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.
I respectfully disagree. A plane does not move itself by moving air. It moves itself by moving through the air. Its forward speed causes air to flow around the wings at different velocities (faster above, slower below), and that in turn creates lift. If the plane doesn’t move forward while it’s on the ground, air is not moved over the wings with sufficient speed to create lift — so the plane doesn’t fly. Based on your premise, we shouldn’t need landing gear or runways as planes should be able to lift off directly from the gate without any ground-relative motion whatsoever. We know it doesn’t work that way, so speed relative to the ground is in fact critical for flight. The plane must move forward relative to the medium upon which it stands, and it must move with sufficient speed to create lift. Until a plane is in the air, it is bound by the same principles that control how cars move. Remember, planes don’t fly on the ground — they are driven on wheels and steered by the same. Think of aircraft carriers for a real-world example of this riddle (planes must reach a certain speed relative to the carrier before they’re able to take flight, hence the catapult and high engine thrust).
You are assuming that the plane will not move forward, but have not explained why you think that. The plane is generating forward thrust. What force acting on the plane (note: NOT the plane’s free rolling wheels) is going to counteract that force and keep the plane from moving forward?
The landing gear are merely a way of eliminating (most of the) friction between the airplane and the runway. How fast the wheels are turning is meaningless. For instance, to take an example from real life, say the runway is coated with ice. The wheels will not be turning as fast as they would on a dry runway. In fact, on a perfectly frictionless surface, the wheel would not turn at all! The only thing that matters if how fast the airplane is moving through the air. The thrust generated by the plane moves the plane forward. The conveyor belt moving backwards spins the wheels backwards at twice their normal rate for that speed on a dry runway. So now the plane is moving forward at 100 knots and the wheels are spinning forward at 200 knots and the runway is moving backwards at 100 knots. So the wheels’ relative speed to the ground is 100 knots, the 100 knots generated by the airplane.
False. Cars move forward by turning their wheels. Planes move forward by generating thrust through the air. The wheels spin as a result. The wheels are free rolling, which means that they are not connected to the engine, and do not work to counteract it.
Actually, the plane must reach a certain speed relative to the air. This is why aircraft carriers point into the wind for takeoffs, as it increases the amount of air moving over the wings, and hence the amount of lift generated by the wings. If an airplane needs to be moving at 200 knots through stationary air in order to take off, and the aircraft carrier is pointing into 200 knot wind (extreme, yes)… the airplane could take off without moving forward on the runway at all… it would just lift straight up.
A plane gets lift from air moving over it’s wing surface. In order for a plane to move air over it’s wing surface it must move forward. If the airplane is not moving forward the only air moving over its wing is the wind.
Seems to me the problem is not properly defined/constrained. Like having two varaibles and only two equations when a minimum of three equations is needed.
Is the airplane’s 100 knots indicated airspeed or ground speed?
If the former, then ground speed is irrelevant. If the latter, then slightly more than ground idle thrust would be sufficient to maintain zero airspeed and 100 knot ground speed.
The only difficulty of taking off at 100 knts indicated airspeed and 200 kts groundspeed is the possibility of tire failure (conveyor example).
An airplane taking off with a 20kt tailwind, lifting off at 100 kts indicated airspeed, will be traveling at 120kts groundspeed. Taken to the absurdity of 100kts of tailwind and the conveyor belt condition is duplicated.
Re: Comment #5; Oops - I meant THREE variables and only 2 equations.
It is meant to say that the airplane is generating enough thrust to move it forward at 100 knots on a stationary surface. So the airspeed is 100 knots, the ground speed (talking about the regular ground, not the belt) is 100 knots, and the “conveyor belt ground speed” is 200 knots (100 knots forward by the plane and 100 knot backwards by the belt double’s the plane’s relative speed to the belt).
The trick here is that backwards movement of the ground doesn’t affect the speed of the plane, because it is free wheeling. The only backwards force is friction… and that’s nothing compared to the thrust needed to move a plane forward at 100 knots. In physics terms, the kinetic motion of the belt gets translated into rotational kinetic energy in the wheel. Because the wheel is free rollling, that’s where the energy flow stops.
I only heard Neal go through this spiel one time. In his description he mentioned that the conveyer belt was rigged to sense the airplane’s speed from the thrust it was exibiting and turn the same speed in the opposite direction. In other words if the plane’s thrust was typical of an airliner traveling (or taking off) at 150 mph then the conveyer belt would roll at a rate of 150 mph in the other direction. This being said, the craft could not possibly take off. Whether it’s a jet plane, a prop plane a car a scooter or a go cart it would sit seemingly idle because any hint of speed it could generate would be counteracted by the belt. An airplane can’t do anything until it generates lift and lift is created by airspeed. What I’ve just discribed is a plane which can’t generate any. The end result is a perfectly good airliner with burnt up wheel bearings sitting at the back end of a conveyer belt in a smoking heep. BTW, this experiment has been done at model airplane airports nationwide with the same results.
Great mind bender. Nomatter where you go on the net everyone agrees that the wheel bearings almost don’t enter into the equation because they exhibit very little drag. So little in fact that let’s just pretend they’re “air bearings” which contribute zero drag, that’s not much of a stretch ok? Let’s look at this whole thing from a different perspective. Let’s say that the jet engines, or props, are shut down on the plane and the conveyer belt is at a dead stop. Then suddenly the conveyer belt instantaneously begins it’s 100 mph backward motion. Remember, the airplane’s engines are off, what happens? Well, the plane’s wheels begin to spin forward at 100 mph and the plane sits perfectly still in respect to the earth. Got it so far? Remember, we agreed that the plane’s bearings are almost drag free and that’s the only thing between the conveyer belt and the airplane. Now, the pilot fires up the plane and cranks the engines to a point that would normally propel the craft at about 100 mph. Remember the plane that was sitting still on the conveyer belt with it’s wheels spinning? You’ve just entered on more thing into the equation…thrust. Thrust is independent of the ground, it pushes against the air behind the plane, the action creates a reaction and the reaction is forward motion. Motion equals lift and lift gets this whole thing in the air. The conveyer belt is just a silly part of this equation that makes the wheels turn faster than they’re supposed to. The end result is a plane that would zoom down the runway pretty much like there was no conveyer belt and takeoff in a normal manner. That is, if the plane’s design would allow it to take off at 100 mph.
Ummm… how can you have lift if there is no air moving across the wing of the plane? The thrusters just move the plane, the air moving across the wing produces lift by creating a pressure difference on the top and bottom of the wing. Think of it this way, if you were in a car going 100 mph while the conveyor belt is going the opposite direction 100mph and you stuck your head out the window, there would be no wind. Because you are not moving relative to the air around you.
One thing many people are forgetting here. The conveyor is matching the speed of the plane. In order for the conveyor to start moving the plane would have to start moving. The tires on the plane are NOT going to start moving without the plane unless the conveyor is cheating and getting a head start. Since it’s fact that the forward thrust of the plane is caused by the propellers and NOT the tires, the plane would actually HAVE to move to make the tires turn! If the plane moves through the air fast enough it WILL have lift. People act like the plane COULD sit still and the conveyor move backwards, well that couldn’t happen because the conveyor is MATCHING the speed of the plane and the plane isn’t moving! Think about it people! The speed of a plane isn’t measured in tire speed it’s measured in air speed, if there is no air speed there is no speed.
Think about it this way if you are driving a motorcycle with a side car on it at 50MPH and the conveyor is ONLY on the side car you can still drive the motorcycle at 50MPH, however the sidecars wheel(s) will be traveling 100MPH. Same principal applies here. The planes motors providing thrust would be the motorcycle in above analogy and the planes wheels would be the side car. It is very possible for the plane to take off.
By the some of your thinking, the motorcycle would not be able to move forward either, which is completely untrue.
Tjamz,
Good analogy!
You guys are too smart for me. I CAN tell you this though. On one of those late night cable shows (the kind of science show that dispels myths or proves them to be true) they proved to me that the plane will take off. They used a childs battery powered airboat, prop driven, very slow. I quess they lacked an airplane. On the boat they attached a set of wheels. They timed it over a 4′ course on the floor and then placed this silly looking vehicle on a grocery store conveyer belt the same length to see if it could match that time. It didn’t but the times were so close that it didn’t matter. It was clear that the differece in time was caused by the really cheezy set of wheels they used as they spun at twice the normal speed because of the belt running the opposite direction. It wasn’t a precise test but it didn’t matter whether the belt was at exactly the right speed or that it was a boat and had no wings. The point is that it zipped right along as if it were on a stationary track and ran off the end of the conveyer. The reason is that it used a prop to move it and this type of propulsion is independent of the ground below it.
Two boats are capable of a 50 mph top speed in still water. One is an outboard and the other is an airboat.
If they were running a race in a river, against a 25 mph current, which would win?
If you said it would be a tie you haven’t got a clue and you probably believe the airplane would never take off from the conveyer.
If you said the airboat would win and go almost twice as fast as the outboard then you are thinking outside the box and are part of the winning team on this debate.
Here’s a simple experiment to prove the airplane WILL fly.
Attach a long rubber band to one end of a table and the other end to the front of a free wheeling Matchbox car. Pull the car back along the table stretching the rubber band. Release the car and it is propelled forward. Now, place a belt sander turned belt up on the table. Pull the car back again stretching the rubber band, place the car on the sander belt and hold it there. Turn on the sander so the wheels of the car are moving forward. Release the car and see what happens. The rubber band (thrust) will propel the car forward regardless of the speed of the belt. The car will not remain stationary unless friction of the bearings (or axles) counteracts every bit of thrust provided by the rubber band.
This means when thrust is applied the plane will move forward through the air at its’ normal speed minus the friction of the wheel bearings which is negligible. Why is this so hard to understand?
Mark is 100% correct. This would have been a great stability project for me when I was a systems engineering student twenty years ago. If I were to model this scenario, I think I’d find a few poles in the left-half plane (not left-half airplane). It is an unstable equation.
The wheels are practically frictionless. The friction in the wheel bearings is the only force countering the thrust of the engine. Let’s say an airplane has 4000 lbs of max thrust. How can you get 4000 pounds of frictional force from wheels that are practically frictionless? By rotating them at extremely high speeds; speeds much faster than the 120 knots needed for the aircraft to take off.
Like I said, the whole scenario presents an unstable equation in which the conveyor speed would probably zip off into infinity before the mathematical airplane became airborne.
You have got to be kidding me, I have 3000 hours in Navy Jets. It’s simple, like one of the responses above….If you stick your head out the window of said airplane are you going to feel wind? No! No wind - no airspeed, no airspeed - no lift, no lift - no fly. Forward motion is what causes air to move over the wing and produce lift. It would be the same as trying to take off with a tail wind equal to your rotation speed. Equate the tailwind to the conveyor and you see the problem is. If you don’t have airflow, which you won’t on the conveyor then you won’t fly.
And you think I’m stupid!
Mark Wilcox,
Just because you fly jets doesn’t mean you understand physics. I sat behind a few pilots who could do advanced basket weaving, but couldn’t fathom the concept of vector analysis. Of course, they were Marine pilots, so that probably explains it (ha).
Answer me this. What force is countering the thrust?
OK, I’ve reread the question. I was assuming the aircraft was stationary compared to the ground. Now I see they are asking if it would remain stationary. If the conveyor were long enough, yes, the thrust would propel the airplane up to the speed required for rotation and would fly. The first time I read this it appeared too obvious, I was assuming a stationary airplane with no airflow over the wings. The conveyor would simply be similar to taking off on ice which we all know happens all the time.
There, I admitted I was wrong, Marine aviators would never do that.
Please if this is your belief please leave aircraft to the pilots. If you happen to find yourself within 100′ of any aircraft get away quick. Wheels,engine,prop are not required for flight. However airspeed is. ever heard of a stall. duh.
Matt,
I’m not sure as to whom you were directing your comment, or to which side of the argument you are on, or even what your point was.
Hey Mark Wilcox do you see what he’s doing ? rethinking.
What’s the point of the conveyor belt!!! we’ve got to generate airspeed to take off. let’s say 60 kts for take off. conveyor speed 60kts .aircraft forward motion “0″.Advance engine power.. yes aircraft moves forward approches 60kts. so we got conv 60kts, aircraft 60kts,little wheels uh 120kts? is take off roll any shorter nope lots of extra wear and tear on L gear you betcha. Tell ya what buy an RC (Radio controlled)aircraft and knock yourself out. maybe I’m all wrong. If it works it would definatly make sence on an a-craft carrier.
Mark W,
I was an EA-6B ECMO. We would just settle this argument by taking a vote.
OK heres my 2 cents. I originally thought plane could absolutely not take off, but then I tried thinking about it from another angle. In the simplest terms, lets take the following circumstances:
1. the conveyor that travels underneath a bridge.
2. you are on rollerskates with airplane wings.
3. you have a magic pole that could grow like Pinocchios nose and at the speed needed for an airplane to take off.
Now lets say you stand on the conveyor and place one end of the the pole against the wall of the bridge, at which point it starts to grow. No matter how fast the conveyor goes that pole will keep moving you up the conveyor. This “pole pushing against the bridge wall” represents “thrust pushing against air”, so in the end, I believe you could take off. Would’nt this make sense? Am I wrong!!?
Those who think the plane will remain stationary still cannot explain what force is countering the thrust. That’s the only answer I want.
The plane will take off. Period.
To prove my point, let’s change things a little. Put a regular old car, say a 2006 Mustang, on the conveyor. Then strap some high lift wings onto the roof of the Mustang. Set the conveyor to exactly equal the velocity of the Mustang with respect to the ground surrounding the conveyor, NOT set to the velocity shown on the speedometer. Jump in and hit the gas. The vehicle MUST move forward, with respect to the ground, for the conveyor to begin moving. When things stabilize, the vehicle speedometer will read exactly 2X the speed of the conveyor. (ie. the speedometer reads 40 mph, the vehicle as seen from the ground is going 20 mph, so the conveyor is also moving 20 mph. 20+20=40!) let’s say the high lift wings need an airspeed of 50 mph to lift the vehicle off the ground. All I have to do is hit the gas and when my speedometer reads 100 mph, it’s up, up and away!
Now if you set the conveyor to match the speed shown on the speedometer, this model falls apart and the Mustang sits on the ground in the same spot as seen by the observer on the ground.
Anyway, in the case of the airplane, you could set the conveyor to match the speed of the tires OR the speed as seen from the ground, the airplane will take off in EITHER case. If it is set to the speed of the wheels, the conveyor will accelerate to infinity very quickly. If it is set to the ground speed, the conveyor wheels will be turning 2X the velocity of the airplane.
OK,OK,I see your point. the interpretation i first received was that this was an attempt to reduce the takeoff roll requirements of an aircraft. i respectfully withdraw my previous comments.an aircraft could get airborne.it would be similar to a sea plane with an opposing water current. am i close?
I started out in the no-fly camp, but did the experiment. I used a toy truck and a laminated nautical chart. Seeing is believing — the plane will fly! With the wheels free to spin, there’s no appreciable force resisting the plane’s forward motion.
Matt, I think the plane on the belt would have an easier time taking off than the seaplane taking off upstream. The pontoons don’t just slide over the water; they are partially immersed in the water. The water moving downstream would apply a force to the pontoon pushing it backward. Unlike the free-spinning wheel, the pontoon is rigidly attached to the airframe, so it would produce a drag on the whole aircraft.
It would be interesting to have to take off with the wind blowing downstream of the river.
The conveyor belt essentially renders the wheels ineffective. No matter if they are spinning at 10 rpm or 1000 rpm, no forward movement of the plane is allowed by design. Therefore, the weight of the plane is acting on the tires, which are in constant contact with the belt. To take off, the plane would have to overcome the tire friction as if the tires didn’t move at all. That is the force acting against the thrust: tire friction.
Regardless, if forcefully matching wheel speed, the conveyor will never allow the wheels to start spinning in the first place. Since the wheels start off at zero, the plane would have to move forward some for the wheels to turn.
Adam,
What do you mean “no forward movement of the plane is allowed by design”? The conveyor is controlled by the forward motion of the airplane not the turning of the wheels, although it doesn’t matter anyway. You are correct though, that “The conveyor belt essentially renders the wheels ineffective”… this is because the conveyor can do absolutley nothing to inhibit the takeoff off the airplane.
If the scenario is that the belt is matching wheel speed, then the wheel cannot make forward motion without breaking the grip of the wheel and the ground. For the plane to move forward while the wheel speed and conveyor speed match, it would have to “skid” across the belt.
Say that the wheel was at maximum speed. The belt is at the same speed. More thrust is applied, but the wheel can’t spin any faster. Eventually, the aircraft breaks the friction between the tire and the belt, and the tire skids across the belt (as if you tried to move the planes when the wheels would not turn at all). This is how the plane would have to move forward if the belt and wheel speed were constantly matched.
Now, if the belt were matching PLANE speed, then the wheels would turn at twice their normal takeoff speed, and the plane would still take off (assuming it’s landing gear could withstand twice the normal speed).
Can you say “infinity”?
Adam,
I suppose technically you are correct. If the belt was tuned to the speed of the wheels, as the aircraft accelerated, the belt would accelerate to infinity quickly. This, of course, would destroy the wheels causing the landing gear to eventually collapse altogether. The aircraft would then be smashed to pieces on the viciously spinning conveyor belt. However, if we assume zero friction wheel bearings, the aircraft would be able to lift off.
I guess it would takeoff, too. What is infinity plus 120 knots?
No, it wouldn’t. Because if the wheels are exactly matching the conveyor, and vice versa, the wheels are stationary in space. Wheel speed - belt speed = plane speed.
Okay, let’s look at the wording of the real question at hand:
“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?”
So thrust is limited to whatever it takes to make the plane normally do 100 knots. Does it take off? No, it doesn’t. Because you have 100 knots worth of inertia in the opposite direction.
The thrust propelling the aircraft forward comes from the props, not the wheels. The wheels can do nothing, short of failing, to stop the forward motion of the aircraft. Are you just mocking us nerdy engineers to try and get us all worked up?
@Adam: If the wheels are not attached to a drive train, then they are not being used to propel the plane forward at all. The only thing propelling the plane forward is its’ thrust, be it jet turbine, propeller, or big inflated baloon. There is no appreciable effect on the plane from the wheels unless the plane’s brakes are being applied. Thus, the force needed to move the plane at 100 knots would still move the plane at 100 knots, even if the conveyer is moving backwards at 10000000000000000000000000000000 knots (unless the tires blew). The force is jet against standing air, not jet wheel against ground.
Adam,
Please do a summation of vectors about the airplane and tell us what force is countering the thrust. If you say the friction in the tires is, then you must think an airplane would roll to a stop WITHOUT BRAKING in the same distance it would take-off. Does that even make sense? Therefore, there must be some other force holding the airplane back, say, a giant invisible hand or a tractor beam. That’s the only way it would not take off.
The tires themselves do have rotational inertia, it may be entirely possible that the energy of the thrust is being conveyed to the rotational acceleration of the tires as the planes attempts to speed up (frictionless or not). If the conveyor belt itself is frictionless, and responds only to the actionary force on the tires, you may get something like this happening:
1)Engine increases in power, infinitesmal thrust is initiated.
2) thrust is transferred in an attempt to increase the momentum of the plane.
3) tires, in response to this desired increase in momentum, attempt to increase in rotational acceleration(requiring energy to do so).
4) this rotational acceleration in turn acclerates the conveyor belt (energy required here as well).
In short, the energy of the thrust can be transferred to an increase in the rotational speed (and energy) of the tires on the plane and the conveyor belt. If this were the case (and I’m not sure if it would be, I don’t know if all the energy of the thrust could actually be conveyed to the tires in a frictionless environment, I don’t want to do the math), all the energy gets expended in an increase in rotational inertia, and the plane doesn’t go anywhere.
As long as not all of the energy of the thrust goes into increasing the rotational inertia of the tires and possibly the conveyor belt, then I’d say yes, the plane will eventually gather speed, and will move along the conveyor belt and gain the desired liftoff speed with respect to the still air surrounding it.
If the treadmill is matching AIRSPEED, the plane takes off.
If the treadmill is matching FORWARD THRUST, the plane does not take off.
I can’t comprehend why anyone still argues against flight here. The conveyor makes absolutely no difference. It could be moving at any speed and still would not be able to keep the aircraft from flying. The only effect it would have would be to increase the speed of the rotating wheels, which will NOT stop the aircraft (Unless, of course, the wheels break!). The conveyor cannot stop the aircraft because the spinning wheels isolate the aircraft from the effects of the conveyor at any and all realistic speeds, that is specifically what they are designed to do!
The premise of the problem is outside the laws of physics. Once one begins mixing physics with arbitrary non-rational constraints, all bets are off.
1) Conveyor belt “instantaneously” matches the wheel speed, thus canceling any horizontal motion.(Arbitrary)
2) engines can provide normal thrust.
Let’s quickly run the engines up to Takeoff thrust whilst applying max braking force to to wheels.
The plane is rockin’ n’ shaking, wanting to hurtle down the runway. Release the brakes. As soon as the plane starts to move forward the wheels turn and the conveyor responds. The plane WILL hurtle down the runway unaffected by the conveyor belt effect. The wheels will quickly reach a very high rotational speed, the over stressed bearings and tires will begin to resist the ever increasing angular velocity to a point where the conveyor-tire contact patches will transition from rolling to sliding friction.
At that point the wheels will decelerate due to reduced friction. Imagine sliding on ice. The conveyor will slow “instantly” (arbitrary constraint) to match the wheel speed. Exactly like anti-lock brakes (but faster), the friction will increase again, the tires will skid and the conveyor will respond.
Assuming the tires don’t blow out and the stressed bearings hold up until the airplane reaches 100 kts indicated airspeed, the wheels will be rolling at much more than 100 hundred knots. The conveyor belt moves opposite the takeoff direction at 100 kts faster than the wheels at takeoff. (Impossible scenario; violates the premise)
Therefore it follows, if the “arbitrary premise” is inviolable (that conveyor belt and wheel speeds are always opposite and equal)the problem itself is arbitrary. An arbitrary condition is neither true nor false, since to be true or false reality (physics) cannot be violated. The problem must be rejected as an irrational hypothesis.
Never mind my post above. Below is a statement of the problem from Airliner Net:
It is really a simple problem. As the plane starts to move due to thrust, the wheels will begin to roll. The conveyor belt will move in “the same direction” and at the “same speed” as the aircraft. At takeoff the wheels will be stationary whilst the conveyor belt is moving exactly at at the speed of the airplane.
However, the wheels will be stationary and the conveyor belt in contact with the tires will be stationary “relative too the tires”. Condition is satisfied, since neither the wheels nor the conveyor belt are moving - RELATIVE TO EACH OTHER.
The plane can takeoff and the wheels will not rotate.
QUOTE:
Those who think the plane will remain stationary still cannot explain what force is countering the thrust. That’s the only answer I want.
________________________________________________
The answer is a combination of GRAVITY and air resistance/DRAG! (EVEN A MOVING PROPELLER PRESENTS A FORMIDABLE DRAG, ON THE FORWARD MOVEMENT OF AN AIRCRAFT!) Thrust needs a ‘COUNTER FORCE’ to ‘affect’ an ‘effect’. If the ground is rolling backwards ‘IN CONCERT WITH’ and NOT PRESENTING A ‘COUNTER FORCE’ to the thrust (through the airframe and the landing gear, and eventually ‘to the GROUND’), then ALL THE THRUST IN THE WORLD is TOTALLY nullified! And, the lack of forward movement fails to produce any lift needed to overcome the combination of gravity, ground effect, and wind resistance/drag!
Just moving the air won’t hack it, in spite of the fact, that your little brain fails to grasp the concept.
Whether or not the plane will ever move is totally DEPENDANT upon the strength of the source, and direction of the THRUST.
Assuming we are talking about a Cessna 150, with a thrust to weight ratio of 0.1 as opposed to an F-15 with a thrust to weight ratio of 5.0 then the plane will NEVER be able to overcome gravity, without the help of the lift provided by the forward movement of the plane. Even then, if the THRUST is not vectored in a downward direction to push against the ground, even the F-15 will never get off the ground!
Quote: “Just moving the air won’t hack it, in spite of the fact, that your little brain fails to grasp the concept.”
Don’t know why you feel the need to insult, especially in a post that clearly identifies you as inept.
Drag and gravity counter thrust?!?!? If the plane isn’t moving,(which is your assertion) there’s no relative air movement(except for the air the prop is pushing), and ergo, there is no drag. There will be drag once the plane starts moving through the air, but not enough to hold back the airplane. Gravity (weight) is a force that is perpendicular to the ground. It cannot counter thrust because it has no horizontal component. Tire and wheel bearing friction would counter thrust a very small amount, but if you took the time to look up the formulas for tire and bearing rotational friction, you’d see that it would be very small compared to the thrust.
BYW, Stephen, airplanes overcome the “FORMIDABLE DRAG” of their propellers hundreds of times a day. Don’t you have any common sense? You certainly don’t have a analytical skills.
Stephen:
If the ground is rolling backwards ‘IN CONCERT WITH’ and NOT PRESENTING A ‘COUNTER FORCE’ to the thrust (through the airframe and the landing gear, and eventually ‘to the GROUND’), then ALL THE THRUST IN THE WORLD is TOTALLY nullified!
Huh? If you admit the moving belt provides no counter-force to engine thrust, how do you suppose the thrust is nullified? When the engines are revved up the plane will want to accelerate forwards following Newton’s Second Law. If it is to remain stationary you must identify a force (acting on the airframe, not just the tires) equal in magnitude and opposite in direction to that of the engine thrust. That is why I changed my mind on this; I could identify no such force. No matter how fast the belt moves, it has no contact with the airframe (just the wheels, which spin freely on their bearings).
Everyone misses the big picture. The plane absolutely WOULD act like a car (providing the wheels are on the treadmill) and also as long as the controls keep the plane level with the ground (just like a plane acts as it zooms down a runway prior to takeoff). Picture it on the treadmill zooming along nice and level. Get the idea?
OK, now picture it sitting on a regular runway with brakes applied so it can’t move and the propeller running at full force.
Got it? Now…if at this point the brakes are released and the plane’s controls are set to rise… the plane will NOT immediately rise and fly. It has to get up sufficient speed.
The only difference between the 2 scenarios is that the plane’s wheels are spinning on the treadmill which, apparently most of you agree, should not affect anything.
It needs some speed to fly - period.
Or it will stall.
“So now we have established that movement of the surface beneath a free wheeling object does not exert a noticeable force on the object…”
So because the plane’s wheels are not geared to the output shaft of the propulsion unit, the plane will happily move about such a conveyor. Really?
After 20 years working on the ground for a major airline, that is going to be great news to the fellas on the ramp. As well as those ignorant manufacturers of 50,000lb aircraft push-tractors. Why, all we had to do was just push the planes around by hand on their free-wheeling gear.
My friend, put aside your narrow view of physics for the moment and revisit the riddle: it takes a SIGNIFICANT amount of energy to move an aircraft forward along the ground before it ever gains the potential to produce lift. Gravity and drag are going to be tugging on your plane just as they would on solid ground, and yes even AFTER it starts rolling. For the record, the puzzle stated the conveyor would match the rotation of the wheels at any given time. under that condition, theoretically the plane could never move forward on the conveyor and therefore could never produce lift.
It seems to me that the question as stated has an unexplained component. The conveyor belt matches the speed of the wheels, right? But the wheels are moving in two different directions, aren’t they? They are rotating on their central axis, rotational speed, and they’re moving forward relative to the speed of the aircraft, forward speed. (Lock the brakes up on your car at 50 mph and you’ll notice that even though rotational speed = 0 mph forward speed is still, unfortunately, very high).
Which speed is the conveyor belt matching?
If the belt is matching the forward speed of the tires, then logically speaking the plane cannot move forward relative to the ground on which both it and the belt set.
But what about if the belt is matching the rotational speed of the tires? What exactly would that mean? Does it mean that the belt makes one full rotation in the same time it takes the tire to make one full rotation? If that’s so wouldn’t the belt be spinning much faster as the distance a point on the belt has to travel to make a full rotation is much greater than the distance a point on the wheel has to travel in the same time?
On the other hand, if the belt is matching the rotational speed of the tire such that for every one rotation of the tire the belt moves in the opposite direction an equal distance, then the belt would be moving much slower than the previous example. But doesn’t this supply the same result as matching the forward speed of the tire?
In other words, if the wheels are not moving forward relative to the ground around it then the plane to which they are connected is not moving forward either, regardless of how much thrust is being generated.
Think of it this way. The belt moves, but the device itself does not relative to the ground on which it sits. Put a mark on the wheels, the belt and the ground such that they all line up.
If the belt is matching the forward speed of the tires then no matter how much thrust is applied the mark on the wheels will not be forward of the mark on the ground and the mark on the belt is irrelevant. If the plane is not moving forward relative to the ground no airspeed is possible (no wind means the plane is moving at the same speed relative to the air and the ground, right?)
If the belt is matching the rotational speed of the tires by traveling one full rotation for every full rotation of the tires then the mark on the tires and the mark on the belt stay together. When the marks on the tires and the belt come together again where would they be relative to the mark on the ground? They’ll either be ahead of the mark, even with it, or behind it. I can’t see any explanation that would demonstrate how the marks on the wheel and belt could be ahead of the mark on the ground. Remember, the parameters of the puzzle say that the belt exactly matches the speed of the wheels, so increasing thrust is a red herring. If the marks on the wheel and belt are not forward of the mark on the ground after one rotation at one level of thrust they won’t be at any level of thrust
Finally, if the belt were matching the rotational speed of the tires such that one full rotation of the tires meant an equal distance of belt passed underneath, the mark on the tires would not move relative to the mark on the ground (after one full tire rotation the ground and tire marks would line up again) and there would be no forward motion.
So it appears that if you define your terms in the first or third fashion the plane does not move forward relative to the ground and thus generate no lift. I’m open to explanations of the problems presented in the second scenario by greater minds than mine.
Not a pilot or an engineer, just overly caffeinated.
you said:
But what about if the belt is matching the rotational speed of the tires? What exactly would that mean? Does it mean that the belt makes one full rotation in the same time it takes the tire to make one full rotation? If that’s so wouldn’t the belt be spinning much faster as the distance a point on the belt has to travel to make a full rotation is much greater than the distance a point on the wheel has to travel in the same time?
My comment:
Interesting theory - but the only possible way this would happen is if the tire AND belt are exactly the same size.
Quote: “After 20 years working on the ground for a major airline, that is going to be great news to the fellas on the ramp. As well as those ignorant manufacturers of 50,000lb aircraft push-tractors. Why, all we had to do was just push the planes around by hand on their free-wheeling gear.”
My dear fellow, you mistake inertia for friction. Even in the weightless reaches of outer space, a 747 would still need a push-tractor (or tractor beam) with significant ass to get it going.
For this problem to make sense, the belt speed has to match the plane speed. It is very confusing, and perhaps nonsensical, to say the belt speed matches the wheel speed.
First, confusion arises because the belt moves with a linear velocity while the wheel has an angular velocity. It seems no one can make heads or tails of what it means to say they have the same speed.
1. If you mean the belt moves at the linear speed of the tire at the tire’s contact patch, then the belt will never move. Think about it: when a wheel turns, the point in contact with the ground is not moving relative to the ground, otherwise it would be sliding. There should be plenty of friction on the belt, so we can assume no sliding. The plane, therefore, rolls down the runway and takes off like normal.
2. Or maybe you mean the belt somehow matches the rotational speed of the wheel. It is hard to envisage what this means. Do you forget that the belt itself affects the rotational speed? That is, as the belt speeds up, it makes the wheel turn faster; now that the wheel turns faster, the belt has to speed up, which then makes the wheel turn faster still. Interestingly, none of this has any effect on the motion of the airframe, as each wheel spins freely on its bearing. It is then a question of whether the aircraft can take off before a massive wheel failure. But that’s kind of a silly answer and I don’t think the intent of the question.
The plane speed. To say otherwise seems to lead to a downward spiral of confusion.
Untrue. The engines will cause the airframe (the wings, fuselage, landing gear struts, etc.) to accelerate forward following Newton’s second law, unless the belt can apply an equal force backward on the airframe. In what way can the belt apply a force to the airframe? As far as I can tell, the belt simply rubs backwards against the tires, causing the wheels to rotate forwards around their bearings. Where then is the force applied to the airframe?
This interpretation seems to require knowing the length of the runway, which isn’t stated in the problem — that is, the belt would have to move much faster on a 10,000 ft runway than on a 2,000 ft runway. The idea of the belt moving different speeds based on the unstated length of the runway should be a clue you are venturing outside the parameters of the question.
The belt moving backwards does not negate the wheel moving forwards. The belt only changes the speed at which it rotates. Consider the source of the motion: the engines pushing the airplane forward. There is no driveshaft spinning an axle. The only reason the wheel would start spinning, in the first place, is the plane moving forward and the friction at the belt pushing backward at the contact patch, causing the tire to rotate.
This assumes the conclusion.
The belt moving backward cannot stop forward motion, because the wheel does not depend on pushing backward against the belt for its forward motion. That’s why the analogy to running on a treadmill isn’t apt.
That’s true, but don’t assume the conclusion.
As someone else pointed out, this requires the belt to have the same length as the circumference of the tire, which is not what was postualated and, well, weird.
Just imagine the plane (and wheels) moving forward, with the wheels spinning faster because of the belt.
I encourage you to do a simple experiment with a toy car and something that slides easily beneath it (but not too slippery to prevent rolling). It will end the confusion.
Wow. Best comment yet. I’m really enjoying watching this thread.
And I just thought of another good way to test this… treadmill, inline skates, a rope around your waist, and someone pulling the rope, advancing you forward on the treadmill. It won’t be significantly harder to pull you forward on the treadmill when it is on as compared to when it is off, assuming your ball bearings are halfway decent.
The backwards force applied to the airframe is the friction between the wheels and their axles/bearings. This friction is minuscule as compared to the forward thrust of the airplane. Now, if you held the forward thrust on the airplane constant, and spun the conveyor belt backwards at a faster and faster speed, eventually, you’d be able to counteract the thrust of the airplane with the friction… but that isn’t this situation.
By the way, for the “matching” version of the problem, think of it like this:
On a flat surface, the plane needs to generate a certain amount of thrust “T” to move forward at speed “X.”
Now, put the plane (still generating thrust “T”) on the conveyor belt and move the belt backwards at speed X. If you increase the plane’s thrust, you make a new speed X … the speed at which the plane would be moving forward on a stationary surface if it generated that new amount of thrust… and it is that X that the conveyor belt matches.
The length of the belt doesn’t matter - it could be 20 feet or twentty miles. The idea of the question - which many people seem to be deviating from in esoteric ways that would make Sir Isaac roll over in his grave, is that the belt enables the plane to be at a standstill (in relation to the ground) while getting full throttle. The question is whether the plane, once the controls are shifted to theoretically enable the plane to rise, will, in fact, fly and rise from the belt any fly away into the sunset to the astonishment of people believing this not to be able to occur.
But is this possible? The answer is of course not.
The only situation I am aware of, as a pilot, for a plane to be level, full powered, and substain altitude (and be at a standstill in relation to the ground) would be for it to ALSO have about a 100MPH headwind adding to my already full-throttle-powered lift - in which case, cruising along, the plane would be close to a standstill in relation to the ground. Since the plane is non-moving (at a standstill in relation to the ground) on a treadmill, this simulates the idea above perfectly - minus the 100MPH or so headwind. It simply cannot immediatly fly from a standstill (on a treadmill).
I can’t believe how such a simple riddle has turned into such a raging debate.
The plane will not take off because there is no air causing lift on the wings. No matter how fast you run on a treadmill you will not feel wind blowing by. Neither will the plane.
Without lift it’s not taking off, period. End of discussion.
Ryan:
I believe you forget the air going over the wings by the propeller. Still, that is not enough to make it fly as I explained above.
Guys, all you are arguing about is what speed is being measured. If it is the linear speed of the plane’s body then yes it will take off as per usual only with the wheels spinning twice as fast at the end of the ‘runway’ as they would ordinarily. However if you are matching the speed of the conveyor to the tangential speed of the wheels then the plane would remain stationary and the tyres would probably end up blowing.
Tam:
The speed of the plane and belt are the same; the idea of this is that, if the plane is sitting there not advancing with full throttle (and subsequent lift over the winds from the propeller) - is this enough to allow it to rise from a standstill and take off? I can’t believe so many people are making arguments that say it can fly…amazing! No way!
The propeller turning (or jet moving air) moves the plane forward unless counteracted by an equal force. What force acting on the plane is counteracting the thrust? You are all saying that the plane is not moving, so that there can be no (significant) lift. That would be true, if the plane were not moving, but you have to prove that it isn’t moving! That’s the riddle… you have to explain why the plane would move forward or why it would not. You cannot just assume that the plane would not move forward and base your argument on that (incorrect) assumption. Yes, we all know that lift is required to take off, and for lift, you need movement of air over the wings. Good, now that’s off the way, we can get down to presenting our arguments as to what the speed of the plane would be through the air.
And once again, this does NOT compare to a human running on a treadmill. It compares to a human on a treadmill wearing inline skates and being propelled forward by a rocket or a a jet or something unrelated to the treadmill.
Seriously guys… take a matchbox car to the grocery store and place it on the conveyor belt. As the belt moves forward, you will be able to hold the car stationary with a feather-light touch. The conveyor belt’s movement only spins the cars wheels.
Looking more closely at the conveyor belt, I see some lettering embossed in the rubber: Manufactured by… “Hogwarts School of Witchcraft and Wizardry!” It is apparently a magical conveyor belt, to the naked eye simply a long piece of rubber, but which, with a wave of Harry Potter’s wand, can exert a force on a 777 equal to that of two GE90 turbofans!
By the way Mark, you were right to correct me for leaving out rolling friction from my analysis. I was imagining some of those GE90s and plumb forgot about it!
Those who think the plane won’t move need to do better explaining why. Looking up the thread I see one poster after another assuming (implicitly or explicitly) that the belt keeps the plane stationary. Yet there is no explanation of how the belt transmits a force to the structure of the aircraft.
Don’t you understand the question? The idea is that the plane is in a situation where the Belt VS the Thrust from the prop is at an equilibrium and the plane is therefore at a standstill. The question is if AT THIS POINT the plane is capable of, from a standstill, taking off and being immediately airborn. To understand the question you have to agree that it is initially not moving either direction and assume that balance has been made.
And the answer, of course, is no.
Also, what is this matchbox car analogy? That has nothing at all to do with the problem.
The equilibrium of which you speak only exists as very low speeds… nothing near what would be needed for takeoff from a regular runway. And that is not the question. The question mentions nothing about a standstill existing. It is merely your assumption that if the prop is generating enough thrust for the plane to go forward at 100 knots on stationary ground, that a conveyor belt moving 100 knots in the opposite direction would render such a plane stationary. And that is an incorrect assumption. The conveyor belt has no significant impact on the plane.
You think your overly clever, pal. Every one of these comments here explains why you are wrong. Nice try buddy, but by trying to be smarter than the average guy, you wind up with a far stupider answer.
No.
Actually, the question posed here is a slight bastardization of the original question at the top of this post and wasn’t made clear. The original question, as posed on the Boortz Show, MADE the assumption that the plane was basically sitting there or a short treadmill and that the engibe was revved up to the point where it would equalize with the speed of the treadmill. The question at that time went further to ask if the plane at that time could just simply…fly. Got it?
No, the question as posed on the Boortz Show did not make the assumption that the plane would be stationary. here is the article that spawned the discussion on Boortz’s show. An excerpt:
Of course, anyone with even a remote understanding of physics knows that the only time the forces are equal are at very, very low speeds (maybe just a hair above idle).
C’mon - that would be like saying that you can only walk very, very slow on a treadmill and not advance.
It appears that what you are suggesting is simply something that you believe cannot happen?
The question (above) again, is: 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 riddle only provides 2 options as an answer: 1) take off or 2) not move in relation to the ground.
Let’s get realistic. If the plane was NOT powered and the treadmill, from a standstill (as described in the question) THEN begins to go back, it would pull the plane with it. Agreed? Good.
Now the plane powers up and moves forward at the SAME speed (thrust) as the treadmill moving backwards. Gravity is holding the plane down, the wheels are spinning like crazy.
Ever hear of cruising speed? Without it, or in the absence of, say, a 100 mph head wind, the plane can’t possibly substain flight.
Common sense, folks.
Db, I’d suggest you not belittle the opposition as it will be quite embarrasing for you when you understand why the plane takes off.
The only effect the conveyor belt has is it will cause the wheels to spin twice as fast as normal. Plane goes 100kts forward, belt goes 100kts backward and the wheels spin as if the plane were doing 200kts on a conventional runway.
For a great article on this question, go here:
http://www.avweb.com/news/columns/191034-1.html
Video demonstration with a fan, a skateboard, and a roll of paper. Note that when he pulls the paper “conveyor belt” out from under the skateboard, it doesn’t slow down, because it is being driven by a fan acting on its body, just like a plane.
Mark:
Nice video try, but I see you tried to pull the wood out at the same speed as the “plane” and, if you look closely, once you start pulling the wood out it stayed at about the same place until all of the wood was pulled out - THEN it kept going. I actually put my finger on the PC screen to prove this - try it. I think you actually proved that it doesn’t move…
It’s not my video. And you need your eyes checked. The skateboard keeps moving forward as he pulls the paper backwards underneath it.
I’ve had the veracity of my answer affirmed by engineers, physicists, and airplane pilots alike.
Answer me this: if the movement of the conveyor belt has an effect on the plane that can equal that of the engines, why don’t aircraft carriers use one to slow planes down on landings or speed them up on takeoffs?
When was the last time you took a college-level physics class? What grade did you get?
First, the video means squat - it has someone manually pulling the simulated treadmill as best they can to equal the speed demonstrated by the fake plane when it moves on the ground. They are using their eyes to mimic what they think is the correct speed. It may or may not be close - that doesn’t matter as the fake plane does move on the fake treadmill BUT it doesn’t really move forward in relation to the ground until it gets OFF the fake treadmill. Check it again - the angle it is filmed at is decieving. Pul your finger on the screen right AFTER they start pulling the fake treadmill (which, you will notice, is not pulled right away).
The funny thing is - this can’t prove it will fly one way or another. Planes fly due to lift; there is no lift in this little creative film - just forward momentum which in negligent.
For the record, I posed this question to a physicist friend here in Dayton Ohio (home of aviation - remember?) who works in this field at Wright Patterson Air Force Base. He kinda grinned and said this question has been floating around for quite a while and that of course it can NOT fly under these circumstances.
Now…if you can get that fake plane in the film to leave the ground - let me know.
The whole issue is about forward movement! The plane moves forward under the power of its engines. You can’t get around that. You’ve repeatedly twisted the scenario, claiming as fact that the plane will not move. You are wrong. The thrust of the engines makes the plane move forward. What is there to stop it? The conveyor belt? How? How does the movement of the runway affect the plane, which is moving forward? What the heck kind of μ factor do you think exists in an airplane’s wheels?
Face it: you don’t know jack about physics. You don’t know what μ is, and you can’t even see the difference between a car and an airplane on a runway. You actually think that the force of friction in an airplane’s wheels is equal to half of its forward thrust. You simply don’t know what you’re talking about, and I’m guessing that your physicist friend was answering the distorted version of the riddle that you keep trying to concoct here.
Db, did you read the article that was posted? Has it still not become clear?
Would there be a difference between this and this scenario: instead of a plane it is a sea plane and instead of a treadmill it is a 100 knot current?
The only difference would be the increased amount of friction. We’ve gone from wheel bearings to water on metal. The increased friction would likely impart some negative velocity in a strong current, but assuming the engines can overcome this and the additional friction, I don’t see the result being any different.
Actually, I would suggest that, due to surface tension and the lack thereof due to the water’s movements, the amount of friction would be much less than you anticipate.
And therein lies the heart of the reason why the plane cannot take off. In order to overcome the rolling friction (whether it’s wheels on a runway or water from a current on a pontoon) a certain amount of thrust has to be generated just to get the plane moving forward.
However, in our scenario this is not the case. As soon as enough thrust is created to overcome the friction and make the plane move forward what happens? The belt (or current) matches the speed of the wheels/pontoons in the opposite direction. This means that friction increases and more thrust has to be generated to overcome the new, increased level of friction.
However, once that new level of thrust is reached the wheels are moving faster and so is the belt and so more friction. This requires more thrust, which creates more friction, etc, etc, infinitie regression and so on and so on.