Headwind/Incline Equivalence

[Psamathe]

Doing my cycling in "flatlandia" I have little appreciation for the effort hills demand. We have a few inclines but they are invariably short (and I do feel them in my legs, not being used to them!).

So I was wondering if people have any ideas about what sort of headwind (ignoring your forward motion) might be equivalent to what sort of hill incline (e.g. headwind of <x> knots/mph on flat around the same as a <y>% incline).

Ian

[karlt]

10mph seems to have about the same affect as 1%; it'll drop me from 20mph on the flat to about 16. But it's going to depend on the individual's setup; inclines work on your weight whilst headwinds on your surface area. A lightweight rider on a carbon bike will suffer far less from inclines than a, erm, larger rider on a full sus BSO, but not suffer much less from headwind.

I've never ridden in anything that slowed me down more than around a 3-4% incline. Round here you can be creaking up hills at 5-6mph, less on the really evil buggers. That'd be like riding into a Force 10.

[Flinders]

This is a really interesting question. I'd say that a headwind of about 10-15mph (according to the Met Office forecast) causes me to drop from about 15 on the flat (okay, I'm a slug) to a point where the same effort gives me about 10-11mph and 12mph can be a real struggle. OTOH, a nice tailwind puts most of that back on the return journey.
However, I am continually irritated by the capacity of the wind to veer and be a headwind on the way back as well as the way out.

Sometimes I end up coming up hills faster than I went down them if the wind actually stays in place. Then I know it really is a wind effect. But if I don't notice a mild headwind on the way out, I can get a bit disheartened by my slower progress and think I'm getting less fit, and it's only when I have it behind me later I realise what the problem has been.

[Mick F]

It's a good question.
Wind tends to be blustery rather than constant, and roads tend to bend this way and that, so we rarely are on a straight road to assess the difference.

Worst is up hill AND against the wind.

I rode up onto Dartmoor a week or two ago up the horrendous Pork Hill. There was a strong easterly against me all the way to Princetown. Purgatory to say the least!

[karlt]

I 'ate it when you climb a hill into a wind, but it's not too bad because you're sheltered by the hill itself, so you comfort yourself thinking of the whizz down the other side, only to be met with a wall of wind trying to blow you back up it taking all the fun out.

[roubaixtuesday]

I think your answer depends on how fast you ride.

First, a bit of basic fluid dynamics
To a first order, air resistance scales as the *square* of speed.
Gravity resistance, however is *constant* regardless of speed.
Power (what you put in on the bike) is resistance multiplied by speed.

So... if you double your speed going up a hill, you need double the power to defeat gravity. Going up at 10mph takes twice the effort of going 5mph. This assumes you’re going so slowly you have negligible wind resistance.

However, if you double relative airspeed – say ride at 10 mph on the flat into a 10mph headwind, you need *four* times the power vs no headwind – the *square* of the change.

Obviously it’s more complex than this in reality, but you get the gist. It also helps explain why it’s so much more wearing riding into the wind than up a hill – you get much less payback for your effort.

[Vorpal]

Wind tends to be blustery rather than constant, and roads tend to bend this way and that, so we rarely are on a straight road to assess the difference.

That depends on where you are. https://en.wikipedia.org/wiki/The_Fens

Up a hill, at least there's and end to it. Across The Fens seems like forever on a windy day.

[Mick F]

Up a hill, at least there's and end to it. Across The Fens seems like forever on a windy day.

Oh yes, I wouldn't say otherwise. It must be awful to say the least!

So the original question is what (constant) wind on the flat is equivalent to what incline in still air.

Answer from me:
Don't know .............. because it's a variable thing when you are in hilly country and subjective too depending on your morale and fatigue.

Only way you could sort of assess it, is by experimenting and using some sort of power meter - Power Tap maybe?
Maybe someone with one knows the answer by comparing one ride against another on flat vs hill.

[Brucey]

Doing my cycling in "flatlandia" I have little appreciation for the effort hills demand. We have a few inclines but they are invariably short (and I do feel them in my legs, not being used to them!).

So I was wondering if people have any ideas about what sort of headwind (ignoring your forward motion) might be equivalent to what sort of hill incline (e.g. headwind of <x> knots/mph on flat around the same as a <y>% incline).

Ian

using this calculator

http://bikecalculator.com/veloMetricNum.html

on its default settings, it suggests that every 1% gradient is roughly equivalent to 10kph of headwind. It feels worse than that to me.....

cheers

[Mick F]

1% gradient is almost flat?
10Kph in English is 6mph (or thereabouts)
I would say that is poppycock.

6mph headwind is much more than the equiv of 1% gradient.
1% is nothing.

[gaz]

using this calculator

http://bikecalculator.com/veloMetricNum.html

on its default settings, it suggests that every 1% gradient is roughly equivalent to 10kph of headwind. It feels worse than that to me.....

I do not pretend to understand the calculator, however I've ridden up a 25% gradient but I don't fancy my chances into a 250kph headwind .

[robing]

I 'ate it when you climb a hill into a wind, but it's not too bad because you're sheltered by the hill itself, so you comfort yourself thinking of the whizz down the other side, only to be met with a wall of wind trying to blow you back up it taking all the fun out.

This! Nothing worse than having to pedal downhill!

[Brucey]

I do not pretend to understand the calculator, however I've ridden up a 25% gradient but I don't fancy my chances into a 250kph headwind .

According to the calculator it is 0.33 kph vs about 1.8 kph for the same (low) power output....

But of course such things, in extremis, quickly become non-linear; an approximation is just that, an approximation. My suspicion is that, in addition, the default settings in the calculator represent a skinny racing type on the hoods quite well, but a typical commuter or tourist rather less well; upping the frontal area to 0.5 or 0.6 m^2 gives results that seem a bit more believable, i.e. where a ~5kph headwind seems like a 1% gradient...

cheers

[Mick F]

..................... a ~5kph headwind seems like a 1% gradient...

Now that, I can believe!

I'd maybe extrapolate it a tad.
1% is hardly anything.

Why not say 5% is equiv to 25kph headwind, or 10% hill is equiv to 50kph headwind?
Or is the formula not linear?

Either way, you need to consider a "noticeable" hill.

[karlt]

1% gradient is almost flat?
10Kph in English is 6mph (or thereabouts)
I would say that is poppycock.

6mph headwind is much more than the equiv of 1% gradient.
1% is nothing.

I wouldn't say nothing. I find that 20mph on flat + a minute for each 50' gives me a reasonable estimate of time which I can these days generally beat by 5-10% if I push on. A mile of 1% rises 50', so that's 4 minutes rather than 3. OK, if it's just a mile I'd probably be looking at more like 3m30s - 3m45s rather than 4, but it's still a significant difference.