[Guest]

This is a very highly debated topic, even though scaled tests have been conducted. The popular Mythbusters show on discovery did it full scale, but some still dispute the way they did it. You can probably find thousands of forums that host this same question, and I wouldn't be suprised if it has even been posted here before. So here goes!

A large passenger jet sits on a tredmill the size of a normal runway that they would normally take off on. When the jet starts up, it climbs in speed slowly. The tredmill matches the jet's speed EXACTLY. For every mile an hour the jet climbs, the tredmill goes in REVERSE that exact amount as-well.

The grand question: Will the plane take-off?

Assume that:

The wind is at 0 MPH

The Jet is powered by turbines

Edited September 6, 2008 by RedRum

[Guest]

Um... not quite.

The pressure in front and behind the engine are the same (both are exposed to the local atmosphere). The thrust is generated by the difference in momentum of the working fluid (air) between the inlet and outlet.

The pressure in front and behind the engine are the same (both are exposed to the local atmosphere). Does it mean that if you stand in front of the engine you will not be sucked into it because "both are exposed to the local atmosphere" ???

[Guest]

No, the plane's wheels are moving faster than the treadmill; the plane is not moving faster than the treadmill. The plane moves at 20 MPH in relation to the ground and 40 MPH in relation to the treadmill. The treadmill moves at 20 MPH in relation to the ground and 40 MPH in relation to the plane. The plane's wheels are spinning 40 MPH.

You keep bringing up arguments in previous posts that I have either conceded or restated, rather than address any new assertion completely.

Above is the fallacy in your argument.

In the above scenario, the plane is moving twice the speed of the treadmill in relation to the ground!

[Guest]

Scraff - are you saying that if I am on a treadmill on a skateboard being pushed from behind until I fall off the front of the treadmill, that I am not going faster than the treadmill? - It's just my wheels going faster?

Edited September 10, 2008 by AAAsn888s

[Guest]

You keep bringing up arguments in previous posts that I have either conceded or restated, rather than address any new assertion completely.

What new assertion haven't I addressed? I bring up you r old assertions because I'm tryingto keep up with what it is you're trying to argue for. I did not see where you conceded anything, but this is a long thread and I may have missed it.

Above is the fallacy in your argument.

In the above scenario, the plane is moving twice the speed of the treadmill in relation to the ground!

The plane is moving 20 MPH in relation to the ground. The treadmill is moving 20 MPH in relation to the ground. They are moving away from each other at equal speed. What is your problem with this situation? I'm not following you.

How is my argument fallacious?

[Guest]

Scraff - are you saying that if I am on a treadmill on a skateboard being pushed from behind until I fall off the front of the treadmill, that I am not going faster than the treadmill? - It's just my wheels going faster?

If the treadmill is designed to exactly match your speed, then that is correct. You are not going faster than the treadmill, but your wheels are going faster than if I was pushing you on the sidewalk.

[Guest]

If the treadmill is designed to exactly match your speed, then that is correct. You are not going faster than the treadmill, but your wheels are going faster than if I was pushing you on the sidewalk.

OK - then how about if I am on the treadmill being held in place - regardless of the speed of the treadmill, we can say it is matching my speed, correct?

The paradox here is that if I am then pushed forward, I am advancing on the treadmill. The speed of the treadmill then becomes irrellevant according to your argument. If the treadmill speed is irrellevant, then what is the point of the OP?

[Guest]

OK - then how about if I am on the treadmill being held in place - regardless of the speed of the treadmill, we can say it is matching my speed, correct?

Okay, you're standing still on a skateboard on a treadmill which is also standing still, and I am going to push you forward by putting my hand on your back and walking forward. This treadmill is designed to match your speed exactly. If I haven't yet put my hand on your back, and the treadmill starts moving, then it is not doing what it is designed to do.

So how are you saying "regardless of the speed of the treadmill, we can say it is matching my speed"?

The paradox here is that if I am then pushed forward, I am advancing on the treadmill. The speed of the treadmill then becomes irrellevant according to your argument.

I have no idea what your talking about. What paradox? How is my argument that the speed of the treadmill is irrelevant? I have repeated myself many times. If I push you on a skateboard, and you and the skateboard are on a treadmill, and I am walking at a speed of 1 MPH, and this treadmill was designed to match your speed exactly, it will be going 1 MP in the opposite direction. Both you and I will be leaving points on the treadmill at 2 MPH and traveling 1 MPH in relation to the ground.

If the treadmill speed is irrellevant, then what is the point of the OP?

It's not irrelevant. A few people in this thread so far believe that if a plane is resting on a treadmill, and that treadmill is designed to match the speed of the plane but in the opposite direction, the plane can't take off. This is also why the folks on MythBusters did the experiment that they did. To bust that exact myth.

This is what you said a few posts back that started this:

"I believe the OP is clearly setting up the scenario #2 - again, because as long as the planes wheels are on the treadmill and it is moving forward - the plane is moving faster than the treadmill - therefore breaching the OP."

Do you see why you're wrong? If the treadmill is designed to match the speed of the plane exactly, the OP has not been breached as you're claiming.

Tell me what you think happens in this scenario:

A plane is on a treadmill. It turns it's thrusters on and a few seconds later, it is going 50 MPH. How fast is the treadmill going in the opposite direction if it is designed to match the speed of the plane?

[Guest]

Please respond to all my posts or we're not going to get anywhere:

"The plane is moving 20 MPH in relation to the ground. The treadmill is moving 20 MPH in relation to the ground. They are moving away from each other at equal speed. What is your problem with this situation? I'm not following you.

How is my argument fallacious? "

[Guest]

Please respond to all my posts or we're not going to get anywhere:

"The plane is moving 20 MPH in relation to the ground. The treadmill is moving 20 MPH in relation to the ground. They are moving away from each other at equal speed. What is your problem with this situation? I'm not following you.

How is my argument fallacious? "

Would love to respond to all of your posts - would like the same courtesy, you keep chopping up my posts, leaving out the pretext or subtext of my arguments and responding to bits and pieces. How about a response to me ENTIRE last post?

NOTE: - With due respect to Scraff - he did exactly this - we were both posting simultaneously and I did not see it...

Edited September 10, 2008 by AAAsn888s

[Guest]

The light bulb just went on.. I swear, I am not dense... For whatever reason, this one got caught in my reasoning loop.

I now understand that I have been adding elements to the puzzle that do not exist. What lit up for me was my reasoning that if the treadmill was going 300 mph, and I was on a skateboard being held in place - it is MY speed that is matching the spead of the treadmill, not vice versa as stated in the OP

If the OP was reversed and the treadmill started up and increased speed to 300 mph and the jet was matching the speed of the treadmill - THEN the jet sits in one place with the wheels spinning - these are not interchangable the way I was reasoning...

Thanks for sticking in there with me - but YOU WIN. You were right and I was wrong. I am man enough to admit defeat...

[Guest]

And if you still think I am not correct - how would I word the OP to create a scenario where the treadmill is screaming along at 300 MPH to have the jet stand in one place?

[Guest]

I'm glad we've resolved a lot, but one more thing:

If the OP was reversed and the treadmill started up and increased speed to 300 mph and the jet was matching the speed of the treadmill - THEN the jet sits in one place with the wheels spinning - these are not interchangable the way I was reasoning...

Lets see. You agree that if the plane moves forward at 1 MPH in relation to the ground, and the treadmill were designed to match its speed, then the treadmill would go 1 MPH in the opposite direction in relation to the ground.

Then you can't think that the jet would stay still if the situation was reversed:

If the jet was designed to match the speed of the treadmill, then once the treadmill is moving 1 MPH, then the jet will have to be moving 1 MPH in the opposite direction. If the jet stays still, it isn't doing what it was designed to do.

It doesn't matter if it's the treadmill that has this special design or the plane. The observer will see the exact same thing happen. Points on the belt and the plane will be moving in opposite directions at 1 MPH in relation to the ground.

And if you still think I am not correct - how would I word the OP to create a scenario where the treadmill is screaming along at 300 MPH to have the jet stand in one place?

When a treadmill moves in the opposite direction of a plane standing on it, it will move the plane along with it to some degree even though the plane is resting on wheels. The plane would need to use its thrusters at just the right degree to keep it still in relation to the ground.

If the plane was designed to stay still in relation to the treadmill, it would need reverse thrusters since once the treadmill started moving backwards, it would not move at the exact speed of the treadmill; its wheels would spin a bit also.

[Guest]

for a while i thought the plane wouldn't move or take off, after a long read and a nice smoke i do have to agree with every1 else. maybe my simplistic view might help.

to begin with nothing is on and nothing moves, as the jets starts this propells the plane forward and the belts start to match the speed of the whole plane. becase the belt moves, this move the wheels and the wheels then spin the same speed as the belt cos of it. the speed of the wheels doesn't effect the speed of the plane as there not connected. as the belt only effects the speed of the wheels and never the speed of the plane, plane will take off normal.

[Guest]

I'm glad we've resolved a lot, but one more thing:

Lets see. You agree that if the plane moves forward at 1 MPH in relation to the ground, and the treadmill were designed to match its speed, then the treadmill would go 1 MPH in the opposite direction in relation to the ground.

Then you can't think that the jet would stay still if the situation was reversed:

If the jet was designed to match the speed of the treadmill, then once the treadmill is moving 1 MPH, then the jet will have to be moving 1 MPH in the opposite direction. If the jet stays still, it isn't doing what it was designed to do.

It doesn't matter if the treadmill has this special design or the treadmill. The observer will se the exact same thing happen. Points on the belt and the plane will be moving in opposite directions at 1 MPH in relation to the ground.

When a treadmill moves in the opposite direction of a plane standing on it, it will move the plane along with it to some degree even though the plane is resting on wheels. The plane would need to use its thrusters at just the right degree to keep it still in relation to the ground.

If the plane was designed to stay still in relation to the treadmill, it would need reverse thrusters since once the treadmill started moving backwards, it would not move at the exact speed of the treadmill; its wheels would spin a bit also.

Just thought of another analogy that really solidified it for me:

Imagine being at the airport, on a skateboard inside the terminal, being pushed along from the side at 2 mph -- you approach the people mover (treadmill,) as a wrong way passenger, the treadmill is going 2 mph in the opposite direction. while it might require more force or thrust, if the person pushing me does not slow down - we continue on at 2mph in one direction while the treadmill moves on in the opposite direction at 2mph - - my wheels are now going 4 mph and the person pushing has to exert more force, but I can still meet the parameters of the OP..

What needs to be conceded is that it would take a subtantially greater thrust of the engines to take off, but yes, the plane would take off!!

Edited September 10, 2008 by AAAsn888s

[Guest]

What needs to be conceded is that it would take a subtantially greater thrust of the engines to take off, but yes, the plane would take off!!

No, it would be minimal, perhaps not even measurable. While the conveyor does exert some modest backward force on the plane, that force is easily overcome by the thrust of the engines pulling the plane ahead. The plane moves forward at roughly its usual speed relative to the ground and air, generates lift, and takes off. The plane on MythBusters did not have to use substantially greater thrust of the engine(s) because almost all the force of the treadmill just made its wheels spin faster.

[Guest]

Sorry boys, still one holdout yet.

Essentially the biggest holdup is defining what you mean by "matching the speed". You are saying that the treadmill is designed to match the ground speed of the plane. The problem with that, as I stated, is that a treadmill designed like that would NEVER KEEP ANY MOVING OBJECT STILL. The only thing in the world that would prevent from moving is a rock (ok, anything that doesn't move). Think about it, you get on a treadmill, it's designed to match your ground speed, you start walking, what happens? Well, if you walk 6 km/h, it starts to accelerate, once it gets to 3km/h it is now matching your ground speed, as 3km/h ground speed + 3km/h treadmill speed equals the 6km/h you're walking. Same can be said of a car, a bike, a snail, it doesn't matter. So why put a plane on that treadmill? Why not anything else? The answer will always be "yes, x can still move despite the treadmill".

Now, if it's a treadmill designed to keep a car still (as we all know is quite possible) it would be matching wheel speed, not ground speed (or engine output or somesuch) to keep it still. Don't go by the spedometer, that just measures wheel speed. So, that treadmill must attempt to match the wheelspeed of the plane.

As I have argued above, and as someone so nicely put into math for me (though I know that wasn't his intention) by doing that, at some (astronomical) speed, we will achieve a point where the force backwards due to bearing friction is equal to the force forwards due to the jets thrust. Is this possible in the real world with current technology? Of course not, but neither are two spaceships approaching each other at the speed of light, but that makes it no less valid of a thought experiment.

(and please let's forget about the mythbusters experiment, current technology prevents us from translating this onto a TV show)

Edited September 11, 2008 by Rheticus

[Guest]

Sorry boys, still one holdout yet.

Essentially the biggest holdup is defining what you mean by "matching the speed". You are saying that the treadmill is designed to match the ground speed of the plane. The problem with that, as I stated, is that a treadmill designed like that would NEVER KEEP ANY MOVING OBJECT STILL. The only thing in the world that would prevent from moving is a rock (ok, anything that doesn't move). Think about it, you get on a treadmill, it's designed to match your ground speed, you start walking, what happens? Well, if you walk 6 km/h, it starts to accelerate, once it gets to 3km/h it is now matching your ground speed, as 3km/h ground speed + 3km/h treadmill speed equals the 6km/h you're walking. Same can be said of a car, a bike, a snail, it doesn't matter. So why put a plane on that treadmill? Why not anything else? The answer will always be "yes, x can still move despite the treadmill".

If you are walking 6km/h on a treadmill, the treadmill is going also 6km/h.

[Guest]

If you are walking 6km/h on a treadmill, the treadmill is going also 6km/h.

No, it isn't, or are you switching out treadmills on me? Everyone is saying "The treadmill matches the planes speed, as in ground speed". Ok, fine, the treadmill will match MY speed as well. My groundspeed on the treadmill is going to be my speed in relation to the outside world. If I was going 6km/h, and so was the treadmill, the treadmill would be going 6km/h and my groundspeed would be 0km/h. That's not how it works, so it must reach equilibrium, which would be at 3km/h.

[Guest]

The plane will not take off. If the treadmill is matching the the speed in reverse, then the plane is getting no air under the wings. Even though the prop is at full speed, the whole principle of a plane is that it needs to have air moving under the wings, creating high pressure under the wings, and low pressure above the wings, generating lift. If you have no air moving, then you have no takeoff.

[Guest]

The pressure in front and behind the engine are the same (both are exposed to the local atmosphere). Does it mean that if you stand in front of the engine you will not be sucked into it because "both are exposed to the local atmosphere" ???

I didn't say that.

When you put your hand out your car window on the freeway, you feel a force. However, the air outside your car is at atmospheric pressure (except in the immediate vicinity of your hand, but that's only because you disturbed the flow). Same goes for the jet inlet. It is the momentum of the incoming air that gets you in trouble.

But, since you mention it, I should clarify: there is a small decrease in pressure at the inlet of the engine, due to the fact that it has been accelerated (its stagnation, or total pressure is the local atmospheric pressure - now is a good time to invoke the spirit of Bernoulli). What I was trying to point out was that the (small) variations in the pressure field at the inlet and outlet of the engine have a negligible effect on thrust.

Anyway, we're getting off topic. PM me if you want to know more...

D.

[Guest]

Essentially the biggest holdup is defining what you mean by "matching the speed". You are saying that the treadmill is designed to match the ground speed of the plane. The problem with that, as I stated, is that a treadmill designed like that would NEVER KEEP ANY MOVING OBJECT STILL.

I have stated that it doesn't matter if we look at it as the treadmill matching the plane's speed in relation to the ground or the treadmill and that is correct because a plane taking off is minimally effected by a moving treadmill. With a person walking it's a different story.

If the treadmill were designed to move at the same speed of a person walking in relation to actual ground speed as seen by an outside observer, then as you say later in your post, if one walks at a speed that would normally be 6 km/h, it would seem to bystanders on the ground that he and the treadmill are moving at 3 km/h in opposite directions.

If the treadmill were designed to move at the same speed of a person walking in relation to how fast those legs moving would have him moving if he were on the ground, if he walks at a speed that would normally be 6 km/h, it would seem to bystanders on the ground that he is still and the treadmill is moving at 6 km/h in opposite directions.

This only matters to people, cars and such. The plane takes off basically the same with either design.

SNow, if it's a treadmill designed to keep a car still (as we all know is quite possible) it would be matching wheel speed, not ground speed (or engine output or somesuch) to keep it still. Don't go by the spedometer, that just measures wheel speed. So, that treadmill must attempt to match the wheelspeed of the plane.

There is no attempt to match. The treadmill is designed to match the speed of the plane exactly. If it said its wheel speed, then it would do that exactly (only there would be no such thing as a match, so the scenario is nonsensical). But this has nothing to do with the plane not being able to take off.

This riddle isn't about a treadmill matching wheel speed of a plane, so lets get back on topic.

[Guest]

There is no attempt to match. The treadmill is designed to match the speed of the plane exactly. If it said its wheel speed, then it would do that exactly (only there would be no such thing as a match, so the scenario is nonsensical). But this has nothing to do with the plane not being able to take off.

This riddle isn't about a treadmill matching wheel speed of a plane, so lets get back on topic.

Actually, I believe the original question DID say "match" and even referred to the fact that it is a dynamic system, meant to respond, and not a preprogramed deal.

Now, if it WAS preprogramed, and if, in fact, it was just a "well, usually a plane accelerates at x, eventually reaching a top speed of y, so lets program the treadmill to do exactly that" then of course the plane takes off, the wheels spin at double the speed, and everyone is happy. But, just from the fact there is (upon my reading, and hearing it before) supposed to be a reactive element to it (reacting to keep the plane at rest) the answer is, in a world with bearing friction, equilibrium would be reached at a ridiculously high speed, and the plane wouldn't move.

As I said before, taking a car, if you say "a car usually goes 60km/h" and put it on a treadmill, that is not going to keep the car still, because there is variation, you could step on the peddle more, etc. In order to create a system that is designed for keeping anything still, it needs to be dynamic, and react to the point of contact between the system and the object to be kept at rest. In the airplane's case, this would be the wheels. And, as I said before, the treadmill would have to be going ludicrous speed in keep the plane still.

That being said, I will concede that the exact way the original question was worded, the plane would take off (because it talks about MPH). My only problems are 1) a car would move under the same rules, and 2) that's not the way I have heard the question posed before, and not the way I think it should be posed (since that is frankly a simplistic and boring answer).

Edited September 11, 2008 by Rheticus

[Guest]

The plane will not take off. If the treadmill is matching the the speed in reverse, then the plane is getting no air under the wings. Even though the prop is at full speed, the whole principle of a plane is that it needs to have air moving under the wings, creating high pressure under the wings, and low pressure above the wings, generating lift. If you have no air moving, then you have no takeoff.

I agree. Regardless of what the wheels or treadmill are doing, the plane needs LIFT to takeoff.

[Guest]

The physics of an aircraft in flight is that there are 4 forces acting on it, lift & weight (or gravity), thrust & drag. On the ground (and for the purposes of this explanation) we can ignore the first two until the point the wheels leave the ground. Drag, (aerodynamical drag) while an aircraft is on the ground is extremely minimal. This leaves us with thrust.

We know that no aircraft has powered wheels, (this is why jets need a pushback from the terminal) so the aircraft does not gain any groundspeed from the wheels. Then what does the aircraft push against if not the ground? We know from Newton that every action has an equal and opposite reaction. It has to push against the air. If the air was on a hypothetical treadmill then the aircraft could take off without moving forward, (which would be cool to see) -- sometimes smaller aircraft can actually do something similar, remain in flight while having zero ground speed. (Ground speed: the velocity of the aircraft with respect to the ground.) The need a good head wind and slow down the engine.

What we have here really, is a race condition (for all you programmers out there). When the engines push on the air, moving the aircraft forward by 1 MPH, without a treadmill, the tires will rotate to let the aircraft move forward that quickly. With the treadmill, the treadmill is now moving backwards 1 MPH but the aircraft is still moving forward that amount, so the tires compensate by rotating at 2 MPH. The planes ground speed in relation to the ground is as per normal, but it's ground speed in relation to the treadmill is double. The faster the plane moves in relation to the ground (not the treadmill), the tires rotate at twice the expected speed (because they're on a treadmill).

When a plane is in the air, how is it staying up? Are the wheels helping it? (No) Is the air itself keeping it up, (without outside help)? Not really. If this was the case, why would an airplane need engines? Gliders DO work this way by always decending. They can climb as well, but they'll never reach their inital peak altitude. (We'll ignore the effect of thermal air currents and cliff effect winds right now.) Gliders need help reaching initial peak altitude, a tow plane or winch. The engines push on the air, moving the aircraft forward. This forward motion "pushes" (not quite) the outside air over the lifting surfaces.

One way to prove that the props (or jets) push against the air is to (hypothetically) anchor the aircraft to the ground with a cable and put a spring scale on it. Fire up the engine(s) and read the scale as the throttle is pushed up. The plane would not really move forward (as much as the cable and spring would allow), thus keeping ground speed equal to "treadmill" speed, zero. I would bet anyone that the spring scale will start to climb.

Facts (prop or jet):

Aircraft wheels do not power (move) an aircraft

Air specifically moved by the powerplant of the aircraft over lifting surfaces provides negligable lift (prop wash or jet wash)

Powerplants push against the air

Air must be moving over the lifting surfaces to make the aircraft climb

I hope this provides some clarity. (I'm also an aspiring pilot and I've been interested in aeronautics for many many years. Being an engineer helps a bit.)

[Guest]

If the air was on a hypothetical treadmill then the aircraft could take off without moving forward, (which would be cool to see) -- sometimes smaller aircraft can actually do something similar, remain in flight while having zero ground speed.

I've flown aircraft in wind tunnels (scale models by remote control - I don't think anybody's crazy enough to actually get in the cockpit), and unfortunately, it's not that exciting.

However, I did see a glider pilot attempt a vertical touch-down once into a 20 kt headwind (its normal landing speed was 23 kts if memory serves). Unfortunately for him, he stalled it about six feet off the ground, damaging his tail. It sure was fun for us spectators though...