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Old 2011-04-13, 04:27 PM   #1
rpt50
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crank length vs. wheel diameter??

Sorry about the newbie question, but how does wheel size affect mechanical advantage on a unicycle? I understand that longer cranks increase leverage. However, if you hold crank length constant (e.g., 125 mm), would you gain a mechanical advantage by using a smaller wheel?
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Old 2011-04-13, 04:41 PM   #2
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Yes you do. You would have better leverage with 125s on a 20 compared to 125s on 36er
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Old 2011-04-13, 05:46 PM   #3
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rpt50,
Welcome to the forums.

The gear ratio (crank length/wheel diameter) is hugely important. Unicyclists can talk for hours about this. This might not be the most fascinating conversation you've ever witnessed, but everyone has their opinions. In fact, there are several threads devoted to this.

Here's one: http://www.unicyclist.com/forums/sho...ighlight=total


Saskatchewanian came up with this beautiful chart of all the different conceivable configurations of available crank lengths and wheel sizes and their resulting gear ratios. He even included the effective wheel diameters of geared 24", 26", 29" and 36" wheels. (Eric, I can't help but mention that now you need to include the 32" wheel. Geared and ungeared, of course. )


Happy reading.

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Old 2011-04-13, 06:27 PM   #4
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Wow! Thanks for the info. That spreadsheet chart is awesome!
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Old 2011-04-14, 02:59 AM   #5
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WOW!!
That is way impressive!
Thanks
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Old 2011-04-14, 04:03 AM   #6
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This may be more than you wanted, but with help from the guys at a physics forum, I found a mathematical description the effects of wheel diameter/crank length:

Yes, smaller wheels offer a mechanical advantage.

The proper way to show it is by knowing that the torque at the crank (c) is the same as the torque at the wheel (w) (since they are part of the same unit):

Tc = Tw
Fc * Rc = Fw * Rw

or

Fw = Fc * Rc / Rw

Assuming the same force at the crank (Fc), the friction force acting between the ground and the tire (Fw) is inversely proportional to the wheel radius (Rw). The smaller the wheel, the larger the force.

Similarly, for speed (V), we know that the angular velocity (w) will be the same for the crank and the wheel:

wc = ww
Vc / Rc = Vw / Rw

or

Vw = Vc * Rw / Rc

Here, assuming the same speed at the crank (Vc), the velocity of the wheel at the ground (hence the unicycle velocity) is proportional to the wheel radius. The smaller the wheel, the lower the unicycle speed.

By changing the wheel or crank radius, you gain force and loose speed (or vice versa).

If you want to know how much torque and speed is possible with your unicycle, you are better using the power approach. The power available by human pedaling is between 200 and 400 W. Power (P) is always constant throughout the mechanical system, so:

P = T * w --> torque and angular velocity is the same for the crank and the wheel
P = Fc * Vc
P = Fw * Vw

So assuming a power of 300 W, if you travel at 8 mph (3.58 m/s),the wheel friction force is 83.8 N. With a 20" wheel (0.508 m), the torque is 21.29 N.m. The angular velocity is 14.1 rad/s (135 rpm). You can find the foot speed and force, knowing the crank radius. These equations are true for instantaneous values or average values.
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Last edited by smackay; 2011-04-14 at 04:04 AM.
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Old 2011-04-14, 04:40 AM   #7
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Quote:
Originally Posted by rpt50 View Post
Wow! Thanks for the info. That spreadsheet chart is awesome!
Quote:
Originally Posted by UniTrac View Post
WOW!!
That is way impressive!
Thanks

Thank Saskatchewanian. He did the math, added the pretty colors and annotated it. I merely cut and pasted it.
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Old 2011-04-14, 04:37 PM   #8
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That is a nice chart, never seen it before, fits my experiences to a "t".

Increasing crank length increases torque, but at a cost in terms of "ease of spin" and the akwardness that comes with having to manage a longer crank (pedal strike, sweet spot/power position, timing)

The only caveats I would add are rider experience/skills and tire size. I have found that both long and short cranks require more "work around" in terms of skill, so starting with cranks that are too long or too short could be a problem. In terms of tires, I was riding 165mm cranks on a 26 x 3 and did fine, but when I went to 26 x 3.8 I found my control and climbing was significantly reduced. I bumped up to a 170mm crank and my control and climbing returned to normal.


Starting muni 24" = 145-150mm, 26" = 150, 29" = 150-160, 36" = 150-165

All of my unis (26 x 3.8, 29 x 2.4, 36 x 2.5) are set up with 170's, this is maybe not optimal for the 36, but I can't find 175's without q factor
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Old 2011-04-14, 06:34 PM   #9
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Saskatchewanian, thanks for the chart. I just ordered some 89mm cranks for my 24" club to act as a stopgap until I save enough for a 36" Coker.
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Old 2011-04-14, 06:56 PM   #10
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Quote:
Originally Posted by smackay View Post
This may be more than you wanted, but with help from the guys at a physics forum, I found a mathematical description the effects of wheel diameter/crank length:

Yes, smaller wheels offer a mechanical advantage.

The proper way to show it is by knowing that the torque at the crank (c) is the same as the torque at the wheel (w) (since they are part of the same unit):

Tc = Tw
Fc * Rc = Fw * Rw

or

Fw = Fc * Rc / Rw

Assuming the same force at the crank (Fc), the friction force acting between the ground and the tire (Fw) is inversely proportional to the wheel radius (Rw). The smaller the wheel, the larger the force.

Similarly, for speed (V), we know that the angular velocity (w) will be the same for the crank and the wheel:

wc = ww
Vc / Rc = Vw / Rw

or

Vw = Vc * Rw / Rc

Here, assuming the same speed at the crank (Vc), the velocity of the wheel at the ground (hence the unicycle velocity) is proportional to the wheel radius. The smaller the wheel, the lower the unicycle speed.

By changing the wheel or crank radius, you gain force and loose speed (or vice versa).

If you want to know how much torque and speed is possible with your unicycle, you are better using the power approach. The power available by human pedaling is between 200 and 400 W. Power (P) is always constant throughout the mechanical system, so:

P = T * w --> torque and angular velocity is the same for the crank and the wheel
P = Fc * Vc
P = Fw * Vw

So assuming a power of 300 W, if you travel at 8 mph (3.58 m/s),the wheel friction force is 83.8 N. With a 20" wheel (0.508 m), the torque is 21.29 N.m. The angular velocity is 14.1 rad/s (135 rpm). You can find the foot speed and force, knowing the crank radius. These equations are true for instantaneous values or average values.
I was in the process of doing the same thing but using LaTex for the equations and making tiny .pdf's to make the equations look nice and pretty thank you for saving me from extra work I really didn't need to do.
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Old 2011-04-14, 07:51 PM   #11
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Quote:
Originally Posted by Nurse Ben View Post
All of my unis (26 x 3.8, 29 x 2.4, 36 x 2.5) are set up with 170's, this is maybe not optimal for the 36, but I can't find 175's without q factor
Wow, finally there is someone out there who likes longer cranks on a 36er than I do. I feel like an odd ball with my 165's. I just switched to my "short" cranks, 152 mm, in preparation of racing season. They're faster all right, but not so much fun riding on steep dirt roads and single track.
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Old 2011-04-14, 08:12 PM   #12
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Geoff,


I've had my Schlumpf put together about a month. I've only had time to put about 20 miles on it. I'm running 137/165's. These cranks are off of my 26" muni. I used the 165 hole for the Chilly Hilly in Feb. I had them on my N36er. At first I didn't like them on the Nimbus. I have since got used to them. Now that I have a guni I will probably leave these cranks on it. Yesterday I hit 16 mph in high gear. I have not used the 137 hole since moving them over to the guni. In 1:1 I have really good control for cutting and zig zagging around people. My commute also involves alot of traffic. When I'm in heavy traffic I will run in 1:1. I am still getting used to high gear. I can shift ok. I don't fall much but my shifting needs improvement. My feet are longer than the 165 cranks. My shoe size is 48 (14 US) I usually end up shifting with my ankle. I would prefer to use my heel.
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Old 2011-04-15, 02:32 AM   #13
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Eric, I can't help but mention that now you need to include the 32" wheel. Geared and ungeared, of course.
Something like this?


48 is about equal to 32 geared up.

I am planning to eventually build up a schlumpfable 48" so I added that to my chart.


Throwing a 32 in there fills the gap nicely eh?

And of course the chart is just a guideline. There are all sorts of other factors, like the fact that big wheels roll better than small wheels, big wheels have more momentum, the fact that I am scared of cranks shorter than 100mm... etc.
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Last edited by saskatchewanian; 2011-04-15 at 02:33 AM.
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Old 2011-04-15, 04:32 AM   #14
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Ha! Magnificent. You've outdone yourself.

Geared 48?!?!?! Dude!
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Old 2011-04-15, 12:39 PM   #15
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how fast could you go on a geared 48?
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