vanesch
Staff Emeritus
Science Advisor
Gold Member
- 5,109
- 20
schroder said:I have already presented my detailed reason why this is NOT a valid inertial reference frame. Either you were missed it or simply chose to ignore it. Let me begin by an example: Place a sailboat in a frame in which the water is calm but the wind is blowing. The sail is up, and the skiff is sailing downwind. Now place the exact same sailboat in an equivalent reference frame, the air is calm, but the water has a current which is flowing in the opposite direction the wind was blowing in reference A. This causes a relative wind to blow which is indistinguishable in frame B from the wind in frame A. The sailboat sails downwind exactly as in frame A. The two frames are equivocal. I go through this exercise not to insult your intelligence, but just to be sure we are on the same page here.
We are.
OK. Now we take this cart, just a wheel with a propeller and hook it up as in the video and run it exactly as we have seen. The turntable spins CW, the cart gets dragged backwards for a short while due to inertia, static resistance but soon enough the apparent wind working against that wide yardarm, as well as the cart and propeller, slows the movement of the cart relative to the movement of the turntable. This slowing causes a relative difference in velocity as seen by the drive wheel, which spins up and via the cable also spins the propeller.
Yes.
The direction of spin and pitch of the propeller is such so that it acts as a true propeller, not a mill, and it propels the cart to move counter to the spin of the table. The cart can be seen advancing against the table. Now, your interpretation is that this is an equivalent reference frame to a stationary table and a true wind blowing on the back of the cart.
Yes.
You also interpret this as the cart going faster than the wind, since it is advancing against the table.
Yes.
Here is where you are wrong: This would ONLY be an equivalent reference frame if the cart were to move in exactly the same direction and at the same velocity, if it were driven NOT by the moving table, but instead by an actual wind blowing on the cart as it stands on a stationary table!
But where is the difference if you look upon this from the reference of the turning table ?
In what way can you say that the table is "really turning" and the air is "really stationary", and not that the table is actually standing still and the air is moving ? This is just a change of reference frame, no ?
(there IS a small difference, and that is the fact that the reference frame of the table also has a rotation which it shouldn't, as an inertial frame. But that can be made smaller with a larger turning table).
I have already shown, and Jeff agrees, that if a wind were to blow on the propeller, with the cart stationary on the table, the propeller will act as a turbine, turning the opposite way, turning the wheels the opposite way, and the cart will try to work AGAINST the wind, not go down wind!
Well, that's wrong. It will of course move with the wind in the beginning, because of the drag of the wind on the system (and the arm which acts as a sail). The propeller always acts as a propeller and not as a turbine. Because if that where the case, the cart on the turntable would speed FORWARD faster than the table and not run backwards. How would you explain that the cart is not running forward on the table, but would so when solicited with an external wind ? Again, it is a transformation of reference frames.
Do you still consider the two frames to be equivalent? Under the same relative environmental conditions, the cart will behave two different ways! That is NOT an equivalent reference frame by any means!
This is because you are wrong with your prediction of how it would behave of course.
As I have said, countless times, you cannot test a cart which is configured for upwind motion and claim that it proves down wind performance!
What is an "upwind configuration" ? If it runs downwinds, it will make the propeller *increase* that motion. If it runs upwind, it will make the propeller increase *that* motion. There could very well be TWO solutions to the equation of motion, depending on the initial conditions. Only, the upwind solution has not been demonstrated.
I have showed you how to set up the cart so that it is a true down wind cart; simply remove the drive cable from one side of the wheel and attach it on the other side that is all that is required.
No, if you do that, you have changed the "gear ratio" and hence you will change the motion.
That is not equivalent. It is as if you changed the gear ratio from p = 1/2 to p = -1/2 in my example. You don't get the same motions.
Now, when you run the test, it will be a TRUE equivocal reference frame with a cart in the wind. What you will find is that the cart on the turntable will run backwards with the table until the wind resistance turns the mill as a turbine, which turns the wheels, and it will indeed go down wind, but it will NEVER exceed the table velocity.
This is correct, but the two are not identical physical situations. Frame-independent quantities (such as the gear ratio) which are the same in every reference frame are now different. In order to have an equivalent frame, you should just apply a uniform velocity vector, and all the rest equal (for a galilean transformation). That's exactly what happens when you go from the turntable to the windtunnel (up to the small rotational motion).
This will PROVE the DDWFTTFW is impossible. Yodu can take that same cart, same configuration, and place a fan behind it and it will go downwind, something the original configuration could NOT do!
It will of course ALSO go downwind on the turntable, but not as much, because in order to act as a "turbine" in the downwind, it actually acts as a propeller making it move slightly with the turning table, and not against it, as was the case with the original cart (before changing the sign in the gearing ratio).
Can you now understand the importance of not mixing and matching reference frames? Test the DW cart on the turntable configured as it would be to go DW. Test the UP wind cart configured on the turn table in the same configuration it will be when going up wind. Please do not mix and match! Is there no one here who understands this?
I think it is you who do not seem to see that equivalent reference frames demand that you just apply a velocity transformation WITHOUT changing frame-independent quantities such as the sign of the gear ratio.
All that comes about because you make a wrong gedanken experiment of what the cart of the original poster WOULD do (according to you) when exposed in a wind tunnel.
You don't change the sails of your boat either when you do the equivalent frame transformation in the sea current versus wind case, do you ?
This is really very similar to the case of the winding of a wire on a wheel while you PULL on the wire. Only because of airodynamics, things are less evident.
Last edited: