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.
Not really.
That way you have 2 separate power sources and that negates the idea of the plane’s thrust doing enough work to get it up and flying - and moving.
To really mess with your mind: how about the possibility of a frictionless treadmill…? Yeah, I’m evil!
I really dont understand what you are saying with not raelly.. that way you have two differnt power sources… It is the same thing as a conveyor belt. heres a little note to his dynometer example. waht would happen to a car if it was running on the dynometer, (wheels spinning not going anywhere) and you or two people came up and pushed the rear bumper… it could move forward…
the frictionless treadmill raelly isnt a hard concept. The plane would take off like normal but the wheels would never turn. theyd slide across the runway
Sooky: the wheels would never turn? Impossible.
I think you are confused with the concept of a frictionless treadmill VS frictionless plane wheels. In both cases the wheels HAVE to turn in order for the plane to move.
well taht certainlly explains why you dont grasp the concept of teh plane taking off.. a planes engine doesnt turn its wheels… the engine pushes air out the back… the only reason wheels will spin is the FRICTION with ground pushing against teh movement of the plane. if there is no friction, what is turning the wheels??
Sooks, you make me feel like a grade school teacher of a Special Ed class.
The term frictionless refers to the item, not its interaction with other items. If a wheel spins frictionless, that means there is no friction on the bearings and it will free spin. Same for a treadmill if referred to as frictionless. When you put a wheel on the treadmill, with the weight of a plane pressing down on the treadmill where the wheel touches, friction or no friction they will spin when movement is involved.
I see what your saying now.. I was actually thinking about a frictionless surface… however the answer is still the same… if there is nothing powering the belt…and the belt is able to spin freely…it will move along with the plane and the wheels wont spin. You do not need to have spinning wheels to move the body of the plane forward. waht would be the case if the belt was moving in the direction of the plane but going faster than the plane was… the wheels would be going backwards…
Sigh.
The ONLY way the wheels won’t spin in this scenario is for the wheels to be locked via a brake or other device.
I see you added an UNPOWERED belt to the equation. That doesn’t make any difference; wheels, by their very nature, will turn (spin) when pulled over ANY surface by virtue of contact.
Which reminds me of the old joke about a guy walking down the road pulling a chain. When asked why he was pulling it, he replied, “Have you ever tried to PUSH one of these things?”
they only turn when there is friction… ok..the surface has friction, the plane bearing has friction… the “bearing” which is the motor or the belt is frictionless. so plane pushes air and center of mass moves. the center of mass of the wheel begins to move.. so the wheel pushes at contact —> since theres friction on the surface the belt pushes back.. but since the belts “bearing” or axis in waht it spins on is frictionless… cant exert and force on the wheel and it will begin to move in the direction of the plane. Its the path of least resistance in a sense.
Nice try, but the reason that idea doesn’t fly (pun intended) - again - is because there is nothing to adhere the wheels to the treadmill - so the wheels will try to move along the treadmill first - hence the wheels will turn and cause the frictionless treadmill to move in the opposite direction. And that doesn’t even take into account the force of the wind generated by the plane also pushing the treadmill into the opposite direction…
NO!!! it cant move the treadmill in the oposite direction.. there is no power in the wheels… the wheels will push the belt horizontally (in the same direction as plane movement) before they can turn. And when it pushes against that belt, the belt cant push back because of the frictionless “bearings” In order for the wheel of a plane to turn..they need motion forward and a resistance force backwards. i.e. it needs torque to turn which implies resistance in opposite directions at 2 points. well the belt cannot impose any force on the wheels.. it has no friction behind it to give it support so to speak.
why would the wheels need power?
the weight of the plan pushing down on the treadmill will cause sufficient contact to cause the wheels to turn as the plane moves forward - there is no reason for the wheels to skid as you suggest or for the treadmill to move in the same direction (unless it is glued to the wheels).
As for you saying: And when it pushes against that belt, the belt cant push back because of the frictionless “bearings†- well, that is wrongo. The bearings have nothing to do with the actual contact of the wheel and treadmill.
no no…i think your misintrepreting what im saying a little bit.. im not saying the wheels will be skidding.. im saying it will push the belt because of that weight on there and the belt cant exert any horizontal force to stop because of the frictionless “bearings”. im not saying that the contact point in the tiresis frictionless and it skids or slides. it will just push the conveyor along with it at the same time.
No problem - I was just commenting on you saying that the wheels will not turn…
The only question to be answered in all this is - does the propellor move the air over the wings. If it does the plane will fly. If it does not it won’t fly. Wheel speed/ ground speed is irrelavent.
If the plane was in a wind tunnel, held on wires and a fan was sucking or blowing air over it, then nobody would question that the plane would fly.
What we have here is a a sort of open sided wind tunnel sucking air from the front and blowing out the back. Due to drag between air molecules all the surrounding air is moved too. The plane would undoubtedly fly.
Yeah.. i was saying that the belt is goingt o be pushed to be moving the same speed as the plane.
pookah..why would the propellor move wind over the wings.. why dont you read all of (or at least a couple of responses) before you state such stupid remarks. the questions doesnt imply that the plane is stationary. That is what..in a sense… the question is truly asking. If the plane can accelerate or not.
nowhere does it ask if the plane can take off while standing still.
A plane taking off transits from a stationary position on the ground, to a diagonal rolling position, to a relatively stable horizontal/pre-lift off position, to lift-off, to complete lift-off, to climb, to stable flight. The conveyor-belt hypothetical is designed to keep the plane in a stationary position relative to the ground by keeping it in a perpetual, diagonal rolling position.
The hypothetical achieves this by canceling the forward thrust of the plane. Theoretically, the plane moves forward by pushing on the air backwards. However, in reality, the weight of the plane is balanced on its wheels, and fixed to the ground. The rev-up of the engines to full-throttle and the time it takes to overcome inertia, unfortunately, is delayed, and therefore would cause the plane to be scraped along the ground -this is why the plane has wheels. A rocket, however, more quickly transits from rest to flight and therefore does not need wheels. In either case, if a plane is preliminarily “attached” to a conveyor belt by the wheel system, or a rocket is “attached” to it’s launch pad by a “rolling conveyor launch pad,” neither object would be a able to make a transition from a stopped position to stable flight because it would be perpetually stuck in a transitory phase.
Now, there are numerous assumptions that must be made, in addition to the “conveyor belt system” to make it work (i.e., keep the plane stationary). These include: (1) the jets/props exert only horizontal thrust; (2) the jets-props divert no air over the wings; and (3) the conveyor system detects change in velocity of the plane and adjusts accordingly SIMULTANEOUS to the change in velocity (this, of course, would have to include predicting the change in velocity of the plane as there is a time lag between the thrust and forward movement).
Some people get stuck on the “friction-less wheels” scenario. This, of course, changes everything. The reason is that if the wheels were indeed “friction-less” then the plane would actually not be attached to the wheels, but would be magically balanced slightly above the conveyor belt system. In such a system, somehow wheels are rolling on a tread-mill without falling off. It is clear, however, that they are not attached to the plane. The weight of the plane (inertia) not being a part of the wheel/treadmill system, allows the plane to “take-off”. How, exactly, the plane is able to magically hover over the system until it reaches the velocity required for flight is not clear.
The basic point is that a plane requires thrust to fly because it allows the plane to achieve lift. If thrust is canceled, then the plane achieves no lift. People get confused by the hypothetical because they forget to include the third factor in solving the problem: time. Once time is included in the hypothetical, it is clear that the plane does not achieve flight because it is unable to transit from a stationary position to a moving position relative to the air, and therefore no lift.
Stick your hand out the window of a car that is COASTING on a conveyor belt and you will feel that there is no lift.
wow…that was simply amazing. First, im really not sure what you are saying wiht this diaganol rolling position…diagnol to what? oh well its irrelevant.
Secondy.. a plane can take off without its wheels… think of a float plane. According to what your saying, this isnt possible? Ive never said the wheels were frictionless, i said they are free spinning, i.e. tey arent powered by the plane like a matchbox car. now just becuae the weight is on the wheels doesnt mean it uses the wheels to move forward. Think if the belt was to match the speed in the same direction… the plane would take off without the wheels ever turning..
And what is your point with the inertia… why cant a plane apply its brakes untill its at fullthrottle like a jet on an aircraft carrier and then release them…
in your last example you say a CAR on a treadmill stick your hand out. Well that doesnt work because a car and plane are different. and a car will standstill.
However most importantly.. you say thrust is cancelled out… you wanna care to explain this one cause this is what really matters, Because the belt does NOT match thrust and negate it. it can only match the speed of the plane and it cannot impart its own forces onto the plane, only a fraction of its force can be imparted through rolling resistance which is not large enough to be equal to the thrust.
They conveyor belt is set to match the **wheel speed**, but in the opposite direction.
The thrust sets the plane in motion, causing the wheels to spin at 5 mph, which is immediately cancelled out by the conveyor running at 5 mph backwards, causing the wheels to spin at 10 mph, so the conveyor belt accelerates to match that, causing the wheels to move at 20 mph, so the conveyor accelerates yet again…
I can’t help but think that this conveyor belt will immediately (or at least very quickly) accelerate to an infinite speed. Assuming all is frictionless, the engine thrust will move the plane forward relative to the air and lift will be generated, and with lift comes flight.
Now… if the conveyor belt was set to match the forward speed of the aircraft itself rather than matching wheel speed, take-off would never happen.
Right?
Well yes and no. you started out on the right track… except for that it doesnt match teh wheels speed… it matches the planes speed from the ground (or to an outside observer) but if it was the case that the plane was matching the wheel speed, you are exactly right, the wheels would go to infinity almost instantly but still take off. however, you kind of went awry when you measured the plane speed saying it wouldnt take off. why do you think that?? if anything it would be harder to take off with matching the wheels speed because it would be experiencing more friction through heat with the wheels spinning faster. with matching the plane speed the wheels will be going just 2x the planes speed and it will take off.
Of course, a plane can take off without wheels. A float plane, however, must travel through the water to obtain lift from the air.
Of course, a plane does not move like a car -wheels generating thrust. However, it could move like a car -for example, a glider being powered by wheels, going towards, and then over a cliff.
Lastly, for those of you who think that somehow (magically, of course) that the plane goes from a stationary position to flying because “air is traveling through the engine:” what if the plane had no wings?!
Does a plane with no wings achieve flight in your “yes, the plane flies off the conveyor belt belief”?! No!
The reason a wingless plane doesn’t achieve flight is because it has no lift, just like the stationary plane in the conveyor belt example.
On the other hand, I would, of course, concede that the plane flies if someone can explain to me how wind travels over the wings in the conveyor belt hypothetical.
The “plane on ice” example does not help because the plane need not “roll forward through the air” because it can “slide forward.” It can ski forward through water or on snow as well. However, I suppose we could modify the conveyor belt to be equipped with snow, water or ice to be moving exactly opposite to, and in anticipation of any relative change in velocity of the airplane thrust.
Now if we are saying that the conveyor belt simply matches the current speed of the airplane -then, of course, the plane achieves flight because the thrust of the plane increases quite dramatically. Thus, e.g., it will go from 0 to 5 to 10 to 20 to 40 to 80 to 160 to 320 knots in, lets say, 7 seconds. On the other hand, if the conveyor belt is matching the current speed only, then it will fail to anticipate increase in velocity, because the plane is accelerating.
On the other hand, if the conveyor belt has sensors attached to the fuel of the plane (to detect change in weight of the plane) the engines (to detect thrust) and the throttle (to detect coming change in speed) then the conveyor belt will be able to negate the thrust of the plane because it negates any change in position by anticipating speed and acceleration in the opposite direction.
For those of you still convinced that the plane achieves flight on the conveyor belt, maybe you should spend your time convincing an airport or the military of your brilliant idea, so they wouldn’t have to build runways or aircraft carriers.
Chris, wind will move over the wings because the plane is moving relative to the air.
The conveyor does not cause the plane to remain stationary. If you think it does, I’d ask you to please identify the force countering the thrust of the engines.
The force countering the thrust of the engines is the plane’s resting inertia. This resting inertia is never overcome because, as the plane attempts to move, it is kept stationary by the corresponding, and opposite movement of the conveyor belt. As the planes attempts to accelerate, so does the conveyor belt, in the opposite direction.
An equivalent scenario, removing the wheels for simplicity, would be to launch a plane into the air backwards at the speed required for flight. Once the plane was in the air, its engines would instantaneously reach maximum thrust. This plane, also, would fail to fly.
No Chris. If resting inertia were enough to counter the thrust of the engines, planes wouldn’t fly at all, would they?
Tell me what force imparted by the conveyor causes the plane to remain stationary. I can tell you there is none, but I’d like you to discover that for yourself.
Inertia is not a force. Inertia just means that an object, unless acted upon with a net force, will not accelerate. We clearly have a force here: the engines. The engines of the plane exert a forward force on the plane. The conveyor belt does not act directly on the body of the plane, but on its wheels. The only way that backwards motion of the conveyor belt is converted into a backwards force on the airplane is through friction in the wheels’ bearings. If you think that the force required to move a plane at 100 knots is only double the force exerted on a plane by a runway moving at 100 knots, you are mistaken. The engines exert more force on the plane by orders of magnitude.
A car would remain stationary, because rearward movement of the conveyor belt acts on the wheels which are connected to the engine.
A plane doesn’t move by turning its wheels. It moves by moving air. The way to get the plane stationary is to give it an equivalent headwind.
So, everyone, at least, concedes that a glider merely resting on top of a car on a treadmill would never take flight.
Would your answer change if the car went “super fast” (like mach 9) on the treadmill, and then kicked into neutral so that “the wheels were not connected to the engine?” Obviously not -the glider would still just sit on top of the car. What if the car kicked into neutral and switched over to “frictionless wheels.” WHAT?! the glider just sits there and does nothing?! Yep. It just sits there, just like your airplane on the treadmill.
What if you had a prop plane on the treadmill, but no wings. Does it take flight? According to you “it flies” people, the wingless prop plane is “moving through the air.”
Now, since the “it flies” people are trying to get the plane of the ground, so to speak, I think you need to present your explanation with a little more explanation than repeating “it flies.” Perhaps it would help you understand that the plane does not fly if you were required to give a little more of an explanation for your answer -such as, at what level of thrust does the plane achieve flight if the plane normally takes flight at 1/3 throttle at 150 knots? For us, “it does not fly” people, the answer is easy: none, because it never achieves flight.
Chris, you’re missing the idea here.
The plane sits on the treadmill. As the engines start and the plane creeps forward, the conveyor moves backward at the same speed. What happens? The wheels simply move twice as fast as they normally would. Say the plane is going 20 knots west relative to the control tower. The conveyor moves 20 knots east and the wheels are now spinning at 40 knots.
That’s all the conveyor does: cause the wheels to move twice as fast.
There is NO force that prevents the plane from moving forward.
Chris, have you ever drawn a free body diagram?
SLOW DOWN AND THINK! At the moment that you believe the plane is moving forward relative to the observation tower, what are the wheels doing in relation to the conveyor belt?
The wheels are not going slower and sliding because the belt maintains relative speed. The wheels are not going faster because, again, the belt maintains relative speed. The problem is that the wheels are connected to the plane and at that point that you imagine the plane moving forward, you have reached an impossible point because the belt has matched speed with the wheels.
So, explain to me how the plane can move faster on the ground than its wheels are spinning in this scenario?
Obviously, if the plane cannot move faster than its wheels are spinning on the conveyor belt, then, by definition, it is stationary because the belt is spinning at exactly the same speed.
Yes, the wind is moving through the engines, BUT IT IS NOT MOVING OVER OR UNDER THE WINGS!
A Cessna would have to move at about 150 knots faster than its wheels are spinning on the conveyor belt before it could lift off. But, the problem is designed such that the Cessna never transitions to anything above 0 knots in relation to the wheel/belt assembly.
Chris I’m really having trouble following you here. I think you’re misunderstanding something.
The belt moves at the same speed as the airplane, but in the opposite direction. So the plane goes west and the belt goes east.
The wheels have absolutely nothing to do with the motion of the airplane. The wheels could be going any speed, and it makes no difference to the airplane. They don’t even have to spin. They’re job is simply to keep the plane from scraping along the ground.
The problem is phrased: “the belt moves as fast as the wheels.” So if the plane were to move, it would be violating the problem because its wheels would have to either be moving faster than the belt or skidding on the belt. -and, if the plane does not move, it does not fly.
In terms of logic: the plane does not fly since the wheels cannot move in relation to the belt, because the belt matches the exact speed of the wheels at any given moment.
In terms of physics: the plane does not move because the wheel/belt assembly operates as a laminar flow that cancels the thrust of the engines by way of drag.
Chris, the problem as it is being discussed recently(and that it is usually phrased) is that the belt matches the speed of the plane.
And once again, what the wheels do doesn’t matter one bit. They don’t affect the airplane.
Ok. Solved.
If the conveyor moves backward in relation to the speed of the plane. Then the wheels simply turn faster to allow the plane to move forward and take off.
However, if the conveyor moves backward in relation to the speed of the wheels, then the plane never moves.
If the conveyor belt moved backwards at the speed that the wheels were moving forward (in relation to the belt), you get a sort of divergence. (This is, of course, not what the question is, but it’s a fun tangent to explore). The reason for this is because you get yourself into an endless loop. If the plane goes forward at 1mph, the runway goes backwards at 1mph, which means that the wheels are now going 2mph (1mph from forward motion, one from backward motion that is matching forward motion). But now that the wheels are going 2mph, the belt has to go 2mph backwards, which means that the wheels are going 4mph which means the belt has to go backwards at 4mph which means that the wheels are going 8mph. And so on, to infinity… while the plane is still generating enough thrust to go forward at 1mph (and only on a stationary runway). Mathmatically, it doesn’t work, because (runway speed) = -(wheel speed) … and (wheel speed) = -(runway speed) + (speed from engines). As soon as the speed of the engines is more than 0, the equations become invalid.
You were on the right track with the car with a glider attached (or a car with wings). That will never fly, because the car isn’t able to gain forward speed (all of its speed is negated by the conveyor belt). Even if you shift it into neutral, it won’t fly… if you put it into neutral, the conveyor belt will no longer act against the engine… but the engine is in neutral, so it isn’t providing any forward thrust that needs to be negated, so you still won’t move forward.
Chris, what mark is saying is correct, if you read some of the posts that are diretly above the one where you satarted we covered this. However, i suspect with the case where we are measuring the wheel speed, the wheels will spin to infinity nearly instantly, yet the plane is still accelerating and i believe it will still be able to take off if to say that all the equipment wouldnt fail.
Sooks,
If the belt accelerated to infinity in the backwards direction, the plane would actually go backwards, because that’s where the net force would be pointing.
Given infinite backwards conveyor belt speed, you would have infinite backwards force (assuming non-zero μ, which would be the case), and no engine in the world can overcome that.
yea..i have debated about that. However, i dont see MU increasing with speed, the only concievable way i see it increasing to the point that its force is increased is that the speed is generating soo much heat within the tires that its increasing mu or the coefficient of rolling friction…..
You’re right, for all practical purposes, Mu is static. But remember, the force due to friction is proportional to the distance over which it is applied. Infinite speed = infinite distance = infinite force. And yes, the tires would melt before you got to infinity anyway.
Interesting thread. I must confess I couldn’t see what would happen until I read your first answer. It was so obvious after that. Interesting how many people still don’t see it though. Just goes to show that sometimes making a leap is not that easy. I’ve seen a lot of people stuck on similar issues in the real world.
Keep up the questions that make you think. We need more of these.
The sad thing is that there are people on both sides firmly convinced that they are correct. All have valid points and arguments and all feel that the other side simply can’t see reason.
Some give the analogy of a wind tunnel proving that a plane can fly w/o moving. Which is ridiculous because, once it emrges from the wind tunnel w/o having achieved sufficient speed to stay aloft, it will sink to the ground.
Bottom line is that, unless it is actualy attempted on a full scale, the answer will remain unknown.
Interesting conversations, though…
I dont mean to sound liek one of those stubborn people you speak of, but i
) but I didnt think it woudl fly at first either. Then
have constantly shown the errors or faults in every example a no fly person
has given. There hasnt been one yet i havent been able to explain.
However, i have yet to have a single no fly person dispute what i have
said. Im not trying to sound all high and mighty (or like someone said
have an ego !!!
i looked at the forces and saw how they acted upon the plane and could see
that it didnt matter, it could still fly. I then went out and used physics
equations to prove it. Yet some peopel dont believe. Well if you truly
dont believe, and you want to end the debate, if you want to prove to me
and prob 95% of the fly crowd, just show how the resistance is equal to or
greater than the thrust force. If you can show that, i will be the first
to admit that i was wrong and congratulate you.
Nothing personal or directed at you, naturally, but…
1) How do you get 95%? It looks pretty evenly split from what I can see.
2) If you honestly believe that a stationary plane, hanging suspended in a wind tunnel will just keep flying off into the sunset after the fan ceases, well…don’t expect this person to be a passenger.
I am a pilot. I have given this original question to commercial pilots and engineers at Wright Patterson Air Force Base here in Dayton, Ohio (home of aviation - remember?) and they all chuckle that people believe that straight physics explains how this should work. You don’t need to show that resistance is equal or greater than the thrust force - it just won’t fly.
‘Nuff Said.
Umm.. i think you misinterpreted me twice. First, i dont think that it will take off from a stand still. otherwise why wouldnt they just do that naturally… im saying it will accelerate naturally with the wheels spinning twice as fast.
as for the other one… i meant 95% of the people who think it wil fly.
as for the physics aspect of it. physics explains whether something or not something will accelerate based on teh forces acting upon it. the only force the belt can act on is through rolling resistance. crf * w. or about .002 * w. its nowhere near enough to stop the thrust or negate it.
acceleration alone does not flight make…as they say poetically on the tarmac.
well if it can acclerate.. and the thrust force is constantly biger than the frictional force it will continue to accelerate untill it takes off. the frictional force is only slightly different than on a normal runway
I’m modifying my previous position: the plane will not fly under either scenario (whether the conveyor moves in relation to the plane or wheels).
Clearly, under the terms of the problem, with respect to the wheels, if the belt moves exactly in relation to the wheels, then the plane can never move because movement would assume that the wheels move faster or slower (slide) than the belt, as the plane moves faster. However, because the terms of the problem require that the belt moves at the exact speed of the wheels, then the plane cannot move. Thus, it cannot fly. To understand this, one nearly apply logic to the problem.
Where the belt moves in relation to the plane, presents more of a problem, because it catches people up in the physics of the problem. They don’t understand, or reject, the that the plane won’t fly because they believe that the thrust of the plane always overcomes the “resistance” of the wheels. This seems reasonable, until one understands that the wheel-belt “assembly” keeps the plane in place because it operates as a boundary layer of laminar flow in the opposite direction. The problem needs to be analyzed using fluid dynamics, in addition to traditional physics. Until this leap is made, those who say it “will fly” will not be brought into the age of flight to understand that it will not fly.
For the “it will fly group” it helps to remember that the belt accelerates in the opposite direction, when you claim that the plane flies because it accelerates.
Obviously, if the belt remained at a constant speed, then the wheels would simply spin at twice their normal speed, and the plane would take off. This is the mindset of the “it will fly people.” However, it cannot be emphasized enough: the belt does accelerate in rotation, as the plane attempts to accelerate by applying more thrust.
Chris, you’re trying to hard to justify an initial visceral reaction. If the belt moves backward at the same speed of the plane, it will take off. If you really still think otherwise, please explain all the forces acting on the plane, and be specific about how the force provided by the engines is nullified. Describe your free body diagram for us.
Isn’t it interesting how some people who disagree with others insist that, instead of showing why the other person is wrong, asks the other person to elaborately justify his position (as in the message above) where it is said: “please explain all the forces acting on the plane, and be specific about how the force provided by the engines is nullified. Describe your free body diagram for us. “.
Geeze…
Chris, Where do i say that the belt doesnt accelerate. it accelerates at the same rate as the plane does.. thus they are always going at the same speed in the opposite direction at any given moment… and then the wheels are going twice as fast…
What the belt does is virtually irrelevant. it cant stop motion of the plane.. the plane isnt like a car in achieving motion. and the belt cant impart a force on the plane of any major significance to slow the plane.
What you state is that the belt is moving backwards, the plane forwards, and that the wheels are simply going twice their normal speed. However, the plane is not moving forwards, because it is stationary. As the plane “tries” to move forward, the wheels do not simply go twice as fast, rather, the wheels proportionately increase their rotation so that the center of the wheels remains fixed. When you say that the wheels are irrelevant to the plane’s motion, I think that you imagine that the plane is not connected to the wheels via the struts. I think it would help the debate if you explained how it is that the plane “separates” from the wheels such that it is able to move. You concede, do you not, that the wheels remain in a fixed position on the conveyor belt? If you can tell me how it is that the wheels, that are connected to the plane, somehow “move” in relation to a fixed point on this conveyor belt, I will concede that the plane flies.
Keep in mind, of course, that as the wheels increase rotation, the belt exactly matches that rotation.
Db, I ask him to explain it so we can understand him and be “enlightened” or so he says. I can surely explain the forces I believe to be acting on the plane, and demonstrate why the plane will take off.
The plane’s weight(a downward force) is negated by the normal force(pointing upward), so our forces in the y direction are in equilibrium.
In the x direction, we have a small frictional force imparted by the wheel bearing in the negative direction, and a very large force generated by the engines in the positive direction. These forces are not in equilibrium and the plane will move along the x axis in a positive direction.
There. Now it’s his turn.
add rolling resistance… coefficient of rolling fiction * weight in negative direction.. little larger than bearing and wind resistance in the negative. which is not any larger than a normal runway takeoff wind resistance. the 3 o them are still much smaller than the thrust force
Sure. And also the forces generated by a spinning object. All of these add small forces related to the plane through the bearings in the wheels. Toss it all under “friction” :).
But like you said, the gist of it is friction
For some reason the “less than” and “greater than” symbols cause the post to not show completely.
Anyway, that post ended “friction is much less than thrust”.
Think of it this way: the plane’s wheels are gears attached to a tooth equipped belt. The thrust of the plane transfers to the wheels to increase their angular momentum. In such a scenario, the belt wouldn’t need to adjust its speed because it would automatically increase with the thrust of the plane, which would dissipate all forward thrust through angular momentum to the wheels and then to the belt. It doesn’t move!
What? Chris, the wheels are spinning freely and impart very little force on the plane. The wheels don’t need to spin at all for the plane to move. The plane really doesn’t care what the wheels are doing.
Chris, your still thinking of it like a car. that is how a car achieves motion, which is different than a plane. a planes wheels are meaningless other than keeping it off the ground. maybe this wil help. which part moves first in a car..and then which part moves first in a plane. a car spins driveshaft..which TURNS wheels which moves center of mass. a plane sucks in air..spits out back moves center of mass.. friction with ground turns wheels.
We’ve been through this before, the lame car does not equal airplane analogy. The argument is similar to arguing that a car runs on gas, a plane jet fuel, a car has wheels, a plane has wings, etc, therefore the plane flies because a car does not.
Now, think of it this way for you who argue “A plane doesn’t care what the wheels are doing” ilk: what about a glider on top of a car. Truly, the glider “doesn’t care” what the wheels of the car are doing. Now, if the car reaches top speed and then kicks into neutral, so that the wheels are not connected to the engine, does the glider fly? No -even though we now have a “frictionless system!”
What you are still failing to acknowledge is that for the plane to move forward, so that it achieves lift, the wheels attached to the plane must somehow move on the conveyor belt. However, under the terms of the problem this is logically impossible because the conveyor belt rotates exactly the same as the wheels! Now, what we have here is a logic problem. It is logically IMPOSSIBLE for the plane to move under the terms of the problem. This is why this argument is so frustrating because if you accept the premises of the problem, you must agree that the plane does not move, and therefore does not fly.
Those of you who argue that the plane flies are rejecting the premises of the problem outright, unsound, or are changing the rules of the problem. THINK!
For a plane to fly it must achieve lift.
A plane achieves lift by air passing by the wings.
For air to pass by the wings the plane must either be moving or the air must be moving.
Here the air is not moving.
Thus, the plane must be moving.
A stationary plane sits on wheels.
When the wheels turn, they move position in relation to the ground.
Thus, when the wheels turn on the ground, the plane moves forward in relation to the ground; regardless of whether the plane is propelling forward or the wheels are propelling forward.
As the plane moves forward, it also moves through the air, achieving lift.
A stationary plane moves its wheels by thrusting; as it thrusts, the wheels spin in EXACT proportion to the ground that is receding, and at the SAME rate.
There are two exceptions to the above principle: The wheels move slower, indicating that the plane is sliding on take off; or the wheels move faster, indicating motorized wheels (not our situation).
Thus, we are left with wheels turning faster and faster, in exact proportion to the receding runway. Normally, the runway is fixed, the plane moves faster and faster through the air that is also fixed or slightly blowing in relation to the runway. In the problem, however, the runway recedes but the plane does not move through the air because the conveyor belt rotates independent of the air.
The only possible way for the plane to move through the air in relation to the fixed, spinning conveyor belt, is if the wheels began to slide or moved proportionately faster than the accelerating belt. IMPOSSIBLE given the problem. Forget the jet engines! LOOK AT THE WHEELS! How is it possible for them to move in relation to the belt?! As I said before, if someone can explain to me how the WHEELS rotate faster or slide in a problem that requires that they do not, then you have not only convinced me, but also violated the terms of the logic problem.
Kevin:
You ARE kidding when you said “The wheels don’t need to spin at all for the plane to move”, right? Can you imagine a plane which takes off with the wheels locked by the brakes?
Perhaps you can explain how it can move on a treadmill WITHOUT the wheels turning…?
Chris, you just aren’t getting it.
Place a plane on a conveyor and tether it in place so it cannot move in any direction. Run the conveyor at 30 knots. What speed are the wheels spinning at? If you said 30 knots, you’re with me so far.
Now, untether the plane and turn off the conveyor. Now push the plane at 30 knots. How fast are the wheels spinning? If you said 30 knots, you’re still with me.
Next, turn the conveyor back on and set it to 30 knots. Then push the plane at 30 knots opposite the direction of the conveyor. How fast are the wheels spinning now? If you can manage to see they’ll be spinning at 60 knots, you’re beginning to understand the riddle.
The point is Chris, the conveyor DOES NOT PREVENT THE PLANE FROM GOING FORWARD. I use caps not because I’m yelling, but because it’s the most important point in dealing with this thought experiment.
Db, if the treadmill were designed to move in the same direction and speed as the plane, the wheels will never turn and the plane will still lift off.
Also, if we had a plane with teflon wheels on ice, we can lock the brakes and take off just fine. You just have to realize wheels are friction reducers.
C’mon, Chris - you can’t arbitrarily add things and change the treadmill to an ice treadmill with teflon wheels on the plane. Or say it is going backwards. Get a grip, man! And the wheels will turn REGARDLESS of the direction of the treadmill anyway once the plane starts to move…
Plane sitting at point 0. Plane tries to move to 1 inch by thrusting, but runway recedes to 1 inch. Plane remains at point 0. Plane tries to move to 1 mile by thrusting equivalently, but runway receds to 1 mile, plane remains at point 0. Whatever thrust WOULD BE REQUIRED to achieve a particular distance, the runway recedes that distance in the equivalent time, and plane remains at point 0. Now, since the plane has not moved beyond point 0, it has achieved no lift and therefore does not fly. Do you at least agree with this analysis? Without applying it to the problem. Now, if you disagree with this analysis, then point out how it is wrong WITHOUT resorting to the problem. On the other hand, if you agree with this analysis, then, and only then, point out how the problem is different.
No they won’t. If the conveyor is going the same direction and speed as the plane, how can the wheels turn?
Think about it this way. Take a toy car in one hand and “drive” it across your other hand. Wheels spin, right? Well, now move both hands in the same direction and at the same speed. Do the wheels turn now?
chris.. waht kevin just said is exactly right.. you seem to think that we are saying that the belt, plane and wheels are all going the same speed. This is important. the belt isnt matching wheel speed, but the speed that the plane itself is moving over the ground. plane speed and belt speed equal each other… wheels twice as fast.
and how can you say the car argument is irrelevant. it is very irrelevant.. because it shows how they accelerate and achieve motion.
Under either scenario: belt turns in relation to plane thrust, or in relation to wheel speed results in the same situation, the plane does not move.
Forget the airplane for a moment.
Suppose we have a wagon (like a child’s toy red wagon) sitting on a conveyor belt. At the front of the conveyor belt there is a motorized winch which is bolted to the ground. The winch is attached to a steel cable which in turn is attached to the wagon.
Let’s unwind the winch completely so that the steel cable is extended to its entire length. With the conveyor belt off, let’s turn the winch on. What happens? The winch reels in the cable and the wagon gets pulled to the front of the conveyor belt.
Let’s unwind the winch again so the cable is extended completely. With the winch off, let’s turn on the conveyor belt. What happens? The wagon stays in place. Is there any speed we can run the conveyor belt which will cause the wagon to move backwards?
Now let’s turn both the winch on and the conveyor belt on. What happens?
Is the wagon different from the airplane?
No Chris, I don’t agree.
The treadmill cannot translate its own motion to the plane directly. The treadmill is acting on the wheels!
I too, at one time, believed the argument that the plane flies because wheels are simplying spinning twice as fast. UNTIL I realized that the plane still does not move because the wheels will spin even faster as the plane tries to accelerate, because the belt equivalently accelerates. I had forgot the rules of the problem, that the belt equivalently ACCELERATES in the opposite direction; not just that the belt is spinning. The problem requires one to keep several points in mind at the same time to realize that the plane does not move. Focusing on one part of the problem usually entails forgetting that the belt or the wheels EQUIVALENTLY ACCELERATE. The algebraic solution that you propose also fails in this exact same respect, and gives the illusion that the plane can move independently of the wheel/belt assembly. This is because it gives an answer for the system at one point in time, and then one imagines the plane moving faster than that. However, the problem must be solved using calculus to account for acceleration over time in the opposite direction.
the wagon example is perfect.. when the belt is on and the wagon stays still. that is the same as a plane where thrust is equal to friction.. (or very little thrust applied.) when you actually pull the wench.. thats the thrust overcoming friction. even if the belt is going the same speed as the wagon..it still moves forward because the cable is getting shorter..it has to move forward
The winch/wagon analogy violates the rules of the problem because the wagon and/or wheels move faster than the conveyor belt in order to move forward. By the terms of the problem, this is not allowed.
chris!!! for the third time.. it matches the planes speed.. NOT the wheel speed. plane = 10.. belt = 10.. wheels = 20
Chris, Chris, Chris…once the plane is powered and begins to move on the treadmill - regardless of the direction of the treadmill - the wheels will turn.
Chris, it does not require calculus!
Let’s imagine the plane is just floating, like a mag-lev train. It’s just hanging out, 2 feet off the ground, not moving anywhere. We place it over our conveyor and have it match the planes speed, but in the opposite direction. When we apply engine thrust we fully expect the plane to fly off. And it does. The conveyor cannot effect the plane because it is very obviously not touching it.
Now, what is changed when we add wheels with good quality bearing? Almost nothing! The frictional forces translated to the plane are very small.
Db, how can you maintain that? I thought for sure you could see this.
Can you dispute my toy car analogy? The car is still moving at some speed relative a stationary observor, but its wheels do not turn.
I’m beginning to wonder if you aren’t just playing dumb.
I cannot make it any clearer. Perhaps this gif will help you visualize the staying in place phenomenon:
http://upload.wikimedia.org/wikipedia/commons/0/05/Muybridge_race_horse_animated_184px.gif
. . . . although, I suppose some could argue this goes to prove that the plane flies because the horse is briefly airborne.
Chris, the fact you’re using a horse as an example proves to me you have no understanding of the problem and have not understood a single thing we’ve been telling you.
The wheels are the key Chris. Hooves are not wheels.
The wheels ARE the key. This, I very clearly understand. I’m glad that the horse gif shocked you out of your obstinance about the plane’s engines so that you could now see that the whole problem revolves around the wheels.
Now, you should understand that because the wheels do not move -neither does the plane.
Chris, the horse gif is completely unrelated to the problem at hand.
To make it equal, we’d have to power our plane with the wheels. Or, we’d have to strap a rocket to that horse.
Chris, one more time. Name the forces acting on the plane. Show me where the force originates that is exactly equal to the of the engine thrust but in the opposite direction.
Chris,
Let’s ignore the airplane/conveyer belt question right now.
In my winch/wagon/conveyer belt example, what happens when the winch and the belt are turned on simultaneously? Let’s just consider this as a separate problem.
how about this…. what if the plane landed on the belt… would the plane instantly come to a stand still… or would the wheels just accelerate rally fast as it coasts toa landing..
The problem with the winch/wagon scenario is that the wheels are moving in synch with the conveyor belt, until the winch is turned on. In which case, the wagon moves forward. How does the wagon move forward? Well, it moves forward because it is DRAGGED ACROSS THE CONVEYOR BELT. The wheels either spin across the belt leaving a skid mark or are dragged across it, leaving a skid mark.
However, if the conveyor belt ACCELERATED to match the speed of the wheels, and the wheels never lost traction, the wagon would NEVER move. The winch would continuously pull harder to match the increasing speed of the treadmill, but would NEVER outmatch it. Now, if you imagine it out pulled the conveyor belt, then the wheels would have to be dragged across the conveyor belt, losing traction by skidding or spinning faster than the conveyor belt. THIS IS NOT ALLOWED -thus you yanked the wagon in violation of the terms of the problem as evidenced by the fact that the wheels skidded and therefore the belt acceleration was not matching the wagon acceleration. On the other hand, if the rope broke, we have not violated the terms of the problem, because the conveyor belt would EXACTLY decrease in velocity such that the wagon remained stationary until the wheels and belt came to rest.
oh my god…. chris.. you keep matching the speed of the belt to the wheels.. for the last time seriously… it doesnt match the wheels.. it matches the speed of the mass. the wheels can rotate faster than the mass is going.. the belt isnt matching them..
The plane would not be able to land on the treadmill. The wheels would not be able to dissipate the forward momentum of the plane into angular momentum. This is why the plane never achieves flight, because it is not able to transfer the angular momentum into forward momentum.
Even if you match the belt speed to mass speed, instead of wheel speed, it doesn’t matter because the wheel speed would be equivalently matched to the belt speed, but just by a multiplying factor. The calculations would be more difficult, but the result the same.
the wheels dont transfer anything…the engine pushes the plane..
If you think it is different (wheels vs. mass) then you at least agree that if the belt is matched to wheel speed, then the plane doesn’t move. You just believe that the plane moves if the belt speed is matched to mass speed. However, you are wrong on this point also.
The obvious problem, here, is getting the “it flies people” to agree. However, they will not agree because they get stuck on particular point (engine thrust, but ignoring momentum, lift, etc) or calculation (that disregards change in time and velocity being matched by acceleration), or disagreements with the premise of the problem (the belt MATCHES speed). This is a reasoning problem on behalf of those people that I cannot address, and so I give up.
umm.. well no… im unsure about matching the wheels speed. That would basically be saying that the planes wheels will go to infinity almost instantly. thus it would raise the crf through heat and if its infintly fast you could say that the crf culd increase to infinity.. so im leaning towards no it wouldnt take off…
but why cant you see the difference matching plane speed. now the wheels are only going twice as fast as they would on a normal runway.. it doesnt hold the plane back.. slight increase in resistance.. thrust is still much greater than the frictional force. it can accelerate and continue to till take off. 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
Chris, no one is disregarding lift or anything else. You’re simply making things up to match your preconcieved notions on how this problem ought to work.
I’d urge you to look at do a search and read up on the riddle. You can start a couple places:
http://ooine.com/index.cfm?CommentID=154
http://www.avweb.com/news/columns/191034-1.html
http://www.straightdope.com/columns/060203.html
Read all three of those and see if you don’t understand then.
im stuck on thrust cause that is the forrce that makes the plane accelerate. and it is constantly bigger than the force resisting it.. if Fnet is positive it accelerates..and continues to untill acted upon a force changing fnet to negative.. in this case it reaches take off speed before this happens
There is no need to resort to physics. It is a logic problem. It is designed such that the plane does not move. This is why I say what we have here is a reasoning problem.
Chris, please read the links I provided. And of course physics can be used. Don’t toss it out simply because it disagrees with you.
This is also why it doesn’t matter if we are talking about a car, a horse, (a boat in a water treadmill with sails or motor) or an airplane. It is a logic problem. There is no forward movement.
Arguments about the airplane’s jet thruster is what tricks people into thinking illogically about the problem.
What the “it flies” people have a problem with, in solving the problem, is the means of propulsion. However, I have faith that one day they will realize that the means of propulsion are irrelevant to the solution of this problem because it is designed such that the object does not move in relation to the treadmill.
Boy, I’m away from an hour and all hell breaks loose here!
Chris: I stil can’t understand why you say that the wheels won’t turn regardless of the direction of the treadmill.
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.
You really can’t see this?
Then how come i have seen lots and lots of people who didnt think it would fly..change their answer… and i havent seen any go from. The problem isnt designed for the plane to standstill… that is what the question is asking.. whteher it will stay stationary or still move.