So one day I thought about how the smaller the front chain-wheel is in relation to the pedal-crank arm, the greater leverage the pedal crank arm has on pulling the chain against the resistance of the rear sprocket. Of course I knew that if you kept the same ratio, then the rear sprocket would get smaller at the same time the front chain-wheel did and counter the added leverage the smaller front chain-wheel enjoyed. But I thought, was the gain or loss with a smaller or larger front chain-wheel directly proportional to the gain or loss with the larger or smaller rear sprocket needed to maintain the same ratio ??? Or was there some small but useful gain of leverage with using the combination with the smaller front chain-wheel?
To answer this I dragged two combinations of parts from my junk-pile from which to take measurements from. One a 52/19 , the other a 43/16 combination of wheels and sprockets. I used a 170mm length for the crank-arm and a 13.5" radius for the complete rear wheel and tire assembly. Then I measured the distance from the center of each sprocket and chain-wheel to half the height of their sprocket-teeth where I thought the roller of the chain would bear.
In the end after using all of the measurements to calculate the gain/loss of the leverages of the front crank/chain-wheel combinations and the change in leverage between the different rear sprockets and the radius of the rear wheel, I found that yes it was absolutely proportional and there was no advantage in leverage or power to be had by using either combination. A friend of mine pointed out that there were fewer chain rollers in contact with the smaller sprockets so there may be less friction, but I countered that the fewer rollers on the smaller sprockets would be under more leverage, strain and pressure than the chain rollers on the larger sprockets and that would make the overall change in total friction also zero.
As long as you are having fun nothing is a waste of time......
