Gratuitous use of "cogent"..."fractal ignorance". Hallmarks of a mountebank.Humber's lack of a cogent argument is based on two problems, only one of which is his communication skills.
No, but 20 seconds later I know that it is an open joke. A prank known by a large community to be a prank. How is that relevant?
Anyone can come on to the internet and imply they have qualifications, eh,humber said:Manipulation of identity.
Doctor?
We can use Newton's impact theorem. Not accurate, but good enough.
Each air molecule strikes the prop over impact time, t
f =ma, so
f*t = ma*t (1)
V= at. ( the wind velocity derived from the acceleration)
f = (mV)/t (2)
During the impact time, N molecules will hit the prop, so the force is
Fd = N*f. (3)
To find the force, we need to know N, and the area hit by those molecules.
The prop has the disk area A. Instant deceleration is impossible, so as the molecules decelerate over time 't', the wind moves distance x. That is, deceleration takes place over a small but finite distance x.
Consider an area, A, of the blade.
Distance = velocity*time
x = V*t
Volume = V*t*x
Combining
N = A*V*t (Number/Volume)
Multiply N by the single molecule force, f.
Fd = m*(Number/Volume)*A*V^2
The density of the molecules (number/volume) can be found from p, the air density. The final product is:
So Fd = p*A*V^2.
That is the force that will accelerate the prop (cart) when in a tailwind, but slow it when a headwind, and does not depend upon "how far the prop moves relative to the air", but only on the amount of air over impact time t.
That equation makes many simplifying assumptions, but when refined as Rayleigh and other did, we get the familiar drag equation.
Fd = 1/2*Cd*p*A*V^2
The headwind slows the cart. If you think that rotation helps because the blade can move the the other way, then you are forgetting that the whole blade move forwards too. When at constant speed, the translation of the surface in the direction of the cart is constant, and independent of the angular velocity of the rotor. Carteers confuse perceptual errors and "insight".
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