Plane on conveyor... Will it ever take off?

It's a problem that demonstrates critical thinking (or a lack thereof). There is a superfluous item, the belt, that has no real impact on the outcome, but is put in there to cloud the problem. The critical thinking part is cutting through the non-relevant junk (the belt) to get at the basic problem. At this point the problem is trivial and either people argue from a skewed perspective (see ATL5p's 4000 or so posts) to hide the fact that they originally got tied up in the junk and will _never_ admit their wrong (again see ATL5p), they argue for a few posts and realize their error and correct themselves or they are just ignorant of the physics involved and argue for the sake of arguing.

FGG

Back to the original problem.

Some airplanes will be able to take off, others will not.

It is easy to tell which can. If the pilot locks the brakes and with the full power setting can skid the tires, the aircraft will be able to take off. Otherwise, it will not have enough power, and the conveyer wins.

It all boils down to physics, and in particular the study of dynamics which is the mathematical analysis of the motion of bodies.

Most posters understand that the prop gives thrust, or a force in one direction. What they tend to discount is the force in the other direction provided by the wheels on the conveyer. This force is proportional to the normal force (the vertical force on the tires as provided by the mass of the aircraft) times the cofficent of friction between the tires and the conveyer belt.

Where most people assume that the only force that the wheels provide is the minor drag from the bearings, they miss the fact that the tires and wheels are in reality are flywheels, where the amount of energy to increase their speed at any point in time depends on the friction. It is this storage of energy that provides the constant force that opposes the thrust from the prop, holding the airplane in place.

However if the prop thrust can overcome this dynamic friction, then the aircraft will start to accelerate forward, and eventually takeoff. With the tires sliding the entire time. Of couse, the cofficient of friction for sliding tires is about half of ones that are not sliding, and the plane will rapidly gain speed, or more precisely airspeed and take off. Albeit, much slower than one not on a conveyer.

Really rather simple problem once you strip away the bs.

So why didn't you?

It's a simple problem, some people think the planes wheels operate the same way as a car.
They don't.
Therefore the plane moves forward. nice simple problem.

Nice and simple problem so far.
But some people can not give up their first assumption that the plane does not move forward and change the problem into meaning the plane stands still.
Looking for ways to keep the plane from moving forward complicates the problem.
As you have.

The original problem even says the plane moves forward.

The only planes that will not be able to take off would be those that already have difficulty taking off on a normal runway - those that are underpowered, significantly overweight, poorly maintained, etc.

No. Planes that cannot cause their tires to skid will still be able to take off pretty easily.

Yes, but I'm suspicious that you haven't done the math correctly.

No. The wheels are attached to the airplane by a low-friction bearing. Thus the coefficient of friction you need to take into account is NOT the friction of the tires on the runway, it is the friction in the bearing itself. There is rolling resistance that must be overcome, true, but most planes can overcome this initial rolling resistance at about 15%-25% throttle setting, and require only about 5%-10% throttle to maintain speed.

So wrong it's sad. The wheels would have to be immense and very dense to have enough rotational inertia to counteract the thrust - or the treadmill would have to accelerate extremely quickly (i.e. >150 km/s/s), which is a physical impossibility.

Even then, consider this: The myth requires that the belt match the speed of the plane. The only way for the wheels to spin is for the plane to move relative to the surface the wheels are in contact with, or for the surface to move relative to the plane. If the plane is stationary relative to the air, then the only way for the wheels to rotate is for the surface to move relative to the plane - in other words, for the belt to cause the "speed" of the plane, rather than MATCHING the speed of the plane.

Still Wrong. The plane will simply accelerate approximately normally, with the wheels rotating twice as fast, and will take off easily.

If you doubt it, watch the Mythbusters episode where they DID IT with a real plane on a real conveyor belt.

It is, but you're insisting on overcomplicating it.

Oh, come on.

This is dead topic. the real question is this: Would a charged plane with half-integer spin ever take off from a treadmill made of absurdium?

We don't need to consider the magnetic moment for this example.