But the cart is motionless in still air on the treadmill. You really are losing me here.
Re:above post, no.
It is too simplistic to conclude that no differential wind = windspeed.
It is not logical to conclude, that because there is no differential wind, the cart is at windspeed.
There are reasons for this: It has been found to work, and more importantly, it can be reasoned to be true, and observed to be true.
I'm sorry, I'm not going to say it again. You seem to have had a very odd physics teacher.
The principle itself is not in dispute.
In what sense does it work? As a tool of convenience to allow simpler calculation, or a mental aid to gain a perspective, yes, but as you say, that changes nothing about the relationship between the relative elements. 'Equivalence' is ubiquitous. It is part of a common background, as are time and gravity. I do not see how invoking this principle changes
one fact about the relationship between the cart and the wind or anything else.
No! If you sit on a missile you can know your velocity, but only if you define a frame of reference! Velocity is meaningless without a frame of reference, that's why I asked you how fast the earth is travelling. You gave the correct answer, but for some reason you think that this is not true for things on earth.
No, it is not redundant. It can be enlightening, because it shows you that you don't have to measure flight in the air only; you can use a wind tunnel.
You are comparing the general to the specific. How is it enlightening to view the cart from the belt? Do you need to invoke a recondite theorem to justify concluding that the wind moves reactive to the ground? Well, it just does, doesn't it?
The Earth's velocity is not significant because the motion is between the cart and the ground; the wind is
the energy conveyor. Yes, the entire solar system is in motion and the galaxies are moving apart. And? There is such a thing as 'locality' to be considered.
In all the math examples I have seen are simplistic. The wind is replaced by a singly-dimensioned vector 'V'.
Statics and Dynamics are equated. Equivalence does not allow for that!.
The wind is not only a dynamic force, it is a system. The air gains energy and momentum from the sun, which is returned as it blows over the road, and other objects. The "equivalence" is much more than the just the relative velocity between the surface of road and the wind, because that is also (one of) the means by which the energy is circulated.
The next step it seems, is to take that vector, and make it manifest by the use of a treadmill. There is no other supporting mathematics or logic that allows for any more equivalence than one superficial similarity. It moves.
It is "observer based" only. Dynamic systems cannot be treated as if they were static, just by means of a new perspective.
It is also an astounding failure of reason. All things may be relative, but that does not mean they are all equal, nor that the absolute magnitude of each becomes unimportant. To 'prove' this failure in a van....
No. As an aerospace engineer I can assure you that this is a failure of your understanding.
To be fair, H'ethetheth, you have made more effort than those you have cited, but I do get tired of the general appeal to authority, especially when the arbiter is that self-same person. There are good engineers and bad engineers. I don't know you. Do you think automatically that you can match me in my fields of expertise?
I do not like to see education used as a weapon, if only because there are those that deserve an explanation despite not having the necessary formal skills. They do not need the pseudo-intellectual posturing of those I refer to as the 'mice'. That's my 2 cents on that topic.
As an aerospace engineer you should be aware that all design and development tools, from software simulations to environmental chambers, undergo a process of verification by comparison with information derived independently of the test object. In use, they are calibrated against standards. The list of failures in this regard are to numerous to mention.
The only force the cart needs to overcome when it is riding at wind speed is the friction in the mechanism. The energy to do this comes from the fact that, in this situation, the ground is passing by at wind speed.
What a happy coincidence it is that we can write;
Required force at windspeed = Stray friction in treadmill.
You are thinking only of the incremental force. In reality, of course, the cart will be constantly changing its velocity as it meets varying circumstances, so making almost continuous demands for significant incremental force. That not withstanding, there must be a static force behind it sufficient to have driven the cart too windspeed in the first place.
The reason that the cart has no 'go' is simple. There is no force at the propeller.
For that to happen, there must a force capable of developing as
differential pressure across the propeller. Obviously, in static air, this is not the case.
The small amount of energy that trickles up from the motor to power the drag of the propeller as it makes a local disturbance, is orders of magnitude below what is actually required.
I have earlier described the treadmills act, but perhaps this is clearer.
Replace the propeller with a tangential impeller, (like a waterwheel
with end-plates, such that it cannot generate lateral forces).
If you spin such a device in the hand, you will feel the opposing drag of the air.
Put this on the cart, and spin the wheel clockwise. The 'prop' will rotate
clockwise, and you will feel the opposing drag.
Turn the wheel CCW, and you will also feel opposing drag.
The cart is trapped in this force 'well'. I cannot so eadily move forward or backwards, so its natural tendency when on the belt, is to stay where it is.
The prop and the drive shaft oppose each other, resulting in an
absolute torque that is the drag of the prop at that particular angular velocity, and a
differential (driving) force of next to zero.
( Assuming there is adequate friction with the belt to transmit that absolute torque)
The real propeller is not symmetrical with respect to drag, though it is turned against its natural bias, so that drag will be dominant. The 'thrust' component will be smaller, as the propeller is not designed to spin in that direction, so the absolute 'drag' will be the result of the difference of those two.
Same process, different 'well' depth. The motion forward I have also previously described, but given that the basic principle is so flawed, I don't feel that it requires more elaboration than has been given
ETA:
To make things clear,H'ethethet, I do not say that vehicles cannot travel faster than the wind, but:
1. A direct propulsion device like this cart, no
2. I have not seem proof that it can, therefore I stick to 1.
3. The treadmill says nothing about the carts capacities, other than the wheels spin
.
