Airplane on a Conveyor Belt
December 8, 2005
11:54 am
A riddle was proposed on the Neal Boortz show today:
If an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots, and the conveyor belt starts moving backwards at 100 knots, will the plane be able to take off, or will it just sit stationary relative to the ground, with the backwards speed of the conveyor belt counteracting the forward thrust of the plane?
Astoundingly, Neal and the rest of his crew took the position that the plane would sit there stationary! Good God… this man is a pilot and has a law degree! I could understand a random high school dropout being fooled by this, but a pilot?
Then I googled the riddle, and found a thread on Airliners.net that has been raging on, with the vast majority of people taking Neal’s position… that the plane would not be able to take off.
Their argument is this, to quote one poster:
Thrust acts accordingly to Newtons Third Law of Motion - every action has an equal and opposite reaction. In the case of an aircraft, the reaction of the engines is that of forward motion, against whatever medium it is stationary. But the ground the aircraft is sitting on in this case is NOT stationary, its providing an exactly CANCELLING force pushing the aircraft back.
The problem here, of course, is that the poster (and Neal) cannot disengage themselves from seeing the airplane as a car. The difference between a car and a grounded airplane is that a car uses its wheels to propel itself forward, and an airplane moves itself forward by moving air. They assume that the runway moving backwards would move the plane backwards. This is what would happen with a car (that is in gear), so why not for an airplane? Well, because an airplane’s wheels are free rolling. There is obviously some friction, so there would be some small backwards force, but it would be infinitely small as compared to the forward thrust of the airplane.
You can test this with a piece of paper and a matchbox car (which has free rolling wheels like an airplane… or like a car in neutral.) Place the paper on a table, and place the matchbox car on the paper. Take your hand, and hold the car still with a lightly placed finger on top of the car. At this point you are providing no forward thrust, and the “conveyor belt” is not moving. The car remains stationary. Now, continuing to hold the airplane with a lightly placed finger, and start to pull the paper out from under the car, in the backwards direction. According to Neal’s logic, the car should push back on your finger with the same force that you are exerting on the paper… but this is not what will happen. You will find that your lightly placed finger is not stressed to any noticeable extent. The paper will slide out, and the wheels will spin, but the car will not be propelled backwards. The reason for this is is that the rotation of the wheels is not related to the movement of the matchbox car except by the very small friction component of the axle, which your lightly placed finger can easily control.
So now we have established that movement of the surface beneath a free wheeling object does not exert a noticeable force on the object. Next, we’ll see what happens when the object is trying to move forward. Attach a string to the matchbox car. Place the car at one end of the paper, and use the string to start pulling the car forward with a steady force. As the car moves forward, start pulling the paper out from under the car, backwards. Do you feel increased resistance as you pull the string? Of course not. The wheels are free rolling! Spinning the wheels does not make the object move!
When an airplane takes off, there is one major forward force… the forward thrust. The main rearward force is air resistance. The turning of the wheels provides a small frictional force, but because the wheels are free-rolling, this friction is very small. Unless the wheels are locked, the friction is always going to be less than the thrust, which means that the overall force is still forward, and the plane will still move.
Gah… people are freakin’ stupid.
Update: There is a variation on this riddle that says that the conveyor belt matches the speed of the plane. It doesn’t matter… the plane still takes off. The conveyor belt could be going 5 times as fast as the plane, and the plane would still take off. You’d get into issues about tires blowing out, but assuming that the wheels can take the strain, the airplane would still take off.
Update: Well here we are more than two years later. The show “Mythbusters” attempted the experiment. And yes, the plane took off. The laws of physics still apply. Back to life as usual.
actually db, if the belt is going the same direction as the plane… and the belt is going the same speed…. the wheels wont turn…
chris…maybe one last example acn help you. take a matchbox car. wheels spin freely.. now, take the treadmill and tip it vertically. now attach a magnet or something just so that it can stay in contact with the belt. now drop the matchbox car. will teh belt hold up the car simply because its matching its speed… or will the car ride all the way down the belt to the ground??
if you say that the belt will hold up the car… then either its pretty much hopeless, or you wont listen and dont understand the problem… cause there istn a possile way the belt can hold up the car.
Sooks - we never said anything about the belt going the same speed as the plane when you said:
“actually db, if the belt is going the same direction as the plane… and the belt is going the same speed…. the wheels wont turn… ”
Chris said that the wheel will never turn regardless of the direction of the belt.
Like I said before: if the treadmill is going in the SAME direction as the plane is pointed, the plane just sits there if it is unpowered. Add power to the plane and it begins to move forward - which causes the wheels to turn.
How can you argue that?
umm…db im getting a little confused on what your saying.. so the plane is just sitting there while the conveyor moves?? say plane is facing east..belt moves to the east..but planes engines are off..
Sooky - I was commenting on Chris’ comment that the wheels of a plane on a treadmill will never move regardless of the direction of the treadmill. Which is flat out, well…damn silly.
yeah i agree..
Chris, you’re simply wrong about this. The only reason the plane flies is because the engine is working against the air and not the treadmill. A car, transfering power through its wheels, will remain stationary. An airplane will not.
Did you read the links I provided? Just answer yes or no. If not, it would really save me some trouble because then it would be perfectly obvious you aren’t interested in actually learning anything.
Chris,
The question does NOT state that the conveyor belt moves fast enough to negate any forward motion. It matches the forward speed of the plane, but in the opposite direction. That is, if the plane starts at X=0 and moves forward to X=100 feet, the portion of the conveyor belt that was originally at X=0 is now at X=-100 feet. The plane has gone 100 feet forward, the runway has gone 100 feet backwards, and the wheels have traveled over 200 feet of conveyor belt.
That’s the setup. The question is merely: can the plane move forward?
Ponder this:
1. The conveyor belt does not move backwards unless the plane moves forward. (You CANNOT dispute that… it’s in the definition of the problem.)
2. If the belt is moving backwards, the plane is moving forward. (Logically follows from #1.)
3. If the plane is moving forward, it has air moving over its wings and can take off. (From a rudimentary understanding of how flight works.)
Q.E.D.
I just solved it without using physics at all. The definition of the problem states that the plane can take off, because the only force that (in a small way) would counteract it only happens if the plane moves forward. If the plane can move forward, it can take off.
How many times does it have to be explained that the plane ***IS*** MOVING FORWARDS JUST AS IT NORMALLY DOES AND THE SPEED OF THE CONVEYOR BELT DOESN’T FUCKING MATTER.
Everyone asserting that if the plane isn’t moving it wont take off is absolutely correct, but not addressing the issue posed. The plane will NOT be stationary unless the conveyor belt is moving backwards at infinite velocity, only then can there be enough force transferred to the plane through it’s frictionless free rotating wheels to create the balancing force.
For crying out loud. Can’t anyone here read?
Just to clerify :
Everyone does agree the plane WILL NOT take off with the given information right?
Kevin, I read your links, the debate is proceeding about the same there, and the individual explanations for “it flies” are wrong. However, thanks for the links, because now I see why you keep repeating the same thing over and over again despite NEW arguments to the contrary. If you could just divorce yourself from repeating, and actually independently think about the problem you would see that the plane does not fly.
Here is another prime example of why the “it flies” people are wrong. They set up an argument that they think the “it doesn’t fly” people are making, and then ridicule it. It turns out, however, the idea they are ridiculing is their own. See these exchanges:
Db at 5:18 p.m. on 2/9/06: “Sooky - I was commenting on Chris’ comment that the wheels of a plane on a treadmill will never move regardless of the direction of the treadmill. Which is flat out, well…damn silly.”
Sooks at 5:21 p.m. on 2/9/06: “yeah i agree..”
BUT . . . . . .
Sooks previously at 4:24 p.m. on 2/9/06: “much teh same way that if you moved the belt so that it was going th same way as the palne the wheels would never spin at all as the plane went to take off”
So, it turns out it was Sooks’ argument [it flies] and not Chris’ argument [it doesn't fly]! I like the congratulatory tone of the exchange where they realize the ideas are “damn silly” -of course, without realizing the ideas were their own that they have been arguing about! It would help to address the opponent’s position, instead of a straw man argument of your own making.
First, I do not think that when the problem says “the belt matches the speed of the plane” it is intended to mean that the plane is moving. I think what it implies is that the belt increases acceleration to match the anticipated movement of the plane were it not on the conveyor belt. If, by the terms of the question, one assumes the plane is moving, well then, I’m not exactly sure what is meant by the question: is the plane given a head start and allowed to accelerate, and after a momentary delay the belt increases rotation?
I think what is meant by the question is that the belt anticipates acceleration and instantaneously matches it, THEREBY canceling it out.
For the “explain to me what is acting on the plane to counter thrust people” . . . I keep telling you the following concepts: (1) resting inertia; (2) laminar flow; (4) angular momentum. Friction is irrelevant to the problem -which is why the “it flies” people keep saying friction is not sufficient to overcome thrust. Please address the concepts raised and not those of your own making.
Chris, Just to tease you hear for a second.. 1 , 2, 4?? hah, prob just a typo. First, i was getting lost at first in what he was trying to debate there so i just gave up after he aid that you had said that the wheels would not spin no matter which way the belt was going. I still do believe that the wheels would not spin if goin gthe same direction as the plane.
Secondly.. how can you say friction doesnt matter in the equation. Have you ever looked a t a free body diagram? you get all the forces acting on the plane, determine the resulting magnitude of the forces and you have a fnet. if fnet is positive.. it accelerates. if they are equal it will remain at a constant speed at whatever speed they became equal. and if it is negative it will decelerate (or accelerate backwards). friction is one of the major forces in the equation. why is angular momentum a huge deal? that would only be relevant if the wheels propelled the plane. i say once again that the wheels dont propel the plane and i think you are stuck on that. Yes, that is important. it acts differently than a car. you never addressed my question about if you notice the difference between that and a car. a plane doesnt need wheels. it can take off without them. it just needs something to limit friction (i.e. keep its belly off the ground.) so the fact that the belt makes the wheels spin does nothing to the forward movement of the plane except create a bit more friction.
Enough is enough.
Just about everyone here (myself included) has been guilty of adding “what if” to the original intent of the question just for shits and giggles.
The original question was the poster’s interpretation of the question as given on Neil’s show a while back.
What I heard when I listened to the show was this:
The idea is simply that the plane is on the moving treadmill, sitting there with the wheels spinning, and the engine going just fast enough to counteract the treadmill and keep the plane in one place. In other words, it is pretty much sitting there full throttle with the wings getting a lot of lift due to the speed of the props.
The question at this position in time is…can the plane at this point simply take off and fly.
Under this scenario, which is the only scenario intended when it was originally asked, my answer is still no way, Jose.
Now, if we go with the EXACT wording of the question above, my answer is yes due to the most important word in the question above: the word LARGE as in large conveyor belt (in this case large can be interpreted as long, obviously). Why? Once the plane starts to inch forward on the treadmill, it will eventually achieve sufficient speed to take off. Simple.
It’s been fun, gang, but I thing we have milked this one enough.
If the plane is not moving relative to the air, of course it cannot take off. But that’s not the result of the conditions laid out in the original riddle. If the belt matches the speed of the plane but moves in the opposite direction, the plane will fly.
Chris “resting inertia” doesn’t make any sense. Besides, if the plane never overcame this “force”, the plane would never move which means the belt would never move(remember, we’re matching the speed of the plane relative to a stationary observor). That argument makes absolutely no sense in the context of the problem.
Lastly, in order for the angular momentum to keep the plane from moving, the belt(and therefore tires) would need to accelerate at something like 8g’s. The plane would be going a not insignificant fraction of the speed of light before it reached the end of the runway. I shouldn’t need to point out to you that no plane is this fast, and therefore the belt would never accelerate at this rate.
You keep naming these things, but you never explain them or show us how the will equal a magnitude exactly equal to that of the engines. Not almost equal mind you, exactly equal.
Put another way: Is it POSSIBLE for a plane to sit in one place while thrusting on a conveyor belt? Think of the conditions under which this would be possible. If you answer yes, then you are beginning to understand why the plane does not fly.
Second point: usually a plane on the runway takes off with full throttle, and achieves flight, if there is enough runway. For those unfamiliar with how a plane actually takes off, check this link: http://64.233.179.104/search?q=cache:MH6kj-_GP-EJ:exp-aircraft.com/library/heintz/testing.html+average+percentage+of+throttle+required+for+takeoff&hl=en&gl=us&ct=clnk&cd=6
Now, keeping that in mind: how does the plane exceed full throttle to take off on this conveyor belt, which, presumably, is, at the very least operating to shorten the runway?!
Lastly, if you are still not convinced, consider this:
1. The forward movement of the plane is directly proportionate to how much thrust is given.
2. The rotation of the wheels is directly proportionate to how far the plane travels on the runway.
3. The speed of rotation of the wheels is, therefore, directly proportionate to the speed of the plane on the runway.
4. Thus, the speed of the rotation of the wheels is directly proportionate to the thrust given.
5. Furthermore, the circumference of the wheels marks the distance rotated by the wheels.
6. Thus, if you matched the distance traveled by the plane by the distance rotated by the wheels, in real time, you would be able to, with direct proportion, match the thrust of the plane.
Consequently, if a belt were designed to exactly match the distance traveled by the plane, in real time, the plane’s thrust would never exceed zero relative to the rotating belt.
Chris, that’s wrong, wrong, wrong.
The rotation of the wheels is NOT proportional to the distance traveled or the speed of the plane with respect to a stationary observor.
HOW would the wheels dictate the plane’s speed?
Try this. Our plane is flying around with its gear down. If another plane nudges up underneath it so it’s roof makes contact with the wheels, and then it slams on the brakes…what happens? Does it make our plane stop or slow down?
If one of the plane’s wheels were on a treadmill moving forward while the other wheel sits on a treadmill moving backward, the plane would take off.
If the plane were on casters instead of wheels, this gets even more fun. The treadmill could be rolling 200 mph to the south, suddenly switch to a standstill, then start moving 50 mph east, then 120 mph to the northwest, etc.
Because the casters/wheels are allowed to spin freely, they exert no force on the plane. An observer in the terminal would see the plane move down the runway and take to the sky, just like a normal takeoff (except for the wheels spinning in strange directions and speeds).
The engines on a plane exert all force through the wheels to the ground by way of angular momentum to overcome resting inertia and friction. Once enough force is exerted by the engines, then the plane begins to move relative to the ground, as the wheels slowly, and then more quickly turn. If the engines are then shut off, the plane will coast to a stop because of these countervailing forces. Air resistance is an additional force acting on the plane in motion. Here, we are considering whether the plane actually achieves motion relative to the ground. So we do not have to consider air resistance.
The answer is the plane does not move because the conveyor belt acts to keep the plane in a state of stationary equilibrium because, as additional thrust is applied, the belt increases rotation to exactly dissipate that thrust, such that resting inertia and wheel to ground friction is never overcome.
It is a redherring to ask “what forces are acting against the jet engines.” The reason this is a redherring is because the forward momentum of the plane is directed solely through angular momentum, rotation of the wheels, to the ground, UNTIL the plane actually starts to move relative to the ground. This angular momentum, upon which the jets are exerting their force, slowly reduces to zero, and reaches zero at the exact moment the plane achieves take off.
Most planes use maximum thrust when they are sitting on the runway in a stationary position, in order to charge down the runway and lift off. Thus, where the conveyor belt dissipates all of the jet thrust which must first overcome the stationary position of the wheels, and here the wheels remain stationary because they rotate freely vis-a-vis the belt, it is hard to imagine the plane ever taking off, or even moving -remember the plane BEGINS at maximum thrust! So, the question to ask is NOT what force is acting on the jets, rather, the question to ask is how are the jets ever able to direct their force other than on initially rotating the wheels?
Chris, humor me with a thought experiment.
Let’s say a plane were flying through the air, three feet above a backwards-moving conveyor belt. Using a handcrank, someone in the plane slowly lowers the landing gear until one small wheel makes consistent contact with the belt.
What happens to the plane? What happens to the wheel?
Chris, it’s becoming increasingly obvious you aren’t up to the task of understanding this riddle. I don’t know what kind, if any, formal education you have in physics, but suffice to say you aren’t using any of it.
The engines push against the air Chris! The engines DON’T CARE ABOUT THE WHEELS. This is such a fundemental concept and you’re completely missing it.
Kevin, the engines do not “push” against the air. The jet engines “compress” the air and as the air expands upon release, it provides thrust. The propellor engines twist through the air like a wing creating a change in air pressure that “pulls” the plane through the air.
Also, the engines “don’t care about the wheels” because the engines do not have feelings.
If what you mean by the emotion of “care” is an analogy to precise physical operations, please spare me the metaphors and, instead, use the formal language that you profess to have.
I think it would help for you to actually read about the physics involved in TAKE-OFF before you continue to ridicule my position. You can read about TAKE-OFF physics here: http://www.centennialofflight.gov/essay/Theories_of_Flight/Performance_Class2/TH25.htm
The problem with a flying plane landing on the conveyor belt is that its airspeed is fast enough such that the weight of the craft is counterbalanced by the lift. Thus, no weight is placed on the wheels. Consequently, there is no friction on the conveyor belt, and the plane will not land, UNLESS, thrust is decreased.
In the hypothetical question, the plane starts from maximum friction, and here what is meant is that the plane never SLIDES on the conveyor belt because the belt accelerates with the wheels, thereby always countering the thrust necessary to overcome friction. Because the plane cannot initially move, it can never increase its airspeed (movement relative to the otherwise stationary air) and therefore all weight remains displaced to the wheels and NOT to the wings.
Weight of the plane is EXTREMELY important for take-off. Those who think the plane flies seem to believe that weight (on the wheels) is irrelevant, which I have time and time again, tried to show is NOT the case.
A plane going from a stationary position on the ground to flight IS NOT THE SAME as a plane in flight coming into contact with the ground. The simple reason for this is that in the stationary position all weight of the craft is on the wheels, whereas in the flying position, all weight is countered by lift (supported by the wings).
Gosh, such technical and totally irrelevant answers to the simple question of what would happen to the wheel. Kevin, you didn’t answer his question. Instead, you went off on a tangent in an attempt to state his knowledge or lack of. As did Chris. Not nice.
Back to his question: his scenario is virtually identical to a landing - minus the decrease in speed that accompanies a landing (he never included anything about the plane slowing up in his question).
Therefore, the wheel would simply touch the treadmill and then (drum roll, please) it would BOUNCE.
Chris, if the weight were too much for the plane to take off, it wouldn’t fly no matter if there were a conveyor or not.
Why do you insist that the plane will not move? It just isn’t true Chris! You still cannot explain to anyone how exactly some mysterious forces come about that exactly equal the thrust of the plane and keep it stationary.
We’re waiting Chris. Explain.
Stolen from “A.Skeptic’s” comment on this topic at mouser.org:
An airplane has skis instead of wheels and is trying to take off from an iced-over lake. The lake is so icy that a person can’t walk on it. Can the plane take off?
Further questions to help elucidate why the plane will not fly:
1. Will the plane fly if the conveyor belt is only 100 feet long? Why not?
2. How long would the conveyor belt have to be for those who think the plane can fly?
3. What if the conveyor belt/wheel system was a cog & teeth system instead of rubber and belt system? For those who think that the wheels are irrelevant to flight, this change in system should not matter should it?
Point on the ice question: doesn’t deal with the friction problem, which point 3 above stresses the importance of.
1. No. A plane requires more than 100 feet to take off.
2. It will have to be slightly longer than a normal runway due to the minor effect of the increased friction between the wheel and the axle.
3. The only reason it would matter is due to the possible increased friction a gear system has over wheels. If we are calling the friction force between the gear itself and the axle of the plane extremely small or non-existant, there really is no difference. Plane still flies.
Still waiting for an explanation of forces Chris. I think you’re avoiding the question because you don’t know.
1. Will the plane fly if the conveyor belt is only 100 feet long? Why not?
Assuming the end of the belt is level with the ground so the wheel can smoothly transition from belt to ground, the plane will fly if the conveyor belt is 100 feet long. It will fly if the runway is a series of 100 foot belts, each moving at a different direction and speed. It will fly if one wheel is on a belt and the other wheel is on the ground. Because the plane’s wheels can freely spin, they transfer no significant force from the belts to the airframe.
2. How long would the conveyor belt have to be for those who think the plane can fly?
Assuming the top of the belt is level with the ground, the conveyor belt can vary in length from 0 to infinity. The length of the belt is inconsequential.
3. What if the conveyor belt/wheel system was a cog & teeth system instead of rubber and belt system? For those who think that the wheels are irrelevant to flight, this change in system should not matter should it?
If the plane’s wheels were toothed and fit into a series of backwards-moving teeth, the plane would move down the runway and takeoff like it does on a regular runway. I’m assuming the toothed wheel can spin freely on its axis– it will transfer no significant force from the “runway teeth” to the airframe.
Clearly, we have a problem here. Bonzo appears to be imagining a plane that can “leap” into the air from a stationary position. This, I believe, no one will agree with they really think about it.
Kevin is more problematic. When I re-read the problem specifically posted on this site:
“If an airplane is on a large conveyor belt and is trying to take off by exerting the thrust needed to move it forward at 100 knots, and the conveyor belt starts moving backwards at 100 knots, will the plane be able to take off, or will it just sit stationary relative to the ground, with the backwards speed of the conveyor belt counteracting the forward thrust of the plane?”
The obvious answer is, yes, the plane will fly. The reason that the plane will fly is that in the above problem, the wheels will skid, and the plane will take flight as normal, but will probably require additional runway -as Kevin points out.
This debate has been raging partly because I didn’t realize that the question posed on this site is DIFFERENT than the question posed on other sites. The ways in which it is different are: (1) it says nothing about the wheels; (2) it says nothing about acceleration; and (3) the plane and conveyor belt instantaneously achieve 100 knots.
I have been debating, assuming the that the belt accelerates to instantaneously MATCH either (1) the speed of the plane (in terms of thrust generally required to achieve a certain speed under normal conditions) or (2) the rotation of the wheels. As a result, the wheels NEVER slide. It is in either of these two scenearios that I believe the plane will NEVER achieve flight; and, in fact, will remain stationary.
That being said, is it at least agreed that if (1) the wheels do not slide; and (2) the belt instantaneously matches the accelerated rotation of the wheels, then the plane will NEVER fly?
Bonzo said nothing of the sort. The plane goes into the air because it moves forward on the ground.
The wheels won’t skid. Take the 100 knot version (as proposed on the Neal Boortz show) or the “matching” version commonly seen around the internet, and also posed in the entry above. The plane flies.
I like the “matching” version better, because the version that was presented on the Neal Boortz show has issues with stuff like “did the plane start from a standstill? Did the runway start from a standstill?”
In the matching version, both start at a standstill, and the runway matches the plane’s forward speed (but in the opposite direction).
This is a normal plane, so we can assume (a) very good friction between wheel and runway and (b) very low friction in the wheels (bearings).
A human being can tow a 747, and planes don’t burn rubber on takeoff, which makes both of these reasonable assumptions.
You keep bringing in acceleration and stuff about the wheels and rotational speed. These are all tangents.
I see two routes to solving the problem:
The first route is a free body diagram. Y-axis forces net zero, so they can be ignored. X-axis forces are the engines (positive), the friction in the wheels’ bearings (negative) and wind resistance (negative). Wind resistance only comes into play if the plane is moving forward, so it’s safe to ignore it. There are three situations: frictional force is greater than the engine’s force, and the plane goes backwards. Frictional force equals engine force and the plane doesn’t move. Frictional force is smaller than engine force and the plane goes forward.
The second route is a logical one that I have already outlined. Because the speed of the runway in reverse is tied to the speed of the plane going forward, the only way that the runway moves backwards is if the plane moves forward. If the plane can move forward, it takes off.
According to you, the plane just sits there with engines blazing. But if the plane is just sitting there, the runway is also just sitting there. If the runway is just sitting there, and the plane isn’t moving, there are no backwards forces acting on the plane. There is no wind resistance. There is no friction. The only force is the engines. So the plane should move forward, and thus it cannot be true that the plane stays stationary. The situation is internally inconsistent.
Something to think about: if the friction in the plane’s wheels is enough to keep it stationary, then why don’t speeding cars screech to a halt when you put them in neutral?
Bonzo appears to be imagining a plane that can “leap†into the air from a stationary position.
Huh? I never said this. If there’s no wind over the wings, the plane will not generate lift and will not take off– I agree with you on this.
No matter the speed or direction of the treadmill, an observer in the airport’s terminal will see the plane advance down the runway and take off, assuming it fires up its engines as normal. To the observer, it will look like every takeoff they have ever seen, unless they’re looking very closely at the wheels, which might be spinning in a strange direction or at a strange speed.
Chris, after thinking of the best way to explain myself, this is the best I can do. Please read this carefully and let me know your thoughts:
If the plane were sitting on a moving treadmill, with its engines off, I believe the plane would not move. The wheel on the landing gear would spin, but the plane would stay in the same position relative to the ground. (Granted, with a little friction, the plane will move slightly in the direction of the treadmill, but this is a very small force on the airframe.)
I think this is where you and I fundamentally disagree– I believe you see the dead plane being pulled across the ground by the treadmill. Am I right?
Chris, to follow up on my previous post…
Given my (crazy!) idea that a plane sitting on a moving belt with its engines off will not move relative to the ground, it should be easy to understand why I believe that this plane will move forward, relative to the ground, when it fires up its engines.
Because the plane’s wheels are allowed to spin freely, they transfer no significant force from the belt to the airframe.
Does this help close the gap between us?
bonzo,
A plane that is stationary where the engines are off and the conveyor starts to move backwards, the plane will then move backwards. there is friction there and even a more significant amount of it because static friction is larger than rolling friction. So if you went back to my calculations using a 747, there is about 10k lbs of friction. from that stand still it would be even larger. so now if the opposing forcec thrust is 0 than you have acceleration in the opposite direction.
Chris,
first off. the key portion your missing is the plane doesnt transfer its power to the wheels. if this wwere the case than a plane with ski’s on snow or ice would never take off. the jets expelling compressed air pushes the center of mass forward. it moves the body of the plane FIRST, then that motion and with friction of the ground, will turn the wheels. You still think the wheels will turn first and push the plane forward.
secondly to answer your questions..
the plane wouldnt take off in 100 ft. Its take off distance is pretty much the same..maybe slightly longer.
your cog teeth example doesnt work because once again, the belt isnt matching the wheels.. but its speed to an outside observer. The wheels or cog teeth will bill be moving twice the rate of the belt.
finally, yes you acn get the plane to be in a state of equillibrium. this would happen only when the thrust forces is equal to the friction forces. so back to that 747 example again.. it would be when the jets are only outputting 10k lbs of thrust or about 1/20th their max thrust. the key there is that the belt doesnt match the force output of the engine.. only its speed. It takes off.
Thanks, Sooks. I’m guilty of oversimplification to make my point. If the wheel were a perfect wheel (infinite friction between the rubber at the belt, 0 friction at the axle), the idling plane would not move as the belt begins to move. Even if it were a real (not perfect) wheel, I imagine you could get the plane to stay in place if the belt acceleration were high enough– sort of like pulling the table cloth out from under a table setting. Is this correct?
However, I don’t want to lose view of the forest as we stare at this tree. In the face of thrusting jet engines, the relatively small amount of friction will not hold the plane back. It will advance down the conveyor belt, with its wheel spinning twice as fast as normal, and take off. I think that you agree with me on this. Because the wheels are allowed to freely spin, they don’t transfer any significant force from the belt to the airframe.
bonzo,
yea.. with a perfect wheel that was frictionless within i believe will not ever move. as to your question if you could instantly speed the belt very very fast, you could get it to stay still. I beleive this could be true much like pullinga tablecloth from under the dishes. however it owuld only be momentary it eventually would start moving.
To you second part.. exactly right.
Chris, you need to pay close attention to the example Bonzo has laid out. I know it changes the question, albeit in a minor way.”If the wheel were a perfect wheel (infinite friction between the rubber at the belt, 0 friction at the axle)” If the engines of a plane are turned off, the plane is dropped on a treadmill, the treadmill is already moving 20mph (either direction), do you honestly believe that the plane will move?!?! This is very simple physics, and the friction force at the wheel might as well not exist, unless you think this force is greater than a JET ENGINE. I don’t mean to accuse you of being intellectually dishonest, but it appears you thought the question referred to the conveyor belt matching the speed of the plane’s wheels, and now are unable to backtrack out of your original position. Back to my example of the off-engined (perfect-wheel) plane dropped on the treadmill, we can most likely agree it isn’t going anywhere no matter how fast the treadmill moves. Now lets turn on the engine…
The answer depends on whether the planes speed is compared to the surroundings or the conveyor. If its the surroundings, then it will take off but take longer. If it is to the conveyor, then it will never take off as it will stay stationary.
Alright. The jet engines fire up. This in turn makes the aircraft roll foward. But as soon as it starts to roll foward, the conveyor belt starts to move at the same speed as the wheels in the opposite direction and the aircraft does not move. Because it is not moving, no air is flowing under and over the wings, and the wing is creating zero lift. No take off.
Lets get silly and apply your “test” to this by attaching a piece of string to the plane and giving it a pull (from the front). The plane will move forward. Why? Because your decreasing the length of the string which is attached to the aircraft and yourself!. This does not at all simulate thrust. The test is useless.
Thrust and the string are forces that act upon the body of the plane. The runway acts upon the wheels of the plane. The plane’s ability to take off is based on its speed through the air, so only things that affect the body of the plane matter. A plane could take off with locked wheels on ice, or with free-rolling wheels on a runway that is moving forward or backward… the wheels simply aren’t relevant. They only act as a method of reducing friction so that the plane can move freely. This friction is small. Doubling it won’t prevent the plane from taking off.
The plane does not move in the “conveyor belt” problem because the question is posed in such a way that the solution to the question is found in the way that it is asked. One does not even need to know physics to understand that the plane does not move.
If they conveyor belt matches the speed of the plane, how could the plane ever move?
Of course, some people overthink the problem. They imagine the plane moving, and if the plane is moving, then it can obviously gain speed relative to the conveyor belt. This error in thought is produced by the way that the question is asked. Perhaps, it would help to pose the question as follows: “as the plane tries to move by adding thrust . . . ” However, adding “tries” would make the answer obvious: the plane does not move. What happens here, is the person solving the problem forgets about the plane moving from stationary to moving: how does this happen?! They simply focus on the word “moving” and imagine the plane moving, which never happens.
Another error is produced by putting a certain speed in the question. As people try to solve the problem they focus on that speed and, for ease of calculation, double the speed and think: “well, the wheels would be just spinning twice as fast.” What happens here, is the person solving the problem forgets about acceleration and the calculus of change over time. Because the conveyor belt proportionately matches the change in tire rotation relative to the acceleration that would be induced by additional thrust, the plane does not move. Using multiplication to solve this calculus results in the errorneous belief that the plane takes flight.
Lastly, those attempting to solve the problem with physics are using a cadillac to kill a fly, so to speak. AS pointed out above, only logic and reason are required to solve the problem. If one tries to use physics, then one really needs to be sure they are taking into account every factor to solve the problem. AS pointed out above, two obvious things that the “it takes flight” people forget in their calculations are: (1) the calculus of change of acceleration over time and the matching rotational change in the belt to compensate for this; and (2) attempted change from a state of equilibrium -zero (instead they imagine the plane already moving).
The third error that these “it takes flight” people commit is to assume that the only force “countering” the thrust of the engines is friction on the tires. Thus, the endless “what about locked wheels, skies and ice” examples. Similarly, the endless “a plane is not a car because the engines operate on the air not the wheels” examples. What these purported physics majors forget to take into consideration is angular momentum. The wheels of a plane not only reduce the friction between a stationary plane and the ground, but also operate to allow the angle of momentum of the plane to change from down to horizontal. Because of gravity the momentum of a stationary plane is straight down, the wheels allow the transition of the plane from stationary to flying by angular momentum becoming horizontal which allows the plane to move relative to the ground, and thus through the approximately stationary air, and achieve lift.
Meditating on this last part will also allow one to start understanding orbit and how it is achieved. Also, it would serve to point out that Wittgenstein was wrong. One can explain how to ride a bicycle other than just simply saying it is one just knows by being one who rides it. Riding a bicycle is explained as follows: one always steers into the direction one is falling with forward motion.
Perhaps it would also serve to help the “it flies” group by meditating on angular momentum here: http://scienceblogs.com/principles/2006/02/pop_quiz_hotshot.php and by reading about how physics majors screw up simply quizzes by overthinking the problem here: http://biocurious.com/the-three-cylinders-problem.
Chris, please show us what rate of acceleration is required to counter the force of the engines through angular momentum.
Also, remember the original question has the belt matching the plane’s speed, NOT the wheels rotational speed. If the plane never moved, the belt would never move.
The rate of acceleration required to counter the force of the engines through angular momentum is that which matches the plane’s speed such that the plane remains stationary with respect to its original position -just like the problem posits.
Let me ask you this Kevin, since you think it is fair to demand that others answer questions to justify their position: Kevin, what additional thrust is necessary for the plane to take off on the conveyor belt such that it will fly and where does this additional thrust come from? Keep in mind, if you are unfamiliar with flight, that when planes normally take off on runways they use maximum thrust.
Chris, planes may be under full power when taking off, but rest assured they are not designed to require full engine power to take off. Otherwise, a tail wind would prevent the airplane from taking off and I’m sure you’d agree this isn’t the case. Also, increased thrust would only be needed if you want to take off in the same distance. Since there is no restriction on the length of our runway, and given the fact a real runway would certainly be long enough to accomodate the increased distance, we can assume everything is ok.
So to answer your question, no additional thrust is required.
You are now the one overthinking the problem Chris. Angular momentum does not change the final answer to this riddle.
Kevin is right here.. the belt isnt matching speeed of the wheels its matching the planes speed. Heres the first problem your encoutering. How does the belt move if the pplane is stationary? your violating the rules of the question. The belt has hardly any impact on the plane. The only interactive force between the two is fricitonal force. which is coefficient of rolling friction * weight. Itt has nothing to do with speed. The only arguement you could have is if the increased speed of the tires increase the CRF. But to hold the plane stationary the crf would have to increase by about 30 times what it is now. And i dont think doubling the speed of the wheels would do that. See my post above if you wnat numbers.
Everyone needs to think this through logically first…. The plane’s engines move the plane, unlike a car…
So really the wheels have no purpose but to simply roll across whatever ground its meant to.
So instead of boggling your minds about a conveyor belt just imagine the plane’s wheels are moving backwards and the plane is in mid-air…
It is the ENGINES that move the plane…
THUS the wheels serve no purpose as they do not propell….the engines propell…it works because there is no force against the propelling engines…
The plane flies folks
Sleep Easy
correct me if im wrong… the prob’s totally ill-defined. (sorry if im duplicating some of the opinions above, there’s simply too much opinions. if mine’s the same as urs == i support ur opinion 2)
1)..by exerting the thrust needed to move at 100 knots:
thrust is a force and 100 knots is a velocity. plane having this thrust doesnt mean its travelling at 100 knots, it just mean its accelerating. i take it that u mean this thrust gives a terminal velocity of 100 knots (and that would mean that the plane is already at 100 knots, and u can’t analyse the plane at speeds lower than that when u need to know the drag coefficient)
2)..conveyor belt matches airplane:
does it matches instantaneously? there should be a slew rate (lag time between conveyor response and aircraft). the result when slew rate tends to zero might be different when slew rate is zero (if u all remember the case where liquid viscousity introduces turbulence whenever viscousity is even minutely small). or r u finding a physical case where it fits the question (question 2 where the conveyor belt dont communicate with airplane)?
the answer quoted by neal is really sloppy, but i believe the plane wont move (there is a case where u can exert a force on an axle of a wheel where there is no frictional torque between wheel and axle).
physics is good, but do u all realise that u didnt draw any diagrams? i dont believe in solving physics problems without a diagram, its bad practice.
Chris, most who are capable of “getting” the answer to the riddle don’t need to draw a free body diagram in order to do so. The diagrams are nice however for explaining to other people, but unfortunately are hard to reproduce here. And don’t forget…you didn’t provide a diagram either :). If you could, explain to us this force that is preventing the thrust of the engines from moving the plane forward through the air.
Chris, Belive me i did the diagrams of every force acting on the plane and used real numbers for a 747 plugged in teh equations just to prove to stubborn people that it will fly. Fact is, the blet has little to no effect on the plane.
Think of it like this. If me and you are on opposite ends of the dinner table. On the table is a tablecloth. On top of that is a plate. I grab the plate, and you grab the table cloth. Now, if we each pull our object towards ourselves at 1 mph. Do you disagreee that at after a short period of time, that i will have pulled the plate off the table, and you will have pulled the tablecloth off the other side.
You should be able to see tahts sorta silly but its the same thing.. the only thing to stop it is friction..and it isnt great enough.
Too many comments, but the fact is this: the plane takes off because what is happening on the ground is irrelevant. If “For every action there is an equal reaction”, then the reaction to a plane’s thrusting engines is the air against which the thrust is pushing: Since the air squeezed through a jet engine is not on a conveyor belt, the jet pushes off against the air. If the air were on a conveyer belt moving at 200 knots (or whatever); specifically, if the air into the engines is moving faster than the engines could thrust against, then the plane would not move forward (though it might still lift off depending on the flow of air under and over the wings). The jet needs air to push against to move forward: that’s it.
Now a rocket in space has no air to push against, since space is a vacuum. Hence, just the expulsion of gas (ignited) from a rocket will change a rocket’s velocity: the ignited gas pushes on the rocket and the rocket pushes on the gas. Thus, movement occurs.
Technically speaking, the person who said above that the engines move the plane is wrong, I think: it is the air that the engines push against that moves the plane (at the engines, of course). So, the only way the plane would not take off from the conveyor belt is if it was anchored to that belt or if it had no air to push against.
Peace.
BG
Technically speaking, the person who said above that the engines move the plane is wrong, I think: it is the air that the engines push against that moves the plane (at the engines, of course). So, the only way the plane would not take off from the conveyor belt is if it was anchored to that belt or if it had no air to push against.
Not meaning to stray off topic, but I disagree with that interpretation. Jet engines push the same way rocket engines do: they throw hot gas out the back, which exerts a reaction force on the engine, which force is then transmitted to the airframe causing acceleration. I don’t see any reason jet engines need to push against “air” (assuming you mean “air” as in atmosphere rather than hot exhaust gas). The only reason jet engines need air is for a source of oxidizer, because they don’t carry one on board. If you put a jet engine in space and plumbed the compressor section to a very large oxygen tank, it could provide thrust as usual until the tank pressure dropped too low or it ran out of fuel.
Matt2,
So we agree, I think. A jet engine will not work in space unless it is retrofitted as a rocket.
But you are right: this is off point. The plane takes off without a problem.
Peace.
BG
Suppose the belt doesn’t match the speed of the plane, but rather the speed of the wheel, and it accelerates with the wheel EXACTLY. If the wheel is turning at 100mph, the belt is turning at 100mph, and there is no relative motion between the two unless the plane is powerful enough drag the wheel across the belt. However, this would be akin to a plane with no wheels dragging metal legs across the ground. Unless the ground was somehow lubricated, this would create an enormous amount of friction, and only a plane that was MUCH more powerful than it would have to be to take off with wheels would be able to overcome this.
Chris, your point of view was rebutted numerous times throughout the thread. Try reading some of the comments. In essence your error is in confusing speed with force, and also in forgetting that airplanes do not need to push against the ground to accelerate forward, unlike a car or a person walking.
The conveyor belt accelerating does impart some small amount of force onto the plane, and if you caused it to accelerate fast enough, the plane would be held in place. I know the plane doesn’t have to push off the ground to accelerate, as I implied in my first post by saying that the plane WOULD TAKE OFF if it could drag the wheels. If the belt matched the speed of the plane, there would be no problem. However, by matching the speed of the wheels exactly, essentially what you get is a plane with its wheels locked that can only move forward if it can drag them.
Of course it flys.
You are dealing with two different energy loops here. One is the energy loop between the wheels and the pavement, and the other is the propeller and the air.
By saying it stays in one spot is saying that the conveyor belt is able to nullify ANY thrust the airplane can output, and thats just wrong. A wheel is designed to be frictionless as possible. How is a conveyor belt running at speed -X impose force -X (in a system built to be frictionless) on thrust component +X.. The conveyor will continue to slip merrily along under the wheel, as the plane continues to accelerate.
How can you say that a conveyor belt is gonna push as hard as a 747’s output only connected at the wheels?
You no fly guys are too stuck in how a car would do it.
The car’s thrust medium IS the conveyor. The conveyor has a direct say.
An airplanes thrust medium IS the air. The conveyor has no say at all other than wheel bearing friction.
Chris, pay attention to Brian’s follow-up (because he is right), but let me explain a little more.
When you say, “by matching the speed of the wheels exactly, essentially what you get is a plane with its wheels locked that can only move forward if it can drag them,” you are making the subtle assumption that the wheels’ means of propulsion is by interacting with the belt, and when the belt moves backward it therefore nullifies the wheels’ source of forward propulsion. But consider that the wheels move forward, not by pushing against the belt, but by being pulled forward at the non-rotating point on their bearings where they connect with the landing gear (which is attached to the airframe, which is attached to the engines, which is where the forward-pushing force originates). This explains how a plane could take off on a frozen lake or, more obviously, how it manages to speed through the air without having to spin the wheels. The wheels are just being pulled along for the ride.
With that in mind, let’s go back to the belt. The engines power up and begin exerting a force on the structure of the airplane, transmitted down through the landing gear to the wheel bearings. This tends to pull the wheels forward with the plane. Given that the wheel doesn’t need to push backward against the belt to move forward, any backward motion of the belt only serves to rotate the wheel faster. It doesn’t “cancel” the forward motion of the wheel. (Although there is some energy lost to friction, the force of rolling friction is small compared to the force an airplane’s engines can generate).
The problem here is test taking skills. The “if flys” group are the type of people that are given instructions to read through a test before taking it, but do not follow that instruction, and proceed to answer every detail until they get to the last page which states: “do not answer any quetions, simply sign your name and turn the test in.” They are then outraged that the test is unfair and that they “correctly” answered all of the questions -even though they ignored the instructions on how to take the test.
In this situation: the test tells you that the conveyor belt exactly matches the wheels. This is all that you need to know to answer the question. There is no need to pontificate about frictionless wheels acting on the jet engine and acting outraged at the “it doesn’t fly people.” A plane reaching flight speed is the normal situation and the runway doesn’t match anything, it doesn’t move at all -zero! The question, however, flips that situation to the opposite extreme. What the “it flys” people forget in their outrage at the parameters of the situation is that for the plane to fly it would have to move forward but that would mean that somehow the wheels rotated faster than the conveyor belt which is impossible given the parameters of the test. Perhaps, in reality, the situation posed by the question would be impossible, but it is a thought experiment and you have to accept the parameters it gives you. YOu cannot change it by saying: “the wheels are frictionless and dragged forward by the thrust of the engines.” Because then the wheels would either be rotating faster than the conveyor belt, or moving slower by being dragged. So, just follow the instructions, sign your name and turn the test back in -don’t argue about how unfair it is or how much you would know if you were given the opportunity to pontificate on questions you wish you were asked instead.
I’m starting to suspect that Chris is a troll. He’s intentionally provoking a reaction from people whom he knows to be correct.
That’s gotta be it, right?
Much as I like to argue, I’m not going to waste my time if he’s going to adopt a condescending, pissy attitude as he does above. Besides which, if you want to adopt a condescending pissy attitude, you really want to make sure you’re on the right side of the argument!
I note in addition to the Avweb article posted long ago, Cecil Adams at the Straight Dope has answered this question. Adams notes something I realized a while ago: the idea of the belt speed “matching” the wheel speed leads to a paradox, because the belt is also a cause of the wheel speed; thus, as the belt speeds up to “match” the wheel speed, it causes the wheels to spin faster. Then the belt has to speed up further still to recalibrate itself to the new wheel speed, ad infinitum.
If your reasoning leads you to the conclusion that both major components of the thought experiment destroy themselves as they try to accelerate to infinite speed, maybe it’s time to reconsider your interpretation of the problem.
SORRY, here’s the correct link for the Straight Dope.
How about a floating plane taking off from a river that is flowing against it at the same speed?
Conveyor belt?! Gah! Now if you had a giant fan that was bolted to the ground, blowing air at the aircraft, then we’d have a different situation.
Okay, I’ll explain this: an airplane uses the thrust generated by the propeller or turbine engines to push forward the airplane, NOT by spinning the wheels. All you would do by putting an airplane on some giant conveyor belt (let’s say the length of the runway) is succeed in getting the wheels to spin twice as fast as they’d need to. The only way the aircraft wouldn’t take off is if you exceeded the speed rating of the tires, causing multiple blow outs and even then you could probably take off (wouldn’t want to be in it when it landed though).
As my old propulsion prof once told me: “put enough thrust behind anything and it’ll fly”
The plane on a river scenario is something else entirely.
A sea plane cannot take off w/o breaking surface tension on the water.
For the plane to ever break ground (river) contact in order to attain a speed needed to take off, it must first attain a speed sufficient to break surface tension - which cannot happen w/o first attaining said speed - which it cannot do w/o…etc etc… Catch 22.
I bet this starts some arguements flowing!
So why don’t aircraft carriers use conveyor belts instead of slingshots? They could have even shorter runways. Has the military investigated this? A conveyor would be expensive, but it could launch something like an F-16 with zero runway.
Im not trying to be mean here..but seriously..cmon dont be stupid. This has been asked so many times.. why dont you research something a bit before you ask it. WHat makes you think that the conveyor belt makes it take off in a shorter distance.. it still has to gain to a certain speed relative to the atmosphere.. if anything..with a bit of increased frictional forces it may make the runway longer…
I realize this is not for the poster, as his head is obviously so far up his ass that there is now way he could read this post.
The airplane flies by creating lift over the wings. it has NOTHING WHATSOEVER with the speed of it’s little wheels or how fast it’s moving over the ground.
Hence tail winds and headwinds are not relevant to the flight abilities of the aircraft, it is only relevant to the GROUND SPEED.
So, if a conveyor belt is moving the wheels, and the wings are not moving forward RELATIVE TO THE WIND, that plane plain aint flying. END OF STORY.
I shudder to think of a licensed pilot thinking otherwise about this subject.
If the wheels are free-wheeling, then the conveyor belt’s contribution of force to the plane is negligible - just bearing friction.
If the wheels’ brakes are on, then the conveyor belt is a problem. Are all the “no-fly” posters thinking this is a problem involving taking off in a plane that’s burning the rubber of of its locked wheels down the runway?
Wow David - not only do you try to self-righteously put someone else’s head up their own ass (your own comment)…you also add the presence of your own foot to your mouth by saying: “…tail winds and headwinds are not relevant to the flight abilities of the aircraft”. You ever try to take off with a really strong tail wind?
And then you add your other foot to your mouth by saying that “flight abilities of the aircraft..is only relevant to the GROUND SPEED”. You ever fly cross-country and find that you arrived sooner than scheduled due to a favorable tail wind?
It sure is a good thing that you don’t think that air is important…’cause you apparently are leaking a lot of hot air.