In practice, things are not lined up in a row. I doubt that you can make all vectors zero, H'ethetheth.
None of that does anything to support zero KE as the basis of a model H'ethetheth, but to suggest that is impossible, and produces an inert result.
It is quite straight forward, and you are changing the playing field. None of these matters have been addressed, and whatever the outcome or interpretation, I have not seen anything other than the over-simplification represented by the equations you posted to me a few posts ago.
I am quite sure an ad-hoc structure can be built, why not, just add more transformations, but that will say nothing about the validity of the model. Mathematics will simply be an obfuscation.
To answer the modeling question, I may as well reply to your earlier post, H'ethetheth.
And if there is no belt? That idea seems magical to me. As yet, nobody has managed to explain how the car can be said to be in motion, or how the KE necessary to meet even the minimum requirements of dynamic modeling is acquired or stored, or how that may be assigned to the belt or anywhere else. (Measurement seems to be impossible without actually supplying it it from test device itself)
The car and belt (or the observer) are not isolated from ground, but share it in common, and are within a common gravitational field. That is for certain, or there would be no power for the motor, to name but one reason. ( Power stations eventually return all current to the ground). It becomes difficult to believe that any KE produced from that source is not relative to ground.
I presume you mean motion other than relative to the ground? That motion at any given time is in the 'background', a common-mode effect. Your fish tank model, and all of our scientific tools are selective, and serve to isolate the desired outcome from that background, or as in your specific case, from water currents too.
I am not traveling in any real sense when not in motion w.r.t the ground, or it could be said that our cemeteries are full of travelers.
The fish may do work against a flow, and yet not move relative to the ground, and so gain no KE w.r.t the ground. This is nor true of the treadmill, as generally, little work is required to stay in one spot, when there is no load.
I did not elaborate on the jets, though I did not have simple vertical jets in mind. Yes, I know it is possible and I could use it, or perhaps something else, may be high-power ultrasonics. Orders of magnitude? I doubt that, and I can still call upon natural phenomenon to do some of the 'calculation', as indeed BMW seem to be doing. I expect that the CFD programme is 'seeded' with real data.
My point H'ethetheth, is that I do not need a belt. Therefore, I can see no reason why the belt could be said to imply motion of any sort.
The belt drags the cart backwards through the wind to be self-limiting, and so stay on the spot. That is not equivalent.
Some emulation of the road/wheel interface and propeller, yes. That is where the similarity ends.
(1)The real wind's power is independent. Whereas on the treadmill, the power available to the cart is limited by the friction to the belt and the reaction of the cart to that. Moreover, the force to the belt is of course, dependent upon gravity. That is not equivalent.
(2) The belt may be capable of providing the necessary power, but as stated, that is limited by the force to the belt. When that limit is reached, the cart's wheels may turn, but it will stay motionless w.r.t the ground ( because of the relative motion of wheel and belt) while the force will be more or less constant from the point. This casts doubt on the claim that the cart is capable of climbing the belt to windspeed.
(3) The treadmill can be modeled by fixing a strip of belt to the top of a long flatbed trolley. The wind-cart is placed on the belt as normal, and the trolley pulled through still air, so as to drag the cart backwards (air against the rear of the propeller). That is the same as the cart moving back with the belt. If the model is at all valid, the cart should make progress along the belt. That would not happen for many reasons;
(3a) The rear of the cart's prop will be met by the air mass, and simply roll on the spot with no motion w.r.t ground, hence no KE.
(3b) Should the propellor turn in that condition, that will serve to drive the cart forward. However, this will self-regulate because the cart is now moving in the forward direction, and so away from the driving force, with the added vexation that the belt and wheels are still in opposite motion. This means that the force is essentially constant, and at a minimum, with little or no motion w.r.t ground. That is the general operation of the treadmill, and the windspeed state.
The cart can never be in motion w.r.t the belt. For the cart to do that, the wheel's axle must move w.r.t the belt, but the opposite motions of belt and wheel prevent that. If force were to be available from the prop, then that would drive the axle forward, away from the driving force. The fact that is does not, shows that there is no net thrust from the propeller.
In fact, the above is a particular example of the general case; a simple wheeled vehicle powered only by the belt, cannot make progress w.r.t that belt.
(3c) That raises questions about distance on the belt. If the perceived travel is said to be velocity above windspeed, that would seem to be valid. The belt represents a velocity plane ( the speed of the belt sets the windspeed) but the distance along the belt itself, as a real belt, has a real dimension, so what does that represent to the treadmill side observer?
The models is strained, but it would appear to be simple displacement w.r.t the ground, for both the real and modeled cases. This also suggests that the cart is not in motion, save for that small displacement.
It is also true that it is not at all comparable. Yes, the fish does stay in one place, that is my point. The fish can gain no KE unless it swims at a velocity w.r.t the ground. The cart does not move relative to the ground at any appreciable velocity, and so can have no KE. In this way, they are similar.
Badly expressed, perhaps. The fish and water could both be at the same velocity w.r.t. the ground, but zero w.r.t reach other. There is no motion relative to the water when not swimming, is what I mean to say.
Yes, that is option(3)of the my earlier post. The others I thought may be closer to the treadmill, which is why I said that (1) was most likely to be comparable.
Yes, the fish is motionless w.r.t the camera, and flowing water would cloud your data, but the fish does swim. The tank rotates to keep the swimming fish fixed relative to the camera. As the tank rotates, there must be some viscous coupling to the water, so a small flow will be generated. I imagine this to be necessary to the experiment, because it stimulates the fish to swim against it. This is nothing like the treadmill.
The fish is self-powered and not from the flow of the water. That is very different from a wind cart. Few would doubt that a battery R/C car would not climb the belt.
That also sounds like magic. Like the fish, the cart it has no KE because it is not in motion w.r.t the ground. The KE is said to exist "relative to the belt" but it seems that a belt is not necessary to the model, so what then? The belt simulates the effect upon the boundary layer of the cart/car passing over the road, but not the motion itself.
In detail, yes. It is hypothetical, but means that it is feasible, and I could eliminate the belt. In any event, I need not model the boundary layer to test other aspects, so how can it be said that the car is in motion if there is no motion at all?
An error margin can be set accordingly. The reproduced boundary layer may perhaps be indistinguishable from the real thing, but definitely not the car's behaviour. The dynamics of motion at speed are no reproduced at all. It is not possible to do this to any significant degree, as the BMW/F1 car is mechanically restrained by attachment to the ceiling. The cart is similarity stabilized, by the method I described and some details specific to the cart's mechanism, but it is quite clearly only just stable. Not the dynamics of a vehicle driven to wind at such speeds,
There is certainly wind passing under the real car. The real wind blows over the road creating a boundary layer, independently of the car. That passes under the car, to be modified by the motion of the car as it travels over the road. There are two components to the boundary at a given velocity; the wind under the car, and the motion of the car over the road. The belt largely provides the pattern of that interaction, but the wind that passes under the car is needed for accurate reproduction. The error in the treadmill belt flow, is a demonstration ( in part) that wind is necessary to that model.
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I went back to read that long long post from humber, just to extract the most enjoyment from it, but I still can't manage to stay awake for more than a paragraph. I think he suddenly realised that no-one is ever going to take him seriously unless he writes an occasional full-length essay.