diagrams.ink / motion studies / 06
Gears don't make power.
They change the trade.
A bigger rear sprocket buys more turning force. A smaller one buys more wheel turns. Follow the chain to see why.
Fig. 06 — Bicycle drivetrain42-tooth front ring / ideal drive
42T chainringCrank + pedalRear sprocketDriven rear wheel
Dark links follow the engaged chain.Pedaling · 60 rpm
Wheel turns / crank turn
42 front teeth ÷ 21 rear teeth
Rear wheel speed
60 crank rpm × 2.00
Wheel torque / crank torque
21 rear teeth ÷ 42 front teeth
Two wheel turns per crank turn. The chain carries 42 teeth past the rear sprocket each pedal revolution. A 21-tooth sprocket therefore turns twice.
Same power, different leverage. Ideal torque and speed ratios are reciprocals: more torque means fewer wheel turns, not free extra power.
ωwheel / ωcrank = 42 / rear · τwheel / τcrank = rear / 42
Ideal, lossless, engaged drive; no coasting. Chain take-up and the shifting transition are omitted. Motion is shown at ¼ speed; rpm readouts are real model values.