A harmless little riddle

the plane will take off only if it is going faster than the treadmill - for example, if the treadmill is going 150 mph, the plane will have to go 150 mph + its takoff velocity.

flying tiger wrote:

thrust from the engines makes a plane move FORWARD Right

air moving over the wings makes it move UPWARD. Right

all the thrust in the world won\'t make it fly if air isn\'t moving over the wings Right

the treadmill moving backwards keeps the plane stationary WRONG

The question does not state that the conveyor\'s movement keeps the airplane over the starting position relative to the ground, just that it moves in the direction opposite to any movement of the airplane.

The people who think it won\'t take off keep saying that the conveyor would overcome the speed of the airplane and it could never get any airspeed; it would never move relative to the ground.

But airplanes do not apply their thrust via their wheels, so the conveyor belt is irrelevant to whether the airplane will takeoff. As I said before, as long as the treadmill is the length of a runway, the plane gains speed relative to the ground, wind speed increases, and the plane takes off.

That being said, the tone everyone is taking on this is pre-adolescent.

I hear what you're saying, but i think we need to work under the assumption the "T-mill" (afraid to spell it wrong) is only large enough to fit the plane.

Someone earlier asked if the a plane was sitting on a runway and there was a 150MPH blowing against it would it take off?????

Answer: yep!

EVERYBODY is missing one thing. That is that the way the riddle is phrased is ambiguous, leading to two possible interpretations. Either the treadmill matches the speed of the plane relative to the ground, or the treadmill matches the speed of the plane relative to it.

As someone has already explained, if the treadmill matched the speed of the plane relative to the ground then the treadmills speed would be exactly half of the speed of the plane relative to it, for any given speed. For example, if the plane started to accelerate from a stop to 1mph the treadmill would move the other way at .5 mph. In this way the plane has a ground speed of .5mph (but moving over the treadmill at 1mph) and the treadmill has a speed of .5 mph. So you would be making forward progress. Friction or no friction the plane can theoretically take off. Friction only comes into it when arguing how much more force it would require to take off versus a normal runway. This satisfies the condition of the riddle under one interpretation.

Under the 2nd interpretation it gets a little more tricky. Under the 2nd interpretation the treadmill matches whatever speed the plane moves over the treadmill, not the ground. This is impossible however. Let me explain. Let's say the treadmill was a frictionless surface. That means that no matter what the speed of the treadmill it will not affect the plane one bit. The plane starts off motionless, not moving over the treadmill at all. So everything is still. Now the plane starts to accelerate to 1mph relative to the ground and the treadmill. What happens to the treadmill? If you say the treadmill moves at 1mph the other way you are wrong. At first the treadmill will move 1mph in the other direction, but if the plane is still moving at a ground speed of 1mph, and the treadmill underneath it is moving 1mph the other way, the speed differential between the plane and treadmill is going to now be 2mph. So the treadmill increases to 2mph. But the plane is still going 1mph to the ground, so with a plane speed of 1mph and a treadmill speed of 2mph the differential is 3mph, so the treadmill increases to 3mph. If this was how the treadmill operated then it would instantly reach an infinite speed even if the plane remained at a constant ground speed of 1mph. That is impossible. Infinity is a concept not a quantity.

Now lets say that the treadmill did have some friction with the wheels. What would then happen is that after the plane accelerated to 1mph the treadmill would accelerate to 1mph the other way, however this would have an effect on the planes speed. the plane would slow to .95 mph (hypothetically) because of the increased friction, so the speed differential would be the planes ground speed of .95 mph plus the treadmill speed of 1mph for a speed differential of 1.95 mph. that would become the treadmills new speed and the plane would slow down to say .91 mph. This would go on and on (instantaneously however) such that for any positive ground speed of the plane the treadmill would always increase its speed until the ground speed of the plane was 0mph. Under this interpretation the treadmill would prevent the plane from even moving. But this intrepretation wouldn't be possible to replicate in reality so it is obvious that the first interpretation is the intended one.

The plane will take off.

Did anyone bother reading this which was posted on this thread on page 3. Perhaps it is because it takes more than 5 minutes to read that most of you haven't even bothererd reading it. Read it and then make new commentary...please.

http://www.avweb.com/news/columns/191034-1.html

It's funny that this site says all the technical people think it WILL fly (and they are correct according to this site) and all the non-technical people say it won't.

Completely opposite from this site. Runners...we know how to turn the world upside down.

the people who are saying it WONT fly while saying it is being driven be its prop are still thinking in terms of a car or runner. They almost have it and thats why it is so confusing to them. Once you understand the treadmill/convor are totally irrevelent to the question and think of it that way you will understandit WILL take off. It would take off if the conveor was going 2, 3, 4, 5, 6 times as fast in the opposite direction because the wheels would simply be moving backwards but the plane would still move forward. I'm glad to finally see some other people are realizing that it will. I will admit at first the question was messing with me and I origianlly thought to myself that it wouldnt but I kept my mouth shut and thought about it for a few minutes and even drew it out on a piece of paper and understood.

Costanza wrote:

I hear what you're saying, but i think we need to work under the assumption the "T-mill" (afraid to spell it wrong) is only large enough to fit the plane.

Someone earlier asked if the a plane was sitting on a runway and there was a 150MPH blowing against it would it take off?????

Answer: yep!

The question said that the treadmill is "enormous"

As you say, the plane in a big wind will take off even though the wheels are not moving at all and the groundspeed is technically 0 (we say "relative to the ground" really as a proxy for the speed of the air over the wings). The ground and the wheels don't matter at all.

If anyone's not read that article, you really should.

For those anti-flight, note that none of the pro-flight folk have argued that the plane will take off by standing still. We argue, rather, that the plane will move forward, as the treadmill is a red herring, with the forward thrust of the plane independent of the freely spinning wheels.

Also, if science isn't enough, Tinman said it will take off, and Tinman's the man.

Let's think about it this way. We're assuming that the tires do not create any friction between the plane and the treadmill. If the engines on the plane are off, no matter what speed the treadmill is spinning at, the tires on the plane will spin, but the plane itself will not move at all relative to the ground.

So say that the treadmill is moving at 150 mph. The tires on the plane will also be spinning at 150 mph. Once the plane starts its engines, air will be pulled through them, causing the plane to move forward, no matter how fast or how slow the engines are going. The tires on the treadmill have no effect on how much air is pulled through the engines, so the engines would function as they normally would on non-treadmill runway.

Now back to the question. The plane and the treadmill are "moving at the same speed", meaning that the engines are running so that on normal ground the plane would be moving at 150 mph, and the treadmill is running at 150 mph in the opposite direction. As I said, as long as the tires are in contact with the treadmill, they will be spinning at 150 mph. But the plane is being pulled through the air at 150 mph, which has nothing to do with how much the treadmill is acting on the tires. So the plane is pulled at 150 mph though the air while the treadmill moves at 150 mph on the tires, not affecting the engines at all. The plane moves forward, eventually gets enough speed and takes off.

Everytime I run on a treadmill I generate copious amounts of wind. Just ask anyone running beside me.

BeNice wrote:

the people who are saying it WONT fly while saying it is being driven be its prop are still thinking in terms of a car or runner.

I agree with you that the wheels act independently of the engines. However, the weight of the plan on those wheels creates traction on the ground. When you start the engines the plane still has a weight on the earth because he hasn't left the ground yet. Again, go to a treadmill, put a skateboard on the treadmill since a skateboard has free rolling wheels like a plane. Turn the treadmill on. Does the skateboard fly off the back or does it stay on the treadmill while the treadmill is moving? It flys off the back, just like a plane would. Just because you turn the engines on doesn't mean the plane gets lifted off the ground. As long as the wheels are on the ground and the weight of the plane rests on the wheels they will move in the direction the treadmill is moving. Once you turn the engines on to match the force that the treadmill is creating then you will have zero movement. Zero movement means their is no wind traveling over/under the plan, which means no lift, which means the plan doesn't fly. The treadmill is important in this situation because gravity is apply force from the plane onto the treadmill. Again, go put a skateboard or a hot wheels car (both have free rolling wheels like a plane) on a treadmill, turn on the treadmill. What happens? Until you do this you won't understand what I'm talking about.

If you have 800 units of force from the treadmill going in the opposite direction of 800 units of force generated by engines on a plane, you wind up with a zero amount of force because they cancel eachother out. Wheny ou have zero amount of force in a direction you get no movement of the plane relative to the ground. No movement of the plane relative to the ground means no wind travels under/over the wings, which means no lift.

If their was no traction (or the amount of traction was so minimal the it is near obsolete) between the wheels and the treadmill (meaning the treadmill couldn't not grip the wheels) then the plane would fly. But on earth we have gravity which pulls the plane down onto the treadmill creating traction, which keeps the wheels incontact with the treadmill, which mean the plane does not move relative to the ground, which means no lift.

How else do you want me to explain it?

Lulu wrote:

Let's think about it this way. We're assuming that the tires do not create any friction between the plane and the treadmill. If the engines on the plane are off, no matter what speed the treadmill is spinning at, the tires on the plane will spin, but the plane itself will not move at all relative to the ground.

Go put a skateboard or a hot wheels car on a treadmill moving at 10 mph and tell me what happens. If they stay in one place on the treadmill then the plan would fly. However, if they fall off the back of the treadmill then the plane won't fly. It's that simple.

*To the poster that said I lost credit siting Jackass as a source, I have found with my Physics students that Jackass is a great show to learn about physics and even biomechanics. You look at the stunts the try to pull and you can tell if they will work or not by looking at the physics of everyone. Like the time they tried to slingshot each other in the pond. Simple physics tells you that it won't work. Low and behold, it doesn't work.

I'm still all over the place on this thing. I've read the article from earlier in the thread and that had me vascillating towards pro-take off. But now I'm wondering how much of this is a semantics thing. PTO (pro takeoff) people are saying the treadmill is a red herring and the plane will be able to attain the proper ground speed relative to the earth to take off. But the plane isn't sitting on the earth. So shouldn't the planes "ground" be the treadmill? And if it's rolling across the treadmill's belt (ground) at takeoff speed it should be stationary and not have any wind going across the wings. Also hurting my brain is this. What are the throttle setting of the plane doing a regular takeoff and the plane supposedly taking off from the treadmill? It's a freaking roller coaster ride inside my head right now.

Jack,

Here's the thing. A plane moves by pulling itself through the air, not pushing itself off of the ground. You are right, the plane would roll off of the back of the treadmill if the engines weren't on and we were taking friction into account. But once the engines are on, it doesn't need the ground to move, it just needs the air, and it will be able to pull itself forward.

To those people who think it will not take off - for the sake of argument, if the wheels were frictionless, do you agree that the plane would remain stationary and that the wheels would simply spin underneath it?

Because those of us who think it will fly can imagine that. From there, it's easy to imagine the engine turning on and the plane going forward. From there it's no big deal if the wheels do have some friction, because we know it's not a lot.

adfgadg wrote:

To those people who think it will not take off - for the sake of argument, if the wheels were frictionless, do you agree that the plane would remain stationary and that the wheels would simply spin underneath it?

Well, if the wheels are frictionless, what's causing them to spin at all? The treadmill below could be turning at infinite speed, but unless there's some friction between the wheels and the treadmill, the wheels won't spin. One can't assume that only parts of the system are frictionless-- either the whole system has friction or you assume that the entire system (and not just selected portions of certain components) is frictionless.

Actually, it will not take off. With the wheels spinning at 300 mph, the tires will explode cause huge damage to the wheels. The plane will then shoot off the back end of the treadmill, killing everybody on board.

You are correct, but I think you know what I meant. Frictionless along the axis that it spins. Obviously the outer surface of a wheel can have different friction than the hole in the middle along which it spins.

Jack Frost wrote:

. . . the weight of the plane on those wheels creates traction on the ground.

WRONG!!!

Go ask anyone you know with an engineering interest what a wheel does. It prevents friction and 'traction' (as you call it) between the core of the wheel (greased up shaft) and whatever turns the wheel (the ground/treadmill belt).