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;">2 </span>+ R<span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;">2 </span>+ H<em><sub><span style="font-size: x-small;">z</span></sub></em><span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;">2 </span>− 2R<i style="mso-bidi-font-style: normal;"><sub>r</sub></i>R<i style="mso-bidi-font-style: normal;"><sub>h</sub> </i>cos (β − α)</span></div>
<div style="margin: 4.7pt 0cm 0pt;">
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><br /></span></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWsv2UwCvUf_ugpLDwGGZkw5pHfD3dTf6xqzWJzmKVr6RJUDozghSGqsBDUvNJyj_OWYX-L1akhzl3C3TtWIqLnriONU9hPf_7voAHzBmGgP3XTSsH7kocBhqY2grC-zoLmFCbP4rc4UQ/s1600/hub.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="391" data-original-width="456" height="273" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhWsv2UwCvUf_ugpLDwGGZkw5pHfD3dTf6xqzWJzmKVr6RJUDozghSGqsBDUvNJyj_OWYX-L1akhzl3C3TtWIqLnriONU9hPf_7voAHzBmGgP3XTSsH7kocBhqY2grC-zoLmFCbP4rc4UQ/s320/hub.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-fareast-font-family: "Times New Roman"; mso-font-width: 105%;">Figure 2. Hub with indicated dimension H<i style="mso-bidi-font-style: normal;"><span style="mso-text-raise: -6.5pt; position: relative; top: 6.5pt;">z </span></i>.</span></td></tr>
</tbody></table>
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"></span></span><div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-fareast-font-family: "Times New Roman"; mso-font-width: 105%;"><span style="color: black; font-family: "times new roman";">
<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;"><span style="color: black;">The<span style="letter-spacing: -0.55pt;"> </span></span><span style="color: black;">unique</span><span style="color: black;"><span style="letter-spacing: -0.5pt;">
</span><span style="letter-spacing: -0.2pt;">way</span><span style="letter-spacing: -0.5pt;"> </span></span><span style="color: black;">to</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">describe</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">a</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">general</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">wheel</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">is</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">to</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">assign</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">starting</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">hole</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">in</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">hub</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">A</span><span style="letter-spacing: -1.45pt;"><span style="color: black;"> </span></span><span style="color: black;">and</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">ending</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">hole in</span><span style="letter-spacing: -0.3pt;"><span style="color: black;">
</span></span><span style="color: black;">the</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><span style="color: black;">rim</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><span style="color: black;">B</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">to</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">every</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><span style="color: black;">spoke.</span><span style="color: black;"><span style="letter-spacing: 0.45pt;"> </span><span style="letter-spacing: -0.15pt;">We</span><span style="letter-spacing: -0.25pt;"> </span></span><span style="color: black;">define</span><span style="letter-spacing: -0.25pt;"><span style="color: black;">
</span></span><span style="color: black;">the</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">parameters</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><span style="color: black;">of</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">wheel:</span><span style="letter-spacing: 0.4pt;"><span style="color: black;"> </span></span><span style="color: black;">H</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>h</sub><span style="letter-spacing: -0.25pt;"> </span></span></i><span style="color: black;">is</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><span style="color: black;">number</span><span style="letter-spacing: -0.25pt;"><span style="color: black;">
</span></span><span style="color: black;">of</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><span style="color: black;">hub</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><span style="color: black;">holes</span><span style="letter-spacing: -0.25pt;"><span style="color: black;"> </span></span><b style="mso-bidi-font-weight: normal;"><span style="color: black;">in<span style="letter-spacing: -0.65pt;"> </span></span><span style="color: black;">one
flange</span><span style="letter-spacing: -1.35pt;"><span style="color: black;"> </span></span></b><span style="color: black;">of</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">hub,</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">H</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>r</sub><span style="letter-spacing: -0.7pt;"> </span></span></i><span style="color: black;">the</span><span style="color: black;"><span style="letter-spacing: -0.8pt;">
</span><b style="mso-bidi-font-weight: normal;">total<span style="letter-spacing: -1.3pt;"> </span></b></span><span style="color: black;">number</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">of</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">rim</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">holes</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">(i.e.</span><span style="letter-spacing: -0.05pt;"><span style="color: black;"> </span></span><span style="color: black;">all</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">holes</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">in</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">rim),</span><span style="letter-spacing: -0.75pt;"><span style="color: black;"> </span></span><span style="color: black;">and</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">S</span><span style="letter-spacing: -1.4pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">number</span><span style="letter-spacing: -0.8pt;"><span style="color: black;">
</span></span><span style="color: black;">of</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">spokes </span><b style="mso-bidi-font-weight: normal;"><span style="color: black;">in<span style="letter-spacing: -0.7pt;"> </span></span><span style="color: black;">one</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">flange</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span></b><span style="color: black;">of</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">hub.</span><span style="letter-spacing: 0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">With</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">these</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">parameters</span><span style="color: black;"><span style="letter-spacing: -0.35pt;"> </span><span style="letter-spacing: -0.15pt;">we</span><span style="letter-spacing: -0.35pt;"> </span></span><span style="color: black;">build</span><span style="letter-spacing: -0.35pt;"><span style="color: black;">
</span></span><span style="color: black;">one</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">side</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">-</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">left</span><span style="color: black;"><span style="letter-spacing: -0.35pt;"> </span><span style="letter-spacing: -0.15pt;">or</span><span style="letter-spacing: -0.35pt;"> </span></span><span style="color: black;">right</span><span style="letter-spacing: -0.35pt;"><span style="color: black;">
</span></span><span style="color: black;">-</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">of</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.4pt;"><span style="color: black;"> </span></span><span style="color: black;">wheel.</span><span style="letter-spacing: 0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">Number</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">of
spokes</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">on</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">left</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">and</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">right</span><span style="letter-spacing: -0.35pt;"><span style="color: black;">
</span></span><span style="color: black;">side</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">of</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">wheel</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">might</span><span style="color: black;"><span style="letter-spacing: -0.35pt;"> </span><span style="letter-spacing: 0.1pt;">be</span><span style="letter-spacing: -0.35pt;"> </span></span><span style="color: black;">di</span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "Arial Unicode MS"; mso-fareast-font-family: "Arial Unicode MS"; mso-font-width: 95%;"><span style="color: black;">ff</span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;"><span style="color: black;">erent;<span style="letter-spacing: -0.25pt;"> </span></span><span style="color: black;">if</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">that</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">is</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">case,</span><span style="color: black;"><span style="letter-spacing: -0.35pt;"> </span><span style="letter-spacing: -0.15pt;">we</span><span style="letter-spacing: -0.3pt;"> </span></span><span style="color: black;">use</span><span style="letter-spacing: -0.35pt;"><span style="color: black;"> </span></span><span style="color: black;">notation</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">S</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>l</sub><span style="letter-spacing: -0.35pt;"> </span></span></i><span style="color: black;">and</span><span style="letter-spacing: -0.3pt;"><span style="color: black;">
</span></span><span style="letter-spacing: 0.2pt;"><span style="color: black;">S<i style="mso-bidi-font-style: normal;"><sub>r</sub></i></span><span style="color: black;">.
</span></span></span><span style="color: black;"><span lang="EN-US" style="font-family: "arial"; letter-spacing: -0.2pt;">For</span><span lang="EN-US" style="font-family: "arial"; letter-spacing: -0.75pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span style="color: black;">each<span style="letter-spacing: -0.7pt;"> </span></span><span style="color: black;">spoke</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">i</span><span style="letter-spacing: -2.5pt;"><span style="color: black;"> </span></span><span style="color: black;">,</span><span style="letter-spacing: -2.55pt;"><span style="color: black;"> </span></span><span style="color: black;">(i</span><span style="letter-spacing: -1.7pt;"><span style="color: black;"> </span></span><span style="color: black;">=</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">1,</span><span style="letter-spacing: -2.55pt;"><span style="color: black;"> </span></span><span style="color: black;">2,</span><span style="letter-spacing: -2.5pt;"><span style="color: black;"> </span></span><span style="color: black;">...,</span><span style="color: black;"><span style="letter-spacing: -2.55pt;"> </span><span style="letter-spacing: 0.25pt;">S)</span><span style="letter-spacing: -0.85pt;"> </span><span style="letter-spacing: -0.15pt;">we</span><span style="letter-spacing: -0.7pt;"> </span></span><span style="color: black;">note</span><span style="color: black;"><span style="letter-spacing: -0.7pt;"> </span><span style="letter-spacing: -0.2pt;">two</span><span style="letter-spacing: -0.75pt;"> </span></span><span style="color: black;">indexes:</span><span style="letter-spacing: -0.05pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">number</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">of</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">hub</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">hole</span><span style="letter-spacing: -0.75pt;"><span style="color: black;"> </span></span><span style="color: black;">A</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>i</sub><span style="letter-spacing: -0.75pt;"> </span></span></i><span style="color: black;">and</span><span style="letter-spacing: -0.7pt;"><span style="color: black;">
</span></span><span style="color: black;">the</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">number</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">of </span><span style="mso-font-width: 95%;"><span style="color: black;">the<span style="letter-spacing: -0.5pt;"> </span></span><span style="color: black;">rim</span><span style="letter-spacing: -0.45pt;"><span style="color: black;"> </span></span><span style="color: black;">hole</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="letter-spacing: 0.15pt;"><span style="color: black;">B<i style="mso-bidi-font-style: normal;"><sub>i</sub></i></span><span style="color: black;">. </span></span><span style="color: black;"><span style="letter-spacing: -0.15pt;">We</span><span style="letter-spacing: -0.5pt;"> </span></span><span style="color: black;">count</span><span style="letter-spacing: -0.45pt;"><span style="color: black;"> </span></span><span style="color: black;">hub</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">and</span><span style="letter-spacing: -0.45pt;"><span style="color: black;"> </span></span><span style="color: black;">rim</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">holes</span><span style="letter-spacing: -0.45pt;"><span style="color: black;"> </span></span><span style="color: black;">in</span><span style="letter-spacing: -0.45pt;"><span style="color: black;"> </span></span><span style="color: black;">a</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">counter-clockwise</span><span style="letter-spacing: -0.45pt;"><span style="color: black;"> </span></span><span style="color: black;">direction</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">starting</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">at</span><span style="letter-spacing: -0.45pt;"><span style="color: black;"> </span></span><span style="color: black;">position</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">β</span><span style="letter-spacing: -1.3pt;"><span style="color: black;"> </span></span><span style="color: black;">=</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">α</span><span style="letter-spacing: -1.55pt;"><span style="color: black;"> </span></span><span style="color: black;">=</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">0 with</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">hole</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">number</span><span style="letter-spacing: -0.45pt;"><span style="color: black;">
</span></span><span style="color: black;">1.</span><span style="letter-spacing: 0.1pt;"><span style="color: black;"> </span></span><span style="color: black;">Index</span><span style="letter-spacing: -0.45pt;"><span style="color: black;"> </span></span><span style="color: black;">B</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>i</sub><span style="letter-spacing: -0.5pt;"> </span></span></i><span style="color: black;">could</span><span style="letter-spacing: -0.5pt;"><span style="color: black;">
</span></span><span style="color: black;">have</span><span style="letter-spacing: -0.45pt;"><span style="color: black;"> </span></span><span style="color: black;">zeros,</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">negative</span><span style="letter-spacing: -0.45pt;"><span style="color: black;">
</span></span><span style="color: black;">numbers,</span><span style="color: black;"><span style="letter-spacing: -0.5pt;"> </span><span style="letter-spacing: -0.15pt;">or</span><span style="letter-spacing: -0.45pt;"> </span></span><span style="color: black;">numbers</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">bigger</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">then</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">H</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>r</sub><span style="letter-spacing: -0.35pt;"> </span></span></i><span style="color: black;">when</span><span style="letter-spacing: -0.5pt;"><span style="color: black;">
</span></span><span style="color: black;">C</span><span style="letter-spacing: -1.25pt;"><span style="color: black;"> </span></span><span style="color: black;">></span><span style="letter-spacing: -1.6pt;"><span style="color: black;"> </span></span><span style="color: black;">1. This</span><span style="letter-spacing: -0.8pt;"><span style="color: black;">
</span></span><span style="color: black;">is</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">OK</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">when</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">calculatig</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">spoke</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">length,</span><span style="letter-spacing: -0.8pt;"><span style="color: black;">
</span></span><span style="color: black;">but</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">for</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">hole</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">count</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">it</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">is</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">more</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">practical</span><span style="letter-spacing: -0.8pt;"><span style="color: black;">
</span></span><span style="color: black;">to</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">have</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">only</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">positive numbers</span><span style="letter-spacing: -0.15pt;"><span style="color: black;"> </span></span><span style="color: black;">in</span><span style="letter-spacing: -0.1pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.15pt;"><span style="color: black;"> </span></span><span style="color: black;">range</span><span style="letter-spacing: -0.1pt;"><span style="color: black;"> </span></span><span style="color: black;">1</span><span style="letter-spacing: -0.15pt;"><span style="color: black;"> </span></span><span style="color: black;">to</span><span style="letter-spacing: -0.1pt;"><span style="color: black;"> </span></span><span style="letter-spacing: 0.2pt;"><span style="color: black;">H<i style="mso-bidi-font-style: normal;"><sub>r</sub></i></span><span style="color: black;">;</span></span><span style="letter-spacing: -0.05pt;"><span style="color: black;"> </span></span><span style="color: black;">therefore</span><span style="color: black;"><span style="letter-spacing: -0.15pt;"> we</span><span style="letter-spacing: -0.1pt;"> </span></span><span style="color: black;">might</span><span style="letter-spacing: -0.15pt;"><span style="color: black;"> </span></span><span style="color: black;">add</span><span style="letter-spacing: -0.1pt;"><span style="color: black;"> </span></span><span style="color: black;">H</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>r</sub><span style="letter-spacing: 0.05pt;"> </span></span></i><span style="color: black;">to</span><span style="letter-spacing: -0.15pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.1pt;"><span style="color: black;"> </span></span><span style="color: black;">zero</span><span style="color: black;"><span style="letter-spacing: -0.15pt;">
or</span><span style="letter-spacing: -0.1pt;"> </span></span><span style="color: black;">negative</span><span style="letter-spacing: -0.15pt;"><span style="color: black;"> </span></span><span style="color: black;">number</span><span style="letter-spacing: -0.1pt;"><span style="color: black;">
</span></span><span style="color: black;">and</span><span style="letter-spacing: -0.15pt;"><span style="color: black;"> </span></span><span style="color: black;">subtract</span><span style="letter-spacing: -0.15pt;"><span style="color: black;"> </span></span><span style="color: black;">H</span><i style="mso-bidi-font-style: normal;"><sub><span style="color: black;">r</span></sub><span style="color: black;">
</span></i></span><span style="color: black;">form</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">numbers</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">greater</span><span style="letter-spacing: -0.55pt;"><span style="color: black;">
</span></span><span style="color: black;">then</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="letter-spacing: 0.2pt;"><span style="color: black;">H<i style="mso-bidi-font-style: normal;"><sub>r</sub></i></span><span style="color: black;">.</span></span><span style="letter-spacing: 0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">Using</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">notations</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">∆α</span><span style="letter-spacing: -1.6pt;"><span style="color: black;"> </span></span><span style="color: black;">=</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">2π/H</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>h</sub><span style="letter-spacing: -0.5pt;"> </span></span></i><span style="color: black;">and</span><span style="letter-spacing: -0.55pt;"><span style="color: black;">
</span></span><span style="color: black;">∆β</span><span style="letter-spacing: -1.35pt;"><span style="color: black;"> </span></span><span style="color: black;">=</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">2π/H</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>r</sub><span style="letter-spacing: -0.45pt;"> </span></span></i><span style="color: black;">for</span><span style="letter-spacing: -0.5pt;"><span style="color: black;">
</span></span><span style="color: black;">angle</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">segments</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">in</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">the
hub and rim respectfully, </span><span style="letter-spacing: -0.15pt;"><span style="color: black;">we </span></span><span style="color: black;">have
the</span><span style="letter-spacing: 0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">equation:</span></span></span></span></span></span><br />
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";">
<br /><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 115%;"><span style="color: black;"> L</span><i style="mso-bidi-font-style: normal;"><sub><span style="color: black;">i</span></sub><span style="color: black;"> </span><span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;"><span style="color: black;">2</span></span></i><span style="color: black;">= R</span><span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;"><span style="color: black;">2 </span></span><span style="color: black;">+ R</span><span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;"><span style="color: black;">2 </span></span><span style="color: black;">+ H</span><span style="mso-text-raise: 7.0pt; position: relative; top: -7pt;"><span style="color: black;">2 </span></span><span style="color: black;">− 2R</span><i style="mso-bidi-font-style: normal;"><sub><span style="color: black;">r</span></sub></i><span style="color: black;">R</span><i style="mso-bidi-font-style: normal;"><sub><span style="color: black;">h</span></sub><span style="color: black;"> </span></i><span style="color: black;">cos (∆β(B</span><i style="mso-bidi-font-style: normal;"><sub><span style="color: black;">i</span></sub><span style="color: black;"> </span></i><span style="color: black;">− 1) − ∆α(A</span><i style="mso-bidi-font-style: normal;"><sub><span style="color: black;">i</span></sub><span style="color: black;"> </span></i><span style="color: black;">− 1))</span></span></span></span></span></div>
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<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";">
</span></span></span><br />
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<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";"><span style="color: black;"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">which
defines spoke length for any spoke </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-fareast-font-family: "Times New Roman";">i </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">and any possible wheel composition.</span></span></span></span></span></div>
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<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";">
<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;"><span style="color: black;">The key point is to define indexes A</span><i style="mso-bidi-font-style: normal;"><sub><span style="color: black;">i</span></sub><span style="color: black;">
</span></i><span style="color: black;">and </span><span style="letter-spacing: 0.15pt;"><span style="color: black;">B<i style="mso-bidi-font-style: normal;"><sub>i</sub></i></span><span style="color: black;">.
</span></span><span style="letter-spacing: -0.15pt;"><span style="color: black;">We </span></span><span style="color: black;">can define them
individually, without calculation, ”by hand”.</span><span style="letter-spacing: -0.5pt;"><span style="color: black;">
</span></span><span style="color: black;">Automatism</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">is,</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">however,</span><span style="letter-spacing: -0.95pt;"><span style="color: black;">
</span></span><span style="color: black;">much</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">appreciated,</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">especially</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">in</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">later</span><span style="color: black;"><span style="letter-spacing: -0.95pt;"> </span><span style="letter-spacing: -0.15pt;">years</span><span style="letter-spacing: -0.95pt;"> </span></span><span style="color: black;">of</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">your</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">life.</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">That</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">is</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">why</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">I</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">wrote
a</span><span style="letter-spacing: -1.05pt;"><span style="color: black;"> </span></span><span style="color: black;">program</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">wheel</span><span style="letter-spacing: -1.25pt;"><span style="color: black;"> </span></span><span style="color: black;">that</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">calculates</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">indexes</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">A</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>i</sub><span style="letter-spacing: -1.1pt;"> </span></span></i><span style="color: black;">and</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="letter-spacing: 0.15pt;"><span style="color: black;">B<i style="mso-bidi-font-style: normal;"><sub>i</sub></i></span><span style="color: black;">,</span></span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">spoke</span><span style="letter-spacing: -1pt;"><span style="color: black;">
</span></span><span style="color: black;">lengths,</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">draws</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">a</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">wheel</span><span style="letter-spacing: -0.95pt;"><span style="color: black;"> </span></span><span style="color: black;">and</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">makes</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">a</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">finite</span><span style="letter-spacing: -1pt;"><span style="color: black;"> </span></span><span style="color: black;">element </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span style="color: black;">model<span style="letter-spacing: 0.65pt;"> </span></span><span style="color: black;">for</span><span style="letter-spacing: 0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: 0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">calculation</span><span style="letter-spacing: 0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">of</span><span style="letter-spacing: 0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">stresses</span><span style="letter-spacing: 0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">in</span><span style="letter-spacing: 0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: 0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">wheel.</span></span></span></span></span></div>
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<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";">
<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;"><span style="color: black;">Indexes<span style="letter-spacing: -0.55pt;"> </span></span><span style="color: black;">A</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>i</sub><span style="letter-spacing: -0.6pt;"> </span></span></i><span style="color: black;">and</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">B</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>i</sub><span style="letter-spacing: -0.6pt;"> </span></span></i><span style="color: black;">are</span><span style="letter-spacing: -0.55pt;"><span style="color: black;">
</span></span><span style="color: black;">calculated</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">as</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">follows.</span><span style="color: black;"><span style="letter-spacing: 0.3pt;">
</span><span style="letter-spacing: -0.15pt;">We</span><span style="letter-spacing: -0.55pt;"> </span></span><span style="color: black;">would</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">prefer</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">spokes</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">to</span><span style="color: black;"><span style="letter-spacing: -0.55pt;"> </span><span style="letter-spacing: 0.1pt;">be</span><span style="letter-spacing: -0.55pt;"> </span></span><span style="color: black;">equally</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">distributed</span><span style="letter-spacing: -0.5pt;"><span style="color: black;"> </span></span><span style="color: black;">over</span><span style="letter-spacing: -0.55pt;"><span style="color: black;"> </span></span><span style="color: black;">the </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span style="color: black;">hub,<span style="letter-spacing: -0.7pt;"> </span></span><span style="color: black;">with</span><span style="letter-spacing: -0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">constant</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">angle</span><span style="letter-spacing: -0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">segment</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">∆γ</span><span style="color: black;"><span style="letter-spacing: -1.55pt;"> </span><span style="mso-font-width: 120%;">=<span style="letter-spacing: -1.55pt;"> </span></span><span style="letter-spacing: 0.15pt;">2π/S.</span><span style="letter-spacing: -0.05pt;"> </span><span style="letter-spacing: -0.15pt;">We</span><span style="letter-spacing: -0.65pt;"> </span></span><span style="color: black;">first</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">find</span><span style="letter-spacing: -0.65pt;"><span style="color: black;"> </span></span><span style="mso-font-width: 120%;"><span style="color: black;">A<i style="mso-bidi-font-style: normal;"><sub>i</sub><span style="letter-spacing: -1.4pt;"> </span></i></span><span style="color: black;">=</span><span style="color: black;"><span style="letter-spacing: -1.55pt;">
</span><span style="letter-spacing: 0.25pt;">j,</span><span style="letter-spacing: -1.1pt;"> </span></span></span><span style="color: black;">i.e.</span><span style="letter-spacing: -0.05pt;"><span style="color: black;"> </span></span><span style="color: black;">a</span><span style="letter-spacing: -0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">hole</span><span style="color: black;"><span style="letter-spacing: -0.7pt;"> </span><span style="mso-font-width: 120%;">j<span style="letter-spacing: -2pt;"> </span></span></span><span style="color: black;">in</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">hub</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">which</span><span style="letter-spacing: -0.65pt;"><span style="color: black;"> </span></span><span style="color: black;">has</span><span style="letter-spacing: -0.7pt;"><span style="color: black;"> </span></span><span style="color: black;">the closest angle to the angle (i − 1)∆γ
of i-th</span><span style="letter-spacing: 1.3pt;"><span style="color: black;"> </span></span><span style="color: black;">spoke:</span></span></span></span></span></div>
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<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 110%;"><span style="color: black;"> A<i style="mso-bidi-font-style: normal;"><sub>i</sub><span style="letter-spacing: 0.05pt;"> </span></i></span><span style="color: black;">=</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span><span style="color: black;">MIN</span><i style="mso-bidi-font-style: normal;"><span style="color: black;"><sub>j</sub><span style="letter-spacing: 0.4pt;"> </span></span></i><span style="color: black;">|(i</span><span style="letter-spacing: -1.6pt;"><span style="color: black;"> </span></span></span><span style="color: black;"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 105%;">−<span style="letter-spacing: -1.45pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 110%;">1)∆γ<span style="letter-spacing: -1.15pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 105%;">−<span style="letter-spacing: -1.45pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 110%;">(j<span style="letter-spacing: -1.1pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 105%;">−<span style="letter-spacing: -1.45pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 110%;">1)∆α|,<span style="mso-tab-count: 1;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 120%;">j<span style="letter-spacing: -0.55pt;"> </span></span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 110%;"><span style="color: black;">=<span style="letter-spacing: 0.1pt;"> </span></span><span style="color: black;">1,</span><span style="letter-spacing: -1.85pt;"><span style="color: black;"> </span></span></span><span style="color: black;"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 105%;">...,<span style="letter-spacing: -1.75pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 110%;">H<i style="mso-bidi-font-style: normal;"><sub>h</sub></i></span></span></span></span></div>
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";">
<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span style="color: black; font-family: "times new roman";"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span style="color: black;">In similar manner, we
would find </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-fareast-font-family: "Times New Roman";"><span style="color: black;">B</span><i style="mso-bidi-font-style: normal;"><sub><span style="color: black;">i</span></sub><span style="color: black;"> </span></i><span style="color: black;">= k</span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span style="color: black;">:</span></span></span></span></span></span></span></div>
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";">
<span style="color: black;"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Sans"; mso-font-width: 105%;"> B</span><i style="mso-bidi-font-style: normal;"><sub><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "Times New Roman"; mso-font-width: 105%;">i</span></sub></i><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "arial"; letter-spacing: 0.6pt;"> </span></i><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Georgia; mso-font-width: 105%;">=<span style="letter-spacing: 0.25pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 105%;">MIN</span><i style="mso-bidi-font-style: normal;"><sub><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "Times New Roman"; mso-font-width: 105%;">k</span></sub></i><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "arial"; letter-spacing: 0.8pt;">
</span></i><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Serif"; mso-font-width: 105%;">|</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Sans"; mso-font-width: 105%;">ϕ<span style="letter-spacing: -1.1pt;"> </span></span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Georgia; mso-font-width: 105%;"><span style="color: black;">+<span style="letter-spacing: -0.35pt;"> </span></span><span style="color: black;">(</span></span><span style="color: black;"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Sans"; mso-font-width: 105%;">i<span style="letter-spacing: -1.1pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Serif"; mso-font-width: 105%;">−<span style="letter-spacing: -1.1pt;"> </span></span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Georgia; mso-font-width: 105%;"><span style="color: black;">1<span style="letter-spacing: -0.35pt;"> </span></span><span style="color: black;">+</span><span style="color: black;"><span style="letter-spacing: -0.3pt;"> </span><span style="letter-spacing: 0.1pt;">(</span></span></span><span style="color: black;"><span lang="EN-US" style="font-family: "arial"; letter-spacing: 0.1pt;">−</span><span lang="EN-US" style="font-family: "arial"; letter-spacing: 0.1pt;">1)</span><i style="mso-bidi-font-style: normal;"><sup><span lang="EN-US" style="font-family: "arial"; letter-spacing: 0.1pt;">i</span></sup></i><sup><span lang="EN-US" style="font-family: "arial"; letter-spacing: 0.1pt;">+1</span></sup><span lang="EN-US" style="font-family: "arial"; letter-spacing: 0.1pt;">C</span><span lang="EN-US" style="font-family: "arial"; letter-spacing: 0.1pt;">)∆</span><span lang="EN-US" style="font-family: "arial"; letter-spacing: 0.1pt;">γ</span><span lang="EN-US" style="font-family: "arial"; letter-spacing: -0.6pt;"> </span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Serif"; mso-font-width: 105%;">−<span style="letter-spacing: -1.15pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Georgia; mso-font-width: 105%;">(</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Sans"; mso-font-width: 105%;">k<span style="letter-spacing: -0.8pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Serif"; mso-font-width: 105%;">−<span style="letter-spacing: -1.15pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Georgia; mso-font-width: 105%;">1)∆</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Sans"; mso-font-width: 105%;">β</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Serif"; mso-font-width: 105%;">|</span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Sans"; mso-font-width: 105%;"><span style="color: black;">,<span style="mso-tab-count: 1;"> </span></span><span style="color: black;">k</span><span style="letter-spacing: -0.3pt;"><span style="color: black;"> </span></span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Georgia; mso-font-width: 105%;"><span style="color: black;">=<span style="letter-spacing: 0.2pt;"> </span></span><span style="color: black;">1</span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Sans"; mso-font-width: 105%;"><span style="color: black;">,<span style="letter-spacing: -1.75pt;"> </span></span><span style="color: black;">...,</span><span style="letter-spacing: -1.7pt;"><span style="color: black;">
</span></span><span style="color: black;">H</span></span><i style="mso-bidi-font-style: normal;"><sub><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "Times New Roman"; mso-font-width: 105%;"><span style="color: black;">r</span></span></sub></i></span></span></span></div>
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<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";">
<span style="color: black;"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Sans";">ϕ<span style="letter-spacing: -1.85pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Georgia;">=<span style="letter-spacing: -1.05pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "DejaVu Sans";">π/H</span><i style="mso-bidi-font-style: normal;"><sub><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "Times New Roman";">h</span></sub></i><i style="mso-bidi-font-style: normal;"><span lang="EN-US" style="font-family: "arial"; letter-spacing: -0.85pt;"> </span></i></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span style="color: black;">is<span style="letter-spacing: -0.8pt;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">offset</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">angle</span><span style="letter-spacing: -0.75pt;"><span style="color: black;"> </span></span><span style="color: black;">between</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">holes</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">on</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">left</span><span style="letter-spacing: -0.75pt;"><span style="color: black;"> </span></span><span style="color: black;">and</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">right</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">flange</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">of</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">hub. </span><span style="color: black;"><span style="letter-spacing: -0.15pt;">We</span><span style="letter-spacing: -0.8pt;"> </span></span><span style="color: black;">must</span><span style="letter-spacing: -0.8pt;"><span style="color: black;"> </span></span><span style="color: black;">add</span><span style="letter-spacing: -0.75pt;"><span style="color: black;"> </span></span><span style="color: black;">this angle</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">when</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">calculating</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">right</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">side</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">of</span><span style="letter-spacing: -0.9pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span><span style="color: black;">wheel,</span><span style="letter-spacing: -0.85pt;"><span style="color: black;"> </span></span></span><b><span lang="EN-US" style="font-family: "arial";"><span style="color: black;">but<span style="letter-spacing: -1.25pt;"> </span></span><span style="color: black;">not</span><span style="letter-spacing: -1.25pt;"><span style="color: black;"> </span></span><span style="color: black;">for</span><span style="letter-spacing: -1.3pt;"><span style="color: black;"> </span></span><span style="color: black;">the</span><span style="letter-spacing: -1.25pt;"><span style="color: black;"> </span></span><span style="color: black;">left</span><span style="letter-spacing: -1.3pt;"><span style="color: black;">
</span></span><span style="color: black;">side</span></span></b><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span style="color: black;">.<span style="letter-spacing: -0.15pt;"> </span></span></span></span></span></span></div>
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<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";"></span></span></span><div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";"><strong>
</strong></span></span></span></div>
<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";"><span style="color: black; font-family: "times new roman";">
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<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;">Example<span style="letter-spacing: -0.45pt;"> </span>1</span></b><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;">.<span style="letter-spacing: 0.65pt;"> </span>Let’s<span style="letter-spacing: -0.1pt;"> </span>first<span style="letter-spacing: -0.1pt;"> </span>give<span style="letter-spacing: -0.1pt;"> </span>a<span style="letter-spacing: -0.15pt;"> </span>simple<span style="letter-spacing: -0.1pt;">
</span>example:<span style="letter-spacing: 0.65pt;"> </span>the<span style="letter-spacing: -0.1pt;"> </span>regular<span style="letter-spacing: -0.15pt;">
</span>wheel.<span style="letter-spacing: 0.65pt;"> </span>It<span style="letter-spacing: -0.1pt;"> </span>has<span style="letter-spacing: -0.05pt;"> </span>H<i style="mso-bidi-font-style: normal;"><sub>h</sub><span style="letter-spacing: -0.4pt;"> </span></i>=<span style="letter-spacing: -0.6pt;"> </span>S<span style="letter-spacing: -0.95pt;"> </span>=<span style="letter-spacing: -0.6pt;"> </span>N<span style="letter-spacing: -0.7pt;"> </span>=<span style="letter-spacing: -0.6pt;"> </span><span style="letter-spacing: 0.1pt;">H<i style="mso-bidi-font-style: normal;"><sub>r</sub></i>/2,</span><span style="letter-spacing: -0.05pt;"> </span>∆α<span style="letter-spacing: -1.35pt;"> </span>=<span style="letter-spacing: -0.6pt;"> </span>2π/N<span style="letter-spacing: -2.5pt;"> </span>,
∆β<span style="letter-spacing: -1.5pt;"> </span>=<span style="letter-spacing: -0.95pt;"> </span>∆α/2<span style="letter-spacing: -0.7pt;"> </span>and<span style="letter-spacing: -0.55pt;"> </span>arbitrary<span style="letter-spacing: -0.55pt;"> </span>cross<span style="letter-spacing: -0.5pt;"> </span>number<span style="letter-spacing: -0.55pt;"> </span><span style="letter-spacing: 0.35pt;">C.</span><span style="letter-spacing: 0.05pt;"> </span>Spoke<span style="letter-spacing: -0.55pt;"> </span>indexes<span style="letter-spacing: -0.5pt;"> </span>are,<span style="letter-spacing: -0.6pt;"> </span></span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;">in compact notation:<span style="mso-spacerun: yes;"> </span>A<i style="mso-bidi-font-style: normal;"><sub>i</sub>
</i>= i and B<i style="mso-bidi-font-style: normal;"><sub>i</sub> </i>= 2(i +(-<span style="letter-spacing: 0.15pt;">1)<i style="mso-bidi-font-style: normal;"><sup>i</sup></i><sup>+1</sup>C) -</span>1,<span style="letter-spacing: -0.7pt;"> </span>and the<span style="letter-spacing: 0.85pt;"> </span>di</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "Arial Unicode MS"; mso-fareast-font-family: "Arial Unicode MS";">ff</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;">erence<span style="letter-spacing: 0.85pt;"> </span>in<span style="letter-spacing: 0.85pt;"> </span>the<span style="letter-spacing: 0.9pt;"> </span>angles<span style="letter-spacing: 0.85pt;"> </span>is:</span></span></div>
<div style="margin: 0cm 0cm 6pt 5.65pt; text-align: justify;">
<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;"> <span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 105%;">∆β(B<i style="mso-bidi-font-style: normal;"><sub>i</sub> </i>− 1) − ∆α(A<i style="mso-bidi-font-style: normal;"><sub>i</sub> </i>− 1) = (−1)<i style="mso-bidi-font-style: normal;"><sup>i</sup></i><sup>+1</sup>C∆α </span></span></span></div>
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<span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;">With numerical<span style="letter-spacing: 0.05pt;"> </span>data for<span style="letter-spacing: 0.05pt;">
</span>a<span style="letter-spacing: 0.05pt;"> </span>32-spoke wheel,<span style="letter-spacing: 0.1pt;"> </span>R<i style="mso-bidi-font-style: normal;"><sub>r</sub><span style="letter-spacing: -0.05pt;"> </span></i>=<span style="letter-spacing: -0.4pt;"> </span>298<span style="letter-spacing: -0.15pt;"> </span>mm,<span style="letter-spacing: 0.05pt;"> </span>R<i style="mso-bidi-font-style: normal;"><sub>h</sub><span style="letter-spacing: -0.2pt;"> </span></i>=<span style="letter-spacing: -0.4pt;"> </span>26,<span style="letter-spacing: 0.05pt;"> </span>H<i style="mso-bidi-font-style: normal;"><sub>z</sub>
</i>=<span style="letter-spacing: -0.4pt;"> </span>20<span style="letter-spacing: -0.1pt;"> </span>mm and<span style="letter-spacing: 0.05pt;"> </span>N<span style="letter-spacing: -0.5pt;"> </span>=<span style="letter-spacing: -0.4pt;"> </span>32/2<span style="letter-spacing: -0.4pt;"> </span>=<span style="letter-spacing: -0.45pt;"> </span>16,<span style="letter-spacing: 0.1pt;"> </span><span style="letter-spacing: -0.15pt;">we </span><span style="mso-font-width: 95%;">get<span style="letter-spacing: -0.45pt;"> </span>spoke<span style="letter-spacing: -0.45pt;"> </span>lengths<span style="letter-spacing: -0.4pt;">
</span>(in<span style="letter-spacing: -0.45pt;"> </span>mm)<span style="letter-spacing: -0.45pt;"> </span>on<span style="letter-spacing: -0.4pt;"> </span>one<span style="letter-spacing: -0.45pt;"> </span>side<span style="letter-spacing: -0.4pt;"> </span>of<span style="letter-spacing: -0.45pt;"> </span>the<span style="letter-spacing: -0.45pt;"> </span>wheel:<span style="letter-spacing: 0.25pt;"> </span>272.7,<span style="letter-spacing: -0.4pt;"> </span>274.9,<span style="letter-spacing: -0.4pt;"> </span>280.9,<span style="letter-spacing: -0.4pt;"> </span>289.7<span style="letter-spacing: -0.6pt;"> </span>and<span style="letter-spacing: -0.4pt;"> </span>299.8<span style="letter-spacing: -0.6pt;"> </span>for<span style="letter-spacing: -0.45pt;"> </span>C<span style="letter-spacing: -1.1pt;"> </span>=<span style="letter-spacing: -0.75pt;"> </span>0,<span style="letter-spacing: -2.15pt;"> </span>1,<span style="letter-spacing: -2.1pt;"> </span>2,<span style="letter-spacing: -2.15pt;"> </span>3,<span style="letter-spacing: -2.1pt;"> </span>4
</span><span style="mso-font-width: 90%;">respectfully. All the spokes on one
side of the wheel have the same length. The other side of the wheel could </span>have
different spoke length, because of di</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: "Arial Unicode MS"; mso-fareast-font-family: "Arial Unicode MS";">ff</span><span lang="EN-US" style="font-family: "arial"; mso-bidi-font-family: Mangal;">erent
dimension H<i style="mso-bidi-font-style: normal;"><sub>z</sub> </i><span style="letter-spacing: -0.15pt;">or </span>different C<span style="letter-spacing: -2.4pt;"> </span>(figure 3).</span></div>
</span><br /></span></span></div>
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<span lang="EN-US" style="font-family: "arial"; mso-font-width: 115%;"><span style="font-family: "times new roman";">
</span></span><br />
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVI29GvG9fBUj04sAJx7YOp0D-6dV6eT8wix75CaejMRpoe9stkgi7X8eX6_B6vDcW129jnFzd2oxy4DqlKKRb0xpvH7wINsCTAPVurrXhJpIZ38Zlz0JQkxe2rmVKqSDS29wtCLIS6_k/s1600/wheel-32.bmp" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="531" data-original-width="609" height="347" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVI29GvG9fBUj04sAJx7YOp0D-6dV6eT8wix75CaejMRpoe9stkgi7X8eX6_B6vDcW129jnFzd2oxy4DqlKKRb0xpvH7wINsCTAPVurrXhJpIZ38Zlz0JQkxe2rmVKqSDS29wtCLIS6_k/s400/wheel-32.bmp" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-fareast-font-family: "Times New Roman";">Figure 3. 32-spoke wheel. H<i style="mso-bidi-font-style: normal;"><span style="mso-text-raise: -6.5pt; position: relative; top: 6.5pt;">h </span></i>= 16, H<i style="mso-bidi-font-style: normal;"><span style="mso-text-raise: -6.5pt; position: relative; top: 6.5pt;">r </span></i>= 32.<span style="mso-spacerun: yes;"> </span>Left side 16 spokes, cross 2.<span style="mso-spacerun: yes;"> </span>Right<span style="mso-spacerun: yes;"> </span>side: 16 radial spokes. Wheel seen from the left side. Spokes on the left side are drawn with solid lines and with dashed lines for the right side. Blue for leading and red for trailing spokes. Rim and hub holes are<span style="letter-spacing: 0.4pt;"> </span>numbered.</span></td></tr>
</tbody></table>
<span style="font-family: "times new roman";">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">Example<span style="letter-spacing: -1.05pt;"> </span>2</span></b><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">.<span style="letter-spacing: -0.1pt;"> </span>Now,<span style="letter-spacing: -0.65pt;"> </span>let’s<span style="letter-spacing: -0.65pt;">
</span>present<span style="letter-spacing: -0.65pt;"> </span>a<span style="letter-spacing: -0.7pt;"> </span>more<span style="letter-spacing: -0.65pt;"> </span>complicated<span style="letter-spacing: -0.7pt;"> </span>case.<span style="letter-spacing: -0.05pt;"> </span>I<span style="letter-spacing: -0.7pt;"> </span>have<span style="letter-spacing: -0.65pt;"> </span>recently<span style="letter-spacing: -0.65pt;"> </span>built<span style="letter-spacing: -0.7pt;"> </span>a<span style="letter-spacing: -0.65pt;"> </span>rear<span style="letter-spacing: -0.7pt;"> </span>wheel<span style="letter-spacing: -0.65pt;"> </span>for<span style="letter-spacing: -0.65pt;"> </span>my<span style="letter-spacing: -0.7pt;"> </span>fixie<span style="letter-spacing: -0.65pt;"> </span>with
32-hole<span style="letter-spacing: -0.15pt;"> </span>hub,<span style="letter-spacing: -0.05pt;"> </span>36-hole<span style="letter-spacing: -0.15pt;"> </span>rim<span style="letter-spacing: -0.1pt;"> </span>and<span style="letter-spacing: -0.15pt;"> </span>16<span style="letter-spacing: -0.1pt;"> </span>spokes<span style="letter-spacing: -0.15pt;">
</span>for<span style="letter-spacing: -0.1pt;"> </span>the<span style="letter-spacing: -0.15pt;"> </span>whole<span style="letter-spacing: -0.1pt;"> </span>wheel,<span style="letter-spacing: -0.1pt;"> </span>which<span style="letter-spacing: -0.1pt;"> </span>means<span style="letter-spacing: -0.15pt;"> </span>with<span style="letter-spacing: -0.1pt;"> </span>parameters<span style="letter-spacing: -0.1pt;"> </span>H<i style="mso-bidi-font-style: normal;"><sub>h</sub><span style="letter-spacing: -0.3pt;"> </span></i>=<span style="letter-spacing: -0.45pt;"> </span>16,<span style="letter-spacing: -2.15pt;"> </span>H<i style="mso-bidi-font-style: normal;"><sub>r</sub><span style="letter-spacing: -0.15pt;"> </span></i>= 36,<span style="letter-spacing: -2.35pt;"> </span>S<span style="letter-spacing: -1.55pt;"> </span>=<span style="letter-spacing: -1.05pt;"> </span>8<span style="letter-spacing: -0.9pt;"> </span>(figure<span style="letter-spacing: -0.65pt;"> 4</span>,<span style="letter-spacing: -0.7pt;"> </span>left<span style="letter-spacing: -0.7pt;"> </span>side).<span style="letter-spacing: -0.15pt;">
</span>Not<span style="letter-spacing: -0.7pt;"> </span>unexpectedly<span style="letter-spacing: -0.65pt;"> </span>however,<span style="letter-spacing: -0.7pt;">
</span>one<span style="letter-spacing: -0.7pt;"> </span>spokes<span style="letter-spacing: -0.7pt;"> </span><span style="letter-spacing: -0.15pt;">broke</span><span style="letter-spacing: -0.75pt;"> </span>after<span style="letter-spacing: -0.65pt;">
</span>about<span style="letter-spacing: -0.75pt;"> </span>200<span style="letter-spacing: -0.65pt;"> </span>km<span style="letter-spacing: -0.7pt;"> </span>and<span style="letter-spacing: -0.7pt;"> </span>another </span><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal;">one after
another 200<span style="letter-spacing: 1.35pt;"> </span>km.</span></span><br />
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span style="font-family: "times new roman";">
<span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 90%;">I made a finite element analysis of the wheel with beam
elements. Loading was 500 N vertical gravitational </span><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-font-width: 95%;">force<span style="letter-spacing: -1.05pt;"> </span>and<span style="letter-spacing: 1.75pt;"> </span>250<span style="letter-spacing: -1.2pt;"> </span>N<span style="letter-spacing: -1.05pt;"> </span>horizontal<span style="letter-spacing: -1.05pt;"> </span>force<span style="letter-spacing: -1.05pt;"> </span>in<span style="letter-spacing: -1.05pt;"> </span>the<span style="letter-spacing: -1.05pt;">
</span>chain<span style="letter-spacing: -1.05pt;"> </span>acting<span style="letter-spacing: -1.05pt;"> </span>on<span style="letter-spacing: -1.05pt;"> </span>the<span style="letter-spacing: -1.05pt;"> </span>edge<span style="letter-spacing: -1.05pt;">
</span>of<span style="letter-spacing: -1pt;"> </span>the<span style="letter-spacing: -1.05pt;"> </span>hub.<span style="letter-spacing: -0.6pt;"> </span>The<span style="letter-spacing: -1pt;"> </span>stress<span style="letter-spacing: -1.05pt;">
</span>analysis<span style="letter-spacing: -1.05pt;"> </span>showed<span style="letter-spacing: -1.05pt;"> </span>that the<span style="letter-spacing: -1.1pt;"> </span>stress<span style="letter-spacing: -1.1pt;"> </span>in<span style="letter-spacing: -1.1pt;"> </span>the<span style="letter-spacing: -1.1pt;"> </span>spokes<span style="letter-spacing: -1.1pt;"> </span>was<span style="letter-spacing: -1.1pt;"> </span>f<span style="letter-spacing: -1.65pt;"> </span>=1.63<span style="letter-spacing: -1.25pt;"> </span>times<span style="letter-spacing: -1.1pt;">
</span>greater<span style="letter-spacing: -1.1pt;"> </span>than<span style="letter-spacing: -1.1pt;"> </span>the<span style="letter-spacing: -1.1pt;"> </span>stress<span style="letter-spacing: -1.1pt;"> </span>would<span style="letter-spacing: -1.1pt;">
</span><span style="letter-spacing: 0.1pt;">be</span><span style="letter-spacing: -1.1pt;"> </span>in<span style="letter-spacing: -1.1pt;"> </span>an<span style="letter-spacing: -1.05pt;"> </span>ordinary<span style="letter-spacing: -1.1pt;"> </span>32-hole<span style="letter-spacing: -1.1pt;"> </span>Wheel.</span></span></div>
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<span style="font-family: "times new roman";">
</span></div>
<div style="margin: 5.05pt 5.9pt 0pt 5.65pt; text-align: justify;">
<span style="font-family: "times new roman";"><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-fareast-font-family: "Times New Roman"; mso-font-width: 95%;">I<span style="letter-spacing: -0.7pt;"> </span>experimented<span style="letter-spacing: -0.7pt;"> </span>with<span style="letter-spacing: -0.65pt;"> </span>different<span style="letter-spacing: -0.7pt;"> </span>wheel<span style="letter-spacing: -0.65pt;"> </span>parameters<span style="letter-spacing: -0.7pt;"> </span>and<span style="letter-spacing: -0.7pt;"> </span>as<span style="letter-spacing: -0.65pt;"> </span>a<span style="letter-spacing: -0.7pt;"> </span>first<span style="letter-spacing: -0.65pt;"> </span>solution<span style="letter-spacing: -0.7pt;">
</span>I<span style="letter-spacing: -0.7pt;"> </span>added<span style="letter-spacing: -0.65pt;"> </span>4<span style="letter-spacing: -0.7pt;"> </span>spokes<span style="letter-spacing: -0.65pt;"> </span>to<span style="letter-spacing: -0.7pt;"> </span>the<span style="letter-spacing: -0.7pt;"> </span>right<span style="letter-spacing: -0.65pt;"> </span>side<span style="letter-spacing: -0.7pt;"> </span>of the<span style="letter-spacing: -0.25pt;">
</span>wheel<span style="letter-spacing: -0.25pt;"> </span>(figure<span style="letter-spacing: -0.2pt;"> 4</span>,<span style="letter-spacing: -0.25pt;"> </span>right),<span style="letter-spacing: -0.25pt;"> </span>which<span style="letter-spacing: -0.2pt;"> </span>reduces<span style="letter-spacing: -0.25pt;"> </span>the<span style="letter-spacing: -0.25pt;"> </span>factor<span style="letter-spacing: -0.25pt;"> </span>to<span style="letter-spacing: -0.25pt;"> </span>f=1.17.<span style="letter-spacing: 0.4pt;"> </span>The<span style="letter-spacing: -0.2pt;"> </span>experiment<span style="letter-spacing: -0.25pt;"> </span>is<span style="letter-spacing: -0.2pt;"> </span>still<span style="letter-spacing: -0.25pt;"> </span>on-going.<span style="letter-spacing: 0.4pt;"> </span>I<span style="letter-spacing: -0.2pt;"> </span>will<span style="letter-spacing: -0.2pt;"> </span>ride </span><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-fareast-font-family: "Times New Roman"; mso-font-width: 90%;">with this wheel until possibly the
next spoke breaks, and then decide about the new wheel configuration. </span></span></div>
<span style="font-family: "times new roman";"><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTi8xl9Vt6Ryo52w0u2sojEnUkWf_Cm58ggbl9KKTpyyPdY0kOD-jPK6htjdSf-c40pNnwy-QitSRIG41akHzI3xF6cDdIbESDk3ldj4-_wNx_4XzoegkStaycw7qRWGDIxbK57kT2Rzg/s1600/wheel-fixie.bmp" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="436" data-original-width="908" height="190" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgTi8xl9Vt6Ryo52w0u2sojEnUkWf_Cm58ggbl9KKTpyyPdY0kOD-jPK6htjdSf-c40pNnwy-QitSRIG41akHzI3xF6cDdIbESDk3ldj4-_wNx_4XzoegkStaycw7qRWGDIxbK57kT2Rzg/s400/wheel-fixie.bmp" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Figure 4. Fixie rear wheel, Hh=16, Hr=36. Left: 16 spokes. Right: 20 spokes.</td></tr>
</tbody></table>
</span><br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy62PSbBy65X0D6gGPmvH6JOP7ohOocKEexI5xOhuPN8euMjOkgNYLOBe1EmnHSzvQhtRCUnI5GLFVEweMF0Q40BbXEyA628aSWhoraFoa9L2iva623w4g_rjUMwaFW_Jq_dVzyFSBK9c/s1600/Fixie.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhy62PSbBy65X0D6gGPmvH6JOP7ohOocKEexI5xOhuPN8euMjOkgNYLOBe1EmnHSzvQhtRCUnI5GLFVEweMF0Q40BbXEyA628aSWhoraFoa9L2iva623w4g_rjUMwaFW_Jq_dVzyFSBK9c/s400/Fixie.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span lang="EN-US" style="color: #4c4c4c; font-family: "arial"; mso-bidi-font-family: Mangal; mso-fareast-font-family: "Times New Roman";">Figure 5. My fixie. Both hubs have 32 holes. Front wheel: 24-hole rim and 16 radial spokes. Rear wheel: 36-hole rim and 20 spokes, mostly cross 2.</span></td></tr>
</tbody></table>
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<br /></div>
<div style="margin: 5.2pt 5.95pt 0pt 5.65pt; text-align: justify;">
<br /></div>
</div>
</div>
iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-9944624690301988102018-03-09T17:44:00.000+01:002018-03-09T17:46:14.729+01:00Minimalist, ECO, under seat bicycle bagThis is a recipe for a dedicated ECO cycling minimalist. A recipe for an under seat bicycle bag. Way back, in the olden years, when buffaloes still roamed the Rocky Mountains, I suggested a handle bar bag, made from Brussels sprouts packaging (<a href="https://iikmisc.blogspot.si/2014/12/ultralight-bicycle-bag.html">link here</a>). It took many years and much more intellectual energy to upgrade this project to include the under seat bag from mesh packaging of garlic. Finally, here it is, revealed freely and costless to you, to the whole world and to adjacent Galaxies. Let the pictures speak for themselves!<br />
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjr929Gxzuyft-aMdBExO_gUhyphenhyphenMANaegnsBTZlyEItKsplLDoRGjSkqCxc7ys5d6xK-TubBot_ephfgKEy4KPmtts1LzGEehimja8Wm2X_UpFvMzuin3vwXn8eJJ0jfzu2I3zqOSbWhwt0/s1600/SAM_0843.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1162" data-original-width="1600" height="290" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjr929Gxzuyft-aMdBExO_gUhyphenhyphenMANaegnsBTZlyEItKsplLDoRGjSkqCxc7ys5d6xK-TubBot_ephfgKEy4KPmtts1LzGEehimja8Wm2X_UpFvMzuin3vwXn8eJJ0jfzu2I3zqOSbWhwt0/s400/SAM_0843.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><br />
Garlic in mesh packaging. Eat the garlic, save the mesh.</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZAA4sXnkH4OgjNVOxskuW8dUVtFLOQNQ79mX9C9DthW9s0AQxRMXGzF9kor7s5bdoq0Dp4OMVeIZJ6j_Ch2Yfrf9GHBxHhcQsSuqo98Ms-X-0R61GFb9NF5HTNIrRflqRZBNRZKP0ohA/s1600/SAM_1258.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZAA4sXnkH4OgjNVOxskuW8dUVtFLOQNQ79mX9C9DthW9s0AQxRMXGzF9kor7s5bdoq0Dp4OMVeIZJ6j_Ch2Yfrf9GHBxHhcQsSuqo98Ms-X-0R61GFb9NF5HTNIrRflqRZBNRZKP0ohA/s400/SAM_1258.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"> Right: garlic mesh with Velcro strap.<br />
Left: ingredients for disaster: spare tube, 4 mm Allen key, tire lever, glue less patches, chain link.</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjussrLLAN9wUbk4oEXAnSQmM2Wk8nPJaFjUJo_UrDIUJmX7pxvmCwSMQpKsI1lhSdZYWgD2aWcZj4QwqHQdsQVGx913nQowW67LXme4cq0SYfVDjinrSHzo1cY08g7gob1AQgM97ts3xw/s1600/SAM_1256.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjussrLLAN9wUbk4oEXAnSQmM2Wk8nPJaFjUJo_UrDIUJmX7pxvmCwSMQpKsI1lhSdZYWgD2aWcZj4QwqHQdsQVGx913nQowW67LXme4cq0SYfVDjinrSHzo1cY08g7gob1AQgM97ts3xw/s400/SAM_1256.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Only 84 g for disaster.</td></tr>
</tbody></table>
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjO96VC4lf85vzt3u8hGOp8wRG7HxFVoL3UkH2bvBoqhDoaqYvHRMfcAeORl5s_y9u-JAIuOT5foAEUTB4vD3QOHzFKgJv0hn0lUuRL9MNEAYVMlvWiEcE8WEK1JF1lDZ3z-Yjxk4a_4js/s1600/SAM_1257.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1200" data-original-width="1600" height="300" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjO96VC4lf85vzt3u8hGOp8wRG7HxFVoL3UkH2bvBoqhDoaqYvHRMfcAeORl5s_y9u-JAIuOT5foAEUTB4vD3QOHzFKgJv0hn0lUuRL9MNEAYVMlvWiEcE8WEK1JF1lDZ3z-Yjxk4a_4js/s400/SAM_1257.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"> The mesh bag, disaster ready, attached to seat rails.</td></tr>
</tbody></table>
<br />iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com2tag:blogger.com,1999:blog-2823816027080391290.post-25845987920757898642016-05-13T15:24:00.001+02:002016-05-16T08:46:20.626+02:00My solution for back pain<br />
<div align="left" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "trebuchet ms" , sans-serif; font-size: small;">The back pain seems to be frequent trouble among cyclists. So much that it produced vast
collection of bike fitting theories, with enormous volume of written and
filmed material, far too big to be manageable. The latest hit in bike fitting is to conduct
a sophisticated test program, as for an astronaut, where they measure your
cycling performance from toe to nose, the final result of the test being a new
cycling position which is a couple of millimeters different from your current
one. Then you are advised to cycle a few thousand kilometers in the new
position until you get used to it. If you don't want to spend <span style="font-family: "georgia" , "times new roman" , serif; font-size: x-small;">few</span> hundreds of
euros for such a treatment, you have one cheaper option from TV sales: for just
39.99 EUR you can get an elastic hamstring band that will miraculously heal
your back pain and which has a fantastic additional benefit that nobody will
notice it under your clothes. If you are too stringent even for that, I have a
costless solution for you, a simple exercise: the plank.</span></div>
<span style="font-family: "trebuchet ms" , sans-serif; font-size: xx-small;"></span><br />
<div align="left" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "trebuchet ms" , sans-serif; font-size: x-small;"><span style="font-size: small;">The plank is a static
exercise for strenghtening your back. Position yourself stretched paralel to
the floor, resting only on your toes and forearms. Hold that position for about
1 minute. Repeat 3 times with 1 minute breaks. That's all. In accordance with
my prefered life philosophy it couldn't be more simple, minimalistic and
lightweight (no equipment needed).</span> </span></div>
<span style="font-family: "trebuchet ms" , sans-serif; font-size: xx-small;"></span><br />
<div align="left" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "trebuchet ms" , sans-serif; font-size: xx-small;"><span style="font-family: "trebuchet ms" , sans-serif;"><span style="font-family: "trebuchet ms" , sans-serif;"><span style="font-family: "trebuchet ms" , sans-serif; font-size: small;">I do it every second
morning. I takes me 5 minutes. It works for me, I have practically no more back
pain – when cycling or otherwise. Contrary to the perception of myself as a
VIP, the facts are regrettingly showing that I am just about an average person, so if it worked for me, it should work for at
least 50% of you.</span> </span></span></span></div>
<span style="font-family: "trebuchet ms" , sans-serif; font-size: xx-small;"></span><br />
<div align="left" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "trebuchet ms" , sans-serif; font-size: small;">This solution has one disadvantage:
you'll have to make an effort. I think it is effective only if you go beyond
the comfort level: do the plank up to the point when you start to shake. You
can make it more enjoyable by taking 1 minute breaks in some simple and
relaxing yoga posture.</span></div>
iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com2tag:blogger.com,1999:blog-2823816027080391290.post-65997987137930109622016-03-05T10:47:00.003+01:002016-04-07T08:59:03.314+02:00Building an unusual wheel<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwo7xWXskWwl56jodhX9hTOlHvosMdt-dXtW3Drxm9FcaTWNYh7TcblBMQz3XJsYxsLeHikHo0uyaFO0uyut6Ybr1sCraJnaF3zsHrlF6eK2B1dsAAW8fAoIxy9FDMpxpRigl5EKPO21I/s1600/My+Pictures3.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiwo7xWXskWwl56jodhX9hTOlHvosMdt-dXtW3Drxm9FcaTWNYh7TcblBMQz3XJsYxsLeHikHo0uyaFO0uyut6Ybr1sCraJnaF3zsHrlF6eK2B1dsAAW8fAoIxy9FDMpxpRigl5EKPO21I/s320/My+Pictures3.jpg" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The bike before (above) and after wheel rebuild.</td></tr>
</tbody></table>
<span lang="EN-US" style="font-family: "times new roman";"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: "trebuchet ms" , sans-serif;">Sheldon Brown said that
building a bicycle wheel is the ultimate test of any bicycle mechanic's
masterhood. If that's true then building a wheel with different number of holes
in the rim and in the hub will make you Dalai Lama of bicycle mechanics. That
is the main reason why I decided to build a real wheel using 24-hole hub, 24
spokes, 32-hole rim and different cross paterns on the drive and non-drive
side. See some intoductory details on my ultralight page:
</span><a href="http://ultralightcycling.blogspot.si/p/equipment-reviews_12.html"><span style="font-family: "trebuchet ms" , sans-serif;">http://ultralightcycling.blogspot.si/p/equipment-reviews_12.html</span></a><span style="font-family: "trebuchet ms" , sans-serif;">. (look for "Cracked Easton rim"). Other reason was that it's
hard to get spare road rims at reasonable price. I guess that time is in shoratage
nowdays, so nobody bothers with rebuilding a wheel and buys new wheelset
instead. But not me! I have plenty of time and I can't imagine any better way
of using it than making a wheel. The more unusual it is, the better.</span></span><span style="font-family: "trebuchet ms" , sans-serif;"> <o:p></o:p></span></span></span><br />
<span style="font-family: "trebuchet ms" , sans-serif;">
</span><br />
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "times new roman";"><span style="font-family: inherit;"><span style="font-family: "trebuchet ms" , sans-serif;">So what we have here is
an old rear wheel with 24 spokes (minus one broken spoke) and cracked rim that
we want to replace. We also have a new rim with 32 holes. How do we go about
rebuilding the wheel with a new 32-hole rim and old 24-hole hub and old 24
pokes? <o:p></o:p></span></span></span></div>
<span style="font-family: "trebuchet ms" , sans-serif;">
</span><br />
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "times new roman";"><span style="font-family: inherit;"><span style="font-family: "trebuchet ms" , sans-serif;">The old rim has an effective
rim diameter (ERD) 595.2 mm, and the new one has ERD 591.2 mm. </span></span></span><span style="font-family: inherit;"><span style="font-family: "trebuchet ms" , sans-serif;"><span style="font-family: "trebuchet ms" , sans-serif;"><span lang="EN-US" style="font-family: "times new roman";"><span style="font-family: "trebuchet ms" , sans-serif;">Old wheel has radial
lacing on the non-drive side of the hub (NDS) with 276 mm spokes and 2-cross
lacing on the drive side (DS) with 286 mm spokes.</span> <o:p></o:p></span></span></span></span></div>
<span style="font-family: "trebuchet ms" , sans-serif;">
</span><br />
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "times new roman";"><span style="font-family: "trebuchet ms" , sans-serif;">First, we have to choose
the lacing pattern so that old spokes will fit in the new rim. There are a
number of spoke length calculators, but probably none
that allows for different number of holes in the hub and the rim. Using the
spoke calculator with ERD of the new rim, the input of 32 spokes and different
lacing patterns, I got the closest spoke lengths with 1-cross pattern on NDS
(277 mm spokes) and 3-cross pattern on DS (288 mm spokes). However, with the
input of 24 spokes the spoke calculator shows that I could use original lacing
pattern: radial on NDS (275 mm spokes) and 1-cross pattern on DS (285 mm
spokes). 32 hole rim has a hole every 11.25 degres, and 24-hole rim every 15
degrees. The maximum difference is 3.75 degres. This is not a big difference,
so the ideal spoke length will be a milimeter or two shorter or longer then
calculated length.</span></span></div>
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZoXBCiLI466VvE6_hBG55-letq6dTmxqqglACo0b8iHL3FrW-21CP-pBIOnX3SdfqRq7xqqvFQCCvUFzYrPLtkimZGL1Ik2QHsOIes7e3m2N_u6ToNKqj_YDHaCkkjmOJqJLLZS05FnY/s1600/SAM_0874.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZoXBCiLI466VvE6_hBG55-letq6dTmxqqglACo0b8iHL3FrW-21CP-pBIOnX3SdfqRq7xqqvFQCCvUFzYrPLtkimZGL1Ik2QHsOIes7e3m2N_u6ToNKqj_YDHaCkkjmOJqJLLZS05FnY/s320/SAM_0874.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">New 32-hole rim taped to the old 24-hole wheel.</td></tr>
</tbody></table>
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "times new roman";"><span style="font-family: inherit;"><span style="font-family: inherit;"><span style="font-family: "trebuchet ms" , sans-serif;">So, despite all this
complicated introduction, the procedure that I used was rather simple. I taped
the 32-rim to the old wheel so that the two spoke holes to the left of the
valve holes of the both rims were allinged. Then, going from this hole in a
clockwise direction, I moved one spoke after another from the old rim to the
nearest spoke hole of the new rim. We can calculate that, with such procedure,
every fourth hole in the new rim, counting from the first alligned hole, will
be empty. In total 8 holes. I covered these holes with a little patch of duct
tape, as a protection from dust and water. Then I used the usual procedure to
true the wheel.<o:p></o:p></span></span></span></span></div>
<span style="font-family: "trebuchet ms" , sans-serif;">
</span><br />
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFwor841yXfRtgtLI6Hzn7MSH_lBFY554u-xy88F2yfyae-fT1dR54U8ntYFV6JXrNgYM-nRaPYORwNQ2_dHVqwioeSrtFohyphenhyphenRhF3I6eiUb74OjFeS68lFq2EXVg8jO0nQ_yoefrMm6ik/s1600/SAM_0876.JPG" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFwor841yXfRtgtLI6Hzn7MSH_lBFY554u-xy88F2yfyae-fT1dR54U8ntYFV6JXrNgYM-nRaPYORwNQ2_dHVqwioeSrtFohyphenhyphenRhF3I6eiUb74OjFeS68lFq2EXVg8jO0nQ_yoefrMm6ik/s320/SAM_0876.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Every 4th hole is without spoke.</td></tr>
</tbody></table>
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "times new roman";"><span style="font-family: "trebuchet ms" , sans-serif;"><span style="font-family: inherit;">The longest segment
between two spokes of the new wheel has 22.5 degrees, opposed to the 15 degrees
in the old wheel. As the new rim has considerably bigger wall thickness, I am
convinced that this will not be a problem. Besides, the new rim miracuously
happened to be 50 g lighter than the old one.</span> </span></span></div>
iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-52184320788685508672015-01-19T09:08:00.002+01:002015-01-19T09:19:31.776+01:00Shortening (QR) skewer<div class="separator" style="clear: both; text-align: center;">
<a href="https://www.blogger.com/" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><br /></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPBVYrDzl202wiwV5CUGVIO5D-tqcJkbJtdm07XVC4WI5OqNq3w66cBj-SgdvxivT-Y1hlBIZqfAg1i4r7vCqcdRXm0FQ2jo7pwOycGmZQEEyrDDmGWow23-WA2K3frFZ921qR89iI3NE/s1600/QR+trimmed.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPBVYrDzl202wiwV5CUGVIO5D-tqcJkbJtdm07XVC4WI5OqNq3w66cBj-SgdvxivT-Y1hlBIZqfAg1i4r7vCqcdRXm0FQ2jo7pwOycGmZQEEyrDDmGWow23-WA2K3frFZ921qR89iI3NE/s1600/QR+trimmed.jpg" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">BEFORE and AFTER<br />
a small bicycle plastic surgery</td></tr>
</tbody></table>
<div style="text-align: justify;">
<a href="https://www.blogger.com/" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a><a href="https://www.blogger.com/" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"></a><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;"><span style="color: black;">Skewer is a rod
(essentially a long bolt) that fits into the hole of a hollow wheel axle and
fixes the axle in the fork dropouts. On one end the rod is threaded and has a
corresponding nut, on the other end it usually has QR (quick release) handle,
but can also have just a hex head. The skewer is often too long, so that the
threaded end extends well past the end of the nut. This is an aesthetic fault
more then anything else, although in some extreme cases – as in the picture
here– it could be considered as a cold weapon, potentially causing serious
injury or damage to the property. The obvious remedy is to cut the excess end of
the threaded end, but many will be reluctant to undertake this task, fearing
that the cut threads would damage the nut. I was sceptical too, but now, after
I pacticed it a few times I can say it is quite safe, if you follow some
simple, logical steps: </span></span> </div>
<div style="text-align: justify;">
<ul>
<li><span style="color: black;"><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">With the skewer on the bike note the length of the threaded end that you want to remove. </span></span><span style="color: black;"><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;"></span></span></li>
<li><span style="color: black;"><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">Remove the skewer from the axle and re-thread the nut past the desired cut point. It is advisable to use another,“heavy duty” nut for this purpose, but the original nut is good too. </span></span><span style="color: black;"><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;"></span></span></li>
<li><span style="color: black;"><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">H</span></span><span style="color: black;"><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">old the skewer in the bench vise and cut the desired length with fine hacksaw.</span></span></li>
<li><span style="color: black;"><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">File the cut surface so that no sharp edges remain.</span></span></li>
<li><span style="color: black;">R</span><span style="color: black;"><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">emove the nut to “clear” the remaining threaded part. Then install the skewer.<o:p></o:p></span></span></li>
</ul>
</div>
<span style="color: black;">
</span><br />
<span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;"><span style="color: black;">By the way, the procedure
is applicable to any bolt that you want to shorten. Weight weenies will be
particularly interested in this, and that is why I add a table showing how much
mass (not<span style="mso-spacerun: yes;"> </span>weight!) in grams you will
drop by shortening a bolt of diameter D by length L= 1cm. For different length
L multiply the number from the table by L expressed in cm.</span></span><br />
<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: currentColor; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 480;">
<tbody>
<tr style="height: 13.55pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background-color: transparent; border: 1pt solid windowtext; height: 13.55pt; mso-border-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 64.65pt;" valign="top" width="86">
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial;">Material<o:p></o:p></span></span></b></div>
</td>
<td colspan="6" style="background-color: transparent; border-color: windowtext windowtext windowtext rgb(0, 0, 0); border-style: solid solid solid none; border-width: 1pt 1pt 1pt 0px; height: 13.55pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 337.65pt;" valign="top" width="450">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial;">Diameter D<o:p></o:p></span></span></b></div>
</td>
</tr>
<tr style="height: 14.4pt; mso-yfti-irow: 1;">
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext; border-style: none solid solid; border-width: 0px 1pt 1pt; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 64.65pt;" valign="top" width="86">
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US"><o:p><span style="font-family: Arial;"> </span></o:p></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" valign="top" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">2
mm<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" valign="top" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">3
mm<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" valign="top" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">4
mm<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" valign="top" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">5
mm<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" valign="top" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">6
mm<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" valign="top" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">8
mm<o:p></o:p></span></span></div>
</td>
</tr>
<tr style="height: 13.55pt; mso-yfti-irow: 2;">
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext; border-style: none solid solid; border-width: 0px 1pt 1pt; height: 13.55pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 64.65pt;" valign="top" width="86">
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial;">Steel<o:p></o:p></span></span></b></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 13.55pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.25<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 13.55pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.55<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 13.55pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.98<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 13.55pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">1.53<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 13.55pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">2.21<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 13.55pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">3.92<o:p></o:p></span></span></div>
</td>
</tr>
<tr style="height: 14.4pt; mso-yfti-irow: 3;">
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext; border-style: none solid solid; border-width: 0px 1pt 1pt; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 64.65pt;" valign="top" width="86">
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial;">Titanium<o:p></o:p></span></span></b></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.14<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.32<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.57<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.88<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">1.27<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">2.26<o:p></o:p></span></span></div>
</td>
</tr>
<tr style="height: 14.4pt; mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext; border-style: none solid solid; border-width: 0px 1pt 1pt; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 64.65pt;" valign="top" width="86">
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-US"><span style="font-family: Arial;">Aluminium<o:p></o:p></span></span></b></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.08<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.19<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.34<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.53<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">0.76<o:p></o:p></span></span></div>
</td>
<td style="background-color: transparent; border-color: rgb(0, 0, 0) windowtext windowtext rgb(0, 0, 0); border-style: none solid solid none; border-width: 0px 1pt 1pt 0px; height: 14.4pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0cm 5.4pt; width: 56.25pt;" width="75">
<div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span lang="EN-US"><span style="font-family: Arial;">1.36<o:p></o:p></span></span></div>
</td>
</tr>
</tbody></table>
iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-84323294362829721652014-12-17T08:53:00.001+01:002014-12-29T09:52:16.388+01:00Ultralight bicycle bag<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="float: left; margin-right: 1em; text-align: left;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaIqtDYDqF0TjOnIIF0N4NdhS_wSnGXkOvTBtI637uSIK4PDtt4YQOhnTPaochursuyu0j5pd_a3uRfOpf3KjzvgmeikLiyFIxTEl-osrHZQDdM4hjp4O3uu4j0LNQ0cKc5jbOnacf_SE/s1600/My+Pictures1.jpg" imageanchor="1" style="clear: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaIqtDYDqF0TjOnIIF0N4NdhS_wSnGXkOvTBtI637uSIK4PDtt4YQOhnTPaochursuyu0j5pd_a3uRfOpf3KjzvgmeikLiyFIxTEl-osrHZQDdM4hjp4O3uu4j0LNQ0cKc5jbOnacf_SE/s1600/My+Pictures1.jpg" height="240" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">What do garlic, plums and Brussels sprouts have in common?</td></tr>
</tbody></table>
<br />
<span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">Have you ever wondered
what garlic, plums and </span><span class="hps"><span lang="EN" style="color: #222222; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">Brussels
sprouts</span></span><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">
have in common? They are all edible by humans of course, but other than that
they have another significant common point: they are all packed in similar
plastic mesh bags. Now, a plastic mesh or a plastic bag immediately rings a
warning bell. Certainly, you've heard emotional stories about huge amount of
plastic in the oceans, endangering the survival of ocean species like <i style="mso-bidi-font-style: normal;">Caretta caretta</i>. The numbers are huge
and menacing. Well, you don't need those stories to realize that people are
producing too much garbage; any week-end wannanbe minimalist can tell you that.
And after seeing thousands of plastic bags hanging from trees after autumn floods
in your country, you can tell that recycling plastics is not working either.
The only way to reduce the garbage madness is to stop using unnecessary
packaging. <o:p></o:p></span><br />
<br />
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">If you think – like many
- that a single person can't do much about it, just look at the numbers: each
of the 8 billions people on Earth using (or reusing) <i>1 less plastic bag only
once in a year </i>(the bag weighing 0.25 g) means more then <i>5 tons less of
garbage every day.</i> My addition to this recommended practice is here: a hint
how to make an ultra light and practically costless bicycle handlebar/under
seat/frame bag. Let it be my present to you for Christmas. </span></div>
<br />
<span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">So, lets get back to
garlic, plums and </span><span class="hps"><span lang="EN" style="color: #222222; font-family: "Times New Roman"; font-size: 12pt; mso-ansi-language: EN;">Brussels
sprouts.</span></span><span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;"> The meshes they are packed in are quite tough and light:
three of them weigh less then a resolution of my scale, which is 2 g. Add an
unpaired shoelace that you somehow forgot throwing away and a buckle of a cinch
chord from a trouser's legging (that any credible ultralighter had cut away and
stored for possible future use) and you've got a not-too-bad-looking handlebar
bag weighing around 4 g that can store almost 500 g of content. In this example
the content is a light wind/rain jacket, a compact camera and a set of tools
(all together 360 g) – which makes a world record content/container ratio of
90.</span><br />
<span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;"><o:p></o:p></span><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxr7J7FpZMfpRdJkaAtxsGqiQsrwr0yoH-ZFRhqY-HP5LbmYspSqcMCCD20TJhwOGQYHKYGxEC-AzxlUGCMQTSmvtzYxLQu5ZstEHjDwj7jbrrEHTcixtINkAc0RdmwQwlxDfTPJPSqic/s1600/P1010244.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxr7J7FpZMfpRdJkaAtxsGqiQsrwr0yoH-ZFRhqY-HP5LbmYspSqcMCCD20TJhwOGQYHKYGxEC-AzxlUGCMQTSmvtzYxLQu5ZstEHjDwj7jbrrEHTcixtINkAc0RdmwQwlxDfTPJPSqic/s1600/P1010244.JPG" height="211" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Mesh is attached to the handlebar with a shoelace and at the lower end to the brake/shifter cables.</td></tr>
</tbody></table>
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXuAv9MsveivC4NvXq2ZiFpMPEXHhbveTLBvENhuZx0Vt5IH-vSUa_pV-mb-oUkN9Ald9SQWc5G79Kz84o4zKyX4u1UWniOqO5uRW1LJ1CTdPUEAhHljlXb8bQiWZEG0MmPFRPRjiH9WQ/s1600/P1010243.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXuAv9MsveivC4NvXq2ZiFpMPEXHhbveTLBvENhuZx0Vt5IH-vSUa_pV-mb-oUkN9Ald9SQWc5G79Kz84o4zKyX4u1UWniOqO5uRW1LJ1CTdPUEAhHljlXb8bQiWZEG0MmPFRPRjiH9WQ/s1600/P1010243.JPG" height="207" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">And here is the mesh in action: holding a wind jacket, compact camera and a set of (mini)tools.</td></tr>
</tbody></table>
<div align="left" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: left;">
<span lang="EN-US" style="font-family: "Times New Roman"; font-size: 12pt;">P.S. If you are truly
dedicated world-saver, you won't go and buy Brussels sprouts to get the mesh;
instead, take a tour in your nearest garbage bin and find your mesh there. It
might also be an eye opening experience, the one you've haven't had for quite
some time.</span></div>
iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com5tag:blogger.com,1999:blog-2823816027080391290.post-45941257912289142352013-04-22T15:02:00.000+02:002013-11-25T11:58:42.385+01:00Numb and/or cold fingersDo you have problems with numb and/or cold fingers? I do! My latest effective solution to this problem comes from p<span dir="auto">sychotherapy</span>. You may know the term "progressive muscle relaxation" (PMR). If not, goggle it. It's an exercise in tensing and relaxing individual muscles of your body. PMR in itself is a good relaxing technique to start or end a day of cycling. But it's also very effective when applied to your numb or cold fingers. It's simple:<br />
<br />
1. Tense or squeeze your fingers and/or fist. You can do this either by holding to the handlebar or not, keeping the fingers straight or bent in the fist. Whatever turns out better for you.<br />
2. Keep your fingers tensed for 7 to 10 seconds.<br />
3. Slowly relax the tensed muscles (in 5 to 10 seconds).<br />
4. Keep the hand relaxed for another 5 to 10 seconds.<br />
5. Repeat points 1,2,3,4 several times. 5 repeats should do in most cases.iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-31181522007123046782013-04-18T16:06:00.001+02:002013-04-22T13:33:10.885+02:00Rain shell gloves<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US">On my other blog (ultralightcycling) I tried to give some advice about cycling in the rain. And I failed miserably! So, the</span><span lang="EN-US"> final solution to cycling in rain is still pending. In the meantime we must satisfy ourselves with partial solutions. </span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US">I have here a solution for your hands; the solution that is both effective and fulfills the rigorous minimalist requirements of <a href="http://ultralightcycling.blogspot.com/">ultralightcycling</a>. The weight of a pair of such gloves is 2 g. They are also inexpensive, costing about 2 Euro cents. Here's what to do:</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<span lang="EN-US" style="mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: 'Times New Roman';"><span style="mso-list: Ignore;">1.<span style="font: 7pt 'Times New Roman';"> </span></span></span><span lang="EN-US">Bend an old spoke to form a U.</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<span lang="EN-US" style="mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: 'Times New Roman';"><span style="mso-list: Ignore;">2.<span style="font: 7pt 'Times New Roman';"> </span></span></span><span lang="EN-US">Take a plastic envelope of a magazine (European A4 size).</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<span lang="EN-US" style="mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: 'Times New Roman';"><span style="mso-list: Ignore;">3.<span style="font: 7pt 'Times New Roman';"> </span></span></span><span lang="EN-US">Heat the spoke over a heat source.</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<span lang="EN-US" style="mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: 'Times New Roman';"><span style="mso-list: Ignore;">4.<span style="font: 7pt 'Times New Roman';"> </span></span></span><span lang="EN-US">With the heated spoke make three cuts in the plastic to make a cubist's approximation of a glove.</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<span lang="EN-US" style="mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: 'Times New Roman';"><span style="mso-list: Ignore;">5.<span style="font: 7pt 'Times New Roman';"> </span></span></span><span lang="EN-US">If you have two hands, repeat the procedure 2,3,4 once again.</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt 36pt; mso-list: l0 level1 lfo1; tab-stops: list 36.0pt; text-indent: -18pt;">
<span lang="EN-US" style="mso-bidi-font-family: 'Times New Roman'; mso-fareast-font-family: 'Times New Roman';"><span style="mso-list: Ignore;">6.<span style="font: 7pt 'Times New Roman';"> </span></span></span><span lang="EN-US">Wait for a rainy day, put the plastic gloves on (optionally over regular gloves), tuck them under your sleeves and enjoy the feeling of dry hands while cycling in rain.</span></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<br /></div>
<div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<span lang="EN-US">You might have some problems with condensation. To overcome them I suggest to make few holes on the palm side of the plastic gloves and to wear only cycling gloves (i.e. not full-finger gloves) under the plastic ones. If the plastic gloves start to tear (this usually happens in the corner between thumb and index finger) </span><br />
<span lang="EN-US">they can be repaired with any heat source.</span><span lang="EN-US">
<table cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTmGKpGxJ5vfB0aL9Q5umEF8Ld2ABWDZvIwM422dEqRMPhpR7rzhwbcqZi5jqstbAy-cpDkFTHL__IyJOIpABm36I5h_Vs9aKrnOGKpV9xyjNV8pgg6TuNTKEHPChsodcYJwbwPQC4p7w/s1600/P1010148.JPG" imageanchor="1" style="clear: left; cssfloat: left; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" dua="true" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTmGKpGxJ5vfB0aL9Q5umEF8Ld2ABWDZvIwM422dEqRMPhpR7rzhwbcqZi5jqstbAy-cpDkFTHL__IyJOIpABm36I5h_Vs9aKrnOGKpV9xyjNV8pgg6TuNTKEHPChsodcYJwbwPQC4p7w/s320/P1010148.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Bent spoke with umbrella tips glued to the ends.</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzfxZa5PyepdcHYeskoKo-L1H9KIetLToLFjFogzKsrmSMvYp9wjV0tRP-jVjKcUs2D5t2k7vdvluGvBq0CHMrVgHpt3_75aXTChX6ij1CZSQb2CSXLVWp8kYo0Kmm0Os9bfUZYMOmVtc/s1600/P1010141.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" dua="true" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzfxZa5PyepdcHYeskoKo-L1H9KIetLToLFjFogzKsrmSMvYp9wjV0tRP-jVjKcUs2D5t2k7vdvluGvBq0CHMrVgHpt3_75aXTChX6ij1CZSQb2CSXLVWp8kYo0Kmm0Os9bfUZYMOmVtc/s320/P1010141.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Plastic cover of a magazine.</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA8aJF4VEDlIdXfhi7LeCW117uC_GoubM6ELkj7qZ6tnGUG14vQWctHi58ThoedAouMxOEM8vGmTjMokEyNoUrPX96dgQx8hf5S3JaUAEuPLy9HaekLQ6gIOamer3ku_7lxkW1cP8Gih0/s1600/P1010142.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" dua="true" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjA8aJF4VEDlIdXfhi7LeCW117uC_GoubM6ELkj7qZ6tnGUG14vQWctHi58ThoedAouMxOEM8vGmTjMokEyNoUrPX96dgQx8hf5S3JaUAEuPLy9HaekLQ6gIOamer3ku_7lxkW1cP8Gih0/s320/P1010142.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">1-2-3 and your plastic glove is ready-made.</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN4NYjbMhFZBM3IkhVNz6fYjo1cN09VsP4afglpcZXvYmjaQnHW0A_HQCbDw9wEjMr4ZG8_X1DAPPtQuzLum7iVgCvl6aso8g1YAWloPVUZjz_d462XbMqqztW7P4NBVVlXOkAKakgGws/s1600/P1010143.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" dua="true" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjN4NYjbMhFZBM3IkhVNz6fYjo1cN09VsP4afglpcZXvYmjaQnHW0A_HQCbDw9wEjMr4ZG8_X1DAPPtQuzLum7iVgCvl6aso8g1YAWloPVUZjz_d462XbMqqztW7P4NBVVlXOkAKakgGws/s320/P1010143.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Your plastic glove in action</td></tr>
</tbody></table>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOYk7FjX-swmtno50WKyXDClBJm6nJB9k_BRobFHYLitaeRrN0m-fl-Lf7mV3ZQLBx0wNkFuydZfgDl2FbvAgyHxX23teMPCAmVn2x6fHQPVpU4DxzKPd_TkRpOW6abkRRi6ej-4D55lE/s1600/P1010147.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" dua="true" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOYk7FjX-swmtno50WKyXDClBJm6nJB9k_BRobFHYLitaeRrN0m-fl-Lf7mV3ZQLBx0wNkFuydZfgDl2FbvAgyHxX23teMPCAmVn2x6fHQPVpU4DxzKPd_TkRpOW6abkRRi6ej-4D55lE/s320/P1010147.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">... and wears better then the usual plastic glove from petrol station of fruit-stand in supermarkets.</td></tr>
</tbody></table>
</span><br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
<br /></div>
</div>
iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com5tag:blogger.com,1999:blog-2823816027080391290.post-80555810171999383082012-03-12T11:20:00.003+01:002012-03-12T11:25:44.389+01:00Cleaning cycling water bottlesPlastic cycling water bottles (bidons) are notorius good growing ground for mould and fungus. However, I am not particularly upset about it, partly because I am not too sensible to dirt, but mostly because I don't recommend the use of cycling bidons in the first place. Ordinary plastic 1L bottle is almost twice lighter then 0.7 L bidon and has more volume. It also has simpler mouthpiece that doesn't attract mould.<br />
<br />
But if, for whatever reason, you insist on using cycling bidons, I have a simple tip how to clean it. <br />
<br />
You don't need any special chemicals, heat treatment or dish washer. Just put a paper towel or a few pieces of (unused) toilet paper in the bottle and stir and rub with a long stiff stick. Instead of a stick you can use the hooked end of a spoke.iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com2tag:blogger.com,1999:blog-2823816027080391290.post-51247069348288733032012-02-29T21:51:00.005+01:002013-01-10T09:17:51.942+01:00Tyre bootTyre boot is a temporary solution for a tyre that is cut or badly damaged, when one doesn't have a spare one. It's a piece of material that is put between the tube and the tyre and which prevents the tube to bulge out through the cut in the tyre and explode. The boot material could be of any kind, as long as it is strong enough to hold the pressure and soft enough not to puncture the tube. It's often recommended to use a piece of the old tyre, although from my experience even a boot made with duct tape did last more then 1500 km (on tarmac). <br />
<br />
My hint is that before putting the boot, it very much helps to sew the tyre. If the tyre casing is cut or damaged, I sew up that part with the needle and thread, just as patching a hole in a sock. Then I apply the tyre boot, which in this case can be as simple as a piece of duct tape or a tube patch, applied from the inside of the tyre. A piece of wrapping material (for chocolate bars, for example) might be just as useful.<br />
<br />
I have such patched tyres on my commuter currently, both at front and rear, as an experiment of how long this would last. This is a road bike with a pressure of 6 bar. I've been riding 18 months now with patched front tyre and 14 months with the back one, but after I'd confessed it, and Murphy is reading it, I suppose I'll have a blowout tomorrow - will let you know.iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com6tag:blogger.com,1999:blog-2823816027080391290.post-48989940011578789242011-10-09T14:18:00.008+02:002011-12-05T15:43:11.602+01:00Climbing a hill on a bicycle<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixS1Rfc8KQxJoWqA7xdaDL-zltdqjO9lWAVAz_YlkNPDHJiRRCSqjI9KeFKaa2VisI8gtskj0xfLSELt_zy7E8RFbj8TiRkbpXceUcEZudVUe5OQ1_lTl049IXf9t_MqYJ2BApMbBNpN8/s1600/Image2004.BMP" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="212px" oda="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEixS1Rfc8KQxJoWqA7xdaDL-zltdqjO9lWAVAz_YlkNPDHJiRRCSqjI9KeFKaa2VisI8gtskj0xfLSELt_zy7E8RFbj8TiRkbpXceUcEZudVUe5OQ1_lTl049IXf9t_MqYJ2BApMbBNpN8/s320/Image2004.BMP" width="320px" /></a></div>Deep down everybody fears hill climbing: the beginners, the veterans and the pro's. It is one of those activities which many people - often including cyclists themselves - find unexplainably masochistic. Why do you climb a hill, when you will come back down again? And if you really insist in climbing, why don't you do it in a car?<br />
I won't go deeper into philosophic essays regarding this subject, although, if you care to think enough about it, you may come to some profound quintessential matter like Universe, Big Bang, Meaning of Life, etc. I will only state some physical facts that may help you to climb the hill easier.<br />
<br />
When you cycle, and in particular when you cycle up hill, the nature is working against you. It is trying to stop you from cycling by imposing various forces that act against your movement. There are three major forces acting against you: the force of gravity (G), the force of rolling resistance (R) and the force of air resistance (A). To move against these forces you have to do some work (W). In mathematical terms the work is a (scalar) product of the force(s) and the path (L) of your movement. When you climb a hill of road length L and of grade N (in %), the work against the gravity is:<br />
<br />
W=M*g*L*<em>sin</em>(<em>arctan</em>(N/100))<br />
<br />
where g is the acceleration of gravity (9.81 m/s^2) and M is a mass of yourself, bicycle and everything on you and on it. You are doing also the work against the rolling and air resistance, but when climbing steeper hills these two represent only about 5% to 10% of the total work, so, for now, we will disregard them for the sake of simplicity.<br />
The energy to do the work is provided by your body, by your muscles. To climb a hill you must produce at least as much energy as the work W. In reality you are producing much more energy, because some of it (some say even 70% of it) is lost in the dissipative processes in your body, and, of course, some is required to keep you alive, even when not moving at all. We will denote this additional energy as internal body energy (Eb). The total energy required is thus (Eb+W). <br />
You will input that energy during some period of time (t) - the time that you climb the hill. Energy divided by time in physical terms is called power (P):<br />
<br />
P=(Eb+W)/t<br />
<br />
When measuring and reporting bicycling power we usually only measure the part that corresponds to the energy W; the part Eb, which is lost due to small muscle efficiency, is usually not measured or reported. So, we are left with:<br />
<br />
P=W/t <br />
<br />
The ability to produce a certain amount of power is in accordance with everyday conception of physical power: trained or stronger people can produce more power. The pro cyclist can produce around 400 Watt to 500 Watt of power when climbing hard. Ordinary cyclists produce 100 Watt up to 250 Watt of power over a period of few hours. According to the above equation, you need more power if you climb the hill faster (in less time), and if you climb the same hill slower, you need less power. Think of it in exaggerated terms: if you had the whole week to climb the hill, you would still need to input the same amount of work W, but you would need so little power that you would probably not even notice there is a hill. The first point to remember is thus: <em>you can climb practically every hill by climbing it slower.</em><br />
<br />
The speed of cycling (v) can be expressed as:<br />
<br />
v = L/t = 2*<span style="font-family: 'Times New Roman'; font-size: 12pt; mso-ansi-language: SL; mso-bidi-language: AR-SA; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: SL;">π</span>*R*c*T<br />
<br />
where (R) is the radius of the wheel, (c) is cadence of pedaling and (T=F/B) is the transmission ratio (where F and B are number of teeth on front and back rings). By substituting the above equations, we have:<br />
<br />
P=M*g*<em>sin</em>(<em>arctan</em>(N/100))*2*<span style="font-family: 'Times New Roman'; font-size: 12pt; mso-ansi-language: SL; mso-bidi-language: AR-SA; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: SL;">π</span>*R*c*T<br />
<br />
What can we say about this equation? It connects the physical quantities (P,M,N,R,c and T) in a definite way. If we change one of those quantities, then at least one of the rest of them will change too. For example, with a maximum power (P) that we can produce, we can climb a steeper hill (=higher N), if we have lower mass, lower cadence, lower transmission or smaller wheel. Conversely, if we cannot change M, c, T or R, then the only way to climb a steeper hill is to produce more power. Incidentally, from the equation you can even see another possible solution: lowering the effective gradient (N) by zigzagging the climb. Of course, any self-respecting cyclist would never do such a thing - it would be as if stepping down on a climb.<br />
<br />
Now, you probably have the feeling that this is perfectly logical, so you may ask why did you have to go through all this math to come to the conclusions that you already know? Well, first of all, it's the proof that physics and common sense sometimes do agree. Second, you can use the equation to calculate, for example, what gearing you require on a certain hill, or what is your power output, or how much will you gain by buying lighter bike, or by loosing 2 kg of fat, or climbing with a MTB instead of road bike. We can very well say that it is the "mother of all cycling equations". Third - and this may be the most important - you may realize that you <em>can</em> climb a certain hill that you considered too hard, and not even that, you may even plan how to climb it without much effort.<br />
<br />
To see that, lets first write the above equation in sipmlified form, like this:<br />
<br />
P=M*g*v*<em>sin</em>(<em>arctan</em>(N/100))<br />
<br />
From this simpler form, you can see that you can climb a steeper hill either by loosing weight (difficult), producing more power (impossible) or lowering climbing speed (quite possible, as we already mentioned).<br />
Lowering the speed probably instinctively makes you think of lower gearing. But even when you run out of lower gears, you still have another ace in your sleeve: lower the cadence. If you lower the cadence down to around 35 rpm you will be surprised how easy it is to climb even the hills that you previously considered impossible.<br />
<br />
However, there is of course a limit: you can climb just as slow as the lowest speed before toppling over. For me it's about 4.5 km/h. By inserting this minimal speed into the equation you can calculate whether you can climb the hill at all (without zigzagging).<br />
<br />
There is another interesting thing that we can conclude from the above equations: that the transmission ratio doesn't really matter. If you could pedal at, say, 10 rpm, you may be able to climb in the big front ring, without the need for any more power than you are usually able to produce. Does it mean that you need only one ring in front? No derailleur, no shifter? It is well worth a try!iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com5tag:blogger.com,1999:blog-2823816027080391290.post-49444200496224702632011-09-30T13:37:00.000+02:002013-02-27T12:47:09.782+01:00Flipping a stem<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
If you are reading this, then you most likely know what is a stem and what "flipping a stem" means and why it is done. For those who came to this page by accident, here are few clarifications: </div>
<ul>
<li style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">A stem is a part of a bicycle that connects the steering tube (which is the top part of the front fork) with the handlebar. There are two types of stem. The <a href="http://sheldonbrown.com/gloss_w.html#wedgebolt">"quill stem"</a> is found on older bicycles and in cheaper today's bikes. Most of today's quality bicycles have the stem as the one in the picture in this post. It connects to the steering tube with two bolts. Usually this kind of stem is not perpendicular to the axis of the steering tube, but is at a certain angle to it - angle <span style="font-family: 'Times New Roman'; font-size: 12pt; mso-ansi-language: SL; mso-bidi-language: AR-SA; mso-fareast-font-family: 'Times New Roman'; mso-fareast-language: SL;">α</span> in the picture. When this is the case, you can raise (or lower) the handlebar by flipping the stem around. </li>
</ul>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFv6nYcfD76eafAlvP5HTv_iNY4lQQj8ub-bZFEfRIBOv4o8RyqmEOmgaaFGWY0Ph1T9GcU_JY3YcFl8KsWk-9Jc6Wxo0FZZYZESOpzXz78o_RwPMYYDFXVH3Om08F3i1PoZy9woLR_WM/s1600/stem.jpg" imageanchor="1" style="clear: left; cssfloat: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="180" kca="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFv6nYcfD76eafAlvP5HTv_iNY4lQQj8ub-bZFEfRIBOv4o8RyqmEOmgaaFGWY0Ph1T9GcU_JY3YcFl8KsWk-9Jc6Wxo0FZZYZESOpzXz78o_RwPMYYDFXVH3Om08F3i1PoZy9woLR_WM/s320/stem.jpg" width="320" /></a><br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
If you flip the stem from the picture around, the point T1 (intersection of the central axis of the stem with the handlebar) will move to point T2.</div>
The question is, how much will you raise the handlebar by flipping the stem. Will it be too high, too low, or is it just not worth the trouble flipping the stem at all? </div>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
<br /></div>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
Well, I've got the answer for you. I will not go into detail of developing all the equations, I'll just state the final result:</div>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
<br />
If the steering tube is at the angle β, the stem has a flip-flop angle α and length L, then, after flipping the stem, the handlebar will move vertically by ΔY and horizontally by ΔX, calculated by:</div>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
<br /></div>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
ΔY=L[cos(β-α)-cos(β+α)], ΔX=L[sin(β-α)-sin(β+α)]</div>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
<br />
Positive values mean that the handlebar will move up and forward, negative values move the handlebar down and backward.</div>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
In the following table are the values of ΔY and ΔX in mm, for some common values of β and α and for the stem length L=100 mm. If you have a stem of different length, multiply the values in the table by L/100, where L is the length of the stem in mm.</div>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
<br /></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-bottom: medium none; border-collapse: collapse; border-left: medium none; border-right: medium none; border-top: medium none; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 480;"><tbody>
<tr style="mso-yfti-firstrow: yes; mso-yfti-irow: 0;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; mso-border-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 54.4pt;" valign="top" width="73"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<br /></div>
</td><td colspan="2" style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 69.45pt;" valign="top" width="93"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">α = 6 º</b></div>
</td><td colspan="2" style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 69.45pt;" valign="top" width="93"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">α = 8 º</b></div>
</td><td colspan="2" style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 75.05pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">α = 10 º</b></div>
</td><td colspan="2" style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: windowtext 1pt solid; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 75.05pt;" valign="top" width="100"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">α = 17 º</b></div>
</td></tr>
<tr style="mso-yfti-irow: 1;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 54.4pt;" valign="top" width="73"><div class="MsoNormal" style="margin: 0cm 0cm 0pt;">
<br /></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">ΔY</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" width="45"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">ΔX</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">ΔY</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" width="45"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">ΔX</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">ΔY</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" width="52"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">ΔX</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">ΔY</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" width="52"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">ΔX</b></div>
</td></tr>
<tr style="mso-yfti-irow: 2;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 54.4pt;" width="73"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">β = 72 º</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">19,9</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" valign="bottom" width="45" x:num="-6.46"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-6,5</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">26,5</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" valign="bottom" width="45" x:num="-8.6010000000000009"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-8,6</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">33,0</span></div>
</td><td style="background-color: transparent; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" valign="bottom" width="52" x:num="-10.73"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-10,7</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">55,6</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" valign="bottom" width="52" x:num="-18.07"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-18,1</span></div>
</td></tr>
<tr style="mso-yfti-irow: 3;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 54.4pt;" width="73"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">β = 73 º</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">20,0</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" valign="bottom" width="45" x:num="-6.1120000000000001"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-6,1</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">26,6</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" valign="bottom" width="45" x:num="-8.1379999999999999"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-8,1</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">33,2</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" valign="bottom" width="52" x:num="-10.15"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-10,2</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">55,9</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" valign="bottom" width="52" x:num="-17.1"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-17,1</span></div>
</td></tr>
<tr style="mso-yfti-irow: 4;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 54.4pt;" width="73"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">β = 74 º</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">20,1</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" valign="bottom" width="45" x:num="-5.7619999999999996"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-5,8</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">26,8</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" valign="bottom" width="45" x:num="-7.6719999999999997"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-7,7</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">33,4</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" valign="bottom" width="52" x:num="-9.5730000000000004"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-9,6</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">56,2</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" valign="bottom" width="52" x:num="-16.12"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-16,1</span></div>
</td></tr>
<tr style="mso-yfti-irow: 5; mso-yfti-lastrow: yes;"><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: windowtext 1pt solid; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 54.4pt;" width="73"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<b style="mso-bidi-font-weight: normal;">β = 75 º</b></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">20,2</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" valign="bottom" width="45" x:num="-5.4109999999999996"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-5,4</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">26,9</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 33.6pt;" valign="bottom" width="45" x:num="-7.2039999999999997"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-7,2</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">33,6</span></div>
</td><td style="background-color: transparent; border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" valign="bottom" width="52" x:num="-8.9890000000000008"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-9,0</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 35.85pt;" valign="bottom" width="48"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">56,5</span></div>
</td><td style="background-color: transparent; border-bottom: windowtext 1pt solid; border-left: #ece9d8; border-right: windowtext 1pt solid; border-top: #ece9d8; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding-bottom: 0cm; padding-left: 5.4pt; padding-right: 5.4pt; padding-top: 0cm; width: 39.2pt;" valign="bottom" width="52" x:num="-15.13"><div align="center" class="MsoNormal" style="margin: 0cm 0cm 0pt; text-align: center;">
<span style="font-family: Arial; font-size: 10pt;">-15,1</span></div>
</td></tr>
</tbody></table>
<br />
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
<br /></div>
<div style="border-bottom: medium none; border-left: medium none; border-right: medium none; border-top: medium none;">
<br /></div>
iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-53927727919317665622010-07-15T15:09:00.005+02:002014-01-15T14:21:04.658+01:00Packing a bicycle for a flight<span style="font-family: inherit;">There are several schools of thought on how to pack a bicycle for a flight. Some like to leave it unpacked so that the baggage handlers will see it's a bike and will treat it gently. Others are convinced that only a hard shell case with steel bracing will do the job. Most of the cyclists take the middle way and put the bicycle in a cardboard box. So let us first start with: </span><br />
<h5>
<span style="font-family: inherit; font-size: small;">Recipe for packing a bicycle in a bike box</span></h5>
<span style="font-family: inherit;">Ingredients:<br />
- 1 road bicycle, size 622 (or 700c) wheels, frame of the size L (or 58), drop bar.<br />
- 1 cardboard box of dimensions 138x78x20 cm.<br />
- several pieces of cardboard (a middle sized cardboard box will do).<br />
- 1 spacer for the fork (or cardboard).<br />
- 1 roll of packaging tape.<br />
- 2 meters of duckt tape.<br />
- 2 or 4 plastic bottles.<br />
- Allen keys 4, 5 and 6 mm.<br />
- 15 mm pedal spanner.<br />
- scissors.<br />
- 1 large beer.<br />
<br />
Procedure: </span><br />
<ol>
<li><span style="font-family: inherit;">Put the beer in the fridge. </span></li>
<li><span style="font-family: inherit;">Tape the bottom of the box with packaging tape, from inside and outside. </span></li>
<li><span style="font-family: inherit;">Reinforce the carrying openings of the box with cardboard from the inside. </span></li>
<li><span style="font-family: inherit;">Shift the chain to the largest rear cog and largest front ring. </span></li>
<li><span style="font-family: inherit;">Put one plastic water bottle in a bottle cage. </span></li>
<li><span style="font-family: inherit;">Unscrew the pedals. </span></li>
<li><span style="font-family: inherit;">Fix one crank arm by taping it to the seat tube with duckt tape. The other crank arm should point down below the front rings to protect them. </span></li>
<li><span style="font-family: inherit;">Remove the seat and fasten back the seat clamp. </span></li>
<li><span style="font-family: inherit;">Deflate the tires slightly. The rear one a bit more then the front one. </span></li>
<li><span style="font-family: inherit;">Lower the rear wheel a bit below the dropout and move the wheel toward the seat tube. Tighten the rear Quick Release. This will give you some more room to fit the bike in the box. You may not need to do this if the box is long enough.</span></li>
<li><span style="font-family: inherit;">Cut the bottom of plastic bottles and protect the rear axle and the rear derailleur with it. This is done in order to prevent the axle </span>puncturing<span style="font-family: inherit;"> the box and as a </span>protection<span style="font-family: inherit;"> of rear derailleur. If you have only 2 bottles, cut them in quarters. </span></li>
<li><span style="font-family: inherit;">Unscrew the stem-steerer bolts and turn the handlebar for 90 degrees in line with the bike. </span></li>
<li><span style="font-family: inherit;">Fasten the stem-steerer bolts back. </span></li>
<li><span style="font-family: inherit;">Turn the bike upside down. </span></li>
<li><span style="font-family: inherit;">Remove the front wheel and remove the front quick release axle. </span></li>
<li><span style="font-family: inherit;">Put a spacer in fork dropouts. You can use a rolled piece of cardboard. </span></li>
<li><span style="font-family: inherit;">Protect the front wheel axle with plastic bottles. </span></li>
<li><span style="font-family: inherit;">Put the bicycle (without the front wheel) in a box. </span></li>
<li><span style="font-family: inherit;">Unscrew the stem-handlebar bolts and remove the handlebar. </span></li>
<li><span style="font-family: inherit;">Screw the stem-handlebar bolts back in. </span></li>
<li><span style="font-family: inherit;">Put the front wheel in the box so that it fits somewhere between the fork and the seat tube. </span></li>
<li><span style="font-family: inherit;">Put the handlebar in the box. </span></li>
<li><span style="font-family: inherit;">Put additional pieces of cardboard between the wheel axles and box sides, and between the front wheel and bicycle frame. </span></li>
<li><span style="font-family: inherit;">From a couple of pieces of cardboard a bit wider then the box width make rolls and put them in the box as spacers. This is not a </span>crucial<span style="font-family: inherit;"> step, but will give you some protection </span>against<span style="font-family: inherit;"> squashing the box. </span></li>
<li><span style="font-family: inherit;">Put the saddle, the pedals and front QR axle into the box and fix them to the bike or the rack. </span></li>
<li><span style="font-family: inherit;">If you have anything else to put in a box, do it now. </span></li>
<li><span style="font-family: inherit;">Shake the box and look for any loose parts. Everything should fit tightly without moving. </span></li>
<li><span style="font-family: inherit;">Close the box and seal it with packaging tape. </span></li>
<li><span style="font-family: inherit;">Have a beer. </span></li>
</ol>
<span style="font-family: inherit;">Time required: 2 hours. </span><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9eaSG630W4ucdYOi7WBa3PAVbslSMvEkvpj2FtVqmffbl7H_wLLc3tpLwCrnT9BIr4F64Vm41gGC1jhgCT8y2GddepwJUSmM1Rdd02dnLt6p_Sq-nCpd_byQVygNg7GAfY_QXGyZtCjA/s1600/pack.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="337px" px="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9eaSG630W4ucdYOi7WBa3PAVbslSMvEkvpj2FtVqmffbl7H_wLLc3tpLwCrnT9BIr4F64Vm41gGC1jhgCT8y2GddepwJUSmM1Rdd02dnLt6p_Sq-nCpd_byQVygNg7GAfY_QXGyZtCjA/s640/pack.jpg" width="640px" /></a></div>
<br />
<span style="font-family: inherit;">If you have smaller bike or wheels (MTB especially) and flat handlebar you can use a smaller box. If the box is too small, you'll have to take the rear wheel off too: in this case the procedure might be considerably different. </span><br />
<h5>
<span style="font-family: inherit; font-size: small;">Other options</span></h5>
<span style="font-family: inherit;">Of course, the cardboard box is not the only way to pack the bike for a flight. Other options are: </span><br />
<ol>
<li><span style="font-family: inherit;">Leave the bike unpacked, just turn the handlebar, lower the seat, deflate the tires and remove the pedals. There is an ongoing debate whether by doing so your chances of getting your bike damaged are increased or decreased. </span></li>
<li><span style="font-family: inherit;">Dismantle the bike and put it in a hard shell travel case. This would certainly be the preferred method if you have somewhere to leave the case upon your arrival. </span></li>
<li><span style="font-family: inherit;">After the procedure as in 1, put a minimal protection made of pieces of cardboard or pieces ob plastic bottles on the sensitive parts: shifters and derailleur. Something like </span><a href="http://www.flickr.com/photos/24563480@N00/228190027/in/set-72157594257325179/"><span style="color: #22aadd; font-family: inherit;">this</span></a><span style="font-family: inherit;">. </span></li>
<li><span style="font-family: inherit;">After the procedure as in 1, wrap the bike in plastic. You can use a roll of food wrapping plastic. A roll of 30cm x 50m should do. The result looks </span><a href="http://www.flickr.com/photos/24563480@N00/228190062/in/set-72157594257325179/"><span style="color: #22aadd; font-family: inherit;">like this</span></a><span style="font-family: inherit;">. </span></li>
</ol>
<span style="font-family: inherit;">Which procedure to use might depend on the policy of the airline company and whether you are starting the tour or flying back. I prefer to start the tour by packing the bike in a box as explained and my preferred option for a return trip is to wrap the bike in food-wrapping plastic. This allows me to cycle to the airport with minimal packaging material and without hassles of finding a box or transportation, preparing the bike and wrapping is quite easy and fast (half an hour) and attracts lot of interested attention at the airport. It also complies with rules of some companies that the bike has to be packaged (to avoid damage to other baggage).</span><br />
<span style="font-family: inherit;"><br /></span>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQvqqVcFgUbC8_YS0K9w3jeVwu1aUKfNVP9ey-xNKSzf2ivf1bUlEsXxiGrtjXoQD9d5zGl6SY63B0vNb4fRwwbP8aww5zI8nYAfTKtfaGJGNJj4v7kmkOV74SJ0nugy-yJqASNoJZXcQ/s1600/SAM_0726.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="426" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQvqqVcFgUbC8_YS0K9w3jeVwu1aUKfNVP9ey-xNKSzf2ivf1bUlEsXxiGrtjXoQD9d5zGl6SY63B0vNb4fRwwbP8aww5zI8nYAfTKtfaGJGNJj4v7kmkOV74SJ0nugy-yJqASNoJZXcQ/s640/SAM_0726.JPG" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">On return trips I usually improvise. More so as I like to cycle all the way to the airport.<br />
This is hardly a school example of the proper packaging of a bike for the flight, but, weighing less then 10 kg it was free of charge on the plane and arrived unscratched to destination after 3 connecting flights.<br />
Ingredients/tools required: a roll of scotch tape, a piece of cardboard and a razor blade.<br />
Pedals and seat were in my hand-luggage, tools & tent spikes (not allowed as hand-luggage) were taped to the rack .</td></tr>
</tbody></table>
Improvisation can save you some money on train (or bus) trips too. As an example, I can tell you my experience on trains Dali-Kunming (seater) and
Kunming-Chengdu (hard sleeper) in China. I bought the biggest bag I could find on the
market, disassembled the bike and put it (stuffed it really) in the bag and
carried it on the train. The bag was too small even only for the frame and rear
wheel, I carried second wheel in the other hand, but nobody in the station or in
the train said anything. In the seater I put the bag in the place between
compartments and in the sleeper under the bed. Everything went smoothly, except
that my arm grew few cm longer after carrying the bag around the stations. See the picture of the bike/bag below.<div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1o9dimT-9Y9jh3nSKpIGskLRrkSZC_cRKFuCaG6jGay8yH1bxXARDMTBwwEGc2WMAXOsJ5loIUHmZSuQTup5tGV2kmXpyf2QBGqSS6ia45GiUpqu8IpuakF_6_blx4cXFhK8evYYVyhs/s1600/Bike+bag.bmp" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="425" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1o9dimT-9Y9jh3nSKpIGskLRrkSZC_cRKFuCaG6jGay8yH1bxXARDMTBwwEGc2WMAXOsJ5loIUHmZSuQTup5tGV2kmXpyf2QBGqSS6ia45GiUpqu8IpuakF_6_blx4cXFhK8evYYVyhs/s640/Bike+bag.bmp" width="640" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">This is hardly a school example of proper packaging of a bike,<br />but it was
free of charge on the train.</td></tr>
</tbody></table>
</div>
iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com10tag:blogger.com,1999:blog-2823816027080391290.post-53451801420926651392010-06-08T15:05:00.001+02:002010-11-05T15:00:33.621+01:00Stiff sole myth<span style="font-family: inherit;">Another in the long line of cycling myths goes approximately like this: "When buying shoes for cycling make sure you get the ones with the stiffest sole you can find." The argument seems to be that the energy is lost by the flexion of the sole, so the one that flexes the least is the best. I must admit that this is a very convincing myth. I myself had fallen for it until very recently. <br />
<br />
But firstly, a clarification of the terms. If by "cycling shoes" we mean special shoes that are fixed to a pedal (SPD or similar clipless system) than this is not a myth but a reality. In this case the force on the pedal is transmitted through small area and if the sole were not strong (=stiff) it would quickly be ruined. However, I think that the stiff-sole-myth had been around before the clipless system hype, so it doesn't descend directly from it (btw, for the reasons explained above the </span><a href="http://iikmisc.blogspot.com/2010/03/clipless-myth.html"><span style="color: #22aadd; font-family: inherit;">clipless system</span></a><span style="font-family: inherit;"> is not an option for me). <br />
<br />
A recent experience convinced me that stiff sole used with ordinary pedals (no clips or straps) might be unfavorable. One Saturday I rode 150 km with two friends in a relatively fast pace. During and after the ride I felt great, the bike fit was perfect, I had no pains whatever. I felt as if I was at the peak of fitness. Next Sunday I rode 80 km "recovery" ride, same bike, same clothes, different shoes. To my surprise on that ride nothing seemed right: I had back pains and the saddle felt uncomfortable. On Saturday I had trainers with soft rubber sole, on Sunday I had shoes for in-door football (which, btw, were up to now my touring shoes) with stiff sole which became sleek and slippery during three years of use. So I am quite convinced that my uneasiness on Sunday was caused by the constant corrections of the position of my feet because the soles of the shoes were slipping on the pedals. If the soles were a bit more flexible they would grip the pedal preventing the slip. <br />
<br />
My conclusion is therefore that the non-slipping contact between the pedal and the sole is much more important then the stiffness of the sole; and this is better attained if the sole is somewhat softer. </span>iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-40649111507008177012010-05-25T15:04:00.000+02:002010-11-05T14:04:59.571+01:0026" vs 700c<span style="font-family: inherit;">The question which wheel is more efficient - 26" or 700C - has already attracted much intellectual energy, probably enough to power a small city for a year. I hope that my little addition to this wasteful practice won't turn you off, especially as you know that up to now the answer to this crucial question was still ambiguous. <br />
<br />
The first stumble-stone is in the question itself. There are a lot of different 26" wheels, as much as 700C's, and certainly you will find a pair to show that either 26" or 700c is the correct answer. We can answer the question unambiguously only if we make some further assumptions - and restrictions. In the following we will consider only the difference which comes from the size - all other things being equal. That means both wheels have the same hubs, spokes (apart from length), rims with tyres (apart from different diameter) and tyre pressure. Both wheels also carry the same weight. Secondly, we consider the efficiency in the following sense: a rider is coasting on a bicycle on flat hard surface (asphalt) with no energy input, so that the bicycle will, from the initial velocity, come to a stop due to various resistances, the wheel which stops later is more efficient. <br />
<br />
The resistances are: resistance from tyres rolling on ground (also known as rolling resistance), air resistance, and resistance in the hub bearings. <br />
<br />
Let's concentrate first on rolling resistance (RR). The cause of the RR is the flexion (deformation) of the tyre. The bigger the flex, the bigger the RR. Both 26" and 700c have the same contact patch A. I conclude this simply because Ap=W and since both tyres have same pressure p and bear the same weight W, the area is also the same. Since the width of the tyre w is the same then from A=wc, c (the length of the contact patch) must be the same for both wheels. But, 26" flexes more. To see this, look at the </span><a href="http://en.wikipedia.org/wiki/Circular_segment"><span style="color: #22aadd; font-family: inherit;">segment of a circle</span></a><span style="font-family: inherit;"> with a chord of length c. You can see it as flattened part of the tyre in contact with the ground. The area of this segment is equivalent to the amount of the flex. Given the fixed chord length c, bigger circle has smaller segment - or smaller flex. And opposite, smaller circle (26") has bigger area=flex. In other words, rolling resistance of 26" is greater. <br />
<br />
The formulas at the Wikipedia page can be used to calculate segment area (equivalent of RR) for any combination of W,w,p,R. I did this for a typical touring situation: W=50 kg, w=35 mm, p=4 kg/cm2 and both wheels (diameters ISO 559 and 622) and I get 10% bigger RR for the 26" (ISO 559). Surprisingly, the result (1.10034) is practically the same as the ratio of wheel diameters (with tyres on): (622+2w)/(559+2w)=1.10016. <br />
BTW, using the same equations we can prove the often stated argument that wider tyres of same diameter and pressure have smaller RR then thinner ones. <br />
<br />
Now, let's look at the resistance in the bearings. It is also in favor of 700c wheels, since on a fixed road distance bigger wheels rotate less times. The bearing resistance of a 26" wheel is then bigger for the factor depending on wheel diameters (with tyres on) - the same factor as above: (622+2w)/(559+2w) =1.10016. <br />
<br />
The air resistance is proportional to the frontal area. Considering just the wheels, the front area of 700C is greater by the same ratio of the wheel diameters: (622+2w)/(559+2w). But we are considering a rider and a whole bicycle (not just the wheels), so this disadvantage is smaller. If the percent of the wheel frontal area to the whole riding frontal area is f, I estimate f=7%, then the advantage of 26" due to smaller air resistance is by a factor 1.0065. <br />
<br />
Our finding is than, that 700C wheels have smaller rolling and bearing resistances, both of about 10%, but have a greater air resistance of about 0.7% because of greater frontal area. It is not difficult now to predict when the 26" wheel will be more efficient. It will be when air resistance force is 0.1/0.07=14,3 times greater then combined rolling resistance + bearing resistance force. The air resistance force increases (nonlinearly) with speed, so we expect that 26" will me more efficient above a certain speed. Using </span><a href="http://www.analyticcycling.com/ForcesPower_Page.html"><span style="color: #22aadd; font-family: inherit;">this calculator</span></a><span style="font-family: Verdana; font-size: x-small;"><span style="font-family: inherit;"><span style="font-size: small;">, starting with the default data, setting slope 0% and weight 100 kg, and playing a bit with the speed, we can see that above 70 km/h the air force is greater than rolling resistance force for a factor 14.3. <br />
So, the conclusion: 26" are more efficient than 700C only at extreme (downhill) speeds. <br />
<br />
<span style="color: #888888;">P.s. Just before 700c (or "bigger is better") enthusiasts start screaming of joy and ordering rounds of beers, let me remind you that situations such as "just size - all other things being equal" don't exist in the real world. Depending on tyre width, tyre pattern, weight, pressure and possibly year of your birthday, 26" might well be preferred.</span></span></span> </span>iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com2tag:blogger.com,1999:blog-2823816027080391290.post-62258864612728409652010-05-01T14:58:00.001+02:002013-12-11T15:25:27.867+01:00Digital maps<span style="font-family: inherit;">Do you like to hang on at the end of the day, with a map spread in front of you, tracing on it the route you've just cycled and contemplating the part that lies before you? It's one of the best feelings isn't it? Well, that's just about all there is good about a map! From a point of view of a light-weight unsentimental cycling warrior - a map is a waste of space. The first urge after this realisation is to cut the map, leaving only the part where you wish to travel. But, there is a much more thorough approach: digitizing a map. <br />
<br />
The idea behind it is rather simple. You can view a map as a colection of points of interest and connections between them. This info can be stored in "digital" form, using alphanumeric characters, in much smaller space then the map itself. The point of it is to store all the information on a small plastified card which is accessible "on the fly", say from a cycling jersey's pocket, without any unfolding, searching, folding and storing. Larger itineraries can be stored on several cards with only one used at any time. Such digital info may not be visualy as clear as a map, but all the info will be there. In fact your card will have much more info then a map, since there will usually be enough space on the card to store info on water points, food, accomodation, camping spots, altitute, passes, check points, usefull phrases, important telephone numbers, repair tips, ... <br />
<br />
There are many ways to make a digitization. I will explain how I do it currently by an example of digitizing Himalaya itineraries in Pakistan, India, China and Nepal. </span><br />
<ol>
<li>Let me start with some definitions. A <i>crossroad</i> is a point where more then two roads meet. A <i>point of interest</i> is either a crossroad or any other feature (e.g. a town, a camping spot) that is on the road and is not a crossroad. A <i>connection</i> is a part of the road between two points of interests, A and B, with the condition that it has no other crossroads on it. Any network of roads can be described as a collection of connections. </li>
<li>The first step is to draw a diagram of the selected routes, showing all possible connections and major points of interests. In the diagram the points of interests are presented as numbers, 0,1,2,... </li>
<li>We represent a point of interest as a name and its number immediately following it. The points of interests are, for example: Islamabad0, Kashi1, Ali2, turn off to north4, Saga3, etc. The points of interests are fully defined by their numbers, the name is not necessary and may be used for clarity. </li>
<li>We represent a connection by its ending points of interest, separated by a dash: Islamabad0-Kashi1, Ali2-Saga3, Ali2-turn off to north4. The connection is fully defined by ending points' numbers, the name may be used for clarity: 0-1, 2-Saga3, Ali2-4, Saga3-t.o.north4. </li>
<li>We first list all the possible connections, using their numbers and names when they are introduced for the first time. As an additional information we add distances of the connections in parenhteses. All the distances will be in kilometers. Example: Islamabad0-Kashi1(1182); 1-Ali2(1323); 2-Saga3(752); 3-t.o.north4(62); 2-4(978). 3-HWY318t.o.5(167); 5-Kathmandu7(231); 5-Tingri.t.o.6(73); 6-EBC8(67). 6-Shegar.t.o.9(48); 8-9(96); 9-Lhatze10(133). 4-10(257); </li>
</ol>
In the second part we add detailed information about the individual connections. We can do that for all of the connections or just the selected ones. The detailed info for one connection looks like this: <br />
<i><b>1-2</b></i>: #315: 200/TL:Yarkand. 65/<u>Yecheng</u>,TR. #219: 25,1500/armyB. 31,1840/V. 15/F. <b>41,3150</b>. 14/F. 5/armyB. 30,3000/Kudi(426). 18,3280/armyB,F. 27,4300/RRS. <b>11,s217,4825</b>. 24,3675/<u>Mazar</u>,TL. 13/F. 35,3860/RRS. 3/F. <b>17,s309,4795</b>. 15/rrs. 16/RRS. 24,3560/<u>Xaidulla</u>(629). 41,3700/t.o.KKH. <b>20,s425,4180/Kosbel</b>. 12,3800/Kangxiwar,RRS. 50,4000/Dahongliutan. 25,4500/RRS. 22,s534,5080,Aksai Chin. 9,4900/tent,f. 34,4735/Tianshuihai. 93,s670,5125. 2,5005/Tielong. 16,s688,5185. 12,5000,Lungmo tso. 15,s715,5090/NP. 5,5140. 10,5090/<u>Sumxi</u>. <b>10,s740,5400/!</b>. 88,4275/<u>Domar</u>(1093). 17,s845,4520. 8,4300/LP. 40,4170/house,f. 2,4150/Nyak tso. 23/H,boats,fish. 15,4150/<u>Rutok Xian</u>,TR. 27,4240/tent. 2,4250/houses. 3,4250/t.o.Rabang. 2,4250/petrogl. <b>53,s1020,4715/Lame</b>. 32,4350/cp. 6,4200/<u><b>Ali2</b></u>. <br />
<br />
The meaning of it is as follows: <br />
<br />
<pre><span style="font-size: small;"><i><b>1-2:</b></i> info on connection 1-2 (Kashi-Ali) follows.
#315: road number 315.
200/TL:Yarkand. after 200 km turn left for Yarkand.
65/<u>Yecheng</u>,TR. 65 km to Yecheng, after that turn right.
#219: road number 219.
25,1500/armyB. 25 km to army base, it's at the altitude 1500 m.
31,1840/V. 31 km to a village, its altitude is 1840 m.
15/F. 15 km to guaranteed food.
<b>41,3150</b>. after 41 km there is a pass, at 3150 m a.s.l. Passes are represented in bold.
14/f. after 14 km there is probable food
5/armyB. 5 km to army base.
30,3000/Kudi(426),CP. 30 km to Kudi. Kudi is at 3000 m altitude and 426 km from the starting point of this connection (e.g. from Kashi).
There is also a Checkpoint.
18,3280/armyB,F. 18 km to army base at altitude 3280 m and guaranteed food.
27,4300/RRS. 27 km to Road Repair Station, at 4300 m.
<b>11,s217,4825</b>. 11 km to a pass at 4825 a.s.l. There is a stone kilometer marker "217" at the top.
24,3675/<u>Mazar</u>,TL. 24 km to Mazar, at 3675 m. Mazar is underlined, which means you can get everything there (water, food, accomodation).
After Mazar turn left.
...</span></pre>
The extent of the detail for individual connections can be different. For difficult routes like the above one, you need detail on food points and altitude. For an easy connection only a connection length may be needed, all other info may not be necessary or might be found while cycling the road itself. The info on all of the usual connections in Hymalaya region can be stored on a card with dimensions 13x8 cm - for a person with good eyesight, that is. The front page of this card would look like this: <br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj23VhDosc634f9DGZPnRCokCyxV5rginXBMZPOCbJo4acyyoobAG4qQPY8GqbNuppgzd7gv8OX6nmVBdxbA2hP0x9QrmsCa9LM_lIi6qOwELAe0wdgXYFdM21XrDeF7vQehVFbARahQaU/s1600/card1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="366" px="true" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj23VhDosc634f9DGZPnRCokCyxV5rginXBMZPOCbJo4acyyoobAG4qQPY8GqbNuppgzd7gv8OX6nmVBdxbA2hP0x9QrmsCa9LM_lIi6qOwELAe0wdgXYFdM21XrDeF7vQehVFbARahQaU/s640/card1.jpg" width="640" /></a></div>
<br />
The opposite side would have info on connections in India and Nepal (between Lahore, Amritsar, Srinagar, Leh, Delhi and Kathmandu). There would be enough space left on that side for personal info and few grace-saving chinese phrases.<br />
<br />
"Digital maps" are an evolving subject: here is the latest one, covering the tour in <a href="http://iikinvietnam.blogspot.com/">Vietnam and China</a><br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLpLPT4Co4HA6k7J3rf72tTSGfqP9tGGolN_HD7a3KuRuBdH5__ilWpeYdFBbcErOOvE7zcp0MttH2sT0xVDOHX7AxnkzuA2aQw5KF4edOlpG7Z5h7ZfdVcuhXTm44_z9ZUxcKRv-KbBM/s1600/SAM_0751.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="265" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLpLPT4Co4HA6k7J3rf72tTSGfqP9tGGolN_HD7a3KuRuBdH5__ilWpeYdFBbcErOOvE7zcp0MttH2sT0xVDOHX7AxnkzuA2aQw5KF4edOlpG7Z5h7ZfdVcuhXTm44_z9ZUxcKRv-KbBM/s400/SAM_0751.JPG" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white;"><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 11px; line-height: 14px;">Iik's latest Navigation App. </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 11px; line-height: 14px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 11px; line-height: 14px;">Note some minor, ingenious upgrades to his cue-sheet (i.e. digital map) concept, </span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 11px; line-height: 14px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 11px; line-height: 14px;">like color-coded items and top-left notch for quick card orientation</span><br style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 11px; line-height: 14px;" /><span style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 11px; line-height: 14px;">(which could possibly be used as bottle opener). </span></span></td></tr>
</tbody></table>
<br />iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-69997935696689985422010-04-15T14:55:00.000+02:002010-11-05T13:56:43.573+01:00Does weight matter?<span style="font-family: inherit;">The basic phisycal equations for the forces on a bicycle rider show that weight has almost proportional effect on the power required for cycling. That is: the required power is greater by the same percent as the percent weight increase of the rider+bike+luggage combination. Interestingly, this fact is the basis for the conclusion that weight doesn't really matter that much: if I weigh 75 kg, my bike 15 kg and my touring luggage 20 kg (a total of 110 kg), then even if I manage to reduce my luggage by 50% (10 kg less - a very difficult task indeed), it would still mean just 9% gain in power. Why then bother with it at all? Well, there are several reasons why light weight might be prefered. I can think of the following: <br />
<br />
- The fatigue life.<br />
- The simplicity.<br />
- The effort.<br />
- The lifestyle.<br />
- The elegance.<br />
<br />
<b>The fatigue life.</b> Weight has large influence on the material of the bike and other equipment. Metals fatigue roughly with 3rd power of stress - and stress is proportional to weight. 5% decrease in weight, for example, results in 16 % increase in fatigue life of the equipment. 20 % decrease in weight = 73 % increase in fatigue life. By reducing the weight one then considerably reduces the likelyhood of equipment breakage. This is the primary benefit and the one that made me go the light way. The stories about cracked rims and broken racks are almost without exception told by 4-panniered heavy-duty tourers. By the way, it seems logical that the weight has similar effect to the body fatigue. The body can heal, of course, but it requires energy to do so. <br />
<b></b></span><br />
<span style="font-family: inherit;"><b>The simplicity.</b> Simplicity is freedom. And freedom means simplicity. They are the same thing. With each thing less you are more carefree. I remember one occasion when I bought a wooden carving in Zimbabwe. From the moment when I purchased an, otherwise outstanding sculpure, I was in a constant worry. How will I transport it on a bike? How will I protect it from the rain? What if they stole it from my tent? How will I take it on the plane trip back home? Will they accept it as hand luggage? And if not how will I package it? These worries made for some miserable nights until the return trip and a 2 kg statue on the the rear rack resulted in a couple of broken spokes (on otherwise already weakened back wheel). <br />
<b></b></span><br />
<span style="font-family: inherit;"><b>The effort.</b> As said above, you need more power to cycle with heavier setup. 9 % more power may seem negligible with respect to the comfort that you're supposedly throwing away. It is a matter of preference: is it important to you to make 10 or 15 km more each day? Or you can cycle the same distance, feel much less tired and have more time in enjoing your rest. Far more effort (in terms of percentage) is saved when you have to carry or push your bike: in this situation your body weight doesn't enter the equation and the effort is proportional just to luggage (and bike) weight. In fact, body weight should not have the same impact as luggage and bike weight. Heavier people are usualy stronger and can produce more power. It is somewhat misleading or "unfair" to compare lugguage weight of differently strong people. But if we take out the body weight from the above equations, then reducing the luggage weight by 50% makes a 29% gain in power, instead of 9%. The real percent gain is somewhere in between. <br />
<b></b></span><br />
<span style="font-family: inherit;"><b>The lifestyle</b> Cyclists like to think of themselves as ecologicaly superior to motorists. By the same line of reasoning lightweight touring is superior to loaded touring. A couple of years involved in reducing the luggage weight had changed my view on many things, unrelated to cycling. I became aware of many redundancies in our everyday procedures and behaviour. <br />
<b></b></span><br />
<span style="font-family: inherit;"><b>The elegance</b> Obviously this is a subjective thing, but a light setup on an elegant bike, preferably set in some spectacular natural environment, is a real pleasure to my eye.</span>iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com2tag:blogger.com,1999:blog-2823816027080391290.post-63926736231038517962010-03-20T13:52:00.002+01:002013-01-22T11:47:49.962+01:00The clipless myth<span style="font-family: inherit;">To start right from the middle: I don't like clipless system. The fact that I broke my arm in a low-speed fall because I failed to unclip may have to do something with this position, but it's not the only reason. <br /><br /><b>Efficiency</b>. I heard claims that clipless system greatly improves cycling efficiency - there were numbers as high as 20%. I was skeptical, so I did my own measurements in a real-world road-cycling circumstances. I was more then disappointed. I measured average speed on two loops of fixed length (60 km and 85 km) with and without clipless system, all the other factors being the same (i.e. the same bike and clothes). The average difference (averaged over 2 and 6 rides) in average speed was less then 0,5%. On one of the sections it was in favor of clipless system, on the other section it was in favor of plain pedals and shoes. The difference was smaller than the difference in individual rides within one system. Thus, my measurements doesn't show any statistically significant advantage of any of the system. <br /><br /><b>Safety</b>. All clipless advocates confess that falling off is part of the learning process. What they do not tell is that you will damage your bike in that process and that an injury is a real possibility. My quick search through the net revealed only 4 voluntarily reported injuries caused by clipless system. When talking to the people after my accident I got the impression that they are much more common - even my physiotherapist had broken the arm. There seems to be a high degree of self-censorship, self-guilt (e.g. "it's MY fault that I couldn't unclip") and the dread of being scoffed at by the "pro"'s. <br /><br /><b>The feel</b>. Nothing is life is all bad or all good. I liked some aspects of clipless system, especially "the feel" and "the look". I suspect that these are the main reasons for its popularity. As for me, I am not going to risk another 2 or 3 months of rehabilitation, just to stay within the "cycling mainstream". The proper cycling technique and a positive feel that your foot is not slipping on a pedal can be trained and learned, without any disadvantages of restrained feet. <br /><br />Every so often I read and hear people comlaining about some additional aspects related to the clipless system: pain in feet, ankles or knees due to restricted movement, water seeping in through the holes in the soles, cold sensation due to heat transfer through the cleats, sorenes in the feet due to pressure in the cleat area, awkward walking, the need for a second footware on a tour. The general consensus, however, is that the benefits of the clipless system override any disadvantages. But what exactly are these benefits? Have they ever been proven in an authoritative research? I know of a few reasearches regarding this issue (</span><a href="http://www.ncbi.nlm.nih.gov/pubmed/18418807"><span style="color: #22aadd; font-family: inherit;">link here</span></a><span style="font-family: inherit;">) and according to them the benefits for a non-proffesional cyclist are so slim (*), that I can only conclude that clipless system is just another market gimmic with huge turnover, exploiting people's urge to follow the fashion. </span><br />
<br />
(*) What this abstract says is: Shoe-pedal interface (flat pedals vs. clippless pedals) does not influence cycling effectiveness during normal (submaximal) exercise. Only an active pulling-up action on the pedal during upstroke increases the pedalling effectiveness, while reducing overall efficiency. <em>It is, really, pretty logical: yes, when you pull up, you will be quicker, but you will loose more energy then if you didn't pull up. So, in brief, there is no free lunch; in fact, the clipless lunch is more expensive.</em>iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com9tag:blogger.com,1999:blog-2823816027080391290.post-42434157153000322442010-03-09T14:47:00.001+01:002010-11-05T15:02:21.180+01:00Repair tipsSome of us like to have our bikes in perfect order, no ticking, skipping, squealing. Here are some things that I learned over the years, by experience or from the net.<br />
<br />
<ol><li><b>Tyre wear at one spot</b> can be the result of a bent or untrue rim. When the bent part of the rim hits the brakes, the part of the tyre which is at the contact with the ground at that instant skips. As this is<br />
always the same point of the tyre (unless you are rotating it regularly on the rim) it will eventually wear out and blow. The thing happened to me in <a href="http://www.blogger.com/kyr.htm">Kyrgyzstan</a>, the explanation is <a href="http://www.sheldonbrown.com/">Sheldon Brown's</a>.</li>
<li><b>Broken brake cable</b> usualy doesn't happen unexpectedly. The individual wires in the cable break first with a warning sound that can be heard, and which usualy happens after a sudden squeeze of the brakes. Check out the cables when such warning comes.</li>
<li>When <b>breaking the chain</b> the pin should not be extruded completely. If this happens however, you can hammer it back by holding it with some narrow tool. Needle plies are the best, but a piece of wood with the hole in it might do as well. The stiff link is loosed simply by bending the side plates of the adjacent links.</li>
<li>If you feel <b>a bump every wheel revolution</b> and the rim is true, it's most probably a tyre bead that is unevenly engaged in the rim or is even pinching the tube. It may also be due to the damaged tyre sidewall.</li>
<li>If the <b>chain stucks in the deraileur</b> seemingly unrelated to the revolution of the cranks, check out the side plates of the chain - they may be broken.</li>
<li><b>Ticking in the handlebar</b> most likely comes from a stem/stearer connection. Grease every part of this connection, including bolts, and tighten.</li>
<li><b>Ticking in seatpost</b>. Check if your seat tube has a metal shim between the tube and the seatpost. Grease all the surfaces that come into contact (shim/seatpost, shim/seat tube). </li>
<li><b>Squeal in the rear derailleur during shifting</b>. Oil the axis of pulley wheels. </li>
<li><b>Ticking in the crankset area</b>. Could be number of things. Check out the simple things first: oil the pedals; tigten cranck bolts; see if cranck is not hitting the front derailleur cable; make sure the sound is not coming from your shoes. The sound could be comming from loose saddle or seatpost.</li>
<li><b>Cracking sounds</b> unrelated with pedal or wheel revolution. When the spokes are too loose they can slip at the points where they cross each other. Happens both when seated or not, holding handlebar or not. Can't happen on radially laced wheels.</li>
<li><b>Squeel when turning the handlebar</b>. Break/shifting cables are fretting in cable stops - oil the cable stops. Cables may fret one against other - tie them with tape.</li>
<li><b>Rattling</b> when going over rough surface. It can be caused by anything that is attached to the bike (bags, lock, pump, water bottle, ...) or anything loose in the bags. If it happens on "naked" bike: check the headset for looseness; check that the shifting or braking cables are not hitting each other.</li>
<li><b>Unusual sounds</b>. Deal with them by eliminatig possible causes one at the time. Is the sound present only while turning pedals? Only while seated? Only while riding a bike (i.e. not when turning the wheel by hand)? Only when holding the handlebar? Only when peddaling forward? Only with bags attached?<br />
With each crank revolution? With each wheel revolution? Sounds may not necesarily come from the bicycle - check the panniers, racks, shoes, things in your pockets.</li>
<li><b>Derraileur adjustment</b> is most easily done when the bike is turned upside down. Just check visually that the pulley wheel runs in the middle of the cog.</li>
<li><b>Rim wear</b> can be drastically reduced by using quality brake pads. The sand particles will embed quickly in most of the ordinary pads. This will act as sand paper, chipping off bit of rim material, which will in turn embed into the pad rubber, resulting in even more wear. Use best pads you can get:<br />
Kool-Stop pads are the best.</li>
<li><b>Brake squeal</b> is reduced by proper toe-in of the brake pads and sand-papering the rim. </li>
<li><b>Cleaning the chain</b> on the road. Find a piece of rug by the side of the road. Start by cleaning the pulley wheels. Then clean the front chainrings. Then start cleaning each chain link: shift the chain to the big front ring and clean the links as they go around the front ring teeth. The chain is not flexing there so you can clean it using one hand only. (This is one operation where I would not agree with <a href="http://www.sheldonbrown.com/brandt/upside-down.html">Jobst Brandt</a><br />
and prefer to do it with the bike upside-down.) Then oil the chain: dip the end of a toothpick into oil and put one drop of oil in the roller/sideplate gap of each chain link. Wipe excessive oil.</li>
<li><b>Carbon forks</b> have a bad reputation for touring. I don't know why. I cover mine with electric tape or with bubble wrap as a protection from scratches. So far, it worked rather good.</li>
<li>Low pressure is bad. Among other things it can result in <b>cracked tyre sidewall</b>.</li>
<li>Tips about reducing probability of <b>punctures</b> are given <a href="http://iikmisc.blogspot.com/2010/11/all-you-never-wanted-to-know-about.html">elsewhere</a>.</li>
<li>If <b>you don't have the appropriate tool</b> try to improvise. Imagine what the procedure would be like if you had the tool. Think about the principle of that tool. You may find a simple substitute that has the same principle.</li>
</ol>iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-77436882139553761722010-02-27T14:39:00.000+01:002013-05-06T08:48:04.836+02:00All you never wanted to know about puncturesTo unacquainted rider punctures come as incomprehensible random events which generally follow Murphy law of happening at the worst possible moment. We will however try to put a trifle of rationality in it, hoping at the same time that vicious Puncture God doesn't take this as a heresy.<br />
<br />
First of all - as heretical as it may sound - every puncture has its cause. This is the founding axiom of puncture science and the most important concept for puncture-free experience. If you have a puncture for which you don't know the cause, you will have lots more of them - and rightly so, since you didn't make an effort to understand it.<br />
<br />
The causes of punctures can be separated into two types:<br />
<ol type="a">
<li><b>external puncture</b> is caused by an external object first protruding through the tyre and then puncturing the tube.</li>
<li><b>internal puncture</b> is one that is not external.</li>
</ol>
Within these types there are variations. We further subdivide punctures as to get a list of every possible puncture cause known to man, woman or child. The following causes are ordered from most likely to least likely cause, based on my experience.<br />
<br />
<ol type="a">
<li><b>external punctures</b></li>
<ol type="1">
<li>external object embeds into the tyre and punctures the tube after several wheel revolutions.</li>
<li>external object protrudes through the badly worn tyre, punctures the tube</li>
<li>external object is pushed through tyre and the tube deliberately.</li>
<li>external object protrudes through tyre and the tube within one wheel revolution.</li>
</ol>
<li><b>internal punctures</b></li>
<ol type="1">
<li>"pinch flat" or "snake bites" when a tyre presses against the tube, mostly when hitting a rock or a pothole.</li>
<li>tube punctures near the valve facing the rim.</li>
<li>tube protrudes through the valve hole and blows out.</li>
<li>tube rubs against an object caught between the tube and the tyre (eg. piece sand, shreds of rim tape, etc.).</li>
<li>tube punctured with a tool when installing it on a rim</li>
<li>tube protrudes through the fault in the tyre and blows out.</li>
<li>tube is pinched between the tyre bead and the rim and blows out or punctures.</li>
<li>deliberately deflated tube (this is not a puncture, but looks like one).</li>
<li>tube patch peels off</li>
<li>tube patch cracked</li>
<li>spoke is too long and punctures the tube from the inside</li>
<li>tube rubs against a fault inside the rim, or against the rim tape.</li>
<li>tube rubs against a fault on the inside of the tyre.</li>
</ol>
</ol>
More often then not you can tell if the puncure is external or internal, or even its subcategory, by a<br />
little forensic study. Use the following procedure:<br />
<br />
<ol type="1">
<li>Before removing the tube from the wheel mark one matching point on both the tyre and the tube. This step is not necessary if you've installed the tyre and the tube correctly (see points 13, 14 and 15 below for installation).</li>
<li>Before removing the tyre look if there are pieces of sand, etc. inside it.</li>
<li>Look if the puncture is at the inside of the tube (the surface facing the rim). If it is, it's an internal puncture.</li>
<li>Examine the rim and/or the tyre at the point that matches with the point of the puncture in the tube. You are likely to find the cause of the puncture at this point. If you don't find it there, go all around the tyre and/or the rim looking for one.</li>
<li>Some punctures (a.2, a.3, b.1, b.2, b.3, b.6, b.7) have no physical evidence of the cause, but some<br />can be identified by the position or appearance.</li>
<li>Type a.2 punctures usualy occur on a very worn tyre thread (eg. so that tyre fabric beneath is showing or if there are a lot of cuts and cracks in the thread). The thread is so thin that the item that punctured the tube (a sharp piece of stone, glass) will not embed in the tyre and will fall off. Changing the tyre is the best remedy.</li>
<li>Snake bites (b.1) are often in a form of double holes about 4 mm apart.</li>
<li>b.2 and b.3 type punctures are at the base of the valve. b.2 punctures are frequently caused by high-pressured tube pressing against the nipple head on single walled rims. (See the solution below).</li>
<li>Some punctures (b.2, b.3, b.6, maybe b.7) can happen when the bike is not in use (e.g. overnight).</li>
<li>A minuscule, slow leaking puncture on the side of the tube is representative of a needle pinch (a.3)</li>
<li>Blowout type of punctures (b.2, b.3, b.6) deflate the tube immediately. b.3 and b.8 leave large holes.</li>
<li>External punctures of type a.1 are often slow leaking.</li>
<li>Rubbing-type punctures (b.4, b.12, b.13) are also slow leaking, at least in the first stage when the tube develops small sracks in the rubbing area. Eventualy these cracks join into a bigger hole.</li>
<li>If you can't identify the cause, record the circumstances for further analysis. If a puncture is particularly mysterious, send the details to me, I am collecting such data.</li>
</ol>
The good news about the punctures is that most of the type b punctures are avoidable. With little care, most of the type (a.1) punctures are avoidable too. Replacing the excessively worn tyre usualy gets rid of the (a.2) punctures. So only with the type (a.3) are we in the mercy of Puncture God, which in this case frequently takes the form of a common man. My advice to puncture-free experience is the following:<br />
<br />
<ol type="1">
<li>Pump your tyres to high pressure. Check and keep the pressure high at all times. Recommended pressure on the tyre sidewall is high enough. If pressure range is indicated, go closer to the higher value. I don't believe in benefits of reduced pressure (e.g. higher traction, softer ride).</li>
<li>Always find out the cause of the puncture and remove it.</li>
<li>Check both tyres regularly for embedded bits of glass, wire, etc. Do this before or after every ride at home and at the start/end of the day on a tour. I always keep a safety pin on my jersey to pick out the bits from the tyre.</li>
<li>Do the above check immediately if you ride through pile of glass, etc.</li>
<li>Do the above check immediately if you hear the sound comming from the wheel at each wheel revolution.</li>
<li>Do the above check always after a puncture unless you are absolutely certain it's an internal puncture.</li>
<li>Don't use any tapes between the tyre and the tube - at least not as a permanent solution.</li>
<li>Use rim tape.</li>
<li>Change the tyre when its sidewall is cracked. As a temporary solution make a tyre boot (duck-tape worked for me).</li>
<li>Change the tyre when its thread wears so much that the tyre fabric beneath is showing. As a temporary measure put a piece of duct tape over these parts.</li>
<li>Few things are important when patching tubes: clean the tube with sand paper before applying rubber cement; let the cement dry before applying the patch!!; press on the patch for 3 minutes; remove the plastic cover from the patch after few hours.</li>
<li>Inflate the tube slightly before puting it inside the tyre. </li>
<li>As a protection against b.2 and b.3 punctures, cut a patch of an old tube and slide it down the valve, so that it covers the valve base (about 2 cm of tube left and right from the valve). Cut a notch on one side of this patch, let's say on the left side.</li>
<li>Most tyres are marked by the manufacturer and brand names only on one side. Install your tyre so that the valve hole is at the middle of this mark and that the mark is on the QR side of the wheel (or on the opposite side, according to the drive direction marked on the tyre).</li>
<li>Put the tube inside the tyre so that the notch mentioned in #13 is to the left when you are facing the tyre mark mentioned in #14. This fixes the relative positions of the rim/tube/tyre combination and hepls in finding the cause of the puncture.</li>
<li>Refrain from using any tools for mounting the tyre on the rim. If this can't be done, it's time to think about different tyre.</li>
<li>With the tube partially inflated go around the tyre and check that the tyre bead doesn't pinch the tube against the rim.</li>
</ol>
iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-2255088235583542732010-01-15T14:26:00.000+01:002010-11-05T13:48:43.187+01:00Calibrating the bicycle calculator<span style="font-family: inherit;">I noticed that my bicycle computer is rarely as accurate as are road markers - usualy it shows few percents more. I was pretty sure this is caused by a wavy bicycle path - until I did some calculations. Let's look at this more closely. <br />
<br />
<i>Question</i>: What distance will be recorded on a bicycle computer on a straight, flat 1 km path if you cycled in a zig-zag fashion, swerving away from the middle line for 10%, lets say a=1 m every L=10 m (i.e. 1 m to the left after 10 m, 0 m after 20 m, 1 m to the right after 30 m, etc)? <br />
<br />
Lets denote a pecent of off-center deviation as f=a/L. Then, instead of every straight L meters you are doing L1=SQRT(L^2+a^2)=SQRT(L^2+f^2L^2)=L*SQRT(1+f^2) meters. Your path is longer for k=L1/L=SQRT(1+f^2) (in percents). So, for f=10% off-center deviation your path is longer for k=0.499 %. In 1 straight km you are doing 1.00499 km or 4.99 meters more. <br />
<br />
The point of this is to show that inaccuracy of the calculator due to the oscilating path of the wheel is negligible (0.5 % for off-center deviations as high as 10%). Manual instructions for calculator set-up are typically innacurate up to +3%. </span>iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com0tag:blogger.com,1999:blog-2823816027080391290.post-4003937732702933632009-12-10T14:22:00.000+01:002010-11-05T13:48:32.451+01:00Steel frame is softer than aluminium one?<span style="font-family: inherit;">Modulus of elasticty, brittleness, strength, stiffness, elastic limit, are standard terms of the theory of elasticity. They are, however, more often than not misinterpreted when used in "technical" debates about bicycles. Many times they are abused as a "scientific evidence" of some natural feel like: "steel is softer then aluminium". Softness, by the way, is not a standard quantity in the theory of elasticity. It can be interpreted as a reciprocal quantity to stiffness. The measure of stiffnes of a material is its modulus of elasticity, or Young modulus, E, which is defined as a ratio of stress vs. strain. In that sense the common bicycle myth that steel is softer than aluminium is a total nonsense. It is not true that steel has relatively low modulus of elasticity, i.e. is a "soft material". In fact its modulus of elasticity (Young modulus) is the highest of all commonly used engineering materials: it is 210 GPa, which is 3 times greater than aluminium (with 69 GPa), 1.75 times greater than titanium (120 Gpa) and at least 1.4 greater than carbon fiber (150 GPa). You can find these figures in a table on Wikipedia page: </span><a href="http://en.wikipedia.org/wiki/Young%27s_modulus"><span style="color: #22aadd; font-family: inherit;">http://en.wikipedia.org/wiki/Young%27s_modulus</span></a><span style="font-family: inherit;">. Steel is the stiffest material to make a frame of, unless you are considering a tungsten or a diamond one. <br />
<br />
It is perfectly OK with me if someone feels a steel frame to be softer than aluminium. But please don't try to prove this by misinterpretation of some half-understood theory. <br />
<br />
<span style="color: #888888;">P.S. I am not a "steel-hater". Steel is the best engineering material for most applications because of its strength, stiffness, ductility, fatigue strength, weldability and price - but certainly not because of it's softness. </span></span>iikhttp://www.blogger.com/profile/08044746367328550812noreply@blogger.com4