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.

I would like to first state that I am an Aerospace Engineer. I normally wouldn't say this, just let my answer speak for itself, but unfortunately there are one or two on the internet who are persuaded by arguments from 'authority'.
Secondly, I ask you this. If you put a free wheeling bicycle on a moving conveyor, like the ones at airports, funnily enough, and hold onto the sides (which don't move), do you go forward, backwards or stay stationary?
You can actually try this yourself with one of those rolling luggage trolleys. When there is no-one else around to be annoyed by your antics, hold the luggage trolley on the conveyor, while you stand off the conveyor (at an end, say). You can quite happily hold that trolley there, can't you? That bicycle doesn't move, does it? Because you are keeping it stationary by an input independent of the conveyor.

The point of this topic's question is this - a though experiment. A thought experiment does not look at the material properties of the bearings in a plane's wheels. A thought experiment does not worry unduly about the rolling resistance of the plane. Of course, you can worry about such things, but you would be missing the point. The idea is that we are referring to a plane here. The 'trick question' is that many might think that a plane is like a car, providing driving force through its wheels. As mentioned in far more detail above, a plane's thrust comes from its engines. The engines act on the air, not the conveyor. Hence, the plane accelerates.

It may take off in slightly less field length than normal due to the boundary layer effect, where air infinitely close to the conveyor travels at the same speed as the conveyor, and further away travels more slowly due to friction with the 'stationary' next layer up. Again, a very small effect, which engineers like to call negligible.

I really appreciate the efforts of those who allow us to see things in a new light, the 'force balance' was lovely, but entirely impractical - the conveyor we are talking about would find it impossible to impart its entire force through the wheels - you would probably find that the materials from the conveyor destroyed themselves before the materials from the plane's ball bearings! If you assume it doesn't, it is incorrect (not unfair, not whimsical, but incorrect) to assume that the wheel's bearings DO have friction.

The problem with reading too far into a problem is that you can lose sight of its purpose - to make you understand that a plane is powered by engines that work on the air, not through the wheels. The problem is pitched at around the level of a 12 year old kid. They aren't interesting in seized ball bearings. They want to learn about aeroplanes!

What exactly was your point?

You didn't ask a single question that you did not answer yourself.

We have liftoff, guaranteed.

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AIRCRAFT WHEELS DO NOT PROPEL AIRCRAFT! There is no linkage. The wheels turn freely with comparatively negligable friction, compared to all the other forces considered. The friction is not non-existent, but it is COMPARATIVELY non-existent. No conveyor belt will stop an aircraft by attempting to match the forward speed of it.
The Boeing 777, for instance, puts out 127,900 lbs of thrust per engine. Times 2 engines, that is more than stage 3 of the Saturn V rocket that carried the Apollo moon mission. Unless you cheat and use your conveyor belt to crash the aircraft before the engines start turning, that aircraft WILL take off. You can spin that belt 10x the forward speed and that wont make a bit of difference against a quarter million pounds of thrust. The wheels will have hot bearings, but it will fly. Hell, you can strap those engines to an office building and it will fly... for a bit, anyway.
Now imagine yourself on rollerskates, on a moving treadmill, holding on to a rope anchored to an engine. So long as you can keep your balance, it doesn't matter how fast that treadmill goes. Your wheels will freewheel and you'll be fine. Now put a prop on that engine, and give it 500 lbs of thrust. Are you telling me that that engine will not pull you forward even with the belt rubbing on your wheels? If you had a Hemi driving that belt, you would still fly.
Now picture an aircraft on skis instead of wheels, and imagine that aircraft on ice. It's the same thing. Wheels, skis, pontoons, skids, they are all just means of keeping the ground from ripping the bottom of the aircraft open on the runway. That's it. That's what they do.

If you can have your method of thrust pull you vertical at 10g's, or pull you through the air at any speed for that matter (and the air puts up a lot more resistance than a set of wheels spinning on low-friction bearings, so does gravity) then you will fly. You will taxi forward and you will have takeoff. You'd better have a straight taxi line and a great pilot, but those engines pull you through the air with such a thrust/weight ratio that no treadmill will stop you.

For gods sake bury this thread.

I had hopes...

It hurts my head how many people think planes lift off because of their wheels moving REALLY fast.

I don't care how many jet engines you put on the plane either, if there is no wind speed the plane is not flying.

Also, unless we're talking about a harrier jet...jet engines on planes are horizontal not vertical. They make the plane move faster so there would be more air pressure so there's more lift.

but if the plane is on a treadmill that keeps it from going anywhere...then no. Not unless this is some kind of magic treadmill that also funnels a shitload of air past the plane at the same speed the wheels are moving...then it might...until it got out of the bubble then it would crash since the plane would be just hovering and not moving

And some guy said it would lift off but couldn't land because the wheels are moving 2x as fast as normal.

First of all, this wouldn't destroy your tires. And second and much more importantly, your wheels are not moving 2x as fast as normal. The treadmill doesn't make them spin faster.....why would you think that?

I think the point of the exercise was to realize that wind speed is what makes a plane lift off...not wheel speed.

It also never said this plane HAS jet engines but okay. Even if it just had propellers you make a good point. Kind of...

But you make a lot of assumptions. For example, that the plane is more powerful than this imaginary treadmill. Why? Why not assume this treadmill can go as fast as infinity.

Also, even if you had your turbines or jet engines maxed out the plane is not going to lift off until it has enough LIFT. And as long as the plane doesn't have lift it's going to be pushing down against the earth with the force of gravity. That's a lot of weight.

So no matter how fast the jet engines push this plane forward, the wheels will just spin and go no where (since it is on a treadmill and this is theoretical so the treadmill doesn't break).

The jet engines might push the plane forward with a lot of thrust but the plane itself isn't moving anywhere. It's wheels are spinning super fast...but the treadmill keeps pushing backwards and the plane moves NO WHERE.

The plane will not move relative to the surrounding air and thus will not get ANY lift and therefore will not go UP at all. It will just go FORWARD up to its maximum speed (full wheels full engines) but the treadmill is still pulling it backwards.


NO WHERE
NOT EVER
NOT IN THIS THOUGHT EXPERIMENT

Another way you can think about this problem is, can a plane take off if it is on a frictionless surface? Again the answer is no. Jet engines, turbines, and propellers are for horizontal thrust. This is not a helicopter, a harrier jet or a rocket ship. It can propel itself FORWARD very quickly but in this example that gets you NO WHERE.

Therefore, the plane goes NO WHERE.
NOT EVER.

Okay I did read one thing that's worth mentioning.

Someone here, an "aerospace engineer" has stated that the plane will overcome any reverse forces of the wheels due to the treadmill due to its propellers, turbines, jet engines etc and move forward and take off eventually anyway.

That might happen. the wheels merely balance the plane and don't actually make it move any faster.

You'd have to look at the weight of the plane and the coefficient of kinetic friction and see how much thrust (wheels and otherwise) would be required to counter that effect.

Then, with whatever you had left over, determine if its enough to lift off the plane.

Basically, to lift off air speed must be x (so its forward horizontal motion must be at least that fast relative to the surrounding air)

The maximum speed of the treadmill (pulling the plane backwards) is y. After this friction breaks down and the maximum speed of the treadmill actually decreases.

the maximum speed of the plane trying to take off with full engines forward is z

Therefore, if z - y >= x then the plane lifts off.
However, if z - y < x then the plane never gets enough lift to pull it off the ground.


To the people who think this means we can make shorter runways...no. this would mean we'd need LONGER runways. Way longer...if these planes could take off at all.

You'd have to do the math but it's probably quite possible the plane will lift off if the turbines or whatever can still propel it fast enough.

I say we test this IRL. Who has a 747 they can afford to crash?

That is the secondary point.
The main point is that the conveyor does not slow the plane down.
So therefore it has the proper wind speed for takeoff.

You say "powerful" then say "fast". Two different things. It doesn't matter how fast the conveyor goes. It can't transmit that power to the plane.

This post has been edited by buttershug on Jan 15 2010, 04:43 PM

Relatively very little.
Think of an ant vs an elephant in a tug of war.

Would you bet on the ant? That's what you are doing with this puzzle.

The real question of the puzzle is does the conveyor stop the plane like it would a car or not?
The answer is not. But somepeople just can't stop thinking the plane does not move forward. The question even says it does. There is nothing in the question that can stop it.