Physics of flight: Plane on a treadmill

[Buddy Spike]

The rudder thread somewhat reminded me of this from another board.

I read it on a car message board sparked from another message board.. Anyway, it made about 400 replies (some of which were absolutely clueless), almost all were from those without a background in aviation, but some were from engineers / physics nerds.

So here's the question:

A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

Will the plane take off? Will it be able to run up and take off?

I believe this was the original thread:

http://community.discovery.com/groupee/for.../7451937218/p/1

This is the thread I'm referring to, but I believe you have to register to post:

http://www.ls2.com/forums/showthread.php?s...ll&pagenumber=1

They're basically the same discussion though.

Discuss.

[ 29. November 2005, 06:43: Message edited by: CrashA10 ]

[Toro]

Plane won't take off. There is no airflow over the wing and therefore no lift.

[USMCAirWinger]

Last time I checked the wheels are independent of the source of thrust. Just imagine that being applied to an f-15 on AB T/O. At the end you may exceed the wheels rotational speed but that bad boy is moving foward.

[Guest MATTUSAF]

This seems like a ridiculous discussion but for some reason I can't keep from posting.

Okay, the conveyor only affects wheel speed right? Our engines will control airspeed. So the jet would still actually move forward on the runway. If the conveyor matches the plane's ground speed as it rolls down the runway the plane should still take off, only with the wheel speed being twice as fast as the airspeed.

So as long as the wheels/tires don't fail from exceeding max wheel speed I think it would still take off.

I was just checking the specs on the endline for the rotory...gurter...I'm retarded.

[USMCAirWinger]

Well, if there's no ground speed and in this case no airflow over the wings there's no lift.

However, this experiment seems impossible to produce due to the high speed required by the belt. Even then, just imagine this on a small scale. Get on a treadmil with rollerblades on and have your buddy push you from behind. I bet you that it wont take a lot to get you moving foward. In other words there wont be enough resistance caused by the free-spinning wheel to keep an airplane from moving foward.

[Rocker]

Huh? The runway is moving opposite of the airplane and no matter how much thrust is applied, the runway just moves by quicker while the relative speed of the aircraft stays zero. In fact, the airspeed indicator would read zero. And what happens at zero airspeed? Certainly not takeoff. Toro's right. UNLESS they have thrust vectoring. It doesn't say that though.

[USMCAirWinger]

All I'm saying that in theory seems to defy the laws of physics and I’m not talking aerodynamics here.

Just answer this. At what speed will the conveyor have to go (taking into consideration the wheel's small resistance, and the fact that the aircraft is yet to experience any form of aerodynamic drag) in order to counter lets say 23,770 Lbs of thrust.

I'm not an engineering major but I will assume that the resistance from a spinning wheel has to stabilize itself at certain point. Therefore no matter how fast the thing is moving; the net force countering the airplane's forward motion will become steady after X many rotations. After this point it will be a matter of the wheels not falling apart and the airplane’s thrust countering this resistance.

[Guest Willy]

Okay, the conveyor only affects wheel speed right? Our engines will control airspeed. So the jet would still actually move forward on the runway. If the conveyor matches the plane's ground speed as it rolls down the runway the plane should still take off, only with the wheel speed being twice as fast as the airspeed

Thats the right answer. The reason this was asked on a car forum is that they are thinking cars where forward momentum is provided by tires (the same thing being countered by the conveyor belt). At any rate, the jet isn't taking off without airflow.

[USMCAirWinger]

That was a lot easier than trying to explain rolling resistance. I was about to bust the formula out.

HP= C W __V__

375

[ 29. November 2005, 08:22: Message edited by: USMCAirWinger ]

[BFM this]

The author of the above question has either come up with a very debatable riddle or has a mental model of airplane thrust that is the same as automobile thrust.

A conveyor could not keep a thrust producing craft from achieving a forward vector. Only tie down chains anchored behind the conveyor could do that. (Unless it was an AIR conveyor (windtunnel)) USMCAW has it there. The conveyor control is moving a speed, not as a function of friction (not mentioned). The only thing that a conveyor could accomplish would be to make the rotational velocity of the wheels twice that of the airplane's velocity.

Makes me wonder if the author wasn't writing a riddle a la "which way would a rooster's egg roll off the farmhouse roof?": IE that a pilot should know that takeoff speed is achieved independent of wheel rotation (watch your nosewheel limiting speed during a SEGo with a tailwind).

[ 29. November 2005, 08:18: Message edited by: BFM this ]

[Guest txaggie_99]

A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

This shit just seems silly, but I couldn't help myself. OK...since this is all based on hypotheticals, it seems we are to assume the conveyor can match the speed of the aircraft should full thrust be applied (thus creating forward movement). Now, with thrust applied, the aircraft will begin movement at which time the conveyor will move matching the forward energy of the aircraft. Seems to me no actual forward movement and any forward energy is expended through the gear's interaction with the conveyor....no forward movement, no airflow, no lift....ain't flyin'...unless it's a Harrier as CH pointed out.

Way too early for that much thought

[Guest mo7stanley]

Plane won't take off because there is not enough airflow over the wings. The plane would not be moving forward. However, if it was a propeller driven aircraft with a big enough engine and a big enough propeller, it could possibly take off. The reason is because of the slipstream which is created by the propeller makes some wind flow over part of the wings, creating lift. However I don't think there is a plane that can do that. If there was a strong headwind a Piper Cub could do it.

I have heard of guys having competitions on windy days to see who could take off fly backward and land on the same runway in the shortest amount of time.

[USMCAirWinger]

I find it hard to believe that accomplished aviators certified by the FAA and US military are getting their arses kicked by this basic question lol

[Guest CrashCB18]

Granted, I'm not a rated pilot, but let's say this idea was tested. Wouldn't the easiest answer be to look at your KIAS dial? Well, even if the wheels were rolling, your KIAS dial would show the amount of airflow going over your wings thus how much lift your wings would produce. Of course this was already said earlier.

Going off of that, I remember a theoritical question asked back in the days of college... A closed system involving a wing inside a closed box with its own air cycle. This source of air movement inside the box and over the wing produced enough airflow for the wing to create lift. However, since there is no air taken from outside the system/box, would the box fly?

EDIT: Spelling

[ 29. November 2005, 13:03: Message edited by: CrashCB18 ]

[USMCAirWinger]

I would say no. Due to fluid dynamics and getting into a vortex ring state (helo dudes can expand on this)

[Guest SuperStallionIP]

Think of the whole escalator or moving walkway in an airport, then try walking in the opposite direction on that escalator or moving walkway. If it could match the speed you could run, then you will have net zero movement in that point in space. Try it next time you fly commercially.

[Rocker]

What happens when you push the throttles up on the ground? The aircraft moves forward. If the aircraft is resting on a big hypothetical conveyor belt that is programmed to match the aircraft's groundspeed in the opposite direction, at the instant the aircraft would start to move forward, the conveyor belt would start moving in the opposite direction under the wheels, and accelerate at exactly the same rate. There is no torque to the wheels here, which is why I think people are getting their brains twisted. It's all thrust, so assuming there is no friction, and by the control of the thrust provided by the engine(s), the aircraft won't move an inch because the conveyor is moving exactly in the opposite direction at the SAME speed. It's like in Tom and Jerry, when Tom the cat runs really fast on a long rug to chase Jerry or something but doesn't go anywhere - the rug just moves under his feet and piles up behind him. Imagine the rug was a big conveyor belt and instead of Tom, it was an aircraft. The only real difference is Tom is applying torque directly to the rug. If he had a rocket pack and rollerskates, it'd be the same effect (though the rug would have to be set up to move on its own, like this hypothetical conveyor belt is). Because in this hypothetical situation the belt matches the speed of the aircraft exactly, it would be impossible for the aircraft to move at all. The relative speed would be huge, twice whatever it would be on a normal runway. But the only way you can get any movement is if the conveyor belt couldn't match the movement of the aircraft (either too much or too little).

How about a conveyor belt going with the aircraft? Let's say it matches exactly whatever forward movement the aircraft makes in the SAME direction? Then the aircraft would accelerate at twice the rate, and take off roll would be half (no wind).

[dmeg130]

I think everyone agrees that airspeed is required to takeoff... the issue the engineer nerds had was if the conveyor matters at all. Their mistake is assuming the wheels are frictionless once the static coefficient of friction is overcome and start rolling.

Imagine an LC-130 on an ice runway. When you run the engines up, it overcomes the friction on the ice and starts moving. If you retard the throttles, the plane should (theoretically) keep moving at its current velocity. However, it will eventually slow down even with a minimal amount of friction (and drag).

The friction in the wheels doesn't "go away" just because you start rolling. The total amount of drag created by the wheels rolling on the conveyor would counter the thrust and keep it stationary. Ergo, no go. It would take one helluva blown wing to make stall speed < 0!

[Guest ericvano]

MattUSAF and Willy had the right answer, I think.

The plane WILL takeoff. Think about it this way. The thrust from the engine will move the plane forward, the conveyor belt will spin the wheels the opposite direction, but as long as you assume that the friction of the wheels will be negligible on the plane, and the pilot doesn't apply brakes, the plane will still move forward and gain enough airflow over the wings to create lift. The wheels should still spin freely, meaning the conveyor belt will have no effect when it comes to keeping the plane from moving. The conveyor belt will only affect how fast the wheels spin.

[USMCAirWinger]

Are you guys kidding me.

This isn't that complicated.

Imagine you were doing a touch and go on the same conveyor belt at 60KTS.

Will you stop automatically?

Will the aircraft slowdown until stopping (with an equal amount of thrust)?

Or will the aircraft be able to perform its touch an go...only that now the tires will be spining at twice the speed.

Last time I checked airplanes don't produce or transfer their thrust via the tires.

[slacker]

It will fly. The wheels will spin at twice the takeoff speed but the plane will fly.

Don't be confused with walking against a escalator or a car on a treadmill because your legs or the cars wheels movements are being negated by the movement of the treadmill-not so with an aircraft.

Experiment 1

tie a rope to your friends truck and around your waist, put on rollerblades and stand on a treadmill. Everything is static- truck in park, treadmill off. Turn on the treadmill to 5 mph, do you go off the back? no because a force outside of your wheels is "holding" you on the treadmill. Turn the treadmill up to 20 mph, your still there with your rollerblades spinning. Have your buddy put the truck in gear and see what happens- you get pulled off the front of the treadmill.

Experiment 2

Find a big ass treadmill and turn it up to 100 mph. now taxi an aircraft to the edge of the treadmill and just put the nosewheel on the treadmill and the mains on the surrounding ground. What happens? the nosewheel is spinning and the mains are sitting on the ground. push up the power and what happens when all the wheels hit the treadmill?

All you have to overcome in order for the plane to fly is the wheel friction. Can you push a 152? how much force do you need to push it? 60-70lbs? so it take 60 lbs of force to overcome the wheel friction. well if a prop produces 700lbs of thrust for the 152 what happens to the other 640lbs of thrust? it generates forward movement of the airframe regardless of the wheels. So if takeoff speed was 100kts the treadmill would be spinning at 100kts the other way and your wheels would be spinning at 200kts. Thrust is independent of the force the treadmill will exert on the wheels.

take a hot rod on too a frozen lake and floor it. what happens? no movement because the wheels are spinning like crazy. Take a plane on the same frozen lake and push up the power, what happens?

[BFM this]

More too the point: those that regularly use the parking brake in a Cessna 172 know that yes, it will keep the plane from rolling all over the parking ramp, but plenty of embarrased pilots out there can attest that said parking brake will not prevent taxi and even take off.

Take the parking brake off, and you could get that hypothetical conveyor moving at mach-snot with a tailwind and a running start, you're still not going to prevent that plane from achieving takeoff velocity. At least until the rubber separates from the wheels, the rims disintegrate and it all comes cartwheeling to an end.

[BFM this]

Originally posted by BigIron:

Think of the whole escalator or moving walkway in an airport, then try walking in the opposite direction on that escalator or moving walkway...

But that depends on my feet (thrust) interacting with said walkway (conveyor). If we separate those two conflicts of interest, say by putting on roller blades and strapping a rotax engine and prop to my back, I could run up and down those moving walkways all day. The only difference being that in one direction , I'd be moving at 10 mph, while my wheels would be spinning 8 mph, and in the other direction I'd move 10 mph while my rollerblade wheels spun at 12 mph.

[Rocker]

Yeah, but take a look at the original question:

A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

As soon as the plane starts moving (actual movement, not relative movement), the conveyor belt moves in the opposite direction. No amount of thrust will make the aircraft actually move, if the conveyor belt matches exactly the aircraft's actual speed in the opposite direction.

Shit, you know what? The more I sit here thinking about this, the less sure I am about it. Good points above, slacker. I'm going to stop thinking about it for awhile so I can continue to believe I'm right...

[Guest kottlows]

You can look at this two ways:

1. There IS kinetic friction in the wheel bearings:

The conveyor speed will be so great that the friction in the wheel bearing will equal the thrust of the engine; no speed relative to the ground and no take-off. Unfortunately those bearings will have to be damn strong and cooled somehow because you are disipating the energy from the thrust via heat from the friction. To enforce the above, keep in mind that friction is linear like drag; more speed=more friction/drag. Thus it is possible to counter all the thrust from the engine.

2. There IS NOT kinetic friction in the wheel bearings (frictionless):

There is nothing to match the thrust in the opposite direction, thus because of action-reaction the plane WILL move realative to the ground, gain airspeed and take-off. The treadmill is worthless if you negate friction.

That's my engineering nerd answer and I'm sticking to it!

-WARHAWK-

[ 29. November 2005, 15:52: Message edited by: Warhawk ]