RE: 747 on a treadmill conundrum..
September 7, 2014 at 5:32 pm
(This post was last modified: September 7, 2014 at 5:33 pm by FreeTony.)
(September 7, 2014 at 4:50 pm)lifesagift Wrote: With problems like this, it's best to examine the extremes, so the moment the jet engines kicked in... from zero km/h to 0.00001 km/h the treadmill would turn and (if in the ideal scenario, could instantly match the planes speed) the plane would be stationary.
No, it wouldn't be stationary, it would still be moving forwards, but with very slightly more drag.
As I was saying before, the plan takes off depending on the programming of the treadmill. It still takes off if the treadmill matches the groundspeed, as long as the tyres survive
However the orginal statement was that the treamill matches the wheel speed.
Mathematically Vw = Vt (Wheel speed = Treamill speed)
However, Vw = Vt + Vp (Vp is plane speed over ground) if there is no tyre slippage.
There are solutions to these equations if:
Vp = 0
or
Vw and Vt are infinite and Vp takes any finite number.
This is why I was talking about an infinite treadmill speed. Whenever we get infinite solutions, there is a problem. In this case it is because the original question doesn't make sense.
It is much better if it is phrased "The treadmill speed matches the groundspeed of the aircraft". In this case the plane will most likely take off.
