20020916, 04:40 AM  #1 
ONE for the...Off Road
Join Date: Jul 2001
Location: West San Fernando Valley, Southern California
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Calculating crank to diameter ratio ?'s
Hi,
When calculating the ratio of cranks to diameter, should I be trying to reach a ratio of 4.0? For example: a crank ratio of 3.9037 would give me more torque than a ratio of 3.859? Or do I have this concept reversed? Can anyone detect this close a difference in torque in real world riding based on using the above numbers? I calculated the diameter from the circumference of the tire using pi. I then converted the diameter to mm and divided by crank length. For example Using 160mm cranks and a diameter of 616.08mm I divided 616.08 by 160 to get my ratio of 3.855. Did I do this correctly? If I did this correctly, a 24 x 2.6 Gazz with 160mm cranks is nearly the same as a 24 x 3.0 gazz with 170mm cranks. The difference is 4 thousandths. Gazz 24 x 3.0 is calculated as 656.08mm/170mm which equals 3.859. Thanks
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20020916, 10:08 PM  #2 
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Re: Calculating crank to diameter ratio ?'s
On Sun, 15 Sep 2002 23:40:35 0500, teachndad
<teachndad.b23hm@timelimit.unicyclist.com> wrote: >When calculating the ratio of cranks to diameter, should I be trying to >reach a ratio of 4.0? To begin with: why 4.0? Secondly, you are talking about "the ratio of cranks to diameter" as if it is a fixed notion, but is it? If not, I would rather use a "crank to diameter" ratio. >For example: a crank ratio of 3.9037 would give me more torque than a >ratio of 3.859? The way you express it, it would be the other way around. While you call your number a "ratio of cranks to diameter", what you actually calculated is the ratio of diameter to cranks. >Can anyone detect this close a difference in torque in real world riding >based on using the above numbers? It is barely 1%. I doubt if it would make a noticeable difference. > >I calculated the diameter from the circumference of the tire using pi. > >I then converted the diameter to mm and divided by crank length. >For example Using 160mm cranks and a diameter of 616.08mm >I divided 616.08 by 160 to get my ratio of 3.855. > >Did I do this correctly? Yes, with the above proviso. For your example, I would proceed as follows: The radius of the wheel is 313.04 mm (half of the diameter). The radius of the crank (a.k.a. crank length) is 160 mm. The crank to diameter ratio then is 160/313.04, which equals 0.5111. That is sort of a leverage factor, meaning that if you push with force x on the pedal (perpendicular to the crank), then the force at the ground contact point will be 0.5111 times x. So you would have more torque (e.g. for climbing) if your crank to diameter ratio is higher (assuming that you could still muster force x on the pedal). Obviously, you can't go higher than a ratio of 1, or your pedals would protrude beyond the tyre. Bonk bonk bonk bonk. Indeed, they would bonk already below 1. Hope this helps, Klaas Bil If you had this signature, I have forged it. 
20020917, 01:28 AM  #3 
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Re: Calculating crank to diameter ratio ?'s
> Hope this helps, Isn't this mostly academic? Example: I want to buy a 24" MUni and I want enough torque to make it up hills with a minimal amount of effort. However, I don't want the cranks so long that my overall ride becomes jerky. I have asked myself, do I want 170 mm or 175 mm cranks? It seems to me that an important factor not included in the equation is the size of the rider. If I were 6'6" tall with rather long legs then the ride would feel very different on 175 mm cranks than with my shorter stature of 5'10" tall. Until I actually ride on the different cranks I won't know anything other than the amount of force represented by x, which doesn't really help or does it? Jason 
20020917, 07:01 PM  #4 
Roland Hope School of Unicycling
Join Date: May 2002
Location: Long Bennington, Lincolnshire, England.
Posts: 6,614

It's dead simple if you think of the cranks in inches  you think of the wheel in inches after all.
Roughly: 100 mm = 4 inches. 125mm = 5 inches 150 mm = 6 inches 170 mm is a shade under 7 inches. Then it's the radius of the wheel which matters, not the diameter, so simplify the calculation here too  the lever acts through the hub. So, on a 20 inch wheel (10 inch radius) with 125 cranks (5 inches) you can express the leverage as 50% (If you prefer: 1:2) On a 24 inch wheel (12 inch radius) with 6 inch cranks, the leverage is also 50% This suggests the two set ups offer similar leverage  although there are many other factors which come into play. On a Coker with a 36 inch wheel (18 inch radius) and standard 6 inch cranks, the ratio is 33% or 1:3. Keep it simple.... count the cranks in inches. I found my Coker with 6 inch cranks would go up some hills my 20 wouldn't go up with 5s on it. I found my 26 with 7 inch cranks (53%) would not go up stuff that my 24 with 6s (50%) would. So, the ratio is a guide only, and the actual wheel size and actual crank size have an effect due to rolling resistance, momentum, angle of attack on obstacles, and ergonomics.
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20020917, 10:48 PM  #5 
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Re: Calculating crank to diameter ratio ?'s
I agree that other factors than just leverage play a role as per
Mikefule's last sentence. He also simplifies the calculations by using round inch numbers but the principle remains the same. And no, it's not academic. When I went from 24" with 125 mm cranks to 20" with 125 mm cranks, I noticed a definite improvement for uphilling. I mounted 150 mm cranks on my 24" wheel and hey presto, an improvement just as big (compared to 125 mm). And guess what, the leverage factor is (nominally) exactly the same. Klaas Bil If you had this signature, I have forged it. On Mon, 16 Sep 2002 16:32:11 0800, Jason Neumann <nospam@nospam.no.no.no> wrote: >Isn't this mostly academic? > >Example: >I want to buy a 24" MUni and I want enough torque to make it up hills >with a minimal amount of effort. However, I don't want the cranks so >long that my overall ride becomes jerky. I have asked myself, do I want >170 mm or 175 mm cranks? It seems to me that an important factor not >included in the equation is the size of the rider. If I were 6'6" tall >with rather long legs then the ride would feel very different on 175 mm >cranks than with my shorter stature of 5'10" tall. Until I actually >ride on the different cranks I won't know anything other than the amount >of force represented by x, which doesn't really help or does it? > > >Jason 
20020917, 10:48 PM  #6 
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Re: Calculating crank to diameter ratio ?'s
On Tue, 17 Sep 2002 14:01:14 0500, Mikefule
<Mikefule.b51yy@timelimit.unicyclist.com> wrote: >I found my Coker with 6 inch cranks would go up some hills my 20 >wouldn't go up with 5s on it. I found my 26 with 7 inch cranks (53%) >would not go up stuff that my 24 with 6s (50%) would. For the second example, OK that's a small difference in leverage factor. Maybe also the 26" was a wider and hence larger tyre than the nominal value? But the Coker example is remarkable, unless either these were real short hills and you could use the greater speed achievable with the Coker to carry you over the top, or the surface was so bumpy that the small wheel got stuck. Klaas Bil If you had this signature, I have forged it. 
20020918, 05:03 AM  #7 
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Re: Calculating crank to diameter ratio ?'s
Klaas Bil wrote:
> > I agree that other factors than just leverage play a role as per > Mikefule's last sentence. Yes. After reading Mikefuls post I find this information much more useful, expressing it in relative percentages such as, "50% (If you prefer: 1:2)". Thanks guys! Jason 
20030927, 09:18 PM  #8 
)O <Neat

There is still one more thing to here. Remember to measure the diameter of the tyre. For example, my 20" trainer has wheel diameter of 20" but my Gazza 24" has diameter of 26". This 2426 diameter only affects 5%, but I think you may feel it.
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20030927, 11:59 PM  #9 
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Location: Texas
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I can't seem to find it on his site right now, but quite a while back i downloaded a cranklength spreadsheet from Roger Davis...still use it a lot, it lets you plug in wheel diameter or circumference and crank length and come up with ratio and lots of other interesting stuff.
Chuck 
20030928, 01:15 AM  #10  


Quote:
Just something to think about. .duaner. 

20030928, 03:00 AM  #11 
Unicyclist

actually, all that stuff is wrong. the center of rotation for rolling objects (wheels) is not the hub. it's where the wheel touches the ground. so to you use the wheel radius plus the crank length instead of just the crank length. and no, i didn't think of this on my own or make it up

20030928, 11:00 AM  #12  
Mostly OKish Unicyclist
Join Date: Jun 2003
Location: Stockon, UK
Posts: 1,446

Quote:


20030928, 02:40 PM  #13 
Unicyclist

um, whoops. that shouldn't be wheel radius + crank length. that should be distance of the pedal from the wheel's contact point, which is wheel radius + crank length only when the crank is pointing up

20030928, 09:21 PM  #14  
dumb blonde
Join Date: Sep 2002
Location: Belper, Derbyshire, UK
Posts: 2,983

Quote:
Why: When the pedals are at 9 o'clock, 12 o'clock and 3 o'clock, the distance between the point where force is being applied and the contact patch is greater than the wheel radius. It's only in a small section of the pedal circle that the pedals are less than the wheel radius away from the ground and that doesn't come near to balancing out the time spent in the other parts of the pedal circle. Being currently a programmer and having forgotten my maths, I wrote a little program to work it out, for a 18 inch radius wheel (coker sized) with 18 inch cranks the effective radius is 22.9 inches, going down to 18.5 inches for 6 inch cranks and tending towards 18 inches as crank length goes to zero. It doesn't matter really though as it doesn't make much difference to the calculations anyway, even in the most extreme practical cases (eg. 6 inch cranks on 20 inch wheel = effective radius of about 22 inches). I'm not sure what happens on a bike, although the small size of rear sprockets might mean it's only a very tiny amount of constant difference in gearing due to the drive being from slightly behind the axle. Joe 

20030929, 09:46 PM  #15 
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Re: Calculating crank to diameter ratio ?'s
On Sat, 27 Sep 2003 22:00:43 0500, ubersquish
<ubersquish.ug44z@timelimit.unicyclist.com> wrote: >actually, all that stuff is wrong. the center of rotation for rolling >objects (wheels) is not the hub. it's where the wheel touches the >ground. so to you use the wheel radius plus the crank length instead of >just the crank length. >[if the pedal is at 12 o'clock] That only holds in a reference frame fixed to the road. So it only applies to someone standing (or walking) on the road. Indeed, if you stand beside a unicycle and want to propel it forward, pushing against the top pedal gives you most leverage, equal to wheel radius plus crank length. However, if you think about a unicyclist riding a unicycle, then you have to consider rotation in a reference frame fixed to the unicycle. Then the centre of rotation is at the hub, and the usual notions about leverage apply. Klaas Bil  Newsgroup Addict  If the crank is moving then it really sounds as if it's loose.  onewheeldave trying to pinpoint the cause of a clicking crank 
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