The arplane on a conveyor belt conundrum

I searched, but couldn't find that it was posted before. There are different variants of the question but they all ask the same thing. Here it goes:

If an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots, and the conveyor belt starts moving backwards at 100 knots, will the plane be able to take off, or will it just sit stationary relative to the ground, with the backwards speed of the conveyor belt counteracting the forward thrust of the plane?

or more simply:

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

The question is:

Will the plane take off or not? Will it be able to run up and take off?

no.

no air flow over the wing = no lift. since airplane remains in the same position (only motion is realative to conveyor belt) and airflow would be related to its relative motion.



Have you heard the one where the plane is 5000lbs (some large arbitrary number) over weight loaded with chickens? If the flight attendent wlaked down the isle continuously scaring the chickens into their short flights do you think the plane COULD fly?

But the wheels don't provide the motion, like a car, the jet turbines do. The wheels don't provide any friction, therefore they don't provide the power. Wouldn't the jet turbines still push the airplane forward, to gain thrust?

I'm still trying to make up my mind and figure it out myself.

But the way you set up the problem it is irrelevant- right? If the airplane is moving relative to conveyor fast enough to stay still relative to the ground- then the AIR is not flowing over the wings so no lift. (that is assuming the ground is the more significant between the conveyor and ground so air is tied to it.

So - yes the engine is what keeps the plane moving relative to conveyor- but it is not moving relative to the air.

Now change the problem so that AIR is being blasted at the plane hard enough to keep it stationary to the ground and you bet ya the thing will fly.


. . . . Now what of the chickens?

The friction on the wheels from the conveyor belt would not be enough to keep the aircraft from moving foreward. The aircraft should get up enough airspeed to fly depending on how much speed is lost because of the friction from the wheels having to rotate twice as fast as normal.

As to those chickens, as long as they were all airborne long enough to rotate the aircraft off the tarmac, but if they all landed the wing loading would be too high and it would desend.

one might think. but it is still no and no.

The plane is getting no air speed if it is staying on the same spot relative to the ground- no air flow over the wings = no lift no matter how fast it moves relative to the conveyor



The chickens either are exibiting downward air pressure on the floor of the plane equal to the weight of the chicken (if stationary in air) or MORE (if actually moving up), even if you say they are jumping with leg power only- you still have equal and opposite reactions. The plane is going to crash at the end of the runway. A good way to see this every day is to weigh a remote control helicopter on a simple bathroom scale with a sheet of plywood- then make it hover a few inches above the scale and plywood- it will read the same thing- i've done it before to prove this in a high school science class.

Way back in college my dynamics instructor loved these sorts of problems on exams- you'd spend most of the time second guessing yourself rather than getting the problems done. class average was around 35%. A good free-body diagram will keep you out of trouble everytime if you draw it right.

[edit on 2-1-2006 by launchpad]

I reckon curme is correct with this one. When considering a car, the wheels turn pushing the ground backwards, therefore the car forwards, to provide the thrust. If the ground were not fixed, i.e. oily, or in this case a conveyor moving backwards, the car would not accelerate forwards as fast, or at all.
With a plane however the thrust comes from the props or jets effectively pushing the air backwards, so the plane forces the air back, therefore the air forces the plane forwards, not the ground. The wheels are simply holding the aircraft of the ground, so can be moving backwards, forwards or not at all; as long as the thrust from the engines can overcome this frictional force.
A more interesting situation would be if the conveyor started before the aircraft, accelerating the aircraft to its take of speed in reverse. Would the plane need twice the thrust to take off then, or would it simply take longer while the plane accelerated from -200Mph through 0 and up to 200Mph; someone else can think about that one…

Originally posted by launchpad
one might think. but it is still no and no.

The plane is getting no air speed if it is staying on the same spot relative to the ground- no air flow over the wings = no lift no matter how fast it moves relative to the conveyor

The aircrafts thrust is not dependant to the wheels turning. If the thrust is high enough the aircraft will move forward and gain airspeed. Think about it. If the wheels spinning twice as fast as they would on the tarmac, and the aircrafts thrust is great enough to overcome this and accelerate the aircraft beyond stall speed, it will most definatly rotate and become airborne.

As to the chickens, it all depnds on th aircrafts construction. If the bottom of the fuselage were made of trusses and bulkheads covered with chickenwire, there would be no ground effect on the fuselage from the chickens wings!

You just have to step outside the box. No one mentioned thrust requirements, or what the aircraft was made of.

What size was your heli? I used to fly a Kyosho .30 and an excell .60!

Maybe we should send this question to myth busters and they can build a working model? for both even. It would be a good show. too bad i probably won't see it without cable tv and all- but it would make a good show. (Keri rocks)

I still say no because thrust or no thrust, until the plane gets lift- which ONLY comes from air moving relative to the wings - the wheels provide a lot more than holding it off the ground. the full weight of the plane will still be squarely on the wheels.

for one: the plane needs the wheels to directionally control it until there is enough air speed relative to the control surfaces to even steer it- especially during taxiing- else it would slide sideways and skid off the taxiway like a hover craft.

How this problem was set up is that the conveyor is keeping it in place- relative to its starting position on the ground. Be it a tail dragger or tricycle gear makes no difference. The wheels do have friction inside them (the faster they spin the more the friction too) and if the conveyor is doing what we set it up to do then we have no lift- so the full weight of the plane still is upon the wheels and it does not fly.

Now, i think that the thrust will be stronger than the little friction on the wheels and it would actually be impossible to keep the plane in place relative to the ground and it will start moving down the conveyor anyway (that is not how we set up the problem though)- then it is moving relative to the ground and getting lift- then and only then it will fly. however, the conveyor will have to be a little bit longer than the planes normal take off run.

I'll have to think about the chickens and the chicken wire floor- i am seeing at least one problem with it- where do we find chicken wire strong enough to support the weight of the chickens that would have overloaded the plane but still be thin enough not to impeed their "thrust" from their wings?


I sadly don't personally own a chopper- though i have a few friends that do. That is an expensive hobby and every bit of my $$$ are going into my shop and Baja race car i am building for the 2010 season. (provided Titor's 2008 war dosen't happen) (( someone should have asked him about Baja 500 in addition to the olympics)) -first titor! en.wikipedia.org...



[edit on 6-1-2006 by launchpad]

But couldnt the pilot still lift the nose of the plane into the air, creating air flow above and below the wings?

no for two reasons:

the piolt is able to raise the nose by down ward lift on the tail surface and he is getting no lift unless moving relative to the ground.

This is pretty funny - First thing I was thinking was how aircraft take off from an aircraft carrier, but the catapult or conveyer is going forward not backwards. Change the direction of your conveyer & you could do 50 & 50 to reach 100 & thus take off from a shorter runway on a small island, mountain etc.

Launchpad is correct - current aircraft use airspeed to create lift - thus you always want to take off into the wind so you get enough airspeed to become airborne before you run out of runway.

The engines don't make a plane fly they push a plane forward, which creates airspeed. That’s why you see some people launching glider aircraft being towed behind a fast moving car or truck.

The air moving past the wings creates lift that makes a plane fly. If you look at the side cutout view of a wing you will notice that the top surface is a greater length than the bottom surface and that creates more air
Pressure on the bottom and results in lift - this is also what results in condensation that you often see coming off the wings as the air mixes back together & releases its moisture. There is also a ground effect when aircraft are close to the ground, as the air has no place to go thus you have more lift when near the ground.

Funny thing is helicopters are the same except the rotor blades are the wings - you will notice they are the same shape as an aircraft wing.

Originally posted by launchpad
the wheels provide a lot more than holding it off the ground. the full weight of the plane will still be squarely on the wheels.

I’m probably reading this wrong, but is that not a bit of a contradiction?

I see where you are coming from with your theory; however I think as long as the accelerating force is not coming from the wheels, they are simply there to reduce the friction between the moving plane and the ground. Imagine it this way.
If the plane was being towed along by tugs which were not on this conveyor, say in front to the left and another to the right, if they were moving at 10Mph and the conveyor at 100Mph, the panes wheels, having very little friction, would move at 110Mph however the plane would only move at 10Mph, with the tugs. This is because the connection between the plane and tugs is fixed, whereas the connection to the conveyor is not - the wheels are allowed to turn.

When instead of 2 tugs providing the forward force you have 2 props pushing against the air, the situation is similar. If the plane is allowed to accelerate first and get a start, and have enough power to overcome the friction of the wheels having to turn faster than normal, then it will accelerate forwards.

If the conveyor starts first then the planes engines would have to fight harder to turn, as they have to overcome the air passing them in the wrong direction, trying to rotate them in the opposite direction.

How this problem was set up is that the conveyor is keeping it in place- relative to its starting position on the ground. Be it a tail dragger or tricycle gear makes no difference. The wheels do have friction inside them (the faster they spin the more the friction too) and if the conveyor is doing what we set it up to do then we have no lift- so the full weight of the plane still is upon the wheels and it does not fly.

Now, i think that the thrust will be stronger than the little friction on the wheels and it would actually be impossible to keep the plane in place relative to the ground and it will start moving down the conveyor anyway (that is not how we set up the problem though)- then it is moving relative to the ground and getting lift- then and only then it will fly. however, the conveyor will have to be a little bit longer than the planes normal take off run.

so your tugs- or props have no relavance on how the problem was set up- stationary air plane does not fly no matter how fast wheels turn. remember we said plane remains in same place!!!!

IF hypothetical conveyor was unable to maintain position of plane relative to the ground then we get air flow over wing and lift. this is how it think it will play out if we build a model and wheels allowed to freespin.

Originally posted by Messi

If the conveyor starts first then the planes engines would have to fight harder to turn, as they have to overcome the air passing them in the wrong direction, trying to rotate them in the opposite direction.

For a helicopter this is called "settling under power" and a BIG problem with heavily laden birds- it happens a lot with gunships since they usually push the envelope at the beginning of missions. a lot of apaches and osprey crashes have been attributed to this.

but it still is not our "problem" we set up.

Originally posted by curme

If an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots, and the conveyor belt starts moving backwards at 100 knots, will the plane be able to take off, or will it just sit stationary relative to the ground, with the backwards speed of the conveyor belt counteracting the forward thrust of the plane?

I see what you’re saying and I think that the problem here is that we are looking at this problem from two different angles. If the plane is kept in the same position, which in my opinion would require it to be tied to something, etc the ground, then of course it would not take of no matter how fast the props turn. The question does not assume this though; it asks if this would happen.

"will the plane be able to take off, or will it just sit stationary relative to the ground".

To which I think yes, it will move and take-off, unless the conveyor was moving so fast that the force exerted on the plane, through the wheels - by the conveyor, was greater or equal to the force of the props pushing the air back. With the conveyor only moving at 100knots though, I doubt this would be the case, unless the wheels were not turning freely.

I do see where you are coming from though and agree with what you said, given the assumption that the plane did stay stationary, which I’m not so sure.

The question does not state if the plane can take off from standing still........ Its basically asking if the plane can still accelerate against the backwards motion of the conveyor belt. The answer is YES. The plane isnt like a car, or bicycle or even a person walking. It doesnt achieve motion through the ground through the wheels. the wheels have nothing to do with the motion of the plane... if the belt was moving forward faster than the plane is moving forward, the wheels would actually be moving backwards while the plane is moving forward. the wheels freespin. the plane is pushed forward from the jet.

Basically what you have to think of is the forces acting onto hte plane. the 4 major forces are thrust say to the right.... drag to the left........ normal force up and gravity down. so to accelerate the force of thrust must overcome the force of drag. the drag forces are wind resistance (which is the same as on a normal runway.) bearing reisistance (which is so minute can basically be ignored) and rolling resistance of the wheel on asphalt. the equation for that is the coefficient of rolling friction.... which is something like ,001 * Weight. the equation hsa nothing to do wiht speed. so basiclaly the wheels mean nothing but to provide a platform of less resistance then if say the wheels were cement blocks. so thrust overcomes the friction and it accelerates to takeoff in probably a little longer distance than a normal runway with the wheels travelling twice as fast as they would normally.

Yep, as I've been saying above, glad someone agrees.
I think this has been put to bed, unless anyone disagrees.

Originally posted by sooks

Basically what you have to think of is the forces acting onto hte plane. the 4 major forces are thrust say to the right.... drag to the left........ normal force up and gravity down. so to accelerate the force of thrust must overcome the force of drag. the drag forces are wind resistance (which is the same as on a normal runway.) bearing reisistance (which is so minute can basically be ignored) and rolling resistance of the wheel on asphalt. the equation for that is the coefficient of rolling friction.... which is something like ,001 * Weight. the equation hsa nothing to do wiht speed. so basiclaly the wheels mean nothing but to provide a platform of less resistance then if say the wheels were cement blocks. so thrust overcomes the friction and it accelerates to takeoff in probably a little longer distance than a normal runway with the wheels travelling twice as fast as they would normally.

Actually, SOOKs the drag of the wheels turning DOES increase with speed.

yes, static friction has a higher coefficient thant dynamic(sliding) friction. (your coefficient of ROLLING friction is not just something you pull off a chart- it is put together from hundreds of varibles in itself: tire material; air pressure; weight of object; WIDTH of tire, material of roadway, number of tires, etc, etc.

However, you are using a basic first year physics equation which does not include all the little things like HEAT generated and parts swell and FLUID friction due to the grease on the bearings, eventual cavitation of the liquified grease, etc, etc. sure it is negliable - to a point. But every basic equation given in the text books is there to get a general point across and later on you find it has tons of little things that go with it- like IF's and at some point they become the deciding factor. (pick up a 'simple' book on bearing design if you do not believe me!)

i guess along those lines: if this experiment goes on long enough - At some point the darn wheels temp will increase sooooo much it/they will pop and that plane if it does not have enough air speed you will have a very spectacular crash as it toubles down the conveyor and then possibly reverses direction. hope it is remote control!

Anyone put this one up to the Myth Busters yet?

The wheels do not propel the plane. The jets do. The wheels prevent friction. The plane would still move forward and lift would be generated. The plane would fly.