Wind resistance and cycling speed

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 another article:

Conservation of energy tells us that (at best) the energy required to lift a heavier bike uphill might be exactly returned going down the other side, but only if you cycle in a vacuum with perfect tyres and bearings.

You can do a simple thought experiment to see for yourself – if you had a bike trailer and put a person on it, you would have (roughly) doubled your mass so your speed uphill for the same effort would be halved.

However, if you imagine freewheeling downhill at 40mph, it’s obvious that the extra body and a trailer would not see you reaching 80mph!

Why a headwind never pays you back when you turn around

On a circular ride, you’ll generally spend a certain proportion of the ride heading into the wind, and a certain proportion with it at your back. In the extreme of a time trial out-and-back route you will literally ride the same stretch of road with the wind at your back and then in your face.

Say our rider plans to stick to 20mph… a 10mph wind parallel to the course would mean riding so many miles at an effective airspeed of 10mph and then the same number at 30mph. It should be obvious that the extra energy required to ride at 30mph far outweighs the energy saved by riding at 10mph!

In reality riders on such a course will naturally go faster with the wind at their backs and slower with the wind in their face. However, covering five miles at 30mph takes just 10 minutes, while riding back at 10mph would take half an hour! This time trial ended up taking 40 minutes instead of 30 minutes for a steady effort at 20mph… even though the wind was in the rider’s face (and at their back) for a “fair” five miles each way…

There are obviously lots of different ways to cut the same cake, but I hope it’s now obvious that all of them result in a slower performance than on a calm day.

Catch on the climbs

Knowing why it takes so much more effort to go a little faster is all well and good, but does it have any practical implications for the average rider?

I’d say so… for instance, if you need a comfort break while riding, it’s clear from the above that you want to do so at the bottom of a stiff climb, where the aerodynamic advantage of the group is largely meaningless.

Even if you’re just trying to catch a single rider, you will get a proportionally much larger return of speed if you have a spare 50W to invest on a climb (paying down gravity) than on the flat (that wind resistance again). It’s tempting to imagine that you’re best to chase on a fast section of road just because of the way it feels to fly along, but this is an illusion!

The following are particularly relevant, on the same vein:

2 Comments

  1. This will get some debate on forums… I’ve often had my enthusiasm for recumbent riding countered with many “ah… buts…” on this topic.

    The wind for many upright riders is treated as an ally as it apparently ‘blows them along’ on the homeward stretch (assuming wind direction doesn’t change). As recumbent riders are ‘too aero’ they loose this benefit (according to these cycling traditionalists). That’s why fast cars are mainly square you see… 😉

    Good to see you’ve escaped your garage for a minute!

  2. Thomas S

    So the reason for having thinner tires is that they lose less power on the back wheel feeling saggy? In fact i prefer my Vittoria rubino pro 25 mm over the 23 mm (Which are training/ alround/simple tires nothing extreme). I cannot tell the difference in rolling resistance, but i always thought that at least on clean roads that the 23 mm should roll better but i never felt the difference.

    But in fact the biggest differce was when I through the original tires on the bike the Vittoria Zaffiero away, they really costed energy and where quite heavy to.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>