Plane on a Treadmill

[NC Hokie]

I may be showing off my ignorance here, but I can't help but wonder...

Aren't the speed of the wheels and the speed of the aircraft equal as long as the wheels remain on the ground?

[Al Sayre]

Under normal circumstances they are, but the wheels aren't connected to the driving force, so on a treadmill, their speed is irrelevant to the aircraft speed.

[Major Lord]

Lt.,

The speed of the wheels in this scenario would be the speed of the treadmill plus the speed of the aircraft, if any. If the aircraft stood still, basically maintaining just enough thrust to stay in one place on the treadmill, the wheel velocity ( To be clear, the speed at which the bottom of the tire travels over the treadmill) would be that of the treadmill.

Major Lord

[N Harmon]

Lt.,

The speed of the wheels in this scenario would be the speed of the treadmill plus the speed of the aircraft, if any. If the aircraft stood still, basically maintaining just enough thrust to stay in one place on the treadmill, the wheel velocity ( To be clear, the speed at which the bottom of the tire travels over the treadmill) would be that of the treadmill.

Major Lord

And the paradox is that the treadmill will always match the speed of the wheels, which is to say for the airplane to have any forward speed then the speeds of the treadmill and wheels won't match...breaking the premise.

I agree......it is theoretically possible to spin the treadmill fast enough to keep the plane from flying.....but the question says it only goes as fast as the wheels move.  I don't think the 100 MPH that the treadmill is moving will be enough to keep a Cessna from flying!

If the treadmill is moving at -100 mph, and the Cessna is taking off, then its wheels are traveling >100 mph. But the problem says the treadmill matches the speed of the wheels so the plane taking off breaks the premise.

[NC Hokie]

Under normal circumstances they are, but the wheels aren't connected to the driving force, so on a treadmill, their speed is irrelevant to the aircraft speed.

So, if we disregard the wheels and have a plane doing, say, 70 knots on a treadmill moving at a speed of 70 knots in the opposite direction, what is the effective speed of the aircraft?

The speed of the wheels in this scenario would be the speed of the treadmill plus the speed of the aircraft, if any. If the aircraft stood still, basically maintaining just enough thrust to stay in one place on the treadmill, the wheel velocity ( To be clear, the speed at which the bottom of the tire travels over the treadmill) would be that of the treadmill.

What makes your situation any different that the original question?  You have a plane "maintaining just enough thrust to stay in one place on the treadmill," but the question postulates a treadmill that is maintaining just enough resistance to keep the plane stationary.  Isn't the end result the same?

[Eclipse]

My turn. 

I saw that Mythbusters and they didn't bust or confirm anything, since despite the assertion of the announcer, the "treadmill's" speed clearly did not match the aircraft's speed - you can see the aircraft physically move forward and continue to accelerate in the opposite direction faster than the treadmill was moving, as evidenced by forward motion.

http://www.youtube.com/watch?v=YORCk1BN7QY

1) An airplane flies because of the motion of air over the wings which creates lift.  Forward velocity is irrelevant to flight except in that the physics of an airfoil require "x" air at "x" speed to pass over to provide lift.  The only way to get that amount of air is forward motion of the aircraft, which is caused by the propeller pulling it forward.  The propeller does not provide lift air over the wings, only forward velocity.

2) In the right theoretical conditions, a given airplane, especially one like a Cessna, could "hover" with a headwind balanced to the power of the engine.  Any discussions that involve vacuum are irrelevant because an aircraft cannot fly in a vacuum.

3) An aircraft tethered to the ground with a source (i.e. huge fan) of air pressure high enough could be made to hover in place with no forward velocity.

4) Any device which impedes forward velocity and thus prevents air from flowing over the wings, would prevent the aircraft from flying.

Thus, the aircraft would not fly, if properly situated on a treadmill which prevented it from achieving forward velocity.

[vento]

^^^ I agree with what Eclise said above, makes sense.
To quote myself in an earlier reply... 

Why is this whole thing so complicated?

A plane will lift off at the specified AIR speed based on weight and balance. As far as I know, air speed is the speed of the air flowing thru the wings. If the airplane is running really fast on a treadmill, then the ground speed could be really fast like say 100 knots, but the air speed is still zero.

The only way an airplane will lift off while on a treadmill is if the airplane and the treadmill is pointed into a strong headwind with a wind speed equal or greater than the air speed required for lift off. 

[SilverEagle2]

I agree with what Eclipse said above, makes sense.

Which really scares me.

The only time a treadmill impedes the forward velocity of the plane is when the speed exceeds the ability of the bearings in the wheels to overcome the friction interior to the bearing. By design, this friction coefficient is many times less than the velocity the plane requires to be air born. The only reason for wheels on planes in the first place is to reduce the friction of the plane on the surface for the plane to become air born and to make it more pleasant on the plane and passengers when the plane lands.

Heck, lets put a plane that requires only 50 knots airspeed to fly on floats and put it in a river flowing in the opposite direction (a pseudo treadmill) at 50 knots. Who cares that the friction of the water passing the floats is far more than tires on a treadmill.

With the planes prop not turning, the plane will float down stream. Turn on the engine and with little effort, the plane will be up on the step of the floats and will then look as though it is sitting still in the water relative to a fixed observer on the shore, effectively balancing the force of the thrust against the friction of the water passing under the floats.

Go full power and it will accelerate. As it gets to 50 knots AIRSPEED it flies. The floats however feel as though they are running though the water at 100 knots (50 from the current, 50 from the forward motion of the plane......equal).

If your explanation above were true, then any plane that needs only 50 knots to fly that is landing at 100 knots would simply stop the instant it hit the ground rather than rolling 1000+ feet to a stop. And that is with the engine at idle.

So where, in a world where the wheels on a plane are FREE SPINNING, does it state that the treadmill is impeding the forward velocity of the plane?

The speed of the wheels (which is matched by the treadmill as stated in the problem) has no required dependency on speed of the plane. They just happen to correlate when the plane is rolling down the runway before take off. Once off, no correlation at all.

A plane in flight with the wheels retracted has a wheel speed of 0. Get them hanging in the slipstream and they may turn a little but not much. So here we have a plane in the air with the wheels not turning.

For those that are stuck on the idea that wheel speed and forward velocity of the plane are related, planes should be falling out of the air all over.

[Eclipse]

I agree with the wheels part of this - they are irrelevant, so the treadmill itself is really a red herring. I would think someone with "skillz" could create a computer model that would prove it once and for all.  Forward velocity has to be completely blocked for this to be a proper test.

But I don't agree on the water, or anything else which impedes forward velocity.  However you prevent forward motion, whether the ground equals the plane, the water equals the plane, or the plane is sitting on ice, as long as the aircraft cannot achieve forward velocity, and thus air pressure over the wings, it will not fly.

Anything that allows the airplane to attain forward velocity, means your test isn't working properly.

Absent the velocity necessary to induce the air pressure, or artificially induced air pressure (big fan), an airplane is not going to just
pop up in air because the prop is spinning.

[SilverEagle2]

OK, what makes a wheel spin on a plane that is on the ground?

Forward Velocity.

If then a plane is on the ground rolling because of forward velocity, causing the wheels to spin, what would be the effect of the treadmill matching the spin speed of the wheels. A doubling of the wheel spin rate. So a 50 knot Vr would simply mean that the wheels were spinning at 100 knots.

If no forward velocity, then no wheel spin then no movement of the treadmill. Of course it won't fly. It is no different than a plane sitting on the runway.

But to satisfy the question in the problem, it has to include forward velocity in order to get a wheel that is spinning for the treadmill to match.

So any model that does not include a forward velocity component is simply showing a plane sitting on a treadmill with zero motion. I can model that any day.

[Major Lord]

Once again, the original question:

" Imagine a plane sitting on a giant conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"

The hypothetical does not state that the airplane cannot move forward, only that the speed (rotation) of the wheels is exactly matched by the treadmill. No one is arguing that the airplane will fly without forward motion into the wind.

Major Lord

[lordmonar]

My turn. 

I saw that Mythbusters and they didn't bust or confirm anything, since despite the assertion of the announcer, the "treadmill's" speed clearly did not match the aircraft's speed - you can see the aircraft physically move forward and continue to accelerate in the opposite direction faster than the treadmill was moving, as evidenced by forward motion.

http://www.youtube.com/watch?v=YORCk1BN7QY

1) An airplane flies because of the motion of air over the wings which creates lift.  Forward velocity is irrelevant to flight except in that the physics of an airfoil require "x" air at "x" speed to pass over to provide lift.  The only way to get that amount of air is forward motion of the aircraft, which is caused by the propeller pulling it forward.  The propeller does not provide lift air over the wings, only forward velocity.

2) In the right theoretical conditions, a given airplane, especially one like a Cessna, could "hover" with a headwind balanced to the power of the engine.  Any discussions that involve vacuum are irrelevant because an aircraft cannot fly in a vacuum.

3) An aircraft tethered to the ground with a source (i.e. huge fan) of air pressure high enough could be made to hover in place with no forward velocity.

4) Any device which impedes forward velocity and thus prevents air from flowing over the wings, would prevent the aircraft from flying.

Thus, the aircraft would not fly, if properly situated on a treadmill which prevented it from achieving forward velocity.

How would the treadmill impeed forward motion?  That is the crux of the problem.

[Eclipse]

How would the treadmill impeed forward motion?  That is the crux of the problem.

It actually prevents it, and causes the airplane to be moving virtually backwards.

Picture this:

Run the treadmill without a motor on the plane.
The plane would move backwards until it hit the end of the runway - no flight.

Engage the engine to the point of equilibrium to the treadmill and the aircraft would stand still - no flight.

Increasing the throttle to exceed the speed relative to the treadmill (as they did on Mythbusters) causes pressure on the wings  - flight - but negates the terms of the test.

You can't compare this action of the aircraft on the ground to it in the air - once airborne, the assumption is a balance of forward velocity and air pressure for lift, but in order to attain that forward velocity, the aircraft has to break gravity, friction, and inertia in order to get the
air moving over the wings in the first place.

The net effect of the treadmill is negative forward motion, thus no lift.

Here's another example - an aircraft can take off from a carrier because it is pushed from behind hard enough for the air pressure to increase enough to lift the airplane (and anyone who has watched a launch knows it's usually right at the edge of stalling).

If the carrier was able to move at the same speed as the steam trolley (in the opposite direction), there would be no actual forward motion of the aircraft, and the plane would just drop into the water like Wile E. Coyote.



Now one question I'd have about a jet is whether its takes off based more on Newton's law of motion vs. a prop plane which
gets its velocity from Bernoulli's principle. If its the former, then forward motion is more like a rocket than a plane, and I don't know whether that makes a difference to this discussion, since rockets don't really "fly" in the Bernoulli sense.

[vento]

If no forward velocity, then no wheel spin then no movement of the treadmill. Of course it won't fly. It is no different than a plane sitting on the runway.

But to satisfy the question in the problem, it has to include forward velocity in order to get a wheel that is spinning for the treadmill to match.

I think we are having a violent agreement or disagreement of some sort. We both agree that AIRSPEED is what makes an airplane fly, no questions here.

I also agree that forward velocity is needed to move the wheels and make the whole airplane move. What we don't seem to agree is that I think the treadmill that the OP proposed will counteract whatever forward velocity there is. So we will have an airplane with the wheels spinning really fast but the plane is in the same spot (Zero ground speed) and it will not fly. This is quite different than your idea of being the same as the airplane sitting on the runway.

That's why I think, the airplane will only fly (float, or lift off, or whatever we call it) if it is pointed into a headwind of equal or greater wind speed than it's required Vr AIRSPEED. The headwind blowing across the wind surface is what creates the lift for the plane to fly, not the speed the wheel is turning. And I think we also agree on this by reading from different segments of your post.

The major disagreement among all of us, is the effect of the treadmill. Some try to explain that the treadmill will never match the airplane in motion and therefore the airplane will eventually accelerate and move forward from the spot of the treadmill, while some argue that the airplane would remain in the same spot, some think differently if in the vacuum, etc. I simply took at as the force that counteracts against the forward movement of the plane and thus keeping the airplane at ZERO GROUND speed regardless of how fast the wheels turn.

My two cents worth...  :angel:

[FW]

^ I agree.  Unless there is a head wind exceeding Vr, the aircraft will not fly.  Case in point.  I recently watched a Gulfstream taxi a little to close in front of a stationary C172.  It was the first time I saw a Cessna go Vertical..... Enough hot air and, up it goes.

[SarDragon]

Now one question I'd have about a jet is whether its takes off based more on Newton's law of motion vs. a prop plane which
gets its velocity from Bernoulli's principle. If its the former, then forward motion is more like a rocket than a plane, and I don't know whether that makes a difference to this discussion, since rockets don't really "fly" in the Bernoulli sense.

Huh???

The aerodynamics of flight are essentially independent of how an aircraft acquires its forward motion to generate lift.

Propulsion

A. Prop plane - big fan in the front (or back - B-36, C-337) drags the plane through the air fast enough for the wings to produce lift

B. Pure jet - suck, squeeze, bang, blow; hot combustion gas pushes on the back of the power turbine and pushes the plane through the air fast enough for the wings to produce lift

C. Turbofan - a combination of A and B above.

D. Rocket - B minus the suck and squeeze, has its own fuel and oxidizer; hot combustion gas pushes on the forward end of the combustion chamber and pushesthe plane through the air fast enough for the wings to produce lift

Now let's talk about airframes.

1. Airplane - wings sticking out the sides, with additional airfoils as needed to maintain control (V-stab, H-stab, etc); may be propelled by A - C-182, B - F-4, C - B-747, and the all important D - X-15. Yes- it is an airplane, because you can fly it just like the other three examples.

2. Rocket - wings (fins) in the back for stability; 2.75 FFAR, point and shoot, unguided (ballistic)

3. Missile - wings (fins) in the back for stability and control, and possibly vectored thrust from rocket style propulsion; Saturn V, not usually controlled in flight by the people flying in it

Move a wing fast enough through the air, and it will generate lift. It doesn't matter what the motive force is.

Fling-wings are left of another discussion.

[Eclipse]

My point was that an airplane won't fly without a wing, but a rocket can (since it doesn't really "fly") its just pushed forward really fast and hard.  Bernoulli has little to do with rockets you don't care about steering.

[lordmonar]

It actually prevents it, and causes the airplane to be moving virtually backwards.

Picture this:

Run the treadmill without a motor on the plane.
The plane would move backwards until it hit the end of the runway - no flight.

Okay...I agree with this. As the treadmill moves back....the aircraft offers it no resistance and so the wheels stay stationary and the entire planes moves to the back with the treadmill.

Engage the engine to the point of equilibrium to the treadmill and the aircraft would stand still - no flight.

Increasing the throttle to exceed the speed relative to the treadmill (as they did on Mythbusters) causes pressure on the wings  - flight - but negates the terms of the test.

Nope.....it illustrates the exact point of the test.  People think that a plane is a car.  That the interface between the ground and the wheels is as important to the plane as it is in a car.

You can't compare this action of the aircraft on the ground to it in the air - once airborne, the assumption is a balance of forward velocity and air pressure for lift, but in order to attain that forward velocity, the aircraft has to break gravity, friction, and inertia in order to get the air moving over the wings in the first place.

The net effect of the treadmill is negative forward motion, thus no lift.

But the speed that you would have to move the treadmill to counteract forward motion of the aircraft would be astronomical which is defiantly a violation of the terms of the test.

Here's another example - an aircraft can take off from a carrier because it is pushed from behind hard enough for the air pressure to increase enough to lift the airplane (and anyone who has watched a launch knows it's usually right at the edge of stalling).

If the carrier was able to move at the same speed as the steam trolley (in the opposite direction), there would be no actual forward motion of the aircraft, and the plane would just drop into the water like Wile E. Coyote.

That is absolutely true....That is because the steam trolly is hardwired to the airplane and for that .02 seconds is the only source of thrust.  So if you are travelling over the water with a tail wind of 100Kts and the catapults shoots you forward at 100Kts your IAS will be zero, no lift, no flying, big splash.

But here is the kicker......it is because you simply pulled the runway out from under the plane.   In the plane on the treadmill test....the question is whether the ground of surface of the ground has any affect on the plane.  The answer is yes.  Friction will tend to slow the plane and resists its forward motion.  But the facts is because the wheels are specifiably designed to reduce this friction and allow the plane to travel over rough asphalt and other terrain.    Once the powerplant is running it will quickly over come the resistance of the bearings and the interface between the treadmill and the wheels and start moving forward.   

[DG]

My turn. 

I saw that Mythbusters and they didn't bust or confirm anything, since despite the assertion of the announcer, the "treadmill's" speed clearly did not match the aircraft's speed - you can see the aircraft physically move forward and continue to accelerate in the opposite direction faster than the treadmill was moving, as evidenced by forward motion.

Thus, the aircraft would not fly, if properly situated on a treadmill which prevented it from achieving forward velocity.

You don't get it.

Refer to the guidance hereinabove "The hypothetical does not state that the airplane cannot move forward, only that the speed (rotation) of the wheels is exactly matched by the treadmill. No one is arguing that the airplane will fly without forward motion into the wind."

[N Harmon]

OK, what makes a wheel spin on a plane that is on the ground?

Forward Velocity.

I look at it as the wheel is spun by a difference between aircraft speed and treadmill speed. After all, if the treadmill and airplane are traveling at the same forward velocity, the wheel speed is zero. Further, if the treadmill and airplane are both traveling backward at different speeds, you will have wheel spin.

Friction will tend to slow the plane and resists its forward motion.  But the facts is because the wheels are specifiably designed to reduce this friction and allow the plane to travel over rough asphalt and other terrain.    Once the powerplant is running it will quickly over come the resistance of the bearings and the interface between the treadmill and the wheels and start moving forward.

The question is can the power plant overcome the rolling resistance in the wheels at any speed? We can posit that if the treadmill were moving backward at a low speed, the aircraft could apply a small amount of thrust to remain stationary in relation to something not on the treadmill. Apply a little more treadmill speed, and you'd need a little more thrust to remain stationary. Rinse, repeat. At some point you're going to reach a limit. The thrust of the power plant is bounded, but the speed at which our theoretical treadmill can spin is not bounded.