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Q: Will an airplane on a treadmill be able to takeoff? ( No Answer,   81 Comments )
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 Subject: Will an airplane on a treadmill be able to takeoff? Category: Science > Physics Asked by: iflytri-ga List Price: \$2.00 Posted: 03 Jan 2006 17:11 PST Expires: 02 Feb 2006 17:11 PST Question ID: 428718
 ```A 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). Will the plane be able to take off?``` Clarification of Question by iflytri-ga on 05 Jan 2006 23:00 PST ```This question tends to generate intense debate wherever asked, and yet intuition tells me there can only be one right answer to this relatively straightforward question: either the plane will move forward and takeoff, or it will not. I am looking for a simple yes/no answer and a logical explanation to support it.```
 There is no answer at this time.

 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 03 Jan 2006 18:00 PST
 ```An airplane's lift is generated by air flow relative to the wings. The speed of the aircraft relative to the runway is, in principle, irrelevant. In fact, let's put it this way: As long as the plane's wheels are free to roll, the conveyor belt can move either forwards or backwards, at any speed, but the engines will exert thrust and the aircraft will aquire airspeed, and will liftoff regardless the belt.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: pinkfreud-ga on 03 Jan 2006 18:03 PST
 ```There is a discussion of this on the Straight Dope Message Board: http://boards.straightdope.com/sdmb/showthread.php?t=348452```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 03 Jan 2006 21:35 PST
 ```If the conveyer belt offsets the plane's speed, then the plane is stationary to the ground and will achieve no more lift than if it was just sitting still on the ground without a conveyor belt. So unless there is a very strong headwind, it will not be able to generate the lift necessary to take off.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 03 Jan 2006 22:09 PST
 ```The point is that the belt cannot play a role in the plane's aquisition of speed due to engine thrust, as long as the wheels roll freely. The rolling wheels decouple the plane from the belt's motion. In fact, for idealised wheels which have no bearing friction, the plane's inertia would prevent it from being carried by the belt even in the absence of engine thrust. In such a scenario it is engine thrust alone which propels the aircraft either forwards or backwards.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 04 Jan 2006 00:55 PST
 ```Qed100, Read the question again. The treadmill plays a crucial roll in the plane's acquistion of speed as long as the plane is not airborne. If it is still on the ground and the wheels are rolling forward at a rate to move the plane at, say 150 mph, the conveyor belt is pulling it backwards at the same 150 mph. So relative to the stationary earth, the plane is going exactly nowhere. This is like going up the steps of the down escalator at the same rate of speed the steps are going down - you get nowhere. And if you are going nowhere and the wind is not blowing, you will not generate any lift at all and therefore will not be able to take off. If wheels do not have any friction, you will slide on them, not roll. This is like a car that slides on the ice. However, the clear intention of the questioner is that the wheels have enough friction to prevent sliding on the conveyor belt. Therefore the plane is not decoupled from the belt's motion. And in the scenario described, will not be able to take off.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 04 Jan 2006 01:12 PST
 ```I should clarify one point. If the belt were accelerating, the plane would roll backwards to some extent relative to the belt and to some extent be carried along by the belt, but if the belt is moving at a constant speed, the plane would not roll back at all. It would be carried by the belt. Again, wheels need to have some friction with respect to the ground (or in this case conveyor belt) in order to roll, not slide. Unless the problem specifically states otherwise, I think we have to assume the wheels roll, not slide.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: poet-ga on 04 Jan 2006 04:39 PST
 ```The plane is driven by the thrust of the engines acting on the air not the ground. It *will* accelerate forward as a result, and acquire speed relative to the air and therefore take off. The friction in the wheels is small enough to be irrelevant. At take of, the runway will be spinning backwards at 2x the forward motion of the plane. The wheels/runway have nothing to do with acquiring airspeed. (for instance imagine it on skids rather than wheels). The runway can spin the wheels fast, but it can't hold the plane still as it creates no force to do so.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: dougw-ga on 04 Jan 2006 08:01 PST
 ```No, the aircraft will not takeoff. As already mentioned lift is generated by the velocity of the flow over the wings. Let's look at it this way - if you are running on a treadmill, do you feel any wind? If you wouldn't then the aircraft's wings wouldn't either.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: frde-ga on 04 Jan 2006 08:13 PST
 ```If the force transmitted via the conveyor belt via the wheels, which presumably use the brakes, is the same as the thrust on the engines .. then it will sit still. Do you know what a 'Backwind' is ? - that is an equivalent, and I was reliably assured that pilots are not trained for it - as they are dead. If you are looking at STOL then Ski Jumps worked for the Harrier, and the idea of a full frontal blast from a static jet on an A/Carrier to lift an aircraft might work - oddly a reverse flush with an internal forward gust might do the trick - I would call that 'Foghorn' - because it looks like it```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ted131-ga on 04 Jan 2006 09:38 PST
 ```"The plane is driven by the thrust of the engines acting on the air not the ground. It *will* accelerate forward as a result, and acquire speed relative to the air and therefore take off." This is the correct answer. Unlike a car, the wheels of a plane play no role in accelerating the plane. All they do is support the weight of the plane until the wings have enough lift to support it. It is engine thrust acting on the air that propels the plane forward. If a plane depended on thrust from its wheels to move, it would have a hard time moving once it left the ground, wouldn't it?```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 04 Jan 2006 10:27 PST
 ```QED is right. If you really want to spend time on this question, read the Straight Dope Message Board that Pinky linked. And before anyone starts talking about the plane's wheels or bearings causing problems, that is also discussed there, with the thoughtful remark that if we are contemplating the existance of such a conveyor belt, then we are also accepting that the wheels and bearings to go along with that exist. That is to say (to Anse1001) that the free rolling wheels has no effect on the plane's forward exceleration. As someone posted on Straight Dope, if the plane were pulled by cable, it would move forward regardless of what the conveyor belt was doing. Same situation with the plane's propellor or jet engines that work against the ambient air. The conveyor belt only makes the wheels turn faster. Need I go on?```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: gargazons-ga on 04 Jan 2006 15:29 PST
 ```Wow. Someone on the Straight Dope message board said they hope this question is a joke, or we're going to need to start taking away voting rights -- I have to say I agree. An object's movement relative to the ground (whether real or on a treadmill) has NOTHING to do with flying! The only thing that matters is the amount of air passing through the wings. If anything, a plane could theoretically fly in a windtunnel while stationary, but treadmills have absolutely nothing to do with flying.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 05 Jan 2006 16:54 PST
 ```Poet and Ted131, you both copied, word for word, the same comment off the internet. The comment is: The plane is driven by the thrust of the engines acting on the air not the ground. It *will* accelerate forward as a result, and acquire speed relative to the air and therefore take off. This comment is wrong. It completely ignores the friction of the wheels on the ground. There are two kinds of friction that are generated by wheels. The first is the friction from the ball bearings. This type of friction is small and irrelevant to the question. The second is the friction of the wheels on the ground, or in this case, the conveyor belt. This friction needs to be great enough to make the wheels grip the road under a variety of conditions. This friction is not so great (nor insignificant) when the wheels roll, but it is dramatically greater when the wheels skid. Once the airplane?s wheels start to roll, the conveyor belt will match their speed, effectively keeping the plane in place. The rotational speed of the wheels and the speed of the conveyor belt will both increase together until the maximum rotational speed of the wheels is reached. As long as the wheels roll without skidding, the plane will go exactly nowhere. For clarity, let?s assume the maximum rotational speed of the wheels is 300mph. Once that speed is reached, if the airplane?s engine still has additional power, the wheels will start to slip. The wheel?s rotational speed, and therefore the conveyor belt?s speed, will both max out at 300mph. Let?s assume the plane needs to achieve airspeed of 100mph to take off. The engine, then, would have to have enough power to make the plane skid on its wheels down the runway at 100mph. How much power is that? If the plane were not on a treadmill, it is equivalent to locking the wheels so they cannot rotate, and accelerating the plane on skidding wheels to 100mph. That would take a LOT of power. And also quickly shred the tires.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 05 Jan 2006 17:20 PST
 ```"As long as the wheels roll without skidding, the plane will go exactly nowhere." That's a bunch of crap. It violates the conservation of momentum. It effectively says that rockets cannot propel themselves through space. And yet they do.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 05 Jan 2006 17:43 PST
 ```Anse1001, You've shown more savvy on other questions. You are describing what would happen with a car on the conveyor belt; the situation of the car trying to advance by the motor turning the wheels. The quoted comment is correct. The 100% friction between the conveyor belt and the tires only spins the tires faster as the plane moves ahead. Give up, you're wrong. I screwed up a couple of days ago on another question and calculated noon to be east instead of west of Greenwich Mean Time 15:30. :-/ Myoarin```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 05 Jan 2006 22:22 PST
 ```Qed001 etal, Regarding conservation of momentum: A rocket going thru space only has the rocket and the exhaust. A plane on the ground has the plane, the exhaust and the wheels in contact with the ground. You overlooked the last item. Therefore it is a false analogy. Let's look at this a little differently for clarity, by looking at the movement of the wheel and the conveyor belt sequentially. If the wheel has a 12 inch circumference, with one rotation it will move forward 12 inches. If the conveyor belt tracks with the wheel it will move backward 12 inches. Since the wheel is on the conveyor belt it will also move back 12 inches. So the wheel ends up in the same place as it started. Whether this takes one second to complete, 1/10th of a second, or 1/100th of a second, the result is the same. The wheel ends up in the same place it started. In reality the wheel and conveyor belt move simultaneously. But if they each make the same amount of movement as they did when they moved sequentially, the result will be the same. And the wheel will go nowhere. They only way the wheel will move is if there is slippage. If the wheel makes one rotation and slips one inch forward during that rotation it will move 13 inches forward. It will move forward 12 inches based on the rotation of the wheel and one inch because of slippage. The conveyor belt will only track with the rotation, not the slippage. So it will only move back 12 inches. So you have a net forward movement of 1 inch. All due to slippage. None of those who have disagreed with me have examined how the conveyor belt will interact with the rotation of the wheel at all. At best, you've just waved your hand at it. If you are right, you should be able to explain in detail how the wheel and conveyor belt interact with respect to the wheel's rotation and slippage and show me where I am wrong. If you can't do that you should agree with me.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 05 Jan 2006 23:05 PST
 ```"Regarding conservation of momentum: A rocket going thru space only has the rocket and the exhaust. A plane on the ground has the plane, the exhaust and the wheels in contact with the ground. You overlooked the last item. Therefore it is a false analogy." Wrong. What we see is that the entire role of freely turning wheels is to eliminate the role of the runway as a source of drag, reducing the dynamics of the system to an engine & its exhaust. The treadmill can run at any rate, forwards or backwards, dragging the wheels with it. All the moving belt does is exert torque on a wheel. The frictional force does work on the wheel. But since the wheel turns, no net work is done on the rest of the airframe. There is no drag. The aircraft will be propelled through the air, and it will aquire lift.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 05 Jan 2006 23:57 PST
 ```Qed001, Have you ever seen an airplane towed at an airport? The vehicle towing a large plane needs to have a fair amount of power to move the plane with the its freely turning wheels. The reason is friction.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: omnivorous-ga on 06 Jan 2006 02:38 PST
 ```Iflytri -- Suggested Google search strategy: downwind takeoff airplane In particular, see the Avweb article that addresses your question directly: "It's The Medium, Manfred," (Durden, Nov. 27, 2005) http://www.avweb.com/news/columns/191034-1.html The answer is that it's "all about the airspeed," as the Rick Durden correctly notes. It's an important concept for pilots, particularly at takeoff and landing. Seemingly small tailwind effects can lengthen both. It's strong enough that some commercial carriers have policies forbidding departures with a tailwind. Best regards, Omnivorous-GA```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: poet-ga on 06 Jan 2006 04:45 PST
 ```Ansel001 1. Could you provide me the link to what I am supposed to have plagiarised? I might be wrong, but I don't recall copying it. 2. You're wrong about the plane. Poet```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 06 Jan 2006 07:59 PST
 ```"Have you ever seen an airplane towed at an airport? The vehicle towing a large plane needs to have a fair amount of power to move the plane with the its freely turning wheels. The reason is friction." Yes, there is some friction in the wheel bearings. But if the wheels were missing from the planes, I doubt that those runway tow vehicles could manage to tow anything. It's a fact that the role of wheels is to elminate friction between road & payload. That there is *some* friction in a well designed bearing is irrelevant. The resistance is tolerably small, and aircraft engines routinely overcome the friction in the wheel bearings every day. I have seen aircaft both being towed and plowing forwards over the runway under their own power.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 06 Jan 2006 15:16 PST
 ```Poet, Upon closer examination, your comment is worded a little differently so it must be your own. However, Ted131 did copy you. However, I respectfully disagree with your conclusion. You might want to consider the implication of one of your own comments. The wheels/runway have nothing to do with acquiring airspeed. (for instance imagine it on skids rather than wheels). The point I raised is that it is only when the wheels start to slip (like skids would) that you get any forward motion of the plane. To the extent the wheels roll rather than skid, the conveyor belt exactly counter acts the forward progress of the wheels. Switching from wheels to skids makes all the difference. You won't acquire airspeed (assuming there is no wind) until the plane starts to move down the conveyor belt. And that will only happen when the wheels start to skid. You made another statement I don't understand. At take of, the runway will be spinning backwards at 2x the forward motion of the plane. Please explain how you arrived at this conclusion. I respectfully disagree with this statement.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 06 Jan 2006 15:33 PST
 ```Iflytri, You are right with your clarification. There must be a way to get everyone off this treadmill. I find it so strange that so many people can't/don't want to understand that airplane propulsion has nothing to do with the plane's wheels. They just support it on the ground, spinning freely, regardless of the conveyor belt. Would it help to point out that if the conveyor belt were running in the other direction, and the wheel bearings had zero friction, that the plane would just sit there with its wheels spinning? Only when the plane's engines are started, would it begin to move. Myoarin```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 06 Jan 2006 19:57 PST
 ```Myoarin, You made the comment: Would it help to point out that if the conveyor belt were running in the other direction, and the wheel bearings had zero friction, that the plane would just sit there with its wheels spinning? Only when the plane's engines are started, would it begin to move. You can do an experiment to check this out. Put on your roller blades, go to the gym and hop on the treadmill. Turn it on and just stand there without holding on. Do the wheels begin to freely spin so that you remain stationary, or does the treadmill carry you backwards off the back end? I guarantee you, you will go off the back end.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 06 Jan 2006 21:12 PST
 ```"You can do an experiment to check this out. Put on your roller blades, go to the gym and hop on the treadmill. Turn it on and just stand there without holding on. Do the wheels begin to freely spin so that you remain stationary, or does the treadmill carry you backwards off the back end? I guarantee you, you will go off the back end." Sure. There's some friction in the bearings. But airplanes do overcome this friction several thousand times each day worldwide. An airplane on a giant treadmill would be capable of the same. It would aquire airspeed, and would aquire lift.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 06 Jan 2006 23:16 PST
 ```Qed100, You seem to have a blind spot on this question. You assume the desired answer as your starting point. You said: Sure. There's some friction in the bearings. But airplanes do overcome this friction several thousand times each day worldwide. An airplane on a giant treadmill would be capable of the same. It would aquire airspeed, and would aquire lift. You seem to think that just because planes can take off on stationary runways, they can take off just as easily on a treadmill that moves backwards just as fast as the wheels of the planes rotate forward. Read your comment above and see what I mean. It contains no reasoning at all. And by the way, it is the friction between the wheels and the treadmill that is important, not the friction in the bearings.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 07 Jan 2006 06:36 PST
 ```I'm sorry, but you've provided no more rigorous analysis than anyone else in this thread. And it cannot be the friction between the wheel surface & the belt surface. Read again what I've said regarding the advantage delivered by wheel technology. The wheel/road friction is rendered moot.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ansel001-ga on 07 Jan 2006 15:47 PST
 ```Qed100, I have read what you said and it's nonsense. I have in the various posts, addressed and refuted all your statements. You have simply ignored mine and waved your hands and restated your "analysis" in which you assume the desired answer as your starting point. This being the case, I see no point in addressing any additional comments you make on this thread.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 07 Jan 2006 21:01 PST
 ```It's way too easy to denigrate an argument with pre-emptive codewords such as "handwaving", "It's not even wrong" and "You haven't been published in a reputable peer-reviewed journal. I see this sort of crap all the time on Usenet, but it doesn't demonstrate your argument. The friction between a runway & the perimeter surface of a wheel is not a source of drag against the progress of the aircraft parallel to the runway. Only friction in the wheel bearing can do this. If the engine exerts thrust which doesn't exceed the bearing friction, then indeed the plane won't go anywhere. If the engine thrust exceeds the bearing friction, then the plane *will* move forwards. It will accelerate as long as the thrust exceeds all sources of drag. Even if drag accumulates with speed, such as with fluid resistance for example, the plane will cease aquiring more speed, but will nevertheless continue to move forwards with constant speed; acceleration due to thrust will be balanced by counter-acceleration due to drag. Terminal velocity will have been reached. The only question is thrust vs drag in the wheel bearing. It cannot be (given a fixed runway) that bearing friction rises with wheel RPM such that it always maintains terminal velocity of less than takeoff airspeed; it's an empirical fact that airplanes achieve takeoff airspeed all the time. It is true that on a treadmill the runway speed can exceed the airspeed. The wheel RPM can be greater on a moving treadmill than on a fixed runway. Does the wheel bearing drag increase with RPM such that the belt can be moved fast enough to create bearing drag sufficient to keep terminal velocity below takeoff airspeed? If it does, then be my guest. Demonstrate.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: egon_spangler-ga on 10 Jan 2006 11:09 PST
 ```in a 1937 study the coefficint of friction for several airplane wheels was measured on different surfaces. I think it's ok to assume that airplane wheels are better but definately not worse than the wheels back then. The worst results they saw on concrete were .035 Now let's take a 747. It weighs roughly 850,000 pounds at max takeoff weight. That means you can calculate it's rolling resistance. 850,000 * .035 or 29750 pounds. (Worst case with tires built in 37) Now that same 747 has 4 engines that produce around 58000 pounds of thrust each. That means that there are 232000 pounds of thrust counteracting that 29750 pounds of friction. That means that only 12% of the total thrust is going towards overcoming the friction again in this worse case scenero of 1937 technology wheels on a really big plane where the rolling friction numbers will be the highest. You can do the calculation for any plane's weight and thrust you want. Check this out for an explination of friction http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html If the plane can overcome it's initial static coefficient of friction it can overcome it's kenetic coefficient of friction.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: cynthia-ga on 10 Jan 2006 17:42 PST
 ```I vote no, the plane will not take off. My reasoning is that as soon as the plane's wheels leave the treadmill and actually starts to MOVE, the plane will hit the wall in front of the treadmill and crash to the floor.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 11 Jan 2006 06:19 PST
 ```"I vote no, the plane will not take off. My reasoning is that as soon as the plane's wheels leave the treadmill and actually starts to MOVE, the plane will hit the wall in front of the treadmill and crash to the floor." This is the most sensible "no" argument I've read so far. Thanks! ;)```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 11 Jan 2006 06:30 PST
 `That is the difference between a Researcher and the rest! :)`
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: brasher-ga on 15 Jan 2006 12:41 PST
 ```I would say that the type of enigne in the aircraft makes a huge difference. If we look at a wing on its own then we must have a relative airflow before the wing produces lift. If there is no airflow, there is no lift and hence the wing wouldn't take off (Lift = 1/2 x rho x Vsquared x S) where rho is air density, v is True Airspeed (TAS) and S is the wing area. If TAS = 0 then Lift = 0). It is lift we reqire to counter weight (thrust counters drag). No lift means the aircraft won't take off. On take off, the Harrier aircraft uses the engine nozzles to produce upwards motion. However, this is pure thrust as there is no relative airflow over its wings. So, in the scenarion you've asked about, if the conveyor could counter any forward motion and there was nil wind then the wing would produce no lift. Say, for example, it was a propellor driven aircraft. Propellors produce airflow over the wings (nothing to do with the conveyor). This lift must oppose the weight of the aircraft and on a normal aircraft would not be sufficent enough to lift the aircraft off the ground. During light aircraft run-up checks we put the brakes on and apply nearly full power. Very little relative airflow so we don't lift off. It is only when we release the brakes and allow the aircraft to accelerate that the aircraft can take off. In this scenario, the treadmill would be countering any acceleration so the aircraft would remain on the ground.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 15 Jan 2006 13:09 PST
 ```iflytri-ga, Re your clarification: you HAVE gotten your answer if you read Qed100's, Poet's and my comments. I thought the example of roller blades on a treadmill would be convincing, but roller blade wheels are actually not as "free wheeling" as they could be, and some fitness treadmills are sloped backwards, so the example is apparently inadequate in some people's eyes. I will assume that you do understand the problem and recognize the correct answer since you refer to the debate it causes. That is more flattering than assuming the contrary. The fact that commenters here and on other sites refuse to accept that the plane's wheels have nothing to do with the plane's forward propulsion from its engines is their mistake. Cheers, Myoarin```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: sooks-ga on 15 Jan 2006 19:47 PST
 ```Alright...i read a little over half the posts before i couldnt take it anymore. The plane will fly plain and simple. The example of the cable attached to it and pulling it along is correct... Here is the reasons why. First of all, it ISNT a car. It doesnt propel itself at the wheels. A car has a drivetrain that spins the wheels and requires the friction of ground to push itself forward. A plane on the other hand, pushes against the air to move forward. A plane doesnt need wheels... thats why it can take off on the snow with skis or on water with floats.. Wheels are there to provide less resistance for the plane. It would act the same as with cement blocks...just would have more friction counteracting it. second... to solve the problem.. simply make a free body diagram. according to newtons laws... Force = mass * acceleration. SO if the net of all the forces is positive...it is accelerating and will continue to till it has sufficient wind over the wings to create lift. There are four main forces acting on it. Thrust (to the right) Drag (to the left) the normal force (up) and gravity (down). So if thrust is greater than drag... it will accelerate. the drag forces are wind resistance (would be the same as on a normal runway). Bearing resistance (too minimal to matter in airplane grade bearings... and rolling resistance. Most people tend to be hung up on this rolling resistance thing... rolling resistance = coefficient of rolling friction * weight. As you can see...this equation has nothing to do with speed. There may be a slight increase, as the extra heat may increase the CRF... but very minimally. Thus the plane will accelerate and continue too untill it creates lift. If someone still doubts that... if you ever want to convince someone....simply show how the drag force is equal to or greter than the thrust force...```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: cynthia-ga on 15 Jan 2006 22:21 PST
 ```Intense debate is an understatement, here's a thread where this very discussion is up to 44 pages: http://forums.flightinfo.com/showthread.php?t=66860 I think someone should contact MythBusters and ler Jamie and Adam get to the bottom of it. At the very least, they will consider it, reference this excerpt from the Transcript of Jamie and Adam's Nov. 10, 2004, Online Chat... ..."Q) Joe: Can I submit a myth to bust? http://dsc.discovery.com/fansites/mythbusters/chat/transcripts/04nov10/04nov10_09.html Answer by Jamie: Absolutely. Answer by Adam: Post it on the Web site. We read every single posting. While we often don't have nearly as much time as we'd like to post replies, we do read every email that comes to us..." (more at the link) If you can somehow design and execute the experiment, AND get it on video tape, you might get on the show: http://dsc.discovery.com/fansites/mythbusters/application/application.html Personally, I like this explanation of why the plane won't fly: http://forum.physorg.com/index.php?showtopic=2417&st=1155&#entry42611```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 16 Jan 2006 04:33 PST
 ```Cynthia, you were right the first time, the plane hits a wall, like this question does. ;)```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: ucabednego-ga on 17 Jan 2006 02:44 PST
 ```First I would like to say that reading this has been very enjoyable for me. I love the way that people got offended, upset, and belligerent all over a theoretical runway. As far as I can tell the plane would take off, but I'm only an Aerospace Engineer, I could be wrong. My laymen's justification is that the problem is very mathematically similar to sailing a boat up a river with swift current. It is possible to sail a boat up a river with no motor, why you say? Why because the thrust generated by the air on the sail is enough to over come the drag of the boat in the water. That's really all I have to contribute...the rest of the math stuff has already been said, I especially liked the reference to 1937 airplane wheels...that guy was on the right track. Also the guy who noted the runway moving at 2x the speed of the plane could be wrong say the it could be more, likely it would be much more because once the plane starts moving the runway will rapidly accelerate without result causing great frustration for the runway and all confused onlookers. Have a blessed day everyone.. matt```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 17 Jan 2006 05:35 PST
 ```ucabednego, Well said.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 17 Jan 2006 14:59 PST
 ```Yes, quite, although now I am beginning to feel that it is a little unfair to those stuck on the treadmill to dissolution them. ;)```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: omnivorous-ga on 21 Jan 2006 09:16 PST
 ```They do all of the time. The "treadmill" or moving runway is called an aircraft carrier. And they move much faster than the treadmills at the YMCA. And you can land on a moving surface too -- http://science.howstuffworks.com/aircraft-carrier5.htm```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: lupulin-ga on 02 Feb 2006 09:27 PST
 ```I just saw this question posed on Cecil Adams' "The Straight Dope." His answer was that the plane would take off. However I and all of my co-workers think it would not take off due to the problem of lack of airflow across the wings to create lift. It's been entertaining reading all the comments here, and there have been several people who agree with my position. However, I have not seen any reasonable refutation to this position. Again, simply put, the plane is not moving relative to the surrounding air. Without airflow over the wings there will be no lift. Without lift the plane cannot take off. Seems pretty simple to me, and again, I have not seen anyone counter this particular argument. The only ways I can see that my position is incorrect is if 1) there is sufficient airflow generated over the wings by the plane's propulsion system (either prop or jet). 2) there is something else besides lift from the wings that allows a plane to leave the ground. As far as I know, the latter is pretty solid, planes fly due to lift created by airflow across the surface of the wings. Number 1 I'm not cartain about, at least for propellers. However, jets are a different matter, they propel the plane forward through the principle of equal and oposite reaction, the plane moving in the opposite direction to the jet's thrust. Therefore, a jet engine, say all the way in the back of the plane, not evem near the wings, shouldn't create any airflow over the wings, so agin, no lift. I particularly like the comparison to a person running on a treadmill. Yo do not generate a headwind by doing so, so if you were a plane, again, no airflow, no lift. If someone has a reasonable counter-argument to this, I'd like to hear it!```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 03 Feb 2006 12:22 PST
 ```lupulin, I'm sorry, but if that's what you got out of this thread, then I'm willing to say that you haven't been paying attention to the whole thread. Skates on a treadmill is definitely not equivalent to an aircraft generating its own thrust.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: johasco-ga on 06 Feb 2006 14:31 PST
 ```There is an unstated assumption here, the invalidity of which gives the answer to the question. I think the reason that folks such as lupulin and his co-workers don't understand the correct answer is that their unstated assumption is never challenged. The unstated assumption is that the airplane on the treadmill, or conveyor belt, will remain stationary in relationship to the conveyor belt. This is not so. The airplane's thrust is not expended against the belt, but against the surrounding air. Thus, treadmill or not, the plane will move forward and eventually achieve enough airspeed for take off. Of course, if the conveyor belt is short, the plane will fall off the end before having achieved enough airspeed to take off, so a passenger jet would need a very, very long conveyor belt! This means that it would also make no difference if the conveyor belt was running in the same direction as the airplane--the plane would still have to develop the same amount of thrust against the air to take off. On the other hand, if one could somehow make the surrounding air move at the same speed as the thrust of the engines or propellers, then the airplane would stand still on the belt (or even on solid ground).```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 06 Feb 2006 16:57 PST
 ```johasco, Very well said. Thanks.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: incrediduck-ga on 08 Feb 2006 08:46 PST
 ```How about this? Apply the brakes on the plane and get the conveyor rolling to its max speed of 100kph. The wind-speed over the wing is now -100kph. Take the brakes off and accelerate the plane to its maximum velocity of 100kph. The wind-speed goes from -100kph to zero. There is no lift, despite the jet or prop 'pushing at the air'. I think this is in the spirit of the question(s).```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 08 Feb 2006 09:37 PST
 ```Just to keep score: 9 say it flies, 5 say it doesn't. Cynthia, Pinkfreud and two commenters posted non-commital comments, as did Omnivorous, but he then seemed to agree that it flies, so I counted him in the 9. Qed and Anse posted almost half the comments. I was a little reassured that the majority think the plane flies, but still wonder what the length of the discussion here and even more so on the other sites says about high school physics education. Cheers, Myoarin```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 09 Feb 2006 15:00 PST
 ```"How about this? Apply the brakes on the plane and get the conveyor rolling to its max speed of 100kph. The wind-speed over the wing is now -100kph. Take the brakes off and accelerate the plane to its maximum velocity of 100kph. The wind-speed goes from -100kph to zero. There is no lift, despite the jet or prop 'pushing at the air'. I think this is in the spirit of the question(s)." This isn't really relevant. It's agreeable that if the plane is dragged backwards at -100 m/h, then accelerates itself forwards a total of +100 m/h, then of course at that point there's no net airflow over the foils, and no lift. This doesn't in principle prevent the aircraft from continuing to accelerate right past that point 'til there is airflow and lift. Interestingly, if the wings' angle of attack were situated properly, being dragged backwards through air at 100 m/h would actually generate a lifting force under the wings.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: rracecarr-ga on 14 Feb 2006 11:32 PST
 ```5 days without a comment--you all should be ashamed. Here's comment #50: Ansel001 is right: most of the rolling resistance of a typical (rubber) wheel on a typical surface comes not from the bearing, but from wheel/road interface. As the wheel rolls, the tire deforms. There is always a flat patch pressed against the ground. There is precious little deformation of the steel bearings. The deformation takes mechanical energy and transforms it into heat: friction. Roller-blade, bicycle, car, 747, doesn't matter. The main source of rolling resistance in all (assuming we're not talking about air drag) is from the movement of the tire on the road. One thing to be clear about is the reference frame relative to which we measure the velocities. I assume we use the airport reference frame. That is, both the airplane speed and the conveyor speed are measured relative to the control tower. In this case, I think it's pretty clear that the plane can take off (sorry Ansel). But actually it would have a (slightly) harder time than than a plane which is not on a conveyor. This is because of the rotational inertia of the wheels. The wheels of the plane on the conveyor are spinning twice as fast at takeoff as are the wheels of the other plane. In order to spin the wheels up to the higher speed, an extra force, over and above that required to overcome the rolling resistance, is needed between the wheels and the conveyor belt. That extra force tries to hold the plane back, and so its acceleration will be a little less, and it will take a bit longer to become airborne.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: rracecarr-ga on 14 Feb 2006 15:03 PST
 ```I just took a look at the Straight Dope link posted by Pinkfreud. The question there is worded a little differently. Instead of matching the speed of the PLANE, the conveyor matches the speed of the WHEELS. This seems to be the definition Ansel has been using. If instead of watching how fast the plane is moving past the control tower, you look at a spedometer attached to a wheel, and match that speed with the conveyor speed, the plane won't move, and it certainly won't take off. As Ansel says, if the wheels don't slip, and the conveyor moves backwards as fast as they spin forwards, then regardless of anything you might say about engines, thrust, etc, the plane obviously goes nowhere. In this scenario, the thrust from the engines goes 100% into spinning the wheels faster and faster. In a very short time, they will be going so fast that the centrifugal force will tear them apart, and then the plane won't roll anymore, and will be carried backward with the conveyor. If you ignore limitations on the strengths of materials, and imagine that the wheels would never break, eventually the speed of their perimeters (and the speed of the conveyor belt) would approach the speed of light, still without the plane ever having moved. However, I think this is the answer to a different question, because to me "the plane's speed" means the speed of the center of mass of the airplane, not the rotation speed of the wheels.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 14 Feb 2006 17:14 PST
 ```Rracecarr, Clever of you to catch that difference in the definitions of the problem, but I don't see that there is any difference in the solution. If the plane can take off at 200 mph, when it starts moving, the conveyor belt will move at the same speed in the other direction, but since we are assuming no material failure and minimal bearing friction, as before, the wheels will just spin faster, and the conveyor belt will still unable to keep the plane from advancing and eventually taking off. Tire failure is, incidentally, a real problem, as someone mentioned. Heard some guys discussing taking off from high altitude airfields, where the thinner air requires a higher speed to achieve liftoff. Apparently the max. speed is marked on all tires. But if we are assuming the existence of the conveyor belt that can run at such speeds (a much more likely failure), then the tires can't be part of the problem.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: rracecarr-ga on 14 Feb 2006 19:45 PST
 ```Hi Myoarin-- If 1) there is no tire slippage, and 2) the speed of the conveyor belt is exactly the same as the speed at which the wheels are spinning, then the plane remains stationary. This is not a statement that has anything to do with the specific nature of airplanes--it is just a mathematical fact. So the problem in your previous post is the phrase "when it starts moving" -- it never does. Forget about the plane for a minute, and just think about one of the wheels. Let's say it has a circumference of 1 meter, and is spinning at 10 revolutions per second. If the conveyor belt weren't moving, the wheel would roll along at 10 m/s. However, the conveyor belt is moving at 10 m/s in the opposite direction, and the wheel just spins in place.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 15 Feb 2006 06:03 PST
 ```Hi Rracecarr, I am a little disappointed with your analysis. What makes the plane move is the engines acting on the ambient air. The fact that it begins to move at all has nothing to do with its form of contact with the ground - beyond overcoming negligable wheel bearing friction. It starts creeping forward, and the belt creeps backwards, making the wheels turn faster (but still slowly at this stage, but hardly braking the advance of the plane). Since the wheels can rotate freely, the plane continues to accelerate, as does the belt, the wheels spinning even faster, much faster than in the other definition of the problem, I admit, and maybe at takeoff at some extremely high speed. As someone has long sinced pointed out, the plane's propulsion by its engines can be compared with its being pulled by a cable parallel to the ground - or your pushing a roller skate forward on a treadmill or conveyor belt. You can do it, despite the counter motion of the belt. Since we are assuming no practical problems (bearings' freezing up, tires' flying to pieces, the existence of the conveyor belt), let's take it to the extreme and assume absolutely no friction from the wheel bearings. It this case, the belt could be flapping along the runway before the plane even starts it engines and the plane would still stand still - no bearing friction, no overcoming of the inertia of the motionless plane. The engines start, the plane moves forwards, regardless of what the wheels and belt are doing. Indeed, by assuming zero friction in this hypothetical situation, they no longer are part of the equation. If the belt were moving in the direction of takeoff, with zero bearings' friction, it would also have no effect on the plane, just allow the wheels to turn more slowly - or even backwards - even at takeoff - if it were moving forward at more than 200 mph. Am I convincing anyone? All hypothetical, of course, but the problem by definition is. Cheers, Myoarin```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: rracecarr-ga on 15 Feb 2006 10:45 PST
 ```Hi again Myoarin, I'm sorry that you're disappointed. But I really think you wouldn't be if you would take two minutes to consider what I wrote. It is very simple, and it is correct. If the plane is rolling forward relative to the conveyor at velocity V, and the conveyor is moving at -V (relative to the airport), then the velocity of the plane (relative to the airport) is the sum of the two. What is V - V? How can you keep arguing that it's not zero? The cable analogy is wrong. It is fine (and helpful for some people I think) for the original problem. But in the case where the speed of the wheels (or alternatively the speed of the plane relative to the conveyor belt) is used to set the speed of the conveyor belt, it isn't. However you try to move the airplane, whether with its engines or a cable, IT WILL NOT BUDGE. However much forward force you apply with the cable or engines, the exact same amount of force will be applied in the opposite direction by the conveyor belt on the tires. That force will act to accelerate the spin of the wheels. And forget about bearing friction (and wheel/surface friction too). Things like that don't belong in thought problems like this. The force the conveyor belt applies to the wheels is not acting against friction. It is acting against the inertia of the wheels. It accelerates their spin. This is the factor that is ignored by the people who say that the the wheels "decouple the plane from the runway". You might ask: "what if I put the plane on the conveyor belt, and then pull it along at 10 meters per second with a cable?" Well, that is a logical impossiblity. You cannot have the wheel speed match the conveyor speed, no wheel slippage, and still move at 10 meters per second. It is like asking what happens if you're tied to an immovable wall with an unbreakable rope, and you start to walk away from the wall at 10 m/s. You can't even start to answer, because the question itself is impossible. All the conditions of the question cannot possibly hold true. In the airplane question, this problem arises if you specify that the wheels are massless, because it doesn't take any force to spin a massless wheel, and so the conveyor belt cannot apply a backward force to the plane. In this case, the question is logically inconsistent. Something has to give. Either the wheels must slip, or the belt must fail to perform as specified. It is pointless to debate what would actually happen, because the question itself is wrong, and everyone can have their own opinion about which part of it should be changed. This has once again gotten to be a longwinded comment. Sorry. Here is the essential point for the 3rd and last (I promise) time: Specifying that the velocity of the conveyor RELATIVE TO THE AIRPORT is equal and opposite to the velocity of the plane RELATIVE TO THE CONVEYOR, is EXACTLY THE SAME as specifying that the velocity of the plane is zero. The answer is in the question.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 16 Feb 2006 08:36 PST
 `I disagree, but 'nuf's enough. :-)`
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: alexb123-ga on 17 Feb 2006 09:53 PST
 ```Anyone who thinks that the airplane will take off is, i'm sorry to say, a complete idiot. Or ignorant. Anyone with a basic knowledge of the principles of lift will know that lift is created as an airstream passes by an airfoil or aerofoil and is deflected downward. The force created by this deflection of the air creates an equal and opposite UPWARD force according to Newton's third law of motion. Because a specific shape of wing will deflect a FLOW of air downwards at a certain force, an equal and opposite force will act on the airplane, giving it lift and allowing it to fly. For this to happen, the airstream needs to be of a sufficient speed - this is the reason planes have to move forward on a runway, or more accurately, move forwards through the AIR. If the plane was on a treadmill in a windtunnel providing a fast airstream it would take off - however, from the wording of the question the plane is in a normal "windless" (or close to windless) situation. It has NOTHING to do with friction in the wheels or any of that crap. An airplane needs AIR moving ACROSS THE WINGS to gain LIFT in order to take off. A notable exception is the harrier jumpjet; but a vertical take-off in this case occurs due to a significant downward force provided by engines, not an airstream moving over the wings. If the plane is not moving through the air (or the air moving past the plane) at sufficient speed it WILL NOT TAKE OFF! There is NO airstream if the plane is running on a treadmill, even if the engines are running. The engines DO NOT push air over the wings; their purpose is to move the plane fast enough through the air to anable LIFT to be generated. The engines can run as "fast" as they want but if the plane is on a treadmill it won't move!!!! Why is this so hard for so many people to understand?```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 17 Feb 2006 19:10 PST
 ```"Why is this so hard for so many people to understand?" Regardless any arguments regarding wheel inertia, etc., it's hard to see why you can't see: an aircraft with airbreathing motors doesn't even ostensibly generate lift by blowing air over the foils directly with the motors. The motors generate horizontal thrust, which propels the craft forward THROUGH THE AIR, thus generating the lift force. The ONLY question in this regard is if the forward acceleration, due to engine thrust, will be negated by the wheels spinning passively on the treadmill. Answer: it won't.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 18 Feb 2006 03:13 PST
 ```Right. QED, if we are so brilliant, why can't we convince anyone? ;-)```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: qed100-ga on 18 Feb 2006 08:54 PST
 `Maybe we're not so brilliant. >:)`
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: doug512-ga on 01 Mar 2006 10:19 PST
 ```Yes, it will take off. However not because of forward movement. As with many hypothetical questions we must assume some things not stated in the question. Let's assume this is a magical converor belt that can run fast enough to keep the aircraft relatively stationary with respect to the ground next to the converor belt. We must also assume that the aircraft tires/wheels will not fly apart (which they likely would). Further, let's assume the intent of the question is that this converor belt has the ability to counter the forward motion of the aircraft. Since the aircraft will tend to move, not as a result of it's wheels roating, but as a result of engine thrust, the only way this magic converor belt can "stop" the aircraft from moving forward is to accelearte so fast that the aircraft engine's energy is all consumed by wheel friction and the initeria of spinning up the aircrafts wheels. Very quickly the converor belt will be moving at impossible speeds, but this is a hypothetical question and if we assume it is possible for a converor belt to hold this aircraft in place we have to assume it can move this fast. So, very quickly after the aircraft attempts to move forward, the conveyor belt is spinning under the aircraft at thousands of feet per second. Friction between the air at the surface of the converor belt and the belt will cause the air to move with respect to the ground next to the belt. At some point the magic belt will be moving fast enough to generate enough airflow over the wings that the aircraft will lift off the belt, again assuming the belt and wheels/tires are magic and do not fly apart. So, yes the aircraft will lift off the belt. What happens next is the subject of another debate.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 01 Mar 2006 18:13 PST
 ```Well, that is a new twist, but the problem states that the belt only moves as fast as the plane.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: rracecarr-ga on 02 Mar 2006 16:22 PST
 ```doug has a point. Myoarin, I think maybe you still haven't understood that there is more than 1 possibility for the definition of the 'speed' of the plane.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: earlesam-ga on 03 May 2006 07:42 PDT
 `no`
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: triangulated-ga on 17 May 2006 23:49 PDT
 ```There are several assumptions made here which render this question unsolvable as currently stated. Let's solve two of the possibilities. 1: Pure fantasy. The airplane engine and power of treadmill are infinite and bearing frictions are 0. The wheel rotation has no effect on the plane and it takes off. 2. Real world. The treadmill exerts a force on the plane via the friction of the bearings in the wheel axle. This friction increases with rotational velocity, as long as the treadmill engine is capable of spinning the wheel at high enough speeds to counteract the thrust generated by the plane engines the plane will remain in one spot and not be able to take off. If the treadmill cannot maintain the speeds necessary the plane will begin to accelerate after the treadmill has reached it's max speed, if the plane engine is strong enough to achieve enough speed to generate the required lift on its wings it will take off. This scenario is easy to simulate with a toy object on a treadmill. Imagine if the toy has very good bearings and you can easily hold it on the treadmill, the wheels will spin up to the treadmill max speed and you will be able to push the toy forward. In this case the thrust generated overcomes the bearing friction and flight would be achieved. Now imagine the toy has really terrible bearings and is very hard to make the wheels move. At the same speeds the treadmill is capable of transmitting a much greater force to the toy and if the friction on the bearings is enough you will not be able to push the toy forward.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: jstrong-ga on 19 May 2006 11:36 PDT
 ```This is somewhat of a "trick" question. Not because it is phrased in a deliberately tricky way, but because people tend to have trouble thinking about the operation of other vehicles apart from cars which they know so well. The heart of the confusion is simply these two important facts: * cars propel themselves by pushing against the ground via friction * airplanes propel themselves by pushing against the air If you can let go of how cars operate and think about what an airplane does, you'll be able to see the problem clearly. One good way of tackling this problem is to find a good analogy. But the analogy must be a valid one else you'll just get more confused. For example, someone posted the analogy of running on a treadmill. Why is that a bad analogy? Because one runs by pushing against the ground via friction between their shoe and the ground. This is how a car propels itself! It is not how an airplane propels itself, by pushing against the air. Bad analogy. Let's use this analogy. Instead of looking at the airplane, let's back up and go into the airport. Suppose you're walking down to your gate and pulling your carry-on bag behind you. It's a nice new bag with low friction wheels. No problem! Up ahead you see one of those moving walkways. You don't see anyone coming, so you decide to do a little experiment. You go over to the walkway that is moving TOWARDS you and place your bag on it. Meanwhile, you step off to the side of the walkway, and still holding on to the handle of your bag, you continue to walk along. In fact, you intentionally walk along at the same speed that the moving walkway is going, just in the opposite direction. Question: does the bag move or does it remain stationary as you keep walking? Obviously it moves with you. So why does your bag move forward when you are walking at the same speed of the conveyor going in the opposite direction? The answer to that question is also the answer to the airplane-conveyor question. To complete the analogy, the pull of your arm is analogous to the force of the airplane engines. The bag's wheels are analogous to the airplane tires. Do the nice low-friction wheels on your bag on the conveyor pull against you anymore than they do when you're just pulling your bag along normally? No, they don't. They are free-wheeling, after all. Meanwhile, you're pulling the bag with the same force in both cases. So in both cases, the bag keeps moving forward. Likewise with the airplane, the pull of the engines doesn't change nor does the force on the airplane imparted by the tires change no matter what the ground is doing underneath the tires. You have the same force imbalance in either case, and since Force = mass x accceleration, you have the same acceleration. Remember, we are talking airplane engines which push against the AIR, not the ground. The acceleration is with respect to the AIR, thus the airplane develops a speed relative to the air and can eventually take off. That's a long winded analogy. Here's a quicker solution. Engineers learn to draw Free Body Diagrams to understand such problems. A FBD is just a block diagram which illustrates the forces acting upon an object. The net force can be calculated from all the contributing forces. If that net force is not zero, the object accelerates in the direction of that force. Let's draw a FBD now. Represent the airplane by a simple rectangle (the shape doesn't matter). Indicate the force of the engines pulling on the plane with a large arrow, labeled "F_e" with e for engines. What force are the tires imparting to the plane? Remember, they spin freely except for bearing friction and rolling friction, which produces forces that are quite tiny compared to the engines. Represent those forces with a small arrow, labeled F_t where t means tire. What other forces are operating? There is a drag force too. But remember this drag force is also small compared to the propulsion of the engines at least at takeoff speeds. Label that F_d. FREE BODY DIAGRAM F_d |----------| F_e <---| Plane |-------------> |----------| <-- F_t So what do we have here? We haven't put numerical quantities on these forces, but instead have just been talking in terms of large and small. That's okay for the purposes of this illustration. It's enough to know that F_e is going to be much greater than F_d + F_t pulling in the opposite direction. If that's the case, we have an unbalanced force on the plane. Therefore, it accelerates. And it accelerates with respect to the AIR, since F_e is produces by the engines pushing against the air. To sum up: Yes, the airplane takes off. The motion of the surface underneath the freely-spinning tires is irrelevant to the acceleration of the aircraft since the tires cannot impart any force to the aircraft (aside from the aforementioned very small rolling and bearing friction). I hope this discussion has helped somewhat and not muddied the waters any further. John Strong Ph.D., biochemical engineering M.S., chemical engineering B.S., mechanical engineering```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 19 May 2006 14:08 PDT
 ```Ah, somebody who knows what he's talking about. Great analogy, not that it will necessarily convince the pedestrians with only their feet to move them. Thanks.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: rracecarr-ga on 19 May 2006 18:29 PDT
 ```Jstrong-- Obviously the plane can take off if you measure the speed of the plane relative to the fixed ground, and match it with the conveyor speed, also measured relative to the fixed ground. But if you measure the speed of the plane relative to the conveyor belt (by using a spedometer attached to the plane's wheels, say), and match that speed with the conveyor belt, the velocity of the plane must always be zero. It will never move forward. Also you're leaving a force out of your diagram--the backward force exerted by the conveyor belt on the tires that goes into accelerating the spin of the wheels. This force is unimportant in the first case (speed measured relative to fixed ground) but not in the second.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: myoarin-ga on 20 May 2006 06:25 PDT
 `Nomen est omen: Rracecarr, all four wheels on the ground and accelerating. :)`
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: vballguy-ga on 23 May 2006 16:37 PDT
 ```Wow - how funny - this seems so simple to me, yet I am sure everyone feels the same way about their answer... The problem is, everyone forgets it is a hypothetical. Lets say you put a skateboard on a treadmill and turn it on to the fastest spead possible as quickly as possible - it will shoot off the back of the treadmill due to the friction of the tires/bearings.... Lets say you attach a string between the skateboard and the front of the treadmill to a device to measure the force.... If you start the treamill ever so slowly, the skateboard will not pull so hard.... if you start quickly there will be more force against the string. This one is hard to underststand but the ACCELERATION in the bearings does cause friction This is the key to the whole puzzle. Do you accept that acceleration of the treadmill does cause more friction. Its a tiny amount but the amount is there. So if you accept that the treadmill can increase the ammount of friction, can it do so infinitly? The force of the engine is huge- I don't think it would be possible to concieve of a treadmill fast enough to hold back a plane - because the resistance provided by the bearings and tire friction is so minute... BUT THIS IS HYPOTHETICAL. If you accept that 1) the treadmill creates friction in the bearing. 2) the friction or force backwards is increased the faster the treadmill accellerates 3) that the force the engines can exert is fixed. 4) the force the treadmill can exert is NOT fixed because it can spead up infinitely fast to an infinite speed Then you see that the plane can never take off. The problem is that the force of the engine would require astronomical amounts of friction from the bearings and this really isn't possible. BUT in hypothetical world we can continue acceleration backwards at impossible speeds. So it really comes down to - does the force exerted by the treadmill increase the faster you accelerate? If you say yes. And you agree that there is nothing to stop the system (its hypothetical) from speeding up, then the plane CAN NOT TAKE OFF.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: jmsteph-ga on 30 May 2006 23:03 PDT
 ```Let's try to come up with a final answer that everyone can agree on... sorry if it's all been said, i haven't read all the posts. quoted from a post by egon_spangler-ga about half way down this page... "in a 1937 study the coefficint of friction for several airplane wheels was measured on different surfaces. I think it's ok to assume that airplane wheels are better but definately not worse than the wheels back then. The worst results they saw on concrete were .035 .... Now that same 747 has 4 engines that produce around 58000 pounds of thrust each. That means that there are 232000 pounds of thrust counteracting that 29750 pounds of friction. ... If the plane can overcome it's initial static coefficient of friction it can overcome it's kenetic coefficient of friction." So....232,000lbs thrust - 29,750lbs friction = 202,250 lbs total force propelling the plane forward. *The important thing to note here is that friction comes from the bearings in the wheels, and bearing frcition does not depend on speed. Here is an quote from another forum Excerpt from SKF Interactive bearing catalog for rolling element bearings: "Under certain conditions (bearing load P » 0,1 C, good lubrication, normal operating conditions) the frictional moment can be calculated with sufficient accuracy using a constant coefficient of friction µ from the following equation M = 0,5 µ F d where M = frictional moment, Nmm µ = coefficient of friction for bearing (Table 1) F = bearing load, N d = bearing bore diameter, mm" (http://www.eng-tips.com/viewthread.cfm?qid=113896&page=5) So, speed is irrelevant for calculating the friction drag on the plane. Only the weight of the plane matters, which is constant. Therefore, the friction force in the plane is always approximately 29,750lbs in the above example. It doens't matter how fast the conveyor belt is moving, it will never (theoretically) prodcue much more drag on the aircraft...the theoretically part comes in when the bearings start to spin faster than their working limit and fail, lock up, and then there'll be lots of friction. So, you can spin that conveyer belt all you want, the 29,750lbs of friction don't do much to stop the 232,000lbs of thrust. The plane will still have plenty of thrust with the conveyor belt spinning to take off. In fact, since the thrust has to overcome the bearing friction force even on a non-moving runway, the added friction with the backward-moving runway is small. The plane would take off, unless the bearings lock up, even considering bearing friction.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: jmsteph-ga on 30 May 2006 23:38 PDT
 ```one addition to the last thing I just wrote... moving the wheels faster does in fact create more "friction force." Rather, it creates some force which opposes the forward motion of the aircraft, not actually friction. This force comes from the inertia of the wheels themselves. It takes some energy to accelerate the wheels, energy which shows itself in the form of an additional drag force on the aircraft. Therefore, if you continue to accelerate the conveyer belt, then yes you can continue to add drag. However, as soon as the conveyer belt stopped accellerating and returned to constant velocity, the drag force would die back down to the bearing friction force, no matter how fast the belt is moving at this point. Since keeping the aircraft stationary under these conditions would require a conveyer belt which could continue to accelerate indefinately, this scenario is impractical. If this was possible, however, the yes the plane would remain stationary and no it would not take off. In reality, this wouldnt work nad the plane would take off.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: pilot737-ga on 02 Jun 2006 11:17 PDT
 `Plane can not take off unless there is a strong headwind :)`
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: deepblue7800-ga on 21 Jun 2006 04:02 PDT
 ```The catergorical answer is YES. The fundamental point to appreciate is that the power from a plane for forward momentum is not through its wheels and the wheels are free to spin. The other point to appreciate is that the questions states that the treadmill is tracking the planes speed and not the other way around. (See scenario B) I think people's yes/no answers depend largely on them ignoring these two points. To clarify, imagine the treadmill runway but with a fixed control tower at the start. Scenario A - Lets assume that the plane tracks the treadmill's speed: The treatmill starts moving at whichever ludicrously high speed you care to mention and the plane's engines are running. For the plane to remain stationary relative to the control tower, the engines would only need to operate at a power to overcome the friction on the free-spinning wheels - as previously quoted by egon_spangler, about 12% for a 747 with the wrong wheels on a concrete treadmill (a whole new question, I feel?). In this instance, will the plane take off? Answer: Absolutely not as there is no airspeed/lift (see everyone elses comments for further explanation) Scenario B - the treadmill tracks the planes speed: The "speed" of the plane would be it's speed relative to the control tower. If the plane accelerates to 100mph, the treadmill would accelerate to 100mph, and the net effect would cause the wheels to spin at 200mph. However, the plane would still be moving forward at 100mph. (For the plane to remain stationary relative to the control tower, there would have to be no speed, and so the treadmill would not move either.) Will the plane take off? Answer: Absolutely yes. Once it achieves the necessary speed relative to the control tower, the airspeed would be sufficient to create the lift. Granted the plane will have to overcome more friction on the wheels than it would on a static runway as they are moving at twice the speed, but the engines would easily overcome this. Different conditions would cause the effects that others are arguing towards, but none apply to this question: If the treadmill was replaced by an windtunnel and the speed of the windtunnel increased to match the thrust of the engines or vice versa, then at the necessary speed, the plane could takeoff and fly whilst remaining stationary relative to the control tower. Alternatively, if you replaced the plane with a car with wings where its forward momentum on the ground is through the wheels, then the treadmill tracking the speed would increase until the car reached it's top speed. The car would remain stationary relative to the tower and it would never take off due to the lack of airspeed. Aside from the treadmill question, I do recognise that a winged car with no means of propulsion once in the air would be pretty rubbish. In conclusion, given the conditions of the question, the plane will take off everytime.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: deepblue7800-ga on 21 Jun 2006 04:21 PDT
 ```If I'd read John Strongs answer before I'd posted my own, then I think I wouldn't have bothered!```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: deepblue7800-ga on 21 Jun 2006 05:04 PDT
 ```I accept Rracecarr's point that there are two interpretations of "speed": relative to the control tower and relative to the conveyor belt. However, as he clearly states, to answer the question based on the latter interpretation is a logical impossibility "You can't even start to answer, because the question itself is impossible. All the conditions of the question cannot possibly hold true." Would this not suggest then, that there can only be one logical interpretation of "speed". Anything else makes the question redundant, which I am sure isn't the point.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: bluegray-ga on 21 Jun 2006 05:30 PDT
 ```First, you have to assume a few things. 1. The conveyor belt can react quick enough to the plane's speed so their speed stays exactly the same. 2. The engine or propeller that powers the plane can only cause the plane to go forward (or backward) but not create any lift. So the only lift generated will be from the wings. 3. The conveyor belt's speed is linked to the speed of the plane relative to the ground and therefore also to the air around it. It is not linked to the turning speed of the wheels. 4. The wheels of the plane does not power or cause the plane to go forward. 5. The wheels can turn freely and without friction, but only in reaction to the movement of the plane or the conveyor belt. Let's start with the plane standing still. The conveyor belt is not moving because the plane is not moving. As the engines start to cause the plane to go forward, the conveyor belt starts to move at the same speed of the plane. But because the wheels are free to move, the conveyor belt has no effect on the plane, only the wheels, so the plane continues to go forward. The faster the plane goes forward, the faster the conveyor belt moves backward, but it's only affecting the wheels, not the plane. The plane will still take off, but the wheels will turn at twice the speed because of the conveyor belt. Because the wheels are free to move and does not affect the speed of the plane, the conveyor belt has no effect on the speed of the plane. If the plane was powered by it's wheels, like a car, and the conveyor belt speed was linked to the speed of the wheels. Then the plane will not move.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: bogdanvarlamov-ga on 11 Sep 2006 23:31 PDT
 ```The people who claim that the wheel will move backwards are overlooking something very important... Put a ball on a piece of paper, now pull the piece of paper forward fast. What happens? The ball spins in a relatively same space? Hmmmm... The fact is the WHEEL which will is modeled by the BALL will start SPINNING corresponding to the motion of the runway...the only way the net movement of the wheel will exceed 0 is either if the wheel spins faster than the runway, or the runway faster than the wheel... The wheel created friction in TWO ways...one is against the runway, the other is against the plane! Friction against the runway transfers motion from the wheel to the runway and from the runway to the wheel...So if the runway moves, the wheel turns but due to friction connecting the wheel to the plane, the wheel doesnt transfer all of the energy because some is lost to friction, so the plane unless it were being pushed forward would move BACKWARDS if the runway was just moving by itself. Now let's assume that the plane has no friction connecting the wheels to the plane. Lets say they have magnetic bearings that just float the plane due to magnatism. The wheels still have normal friction to the runway, but now when we turn on the runway the wheels spin, but the energy isnt transfered to the plane...so the plane doesnt move no matter how fast we spin the wheels... So now...let's assume that when the plane turns on its engines, forward thrust is created, this creates a force forward and the plane will start moving forward. This forward motion pushed forward on the bearings of the plane, which push forward on the wheels (without friction, but with magnetism) but since the wheels are touching the runway friction prevents them from just sliding forward (There is a forward force on them remember?). They must ROLL to move forward in reaction to the force... When the wheels roll they exert a force on the runway in the opposite direction of their movement (just as you do on the earth when you walk across it) but when you move push agains the earth, the earth pushes back and you move. In this case the runway does NOT push back but absorbs that force as it turns. So when the force is absorbed (kind of like you trying to jump on a floor that falls through right when you apply force to it, you will stay in the same place as the floor falls under you, and then gravity will take over and you will fall too) The plane will not be able to provide enough force to the wheels to make them move as all of the force will be cancelled out by the moving runway. BUT the plane's engine do NOT only apply force to the WHEELS!!! There is a force pushing on the rest of the plane, and unless this plane is in a wind tunnel that has air blowing on it to create enough resistance to counteract the force of the cockpit pushing against the air, the REST OF THE AIRPLANE will move forward. So what happens then? The wheels stay in one place, the rest moves forward? The plane begins to rotate around the stationary point(s) (this being the wheels) and this means the plane starts pointing towards the ground. Think of it this way, you are running on a treadmill as fast as you can, your feet are literally being swept under you as fast as you can place another one on there. There is no way they are moving forward anymore. Now I come up and push your head forward. What happens? Do you move forward? NO you cant! Your head travels faster than your feet, but since you are connected your head doesnt travel straight forward but is pulled by the rest of your body like a ball on a tether and travels in an ARC, downward and then you fall. Same thing with the airplane, the wheels cant move, the rest of the plane doesnt have any forces to prevent it from moving (aside air friction) so the plane starts moving like a ball tethered to a pole (the pole being the wheels) IT starts rotating towards the earth, ultimately around the front wheel as when it tilts slightly the back wheels will come off the ground and then only the fast spinning front wheel will keep it from moving. So inevitably the plane rotates until it is pointing down into the ground enough that the tip of the nose catches the runway and thats the end of that flight. Then of course the other scenario is that this plane can generat STATIC lift by the engines. IF the engines can move enough air from the front of the plane to the back of the plane while the wheels do not move, then the air flowing under the wings could generate the lift it needs to get the wheels off the ground. Another thing to consider is that in our universe by our laws of physics nothing can travel at the speed of light so assuming that the engine can generate infinite energy is unrealistic, and then to assume the runway could rotate at infinite speeds is unrealistic too. This question does not have enough information to be reasonably answered. IF the engine and the runway can only go so fast, then the scenario I described will occur and the plane will tip over and crash. IF they wheels and the runway can move infinitely fast than they will reach the speed of light almost instantly and physicists arent smart enough to figure out what happens yet, some say that its impossible to accelerate to a speed faster than that of light so... then the wheels and the runway would be spinning at the speed of light creating massive gravitational forces and just things that this question wasn't meant to ask. IF they COULD spin faster than the speed of light they would end up traveling back in time... Then what? the plane wouldnt have any wheels and runway to get in its way and take off? HAHA (no because the mass of an object moving near the speed of light would crush the plane, so the plane would be crushed by the gravity of the runway and the wheels spinning so fast). There ya go... THAT is what would really happen.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: hintz-ga on 03 Nov 2006 18:13 PST
 ```Very interesting. I am going with the notion that it doesn't take off. If the conveyor is moving backwards at the speed the plane is thrusting forwards, it will esensially be at a stand still (much like the aformentioned escalator theory). Even if you suddenly stopped the conveyor moving, whilst the plane is still thrusting, the plane would still need to cover a certain distance to gain the velocity needed to have lift. Also, another thing that corssed my mind. If you had the conveyor matching the thrust speed of the plane, and the conveyor was dropped from underneath the plane, the plane would fall with the conveyor. I suppose its the same principal that comes with having a fly in your car flying around, yet you are doing 100mph. I have no qualifications, and was a school drop out at 16, so if my answer seems a bit primitive, that's why. But i have a good understanding, and the common sense to see that the plane would not take off.```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: hintz-ga on 03 Nov 2006 18:24 PST
 ```Ok, I've just changed my mind lol Thinking about it, when a plane thrusts, it thrusts against the atmosphere, not through the wheels on the belt. lol I can see why this is a bhig debate, There's not really any solid way of proving which is right or wrong unless its actually tried. How about thinking of it the other way? If you sat the plane on the conveyor belt, but diddn't switch it on......then you thrust the plane to take off.....would the belt move in the opposite direction of the plane? Like if you were on a free running tredmill, if you exert a force to start sprinting with your legs, the belt will move the opposite way. Most confusing, and i'd love to know the answer :)```
 Subject: Re: Will an airplane on a treadmill be able to takeoff? From: commonsense4u-ga on 29 Nov 2006 10:02 PST
 ```Hmmm...for an experiment we simply need a device large enough moving in the opposite direction under the airplane. Let's use planet earth. Will an airplane, pointed against the rotational direction of the earth, have difficulty taking off? No. BTW the earth would be spinning approx 1070 mi/hr against the plane if at the equator. If you believe the drag is great enough to prevent the plane from taking off then the same would apply when the plane is landing. As soon as the wheels touch down then plane should come to a halt on it's own but this is not true and major brakes must be applied because there is not enough friction to stop without them.```