Plane on a Treadmill

[N Harmon]

If you're in the pilot's seat, traveling at 50 knots in relation to the stationary ground (not the treadmill), and the treadmill is moving backward at a speed of 50 knots in relation to the stationary ground but 100 knots in relation to you,... then what speed would your wheels be at....

I need to think about this some more...

[Major Lord]

Nope, still wrong!  The aircraft is only incidentally rolling: it is primarily an object propelled through space by compressed air from the prop. The wheels are just dragging along at the speed of the aircraft Plus not Minus the treadmill speed. As the aircraft increases in speed to reach VR, the belt will increase in speed to match the speed of the wheels, but it won't dramatically effect the speed over ground of the aircraft. The presence of the observer is irrelevant. The model of this as a hamster running in a cage or walking in place on an escalator is just not accurate, these models only apply to operations on treadmills wherein the motion is imparted by the wheels ( or legs, in the above cases) rather than by being pushed by a frictionally unrelated power source.   In fact, I doubt you could even cause an aircraft at full power to stand static like this on a treadmill if you tried, since the rolling resistance is so slight, that any amount of throttle, high or low, would cause you to drift forwards or backwards.

Major Lord

[lordmonar]

If you're in the pilot's seat, traveling at 50 knots in relation to the stationary ground (not the treadmill), and the treadmill is moving backward at a speed of 50 knots in relation to the stationary ground but 100 knots in relation to you,... then what speed would your wheels be at....

I need to think about this some more...

The wheels move because the thrust of the aircraft is converted to rotation by the friction with the ground.

If the plane is stationary and held in place by rope....and the treadmill moves (V_c)...the wheels will turn...(V_b) thus V_b=V_c.  If The ground is stationary and the plane move V_w then the wheels will turn and give you V_b=V_w. 

That is how the wheels turn....and give you wheel speed.  The do not turn on their own.  They only turn when either the ground moves or the plane moves.

So basically the speed of the wheels is V_b=V_W+V_c

So the premise says....the treadmill moves at the same speed (but opposite direction) of the wheels V_c=V_b.  But if the ground moves that movement increases the movement of the wheels...which increases the movement of the ground...and so on...until in theory treadmill speed goes to infinity....even if the wheels only turn a fraction of an inch...so long as it maintains the initial speed then the treadmill will ramp up to light speed in a fraction of a second (assuming instantaneous feed back)....that is the problem with a positive feedback loop.  V_c=V_w+V_c

You cannot solve for V_c unless everything is zero. 

It is mathematically impossible.

It is practically possible....because there in always some lag in the feedback loop.  The speed of the lag will determine what will happen.  If the lag is slow....the airplane will get airborne and fly away.  If the lag is fast then the speed of the treadmill and the speed of the wheels will increase to a point where something will fail and break apart before the aircraft has enough air speed to get airborn.  If the lag is instantanious the threadmill goes to light speed and create a black hole and then just suck everything in and that will be the end of the experiment!

I think what our problem is.....is that we are reading too much into the premise.  The guy who wrote it was probably trying to see if people knew how an aircraft developed forward motion.  In a car you can do this treadmill thing because thrust comes from engine to the axle and then resistance between the tire and the ground pushes the car forward.  A treadmill moving backwards will absorb the energy (that is the law of conservation of energy) and the car will remain stationary.  If you are trying to catch people into not thinking where a planes thrust comes from....they would assume that if a car stay stationary then a plane must do so also.  But that is not the case.  A plane's thrust comes from the prop pulling on the air in front of it....or a jet/rocket directing its blast to the rear of the aircraft.  The treadmill has no effect on either of these things.  So the only affect if could possible have on the aircraft is through friction with the wheels.


Mathematically in can't fly.....but that is because the premise of the math equations is only solveable where the velocity is zero.  It is a faulty math problem.  In reality it will fly.  The wheels will freely turn no matter what anything else is doing.  The feedback lag will be slow enough for the plane to get airborn or at the very most something will explode in an orgy of sparks and burning rubber.

This reminds me of the old mathematics problem of the turtle that is 100M away from his home and covers half the distance between itself and home every second.....How long does it take him to get home.

Mathematically the answere is never....but in reality the distance is so small we just say "Lucy I'm home!".

Same thing here.  Mathematically we instantaneously spin the wheels to the speed of light and the universe comes to an end.....in reality the plane takes off and flies away, because a bunch of engineers made some good bearings and high strength rubber tires.

[Short Field]

This is a "How many angels can dance on the head of pin" type question.....

[lordmonar]

This is a "How many angels can dance on the head of pin" type question.....

That one is easy....measure the dance area of an angle.....measuer the area of the head of a pin....divide one into the other.....QED

[DG]

If you're in the pilot's seat, traveling at 50 knots in relation to the stationary ground (not the treadmill), and the treadmill is moving backward at a speed of 50 knots in relation to the stationary ground but 100 knots in relation to you,... then what speed would your wheels be at....

I need to think about this some more...

The wheels move because the thrust of the aircraft is converted to rotation by the friction with the ground.

If the plane is stationary and held in place by rope....and the treadmill moves (V_c)...the wheels will turn...(V_b) thus V_b=V_c.  If The ground is stationary and the plane move V_w then the wheels will turn and give you V_b=V_w. 

That is how the wheels turn....and give you wheel speed.  The do not turn on their own.  They only turn when either the ground moves or the plane moves.

So basically the speed of the wheels is V_b=V_W+V_c

So the premise says....the treadmill moves at the same speed (but opposite direction) of the wheels V_c=V_b.  But if the ground moves that movement increases the movement of the wheels...which increases the movement of the ground...and so on...until in theory treadmill speed goes to infinity....even if the wheels only turn a fraction of an inch...so long as it maintains the initial speed then the treadmill will ramp up to light speed in a fraction of a second (assuming instantaneous feed back)....that is the problem with a positive feedback loop.  V_c=V_w+V_c

You cannot solve for V_c unless everything is zero. 

It is mathematically impossible.

It is practically possible....because there in always some lag in the feedback loop.  The speed of the lag will determine what will happen.  If the lag is slow....the airplane will get airborne and fly away.  If the lag is fast then the speed of the treadmill and the speed of the wheels will increase to a point where something will fail and break apart before the aircraft has enough air speed to get airborn.  If the lag is instantanious the threadmill goes to light speed and create a black hole and then just suck everything in and that will be the end of the experiment!

I think what our problem is.....is that we are reading too much into the premise.  The guy who wrote it was probably trying to see if people knew how an aircraft developed forward motion.  In a car you can do this treadmill thing because thrust comes from engine to the axle and then resistance between the tire and the ground pushes the car forward.  A treadmill moving backwards will absorb the energy (that is the law of conservation of energy) and the car will remain stationary.  If you are trying to catch people into not thinking where a planes thrust comes from....they would assume that if a car stay stationary then a plane must do so also.  But that is not the case.  A plane's thrust comes from the prop pulling on the air in front of it....or a jet/rocket directing its blast to the rear of the aircraft.  The treadmill has no effect on either of these things.  So the only affect if could possible have on the aircraft is through friction with the wheels.


Mathematically in can't fly.....but that is because the premise of the math equations is only solveable where the velocity is zero.  It is a faulty math problem.  In reality it will fly.  The wheels will freely turn no matter what anything else is doing.  The feedback lag will be slow enough for the plane to get airborn or at the very most something will explode in an orgy of sparks and burning rubber.

This reminds me of the old mathematics problem of the turtle that is 100M away from his home and covers half the distance between itself and home every second.....How long does it take him to get home.

Mathematically the answere is never....but in reality the distance is so small we just say "Lucy I'm home!".

Same thing here.  Mathematically we instantaneously spin the wheels to the speed of light and the universe comes to an end.....in reality the plane takes off and flies away, because a bunch of engineers made some good bearings and high strength rubber tires.

Ahhhh......,

were you doing undercover work, in Mendocino County?

[N Harmon]

So basically the speed of the wheels is V_b=V_W+V_c

So the premise says....the treadmill moves at the same speed (but opposite direction) of the wheels V_c=V_b.  But if the ground moves that movement increases the movement of the wheels...which increases the movement of the ground...and so on...until in theory treadmill speed goes to infinity....even if the wheels only turn a fraction of an inch...so long as it maintains the initial speed then the treadmill will ramp up to light speed in a fraction of a second (assuming instantaneous feed back)....that is the problem with a positive feedback loop.  V_c=V_w+V_c

Right, but from the perspective of the pilot V_w is always zero, right? I mean, unless the guy is walking to or from the lavatory, the relative velocity of the pilot and airplane is zero. Or are we missing something?

[lordmonar]

So basically the speed of the wheels is V_b=V_W+V_c

So the premise says....the treadmill moves at the same speed (but opposite direction) of the wheels V_c=V_b.  But if the ground moves that movement increases the movement of the wheels...which increases the movement of the ground...and so on...until in theory treadmill speed goes to infinity....even if the wheels only turn a fraction of an inch...so long as it maintains the initial speed then the treadmill will ramp up to light speed in a fraction of a second (assuming instantaneous feed back)....that is the problem with a positive feedback loop.  V_c=V_w+V_c

Right, but from the perspective of the pilot V_w is always zero, right? I mean, unless the guy is walking to or from the lavatory, the relative velocity of the pilot and airplane is zero. Or are we missing something?

I don't know where  you are going on this at all?

If you want to bring reletivity into this......okay....but why?

The airplane and the wheels will be pulled forward by the power plant as soon as it developes enough thrust to break the friction of the wheels.  The treadmill will not induce enough drag through the wheels to prevent the power plant from moving the airplane forward.

Reletive speeds and frames of references have very little do with the problem.

[N Harmon]

If you want to bring reletivity into this......okay....but why?

Woah. Don't blame me! The issue of relativity was brought up by SilverEagle2 at the end of page 6.  :angel:

[SilverEagle2]

My mistake. It was a long day of frustrating circumstances which led to the thought. It won't happen again.

The effective speed of the treadmill is increased by the forward motion of the plane. Adding the planes velocity to the speed of the treadmill, it will equal the speed of the wheel rotation.

But then that will be argued as invalid by those that say it is not matching the wheel speed despite the continued 1 to 1 distance of the tire rotating across the surface of the treadmill.

[Major Lord]

Those who would argue that the invalidity of the premise could  reread the beginning premise:

"The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction."

In the real world, both the airplane and the treadmill need time to accelerate, but the premise of the question shows us that the treadmill will adjust itself to the speed of the wheels, and so we accept that as a fixed factor. We cannot assume that the velocity changes of the treadmill and the wheels happens instantaneously, because that does not happen in the real world. The wheel velocity on the other hand, is for the most part, a direct function of the treadmill velocity plus the aircraft forward velocity, their inertia and friction is one of the limiting factors on the ability of the treadmill to change velocity.

Major Lord

[Brad]

Ok, my turn to join the masses of the yes people. That and post on this thing again after something like a year-absence, haha! (Had to update my signature entirely, not even an AEO anymore, heh)

Anyways, here's why it is yes, and this explaination probably has already been posted, but it's 3 am and I don't want to do math at this time of the morning.

Ok, as was stated before, airplane wheels are not directly powered. They only move because the prop pulls the plane forward and they move against the ground due to friction, electron repulsion on the atomic level, and invisible little green men :-P

So, let's say that the wheels are rotating at a factor of 10 kts. This hypothetical perfect treadmill is therefore instantly rotating at -10 kts relative to the same direction, since it's moving in the opposite direction. Ok so now the wheels will no longer be rotating since they have lost their rotational velocity. However since they don't directly influence the plane, they are just "support and cushioning", the plane will continue to accelerate by the action of the prop pulling the plane through the air. The treadmill will increase in speed to keep the wheels at 0 kts, but again this doesn't matter. The plane will continue to accelerate. Your wheels may leave skidmarks and may even burn off some, and the plane may end up with a higher VR, but once it reaches that VR, physics says lift will overcome weight to the degree that the plane will fly.

[a2capt]

Okay, if the airplane is stationary, absolute and the treadmill is going backwards suddenly at 60kts.

Is the air moving over the wings at 60 kts?

Thats the part of this I just don't get. The TV clip definitely showed the airplane moving forward. In which all they did was accomplish a really short field take off somehow.

Unless the power plant is run up at the same constant that the treadmill runs backwards, the airplane will not stay in the same place, and the moment it comes off the treadmill it has to go forward or it will just come back to the ground.

But again, the air flow has nothing to do with the treadmill movement.

[Flying Pig]

The myth busters episode had some serious flaws.  If the plane was on a true tread mill that equally matched the speed as the tires rolled, the airplane would not gain any forward airspeed.  Gents.....unless your a Harrier, a helicopter or an F-35, your not flying without forward airspeed.

Mythbusters used the argument that because the power of the airplane is not tied the the wheels like they are in a car, that it is possible for a plane on a treadmill to fly.  In that segment, the airplane was accelerating forward because the ground under the tarp they were pulling was still providing enough friction for the airplane to gain forward motion.  On a true treadmill, where the tread mill exactly matches the speed of the rolling tires, the plane would go nowhere.

[lordmonar]

Flying Pig.

The plane will move!  The power plant pulls the aircraft forward.  Unless the friction/drag from the tread mill is so great that it will counter act the thrust of the power plant it will move.

The way the OP question was posted....the treadmill only moves as fast as the wheels.

In that scenio it is either talking about speed of the rotating tire....in which you end up with a positive feedback loop that will quickly go to the speed of light (mathmatically) or it matches the speed of the axil as it moves forward...in which case...it is moving forward which implies air flow...and the plane will fly.

The other way the treadmill can move is in the same direction as the aircraft (keeping the wheels from turning).  In that case the airplane is still moving foward through the airmass, generating lift.

So....bottom line.  The only way to keep the plane from flying is to move the treadmill so fast that it overcomes the thrust of the engine.  The speed to do this would be much greater then the speed of the tires that the OP has stipulated in his original question......so one again....the plane will eventually overcome the drag from the treadmill and gain enough airspeed to take off.

[Short Field]

paraphrased from another site:   The airplane on a treadmill problem contains a basic ambiguity, and people resolve it one of a couple different ways. The tricky thing is, each group thinks the other is making a very simple physics mistake. So you get two groups each condescendingly explaining basic physics and math to the other. This is why, for example, the airplane/treadmill problem is a banned topic on some forums (along with argument about whether 0.999... = 1).

[ßτε]

Can anyone explain how the treadmill can exert any force on the airframe which can at all counteract the thrust developed by the powerplant/propeller?

That is going to be the only way that it can keep the airplane from flying.

By the way, be specific. If you say it is friction, be specific about the source, how it gets transferred to the plane, , the direction, and the magnitude.

[Major Lord]

There is really no ambiguity about it, other than those introduced by persons introducing completely theoretical factors. Wheels spinning to infinity, frictionless environments, changes in velocity occurring outside of time, etc. etc. One group is thinking like theoretical physicists, ardently arguing that bees can't fly, and if they do in real life, its merely because we engineers are too dumb to understand the physics, or that we gamed  the question and now duck the math. The other group sees the problem as just how it was initially posed, and the answer ( as is so often the case when the question is fully understood before seeking the answer) is that of course the airplane can take off. To take a liberty with the initial question, in the real world ( no vacuums, magic, frictionless loops, or Heisenberg uncertainties) could you possibly create a situation in which you could cause an aircraft ( or lets call it a propeller driven car if you prefer) to stand perfectly static on a treadmill as the power of the propeller thrust is increased? Not a chance. The lag time between treadmill response and vehicle thrust would cause some degree of fore or aft motion. How about this;  If you landed your plane on a treadmill that exactly matched the reciprocal speed of the wheels of the aircraft, would the plane instantly stop because the wheels were accelerating to the velocity of the treadmill? Nonsense.

BTE, No one can explain to you how the treadmill can exert the force necessary without using introducing a religious argument to do so.

The funny thing is in this whole durn organization of aviation enthusiasts we don't seem to have a single real aerodynamics engineer. We should all just join the Coast Guard Aux, cause fluid dynamics is easier with water than air......

Major Lord

[N Harmon]

This isn't an engineering question. It's a physics/logic question, and there is a huge ambiguity to it.

Can anyone explain how the treadmill can exert any force on the airframe which can at all counteract the thrust developed by the powerplant/propeller?

You asked this on page 6, and I answered it. As for being specific, which one would you like to discuss first?

[ßτε]

This isn't an engineering question. It's a physics/logic question, and there is a huge ambiguity to it.

Can anyone explain how the treadmill can exert any force on the airframe which can at all counteract the thrust developed by the powerplant/propeller?

You asked this on page 6, and I answered it. As for being specific, which one would you like to discuss first?

Yes I did ask before, but I have to admit that your answer did not actually answer my question. I really want to know how the forces can be exerted by the treadmill in such magnitude and direction to counteract the force provided by the propeller.