- #316
zoobyshoe
- 6,510
- 1,291
First: just clarify for me if you are talking about an outdoor wind test or swerdna's table?vanesch said:The problem is again that your v^3 is dependent on the reference frame in which you are looking. If you are looking in the ground reference frame, then the only "moving medium" is the wind, but there's no problem: the wind is blowing at a steady pace.
Now, when you are looking at the situation from the cart's perspective (when it is exactly at the wind speed), then it is right that the *wind* medium doesn't allow any extraction, but in this reference frame, the floor is moving, and from *that* movement you can extract energy (like you can when you would have a running treadmill and you would put a wheel with a dynamo on it: you can extract power from this moving floor.
The problem is that you are applying your energy balance by using movements as seen in two different reference frames: you say that you cannot extract power from the floor (which is correct in the floor reference frame) AND you say that you cannot extract power from the air (which is correct in the cart's frame). So you say: there's no power source anymore (the floor is not moving, and the air is not moving). But you should do your balance in one and the same frame. It doesn't matter which one (although there will always be one where things are simpler), but once you've chosen it, you have to stick to it.
As pointed out already several times, when you reach the point where the cart is at (or beyond) windspeed, the propeller is DELIVERING power to the wind in the cart's frame, and TAKING that power from the motion of the floor (again, in the cart's frame). That's because it is *accelerating* the wind in its frame.
You get a similar analysis when you look at it from the wind's frame (but the numbers are different).
When looking at is from the floor's frame, the propeller is TAKING power from the wind (because in *this* frame, it is slowing down the wind). As in this frame the floor isn't moving, there' s no power to or from the floor.