Shoe

Ben,

For the most part, I think we agree on the underlying physics. I think perhaps where we aren't in agreement is in the question itself. If the limiting factor for the treadmill to exert a force on the wheels is the frictional force, then I think we're talking about a different question that really doesn't need to involve a treadmill. Essentially the question becomes: Can an airplane take off with its parking brake set? or Can an airplane take off if you replace its wheels with skids? The answer to those questions is yes, SOME airplanes certainly can, but I think the interesting treadmill question arises when the airplane can't produce enough thrust to overcome the maximum available static frictional force between its wheels and the ground. This is a relevant question because MOST full scale airplanes can't overcome the friction between their wheels and the ground with thrust (to overcome the maximum frictional force of rubber tires on dry concrete, for example, a plane would need a thrust to weight ratio of about 1 to 1). You said that "An airplane is designed to minimize friction between tire and ground... ". I couldn't disagree more. When it's time for an airplane to stop (either on landing or during an aborted takeoff), the airplane needs all the friction it can get between tire and ground.

I agree that a plane will fly under the Mythbusters' statement of the problem (although I don't think they even achieved those conditions on the show). But in my opinion that's kind of a silly question to ask... of course the airplane can take off... it's wheels will simply be rolling twice as fast when it does. I also agree that for high thrust-to-weight ratio airplanes, you can overcome the kinematic constraint I described by skidding the wheels.

Again, I think the interesting case occurs when the airplane can't produce enough thrust to overcome the maximum static frictional force between its wheels and the treadmill. For this case, there is no need for the treadmill to violate any physical law to keep the airplane from moving forward or aft. The treadmill-wheel contact point certainly doesn't have unlimited force producing capability, but in this case it will always have enough to counter the airplane's maximum thrust. I think we would agree that under these conditions, the kinematic constraint I described would apply. The treadmill would be able to keep the airplane stationary by exerting a force on the wheels equal to the thrust (thereby accelerating the wheels), and forcing the airplane to initiate its takeoff with a purely vertical motion. The constraint would break down only when the treadmill reached its maximum speed or the wheels flew apart.

There is no right or wrong way to pose this question, I just think that this version involves more interesting physics.

On a side note, I don't think that in the "skidding problem", the sliding friction force of the skid-treadmill interface would be proportional to the speed. Instead, I would expect the the sliding frictional force to be roughly constant, and about equal to the coefficient of kinetic friction times the normal force (in this case, the weight).

Thanks for the thoughtful reply!

Shoe

Phlip

So you've taken a question that has an obvious answer (although it is amazing to me how many people , including the pilot on the Mythbusters episode, don't get it) and changed the phrasing of it until it is about physical and logical impossibilities and chosen to argue that instead? Why not just revive the old question, "If God is all powerful, can He create a boulder that is so big He can't pick it up?"

I apologize if I sound like a smart alec. I've stayed out of this discussion since early on in the original discussion before Mythbusters ever broached the subject. I thought, when they got the question right and demonstrated the truth that this topic would die a well deserved death. But it amazes me that some people don't believe it even when they see it! It's like the cheating spouse who gets caught with his mistress saying to the wife, "Who are you going to believe, me or your lying eyes?"

combatpigg

My Feedback: (3)

The Mythbusters plane's landing gear legs loaded up with tension and wheel hopped the plane into the air. Their belt is a far cry from the belt system of the idealized concept. They also chose a plane that will take off from the palm of your hand. Their set up was a horrible waste of time. Bad example.

A Nordic Track with a 1 ounce plane bouncing along with pizza cutter wheels is also short of the visualized concept. If anything, set the Vapor up with a pair of tires heavy enough to give it better traction with the belt and enough of an extra load to bring it's take off speed up to the tread mills' max. Spray copious amounts of 3M77 on the belt and tires to simulate perfect traction, then turn the Vapor loose.

Top_Gunn

My Feedback: (6)

We start with a stationary plane on a stationary treadmill. If the plane doesn't move forward, the wheels won't start to turn, and so the treadmill doesn't start to move the other way. If the plane does move forward first, you've violated your notion that the plane will be stationary. If the treadmill moves first, you've violated the "match the speed of the wheels" condition. Saying "absolutely not!" doesn't make these paradoxes vanish. The treadmill in this version must go instantly from zero speed to infinity. You won't see that one tested on TV.

Combatpigg still seems to think the plane won't be able to move forward even if the treadmill moves only at the plane's takeoff speed. This is wrong, as the wheels can roll along the treadmill, and nothing stops them from rolling faster than the treadmill is moving unless we get into that infinite-speed treadmill stuff. If you disbelieve that, you'd have to think that wheels on a stationary treadmill couldn't roll at all; that's just silly. Picture someone standing on roller skates on a treadmill, and holding on to a rope attached to a wall in front of the treadmill. Can this person pull himself forward? Of course. All the traction in the world won't prevent the wheels from turning. Just as the tug on the rope pulls the roller skater forward (without "jumping off the treadmil') the thrust from the engine pulls the plane forward. I think this is generally recognized, at least on this thread. (I borrowed the roller-skater example from a thread on a different forum. Lots of groups have discussed this problem, usually without making clear which version they have in mind.)

combatpigg

My Feedback: (3)

As soon as the rollerskater begins to pull himself forward the wheels of his skates can no longer roll at the belts' rate of feed.
The skaters wheels must roll faster than the belts' rate of feed. Think friction.
The wheels will need to churn, grind, chew.....etc., to advance on the belt. This is not in keeping with the concept, no grinding allowed.
The ideal belt system senses the advance of the rollerskater and puts him back in his place.
So far no re-enactors of this concept have been able to duplicate the infinite belt drive with infinite traction.

Top_Gunn

My Feedback: (6)

Well, let's think about this when the belt's "rate of feed" is zero. If you're right, the skater can't roll forward by pulling on the rope unless the wheels "churn, grind, etc." But that's not what would happen. It is true that the wheels will roll faster when the skater pulls on the rope. So what? They can do that. The wheels of a plane rolling along the runway roll faster than the (zero) speed of the runway. They don't for that reason chew it up.

Go somewhere where there's a treadmill. Take a toy car with wheels that are free to turn. Start the treadmill, then push the car forward. It will roll. Or do the roller skating thing.

The belt I'm talking about is the one that moves at the plane's takeoff speed; this was what the Mythbusters people were testing. If you're discussing infinite-speed belts, that's a different matter.

Ben Lanterman

Shoe you say, "Again, I think the interesting case occurs when the airplane can't produce enough thrust to overcome the maximum static frictional force between its wheels and the treadmill."

Why would that be the interesting case? It automatically means the airplane can't take off. So what. Make the problem one that has the potential to take off. Vertical takeoffs are not valid as they are not in the spirit of the problem either. I don't understand why this becomes the more interesting problem.

Combatpig - you say...

A Nordic Track with a 1 ounce plane bouncing along with pizza cutter wheels is also short of the visualized concept. If anything, set the Vapor up with a pair of tires heavy enough to give it better traction with the belt and enough of an extra load to bring it's take off speed up to the tread mills' max. Spray copious amounts of 3M77 on the belt and tires to simulate perfect traction, then turn the Vapor loose.

Well it actually is pretty good. I have spent a life time of testing airplanes in various conditions and the test is valid. The tires don't have to be heavy to turn at the same speed as the treadmill. The light tires turned just fine. Why does it's take off speed have to be handicapped to the treadmills max speed? That is simply nonsense. Why do you think there must be perfect traction? In the real world the so called perfect traction breaks down when the frictional force reaches the maximum that the system can produce. Gluing the airplane to the treadmill is not quite in the spirit of the problem.

You say....

As soon as the rollerskater begins to pull himself forward the wheels of his skates can no longer roll at the belts' rate of feed.
The skaters wheels must roll faster than the belts' rate of feed. Think friction.

You are missing something here. As long as the skaters wheels are in contact with the belt with no slipping, the point of contact of belt/wheel is moving at the same speed. The measured rate of feed at the belts turnaround rollers doesn't equal the roller skate's wheels but they don't have to.

The wheels will need to churn, grind, chew.....etc., to advance on the belt. This is not in keeping with the concept, no grinding allowed.
The ideal belt system senses the advance of the rollerskater and puts him back in his place.
So far no re-enactors of this concept have been able to duplicate the infinite belt drive with infinite traction.

There is no need to churn, etc. That is an easy thing to do in the basement and it is a smooth process. Roller Skates move nicely on a treadmill at any speed. The ideal belt system can't put him back in place as long as he is holding the rope! Just how much friction do you think the ball bearings in the wheels have??

The question is never asked such that the belt has infinite traction. The question is asked in such a way that anyone can do the experiment with any treadmill and a suitable airplane. Normal things with normal physical properties.

It is that simple.

Ben

combatpigg

My Feedback: (3)

Without an idealized belt and interface with the plane there is nothing to consider, nothing to discuss.
This is not a "real world" type question. Discussing a plane running on top of a conveyor belt disqualifies it right away from certain real world considerations.
If the belt isn't capable of exceeding the plane's takeoff speed, then there is ABSOLUTELY nothing to discuss. Just equip the plane with enough power and it will defeat any contraption designed to hold it in place.

Shoe

Ben,

I still think the interesting case occurs when the airplane can't produce enough thrust to overcome the maximum static frictional force between its wheels and the treadmill.

You asked: Why would that be the interesting case? It automatically means the airplane can't take off.

It doesn't mean the airplane can't take off. Most of us have flown in airplanes that can't produce enough thrust to overcome the maximum static frictional force between the airplane's wheels and the runway. Such airplane are able to take off because their wheels roll rather than slide on the runway. The inability to overcome the max frictional force simply means that the airplane can't use thrust to make its wheels slip.

Strat2003

My Feedback: (1)

It's a poorly stated, paradoxical trick question, not a real world problem. If the airplane moves forward relative to the air (or the non-moving sides of the treadmill) the initial conditions have been violated. The treadmill is no longer "matching the speed of the airplane".

Imagine this problem: A B52 bomber is held stationary on the runway by a length of 5 pound test monofilament line. Can the B52 take off?

The initial conditions state that the bomber is held stationary, despite the fact that in the real world that peice of fishing line couldn't hold it back. No use arguing about how much thrust the plane produces or how strong 5 pound test line is, the problem stated that it's held stationary.

Top_Gunn

My Feedback: (6)

Huh? Suppose the plane moves forward at 40 mph and the top of the treadmill moves backward at the same speed. The treadmill is "matching the speed of the airplane," isn't it?

The versions where the treadmill is supposed to "match the speed of the wheels" are ambiguous and, in some cases, impossible, But the Mythbusters version is straightforward. (And the plane in that version will take off.)

I've seen one version in which the treadmill was supposed to move in such a way as to keep the wheels from turning. That's easy too, as the top of the treadmill there would have to be moving forward, along with the plane, to keep the wheels from turning.

da Rock

However, the false premise is that by matching the movement of the airplane wheels, the treadmill will somehow stop a plane from moving foreward that isn't going to be moving forward because it's wheels are holding it back.

Unless the plane moves, the wheels won't turn to begin with. If the plane doesn't move, the wheels won't roll and the treadmill won't either.

Phlip

GOOD ONE!!!

I think it couldn't take off because a stationary B52 can't fly.

Ben Lanterman

Since in the problem the wheels are always allowed to roll then the maximum frictional force in the problem is only the rolling friction of the wheels - which is very small - it is easy for the airplane to overcome that force. Looking at the wheels locked case with enough thrust is also a similar case. But the rolling case is the one we are talking about.

And if that is the case are you finally saying that the airplane will indeed takeoff?

Strat2003 -
The Mythbusters statement of problem was, "An airplane cannot take off from a runway which is moving backwards (like a treadmill) at a speed equal to its normal ground speed during takeoff." That statement of the problem is very nicely put and I think they probably put a lot of thought into it to eliminate the things like the fuselage must be stationary and the like.

The fact that the MythBusters could test the problem and that I could test the problem means that it isn't a trick question. It is a good question and does require a little simple thought. But it is a testable and therefore good question. After all they "wasted" a lot of time on it otherwise.

The problem as put by the MythBusters is good and the answer is yes. Other attempts to get around it by changing the problem or bringing up things that are not physically possible are simply attempts to rationalize initial bad answers - aren't they????

Ben

Shoe

Ben,

I think we're converging on common ground. One point of my original post was to suggest that there is a mechanism that would allow a treadmill to exert a force on an airplane's wheels even in the absence of rolling friction. Without rolling friction, any force the treadmill exerts on the wheels will simply cause them to rotate faster (quantitatively, the angular acceleration of a wheel will be equal to the force exerted on it by the treadmill times the wheel radius divided by the wheel's moment of inertia about its rotational axis). As long as the wheel has some finite moment of inertia (and even wheels without rolling friction have to have a non-zero moment of inertia), the wheels won't instantaneously accelerate to infinite speed as has been suggested, they will just accelerate at some finite rate.

If you had an "agile treadmill", and you used feedback control to modulate its speed very precisely, I think you could keep an airplane in place (or VERY nearly in place) until the treadmill reached its top speed (or the wheels flew apart). I'm not suggesting some unrealizable hypothetical treadmill, but something that could actually be built. This treadmill's behavior would be considerably different than the treadmills suggested in some earlier posts. If you were to put an airplane on the treadmill and give it a steady push, the airplane would NOT move forward. Instead, it would remain in place while pushing back at your hand with an equal and opposite force. In order to keep the plane in place, the belt would be accelerating. If you pushed harder, the belt would accelerate faster, but the airplane wouldn't move. Yes, at some point you would reach the treadmill's top speed, but until then the airplane would stay in place as you pushed on it. No physical contradictions required to build such a device.

Again, thinking in reverse, if you were to hold the airplane in place as you accelerated and decelerated a treadmill, you would need to exert a range of forces on the plane to keep it from moving. From this point of view, there is nothing mysterious about the treadmill exerting a force on the airplane.

Shoe

andrew66

mythbusters forgot that ground speed is only used for flight planning and trying to stop with sufficient runway left (landing) as i stated b4 that its the relative wind and airspeed that makes the plane fly. Kinda funny how that spinny thingy in the front (prop) kinda works on the same principles as the wing. the belt doesnt affect this. so they really didnt need to do the experiments. basic knowledge of aerodynamics could have told them what was going to happen. but i guess they had fun and people watching probably enjoyed it, so it wasnt a complete waste of time

Phlip

Shoe, this is actually the best description that I have seen of where somebody with your point of view is coming from. The only problem that I see with it is that there is nothing in the original problem that says the conveyor belt holds the plane stationary. It only says that it moves backward at a speed equal to the plane's forward speed. As you said before, given those conditions, the problem is a no-brainer. What plane with wheels can't take off with a ground speed equal to two times its air speed? It just has more ground pass under it in the time it takes to take off.

15thAF

I'm not suggesting some unrealizable hypothetical treadmill, but something that could actually be built.

But, in fact, you are suggesting an unrealizable hypothetical treadmill - you are restating the problem so that the issue becomes 'can a treadmill be built that can exactly match the speed of the wheels' and the answer is "No". A feedback control system, by definition, reacts to the error between the process variable and the setpoint. Are you also going to restate the problem such that the wheels are not allowed to accelerate? The control system can only react to the acceleration - it cannot magically predict that acceleration is about to occur and instantaneously match it. If the wheels accelerate, the airplane has moved forward. If you can build a control system that can do so, you will become very wealthy in the process controls industry. Until that time, you are suggesting an unrealizable hypothetical treadmill.

Shoe

That's why I said the treadmill would hold the airplane "very nearly in place". Yes, there would need to be some position error for the treadmill to respond, but with an "agile treadmill" you could make this quite small. The point is not to hold the airplane exactly in place, but very nearly in place... in the same way that the thermostat in your house keeps it very nearly at constant temperature.

I just think this is the more interesting statement of the problem. It makes you wonder if you could hold an airplane "in place" with a treadmill. I think you could with the right treadmill (until you hit some limit such as max belt speed, or wheel strength). Many other statements of the problem (like the one addressed by the Mythbusters) are really no-brainers.

Sport_Pilot

So what! Half my Calculas and physics test questions were not real world either. It's just fun to discuss. So it's not nothing to discuss.

Sport_Pilot

Unless the brakes are locked wheel friction would be very low, their would be almost noting holding it back.

propbuster

My Feedback: (1)

Am I missing something here or what? Why the heck would the airplane care what the wheels are doing, the Prop acts like a screw in the air and pulls it foward. It's AIR speed that make it take off not ground speed.

rmh

Shhhh!
I said that once and got yelled at ! It's true -of course - the entire question is a canard

Ben Lanterman

Dick you deserve to be yelled at most of the time :-)

Shoe, I finally see what you are talking about. I think the thing is that the aft force from that phenomena can be negated in real by having a wheel with an extremely low moment of inertia, low weight, etc. Since we might consider this in theory, make the wheel massless with zero inertia. Then it has no input other than friction due to the tire/belt interface due to airplane weight and that does have a definite limit that is usually small compared to the power available. Then the belt is in a catchup mode.

The original problem was stated such that the wheel motion phenomena wouldn't be a part of it. They just wanted to trick the viewer into thinking the motion on the treadmill is to be considered like the rolling motion of a car (which is what most viewers would do) and see if the reader would think of them (car and airplane) as being the same.

Since the propulsion comes from different sources the results are what we see, the airplane can take off.

Ben

habendanio

Do you guys realize that the heads in your hardrives fly across the platter. They are tethered to the control arms but the platter spins at thousands of RPM creating a cushion of air for lift. If you ever get a big treadmill to spin fast enough to hold an airplane against its thrust it would probably just lift from the ground effect.