How does a headwind affect speed and power output?

[Jon in Sweden]

I was wondering if anyone had any concrete data for how headwinds reduce speed/increase power output?

I had a savagely tough ride yesterday. We needed to be in Växjö by late afternoon to pick up my wife's friend from the station. I decided to cycle it, for no other reason that I could. I rendezvoused with them in Växjö and we continued our afternoon.

I cycle 90km into a 16kph headwind. I was cycling absolutely squarely into it for the first 50km and then turned slightly, so maybe was only getting 70% of it for the remainder.

Some late night searching on the tinterweb suggested that such a headwind might have almost doubled my power output to maintain 30kph (30.1 actually ), with two calculators suggesting 350-370w as an average. I don't have a power meter and I'm 104kg, but I can't imagine that the output was that high?

It was character building though. To cycle at full whack for three hours knowing that I was never going to make the turn and ride the tailwind home again!

This is the ride in question:

https://www.strava.com/activities/8097234216

[roubaixtuesday]

I was wondering if anyone had any concrete data for how headwinds reduce speed/increase power output?

I had a savagely tough ride yesterday. We needed to be in Växjö by late afternoon to pick up my wife's friend from the station. I decided to cycle it, for no other reason that I could. I rendezvoused with them in Växjö and we continued our afternoon.

I cycle 90km into a 16kph headwind. I was cycling absolutely squarely into it for the first 50km and then turned slightly, so maybe was only getting 70% of it for the remainder.

Some late night searching on the tinterweb suggested that such a headwind might have almost doubled my power output to maintain 30kph (30.1 actually ), with two calculators suggesting 350-370w as an average. I don't have a power meter and I'm 104kg, but I can't imagine that the output was that high?

It was character building though. To cycle at full whack for three hours knowing that I was never going to make the turn and ride the tailwind home again!

This is the ride in question:

https://www.strava.com/activities/8097234216

Roughly, air resistance is proportional to the square of speed relative to the wind (for all subsonic turbulent flow, not just cycling).

Power is force x speed.

So you to increase relative speed from 30 to 46, you expect power to increase by a factor of (46/30)^2 = 2.4

You might expect a bit less as not all resistance is wind resistance. I'd say your calculator is about right.

See for instance https://www.sheldonbrown.com/rinard/aero/formulas.html

[DaveReading]

I was wondering if anyone had any concrete data for how headwinds reduce speed/increase power output?

I had a savagely tough ride yesterday. We needed to be in Växjö by late afternoon to pick up my wife's friend from the station. I decided to cycle it, for no other reason that I could. I rendezvoused with them in Växjö and we continued our afternoon.

I'd have thought that picking up someone on a bike had a far greater effect on speed than any wind.

[Jon in Sweden]

I was wondering if anyone had any concrete data for how headwinds reduce speed/increase power output?

I had a savagely tough ride yesterday. We needed to be in Växjö by late afternoon to pick up my wife's friend from the station. I decided to cycle it, for no other reason that I could. I rendezvoused with them in Växjö and we continued our afternoon.

I'd have thought that picking up someone on a bike had a far greater effect on speed than any wind.

Haha! Well indeed!

Roughly, air resistance is proportional to the square of speed relative to the wind (for all subsonic turbulent flow, not just cycling).

Power is force x speed.

So you to increase relative speed from 30 to 46, you expect power to increase by a factor of (46/30)^2 = 2.4

You might expect a bit less as not all resistance is wind resistance. I'd say your calculator is about right.

See for instance https://www.sheldonbrown.com/rinard/aero/formulas.html

That's mad. I didn't think I'd be able to sustain that kind of power for anywhere near that kind of time. I am much bigger than your average cyclist, and have a weight lifting background, but still.

My heart rate average for the three hours was 153. Anything approaching 150 is fairly hard work for me.

[Jdsk]

Drag goes up as the square of airspeed. Power goes up as the cube.

Jonathan

[roubaixtuesday]

Drag goes up as the square of airspeed. Power goes up as the cube.

Jonathan

I tried to be careful how I worded my response.

Your statement is true relative to the speed of the air

However, in this case the OP is riding the same speed relative to the ground. for the with and without headwind scenarios

So both resistance and his power are relative to the square of the net (cyclist speed + headwind)

It would be the cube of his speed if there were no headwind, but his own speed varied.

[I've probably garbled this, but I'm confident we agree on the physics]

[Nearholmer]

Yes, we’ve got three things at play: ground speed, air speed, and cyclist-output power.

If ground speed remains constant while air speed increases, air resistance rises by a square, and cyclist-output power by a cube.

In my case that doesn’t happen, what happens is that as head-wind increases cyclist power output remains constant at c0.85 absolute maximum, and speed decreases dramatically, in a losing battle to maintain air resistance the same while remaining upright and not going backwards. It’s the same with hills!

I went out the other morning and thought I seemed unusually fit, ticking along a couple of cogs up from the usual. It was only when I turned round to come back that the horrible truth dawned on me: I’d had the wind at my back, and now it was at my face.

[backnotes]

There's a graph in the book Bicycling Science that shows how different head/tail wind speeds affect the air drag power you have to overcome at different riding speeds. This is for a "fairly large rider in a nonaerodynamic position" but it gives a general picture.

It doesn't explain why you can do whole days in The Fens when the wind feels against you, but I suspect that is all in the mind. It also fails to account for those lunch stops during which the anticipated tailwind home mysteriously goes away or even seems to swing by 180 degrees during the stop.

[Jon in Sweden]

Thanks for all the incredibly useful contributions.

All the calculators (and that graph) seem to suggest that I was indeed pushing 350-370w for three hours.

Firstly, it renders the estimated power figures on Strava utterly useless. It appears that Strava makes no account of wind speed or direction despite referencing it on the summary.

Secondly, whilst the figures seem quite high, for me at my bodyweight, it's only 3.4 - 3.5w/kg.

Nevertheless, I did not think I was able to do those sorts of numbers and makes me think that if I properly leaned out (I probably have 5kg of spare fat I could lose), that I would be going a lot faster.

I'm only 6.5 months back into training, so I also have a lot of work to do with my base fitness, lactate threshold and anaerobic capacity.

I love statistical analysis!

[Jdsk]

As above: Bicycling Science is by far the best primer that I know, and in some areas it goes way beyond being that.

Rating: Mandatory.
: - )

Jonathan

[roubaixtuesday]

It doesn't explain why you can do whole days in The Fens when the wind feels against you, but I suspect that is all in the mind.

First, a disclaimer that I've never ridden in the Fens!

But I suspect it's not in the mind.

If you take the case of a side wind of equal speed to your normal cycling speed, by my calculation that adds full 40% (square root of two) drag. It's *much* harder to ride in a side wind than with no wind, so it genuinely is that the wind is normally against you, even when it isn't!

It's probably actually much worse even than this, because your effective drag coefficient will be far worse side on, as your projected area is much larger to the side. I'd guess maybe double? If that's the case, it gives 80% more effort needed in a side wind than no wind, and the wind only feels behind you (net reduction in effort) if you are within 60 degrees of a true tailwind. ie 2/3 of the time, it feels like a headwind, even if you've ridden a perfect circle in a completely steady wind.

Above calcs subject to arithmetic errors and gross assumptions.

[mattheus]

There's a graph in the book Bicycling Science that shows how different head/tail wind speeds affect the air drag power you have to overcome at different riding speeds. This is for a "fairly large rider in a nonaerodynamic position" but it gives a general picture.


IMG_2006.jpg

That's a mic-drop post

Because:
- that's a brilliant book (is it still in print?!?); and
- that graph pretty much answers all the questions (especially if you're not that comfortable with the applied maths, equations etc).

[Jdsk]

There's a graph in the book Bicycling Science that shows how different head/tail wind speeds affect the air drag power you have to overcome at different riding speeds. This is for a "fairly large rider in a nonaerodynamic position" but it gives a general picture.

That's a mic-drop post

Because:
- that's a brilliant book (is it still in print?!?); and
- that graph pretty much answers all the questions (especially if you're not that comfortable with the applied maths, equations etc).

Fourth edition, 2020:
https://mitpress.mit.edu/9780262538404/ ... g-science/

Jonathan

[Jon in Sweden]

So I guess my follow on question is how do I convert my obviously very high power output into faster cycling?

I am far from quick on the bike. I don't think I could get much under 100kg without looking daft. Think Connor from GCN (he's a centimetre taller than me) but I'm broader across my top half.

Tall people are basically just walking, talking windbreaks in the pelaton!

[Cugel]

So I guess my follow on question is how do I convert my obviously very high power output into faster cycling?

I am far from quick on the bike. I don't think I could get much under 100kg without looking daft. Think Connor from GCN (he's a centimetre taller than me) but I'm broader across my top half.

Tall people are basically just walking, talking windbreaks in the pelaton!

Reduce your drag through the air. This means getting your front half long and low - see that Connor you mentioned for the position I refer to. Basically, a flat back and a narrow grip o' the bars. No knees flailing out, mind!

The question is: can you be comfortable enough in such a position to maintain your maximum sustainable power (your FTP)? I know I can't, now or then; or even before then. You'd need some serious flexibility and a very skinny waist. And probably other bodily features, some of which might be built-in courtesy of your genetics and some of which can be trained for, by who-knows-what contortionary procedures!

Cugel