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#21
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Deriving a unicycle crank length formula?
Having been bred an engineer, I spent some time thinking about this and I offer the following. What we want to know is how will a given crank on a given wheel feel in terms of power and control. Where feel means many things as mentioned in the strings referenced--control, speed, torque, rotational diameter, power, knee pain...etc. Work equals force times distance. For different wheel sizes on different rims to feel the same, will essentially require that the rider be accomplishing the same amount of work. Each wheel size has a different diameter, when circumference is calculated...Pi times diameter, you can obtain a number for each wheel size. Then by multiplying by 2.54 you can determine the circumference in centimeter. 20� diameter times Pi equals 62.80 in or 159.51 cm 24� diameter times Pi equals 75.36 in or 191.41 cm 26� diameter times Pi equals 81.64 in or 207.37 cm 29� diameter times Pi equals 91.06 in or 231.29 cm 36� diameter times Pi equals 113.04 in or 287.12 cm By accomplishing a ratio of circumference divided by crank length in centimeters, you can determine a ratio for comparison. Using this approach each crank length and wheel diameter can be compared in a grid. I hope the chart works on the internet... Wheel -- 20 24 26 29 36 Crank 85 -- 188 225 244 272 338 110 -- 145 174 189 210 261 114 -- 140 167 182 203 252 125 -- 127 153 166 185 230 140 -- 114 137 148 165 205 150 -- 106 127 138 154 191 165 -- 97 116 126 140 174 170 -- 94 113 122 136 169 175 -- 91 109 118 132 164 These numbers provide a referenced baseline for the work of a given crank/wheel combination for the same distance output. Similar numbers between columns will represent similar feel in terms of unicycle performance--given that each of us has a different comfort level and range of comfortable skill. Note that a 20 inch with a 125 crank gives a rating of 127...which compares in terms of work and feel to a 24 inch with a 150 (similarly a 127 work rating). Likewise a 26 inch with a 165 crank should feel about the same in terms of work but recognizing that the larger rotation of the longer cranks has a subjective impact. As I look at it, the ratio of around 125 to about 175 covers the range of most riders comfort zones. The higher number being harder to pedal with a smaller pedal arc and the opportunity for greater speed. The lower number makes it easier to pedal a give distance due to increases lever arm resulting in probably lower speeds due to larger pedal arcs. As the crank to wheel size ratio goes down to about 100, the torque skyrockets and traction probably becomes the limiter...although large pedal arcs may be less comfortable. In the opposite direction, as the ratio goes up...the opportunity for speed due to shorter pedal arcs increases with a penalty in power and hill climbing ability. Note that AspenMike, who as I recall, rides 175s on his 36 inch Coker, carries a tougher pedal stroke than someone who rides a 20 inch unicycle with 110s--making his performance on the Iron Horse all the more remarkable. This chart should give riders the chance to decide how cranks compare on different wheel sizes--recognizing that every one of us will have a comfort zone on this chart of varying width based on skill and strength. I bought a 24 inch Torker LX with 150 cranks (work ratio 127) and quickly went to 114s (work ratio 140) which are more comfortable in my riding situation. On the KH29XC I bought with 29 inch wheel and 150 cranks (work ratio 154), I also want to optimize for speed so I bought a set of 125 cranks (work ratio 185). By comparison, the 29 inch with 150s starts me at a higher work ratio than my previous riding situation (harder cranking, less control, less power) and my decision to learn to ride the same unicycle with only 125s is a commitment train to even less control and power but this is offset by the ability for a better spin and higher speed. Hope this helps. Any subjective opinions on the field application of this rough science is welcome. Carey -- Carey ------------------------------------------------------------------------ Carey's Profile: http://www.unicyclist.com/profile/9910 View this thread: http://www.unicyclist.com/thread/43478 |
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#22
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Deriving a unicycle crank length formula?
Having been bred an engineer, I spent some time thinking about this and I offer the following. What we want to know is how will a given crank on a given wheel feel in terms of power and control. Where feel means many things as mentioned in the strings referenced--control, speed, torque, rotational diameter, power, knee pain...etc. Work equals force times distance. For different wheel sizes on different rims to feel the same, will essentially require that the rider be accomplishing the same amount of work. Each wheel size has a different diameter, when circumference is calculated...Pi times diameter, you can obtain a number for each wheel size. Then by multiplying by 2.54 you can determine the circumference in centimeter. 20 in diameter times Pi equals 62.80 in or 159.51 cm 24 in diameter times Pi equals 75.36 in or 191.41 cm 26 in diameter times Pi equals 81.64 in or 207.37 cm 29 in diameter times Pi equals 91.06 in or 231.29 cm 36 in diameter times Pi equals 113.04 in or 287.12 cm By accomplishing a ratio of circumference divided by crank length in centimeters, you can determine a ratio for comparison. Using this approach each crank length and wheel diameter can be compared in a grid. I hope the chart works on the internet... Wheel -- 20 24 26 29 36 Crank 85 -- 188 225 244 272 338 110 -- 145 174 189 210 261 114 -- 140 167 182 203 252 125 -- 127 153 166 185 230 140 -- 114 137 148 165 205 150 -- 106 127 138 154 191 165 -- 97 116 126 140 174 170 -- 94 113 122 136 169 175 -- 91 109 118 132 164 These numbers provide a referenced baseline for the work of a given crank/wheel combination for the same distance output. Similar numbers between columns will represent similar feel in terms of unicycle performance--given that each of us has a different comfort level and range of comfortable skill. Note that a 20 inch with a 125 crank gives a rating of 127...which compares in terms of work and feel to a 24 inch with a 150 (similarly a 127 work rating). Likewise a 26 inch with a 165 crank should feel about the same in terms of work but recognizing that the larger rotation of the longer cranks has a subjective impact. As I look at it, the ratio of around 125 to about 175 covers the range of most riders comfort zones. The higher number being harder to pedal with a smaller pedal arc and the opportunity for greater speed. The lower number makes it easier to pedal a give distance due to increases lever arm resulting in probably lower speeds due to larger pedal arcs. As the crank to wheel size ratio goes down to about 100, the torque skyrockets and traction probably becomes the limiter...although large pedal arcs may be less comfortable. In the opposite direction, as the ratio goes up...the opportunity for speed due to shorter pedal arcs increases with a penalty in power and hill climbing ability. Note that AspenMike, who as I recall, rides 175s on his 36 inch Coker, carries a tougher pedal stroke than someone who rides a 20 inch unicycle with 110s--making his performance on the Iron Horse all the more remarkable. This chart should give riders the chance to decide how cranks compare on different wheel sizes--recognizing that every one of us will have a comfort zone on this chart of varying width based on skill and strength. I bought a 24 inch Torker LX with 150 cranks (work ratio 127) and quickly went to 114s (work ratio 140) which are more comfortable in my riding situation. On the KH29XC I bought with 29 inch wheel and 150 cranks (work ratio 154), I also want to optimize for speed so I bought a set of 125 cranks (work ratio 185). By comparison, the 29 inch with 150s starts me at a higher work ratio than my previous riding situation (harder cranking, less control, less power) and my decision to learn to ride the same unicycle with only 125s is a commitment train to even less control and power but this is offset by the ability for a better spin and higher speed. Hope this helps. Any subjective opinions on the field application of this rough science is welcome. Carey -- Carey ------------------------------------------------------------------------ Carey's Profile: http://www.unicyclist.com/profile/9910 View this thread: http://www.unicyclist.com/thread/43478 |
#23
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Deriving a unicycle crank length formula?
Didn't mean to put that in twice. Carey -- Carey ------------------------------------------------------------------------ Carey's Profile: http://www.unicyclist.com/profile/9910 View this thread: http://www.unicyclist.com/thread/43478 |
#24
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Deriving a unicycle crank length formula?
As you said, there have been many, many threads discussing crank length throughout the years here on this forum. My personal belief is that there is no way to quantify all of the variables involved and derive a useful formula for this. I looked at the site you listed about bicycle crank length, and to be honest, I disagree with the writer's basic premise even for a bicycle. If I were to follow his formula, I would have 188mm cranks on my bike. I can't imagine how uncomfortable that would be even if I could find a crankset that long! I use a 165mm crankset on my fixed-gear, and 170mm on my commuter. I often wish I could find a crankset with much shorter cranks to experiment with on my bicycles. On a bicycle, leverage isn't nearly as big a factor as it is on a unicycle, since gearing is easily manipulated. A standard unicycle always has a 1:1 gear ratio. Every time your feet make a circle, the wheel makes a circle. The only way to manipulate gear/inches is to change the size of the wheel. Optimum crank length is based more on individual strengths and preferences. I prefer fairly short cranks on my unicycles, but many stronger riders prefer even shorter cranks. I use 125mm on my Coker, and 110's on my 29er. I don't have a 24x3 muni anymore, but when I did I discovered that I didn't like the 170mm cranks that came on it, and that I could ride it much better using 150's. With 170's I felt like my knees were trying to hit me in the chin! This is just one old mans humble opinion, but I don't think that there is any formula that could determine an ideal crank length for a unicycle or a bicycle. Individual preference, strength, skill level and the terrain that you ride determine what crank length is "right". Chuck -- Chuck Webb ------------------------------------------------------------------------ Chuck Webb's Profile: http://www.unicyclist.com/profile/1450 View this thread: http://www.unicyclist.com/thread/43478 |
#25
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Deriving a unicycle crank length formula?
Chuck, Your preferences chart out at 210 and 230, the top right portion of the chart--in my book a power rider! A work ratio of over two hundred looks to me like it would take strength as well as skill. Carey -- Carey ------------------------------------------------------------------------ Carey's Profile: http://www.unicyclist.com/profile/9910 View this thread: http://www.unicyclist.com/thread/43478 |
#26
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Deriving a unicycle crank length formula?
Roger from unicycle.com UK worked up a spreadsheet a few years ago somewhat along those same lines, Carey. I don't know if it is still available on his website, but it is fun to play with. It calculates the relationship between wheel size, crank length, speed, cadence and footspeed. I've got it somewhere, I'll try to find it if you are interested. Chuck -- Chuck Webb ------------------------------------------------------------------------ Chuck Webb's Profile: http://www.unicyclist.com/profile/1450 View this thread: http://www.unicyclist.com/thread/43478 |
#27
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Deriving a unicycle crank length formula?
On Sat, 24 Sep 2005 18:08:19 -0500, "Carey" wrote:
For different wheel sizes on different rims to feel the same, will essentially require that the rider be accomplishing the same amount of work. Using such a table is a fruitful approach, and it is useful, in that if I look up to different set-ups with the same work ratio and imagine riding them, they would indeed feel about the same. However, I don't buy the logic on which the table is based (i.e. your copied statement above). In the first place, the actual work done is larger than you assume, because both legs exert force on the pedals, and moreover it happens in a sort of erratic way (in the time domain), as required to keep balance. But more importantly, I think that a skilled rider cruising along a horizontal path will not be bothered about power, as the required power output is generally lowish. He'll be more concerned with control and log movement. It now happens that if you take the reciprocal of each "work ratio" in your chart, you end up with numbers which are proportional to what others have called "gearing ratio". One definition of gear ratio (by Mikefule I think) is crank length divided by wheel radius, both in the same length units. E.g. for a 20" unicycle with 5" cranks (a very common combination), the gearing ratio is 0.5. For a 24" unicycle with 6" cranks, the gearing ratio is also 0.5. And indeed (I think) these two combination feel about the same, or let's say, you can't make them feel more similar by changing cranks. The reason for that, I think, is that gear ratio determines how easy a unicycle can be controlled, and not so much that the required power is the same. This breaks down at the point where too high crank lengths make pedaling uncomfortable in itself. All in all, I think that gear ratio would be a good indicator of unicycle "feel" with various wheel sizes and cranks. Also, the numbers nicely vary between 0 (pedals at axle like a BC wheel) and 1 (pedals at circumference of wheel), and are therefore easily understandable. Klaas Bil - Newsgroup Addict -- "Unicycling is like glue: you have to stick with it, and it's not to be sniffed at - Mikefule" |
#28
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Deriving a unicycle crank length formula?
Klaas Bil, I think you are right. The work ratio I mention is an imprecisely defined approximate for comparison reasons only, with the ratio numerator and denominator randomly selected but consistently applied. The logic of a 0 to 1 scale is a good approach. In fact, it sounds like the gear ratio you mention is a similar ratio that works from only diameter and crank length...which makes sense since Pi is a constant in the equation. It would be a comparable estimate to my effort--and I notice, makes the same point about a 20 with 125s and a 24 with 150s. All this data aside, what I know is that the 150s on my 24 are very powerful and precise but too much arc, the 114s made it smooth and fast, and I can still control it well. The 150s on the 29 feel good now but as I get better on it I will move to 125s. Kind of scary as I UPD'd off the front last night at pretty high speed and was barely able to keep my feet. I am looking for speed that makes me immune to mosquito attacks here. Chuck--If you can find that chart, I'd be interested in it. Sounds like you guys have thought about this in depth before. My approach was to give me a feel for where I would start with cranks on different wheel sizes, given that I knew what I liked on one. Carey -- Carey ------------------------------------------------------------------------ Carey's Profile: http://www.unicyclist.com/profile/9910 View this thread: http://www.unicyclist.com/thread/43478 |
#29
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Deriving a unicycle crank length formula?
On Sun, 25 Sep 2005 09:49:50 -0500, "Carey" wrote:
Chuck--If you can find that chart, I'd be interested in it. Sounds like you guys have thought about this in depth before. My approach was to give me a feel for where I would start with cranks on different wheel sizes, given that I knew what I liked on one. I've seen Roger's chart (it was a spreadsheet) but not saved it. I have made one in Dutch that is roughly similar - you can have it if you want. But you can make one yourself easily, the calculations involved are very simple. Klaas Bil - Newsgroup Addict -- "Unicycling is like glue: you have to stick with it, and it's not to be sniffed at - Mikefule" |
#30
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Deriving a unicycle crank length formula?
Chuck Webb wrote: *Roger from unicycle.com UK worked up a spreadsheet a few years ago somewhat along those same lines, Carey. I don't know if it is still available on his website, but it is fun to play with. It calculates the relationship between wheel size, crank length, speed, cadence and footspeed. I've got it somewhere, I'll try to find it if you are interested. Chuck * That spreadsheet of Roger’s is useful and it’s here; http://www.unicycle.uk.com/Cranklength.xls -- unicus - EMUnicyclist 'Photos' (http://gallery.unicyclist.com/Photos-from-unicus) 'Videos' (http://gallery.unicyclist.com/unicus) ------------------------------------------------------------------------ unicus's Profile: http://www.unicyclist.com/profile/869 View this thread: http://www.unicyclist.com/thread/43478 |
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