Thread: Answer to the aeroplane problem on Facebook

Let me clarify something first – there are two popular quizzes circulating over the internet. And there are two different answers for them.

The first goes like this “Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?”
Answer: preassumptions cause this situation to be physically impossible.

The second – as shown in Mythbusters – is a little different: “An airplane cannot take off from a runway which is moving backward (like a treadmill) at a speed equal to its normal ground speed during takeoff“.
Answer: the plane will takeoff

Note the difference. It is important.

Originally Posted by Tombie

Let me clarify something first – there are two popular quizzes circulating over the internet. And there are two different answers for them.

The first goes like this “Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?”
Answer: preassumptions cause this situation to be physically impossible.

The second – as shown in Mythbusters – is a little different: “An airplane cannot take off from a runway which is moving backward (like a treadmill) at a speed equal to its normal ground speed during takeoff“.
Answer: the plane will takeoff

Note the difference. It is important.

Plane will still take off, what the wheels are doing is completely irrelevant. only thing with the first one is the wheel bearings may cook before liftoff.

If the opposing speeds of the conveyor belt and the wheels are the same, isn't the plane stationary?

Originally Posted by Homestar

Plane will still take off, what the wheels are doing is completely irrelevant. only thing with the first one is the wheel bearings may cook before liftoff.

Sorry Gav, but it won’t...

Preassumptions prevent that from happening.

It can NOT take off *whilst meeting* the preassumption criteria.

So the answer is No, it will not fly.

...And if it could do this, the belt reaching infinite speed would see the aircraft collapse to the ground long before it could generate airspeed...

(The important part is to understand that you must meet ALL criteria, not a logical outcome)

Originally Posted by DiscoMick

If the opposing speeds of the conveyor belt and the wheels are the same, isn't the plane stationary?

The way Gav is looking at it is thus...

Plane moves via engine thrust
Wheels are just rollers keeping it off the ground until it hops into the air
Thrust moves air, so wheel speed is irrelevant.

The catch in the question is:
The wheel speed and conveyor speed will always match.

Originally Posted by Tombie

The way Gav is looking at it is thus...

Plane moves via engine thrust
Wheels are just rollers keeping it off the ground until it hops into the air
Thrust moves air, so wheel speed is irrelevant.

The catch in the question is:
The wheel speed and conveyor speed will always match.

If the engines are roaring, but the opposing speeds of the wheels and the conveyor belt are the same, isn't the plane just sitting stationary with the engines roaring? If the plane is not moving there is no uplift on the wings so the plane can't take off. It will just sit there roaring its' engines, like a vehicle left in neutral transmission, until it runs out of fuel.
Isn't that right?

Wheels on a plane are only holding it up of the ground and giving it something to land with after flight. What ever speed the wheels are doing is absolutely irrelevant.

Originally Posted by 67hardtop

Wheels on a plane are only holding it up of the ground and giving it something to land with after flight. What ever speed the wheels are doing is absolutely irrelevant.

Read the question and the Preassumptions...
It’s NOT irrelevant when phrased as such.

Explanation:
The conveyor belt is designed to exactly match the speed of the wheels
This is the problem! The wording of this quiz is wrong and makes it physically impossible.

Divide this situation to several steps. At first, everything is just the same as in my explanation above. We apply thrust and we run the conveyor belt in the opposite direction. The wheel starts turning. As the plane moves forward – the conveyor belt accelerates. Keep in mind the preassumption “conveyor belt is designed to exactly match the speed of the wheels”.

When the aircraft moves forward then its wheels have to travel further than the conveyor belt has moved back. But this is impossible in this situation. The conveyor belt is designed to match the speed of the wheel – so it will increase the speed. But the plane still moves forward – there is again a difference between the speed of the wheel and the speed of the conveyor belt. But we do not allow such situation! So we increase the speed of the conveyor belt!

Actually, this is not a process that happens in steps – all of this happens simultaneously – the plane tries to accelerate and the conveyor accelerates to keep up with the wheels. Adding to the speed of wheels. And the wheels accelerate even more. So the conveyor belt…

It lasts until wheels and conveyor belt speed reaches infinity. Or until they reach the speed of light. If you wish to know what happens then – consult the screenwriters of Start Trek or Star Wars.

The wording of this quiz is wrong! This case is impossible. It is impossible right from the very beginning where the preassumption is that the speeds will always match. If we know (and we know!) the forces applied on the plane we know that during the takeoff there is a huge imbalance of forces. So quoting the Newtonian law:
*An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.*

The object will not stay motionless because we have unbalanced forces. So we can not design the conveyor belt to move at the same speed as wheels.

THEREFORE: Question is invalid..