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• # Human power gear calulation?

Discussion in 'Calculations' started by jawnn, Jun 7, 2012.

1. ### jawnnWell-Known Member

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Does anyone understand this, and is it correct?
Shelton Brown has a way of calculating gear ratios that I do not understand.
http://sheldonbrown.com/gain.html

Radius ratio x gear ratio = gain ratio

But can it be applied to ground speed in reliable way? Or is it purely for comparison?

My MTBâ€™s lowest gear:
(330.2mm tire / 175mm cranks) x (22/34) = 1.22 gain ratio
(80467.2 / 1.22) / (175 x 2 x 3.14) = 60 rpm cranking to move at 3mph

My recumbent bikeâ€™s lowest gear:
(323.85/170) x (24/34) = 1.344 ratio
(80467.2 / 1.344) / (170 x 2 x 3.14) = 56 rpm at 3 mph
and at 4mph =74.77 rpm

2.
3. ### Auto EngineerActive Member

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It would seem quite easy to prove or disprove his theories, therefore draw a chalk line on level ground and follow his examples, if the cycle travels the distances expected then his theory works.

4. ### ErichWell-Known Member

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All he is doing is adding the effect of the crank arm length to his calculation of a new bicycle "gear ratio"

He is computing a pure ratio of the distance traveled by the bike to the distance traveled by your foot as is goes in a circle around the bottom bracket.
Its an interesting viewpoint but ultimately of little real use. Calculating the effective diameter of a wheel always worked for me and gave me the understanding of which gears were taller than others.

5. ### jawnnWell-Known Member

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I think this could be used to calculate how much of a lower gear I need for shorter crank arms....but I am probably wrong...?

6. ### ErichWell-Known Member

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If you have a bike with a given length of crank and you change to a shorter crank, to keep the same pedal effort your gear ratios need to decrease by the ratio of the lengths of the crank arms.
It is not any more complicated than that.

7. ### StefanoNew Member

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It seems methematically correct if one neglects the wheel deformation.

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His terms are not properly defined - how about a diagram?

9. ### MikeNew Member

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The "Gain Ratio" is simply the ratio of the distance the circumference of the wheel (or the bike itself) moves for every inch you foot moves in the circle of the crank. If you already know your road speed (as my daughter does with her speedometer), it will tell you your foot speed. It is also the ratio of how much force is exerted on the pedal for every pound of tractive force the wheel exerts against the ground.

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Thanks Mike, I would therefore propose the following equation for Gain Ratio:
Road Speed / Foot Speed = (Large Sprocket Radius / Pedal Radius) * (Tyre Radius / Small Sprocket Radius)
I believe that this fits with the basic laws of lever kinematics with a chain drive. It is identical to
Road Speed / Foot Speed = (Tyre Radius / Pedal Radius) * (Large Sprocket Radius / Small Sprocket Radius)
which is in the form set out by the original questioner and therefore correct. I hope that this helps !!!