marius-ciclistu bicycle transmission calculator
For this demonstration I compared three kids bikes for their lowest gears:
- (A) 20x2.125 inch (518 mm diameter) 36–34 teeth 140mm arm => 0.51058903149534 force coefficient
- (B) 24x1.75 inch (554 mm diameter) 28–32 teeth 130 mm arm => 0.53609506310588 force coefficient
- (C) 20x1.75 inch (482 mm diameter) 24–28 teeth 120mm arm=> 0.58047246004515 force coefficient
using https://marius-ciclistu.ro/biketransmissioncalculator.php.
As you can see the force coefficient is within a ~ 0.07 range.
An example of force coefficient: if the biker applies X force into the pedals, then X * force coefficient = propelling force.
That translates into:
For transmission A to generate same propelling force as transmission C, the biker needs to apply 13.7 % more force into the pedals.
For transmission B to generate same propelling force as transmission C, the biker needs to apply 8.3 % more force into the pedals.
For transmission A to generate same propelling force as transmission B, the biker needs to apply 5 % more force into the pedals.
If we consider all 3 cases having the same total mass, then the above 3 sentences can be translated into:
For transmission A to generate same acceleration (FORCE/MASS) as transmission C, the biker needs to apply 13.7 % more force into the pedals.
For transmission B to generate same acceleration (FORCE/MASS) as transmission C, the biker needs to apply 8.3 % more force into the pedals.
For transmission A to generate same acceleration (FORCE/MASS) as transmission B, the biker needs to apply 5 % more force into the pedals.
Note that the above-mentioned acceleration and force are not the resultant acceleration and force, but only the generated/potential acceleration and force. This is what we are interested in when comparing because the resultant ones are influenced by the environment resistive forces that are the same for all 3 cases if their masses are the same (the gearing being the lowest, we don’t consider the air friction and tire hysteresis force as resistive forces).
If the weight differs then the acceleration comparison is more accurate than the force comparison and the % differences must be multiplied by the mass ratio.
In any case, notice what is not present? Power … Meaning we don’t have to calculate it for our research/comparison, as we don’t need to look at it in any transmission.
