Seriously, are you serious? This is what your faith in DDWFTTW rests on, and there are people out there who actually believe in this? There are people out there who look at this so-called “math” and don’t fall over themselves laughing?
OK, I’m going to make this short as possible and just use nice round numbers to bring a bit of enlightenment to the masses.
Thrust is 160 Newtons and the cart is supposed to move at 9 m/s, so it requires 1,440 Joules/sec, that is 1,440 Watts of Power.
You started out with 750 Watts at the wheels, only the Good Lord knows where it came, from (ground power) but I know the only place it could have come from is the cart’s very own kinetic energy, assuming it is somehow already moving at 9 m/s without explanation of how it got there. So, at 295 kg it would have 12 kilo joules of ke, right? Now you steal maybe 850 of that to get your 750 watts at the wheels ( nothing is 100% efficient, you know) Scorecard reads, minus 100, gone to heat and unrecoverable. (bye bye). Next, you send that up the long twisted chain held in place with pieces of skateboard, and 600 Watts arrives at the propeller shaft, so you lost another 150 Joules. (not looking good is it?) Now the propeller gets into the act, and with 52% efficiency (your number, not mine) it puts 312 watts of power into working on the air. Ah, lets make that 350 watts just to give this thing a fighting chance. Scorecard reads minus 500 watts. That is minus 500 Joules per second of precious kinetic energy and you know what that means don’t you? The cart is slowing down. What do propose as a solution to this quagmire? In order to push with that thrust of 160 N and move at 9 m/s, the cart needs 1,440 watts of power. After burning off 500 watts, it has 350 watts at the propeller to do some magic on the air. Now think about where we are here: the cart wants 1,440 watts to do what you claim, but it has already lost 500 watts trying. Now it needs 1, 940 watts to do what you claim and it has a grand total of 350 watts to do it with. BLEAK, VERY BLEAK.
What can the cart do to get out of this big hole it has dug for itself? It can slow down some of that wind that is out there somewhere, but going slower than the cart. OK let it do that! 160 N of thrust and 350 watts, with F = ma, a simple back of the envelope calc says it slows down at most 72 kg of air by 2.2 m/s (72 x 2.2 ~ 160, close enough for this nonsense). That wind will lose some energy during the slow down of 2.2 m/s, with respect to the ground it loses about 1000 joules per second, that is 1000 watts absolute Maximum. IF that ALL went to the cart, the cart would have 1,350 watts when it needs 1,940 watts. But as we all know, no process is 100% efficient and there is no way all of that wind energy goes into the cart but it doesn’t matter anyway as the cart is dead meat, slowing down and it will not stop slowing down until it is well below the wind speed.
Still some believers out there?
I agree with one thing you said A total piece of crap