Physics challenge!

You have shown nothing. The fact that your model gives 253kg vs 252 max takeoff weight suggests you have 1kg extra for acceleration, otherwise known as this thing accelerates at 1/253 m/s^2 during takeoff. Then if your efficiency is below 99.5% or so, then you have absolutely no lift at all and it wouldn't leave the ground.

What's more realistic, 400kg of thrust, at 80% efficiency leaving you with 320kg effective thrust on a 250kg platform, giving ~70kg worth to accelerate you at approx 0.3 m/s^2. Or 253kg of thrust at 100% efficiency giving you 1kg effective thrust accelerating you at approx 0.003m/s^2?

Essentially, you have worked out a simple model, the model underestimates the thrust by a factor of (4)^(1/3) compared to the more accurate simple model. It just so happens that when you factor in how efficient the real system is and various other real world quantities, that your method *looks* more accurate for /some/ thrust values. Once you begin to factor in these relevant real world factors, the model on wikipedia is more accurate, and yours underestimates the thrust.

It's a hoverboard my man, it's not designed to accelerate fast because that will throw the guy off. As I said you have no proof that the thing flies at 16 mph at max takeoff weight. You have also failed to explain the result for the commercial ducted fan. That 2850g wasn't listed as max takeoff weight but merely the thrust. And I already told you that contra-rotating props are 10-15% more efficient than normal props so we are actually looking at 90-95%. Even a normal ducted fan can easily push out over 90% efficiency because this isn't 1907 anymore. 82% efficiency is what the Wright brothers got with their propeller.

There are 16 aliens on a house. The house is orange and weighs 10000kg. The aliens' height range is 120cm - 190cm as a Gaussian distribution.

Using the above numbers and physics, calculate how many strands of hair the aliens have on their head.

P.S. If you can't do this simple calculation you have no chance of getting into Oxbridge.

There is a difference between accelerating fast and not accelerating at all. 0.3 m/s^2 is not a quick acceleration. It does not need to fly at 16 mph on takeoff. It merely needs to be able to get to that speed at some point. With your thrust, that would take something like 10 minutes of acceleration to reach that speed, which is plainly ridiculous. And that is still assuming 100% efficiency which is clearly not going to be the case.

As for the ducted fans, 1 out of 3 of those appeared accurate, the others did not. As with before, that's not taking into account efficiency in your calculations. You'd expect a simple method to over-state measured thrust because it doesn't take into account any loses of power.

As for 82% efficiency for the Wright brothers: "... The finished product produced a maximum efficiency of 66%... " - source.

Technically it would have a mass of 10000kg (a weight of ~98.1 kN), weight is measured in Newtons and is the force caused by gravity acting on mass. :P

If you didn't spot that you have no chance of getting into Oxbridge.