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Plane on a conveyor belt (41) Mon, Jun 26, 2006
The case of the plane on a conveyor belt has been extensively discussed in the online world, and still doesn't have a definite conclusion.  Or rather, there are two opposing sides which believe wholeheartedly in their explanation, and these sides will never agree.  The question is this: 
A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?
I've read a thousand people's opinions about this and heard every comparison ranging from a skateboard on a treadmill to a weightless car on a sheet of paper.  Taking into account some major assumptions (a plane on a conveyor belt is actually plausible; frictionless wheels, bearings, conveyor belt; no wind; ideal/instantaneous control system), my take on it is this:  The plane won't take off [Edit:  I changed my mind].  Here's my reasoning: 

1.  In order for a plane to take off, it needs to have air passing over its wings at a certain speed.  This air can come from the plane moving down the runway, or it can come from wind.  Theoretically, a plane can take off while sitting completely still, as long as there is a significant amount of headwind.  However, since there's no wind in this example, the plane must be moving forward at a considerable velocity. 

2.  A plane's wheels are "dumb".  In other words, they're only there to reduce friction.  A plane could just as easily have no wheels and just rest on its belly on the runway.  It could still take off because its motion is produced by thrust from its engines or the movement of air from its propellers.  The wheels will spin when the plane is in motion and in contact with a surface. 

3.  As many people have pointed out, the question's wording can be confusing. 
a.  If "plane speed" means "angular velocity of the wheels with respect to a stationary/ground observer", the conveyor belt would spin at an infinitely increasing rate, which is logically impossible.  For example, if the wheels started to spin at 100 rpm, the conveyor would ramp up and spin at 100 rpm.  But this would cause the wheels to actually be spinning at 200 rpm from the point of view of a stationary observer because the ground is no longer stationary but is moving at 100 rpm in the opposite direction.  This would force the conveyor belt to spin at 200 rpm, 400 rpm, 800 rpm, etc., ad infinitum. 

b.  If "plane speed" means "angular velocity of the wheels with respect to the conveyor belt", the velocity of the conveyor belt would always equal the velocity of the wheels, no matter what.  This means that the plane wouldn't move, no matter what.  If the wheels started to spin at 100 rpm, the conveyor would ramp up and spin at 100 rpm.  From the point of view of the conveyor belt, the wheels would still be spinning at 100 rpm even though they're actually spinning at 200 rpm from the point of view of a stationary observer.  No matter what speed the wheels spun, the conveyor would always be spinning at the same speed as the wheels.  This would prevent any forward motion of the plane. 

c.  If "plane speed" means "linear/horizontal velocity of the plane with respect to a stationary/ground observer", the plane speed would always be zero because the conveyor belt would always cancel out any forward motion of the plane.  For example, if the plane started moving at 100 mph to the right (with motion derived from thrust), the conveyor belt would immediately begin moving at 100 mph to the left.  Although the wheels would be spinning at an incredibly high rate (the wheel diameter doesn't equal the conveyor belt diameter, so the conveyor belt speed of 100 mph would translate to a wheel speed of something like 100,000 rpm [total guess, but the concept is there]), the plane would not change position from the point of view of a stationary observer.  If it started at point A, it would stay at point A.  This is the same result as part b. 

d.  If "plane speed" means "linear/horizontal velocity of the plane with respect to the conveyor belt", it's the same as part a.  The conveyor belt would spin at an infinitely increasing rate. 
So in conclusion, the plane wouldn't take off because it wouldn't move from its original location. 

Part of the reason this whole thing gets me so riled up is the attitude of the people who think they're right.  Cecil Adams said, "Everything clear now?  Maybe not.  But believe this:  The plane takes off."  Thanks for your mediocre and confusing explanation, followed by an unqualified, unproven conclusion.  Michael Buffington said, "Jason's Case of the Plane and Conveyor Belt riddle is confusing very smart people, so I thought I might explain it."  Thanks, Michael.  Obviously you know everything and everybody else knows nothing.  Without you, we'd be nowhere. 

This is my explanation.  I put a lot of thought into it, and I even lost some sleep over it last night.  I sort of think I'm right, but I'd be willing to be proven wrong if somebody has a good explanation.  I'd also love to see this on MythBusters. #science

Comments:
Dave Brown Mon, Jun 26, 2006
Dave, my only question with your analysis is: By what mechanism does the conveyor belt restrain the plane from moving forward? It's really just an equilibrium problem. If the jets or propellers are on, then there's a force being applied pushing the plane forward. If the brakes aren't on and the wheels are frictionless, then the motion of the ground is absolutely irrelevent to the equilibrium of the plane. In other words, the ground doesn't apply any forces parallel to the ground. The only force resisting the thrust of the engines is the resistance of the air, which as you described also pushes the plane off the ground. I should have used this as an example in a statics review.

Dave Mon, Jun 26, 2006
I agree with what you're saying.  If we drew a free body diagram, there would be weight pointing down, normal force pointing up, thrust pointing right, and friction pointing left.  If there's no friction, there's nothing counteracting the thrust, which means the plane would move.  I agree with this is theory, but I just don't agree with the conclusion.  Maybe it's because the conveyor belt acts as a moving frame of reference.  Sure, the plane would be moving with respect to the conveyor belt.  But because the conveyor belt is moving backwards, the plane isn't moving with respect to a bystander.  I just can't get past that part.

Dave Brown Tue, Jun 27, 2006
If the wheels are perfectly frictionless, the conveyor belt can be moving at any speed forward or backward and the plane will not move. The wheels prevent the conveyor belt from applying any force to the plane in that direction. All of your assumptions are correct except for the assumption that the plane is not moving with respect to a bystander. The plane WILL move with respect to the bystander as soon as the thrust is turned on. The conveyor belt is not capable of preventing the plane from moving. The conveyor belt is a red herring and it can move at any speed in either direction without having any effect on the plane whatsoever. If a plane's ability to accelerate was dependent upon the motion of the ground then no plane would ever be able to fly. It would always fail as soon as it left the ground. That's just one of the many reasons why all those bicycle powered planes in those old videos could never have worked.

Dave Tue, Jun 27, 2006
In the course of 24 hours, I've completely changed my mind about this. 

Mr. Dave Brown said, "If the wheels are perfectly frictionless, the conveyor belt can be moving at any speed forward or backward and the plane will not move."  I agree with this point.  If the plane's engine is off and it's just sitting on the conveyor belt, if the belt were to move to the right or to the left, it wouldn't cause the plane to move.  This is because the conveyor belt doesn't have the ability to impart velocity to the plane because the points of contact between the belt and the plane are frictionless.  If it can't impart velocity to the plane, it also can't take it away.  So if the plane starts to move at 100 mph by pushing on the air, and the conveyor belt moves in the opposite direction at 100 mph, this will have no effect on the speed of the plane.  The plane will continue to travel at 100 mph because the conveyor belt can't possibly have any effect on the speed of the plane. 

So part 3b and 3c from my explanation weren't completely true:  The motion of the conveyor belt won't affect the motion of the plane.  Therefore, the plane will move, it will gain enough velocity to become airborne, and it will fly. 

I totally changed my mind.

Wendy Wed, Jun 28, 2006
you should send this in to Mythbusters...

Rich Wed, Jun 28, 2006
I'm loving these posts recently...  I feel the need to weigh in on this once again. 
I could be really annoying and give the quick useless answer, or I could be long winded and give a more complete answer.  I think I'll be even more long winded and give both!
1. Useless answer: You did not define what type of plane this is.  I therefore define the plane to be a harrier.  It can take off because a harrier can take off vertically.  Nyea

2. And here we go...
The original prompt did not specify frictionless wheels, and this matters a great deal, so I will address both the case of frictionless wheels and wheels with friction.  I will assume that the plane's engine can exhaust air at an arbitrary speed and ignore transonic effects if such speeds are necessary.  I will also assume that the conveyor belt can move at an arbitrary speed, is of infinite length, and that its control system can adjust its speed instantly.  (And if you want the quick answer, yes, the plane takes off.)

2a: With frictionless wheels:
This premise is almost untenable.  Such a control system could not exist as to keep the belt moving at the same speed as the wheels.  All of the linear momentum that the belt transfers to the wheel is used up by the wheel as angular momentum.  Nothing is transferred to the plane.  In this case, the only force on the plane in the x direction is forward, and is from the exhaust air pushing on the back of the fan blades (I'm assuming a standard turbofan, but this works for whatever).  Thus, the plane will begin to move forward (relative to a stationary observer not on the belt), and smoothly accelerates to a takeoff.  Before takeoff, though, interesting things are happening to the wheels and belt:  This process spins the wheels faster, forcing the belt to move faster (though at any point in time it simply CANNOT actually move fast enough to match the speed of the wheels rotation).  The belt will then continually accelerate trying to compensate for the fact that the wheels will always be spinning a little faster due to the plane's forward motion.  However, the acceleration is not without an upper bound.  What will happen before too long is that the coefficient of static (if you think this should be kinetic, you should read up on how a wheel actually works) friction will be overcome, and the wheels will skid.  I originally thought that this would slow the plane down, but, again, the frictionless nature of the wheels means that the dragging from the belt only serves to slow the rotation of the wheels.  What happens next depends on how this perfect control system works.  If it is measuring the rotational velocity of the wheels, then it will slow down since the wheels slowed during the skid.  As the belt and wheels both slow, they will reestablish static friction, and the wheels will roll again, and the belt will speed up again.  This will continue to modulate, not affecting the plane's forward motion, but putting a ceiling on the speed of the belt.  Then, the plane takes off, and the belt and wheels can finally slow down to rest.  (Yes, I know I overanalyzed what was happening to the wheels and belt, but I thought it mattered for a while, and it comes into play below.)

2b: The wheels have some friction:
The plane takes off, but not for the reasons you most likely think.  The forward force from the exhaust air causes the plane to start to roll forward, which causes the belt to speed up, spinning the wheels faster.  Since there is friction in the wheels, this does create a backward force on the plane.  Since the belt is controlled to match the speed of the wheels, then this backward force will always be equal and opposite to the force applied by the air.  By definition, the controller will not allow the wheels to outpace the belt, so they cannot roll forward.  The plane will stay stationary with respect to an observer not on the belt.  If the observer is anywhere nearby, they are likely to be deafened, as the belt's motor and plane's engines scream as they continually put out more power seemingly without bound.  However, this actually does not go on forever.  At some point, the wheels will skid for much the same reason as in 2a.  The coefficient of static friction will be overcome by the force applied by the accelerating belt.  Since the coefficient of kinetic friction will be lower, the plane begins to move forward, dragging its wheels the whole way.  (I'm assuming the tires won't be worn out, and that the coefficients of static and kinetic friction remain constant despite the drastic heating that is likely occurring at this point.)  At this point, the rotational speed of the wheels determines what happens.  The forward motion of the plane, and the rearward motion of the belt are both contributing to the rotation of the wheels.  The efficiency with which their linear momenta are translated into rotational momentum is dictated by the coefficient of kinetic friction.  This spawns 3 cases: 2b1, 2b2, and 2b3.  (In each case, the plane takes off, but I'm trying to be thorough)

2b1: The coefficient of kinetic friction is so low that the wheels slow down.  This causes the belt to slow, until the point that static friction is reestablished, and the wheels roll again.  However, the belt and wheels are going far too slow to balance the thrust that the plane is putting out at this point, so the plane continues forward, causing the wheels to roll faster, which once again overcomes static friction, and we are sliding again.  All this serves to do is possibly momentarily hinder the plane's acceleration, so it still takes off. 

2b2: The coefficient of kinetic friction is at exactly the right value that the wheels spin with constant speed, so the belt moves with constant speed as well, maintaining the regime where the wheels are skidding.  The plane continues to accelerate smoothly and takes off.

2b3: The coefficient of kinetic friction is high enough that the combined effect of the plane's forward motion and the belt's rearward motion cause the wheels and belt to accelerate without bound until the plane takes off.  During this time, we are still skidding, so the plane will accelerate smoothly and take off (putting the wheels and belt out of their misery). 
And with that, I put you out of your misery as well.  Sorry it was so long, but I think I've covered all the main sticking points.

Dave Wed, Jun 28, 2006
I searched on the MythBusters message boards, and confirmed that this idea has been submitted in the past (perhaps multiple times).  One interesting comment in the forums compared the situation to a seaplane.  It said, "A seaplane can't takeoff unless it overcomes the relative motion of the water."  I see that point and agree with it.  But I think this case is different from that of the seaplane because water traveling around/beneath a seaplane is causing friction (I think), whereas the interface between the wheels and the belt is frictionless. 

Rich, thanks for being long-winded.  That's what I was hoping for.  I think your most important point was, "All of the linear momentum that the belt transfers to the wheel is used up by the wheel as angular momentum. Nothing is transferred to the plane."  That's basically the conclusion I came to before, but without the fancy explanation.

Rich Wed, Jun 28, 2006
Frictionless wheels (or pullies) refer to the bearings being frictionless.  If the interface of the wheel and the belt was frictionless, then the wheel would not turn at all; the plane would just slide along frictionlessly.  There is friction between the belt and the wheel, and you are correct that there is friction between the water and the hull of the sea plane.

Dave Thu, Jun 29, 2006
Good point.  I should've said, "The forces at the interface between the wheels and the belt don't overcome static friction".  This makes it sound like the whole problem has changed, but it hasn't.  Actually, whether there's friction at the interface or not doesn't make a difference.  My main point is still true:  If the plane is stationary and the conveyor moves, the plane won't move.  Therefore if the plane is in motion and the conveyor belt moves, the plane's motion won't be affected by the conveyor belt.  In conclusion, the plane will move and take off.

Wendy Fri, Jun 30, 2006
rich, i like that you put in the universal geek reply "Nyea"

At Last, Correct Ray-Traced Depth of Field in LW9! - Page 7 - NewTek Discussions Mon, Jul 17, 2006
[...] Originally Posted by jameswillmott  If the wheels were fixed ( nonrotating ) and bolted to the conveyor which matched the thrust of the engines, rather than the speed of the wheels, then the plane would remain stationary.    Then the landing gear would just snap off... and the plane would probably crash into the conveyor belt  I'll leave it at that and point to: http://ddhr.org/2006/06/26/plane-on-a-conveyor-belt/  Cheers, Mike    __________________ blessed are the sheep, for they shall inherit the grass Now shipping: infiniMap Pro [...]

Dave Wed, Jul 19, 2006
A video of a fan on a skateboard that proves it!

Peter Wed, Aug 23, 2006
I got a little lost reading the comments, but I thought I'd offer my own simple way to figure this out.

Whether an airplane can fly or not is all about airspeed, that is, the speed of the plane relative to the air. If a plane is sitting still on the runway, but is facing into an 80 MPH wind, it could take off without moving relative to the ground because its airspeed is sufficient for takeoff. If the wind is going the opposite direction, then the plane has an airspeed of -80 MPH. To take off, it would have to reach a groundspeed of 160 MPH.

When you think about the models designers use to test the aerodynamics, you think of them as being stationary in a wind tunnel. So assuming these tests aren't useless, it shows that the plane doesn't have to move relative to the ground; it just has to have the appropriate airspeed.

The conveyor belt is, as someone else said, a red herring. Groundspeed, whether real or apparent, is always irrelevant when it comes to figuring out whether a plane can take off. It is relevant when the plane practically wants to take off or land, because you have to start from (or finish at) 0 groundspeed, not airspeed. That's why planes take off and land into the wind.

Dave Wed, Aug 23, 2006
Sorry Peter, but I don't think your comment clarifies anything.  My first point in the post was that a plane can take off when not moving relative to the ground.  I don't think anybody disagrees with that.  But the part you left out is how the plane develops this velocity assuming there isn't sufficient wind to cause liftoff while the plane is stationary.  And that's the part I had trouble understanding at first.  Originally, I thought the conveyor would prevent the plane from developing speed relative to the ground.  But then I realized that the conveyor has no effect on this speed (see above).  And if the plane can develop ground speed, it can develop air speed, and it'll take off.  I'm assuming you were getting at that too, but you didn't state it.

David Pontzer Wed, Sep 20, 2006
If the plane does not move relative to the air, no flying happens.

Shara Thu, Sep 21, 2006
I think this post has the most comments.  I don't really even know what it's all about...well, obviously a plane on a conveyor belt.  I figured since basically everyone else that visits your site left a comment, I would too.

Shara Thu, Sep 21, 2006
Okay, I just wanted to say that I don't think that everyone that visits your site left a comment about the plane on a conveyor belt.  I'm sure a lot more people read your posts.  I do think, however, that all of the "Daves" that visit your site have left a post.  :)

Dave Thu, Sep 21, 2006
Yeah this is kind of a heated debate, especially for people who have studied engineering or tend to use logic to figure things out.  I think there's really good logic on both sides of the argument, and all kinds of math and physics can be used to prove everybody's points. 

But David Pontzer, I'm gonna have to disagree with what I think you're saying.  I agree that if the plane doesn't move relative to the air (or the air relative to the plane), no flying happens.  But I think the plane does move relative to the air because the conveyor belt doesn't have the ability to add to or take away from the plane's motion.  Sorry to keep restating my point, but it's my main point and I think it's right. 

And yes, I've gotten comments from Dave Brown, David Pontzer, and me.  I'm waiting for Dave Chappelle or Dave Coulier to comment.  They probably read my site.

Rich Fri, Sep 22, 2006
My only question is: what debate?
I think I was pretty clear, if somewhat lengthy, in my explanation of exactly what physical processes come into play, and why the plane takes off.  I also pointed out the different conflicting assumptions that are being made, and how those could affect the outcome.  If we were debating this, someone might have actually cited a point someone else (namely me) made and refuted it.  This has not happened.  So, I will restate the quick answer from before: the plane takes off.  If you don't agree, find a flaw in my logic above, and point it out.  Dave, I think our opponents are just intimidated by our obvious nerd prowess.  You shouldn't have to restate your point.  The person who disagrees with you should, and then explain why they think you are wrong (which you aren't, since in my humble opinion we are right ;-p).  Then a debate really could ensue.

Dave Fri, Sep 22, 2006
The reason it's a debate is because people don't agree with you (and me).  And even I'm not fully convinced that I'm right.  I could definitely envision a person not agreeing with your logic but also not being able to find a specific fault in what you said. 

And for the ignorant yet true statement of the day:  Just because you prove something with science doesn't mean it's true.  Some people need to see physical proof.  I'm still holding out for MythBusters.

Rich Fri, Sep 22, 2006
I think you and I have differences of opinion on the definitions of some words.  I tend to think of a debate as two opposing views that use logic to attempt to prove themselves right and the other wrong.  I think of two people who just don't agree as arguing rather than debating.  As you can probably tell from my language, I'm pretty sure that we are right, and I would really like to see anyone pick apart my reasoning or basic assumptions. 
I conditionally agree with your ignorant yet true statement of the day.  It all depends on the definitions of "prove" and "true" (and unfortunately, in the wrong hands, "science").  To my mind if you "prove" something, that means it's true becasue that's my definition of prove (and dictionary.com's #1 definition as well: "...to establish the truth or genuineness of, as by evidence or argument: to prove one's claim.")  "True" gets real interesting when we get into the area of opinions, which is interesting, since truth only deals with facts.  Facts can be true or false; opinions are not nearly so constrained. 
The actual logical problem with the statement is that science does not, has never, and never claimed to "prove" anything.  (Mathematics on the other hand does so all the time.)  In science, we have hypotheses, theories, and even laws.  On the surface, one would figure laws are proven, but the best definition of a law in science that I've ever heard is simply a theory that is supported by all known experimental data.  If you ever hear a scientist saying "...and that proves..." he's either embellishing to make a point, speaking informally (and will admit if questioned that there can be no proof), or, if he really means it, is full of hot air.

Shara Mon, Sep 25, 2006
Why would the plane be on a conveyor belt to begin with :)?

The_dude Sat, Dec 30, 2006
I have had this argument so many times with people of varying intellect and ego blockage.  I am not going to be able to add anything that anybody else hasn't already mentioned.  Often times these threads fail to mention that a wheel and a treadmill always move at the same speed.  There would be no "programming" required.  A relationship exists between the wheel and the conveyer.  Say the conveyer belt made a 1000 ft. (or just short of) runway making the belt 2000 ft. lets say your plane wheel travels 1 ft. per rotation.  You have a solid unbreakable relation of  2000:1.  That means no matter what the rate of the plane speed is in relationship to the ground speed, the wheels will (in this example) spin at a rate of  1 rotation of the conveyor belt to 2000 revelations of the plane wheels.  If we are to believe that Newton's third law is correct,  then the conveyor belt  will never actually have to move.  The wheels will achieve flight 1000 ft down the runway, spinning 1000 times, with the ration remaining at .5 rotations of the conveyor belt to 1000 rotations of the wheel.  The plane moved across half of the conveyor belt the full length of the runway.  This is irrelevant to the speed in which the plane is moving across the ground.  Wheels and conveyors move in terms of RPM not MPH.

That said I have heard people try to argue that the questions was worded improperly and that it is sometimes stated that the conveyor belt matches the speed of the plane.  Then the only required understanding is that once the planes thrust exceeds the friction coefficient then plan will move forward.  You and your buds can prove this with a pair of roller blades, a treadmill, a water-ski rope, a fishing scale, and a 4 pack of really good Russian imperial stout.  Attach the scale to the wall, the ski rope to the other end of the scale.  Have your friend don the roller blades, climb on the treadmill, and power up the treadmill. The beer should be obvious.  Note that only a small amount of pressure will be exerted on the fish weight scale.  That will be true no matter what the setting is on the treadmill or even if he pulls himself forward. 

Plane move through the air in relationship to the ground.

Mike Thu, Oct 25, 2007
So I'm kinda lost with everyone trying to over-analyze this. 

I think people are reading too much into the test/myth.  The point of the question revolves around the fact that if the airplane was to have no relative ground movement would it still take off at full power?  The friction this, friction that, and whether or not it will move relatively was too much insight from the original idea. 

The fact (as it has been mentioned before) is that if there is no relative air movement...then there is no lift generated by the wings...thus no flight...unless you have a rocket with enough thrust to weight ratio to become airborne.  You mean to tell me that if we were to suspend an aircraft in the air to hold it in place with full power it would still fly?  I don't think so. The air movement produced from the propeller (or jet engine) is not signifcant enough to get the plane of the ground...thus you must have a proper "airspeed" not ground speed to fly.  We all know how an aircraft flies right?  so this should be a moot point thus pointless to philosophize about.

If it somehow got airmovement over the wings an airspeed relative to the takoff performance of the specific aircraft it would fly.  But if the conveyor belt kept it from achieving that airspeed...which in a no wind situation would be somewhat true...then no flight.

Dave Mon, Dec 10, 2007
This will be on MythBusters this Wednesday (Dec. 12, 2007) at 9pm EST.

Dave Thu, Dec 13, 2007
Just kidding.  Thanks, Discovery Channel, you bunch of jerks.  The new date is January 30, 2008 at 9pm EST.

Dave Mc Wed, Jan 16, 2008
It is as some have said before, depends on how you look at the question. If we are saying the conveyor belt CAN impart enough force against the plane due to friction of the wheels to overcome the propulsion force of the plane through the air then you have a sum of zero force, so no movement, and no airspeed over the wings = no lift = no flight.

However, as Rich pointed out, that coffecient of friction is not possible,nor is it claimed in the scenario. So at some point the propulsion force against the airframe through the air overcomes the force from friction against the wheels and the plane moves in relation to the static air, and you get wind speed over the wings and lift = flight. If you look at the question in the form of wheel rpm, at some point the wheels will hit the point where they spin no faster, but the plane keeps moving forward with respect to the static air because of the propulsion force thru the air. The wheels rpm is not tied directly to the speed of the plane thru the air, but to their relative speed against the conveyor belt, via friction of the tires against the belt. The force against the plane is related to the friction of the tires wheel bearings against the airframe. Given wheels on airplanes won't generate that much force against the plane, the treadmill hits a speed where the wheels are no longer gaing rpm as the airplane moves forward thru the air because the wheel bearings are not imparting enough frictional force against the wheels to make them gain rpm. The bearings are just skidding around the hub, which allows the airframe to move forward through the air, because the wheels themselves gain no rpm due to the airframes increasing forward motion. But that's just my opinion given my understanding of physics and wheels.

Rich Thu, Jan 17, 2008
Dave Mc:
Exactly!
Here's a prediction: Mythbusters will say the plane does not take off, because they will overlook the fact that the friction between the conveyor belt and the wheels must inevitably be overcome if the thrust the plane produces increases without bound.

Jeff Tue, Jan 29, 2008
Let's forget about the wheels.  Lets just say the plane is tethered with an unbreakable rope at the tail to an anchor a hundred feet away.  Now the real question is, do the engines themselves draw air over the wings fast enough to create lift.  I think they just might, depending on the engines.  The plane will be stationary, but the engines will still be sucking air, creating wind. I'm not sure if it will be enough wind, but that is the question.  It has nothing to do with the conveyor belt.

bvbellomo Wed, Jan 30, 2008
I just wanted to post I felt really cheated by the mythbuster's episode, and as many have pointed out, interpreting the question is harder than knowing the answer.

Either way, it is obvious (as mythbuster's proved) that a plane can take off from a conveyor belt if the conveyor belt moves very slowly.

The way I interpreted the question, is if the conveyor is capable of putting enough force and exactly the right amount of force on the plane to keep it completely stationary relative to the air, can it take off?  The obvious answer is no.  But doing the experiment is nearly impossible (a ridiculous amount of force from the conveyor to keep the plane still is needed).

Another interpretation is if the plane is moving forward relative to the air at the same speed the conveyor is running.  Obviously, the plane still takes off.

I am confused so many people are interested, but really felt all the mythbuster's proved is they didn't think about the question.

Jorge Wed, Jan 30, 2008
I agree with bvbellomo, I feel myself cheated by the Mythbusters, used to trust on them a lot, but it is obvious that they didn't think so much about the question, and also the experiment is wrongly executed, if you watch the episode again, put close attention at the propeller, it starts to accelerate, obviously that will create acceleration and obviously speed respecting to the air, and obviously the plane takes off, the idea is to test the myth without the help of the plane's engine.

So, I would say the answer is:
- The plane takes off if and only if you accelerate the plane's engine, otherwise, it will not take off, the velocity of the wheels has absolutely nothing to do with about the plane taking off or not, they are just "friction reducers".

Jorge

Dave Fri, Feb 01, 2008
I actually thought the MythBusters proved it conclusively in the first few minutes of the show.  Their little model airplane flew off the treadmill.  Instead of having a plane moving at one speed and a conveyor belt moving at the same speed in the opposite direction, they had a treadmill moving at one speed and a plane not moving at all.  Since the plane was able to move even though the ground beneath it was moving backwards, it proves that the plane would take off no matter how fast the treadmill or conveyor belt was moving.

Rich Fri, Feb 01, 2008
bvbellomo: Regarding your interpretation - you are assuming that the conveyor belt can continue to put ever-increasing force on the plane.  This is inaccurate.  Certainly we can let it run at an arbitrary speed, but at a certain point, the force will exceed the coefficient of static friction of the wheels, and they will skid, which reduces the force that the conveyor belt imparts on the plane, and allows it to take off.  I feel like a broken record, but this is the key point that people seem to be disregarding.

Sammy Sat, Feb 02, 2008
OK, the premise put forward by the MythBusters was that the conveyor belt would be moving backward at the same speed as the plane was moving forward, and the plane would just sail right off into the air - or not.    It's obvious that they didn't accomplish this, as one could easily see that the plane was moving forward, relative to the cones they had positioned alongside the tarpaulin.

In reality, their premise would not be significantly different from that of a plane revving its engine & propellor to full flight speed with its brakes fully locked.  If the thrust of the propellor is all that's needed for flight, we'd have no need for a runway - planes could sail right off into the sky from a stationary point.  But they don't - you've got to have forward movement, with air moving over the airfoil of the wings, generating lift.  Bernoulli's Principle and all that,  you know...

Jason Sun, Feb 03, 2008
The fact of the matter is the original question does not state the aircraft is held stationary. It only states that the conveyor belt is moving at the same speed of the wheels meant to imply the question "Will it keep the aircraft stationary?" The 4 basic forces affecting an aircraft are Lift, Gravity, Thrust, and Drag. The conveyor belt is assumed to be contributing to Drag, which is the opposing force to thrust. I don't have numbers to back up what I say, but I have plenty of experience with flying, including 1100 hours as a crewman in an H-60 Seahawk and witnessing at least 5000 aircraft carrier take offs and landings. I can almost promise you that no amount of friction in the bearings of the wheels will ever create enough "drag" forces to overcome the power of thrust. Depending on the aircraft itself, some could even take off with the brakes locked and dragging the tires arcoss the runway. You will not impart any more friction in the direction of drag than that scenario on the wheels.

Kevin Mon, Feb 04, 2008
At first I was disappointed by how the Mythbusters handled this test because I, like many of the posters here, wanted to see the plane sit still relative to the ground and take off somehow (which I doubted would be possible because there wouldn't be enough air flowing over the wings to cause lift). However, after reading these comments, I understand that there is no way a conveyor belt could match the plane's speed and force it to sit still because the wheels are nearly meaningless when it comes to the plane's acceleration. No matter how fast the conveyor belt goes, the plane can always move forward relative to the ground, thus causing air to flow over its wings, followed by flight. This was confirmed by the Mythbusters.

I think the problem is that the other posters haven't come to the realization that the conditions of the myth itself are impossible. If the INTENTION of the myth was to ask if a plane could take off without moving relative to the ground (and without the assistance of wind), then putting a plane on a conveyor belt does not prove anything. A better test would be what another poster mentioned: tie the plane to a wall so that it CANNOT move forward, and see if it lifts off of the ground. However, if the intention of the myth was to test whether enough friction can be exerted on the wheels of a plane to keep it from taking off, then it has been busted by the Mythbusters.

Jason Mon, Feb 04, 2008
With the impossible or near impossible conditions that the conveyor belt needs to meet, I think the best compromise to test the true intention of the question is to have the conveyor belt move in the opposite direction at the ground speed equivilant to the airspeed required for a particular aircraft to take off. So if a particular aircraft needs to reach 100 knots indicated airspeed to attain flight, and not factoring in windspeed or direction, to have the conveyor belt move 100 knots in the reverse direction. I don't see how anyone could argue against that as a fair demonstration, because the speeds will be matched at the critical point.  But I am sure you will find that the aircraft would still take off.

ML Sun, Apr 20, 2008
Okay, so, I just saw this episode and was a bit disapointed.

Let's take this even more theoretical. What if the airplane was bound to the treadmill. So, the airplane was not moving with respect to the treadmill surface. What is your prediction then?

This removes (or perhaps furthers the idea) of the friction being infinite and allows one to remove the worry about skidding reducing the friction at some point

Triffid Sat, Jan 02, 2010
When I first watched this episode I admit I thought the challenge involved an aircraft rendered stationary by a moving treadmill, and I thought the experiment was flawed when I saw the plane moving forward. True, I am NOT a pilot, nor do I claim to have a firm grasp on the laws of aerodynamics, but I should not have jumped so quickly into such an erroneous conclusion. I soon realized my mistake when I read the phrase " A treadmill CANNOT prevent a free-rolling plane from moving forward. The propellers PULL the plane through the air, thus creating lift. The plane WILL take off!"

The analogies of attaching a rope to the back of the aircraft, or holding a toy car stationary with your hand do not apply. THE PLANE WILL MOVE FORWARD AND TAKE OFF! Luckily, I realized my mistake before I posted any letters to the contrary.

I cannot call it a trick question, like the rooster laying an egg on top of a barn, but at first glance it can mislead.

Kind of reminds me of this one...If a space ship traveling at the speed of light turns on its' headlamps, how fast does the light from the headlamps travel!

Well, maybe not.

Anyway...Naysayers, for a short time I was one of you. YOU ARE INCORRECT !

Roy Tue, Oct 05, 2010
Honestly it was economics and not physics that made me pretty sure something like what happened in mythbusters would happen.  I didn't understand about the freestanding wheels, but I did think that, if a plane could take off while not moving relative to the ground, then no airport would ever pay a bloody fortune for land for runways.  Obviously they do, so obviously that can't be done. 

So I thought it wouldn't take off, but I didn't think about the fact that the treadmill basically can't keep the plane stationary because the plane doesn't depend on its wheels.  The Mythbusters subtly changed the conditions to the treadmill going backwards at the same speed as the plane was going forwards..of course the plane just accelerated to twice the speed relative to the treadmill and took right off.

If you designed a plane which took off by using a car engine driving the wheels to get up the necessary speed, then the treadmill could prevent it from taking off.

builders merchants Fri, Nov 19, 2010
Interesting thing - and I've just confused my office with the plane on a conveyor belt question. I think we'll all be discussing it for the rest of the afternoon. I can't see that the plane would move because surely for something to move the force pulling it has to be greater than the force pushing it in the opposite direction? Surely it would just sit in one place?


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