Airplane on a Treadmill

I can’t believe that this has actually turned into such a huge thing.

The question of the month appears to be this. If you put an airplane on a treadmill and get it going really fast (working up a heck of a sweat, mind you), will it eventually take off?

Upgrade: Travel Better points out that David Pogue of the New York Times even picked this one up a few days ago (and that’s where this picture came from, though the headband addition was mine). So what’s the answer?

No, it won’t.

Now I’m amazed at how many conflicting opinions there are on this thing, because it seems very basic to me. Let’s say you get that treadmill humming in a really big gym (with no wind around) and the plane has full takeoff power going. Those wheels are racing on the treadmill, but it doesn’t matter what the wheels do here. Aircraft get lift from air passing over the wings, and in this case, there isn’t any.

If there’s no wind in the area and the plane isn’t moving through the air, then there will be no air passing over the wings. It’s that simple. Now if there happens to be a 200 knot headwind, you’re going to get airborne whether your engines are on or not, but I’m assuming that’s not part of the question here.

Ever wondered why airplanes take off on different runways at different times? Well, they always want to take off into the wind. The reason for that is once again that ground speed doesn’t matter – it’s airspeed that does.

For simplicity’s sake, let’s say you need 100 knots of airspeed to get off the ground (meaning the air is moving over your wings at 100 knots). If the wind is blowing 10 knots down the runway and you take off into it, you only need to be going 90 knots on the ground, because 90 knots plus the 10 knots that the air is already moving will get you where to need to be.

Conversely if you took off the other way, you would need to be going 110 knots because you’ve already got 10 knots at your back. Only when you get to 110 knots on the ground would you have 100 knots of airspeed.

On that treadmill, air is not moving over the wing at all so it’s not taking off.

Brett

15 responses to “Airplane on a Treadmill”

Better Living Through Miles

Dec 15, 2006

Quite correct.

And I love your mad photoshopping skillz. It’s the Bjorn Borg of airplanes.

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Anonymous

Dec 15, 2006

Go Cranky! You show them who’s boss.

(BTW, that would be one helluva treadmill…)

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Anonymous

Dec 19, 2006

It certainly would take off. On an airplane, the wheels are decoupled from the thrust. So they would just spin forwards faster, but the plane would move forward at exactly the same speed as if it was on a normal runway.

For a vehicle like an automobile, where the wheels provide the thrust, it’s a different story and the automobile would stay stationary.

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The CF

Dec 19, 2006

I suppose I could be simplifying the problem too much here (I’ve seen some impressive email threads on this subject go on for days), but here is my basic understanding of the issue.

What matters is the movement of air over the wing. Let’s assume that the aircraft is using full thrust. Let’s also assume that the treadmill is a power treadmill that is going in the opposite direction at just the right speed so that the airplane doesn’t move forward even with full thrust.

I believe the last comment was stating that since the wheels don’t power the aircraft, the aircraft would move forward (and right off the treadmill), but I don’t think that was the point.

I think the point is that the airplane isn’t moving forward on the treadmill. The counter force from the treadmill is enough to offset the thrust from the airplane (even though the wheels don’t power the plane) so that it acts like a person does on a treadmill. In that case, the plane isn’t going anywhere.

If you do assume that the plane would just run right off the treadmill and go forward, well, then it would fly, but that doesn’t seem like a very interesting problem to me.

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Anonymous

Dec 19, 2006

Anyone who thinks the plane would take-off is either crazy, stupid, or trying to play games by changing the problem. Airplanes fly by creating lift under the wings. That only happens with relative wind (usually speeds in excess of 100 mph but depends on the plane). The motion of the wheels are irrelevant. The floats on seaplanes stay stationary whether the plane is flying or not.

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Anonymous

Dec 19, 2006

The engines are pushing against the air, not the treadmill, so it only matters what the surrounding air is doing, not how fast the wheels are spinning. There is hardly any counterforce from the treadmill going, they are wheels on the plane after all and roll freely.

Bottom line, a plane on a treadmill runway will only need a little extra thrust to take off to counteract the slightly higher friction the wheels are experiencing.

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Anonymous

Dec 20, 2006

The air over the wings thing is missing the point: no matter how fast the treadmill goes backwards, there’s no way you can keep the plane stationary. It will move forwards just as it would on a runway. Given that the plane can move forward, air will go over the wings as normal and it will take off, as normal.
To reiterate: you can’t build a treadmill that will result in a stationary airplane.

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William

Dec 30, 2006

It’s hard to believe this “debate” has surfaced again. The plane obviously takes off. The treadmill has zero impact on the airplane, assuming the wheels are normal, free-spinning aircraft wheels. The airplane is propelled forward by the engines acting against the body of air. The only thing you could do with the treadmill to keep the airplane from flying would be to pick it up and swat the airplane out of the sky with it.

If the treadmill is specified as “matching the speed of the airplane in the opposite direction”, then the speed of the surface of the treadmill will be 2X the relative ground speed at the moment of takeoff. The ground speed will be the same as it would be without the treadmill, as would the airspeed required for takeoff (V1).

If you disagree well, sorry. You need to think it through again. Suggesting that those of us who know it will fly are “crazy or stupid” isn’t a particularly convincing argument. I am, in fact, a pilot. The speed of an airplane relative to anything other than the body of air it sits in has zero effect on lift and the subsequent ability to take off.

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The CF

Dec 30, 2006

Ok, I think everyone agrees about the aerodynamics involved here. It’s all about how the plane moves through the air.

One point of view is that the treadmill would move counter to the wheels so that while the airplane may have ground speed at V1 or higher in relation to the treadmill, the airspeed assuming no wind (and ground speed in relation to the ground underneath the treadmill) would be zero. That’s like someone jogging on a treadmill.

The other point of view, if I’m reading this right, is that since the power source is not related to the wheels in any way, the aircraft would move forward right off the treadmill and it would take off. This means the treadmill wouldn’t function like a treadmill at all and would just be another piece of ground for the airplane to run over.

I tend to think that the problem was devised to assume the former to be true, and it was more of a question for people who don’t understand aerodynamics. Really though, there’s only one way to settle this.

Who has the money to build a 2 mile long treadmill in the desert?

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Know it all

Jan 28, 2008

There is no way the problem would just imply that the plane remain stationary. If that was the case, anybody could answer it. Heres a clue. They actually went through all the trouble of inventing vertical lift planes to get around the problem some of you are presenting. Why, because its not possible for a plane of traditional design to take off from a stand still. No need for any experiments.

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Peter

Apr 20, 2008

The answer is: Yes, an airplane CAN take off from a treadmill if the treadmill is countering the velocity of the airplane’s normal take-off velocity.

The physics of the matter is: The airplane taking off depends upon air-flow over the wings. And the forward velocity of the airplane is dependent upon the thrust of the engines through the air.

Thrust on the airplane is equal to the mass of the air being propelled backwards by the engines. This will push the airplane forwards with relationship to the air.

The treadmill has very little to do with the matter.

The only effect of the treadmill on the motion of the airplane is through the wheel bearings.

Now — if you could get the treadmill to go so fast in reverse of the airplane’s motion that the wheel bearings would burn out before the thing took off, then you might have an issue.

But since the plane takes off in a span of about 10 to 15 seconds, it’s doubtful that your treadmill would be able to have much of an effect.

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Nicholas Barnard

Apr 20, 2008

My cousin and I argued on this for days. It came down to a misunderstanding of physics terms. Without delving wholly into whichever version of the problem you’re thinking about my understanding of the bottom line is that:

If the treadmill moves in reverse to the ground speed of the airplane it does take off.

If the treadmill moves in reverse to the force created by the engine it does not take off.

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Benjamin Schwartz

Apr 20, 2008

Actually Nick (I’m the cousin!), if the treadmill moved at the same speed as the wheels that would create an impossible situation. If the wheels spun 300 MPH forwards, then the treadmill would go 300 MPH backwards which would make the wheels spin at 600 MPH so the treadmill would have to go 600 MPH backwards which would make the wheels spin at 1200 MPH etc.

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Rabon

Jun 30, 2008

Ok, think about this:

Planes are frequently taking off from Aircraft Carriers. These carriers are basically giant treadmills on the ocean. Sometimes they move in the opposite direction from takeoff. So the planes are already moving at however many knots completely in the wrong direction. The planes have to overcome this and get up to takeoff speed before they can leave the carrier, yet they do it all the time. If the plane wouldn’t take off with the treadmill running counter to the wheels, how could they overcome a speed greater to their starting speed and take off?

The major problem with understanding this question is that people don’t realize that thrust comes something not touching the ground. Yes, the relative airspeed is what gets them off the ground, but the wheels have nothing to do with getting them up to this speed. Imagine putting a Hot Wheels car on a treadmill. Have the treadmill go much faster than your hand, and slide the car up the treadmill. The engines on a plane work much the same way. The thrust is like an invisible hand pushing the plane along at faster and faster speeds until it can take off.

As I understand it, the original problem was not about matching the wheel speed but the speed of the plane, so this would make the wheels spin twice as fast as takeoff speed and no more. Unless, as Peter said, you happened to burn up the bearings before takeoff (causing the plane to fall to the ground), the plane would be unaffected.

So, yes, the plane will take off.

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Matt

Jan 16, 2010

Matter of airspeed, not ground one.

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