How does a headwind affect speed and power output?

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

Post by Jdsk »

roubaixtuesday wrote: 13 Nov 2022, 5:39pm
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.
I have offered you a step by step approach already.

You insist that distance must be measured relative to air speed.
...
Yes, we're at the first step. No cyclist, no ground, just an arbitrary object moving in an airstream. To get the equation for work (or energy) we need a distance. That distance is distance through the air that is exerting the drag force. What else could it be?

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

Post by Jdsk »

roubaixtuesday wrote: 13 Nov 2022, 5:41pmRelative to the frame the question itself uses for distance. The ground.

You're using two frames of reference inconsistently.
There is no ground in the first step, only an object moving in airstream.

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

Post by roubaixtuesday »

Jdsk wrote: 13 Nov 2022, 5:45pm
roubaixtuesday wrote: 13 Nov 2022, 5:41pmRelative to the frame the question itself uses for distance. The ground.

You're using two frames of reference inconsistently.
There is no ground in the first step, only an object moving in airstream.

Jonathan
We agree that the cube is the right answer for an object in stationary air.
. The question at hand is what is the relationship vs headwind for an object maintaining constant speed relative to the ground.

You are using the wrong velocity.
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

roubaixtuesday wrote: 13 Nov 2022, 5:47pmThe question at hand is what is the relationship vs headwind for an object maintaining constant speed relative to the ground.
There is no ground in the consideration of an arbitrary object moving through an airstream. If we can derive the appropriate distance and the energy equation for that we can move on to the next step.

But I suspect that we're now stalled (!).

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

Post by Jdsk »

roubaixtuesday wrote: 13 Nov 2022, 5:47pm...
We agree that the cube is the right answer for an object in stationary air.
...
Yes.

It's also the relationship between power and aerodynamic drag for whether the air is moving relative to the ground or not as long as the velocity used is the airspeed of the object (or "relative velocity of the object through the air ").

Jonathan
Last edited by Jdsk on 13 Nov 2022, 6:56pm, edited 1 time in total.
roubaixtuesday
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Re: How does a headwind affect speed and power output?

Post by roubaixtuesday »

OK, I'm going to leave it here.

I've tried and failed to explain the correct answer.

I'd ask you to critically consider why your method gives unphysical results at zero speed, and disagrees with available online calculators.

Please use your curiosity to critically engage with these questions!
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Chris Jeggo
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Re: How does a headwind affect speed and power output?

Post by Chris Jeggo »

We're agreed that drag force is proportional to the square of relative wind speed.
The question is, what speed is the correct one to use in
power = force x speed

The answer is that it depends. It depends on how the propulsive force, that counteracts the drag force, is generated.
If the propulsive force is generated by the tyre pushing backwards against the road then the correct speed is the road speed because all the action takes place at the road surface.
If the propulsive force is generated entirely by an aero engine pushing backwards on the air then the correct speed is the relative wind speed because all the action takes place in the air.
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

The power required to overcome the aerodynamic drag of an object moving through the air and its relation to relative air velocity is independent of the means of propulsion.

The drag force is:
Screenshot 2022-11-13 at 21.31.20.png
Screenshot 2022-11-13 at 21.31.20.png (6.32 KiB) Viewed 545 times
The power is:
Screenshot 2022-11-13 at 21.32.24.png
Screenshot 2022-11-13 at 21.32.24.png (7.74 KiB) Viewed 545 times
where that velocity term is the velocity of the object relative to the fluid throughout.

...

The force and the power required depend on the molecules of the fluid and how big the object is and what shape the object is and how fast it hits the molecules. None of these are affected by the means of propulsion.

Jonathan
Last edited by Jdsk on 13 Nov 2022, 9:58pm, edited 2 times in total.
roubaixtuesday
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Re: How does a headwind affect speed and power output?

Post by roubaixtuesday »

Chris Jeggo wrote: 13 Nov 2022, 9:20pm We're agreed that drag force is proportional to the square of relative wind speed.
The question is, what speed is the correct one to use in
power = force x speed

The answer is that it depends. It depends on how the propulsive force, that counteracts the drag force, is generated.
If the propulsive force is generated by the tyre pushing backwards against the road then the correct speed is the road speed because all the action takes place at the road surface.
If the propulsive force is generated entirely by an aero engine pushing backwards on the air then the correct speed is the relative wind speed because all the action takes place in the air.
It doesn't matter. Either can be used, as long as you're consistent in applying the speed and distance terms.

If you use constant air speed as the frame of reference, you can't then use the ground speed in the same calculation. That's what's happening here - in a calculation of what will happen if ground speed is constant, constant air speed is being applied to the formulae.
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Cowsham
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Re: How does a headwind affect speed and power output?

Post by Cowsham »

When going uphill into wind on a straight road is easier than going down the other side, that's a strong wind.

I've reached the top of a hill facing into wind only to find the wind at the top is so strong it almost brings proceedings to a halt and that I'd been sheltered by the hill I'm going up.
I am here. Where are you?
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Chris Jeggo
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Re: How does a headwind affect speed and power output?

Post by Chris Jeggo »

Jdsk wrote: 13 Nov 2022, 9:35pm The power required to overcome the aerodynamic drag of an object moving through the air and its relation to relative air velocity is independent of the means of propulsion and whether some part of the object touches the ground or not.

The drag force is:
Screenshot 2022-11-13 at 21.31.20.png
The power is:
Screenshot 2022-11-13 at 21.32.24.png
where that velocity term is the velocity of the object relative to the fluid throughout.

...

The force and the power required depend on the molecules of the fluid and how big the object is and what shape the object is and how fast it hits the molecules. None of these are affected by the means of propulsion.

Jonathan
That is the power which is transferred to the air. It is not equal to the power expended by the cyclist.

My argument is true in two special cases. Yours fails in one of them, in that we have been arguing solely about the power expended by the cyclist.
Case (1): No headwind - still air. Both arguments true.
Case (2): Stationary trike in headwind - cyclist stops trike rolling backwards by pressing down on forward pedal. Cyclist does no work because pedal is not moving downwards - no work, no power.

There are texts on dynamics which carefully define force, work, energy and power. They are available in book shops, libraries and online.
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Chris Jeggo
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Re: How does a headwind affect speed and power output?

Post by Chris Jeggo »

Incidentally, note that the final airflow depends on whether propulsion is provided by cyclist or aero engine, because the vehicle creates a draggy, forward-moving wake but the aero engine also creates a backward-moving efflux. Hence the difference in the power results for the two cases.
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

Chris Jeggo wrote: 13 Nov 2022, 10:24pm...
That is the power which is transferred to the air. It is not equal to the power expended by the cyclist.
...
That's *the general drag equation.And the power to overcome drag.

Jonathan

* And it will be near the front of those textbooks. : - )
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Chris Jeggo
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Re: How does a headwind affect speed and power output?

Post by Chris Jeggo »

Jonathan, please quote the source of your two screenshot equations.
Jdsk
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Re: How does a headwind affect speed and power output?

Post by Jdsk »

Chris Jeggo wrote: 13 Nov 2022, 10:24pm My argument is true in two special cases. Yours fails in one of them, in that we have been arguing solely about the power expended by the cyclist.
Case (1): No headwind - still air. Both arguments true.
Case (2): Stationary trike in headwind - cyclist stops trike rolling backwards by pressing down on forward pedal. Cyclist does no work because pedal is not moving downwards - no work, no power.
The general drag equation is valid throughout. The relative air velocity varies across scenarios, and is taken into account in the force and power equations.

Jonathan
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