I would say that the plane wouldn’t be able to take off because the speed of the plane relative to the air would be 0. To be able to take off, the plane needs to be able to generate lift from the movement of air over the wing. Therefore the plane wouldnt be able to take off.

Maybe I’m missing something though :)

ps great blog – have been reading for a while now

Here’s an indirect hint to help think things through. If you stuck wings on a car, put in a 1000hp engine and removed its spoiler and gunned it down a non-moving runway – it still wouldn’t fly. It might lift off momentarily, but it can’t fly. Why? What’s different between this car and a plane? How does this difference factor in to the problem scenario?

Am I being pendantic? The riddle says the plane is “moving in one direction” which means it’s moving on an axis, not just sitting still with the wheels spinning. Doesn’t that already undo the riddle? Maybe I am being too pedantic. =/

Anyway I think it would fly. Even if the plane’s speed relative to the air was ‘0’ – the fact is that it has jet engines (or whatever) which would be pushing the air through at a high speed anyway, and isn’t that where the lift comes from? In fact this could be a brilliant idea for miniature airports!

To put it clearer: The point of the runway is to get the engines up to speed, not the plane itself. Am I right?

No. Though the plane’s engines could be spun up to full speed, there would be no motion of air over/around the wings. By creating a lower pressure above the wings and a higher pressure above them, a plane is able to take off. However, because the plane is stationary on its x-axis (assuming this is two-dimensional, which is all it needs: KISS), there will be no airflow other than normal under/over the wings. A plane takes off because the speed it gathers allows the wings to generate a significant pressure difference above/below the wing; this does not work if the airflow is normal (there is not enough of a pressure difference between the top/bottom of a wing). Of course, I am completely unaware as to how much air a jet engine can move, so I am excepting that from my logic. Considering most are turbofans, however, I am fairly sure they cannot operate at full efficiency/power under sea-level atmospheric conditions; their air displacement rates at sea-level may not be enough to move without having to taxi.

Pick my logic apart, please. I’m curious as to how I am wrong if I am.

That is absolutely right, you need airflow via forward movement over wings to give a plane lift (upwards force) so thrust (forwards force) from the engine just by itself does not give a plane lift… if the plane is stationary but the engines are full throttle, no lift is produced and the plane will not fly.

So, if I reckon the plane will still be able to take off, what (erroneous) assumption have you made about this scenario?

Ok I know where this is going now :)

So what you are saying is that when the engines are working the plane will move forward with respect to the ground and will therefore take off. This is because even if the conveyor belt speeds up to compensate then all it will do is turn the wheels faster. ie the force being applied to the plane by the engines CANNOT be counteracted by the conveyor belt. Is this correct?

Fascinating.

You got it! :)

As long as the plane appears stationary relative to the air around it, it will not fly. Flight in a plane is generated by air rushing over its wings. The nature of the wing, with its curved superior surface allows the air to flow at a faster rate over the top of the wing than under.

This creates a lower pressure above the wing (Bernoulli Effect) giving it lift. That is why a kite will fly on a windy day without any self propulsion. A car with wings if travelling fast enough will take off, however once its wheels leave the ground, its speed will drop and it will come down again. The jet engines or propellers are just to generate continuing forward thrust and therefore motion relative to the air. Please note that a jet engine that generated some vertical thrust will fly without wings (Newton’s Third Law) or able to take off vertically (Harrier Jump Jets) However here we are talking about horizontal thrust.

There isn’t enough information to accuratly answer the question. The total coefiicient of friction of the airplane needs to be known. Since this is a thought experement, if you assume that there is no friction between the wheels and the axels, and no friction between the tires and teh conveyor belt runway, then the conveyor belt wouldn’t be able to exert a force on the plane, therefore, the plane would gain speed as it throttled up, and would take off. If, however, the friction is high, the plane wouldn’t be able to gain enough speed to take off.