The major problem in trying to debunk the "plane on a conveyor belt" dilemma

The "plane on a conveyor belt" dilemma (or various variants of such a name) is the question of whether a plane can take off from a conveyor belt that's running backwards matching the speed of the plane.

Quite famously the TV show Mythbusters tried to demonstrate that of course it can, there's no doubt about it. Later also Adam Savage made a YouTube video further explaining the myth and why the idea that the plane couldn't take off just doesn't work.

One of the major problems with the proposition, and the attempt at debunking it, however, is that the problem is quite often presented in an ambiguous manner, using ambiguous wording.

The ambiguous wording is that the conveyor belt "matches the speed" of the airplane. The problem with this is that the idea is very easily misunderstood.

And that's exactly what happened with the Mythbusters episode. They interpreted it to mean that if the plane, for example, sets its throttle so that the plane ought to go at, let's say 50 mph, then the conveyor belt should go backwards at 50 mph.

But that's not the idea in the dilemma. The conveyor belt is not supposed to look at what the throttle of the plane is set at, and use the same speed.

When people say that the conveyor belt should "match the speed" of the airplane, what they really mean is that the conveyor belt should always move as fast as to counteract any movement by the airplane. In other words, if the plane starts moving forward, the conveyor belt should quickly accelerate up until the plane stops. It doesn't matter if the conveyor belt needs to go at 10 thousand mph to stop the plane, that's the very idea.

In other words, the idea in the dilemma, which is usually very poorly expressed, is that if the conveyor belt always accelerates as much as necessary to keep the plane in immobile, can it take off? It doesn't matter if the conveyor belt moves at 100 mph, or a million mph, it always accelerates to a speed that keeps the plane immobile. In other words, it always "matches the speed" of the plane in the sense that it will always go as fast as necessary to keep it still.

Ostensibly this should theoretically make the airplane incapable of taking off because wheels cannot have zero friction, and the conveyor belt will always be able to take advantage of this friction to stop the plane from moving. (In practice the friction could generate so much heat that the wheels would melt and burst, but this is a hypothetical scenario anyway.)

So no, I don't think Mythbusters proved the myth as false. They merely misinterpreted and misunderstood what the myth is about (this no doubt helped by the fact that very few people can actually clearly and unambiguously express the scenario properly.)