Physics of flight: Plane on a treadmill

[R-Dub]

Originally posted by slacker130:

It will fly...tie a rope to your friends truck and around your waist, put on rollerblades and stand on a treadmill.... 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?

Agreed. Good example, Slacker...taxi onto an ice patch, bring the aircraft to a complete stop, lock the parking brake, and run the engine up to redline...what happens?!?! You definately move forward. Wheel motion is completely independant of the relative airflow, but only when your thrust producer is independant of the wheels. Your thrust from your car is completely dependant upon coefficient of kinetic friction...aircraft thrust isn't.

Now, after this , it's time for a !

[Guest cbire880]

Its all about the friction. The big assumption is whether or not the friciton is limitless. In reality, friction has a limit. Think of pushing a box along the floor, you push so hard until it starts moving, then it suddenly becomes easier to move b/c you overcame the friction force. The airplane on the conveyor belt works the same way (albeit in a more complicated manner). When the thrust exceeds the rolling friction potential of the tire/ground (assuming no bearings, but that would just add another layer of force transfer), the airplane will start to accelerate. Generally at this point, your wheel/bearing will destroy itself and other bad things will happen, but its effectively the same as holding the brakes and waiting till the airplane skids.

Friction is linear to a point, but once you reach the limit, it becomes nearly constant. So, in theory you could prevent the airplane from moving, but you'd need some pretty badass wheels.

Like all engineering problems, it comes down to your assumptions...and we all know what happens when you assume.

[Guest mo7stanley]

After much deep thinking brain things going on inside my head along with the preponderance of the other deep thoughts and thinking of the people on this board, I have come to the conclusion that the guys who say that it will take off are correct.

[CrateOfThunder]

In most engineering problems, bearing friction is assumed to be negligible, therefore it is probably not really a factor here. I think the only real friction is between the wheel and the ground F= Normal x Coeff of friction. This is independent of velocity. Once an airplane gets rolling, it is past the static coefficient of friction and becomes realiant on the kinetic coefficient of friction. Therefore, an airplane capable of overcoming static friction on a stationary runway will be able to overcome it on a moving runway. It will take longer to accelerate to rotation speed but eventually the plane will take off!

[BFM this]

For all those that insist that this airplane cannot overcome the awesome force that this treadmill puts on an airplane, riddle me this:

If the airplane isn't moving (hasn't achieved any forward vector), how fast is the conveyor moving?

Airplane speed = 0

Conveyor speed = 0

Airplane speed = rotation speed in one direction

Conveyor speed = rotation speed in the other direction.

Wheels = rotation speed times 2

[ 29. November 2005, 21:10: Message edited by: BFM this ]

[Guest TomandFle]

Here's my theory, if anyone still cares enough to keep reading this thread.

The plane won't take off. Once the wheels are spinning, it's just like the plane taking off on a very, very icy runway (essentially a frictionless surface), EXCEPT...

the "icy runway" is moving backward at the same speed the plane moves forward. Still no relative wind, therefore no takeoff.

Can we have a vote please?

[Guest MATTUSAF]

Dude you guys are killing me. Think about this if the plane velocity = 0 then the treadmill velocity = 0.

So once the plane starts moving forward at 1 knot the tread mill moves backward at 1 knot.

Plane forward speed = 1 knot, plane wheel speed = 2 knots.

Then the plane and the treadmill will continue to accelerate at the same rate in opposite directions until Vrot.

[Guest egovolo]

Here is another thought. Replace the runway with an artificial river, and the aircraft on wheels with one on floats. The river somehow has the ability to sense the aircraft's forward movement and will adjust the water flow accordingly. If the aircraft moves lets say 1kt in relation to a fixed object on shore, the velocity of the river will also increase by 1kt. On the other hand, I think I'll just have another beer.

[ClearedHot]

Ok, I decided to settle this once and for all. I had a few beers last night and I went to the airport and jumped on the moving walkway going the opposite direction. No matter how fast I ran and how hard I flapped my arms, I did not take off, case closed.

[Guest rotorhead]

UNBELIEVABLE.

I can't sit back any longer.

The airplane WILL fly.

We need airspeed...to get that, we need to move forward...to do that, we need more thrust than drag. Easy.

Put a kids toy truck (with freespinning wheels)(representing your airplane) on a treadmill. Put your hand flat against the back of the truck (representing your engine, which is an outside force not connected to the treadmill, nor driving the wheels) and turn the treadmill on. Set the treadmill to 1 mph...your single hand will keep the truck from moving backward. Now speed the treadmill up to 10 mph,...your single hand will keep the truck from moving backward. With the treadmill at max speed, take your single hand and push the truck forward. Not too difficult, huh? Forward speed would give you AIRSPEED, and ultimately, lift. You could run the treadmill at 100 mph, and your single hand could push the toy truck forward.

All we need to do is overcome the drag of the wheels (tires, bearings, etc.) which you easily do every day (or you couldn't begin a takeoff roll).

Yes, taken to the extreme, there would perhaps be some huge wheel/treadmill speeds, and huge bearing heat, but that's for a geekier forum to calculate.

We flingwingers don't bother with these odd constraints like "forward airspeed" !!!! Sitting on the treadmill, our wings already have several hundred knots of "forward airspeed". Just raise the collective, and lift off of the stupid treadmill. ;)

[ 30. November 2005, 06:30: Message edited by: rotorhead ]

[slacker]

Originally posted by herk28:

The plane absolutely WILL NOT TAKE OFF!

The way the question is asked, it's basically saying the plane is on a TREADMILL. When you're on a treadmill, you go NOWHERE, thus there is no airflow over you. The plane in this question may be moving forward relative the conveyor belt that it is on, but relative to the rest of the world, it is NOT MOVING, thus NO AIRFLOW, thus airspeed indicator reads ZERO, thus NO Vrot.

You're relating it to you on a treadmill, it's completely different. You produce "thrust" through your legs and feet which the treadmill works directly against. An aircraft produces thrust independent of whatever happens to the wheels. Don't get fooled into think of this relative to a car or yourself on a treadmill, it's completely different. How about this, put a car on a treadmill and tie a chain to the car and to your buddy's truck. Put the car in neutral and start the treadmill slowly, what happens, the wheels spin and the car stays in the same position. Now run the treadmill up to 100mph and have your buddy put his truck into drive. I bet he doesn't even have to press the gas pedal to pull you off the front of the treadmill, because his truck is not being effected by the treadmill except to overcome your tire/bearing friction (which is minimal). It's the same with a prop or jet, the power plant has to overcome the wheel/bearing friction and that's it, the plane moves forward. The treadmill cannot effect the thrust of power plant thru the wheels of a plane.

The bigger question is if you put a plane equiped with skis on a nordic track cross country ski machine, will anyone give a f#ck?

[slacker]

Here's an article about the treadmill debate. Enjoy

avweb

[hindsight2020]

The 'other' forum had this thread go on for ages, I followed it until I got tired of writing a thesis to the non-believers, you guys probably saw the long a$$ thread and how it got out of control...Slacker your analogy is very similar to the one I gave early on the 'other' board, good choice :D

All that said,I love this thread here on baseops...the mere fact that currently rated AF drivers got hung on this one makes ME feel better about my non-selection letters, all the self-validation I needed :D

[BFM this]

Originally posted by slacker130:

Here's an article about the treadmill debate. Enjoy

avweb

"To borrow from Winston Churchill, never have so many argued so long and so hard over so little. "-Rick Durden, similar AVWEB artical about debate over flaps

[Guest Demeeta652]

It's basically the same as having a really strong tailwind on takeoff with an infinitely long runway if you think about it. Theoretically, the wheels provide negligible drag against the thrust of the engines, so why should it matter how fast they are rotating? Your engines are still pushing against a static air stream.

[JS]

Thread revival - I have been meaning to reply to this one for a few weeks, but have been out of pocket.

The reason why so many people disagree on this problem is because the question is worded very poorly and very vaguely - as Mr. Durden himself points out in his Avweb article.

"On a day with absolutely calm wind, a plane is standing on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. The conveyor has a control system that tracks the plane speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction). Can the airplane ever take off?"

First off, when he says "The plane moves in one direction," is he talking about the wheels of the plane, or the actual fuselage (and pitot tube and airfoil) of the aircraft? If we are assuming that the conveyor matches the speed of the wheels, then the plane will generate relative motion and airflow over the wings after you add thrust, and Slacker130 would be correct:

Originally posted by slacker130:

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

And MATTUSAF would be correct too:

Originally posted by MATTUSAF:

So once the plane starts moving forward at 1 knot the tread mill moves backward at 1 knot.

Plane forward speed = 1 knot, plane wheel speed = 2 knots.

Then the plane and the treadmill will continue to accelerate at the same rate in opposite directions until Vrot.

And BFM would be correct:

Originally posted by BFM this:

Airplane speed = 0

Conveyor speed = 0

Airplane speed = rotation speed in one direction

Conveyor speed = rotation speed in the other direction.

Wheels = rotation speed times 2

All 3 basically said the same thing.

HOWEVER, if the treadmill is matching the speed of the rest of the aircraft (say through some kind of motion detection laser or something), then the aircraft will never move relative to the ground and will not take off. As soon as the wheels inched forward a millimeter and the fuselage of the aircraft moved forward one millimeter, the conveyor would start in reverse and would not stop until the aircraft was back at the original speed that the conveyor/laser system was trying to maintain - in this case 0 knots. As more thrust was added, the conveyor would speed up in reverse until the tires oversped. Again, under this assumption the conveyor is ignoring the speed of the tires and only trying to match the speed of the metal of the wings of the aircraft.

As a matter of fact, in order to satisfy the original condition, which has the aircraft initially at rest, the conveyor would HAVE to keep the body of the plane at zero ground speed if it truly "tunes the speed of the conveyor to be exactly the same (but in the opposite direction)" as the original description indicates.

By sheer engineering definition, if a system is going to exert an unlimited force to maintain an opposite speed of an object, then the objects speed could never change. If the experiment started at 0 kts, that speed could not change by definition of the experiment. If the experiment started at 120 kts, as in the example of the plane doing a touch-and-go on the treadmill, then the treadmill will keep it at 120 kts - the original speed. Again, it is all in the wording and assumptions of the definition of the problem.

In my second example/assumption, no external forces would help the plane move forward, because, again, the conveyor system is overcoming any forces that are trying to move the fuselage of the plane forward, and not the tires.

In that case, the following would be incorrect:

Originally posted by slacker130:

Experiment 1

tie a rope to your friends truck and around your waist, put on rollerblades and stand on a 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.

After you put the truck in gear, you have added an external force to the fuselage of the plane, and the conveyor system in the 2nd assumption will match that force and keep the plane at it's original speed - 0 knots.

This would also be incorrect:

Originally posted by slacker130:

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?

Again, no matter where the thrust came from -whether it was from "your buddy's truck," your legs, the tires of a hot rod, or the thrust of an F-15 or C-172 - the minute the fuselage of the plane moved a needle-width forward, the conveyor would put out it's max effort (if necessary) to keep the plane's fuselage from moving. In engineering terms, it is called a closed-loop system with the position loop being closed based on some sort of feedback.

Rocker would be correct in this second assumption:

Originally posted by Rocker:

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.

Let's not forget that, Mr. Durden, the author of that Avweb article that states that the plane will take off, is a lawyer. I guess that is what lawyers do - they take an ambiguous paragraph or problem and convince others of a specific answer, regardless of the specifics (or lack thereof) stated in the original problem.

As an engineer, I can say that you cannot come to a solid conclusion on this one without first making some assumptions and/or clarifications in the original definition of the problem.

[Guest Sundowner]

As an engineer myself, I'm going to stick my neck out and say that you're wrong, the plane will take off. Let me just preface this by saying that I didn't read all of the previous posts, but here's how I would put it:

It doesn't matter how fast the ground moves beneath you. If the "conveyor" doubled whatever speed it detected you moving at you would still take off. Here's my example. A prop (a jet works the same) pulls you through the air. If you were in a wheelchair you could pull yourself forward along a rope the same way a prop would pull you forward. If we put you and your wheelchair on a conveyor you would move backward with the conveyor. If we gave you the rope you could hold yourself in place while your wheels spun beneath you. But if you wanted to, you could pull yourself forward along the rope using the same amount of force it would take before regardless of how fast the floor moved beneath you. Hope that makes sense.

[JS]

Originally posted by Sundowner:

As an engineer myself, I'm going to stick my neck out and say that you're wrong, the plane will take off

As you can tell from my post above, I said the plane WILL takeoff and it WILL NOT take off, depending on how the problem is defined and where the feedback device is that is "moving the conveyor in the opposite direction."

So, "as an engineer," I wholeheartedly agree with you that I am wrong. I also wholeheartedly disagree with you that I am wrong.

Originally posted by Sundowner:

If you were in a wheelchair....If we gave you the rope you could hold yourself in place while your wheels spun beneath you. But if you wanted to, you could pull yourself forward along the rope using the same amount of force it would take before regardless of how fast the floor moved beneath you.

Again, you are considering only the speed of the wheels of the wheelchair and you are assuming that the speed of the conveyor will remain constant when you applied the extra force of pulling on the rope. By definition of the problem, the minute you pulled on the rope, the speed of the conveyor would increase to keep the wheelchair at it's original relative speed - 0 kts - regardless how fast the wheels were spinning.

[jcollins]

As an engineer...JS I have to say you nailed it. The question is kinda ambiguous (to say the least)

And, as a MX guy...I have to say that in any case my bird is probably going to break...which is going to cause us (actually, those poor crew chiefs) grief...

[ 24. December 2005, 16:52: Message edited by: jcollins ]

[Guest DirtyMaintainer]

I would set the parking brake so I could get off of the treadmill. Then, I would taxi to the right and take off. Thread over. :D

[Riddller]

JS-

Good post, except for the idea that the belt moving in the opposite direction as that of the fuselage will actually have any effect on that fuselage. The force that can be exerted by the tires to the aircraft in the horizontal direction is limited by one thing: coefficient of friction times weight. This is a constant number. You assert that it would be possible to turn the belt at a fast enough speed to counteract the thrust of the motors, not so. As long as the motors can produce more thrust than the coefficient of friction times weight, the plane WILL move forward. The force exerted by the tires to the plane is independent of the velocity of the belt, once they are in motion.

Plus, if you really want to get into it, if there is friction, then a runway sized conveyor belt rotating at any appreciable velocity will drag a HUGE amount of air with it. I won't get into the formulas describing the depth of the laminar and turbulent boundary layers of a fluid over a flat plate, but take my word that the air flow created over the wings from this situation would (significantly) further reduce the 'weight' on the wheels with a corresponding decrease in friction force generated.

There is NO possibility for the belt to be moving at a fast enough speed to prevent the aircraft from taking off, regardless of what that speed is referenced to.

[john]

not to beat a dead horse. but mythbusters is supposed to test this next week. 1.30.08.

[RangerMateo]

not to beat a dead horse. but mythbusters is supposed to test this next week. 1.30.08.

Good! I have to get my vote in then =)

Assuming no mechanical breakdown in the wheels, plane takes off at normal IAS while wheel speed is equal to IAS+GS. (To account for any head/tail winds).

This is basic Newton's Third here. Car's work by pushing against the ground and the only effect of wind is aerodynamic drag. Airplanes push against the air and the only effect of the ground is frictional drag. This is tantamount to claiming that a car placed in a wind tunnel where the opposing wind speed increased equal to your ground speed would never go anywhere. It'd still go...

Here's another way of thinking about it. The only part of the treadmill that matters is the part that is immediately in contact with the wheel (ignoring any fringe gravitational effects the asphalt might have forward and aft...which would actually draw the aircraft forward since most likely there is a higher mass concentration ahead than behind...think you can't measure that? LIGO). Anyway, the only part that really matters is the patch of tire that is on the patch of treadmill...what is in effect spinning the tire in conjunction (opposition) with the thrust from the engines. So take a C-172 at 5,000 AGL and sneak up under it with a wheel mounted on an electric motor and put it in contact with the tires. Use it to spin the tires backwards at the forward speed of the aircraft. Will it fall out of the sky? Perhaps this is why most military aircraft have retractable gear, to prevent the enemy from using their SA-13 anti-wheel-spinnything missiles.

The other logical extension of this illogical theory that the treadmill prevents flight is that you could take off by hoisting the a/c just above the ground then spinning the tires up by some external means. Maybe you could even do this internally...wonder if Skunkworks is already onto this...I hope we're not treading into OPSEC again...

Bet you can't guess my major =)

[Guest alfakilo]

When a car is run on one of those dynamometer things to measure horsepower output and the car is at max RPM, how fast does the speedometer say it's going?

[Guest]

car speed is measured by the wheels, not by pitot/static system.