What goes up, doesn’t come down (as fast)
And a headwind never pays you back when you turn around…
The forces that resist a cyclist’s progress do not increase linearly with speed.
If they did, since 100W
What goes up, doesn’t come down (as fast)
And a headwind never pays you back when you turn around…
The forces that resist a cyclist’s progress do not increase linearly with speed.
If they did, since 100W of pedalling effort will move a rider at over 10mph, a Tour sprinter like Cavendish putting out ~1600W at the end of a stage could expect to hit over 160mph.
In reality, even with a lead out line he will “only” reach ~45mph.
This is because the main source of resistance, pushing bike and body through the air, increases
exponentially polynomially (thanks to Iain B for the correction!) with speed. That is, if a rider doubles their speed, not only will they ‘hit’ the air molecules in front of them twice as hard, twice as many air molecules must be pushed aside every second.
The result? Drag squares with speed (doubling speed increases drag fourfold).
Now think about the power requirements of the rider. We’ve seen that per metre travelled, there is now four times as much resistance. However, twice as many metres are being covered each second, so the energy that must be spent per second is doubled too. This means there is an eightfold increase (fourfold doubled) in the wattage required from the rider’s legs to double their speed.
This is why, given an average road bike, an amateur could expect to travel perhaps half as fast as a professional despite putting out a fraction of the power. It’s also why recumbents (and to a lesser extent, time trial bikes) are so effective at turning any given wattage into forward speed.
Wind resistance (yellow) and other losses (purple)
An aside on other sources of drag
You may be thinking “hang on, if 100W gives 10mph, how come I can ride at 20mph without needing to sustain 800W?”
At 10mph most of the energy a rider requires is actually used to overcome the other aspects of resistance (rolling resistance of the tyres, bearing losses, and so on) and the wattage needed to overcome wind resistance is still very low. It has increased eightfold for each doubling of speed up to 10mph, but 8x not much is still not much (for a while!).
The numbers just happen to get very large very quickly at around the speeds that we cycle. (This is no coincidence; if we lived on a planet where the air was half as thick, cyclists would rapidly get up to 20mph and then complain that wind resistance gets large at just the speeds they ride at…)
What wind resistance tells us about hill strategy
On a hill of any significant gradient, the main force that must be overcome is gravity, not wind resistance. As gravity is a constant force regardless of your speed, this makes “climbing maths” fairly straightforward.
Say your total weight (rider plus bike) is 10% more than another rider in your group. To climb at the same speed, 10% more power is required from your legs than his. So far, so good.
When descending, you can think of gravity as giving back each rider so many watts per kilo which they can use to overcome wind resistance as they descend. So on the other side of the hill, the rider who weighs 10% more will effectively be “pedalling” (albiet virtually) 10% harder.
However, where doubling your power will double your speed on a climb, we’ve just established that you need to increase your power eight times over to double your speed when you’re being held back by air resistance.
The extra power gravity gives to the heavier rider is pretty much worthless – it’s a con!
For another explanation of this, see this recent comment I made on anothe