schroder said:
Let’s look at your “calculations” in a bit more detail: You start out by saying the propeller, in order to grab those air molecules, needs to exert a certain amount of Force equal to mvn/s. Let’s put some numbers in there to bring this fantasy to life, shall we? Let’s use those heavy air molecules you mentioned that weigh 1 kg each and let’s start out at wind velocity of 10 m/s and we need to throw 10 of those molecules back every second, so n = 10. Fair enough? That will be (1kg) (10m/s) (10 molecules/s) = 100 Newtons of Force.
Ok.
This is the amount of Force the propeller needs to provide to throw those heavy air molecules around.
No, the propeller doesn't "need an amount of force". Its interaction with the air *results* in an interaction force, which is this 100 Newtons. The propeller exerts 100 N on the air, and hence the air exerts, by reaction, 100 N on the propeller.
Now, you speak of “deciding” to use just half of the force that the propeller needs to provide?
No, Atom Man wonders whether he can have an ENERGY balance if he doesn't have larger drag generated than half of this force by the generator. So he DECIDES to build a generator that will have half of this force as a drag, and is then going to find out how much energy he can get from that generator.
Why don’t we just calculate the energy and power we need to provide to the propeller?
But that is exactly what he's doing! He's just trying to find out what is the CONDITION for the drag needed not to exceed half of the propulsion force of the propeller.
KE = 1/2 mv^2 so at 10m/s the KE is 50 Joules. The power = Energy/time or Energy x n = 50 J x 10 = 500 Watts. So our generator needs to be able to provide 500 Watts to the propeller.
Exactly.
Now, would you care to continue this story? Where do you propose to find this 500 Watts? Do you propose to use just half of the Force needed at the propeller to run the generator?
Well, that's simple. The car is running at 25 m/s (say that is wind speed, and the car is runing at windspeed). The wheel is hence turning at a rotation rate which is such that at its rim, the velocity is 25 m/s. (let's not go deep down the trench here, please) Now, if you put a generator on the axle of the wheel which
delivers 500 W, then that will generate a DRAG equal to 500 W / 25m/s = 20 N.
So powering a generator with the wheel gives you a drag force of 20 N, far below the limit of 50 N we set ourselves.
So we cause a drag force of 20 N by the wheels, while the propeller pulls forward with 100 N. Net force on the car: 80 N forward.
EDIT: I just realize that you gave a windspeed of 10 m/s while I took arbitrarily 25 m/s. No problem, the 10 m/s is handled next...
Do you believe that a motor which requires 500 Watts of power input to produce 100 Newtons of Force can be tapped into to use 50 Newtons of that Force to run a genset which then in turn produces the needed 500 Watts?
Yes, of course. What do you think is the drag caused by a generator delivering 500 W on an axle of a wheel that runs at 25 m/s ?
Imagine that this is not a FDDW car, but rather a normal sailing car (to remove temporarily any mental block), and that the user has installed a generator on the axle of the wheels to power the headlights and make the stereo play. What do you think is the drag force that such a generator will generate if it delivers 500 W and if the car is going at 25 m/s ?
EDIT: Or still another way of seeing this: imagine that you are an engineer and that you have to design a BRAKE for a car that will run at 25 m/s and that will need a braking force of 20 N. How much power are you going to dissipate in the brake and how much cooling do you have to foresee ? Answer:
to have a braking force of 20 N (drag) on a wheel that runs at 25 m/s, no matter what I do, I will have to dissipate 20 N x 25 m/s = 500 W of heat.
Say that you are an engineer working in the aeronautical industry, and that you have to design the brakes for an airplane that will touch down at 25 m/s and that you need a braking force of 100 N. What cooling do you need ? If you think that only 500 W will be dissipated, and you design the cooling of the brakes that way, *your brakes will melt* and you will have committed a professional error. 100 N at 25 m/s will dissipate 2500 W ! So this is important to understand for an engineer.
Now, to come back to Atom Mans' case, as we are throwing the balls at 10 m/s, and the condition he found was that we should throw them SLOWER than the wind speed (at ground level) for his condition of half drag force, then this means that we should just arrive at 50 N drag when the cart (and the wind) is actually doing 10 m/s. Let us check.
We still need 500 W, but this time the wheels are only running at 10 m/s. The drag that a 500 W generator will cause this time is 500 W / 10m/s = 50 N. Indeed.
When we throw the balls at exactly wind speed (on the ground) when the cart is running at wind speed, the drag force is half of the propeller force.But, but but, you say, there MUST be something wrong, I don't know what, but the result CAN'T be that I have a thing that *generates* me 100 N, and that only *drags* 50 N, because such a thing would speed up all by itself, right ? It is a PMM, right ? I don't know where, but you MUST be playing a trick on me somewhere ?
Let us have Silly Man, who has heard over the whole thing, and thinks he's now going to become rich with a PMM based upon Atom Mans invention. He puts a similar cart on a large track on a windless day, and tries to speed up "for nothing". Just to get going, he asks his assistant to speed him up to 20 m/s. He will throw the molecule-balls also at 10 m/s. "It's even easier" he thinks, now that this is a windless day, the molecules come in at 20 m/s!
So he STOPS the molecules, and throws them back at 10 m/s. He needs 500 W for the throwing, and he will have a drag on the wheels of 500W / 20m/s = 25 N, but he will have a forward force from his throwing of 100 N, so he will "speed up" for nothing, right ?
Not right. This time he STOPS the molecules which CAME IN at 20 m/s. So he has to stop 10 molecules of 1 kg per second, and he will have to exercise hence a force of 200 N on them to stop them. By reaction, this will cause a backward force of 200 N on him, and hence he has: 100 N forward (throwing), 200 N backward (stopping), 25 N backward (drag) = 125 N backward! His car quickly stops.
Mm, he says, that's normal. The balls come in faster than I can throw them, so in fact I slow them down. That's not a good idea. So this time he asks his assistent to have the car only sped up at 5 m/s. Then the balls come in at 5 m/s and he will accelerate them to 10 m/s. Let's see what this does. At 5 m/s, to generate 500 W, you need a drag of 500 W / 5 m/s = 100 N.
The balls come in at 5 m/s and he STOPS them. So this will result in a backward force of 50 N. He has hence: 100 N forward, 50 N backward, 100 N drag backward = 50 N backward. Again, his car stops. Because the car is too slow of course, he says.
At 8 m/s, we have: drag: 500 W / 8m/s = 62.5 N ; stopping: 80 N, so we have:
100 N forward (throwing), 80 N backward (stopping), 62.5 N drag = 42.5 N backward, stops again!
And for years, Silly Man tries to find the right combination of throwing speed, car speed, etc... and ends up ruined and locked up in an asylum.
The trick was that because of the wind, the molecule balls came in GENTLER (in our case, were even at rest) in the car than that they could be thrown out, while nevertheless throwing them out at a velocity lower than ground speed. That is due to the fact that there was wind.
If we look at the energy balance in the ground frame: the affected molecules had initially 10 m/s of speed (wind), and by the throwing back, they ended up at rest. So those molecules lost 500 W. That's where, ultimately, the power comes from...
If originally, the molecules don't have any kinetic energy in the ground frame, you won't be able to use it.
Brilliant !
