How does a headwind affect speed and power output?

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Chris Jeggo
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Re: How does a headwind affect speed and power output?

Post by Chris Jeggo »

roubaixtuesday wrote: 12 Nov 2022, 6:50pm
axel_knutt wrote: 12 Nov 2022, 6:46pm
roubaixtuesday wrote: 12 Nov 2022, 6:13pm
The total energy input is force x distance (this is a completely general equation).

The power is energy/ time.

So power = force x (distance/ time)

(Distance / time) is speed.

The force is proportional to the square of relative wind speed, so the power must be too
Force is proportional to square of relative air velocity.
Energy is force on the bike multiplied by distance the bike travels along the road surface that the wheels are pushing against, (if the bike's not moving, there's no power even when the wind's blowing a hoolie).
Power is energy/time = force x bike distance/time = force x bike velocity
Power vs Wind.png
We agree.
We three agree.
Dingdong
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Re: How does a headwind affect speed and power output?

Post by Dingdong »

From a real world scenario, we rolled out about 50 miles last weekend into a nearly continuous stormy headwind, with the odd bit of rain. It was awful and one if the guys we regularly ride with was really struggling. On the return leg, I got what I imagine electric bike owners get: that effortless pedalling sensation with a direct in the tail tailwind.
DaveReading
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Re: How does a headwind affect speed and power output?

Post by DaveReading »

Dingdong wrote: 13 Nov 2022, 7:36amFrom a real world scenario, we rolled out about 50 miles last weekend into a nearly continuous stormy headwind, with the odd bit of rain. It was awful and one if the guys we regularly ride with was really struggling. On the return leg, I got what I imagine electric bike owners get: that effortless pedalling sensation with a direct in the tail tailwind.
It would be interesting to see the energy/work/power relationship given a tailwind.

Re the headwind case, coming from an aeronautical background I'm struggling to see the difference between maintaining a constant speed into a headwind that has got x knots faster, and increasing speed by x knots into a constant headwind.

Must be something to do with the road. :)
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

I finally got my mind round the difference between the two formulations. And why working on distance produces it.
roubaixtuesday wrote: 12 Nov 2022, 5:51pm
Jdsk wrote: 12 Nov 2022, 5:46pm Thanks for those replies.

The cyclist related questions are too complicated for me at the moment. I'm sure that we'll get there when we've done some more agreeing.
They are not cycling related! Here they are again, with all cyclists removed, and simplified.

Please indicate which you agree with.

The total energy input is force x distance (this is a completely general equation).
Agreed. And for any arbitrary object experiencing aerodynamic drag the force is the aerodynamic drag and the distance is the distance that the object moves through the air.

And this is the crucial point, and it needs to be discussed as early as possible. By taking the general case it's easier to see that the distance moved though the air is the relevant distance. What other distance could it be?

Jonathan
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

DaveReading wrote: 13 Nov 2022, 8:11am ...
Re the headwind case, coming from an aeronautical background I'm struggling to see the difference between maintaining a constant speed into a headwind that has got x knots faster, and increasing speed by x knots into a constant headwind.

Must be something to do with the road. :)
That smiley is doing a lot of work!

: - )

Jonathan
roubaixtuesday
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Re: How does a headwind affect speed and power output?

Post by roubaixtuesday »

Jdsk wrote: 13 Nov 2022, 8:31am I finally got my mind round the difference between the two formulations. And why working on distance produces it.
roubaixtuesday wrote: 12 Nov 2022, 5:51pm
Jdsk wrote: 12 Nov 2022, 5:46pm Thanks for those replies.

The cyclist related questions are too complicated for me at the moment. I'm sure that we'll get there when we've done some more agreeing.
They are not cycling related! Here they are again, with all cyclists removed, and simplified.

Please indicate which you agree with.

The total energy input is force x distance (this is a completely general equation).
Agreed. And for any arbitrary object experiencing aerodynamic drag the force is the aerodynamic drag and the distance is the distance that the object moves through the air.

And this is the crucial point, and it needs to be discussed as early as possible. By taking the general case it's easier to see that the distance moved though the air is the relevant distance. What other distance could it be?

Jonathan
It's the distance along the ground.

The source of the retarding force, being aerodynamic, frictional, gravitational or anything else is entirely irrelevant.

Whatever the source of the force, the work done by the cyclist is the distance the cyclist travels multiplied by the force he overcomes.

Think about your claim.

If a cyclist is going uphill, and experiencing an aerodynamic drag equal to the gravitational force, do you

a) calculate the work by distance x (sum of the forces) or

b) calculate the work by somehow weighting according to windspeed?

The object doing the work does the same amount of work regardless of the reason for the retarding force.

[You can do the calculation as you suggest, using a moving frame of reference. But by doing so , you need to calculate using a different distance, as the distance depends on windspeed]
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

roubaixtuesday wrote: 13 Nov 2022, 2:17pm
Jdsk wrote: 13 Nov 2022, 8:31am I finally got my mind round the difference between the two formulations. And why working on distance produces it.
roubaixtuesday wrote: 12 Nov 2022, 5:51pm They are not cycling related! Here they are again, with all cyclists removed, and simplified.

Please indicate which you agree with.

The total energy input is force x distance (this is a completely general equation).
Agreed. And for any arbitrary object experiencing aerodynamic drag the force is the aerodynamic drag and the distance is the distance that the object moves through the air.

And this is the crucial point, and it needs to be discussed as early as possible. By taking the general case it's easier to see that the distance moved though the air is the relevant distance. What other distance could it be?
It's the distance along the ground.
...
There is no "ground" for an arbitrary object experiencing aerodynamic drag. Just the object and the air.

Jonathan
roubaixtuesday
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Re: How does a headwind affect speed and power output?

Post by roubaixtuesday »

Jdsk wrote: 13 Nov 2022, 2:58pm
roubaixtuesday wrote: 13 Nov 2022, 2:17pm
Jdsk wrote: 13 Nov 2022, 8:31am I finally got my mind round the difference between the two formulations. And why working on distance produces it.

Agreed. And for any arbitrary object experiencing aerodynamic drag the force is the aerodynamic drag and the distance is the distance that the object moves through the air.

And this is the crucial point, and it needs to be discussed as early as possible. By taking the general case it's easier to see that the distance moved though the air is the relevant distance. What other distance could it be?
It's the distance along the ground.
...
There is no "ground" for an arbitrary object experiencing aerodynamic drag. Just the object and the air.

Jonathan
The speed of the cyclist is defined relative to the ground.

You are doing a calculation applying different frames of reference to different parts of the calculation.

Again, work = force x distance

It matters not a jot what the source of the force is, the law still applies.

Your approach breaks the laws of physics.
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

roubaixtuesday wrote: 13 Nov 2022, 5:12pm
Jdsk wrote: 13 Nov 2022, 2:58pm
roubaixtuesday wrote: 13 Nov 2022, 2:17pm
It's the distance along the ground.
...
There is no "ground" for an arbitrary object experiencing aerodynamic drag. Just the object and the air.
The speed of the cyclist is defined relative to the ground.

You are doing a calculation applying different frames of reference to different parts of the calculation.

Again, work = force x distance

It matters not a jot what the source of the force is, the law still applies.

Your approach breaks the laws of physics.
We'd just agreed that there wasn't a cyclist:
roubaixtuesday wrote: 12 Nov 2022, 5:51pmThey are not cycling related! Here they are again, with all cyclists removed, and simplified.
Jonathan
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

roubaixtuesday wrote: 13 Nov 2022, 5:12pmYour approach breaks the laws of physics.
My approach is the fundamental equation of drag. For an arbitrary object in an airstream:

Force (of the drag) is proportional to the square of the speed of the object through the air.

plus:
Energy (or work) = force x distance.

And distance here is the distance that the object travels through the airstream. What other distance could it be?

Jonathan
Last edited by Jdsk on 13 Nov 2022, 5:26pm, edited 2 times in total.
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

If at this point any one is interested in why the distance matters I'm happy to explain, but I'd rather work through it one step at a time.

Jonathan
roubaixtuesday
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Re: How does a headwind affect speed and power output?

Post by roubaixtuesday »

Jdsk wrote: 13 Nov 2022, 5:24pm
roubaixtuesday wrote: 13 Nov 2022, 5:12pmYour approach breaks the laws of physics.
My approach is the fundamental equation of drag. For an arbitrary object in an airstream:

Force (of the drag) is proportional to the square of the speed of the object through the air.

plus:
Energy (or work) = force x distance.

And distance here is the distance that the object travels through the airstream. What other distance could it be?

Jonathan
Here we are discussing an object whose distance is measured vs ground, not vs airstream.

You can't use the velocity vs airstream to calculate work, and say the velocity vs ground is constant.

That's your fundamental error - you're using two different frames of reference in the same calculation.

If you do the calculation with a single consistent frame of reference you'll get the correct answer.

Try it!
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

roubaixtuesday wrote: 13 Nov 2022, 5:35pm
Jdsk wrote: 13 Nov 2022, 5:24pm
roubaixtuesday wrote: 13 Nov 2022, 5:12pmYour approach breaks the laws of physics.
My approach is the fundamental equation of drag. For an arbitrary object in an airstream:

Force (of the drag) is proportional to the square of the speed of the object through the air.

plus:
Energy (or work) = force x distance.

And distance here is the distance that the object travels through the airstream. What other distance could it be?
Here we are discussing an object whose distance is measured vs ground, not vs airstream.

You can't use the velocity vs airstream to calculate work, and say the velocity vs ground is constant.

That's your fundamental error - you're using two different frames of reference in the same calculation.

If you do the calculation with a single consistent frame of reference you'll get the correct answer.

Try it!
What other frame of reference is there for an arbitrary object moving though an airstream?

Thanks

Jonathan
roubaixtuesday
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Joined: 18 Aug 2015, 7:05pm

Re: How does a headwind affect speed and power output?

Post by roubaixtuesday »

Jdsk wrote: 13 Nov 2022, 5:25pm If at this point any one is interested in why the distance matters I'm happy to explain, but I'd rather work through it one step at a time.

Jonathan
I have offered you a step by step approach already.

You insist that distance must be measured relative to air speed.

If, for instance, the headwind is the same as the object's speed this means you have doubled its speed.

Which means the speed is not constant - which is the question at hand; what is the relationship between power and headwind for an object at constant speed.

Work is force x distance regardless of the force. You are breaking this physical law.

Also, when your answer is different to all the online calculators available, could I suggest asking yourself the question "where have I made my mistake" will get you to an answer.
roubaixtuesday
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Re: How does a headwind affect speed and power output?

Post by roubaixtuesday »

Jdsk wrote: 13 Nov 2022, 5:37pm
roubaixtuesday wrote: 13 Nov 2022, 5:35pm
Jdsk wrote: 13 Nov 2022, 5:24pm
My approach is the fundamental equation of drag. For an arbitrary object in an airstream:

Force (of the drag) is proportional to the square of the speed of the object through the air.

plus:
Energy (or work) = force x distance.

And distance here is the distance that the object travels through the airstream. What other distance could it be?
Here we are discussing an object whose distance is measured vs ground, not vs airstream.

You can't use the velocity vs airstream to calculate work, and say the velocity vs ground is constant.

That's your fundamental error - you're using two different frames of reference in the same calculation.

If you do the calculation with a single consistent frame of reference you'll get the correct answer.

Try it!
What other frame of reference is there for an arbitrary object moving though an airstream?

Thanks

Jonathan
Relative to the frame the question itself uses for distance. The ground.

You're using two frames of reference inconsistently.
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