Classic Connundrums: Airplane on a Treadmill
Published by Joel November 3rd, 2006 in Games. Share ThisA plane is standing on a runway that can move (like a giant conveyor belt). This conveyor has a control system that tracks the plane’s speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction) instantly.
Will the plane be able to take off?
Obviously, the answer is “Yes, the plane can take off.” Despite the fact that the plane isn’t moving relative to the surrounding landscape, it is still increasing its speed relative to the air directly impacting its wings.
Or wait, it isn’t. So obviously the answer is no—it’ll just sit there.
Right?
44 Responses to “Classic Connundrums: Airplane on a Treadmill”
- 1 Trackback on Dec 12th, 2006 at 6:36 am
http://www.straightdope.com/columns/060203.html
No.
Errr. . . Yes.
Banana?
Who cares about the treadmill? The treadmill is only relevant if the plane moves itself forward using the wheels. It doesn’t, it uses its engines. The treadmill could be moving at the speed of light in the opposite direction (Never mind the wheels catching fire) and it would just make the wheels spin faster as the plane took off.
Yes, the plane will take off:
http://www.straightdope.com/columns/060203.html
Umm…isn’t this how wind-tunnels work? They dont use mile-long runways and yet the aircraft that they place in a wind-tunnel (even though they’re usually bolted down) exhibit the same characteristics as a flying aircraft, right?
Ah-ha! Of course Cecil would have already had the answer. I feel sheepish for not consulting him first.
But of course it will!
http://www.kottke.org/06/02/plane-conveyor-belt
You said:
Obviously, the answer is “Yes, the plane can take off.” Despite the fact that the plane isn’t moving relative to the surrounding landscape, it is still increasing its speed relative to the air directly impacting its wings.
Or wait, it isn’t. So obviously the answer is no—it’ll just sit there.
Right?
—————
But there’s a fallacy in there.
Because the plane uses engines to move forward, not the wheels, the plane WILL move forward relative to the surrounding landscape and WILL take off.
Actually, Cecil has it wrong or at least he has it wrong absent the existence of a very high headwind. An airplane “takes off” based on the creation of lift from air moving over the wing, i.e., takeoff speed is not measured relevant to the surrounding land but as the differential between the movement of the airplane and the surrounding air. Think trying to launch a kite by running with the wind–nothing happens. Because the airplane’s engines are not connected to the wheels, there is nothing (in the absence of wind) that will cause the treadmill to move no matter how much thrust is created by the engines. The plane will only move forward relative to the treadmill at the speed of the head wind. (the other attractive wrong answer is that the engines create the headwind–they don’t) Put even more simply–Do you feel the wind in your hair when you run on a treadmill indoors?
I didn’t expect to see this here.
I’ve wanted to punch people in the face over their stupidity in answering this before.
Big words, Honad: What’s your answer?
How long is the treadmill? Is it infinitely long? Or is it just the length of the plane?
If the plane isn’t moving forward relative to the ground (not the treadmill mind you, but the ground on either side of the treadmill), then no air flows over the wing, and no lift occurs.
So, if the treadmill is the length of the plane, then the answer is “NO”.
So, if the treadmill is infinitely long, then the answer is “YES”.
No wind moving over the wing = no lift
no lift = no flight
If the force of thrust is negated by the force of drag “the direction of the treadmill” no lift can occur, because no air moves over the lifting surfaces of the aircraft.
MYTHBUSTERS!!!!
The ground has *absolutely nothing* to do with the equation. There is no propulsion attached to the plane’s wheels - they’re free-rolling (as long as brakes aren’t applied), so the plane will take off.
Real world example? A sea plane taking off against a current - as long as the plane can overcome the drag of the water and get enough airspeed over its wings, there’s no problem. Unlike the sea plane, however, wheels on a treadmill have a much lower coefficient of friction. In other words, if a sea plane can do it, a plane on a treadmill definitely could.
If planes flew because their wheels spun really fast then, yes it would take off.
But I’m pretty sure it has something to do with the wings not the wheels.
-Bob, aren’t all treadmills infinitely long?
/wiseass
P
Garth and Bob Roberts have it right. If the plane is not moving forward them no lift is being generated by the wings. A plane can fly because the design of the wing forces more air under the wing than over it, generating lift. The engines only produce thrust in order to push the plane forward so that air can be pushed over and under then wing.
If its on a treadmill forcing it to be stationary it will not fly.
Rather than tediously reproducing my comment to the Kottke thread on the same topic, how about an alternate scenario?
In this version, the treadmill still tracks changes in the plane’s speed, but instead of making the treadmill run in the opposite direction at the same speed as the plane, it runs in the *same* direction at *twice* the speed of the plane. Does the plane take off faster?
The answer is “no”. Assuming the plane’s wheel’s aren’t locked, their main effect is to reduce the plane’s friction against the surface. The force generated by the plane’s jet engines or propeller is strong enough to dominate the small force applied to the plane via the treadmill’s action on the wheels.
So, in the original version, the plane will take off as normal, but with the wheels spinning about twice as fast as normal. In my modified version, the plane still takes off normally, but with the wheels spinning *backwards*.
:)
It helps if you think of air as a fluid.
I’m gonna have to say no, the plane can’t take off.
Gliders can still fly even though they have no engines, so the straightdope article is wrong, because it assumes that jet engines move air over the wings of an aircraft. They don’t. They provide thrust which moves the plane forward, causing air to move across the wings generating lift. If the plane is not moving it will not take off. This is also the reason you have to run with a kite, or throw it high into a strong wind to get it aloft.
Wind tunnels work because they provide enough wind across the wings to generate lift in a controlled space. If a suitable fan were constructed you could get a plane off the ground, but as soon as it cleared the jet stream of the fan it would crash back to earth.
a treadmill with a plane is irrelavent. the wheels do not drive the airplane. If a plane got onto a treadmill, as in this experiment, they would not rotate at all, since the treadmill only matches the speed of the wheels (which cannot rotate on their own.)
If the nature of the experiment is a question of whether the thrust of the plane would be sufficient to move the plane off the treadmill so that it could taxi and take off normally, then yes it would do that.
The money spent and the existence of craft like the Harrier Jump Jet and the V22-Osprey are also proof that this theory doesn’t work. We wouldn’t have had to spend billions of dollars in R&D on these machines if we could have been just putting planes on treadmills all this time.
I think this question works if the follow assumption is made:
the engine of the aircraft is bolted underneath the plane, and as the engines create thurst, this forces air from the front, throwing it underneath the wings. This creates a faster flow of air beneath the wings compared to the top of the plane, thus creating an upward lift which is what an airplane requires to overpower the gravitational force in order to be airborne.
however that said, as the aircraft will be ’stationary’ with comparison to ground speed (as Bob Roberts mentioned) you do not have any air movement to aid in creating this lift, and all forces will be from the thrust of the airplane alone. the engines will probably be very powerful with on a light aircraft for this to work.
If you take a gilder plane, have a truck drag it, and the truck and gilder both on the treadmill, the glider will NOT lift.
jack
Wrong
An example of why you are wrong is a aircraft carrier catapult if the treadmill is moving in the same direction it would provide a similar effect and throw the aircraft faster in a shorter distance than it would normally be able to under it’s own power and would reach the requirements for lift faster.
Assuming frictionless wheels, there’s no way that the conveyor belt can overcome the force of the jets. The problem with some of these answers is the assumption that the conveyor belt can somehow keep the plane stationary.
Think of a toy car on a treadmill. Turn the treadmill on full speed while holding the car stationary. You are overcoming the friction in the wheels by holding the car, if you apply just a little more force than the friction, you’ll force the car to go forward. No amount of increase in the speed of the tradmill will counteract that force. With frictionless wheels, you’d barely have to push.
Same with the airplane. It takes off. It CAN’T be stationary. Doesn’t matter how fast the conveyor is going. The wheels will blow off a real plane, but it won’t be stationary.
Get on a treadmill with a Kite.
If you can fly it running at your fastest, then the answer is yes. The plane will take off.
If you cannot fly it running at your fastest, then the answer is no.
Bob Roberts is the only one in this thread who does not deserve to be kicked in the nuts.
Especially Murph. Murph apparently thinks the point of jet engines is to proivde downforce like a giant finger.
And especially Clay. Clay apparently believes that a light breeze that could fly a kite can also lift an airplane.
And most especially me for posting this and not just pointing and laughing.
“there’s no way that the conveyor belt can overcome the force of the jets. The problem with some of these answers is the assumption that the conveyor belt can somehow keep the plane stationary.”
I used to be on the “no take-off” side, for precisely that (incorrect) reason. But he doesn’t even get it quite right; the conveyor CAN keep the plane stationary if it moves fast enough, but it doesn’t; it only moves as fast, backwards, as the plane moves, forwards.
My scenario: airplane with engines running, low-friction wheels. Conveyor matches ground speed of plane (in reverse). What happens? Regardless of the situation with the wheels/conveyor/air resistance system, the engines produce forward thrust, moving the aircraft forward faster until it attains lift-off. Throughout the take-off process, the conveyor matches the ground speed of the airplane (but in reverse), thus when the airplane is moving forward at 5mph, the conveyor is moving backwards at 5mph and the wheels spin at 10mph. The plane still moves forward. At take off, the wheels spin twice as fast as the take-off speed, but the plane is still moving at take-off speed and still lifts off.
UNLESS: If you take the question a little differently (the way I used to), the conveyor can move infinitely fast, and it will always attempt to _keep the airplane stationary_ (that’s the difference).
Imagine scenario 1: airplane with engines off, frictionless wheels. Conveyor starts moving at an arbitrary speed. What happens? Due to the inertia of the plane, it stays stationary and the wheels/treadmill can spin as fast as they want.
Scenario 2: airplane with engines running, frictionless wheels. Conveyor starts running at an arbitrary speed. What happens? Due to the forward thrust of the engines, the plane moves forward and gathers speed with respect to surrounding environment until it lifts off. The wheels/treadmill can spin as fast as they want without affecting this.
Scenario 3: airplane with engines off, low-friction wheels. Conveyor starts running at an arbitrary speed. what happens? Initially, the plane’s inertia will resist moving with the conveyor, but slowly the friction from the wheels will cause the plane to move in the direction of the conveyor. The backwards speed of the plane will continue to increase until the wheels/conveyor/air resistance system is in equilibrium (in an airless environment, equilibrium would obtain when the wheels became motionless with respect to the conveyor surface).
Scenario 4: airplane with engines running, low-friction wheels. Conveyor starts running at an arbitrary speed. What happens? Because the wheels are NOT 100% frictionless, the friction from the wheel/conveyor system will overcome the forward thrust from the engines at a given speed. The conveyor will have to move really, really, really fast to cause the wheels’ friction to overcome the thrust of the jet engine, but in a theoretical sense, it happens. Thus, no forward motion for the plane, no lift, no take-off. That used to be my answer, until I read the question correctly.
Ahhhh hahahahahahaha. Most folks first answer would be, I think, “It stays still and doesn’t take off.” Thing is - word the question however you like, but if you don’t know how an airplane’s wheels work, then chances are you’re going to answer that “it doesn’t take off.”
It’s pretty simple actually, no need for physics unless you really really want to get into it.
An airplane’s wheel are free-rolling - that is, they are not like the wheels on a car. They’re like the wheels on a… stroller. They just roll free.
The conveyer and the airplane wheels are red herrings, because an airplane does not rely on it’s wheels at all to take off - the wheel are just there, in a simple sense, to allow the plane easy movement relative to the surface it is sitting on. That is, an airplane does NOT rely on the speed of its wheels to take off (that implies it’s acting like a car, using an engine to drive it’s wheels) - it relies on the speed produced by its engines. The engines push the plane through the air.
Best way to demo this for yourself is with a toy car - I sent my folks this question and it had them arguing. =) So here’s what I showed them:
A Matchbox car, a long strip of paper, and your fingers. First, hold the car steady between your fingers, and pull the paper out from under the car. The car’s wheel are free spinning, so the paper slides easily out from underneath. This is somewhat representative if a REAL car was in this conveyer situation - it would stand still because it’s engines will propel it forward relative to the ground (moving or not!)
Now, do the same thing, but instead of holding the car steady with your fingers, push the car forward as you pull the paper out from under it. The car moved forward relative to its surroundings, right? This is because your fingers are now acting as the JET’S ENGINES. A jet’s engines work by moving air, NOT by acting upon the ground. That’s how a plane moves along the ground. The plane’s wheel dont have little engines in them - the plane’s big turbine engines suck in air, push it out the back and propel the plane forward.
Hell, if holding the toy car with your fingers doesn’t do it for you, attach the car to a string. As you pull out the paper, pull the car forward - you pulling the string represents the jet’s engines, because the jet’s engine produces forward thrust completely independently of whatEVER the hell the ground is “doing” - whether it’s a conveyer belt, ice, frictionless magic surface, etc.
JustinD is completely right. As to the infinite treadmill vs. short treadmill debate, the only difference is:
On a treadmill that is long enough for the plane to achieve V2 (safe rotation speed) while still on the treadmill, the plane will accelerate and lift off normally.
On a treadmill of shorter length, the plane will reach the end of the treadmill at ground speed X with its tires rotating at whatever rotational velocity that would correlate with ground speed 2X. Hence, when the plane reached the end of the treadmill, you would see a large cloud of tire smoke as the wheels immediately decelerated to half their rotational velocity, but the plane would continue as normal, reaching v2 and rotating (assuming 1) no mechanical failure due to the rapid deceleration of the wheels and 2) sufficent space AFTER the treadmill for the plane to achieve sufficient velocity.)
Some of you have been distracted by the red herring of “a jet engine does not produce airflow over the wing”, using that statement to discount arguments that suggest take-off is possible. While it is true that jet engines do not produce airflow over the wing, they do provide forward thrust to the airplane, which enables the movement that, in turn, creates airflow over the wing, an area of low pressure above the wing, Bernoulli’s principle, magic flying pixie dust, et. al. (Although, technically, Bernoulli’s principle does not thoroughly explain the lift created by an airplane’s wing–it’s an easy (for the layman) to understand explanation that comes close but relies on the fallacy of equal transit times…wings actually create lift because they force air downwards. For more info, check this out: http://home.comcast.net/%7Eclipper-108/lift.htm) The forward thrust that the engines create is INDEPENDENT OF THE WHEELS, THE GROUND, AND ANYTHING OTHER THAN THE AIR SURROUNDING THE AIRCRAFT, any way you slice it. The airplane does take off–not because of jet engines creating airflow over the wings, but because of the ground-independant forward thrust they provide.
*independent. Apparently I can understand aerodynamics, but I can’t spell.
hello im a boeing engineer, and they whole thing with this about the wheels is that if you take into effect that the thrust turns the wheels and the thrust in turn determines the speed of the wheels, and if the treadmill is equally going the opposite direction, in turn the plane is not moving at all.
sop if the plane is not moving, you will not creat any lift, and inturn the plane will not leave the ground. and as someone stated your engines do not create any life is entirely correct, a plane is pretty much a rock that you threw a rocket on and hope for the best.
but since the aircraft is not moving the slats and flaps will not do their job of making an air bubble under the wing that lifts the wings and in turn lift the plane, positive airflow over the wings is what creates this pressure difference that lifts the wings. so you need enough forward movement to create this differenc to lift the plane.
thank you i was great
Actually no, the plane will not take off.
Assuming the treadmill effectively increases speed to an indefinite number or at least very high, the friction of the rubber on the treadmill will be so high that the tires will burst. The tires will have exceeded the maximum tire speed (published for transport category aircraft). At that point the plane will be resting on metal stumps, on a stationary treadmill. Given that the thrust rarely exceeds the breakaway force required from the metal on treadmill combo, the plane will not lift off.
Chris,
You’re right–in a practical application that’s what would happen, and you’d have a fiery, terrific crash.
However, assuming a frictionless/extremely-low-friction environment (as one often does when attempting to divine the physics behind a practical experiment), my previous statement still stands.
And, uh, Andy? The thrust doesn’t turn the wheels. The thrust pushes the plane forward, and the forward motion of the airplane turns the wheels. They’re just there to reduce friction.
I think the issue here is whether the we are to assume that the plane is motionless relative to the ground. I do not know enough about the wheels on the plane but the premise seems to say that the treadmill is counteracting the plane’s thrust and therefore there is no relative motion and the size of the treadmill is irrelevant. If this is true then the plane does not take off because without strong airflow around the wings there is no pressure differential between the top and underside of the wings that creates lift. (I’m an electrical engineer but I remember some of my fluids from physics.) If the premise does not mean that the plane is stationary relative to the ground, then assuming that the treadmill is long enough, it can take off.
The problem states “the plane isn’t moving relative to the surrounding landscape.”
If this is the case, the plane won’t ever reach the end of the runway, because all of it’s forward energy will be cancelled out by the magical frictionless treadmill.
Grab a glider at Toys ‘R’ Us (or make a paper airplane), hop on your treadmill, and crank it up to as fast as you can run. You’re the jet engine, you’re the wheels. Hold the glider over your head and let it go. If it’s heavy, you should wear a helmet or be prepared to dodge, because it’s going to fall straight down.
hey joe,
i know the wheels are not powered by the thrust, that they are just there for the plane to be able to taxi and brake when needed, im not stupid, but the thrust does turn the wheels cause of the forward motion that is created by the thrust. you know there are planes with out wheels too what about if we had a plane with skis on it, if you had that on the treadmill, guess what, you would still be sitting still and not moving. the wheels are irrelevent to the whole thing cause of the treadmills motion canceling them out. this is just like a plane sitting on the ground doing an engine run, breaks set and chocks ion place. the plane will not leave the ground
Andy,
As I made explicitly clear in my last post, all my answers assume a frictionless/low friction environment. Hence, it’s NOT like a plane sitting on the ground, doing an engine run with the brakes on and the chalks in place. In that scenario, the friction of the rubber on the ground (held motionless), the grip of the groundbrakes, and the force of the chalks against the tires is enough to hold the plane in place.
In the treadmill conundrum, it’s absurd to take friction into account; if we do, the whole exercise is useless as the friction of the wheels spinning at 2X ground speed would quickly destroy the entire undercarriage.
So…assuming no friction, nothing would hold the plane in place, the wheels would spin at a rotational velocity that corresponds to twice the airplane’s ground speed, and the engines would act on the air surrounding the plane to create thrust and push the plane forward. See JustinD’s explanation for a practical exercise you can do to prove this correct.
This is just silly. The fact is that the friction of the wheels doesn’t matter one way or the other.
All that matters is the wind speed relative to the airplane (and, more specifically, the airplane’s wings). Hypothetically, if you pointed a really powerful fan at an airplane, coming from directly in front, you wouldn’t even need the engines to generate the thrust (which, in turn, would increase the wind speed over the wings and therefore generate lift). This is what happens inside a wind tunnel during testing. On the other hand, since in the example the plane is not moving, there is no positive airflow past the wings and thus no lift is generated.
The plane does not take off.
I’m shocked by the comments here, but even more so that Cecil was actually wrong about something. I was expecting some ingenious explanation of why this example is counter-intuitive (like the Door-Picking exercise in “Let’s make a deal” that Cecil mentions in the article), but instead, this…?!?!!?
This whole question is flawed. It seems the question gets you all concerned about the movement of the treadmill. If the only effect the treadmill gives is spinning the wheels of the plane, then it will have no effect on the plane taking off. So, take the treadmill out of the equation all together. If a plane sat still on runway with its wheels locked and its engines going full blast would it take off. Of course not.
How about a treadmill moving the same direction as the plane. The wheels couldn’t be free spinning. If this was the case the treamill would have little effect. The wheels would have to move only in the forward direction. This reminds me of a conveyor in an airport that people walk on. You move twice as fast. Of course this wouldn’t make the plane take off while standing still, but it should cut the runway length drastically. Sort of like the sling shot device used on carriers.
In the real-world with regular planes and regular treadmills (large as they may be) there is nothing to stop the plane from moving forward (relative to an observer on the ground) and taking off. Meaning the plane will always be able to generate forward thrust and move forward.
If you think of the wheels as a sprocket and the treadmill as a chain and assume the “sprocket-tire” can never jump out of the chain then you increase the force of the plane’s forward thrust on the treadmill-chain. But then you really don’t have an airplane on a treadmill, you have an airplane engine driving a sprocket-chain assembly. Not the same thing.
Real-world example with existing items, the plane takes off. Fantasy land where you can introduce some way to anchor the plane to the treadmill (sprocket-chain), the thrust is diverted towards driving the treadmill instead of pulling the plane forward.
This is the wrong question. The original question says speed of the wheels. If it is designed to match the speed of the plane it takes off. Becuase if the plane is going 100mph the wheels spin at 200mph.
The original question where it matches the wheels. The answer is its impossible so why are we arguing.