Thread: Something to think about

A jet moving forward on the ground or a treadmill is not the same as running on a treadmill. Running on a treadmill is only possible due to the pressure that your feet are applying on the treadmill. It is that interaction of your feet being faster than the treadmill that moves you forward (as running at the same speed keeps you stationary). This is different than a jet engine. A jet engine works by applying a force that moves you forward through space, through the air. With free-rolling wheels, the jet might as well be hovering in space, on its own. It is not connected to the treadmill by friction, it is merely sitting there because of gravity. The reverse thrust of afterburners, in the air, is going to move the jet forward, as long as the wheels are free-rolling and don't provide enough friction (by way of lock-up) to stop the jet from forward motion.

From someone who has taken courses in aerodynamics and put them into practise, this thread is funny...

By the way, this is the shortest conventional take-off I know of...

http://www.youtube.com/watch?v=iYdo4...elated&search=

Originally Posted by Spartiate

From someone who has taken courses in aerodynamics and put them into practise, this thread is funny...

By the way, this is the shortest conventional take-off I know of...

http://www.youtube.com/watch?v=iYdo4...elated&search=

I'm not sure I understand:

Sure, aerodynamics would have everything to do with generating the lift required to get the plane of the ground, but this problem seems to have more to do with generating the speed.. There is no debate that the plane would have to generate enough speed for the aerodynamics to come into play, but why do you not feel that a jet engine could create enough forward momentum to gather forward velocity, when the plane is rolling on a treadmill that matches wheel-speed?

To put this into the perspective of how I (now) see it: If we set up a vertical treadmill beside the space shuttle, and attached a set of wheels to the space shuttle that would lean against that treadmill, the thrust generated by the space shuttle wouldn't cause the shuttle to lift off, even if the treadmill was moving downward at a speed that perfectly matched the wheels? Would the wheel-to-treadmill variable even matter, when there is enough thrust to lift the space shuttle into the air?

Likewise, would the movement of a treadmill under a jet with free-rolling wheels even matter, if the forward thrust is generated by a rocket/jet that acts against the air and not the ground?

Originally Posted by Oneironaut

Likewise, would the movement of a treadmill under a jet with free-rolling wheels even matter, if the forward thrust is generated by a rocket/jet that acts against the air and not the ground?

But that's not so. Unless the jet is experiencing lift (which can only be generated by the movement of air across the airfoil wings) then its weight is being supported by the treadmill. It's the same thing as a plane taxiing along the runway: until it starts to lift itself, its weight is being supported by the ground/treadmill.

Imaging the plane sitting on the treadmill but being held still by a rigid frame. Now image the treadmill being run so that it causes the plane's wheels to spin. This is the exact same condition being experienced in the example we're talking about. The only difference is that there is no rigid frame; instead it is the plane's engine keeping it stationary.

It is not the same thing as what you are thinking it is.

Originally Posted by Oneironaught

But that's not so. Unless the jet is experiencing lift (which can only be generated by the movement of air across the airfoil wings) then its weight is being supported by the treadmill.

That's my point, though. It seems that people (as I was, in the beginning) are focusing only on the lift. There is no argument that, once the jet gets to a certain speed (in relation to the air around it) it can raise the wing foil and generate lift. I understand that part completely.

We are simply talking about forward motion, here. That's all, because it's agreed that once forward motion can be generated, lift is possible at a certain speed.

So, imagine this plane is attached to a wench that is hooked onto the nose of the plane. Under this jet is a treadmill. Imagine this treadmill is going 25,000 miles per hour (about as fast as the space shuttle travels), and the afterburners of the jet are not active. The jet would be sitting stationary, because it is being held in place by the wench. Regardless of how fast the treadmill is, the jet would be sitting in one spot.

Now, imagine the pilot activated the afterburners at full speed. There is nothing holding the jet from the rear. I believe that the jet would begin moving forward, no matter how fast the treadmill is going, because the thrust is being imposed upon the air, itself, regardless of how fast or slow the wheels are turning. Eventually, the jet plane would reach whatever velocity the afterburners permit, because it would not matter how fast or slow the wheels are moving along the ground. They spin completely independently of the jet's propulsion, itself.

This would not create a forward motion? I honestly don't understand why not. But the again, I really don't know that the weight of the plane is enough to counteract the force of the afterburners. (Haha, damn. Now I really wanna know the answer to this. )

Originally Posted by Oneironaut

This would not create a forward motion? I honestly don't understand why not. But the again, I really don't know that the weight of the plane is enough to counteract the force of the afterburners. (Haha, damn. Now I really wanna know the answer to this. )

I see what you're saying but I honestly think you're confused. Yes, the thrust is acting upon the air, thereby creating and opposite force upon the plane. But, the key issue is that the air flow across the wings is not there. The only forces acting on the plane are a push from the rear. But that push is only serving the function of keeping up with the treadmill, not creating an air current across the wings (only through the engines).

Yeah, I'm completely stumped on this one. I can see it working both ways, but, given that I can't really imagine the fictional variable of the treadmill keeping up with the plane (not the other way around) I simply don't know what would happen.

I'm trying to think of analogies, though, but they all do kinda point to what you are saying (and what I was saying in the beginning, before I started seeing things the way Phobia stated), such as:

If someone were in an air boat, and they were floating backward down a river that was going 50mph, and then they turned on the fan to 50mph, they would, eventually, seem to stay in one spot, I would imagine.

Likewise, if someone was in a giant slingshot on the back of a semitruck that was going 50 mph, they were facing backward, and the slingshot had a firing velocity of 50 mph, they would landed in the same horizontal position that they were launched from. I can see that.

But, still...I just don't know. Somebody give me the damn answer before my head explodes. Lol.

Originally Posted by Oneironaut

If someone were in an air boat, and they were floating backward down a river that was going 50mph, and then they turned on the fan to 50mph, they would, eventually, seem to stay in one spot, I would imagine.

Exactly. The same analogy applies to the plane/treadmill scenario, because we are dealing only with a pushing force in each case.

Originally Posted by Oneironaut

I'm not sure I understand:

Sure, aerodynamics would have everything to do with generating the lift required to get the plane of the ground, but this problem seems to have more to do with generating the speed.. There is no debate that the plane would have to generate enough speed for the aerodynamics to come into play, but why do you not feel that a jet engine could create enough forward momentum to gather forward velocity, when the plane is rolling on a treadmill that matches wheel-speed?

To put this into the perspective of how I (now) see it: If we set up a vertical treadmill beside the space shuttle, and attached a set of wheels to the space shuttle that would lean against that treadmill, the thrust generated by the space shuttle wouldn't cause the shuttle to lift off, even if the treadmill was moving downward at a speed that perfectly matched the wheels? Would the wheel-to-treadmill variable even matter, when there is enough thrust to lift the space shuttle into the air?

Likewise, would the movement of a treadmill under a jet with free-rolling wheels even matter, if the forward thrust is generated by a rocket/jet that acts against the air and not the ground?

I suppose we could go on and mingle forever about the intricacies of the whole "treadmill" scenario... I simply took it as meaning that the airplane's forward motion = 0 while the wheels are moving at x speed and the engines are at full power. In this case, no forward motion means no flight, unless you have a 120 knot head wind ...

I just want to add a couple more things I thought of. The argument that the plane won't take off, it will stand still relies on the fact the treadmill instantaneously matches the speed of the plane. If the plane starts at a standstill and the treadmill matches the speed (defining this as making the treadmill move at a speed so that it matches the speed of the wheels so basically the wheels stay in the same place just spinning around) then you are correct that it will not take off. In fact nothing will happen. In order for the treadmill to move the plane must have speed and in order for the plane to have speed the treadmill must be spinning the same speed underneath. Since neither start out moving, neither can start moving. (Thats confusing- basically your argument is that the plane won't move at all, so if the plane doesn't move then neither will the treamill.)

The other interpretation which is the one I took (since something actually happens this way). The plane will increase in speed and then the treadmill will match that but not instantaneously. This way is as explained in my last post where the wheels will increase speed and then the treamill will and they will keep accelerating into infinity. Meanwhile the plane will be moving because the thrust is independent of the wheels.

Overall this problem is very poorly set up and arguments can be made either way depending on the interpretation.

Originally Posted by ThePhobiaViewed

The other interpretation which is the one I took (since something actually happens this way). The plane will increase in speed and then the treadmill will match that but not instantaneously. This way is as explained in my last post where the wheels will increase speed and then the treamill will and they will keep accelerating into infinity. Meanwhile the plane will be moving because the thrust is independent of the wheels.

Well it won't really accelerate to infinity, given that the plane has a maximum amount of avaible thrust. F= ma my friend...

Originally Posted by Spartiate

Well it won't really accelerate to infinity, given that the plane has a maximum amount of avaible thrust. F= ma my friend...

I'm not completely sure about the math but I think that the wheels and treadmill would accelerate much more than the plane but I could be wrong. Obviously it would not be to infinity but I think it would be to a point where in real life it would make the wheels explode.

This question assumes we are dealing with a regular jet plane.

The plane would actually take off, since its forward motion is provided by the jet engines themselves (pushing against the air/atmosphere), and not by the wheels pushing against the ground.

The plane would therefor have forward motion, movement over the wings, and lift to take off. The wheels would simply spin faster than normal until the plane left the runway.

The conveyor belt runway doesn't even come into the equation

Lol Damnit I thought so! (Well, not until Phobia said something, but I had a feeling he was right. Lol.).

Originally Posted by ouija

This question assumes we are dealing with a regular jet plane.

The plane would actually take off, since its forward motion is provided by the jet engines themselves (pushing against the air/atmosphere), and not by the wheels pushing against the ground.

The plane would therefor have forward motion, movement over the wings, and lift to take off. The wheels would simply spin faster than normal until the plane left the runway.

The conveyor belt runway doesn't even come into the equation

I don't see how you can figure that the plane would get forward motion ? The supposed treadmill is set to match the speed of the airplane (lets suppose this is done instantly). On the ground, the wheels move at a speed relative to the aircraft's, it's not independant, or else you would get slipping/skidding.

It's really the same principal as an actual person on a treadmill. Say you're running at 10 mph towards a treadmill that is going backwards at 10 mph. Once you get on the treadmill, your forward motion relative to the ground will be nullified.

Originally Posted by Spartiate

I don't see how you can figure that the plane would get forward motion ? The supposed treadmill is set to match the speed of the airplane (lets suppose this is done instantly). On the ground, the wheels move at a speed relative to the aircraft's, it's not independant, or else you would get slipping/skidding.

It's really the same principal as an actual person on a treadmill. Say you're running at 10 mph towards a treadmill that is going backwards at 10 mph. Once you get on the treadmill, your forward motion relative to the ground will be nullified.

It's not the same, though, Spartiate.

A person on a treadmill has the forward velocity and movement of their entire body dependent on what their legs are doing. A plane on wheels is different.

If you are on a treadmill, wearing roller-blades, and holding on to the arm of the treadmill, your body will not move. You can crank the treadmill up to 100 mph and, as long as you are applying the slightest bit of resistance by holding onto the arm of the treadmill, your body is not going to move. While that treadmill is going 100mph, all I have to do is walk up to you, grab you by the shirt collar, and pull you toward me and, guess what, you're going to roll toward me, even if the treadmill is going 100mph in the opposite direction, because you are wearing skates.

Originally Posted by Oneironaut

While that treadmill is going 100mph, all I have to do is walk up to you, grab you by the shirt collar, and pull you toward me and, guess what, you're going to roll toward me, even if the treadmill is going 100mph in the opposite direction, because you are wearing skates.

But you see, that would increase the speed at which the wheels are turning, which the treadmill would in turn negate...

This would only affect the wheels, not your body. What is happening to the wheels is irrelevant.

If you were wearing skates on a treadmill, and you were handcuffed to the arm of the treadmill, at what speed of the treadmill would the handcuffs snap, due to the speed that your wheels were turning?

Answer: They would never snap, because (as long as your wheels can take the rate of rotation without being destroyed) it does not matter how fast your wheels are going. You could be handcuffed at 100mph and then crank the treadmill up to 400mph (assuming, for the sake of argument, that the wheels are that strong) and you would not experience a force that is strong enough to break the handcuffs. They would hold you right where you're standing. You are being held in place by a force (the handcuffs) that works independently of what is going on on the ground, beneath your wheels.

Heh, this is harder to explain than I realised ... I'm starting to see what you're getting at, but there are some differences, with this situation. I can visualise it so well, so I'll try my best to describe how I see it... Say we forget about the conveyor belt thing, instead, we'll use an aircraft carrier. In the water, right next to where the plane is positioned for take-off, there is a stationary buoy. When the plane takes off, the carrier accelerates equaly in the opposite direction (impossible, I know, but for the sake of argument...). So if both move in opposite directions at equal acceleration, does the plane move relative to the buoy? Here's a sketch to demonstrate:

If it were a car on the carrier, in which case the propulsion would depend on the engine's force upon the tires and the tires' force upon the ground, I would say 3 would be the correct answer. But, in the case of a jet plane, in which case the propulsion is strictly a matter of being pushed through the air,by the air resistance, regardless of what free-rolling wheels are doing, I'd say 1 would be the closest answer (even though the aircraft carrier would be moving in the opposite direction - which that picture doesn't show- as is the case with the treadmill).

Originally Posted by Spartiate

Heh, this is harder to explain than I realised ... I'm starting to see what you're getting at, but there are some differences, with this situation. I can visualise it so well, so I'll try my best to describe how I see it... Say we forget about the conveyor belt thing, instead, we'll use an aircraft carrier. In the water, right next to where the plane is positioned for take-off, there is a stationary buoy. When the plane takes off, the carrier accelerates equaly in the opposite direction (impossible, I know, but for the sake of argument...). So if both move in opposite directions at equal acceleration, does the plane move relative to the buoy? Here's a sketch to demonstrate:

For this to be similar to the treadmill problem we will assume that the carrier is stationery at the start and the plane is lined up with the buoy. If the matching of speed is instantaneous, you would think the plane will not move relative to the buoy. I think it goes back to what I said earlier though. For this situation they all have to start out stationery. In an earlier post I said that neither would be able to move at all because for the treamill to start moving, the plane would have to be moving which goes against the argument for this situation that the plane is stationery so therefore it can't take off. This again depends on the wording about matching the speed of the plane. If it is indeed the speed of the plane then neither will start to move. Yes it is correct the plane will not take off or move relative to the buoy because nothing will happen at all. This means this whole question is very stupid.

If the matching is not quite instantaneous then the plane will still not take off because it will run out of room and fall into the sea. If the carrier is infinitely long then the plane would indeed take off and it would be the same situation where the wheels increase speed and then the ground catches up and that continually happens as the plane gains speed.

Originally Posted by ouija

This question assumes we are dealing with a regular jet plane.

The plane would actually take off, since its forward motion is provided by the jet engines themselves (pushing against the air/atmosphere), and not by the wheels pushing against the ground.

The plane would therefor have forward motion, movement over the wings, and lift to take off. The wheels would simply spin faster than normal until the plane left the runway.

The conveyor belt runway doesn't even come into the equation

Originally Posted by And Oneironaut

...

Oh, gee... Now we're back at square one, running over the same thing once again...

How can a plane - on a treadmill, runway, Interstate I-4, anywhere - that's sitting on something (anything) move forward without its wheels rotating? It can't. In this case, the wheels HAVE to spin in order for the whole treadmill scenario to even be part of this discussion. If not then we have a plane being pulled backwards by the moving treadmill belt. A plane is not weightless (even in flight).

Originally Posted by ouija

The plane would actually take off, since its forward motion is provided by the jet engines themselves (pushing against the air/atmosphere), and not by the wheels pushing against the ground.

That is false. The jet engines are ONLY countering (compensating for) the movement of the treadmill, not creating forward motion. The treadmill is matching the speed of the plane, meaning the plane goes nowhere at all. It simply sits right where it is. The engines are ONLY acting to prevent the plane from moving backwards. It's absolutely no different from a tether or backstop.

No movement = no take off. The jet engines only push the plane, not move air across the wings, not move the plane forward, not create lift, not make the Easter Bunny lay a Cadbury Creme Egg - nothing at all. The engine only provides the energy to hold the plane in its relative position. Nothing more - nothing less.

Engine (pushing forward) + treadmill (pushing backwards) = standing still (no movement).

In other words: only the ground is moving, not the plane. A plane doesn't take off just because the ground is moving (independently of the plane at that). Say we were use the Schwartz and magically levitate the plane (so that we eliminate the treadmill and engine). We find that the plane is still sitting in one spot and still no take off because the plane isn't moving. Remember, the only function the plane's engines were serving was to prevent the plane from being pulled backwards by the ground (treadmill) movement. A plane HAS to have forward motion with respect to the surrounding air for anything to happen.

Yeah, I see what you're saying, but hell I just dunno. I'm just going to have to leave it with not being able to decide.

I see what you are saying but, even though the plane is not weightless, it is not imposing its full weight, as resistance. A single man cannot push a truck with no wheels - but he can push a truck, that ways more than three times his bodyweight, if that truck has wheels and is in neutral.

The plane is not trying to compensate for the treadmill. It is the other way around. Once the boosters are activated, the jet is going to jump forward, regardless. It would be up to the reverse momentum of the treadmill to travel through the wheels and first slow the jet down. It is the same as if you stack a book on top of a bottle, and swipe the bottle out from under the book. Inertia. The book doesn't fly backward with the bottle, it drops down in the same spot. It takes time and continuous friction for the object on top to catch up to whatever the momentum below is doing.

If a Jet was sitting on a treadmill, with its afterburners off, and the treadmill were to suddenly shoot off to the rear at 600 miles per hour, would the jet sling backward at 600mph, at the same time? No. The wheels would spin and spin while the jet slid backward, slowly at first, and gradually caught up to 600mph...this could take however many feet/yards to do.

In the case of the given problem, with force blasting from the afterburners while the jet is sitting at a standstill, I believe it's going to jump forward, as the plane sped up, the treadmill would speed up, but I think there would be a difference between how fast the treadmill is going and how fast the jet body is able to move through space, until there is enough friction built up between the wheels and axles of the jet to cause the jet to succumb to the backward momentum of the treadmill.

In that time, it is very possible that the jet might have had enough speed to take off, but that all comes down to a hypothetical, as I don't know how much speed is needed for the jet to take off, and how long it would take for the backward momentum of the treadmill would keep it from reaching that speed.

Originally Posted by Oneironaut

The plane is not trying to compensate for the treadmill. It is the other way around.

But, regardless of cause and effect (or chicken/egg discussions), we're assuming the treadmill to instantly and perfectly match the thrust of the plane.

Once the boosters are activated, the jet is going to jump forward, regardless.

Under normal conditions, yes. But not under these idealised, hypothetical conditions. Otherwise there'd be no point in talking about the treadmill to begin with. The original puzzle is to decide the effects of a plane on a treadmill that magically and instantaneously matches the forward thrust of the plane. In that model, zero forward movement can ever take place. So, by extension, we're necessarily only considering whether lift can be generated by a stationary plane (and assuming no air to be forced along it, as would be the case in a wind tunnel).

It would be up to the reverse momentum of the treadmill to travel through the wheels and first slow the jet down. It is the same as if you stack a book on top of a bottle, and swipe the bottle out from under the book. Inertia. The book doesn't fly backward with the bottle, it drops down in the same spot. It takes time and continuous friction for the object on top to catch up to whatever the momentum below is doing.

Right, but not in our ideal treadmill scenario.

To recap: if the plane is allowed to move forward (or if enough air is forced at it) then it can gain lift. If not - as in our model - then it cannot.