(September 5, 2014 at 5:53 pm)FreeTony Wrote: Honestly, the answer is yes. It is a very straightforward problem. Wheels on airliners are free-spining.




It was even done on Mythbusters

https://www.youtube.com/watch?v=YORCk1BN7QY

The point here being that because the plane's speed is air driven and independent of it's wheels the plane does move forward relative to the cones and more importantly the air. So it takes off.

(September 6, 2014 at 5:58 pm)FreeTony Wrote: [
If however the treadmill starts at a backwards speed of Vrotate (the speed the a/c lifts off) and maintains this, the aircraft will probably take off fine as long as the tyres can handle it. In this case the maximum tyre speed is 2*Vrotate.

When considering whether an aircraft's tires can handle the stress of rolling at twice the normal rate of rotation at take off, keep in mind that take off run is not the most stressful part of the an airplane tire's designed duty cycle.

By far the most wearing part of the an airplane tire's duty cycle is at the moment of landing, when a non-rotating tire hits the ground carrying the entire aircraft's downward momentum upon it, and has to be spun up to its rolling speed in a short distance by the drag of the runway contact. This is when you typically see a big puff of smoke coming off of the tires of a 747.

As a result, The lifespan of an large airplane's tires are not rated in terms of how many miles it had rolled on the ground, or how many take off runs the tires had made. Instead it is rated based on how many full load landings the tire can sustain. During early jet age, a main landing gear tires have life span as short as 12-15 landings. Then the tire would be worn out and has to be replaced. Modern civil airliner tire lives are much longer, but the limiting factors remains how many landings, not how many takeoffs.

It could well be that the stress on the tire of rolling at twice its normal designed rate is nothing compare to the stress of the initial ground contact when the plane makes a hard landing. In that case, running the plane on a treadmill during takeoff would be nothing to the tires.

For me, there are two incompatible notions here.

1. the thrust from the jets act on the air, they don't care whether there are wheels, ice, or even if the plane is superglued to the floor!
2. The conveyor does not drive the plane backwards and is designed in the question to represent what would happen if you were to walk or cycle at speed x, the treadmill would match that and you would stay stationary.

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.

However, the engines are still thrusting us forward, so the plane would again move forward, but this time from 0.00001 km/h to 0.00002 km/h, and the treadmill will instantly match that, and we'd be stationary.

This then is repeated until the wheels and treadmill reach an infinite speed... so no take off.

This is how I imagined the questioner structured the original question.

(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.

The thing is... as soon as the plane is moving, the wheels are spinning... the treadmill only makes the wheels move faster, but the plane keeps going forward.

Yep the wheels have almost nothing to do with the plane's movement. They aren't connected to the engine.

Hence why the two notions can't exist together. So the point of the question is to fid out why they can't coexist in the same conundrum.

(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.

Are we over analyising the question?

Tyre performance is irrelavent. and we all agree that the engines will push the plane through the air...

What does the question want to get at? I suspect that the treadmill will pre-empt the movement and counter it in an instant.

(September 7, 2014 at 5:46 pm)lifesagift Wrote: Are we over analyising the question?

Never. It is a serious question that requires some serious discussion, especially by those of us who are not rocket scienfical aeronautical engineers.

(September 7, 2014 at 6:00 pm)naimless Wrote:

(September 7, 2014 at 5:46 pm)lifesagift Wrote: Are we over analyising the question?

Never. It is a serious question that requires some serious discussion, especially by those of us who are not rocket scienfical aeronautical engineers.

Of course, but what i'm saying is are we missing the point?
We could ask all sorts of questions like "how fast could I swim to the moon", but it doesn't make it valid just because you asked it.

Often with a conundrum you have to reassess how you approach an answer..

That's all!