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Mess with your minds: A wind powered craft going faster than a tail wind speed.
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PlainName:

--- Quote ---Do you agree air is a compressible gas ?
--- End quote ---

Yes, but I don't think it's relevant. Without air there would be no puzzle since there would be no wind to move faster than :)

I think the crux of it is that you're missing the effect of the wall of air. That wall could be a moving sail, being pushed back by the vehicle, except that there is a finite distance to which it could be pushed. With air, there is no limit because there is always air in front of you to push back. There is no infinite mechanism to do the same for a sail.

But let's assume for the moment that it is a sail, and the vehicle is infinitely long. The sail starts at the front and moves backwards at 1ms, say. There is a wind pushing the vehicle at 2ms. But that's pushing against the sail, so the wheel speed across the ground is actually 3ms - the 2ms wind plus 1ms sail.

That's how it works. The vehicle speed across ground is the wind speed plus the prop wash speed. Simple as that.

Ah, but the prop is powered by the wheels. Which is fine because the real vehicle speed will never reach the theoretical maximum. As has already been discussed, as the max is approached the wind power drops off and the speed stops increasing. So, in our example above, the vehicle may be doing 2.5m/s and can't go faster because of the lack of power as the vehicle-prop velocity approaches wind speed. But, as also noted, as the vehicle speed drops the apparent wind power will increase. Given the available wind power (acting against the diameter of the prop wash) is greater than the frictional losses of pushing the wheels to turn the prop, the realised speed can be higher than the winds ground speed (which is what all this is about).
electrodacus:

--- Quote from: dunkemhigh on December 24, 2021, 05:59:39 pm ---
--- Quote ---Do you agree air is a compressible gas ?
--- End quote ---

Yes, but I don't think it's relevant. Without air there would be no puzzle since there would be no wind to move faster than :)

I think the crux of it is that you're missing the effect of the wall of air. That wall could be a moving sail, being pushed back by the vehicle, except that there is a finite distance to which it could be pushed. With air, there is no limit because there is always air in front of you to push back. There is no infinite mechanism to do the same for a sail.

But let's assume for the moment that it is a sail, and the vehicle is infinitely long. The sail starts at the front and moves backwards at 1ms, say. There is a wind pushing the vehicle at 2ms. But that's pushing against the sail, so the wheel speed across the ground is actually 3ms - the 2ms wind plus 1ms sail.

That's how it works. The vehicle speed across ground is the wind speed plus the prop wash speed. Simple as that.

Ah, but the prop is powered by the wheels. Which is fine because the real vehicle speed will never reach the theoretical maximum. As has already been discussed, as the max is approached the wind power drops off and the speed stops increasing. So, in our example above, the vehicle may be doing 2.5m/s and can't go faster because of the lack of power as the vehicle-prop velocity approaches wind speed. But, as also noted, as the vehicle speed drops the apparent wind power will increase. Given the available wind power (acting against the diameter of the prop wash) is greater than the frictional losses of pushing the wheels to turn the prop, the realised speed can be higher than the winds ground speed (which is what all this is about).

--- End quote ---

You just try to delude yourself with a crazy explanation.
What you call that wall of air is the wind (air particles moving in the same direction in average) and once your vehicle exceeds that the vehicle will face the opposite as not vehicle is no longer pushed by wind (but needs to travel with the equivalent of a headwind).
So not only there is no wind power available to vehicle but it has to deal with air moving in the opposite direction relative to the vehicle.

You all have this same insane explanation that you can output higher power at the propeller than you take from the wheels.
You are describing an over-unity device so the wrong explanation of how the vehicle actually works.
IanB:

--- Quote from: electrodacus on December 24, 2021, 05:36:09 pm ---Do you agree air is a compressible gas?
--- End quote ---

No, I don't agree. All of the wind turbine power equations you have posted treat air as an incompressible fluid. All the equations you have posted have a constant density for air, which you state as 1.2 kg/m3.

If air were to be considered a compressible gas then the density would vary as a function of pressure, and this would appear in the equations. Since none of your equations have a variable density in them, you are stating that air is modeled as an incompressible fluid.

So if you try to say air is a compressible gas you are contradicting yourself.
electrodacus:

--- Quote from: IanB on December 24, 2021, 06:17:37 pm ---
--- Quote from: electrodacus on December 24, 2021, 05:36:09 pm ---Do you agree air is a compressible gas?
--- End quote ---

No, I don't agree. All of the wind turbine power equations you have posted treat air as an incompressible fluid. All the equations you have posted have a constant density for air, which you state as 1.2 kg/m3.

If air were to be considered a compressible gas then the density would vary as a function of pressure, and this would appear in the equations. Since none of your equations have a variable density in them, you are stating that air is modeled as an incompressible fluid.

So if you try to say air is a compressible gas you are contradicting yourself.

--- End quote ---

That equation I posted shows the available wind power the stored energy is a separate equation that makes no sense to talk about until you understand that vehicle has no wind power available once wind speed is exceeded.
In my video I show the way energy is stored in compressed air and how vehicle gets to exceed wind speed.  It is for ideal case so no losses but those can also be added for a more accurate real world result and to show the deceleration after vehicle got to peak speed.
I also linked to a proper calculator that is designed for the air pressure against a fixed wall or parapet and that clearly shows different pressure levels behind the wall thus clearly illustrating the air as a compressible fluid.
Here is the link again   https://eurocodeapplied.com/design/en1991/wind-pressure-freestanding-wall
And there is obviously one of my replays above sowing the pressure differential for an axial fan.
Labrat101:
I gave the formula in reply #1071
key parameters in propeller design, the main ones being the power to drive the propeller,
 and the thrust that the propeller delivers.
    • The angle between blade chord and propeller plane is the geometric pitch (blade angle β
    • )
    • Angle of attack of the blade element α=β−Φ
    • The effective pitch angle is Φ=arctan(V/ω∗r)
. This is often given relative to rotational speed n = rounds per second of the propeller, and the propeller diameter R:
Φ=arctanVn⋅D∗1π⋅r/R
The advance ratio J of the propeller is
J=Vn⋅D
Induced velocity should be constant over the blade, implying that β
decreases linearly with increasing r: the propeller blade twist. Because the twist changes linearly, one point on the blade can be taken as the representative blade β
, and this is usually taken at either 70% or 75% of the radial distance.
It can be shown that for a given blade geometry, the power and thrust coefficients CP
and CT of the propeller are determined only by J and β0.75. If tip speed is below speed of sound and the blades are not stalled, Mach and Reynolds number effects are negligible.
CP=Pρ⋅n3⋅D5
CT=Tρ⋅n2⋅D4
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