Biomechanics
Before shaving grams off your wheels, learn to pedal
The geometry of the pedal stroke
Two cyclists can push just as hard on the pedals without transmitting the same power. The difference comes down to the direction of the force applied to the pedal. Here's the demonstration, with numbers.
1 — The principle
Only the tangential component produces a moment
The crank is a lever. A force on the pedal always breaks down into a tangential component (perpendicular to the crank) and a radial component (along the crank). Only the tangential component produces a moment; the radial component pushes on the axle and turns nothing.
The moment of a force, or torque, depends on 3 things: the length |r| of the crank, the magnitude |F| of the force applied to the pedal, and the angle θ between the crank's direction (axis) and the direction of the force applied to the pedal.
Moment = |r| × |F| × sin(θ)
Since the force stays close to perpendicular to the crank, we measure its deviation δ from that perpendicular, i.e. θ = 90° − δ. Since sin(90° − δ) = cos(δ), the moment can be written in terms of the deviation angle δ:
Moment = |r| × |F| × cos(δ)
This factor cos(δ) depends only on the direction of the force. It is greatest, and equals 1, when δ = 0°, i.e. when the force is applied perpendicular to the crank, hence tangent to the circular path traced by the pedal.
The power delivered to the drivetrain is this moment multiplied by the angular velocity |ω| — the well-known pedalling cadence:
Power = Moment × |ω| = |r| × |F| × cos(δ) × |ω|
At equal cadence (i.e. |ω| fixed), equal force magnitude (i.e. |F| fixed) and equal crank length (i.e. |r| fixed), the factor cos(δ) carries straight over to the power: it's what sets the watts. The larger the deviation (δ), the smaller the power, all else being equal.
2 — The gesture
Two cyclists, same force, different direction
A perfect pedal stroke keeps the force tangent to the circle throughout the turn (δ = 0°): at the top you push forward, on the downstroke down, at the bottom you pull back (as if scraping your shoe), on the upstroke you pull up. On the right, the same cyclist applies the same force magnitude but with a deviation δ: the tangential component drops to |F| × cos(δ), and the rest goes radial — |F| × sin(δ) — which produces no moment.
3 — The numbers
What a constant deviation takes away
Take a constant deviation over the whole turn, all else equal. The factor cos(δ) applies at every instant. On a base of 250 W delivered with perfect direction:
| Deviation δ | cos(δ) | Power delivered | Reduction |
|---|---|---|---|
| 0° (perfect) | 1.00 | 250 W | 0 % |
| 10° | 0.98 | 246 W | −1.5 % (−4 W) |
| 20° | 0.94 | 235 W | −6.0 % (−15 W) |
| 30° | 0.87 | 217 W | −13.4 % (−33 W) |
The power loss is negligible for small angles, then grows as the square of the angle. Doubling the deviation (10° → 20°) quadruples the power loss. A slight imprecision costs very little; a marked deviation is paid for dearly.
Key takeaways
- A force on the pedal = a tangential component (produces the moment) + a radial component (no moment).
- Only the tangential force moves you forward; the radial force is wasted.
- At equal force magnitude and angular velocity (pedalling cadence), the power loss ranges from 1.5 % to 23.4 % for deviation angles (δ) from 10° to 40°.
- Power loss grows as the square of the deviation angle δ.
The most accessible gain isn't in your equipment, it's in your technique: learn to pedal before shaving grams off your wheels.
Arnaud Collet, PhD, CPSS®