The formula
P = (Crr·m·g·cos θ + m·g·sin θ + ½·ρ·CdA·v²) · v ÷ efficiency
Where it comes from
The power you have to put out is the sum of three resistances that behave very differently. Rolling resistance is nearly constant and counts for little. Gravity only shows up on a climb, and there it dominates: at eight per cent it takes more than eighty per cent of the effort. And air resistance grows with the square of speed, so the power to overcome it grows with the cube: past about twenty-five an hour on the flat almost all the work is pushing air, and that is why going twenty per cent faster costs nearly twice the watts.
How to work it out by hand
- Convert the speed to metres per second by dividing by 3.6
- Work out the three forces: rolling, gravity and air
- Add them and multiply by the speed for watts at the wheel
- Divide by drivetrain efficiency, around 97 per cent
What is worth knowing
CdA is what you can improve most without training: 0.40 m² sitting up on the tops, 0.32 in the drops and 0.25 in an aero position. Going from 0.32 to 0.25 is about twenty watts saved at thirty-five an hour, which is more than a far more expensive bike buys you. On a climb aerodynamics stops mattering and total weight takes over: that is why climbers are compared in watts per kilo and rouleurs in raw watts.