>>11448905The mythbusters test did not replicate all the conditions of the thought experiment. Most egregious was the use of a prop plane, which generates left even when not moving forwards from the backdraft of the props going over the wings. A jet plane generates lift only by forward movement. If the treadmill matches the wheelspeed this forward movement will remain at zero. However none of this works in reality outside of the troll physics of the thought experiment as I will attempt to outline...
>>11449174Bingo and you have just solved why the experiment makes no sense in reality. The plane would have to be glued to the runway somehow otherwise it would just end up skipping over the runway, not making contact properly which would allow it to gain forward speed. If this speed reached what is required for take off, so it will, otherwise not.
Let's just take the wings out of the equation for a second. Instead of a plane, we have a toy car and a personal treadmill. There are sensors in the car wheels so that the treadmill can match the speed. Now, if you attempt to push the car forwards whilst pressing down very hard, you will likely not be able to move the car forwards. The friction and backwards movement of the treadmill will create an equal pushback stopping you from going forwards. If, however, you exert all your force on moving the car forwards and going in a straight line, you will probably be able to achieve forwards movement as the car will skip along the treadmill, not constantly making contact with it. That is because the treadmill is not stuck to the car in any way.
tl:dr the probably won't be able to get to take-off velocity despite being able to move forwards. The wheels would essentially be skimming the material of the treadmill in order to be able to move and to get to takeoff velocity would require insane amounts of power and the wheels would likely disintegrate before it could happen anyway.