[Closed] Does a headwind hurt more than a tailwind help?

Yes, wind resistance increases with the square of the speed.

there are no tailwinds, just spells when you feel good

definitely. But slogging into a headwind makes you feel like a flandrian hero

Eat more beans.

Not only does it hurt, but it takes longer to cover the same ground so it hurts for longer.

Yes. For example, if you can maintain 20 mph in still air and do a 20 mile ride, it will take you 1 hour. If you have a 5 mph headwind on the first half and a 5 mph tailwind on the return journey, the first half will take you about 40 minutes and the return journey about 24 minutes, so you'd lose 4 minutes. If you have a 10 mph wind, it would take 1 hour for the outward journey and 20 minutes for the return, so you'd lose 20 minutes. With a 20 mph wind, you would never complete the outward journey.

Yes. I’ve just done an out and back, which is usually a 20k gentle climb and a 20k tt back down a fast road with a bit of descent. I was a lot quicker up than down... brutal. Probably 5-10 minutes slower than usual overall.

Just made a spreadsheet to prove it:

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With a headwind of ~10mph a nominal ~20mph TT effort ends up taking about 1/3 longer.

With a 20 mph wind, you would never complete the outward journey.

If that were the case, I'd never get any riding done around here.

Every pedal stroke you make moves you forwards by a set amount depending on the gearing, it is simply that normally this generates momentum which makes the next pedal stroke easier. The strong headwind robs you of some or all of that momentum, it doesn't halt progress altogether.

Effectively it's the same as riding up a steep hill, but on the flat (and this week, downhill) as well.

[edit] should have said "with a ~10mph dead on headwind on the outward leg and the same tailwind on the return" not a constant ~10mph headwind.

Have a look at www.mywindsock.com
Sync it to your Strava account and it'll show you the penalty for riding into the wind. My 23 mile commute had a 9 mile penalty every morning these last two weeks!

Given a ride that would normally take an hour, in still conditions, a headwind would make it last for longer than an hour and a tailwind would make it last for less.
So, the headwind is working against you for more time than the tailwind is helping - I'd say that this makes the headwind outweigh the tailwind by some margin

It’s never nice to be in someone else’s tail wind.

Most people don't ride in a straight out and back so you have lots of crosswinds that also hamper your forward progress on top of headwinds.......then you experience non windy silence and feel like a riding god as the recent up to 40 to 50 mph consistent westerly tailwinds kick in.

The bummer is that side winds also slow you down, I seem to remember reading (and some vector analysis would seem to corroborate without having worked it out) that a wind had to be from your rear quarter or rearwards to help. So given a random distribution of angles in the real world most of them will be a hindrance. The above about head on winds is true (it's also why the downhills on hilly rides don't cancel out the climbs) but you're also hindered by angles.

Most people don’t ride in a straight out and back so you have lots of crosswinds that also hamper your forward

There's also quirks in the aerodynamics to account for. Like for example some wheels actually generate thrust at certain crosswind angles, and considering most of the time the riders speed is much more than the windspeed most of the ride is actually at the shallow angles that this occurs. Doesn't help the rider on top get through the air, but it's not as simple as assuming something like:

F = Cda (net airspeed)^2 A / 2 * cos (net yaw angle).

[Not a real equation, just what a simplified drag equation would look like, e.g. for a sphere]

After today I can guarantee it hurts more. The worst thing was that it was like a huge hill but at the end there is no decent view to reward you.
30 miles on the flat on a singlespeed on the roads in Oxfordshire today. And angry.

Effectively it’s the same as riding up a steep hill, but on the flat

There's an important difference. The power required to climb a steep hill increases pretty much in direct linear proportion to the speed because you are going so slowly that aero drag is negligible. However, the power required to overcome aero drag on the flat increases by the cube of the speed, so doubling your speed requires eight times the power.

The force required to overcome the aero drag increases by the square of the speed (and then you need to multiply by the speed again to get the power, hence the cubic increase in power). This means that you will quickly run out of gears riding into a headwind because shifting up a gear requires much more than a linear increase in power.

Also, my example above wasn't meant to be literal, just an illustration of why a headwind/tailwind will slow down your average. You can think about it like this: At some point the headwind will be strong enough that it will slow you so much that the section of your journey going into the headwind will take as long as the entire journey does when there is not wind. It is impossible to complete the rest of the journey in zero time, so the entire journey must take longer.

Yes. For example, if you can maintain 20 mph in still air and do a 20 mile ride, it will take you 1 hour. If you have a 5 mph headwind on the first half and a 5 mph tailwind on the return journey, the first half will take you about 40 minutes and the return journey about 24 minutes, so you’d lose 4 minutes. If you have a 10 mph wind, it would take 1 hour for the outward journey and 20 minutes for the return, so you’d lose 20 minutes. With a 20 mph wind, you would never complete the outward journey.

That is not the correct way to work it out . That would only work if aerodynamics was the only factor that you had to consider but it isn't . A 20mph headwind would not stop you from going forwards on a bike as you are suggesting . https://www.sheldonbrown.com/brandt/wind.html

Tail wind you say, lucky buggers plenty of places where it just swings round when you turn around. Double headwind for the win!!

That would only work if aerodynamics was the only factor that you had to consider but it isn’t .

No, but aerodynamics is the dominant thing. Rolling friction increases fairly linearly, aero drag as a cubic function.

I think the correct equation for how fast you could ride into a headwind would be as follows, assuming you could sustain 20 mph on the flat in still air:

P = G * (G + W)^2

Where:
P = Power
G = Ground speed
W = Wind speed

When there is no headwind or tailwind, W = 0, G = 20
Therefore P = G^3 = 800

With a headwind of 20 mph:
P = 800
W = 20
G = ?

So
800 = G * (G + 20)^2
800 = G^3 + 40G^2 + 400G

G = 1.7 mph

So, to ride 10 miles at 1.7 mph would take about 6 hours if you didn't stop for a break. I doubt that many people would persist that long, so in most cases my money would be on you never completing the journey.

Apologies if my maths is wrong, happy to be corrected.

I wouldn't have a clue how to work out the difference a headwind makes to a cyclist but real world experience says that a 20 mph headwind will not slow you down anything like that much . Take a look at the link that I posted particularly figure 4 it tells you that a rider who can do a 25 mile TT in an hour on a still day will take just over 63 minutes with a 10mph headwind , 67mins with a 15mph headwind , 73 minutes with a 20 mph headwind and 81 minutes into a 25 mph headwind that by your reckoning would have him not able to move .

Oops, basic mistake in the arithmetic above, 20^3 = 8000, not 800.

Fixing that, G = 9.3 mph.

So, basically the outward trip would take as long as the round trip in calm conditions.

With a 25 mph headwind, speed would drop to 7.5 mph.
With a 30 mph headwind, speed would drop to 6.1 mph.
With a 35 mph headwind, speed would drop to 5.0 mph.
With a 40 mph headwind, speed would drop to 4.1 mph.

I live on a small Island in the middle of the Irish Sea and believe me we have more than our share of wind and I can tell you that your figures there are still not correct . Perhaps your formula is wrong not your arithmetic . Why don't you just accept that the link to Sheldon Brown that I have supplied is correct .

Perhaps your formula is wrong not your arithmetic

It may well be wrong. Please correct it if you can see a problem with it. I worked it out in my head when I went for a ride yesterday morning, hence the error in the arithmetic. Having posted a basic arithmetic mistake, I figured the least I could do was to correct it.

My original post wasn't meant to be taken literally, just as an illustration of how a tailwind won't compensate for a headwind, I should have been clearer about that. In the real world, things will be much more complex, but the basic principle will stand.

Tailwinds add joy.
Headwinds suck the soul out of you.

I live in East Anglia, we’re due our day without strong winds around July. Can’t wait.