Airplane and Conveyor Belt Debate

[FredGarvin]

y'know for a physics forum, this place doesn't use the laws of physics very much to solve 'em.

Care to revise that statement?

We'll believe AvWeb, but we won't believe the physics board. What has the world come to? At least they had the means to actually perform representative tests.

 

[russ_watters]

This is the most literal interpreation of the original question. However, such a system would not keep a car from moving, much less a plane, as I remarked earlier. For instance, if the car moved west relative to the Earth at 30 mph, the conveyer would move east relative to the Earth at 30 mph, making the speed of the car relative to the conveyer 60 mph.

That's true, but a treadmill could also be programmed to keep a car stationary (or going whatever speed it wants), while it could not be programmed to keep a plane stationary.

For the plane, the only way anything even happens is for the treadmill to respond to the forward motion of the plane. ---because (as has been pointed out a good dozen times now) the car drivetrain is directly connected to the treadmill, whereas the plane's engines are not.

So the scenario you and w_benjamin are describing would simply be pointless - nothing at all would happen. That's why I don't think that's likely to be the correct meaning of the (as I've said - not well written) scenario.

 

[Danger]

May I humbly request that this thread be locked before I'm forced to wriggle my fingers through the ADSL line and choke someone?

 

[ukmicky]

.
What vorticies are going to be created by the engines? We work very hard with airframers to make sure that flow is as undisturbed as possible on both the inlet and exhaust. The wings and fuselage are the most probable sources of vorticies and those are usually restricted to the wing tips and roots.

However we are dealing with a plane which is not flying but standing still with its engine on full power, pulling in and pushing out large quntaties of the surrounding air. so to say there will be no vorticies created around the wing is madness

 

[russ_watters]

I feel the need to add some more. Those who are saying that the plane would not take off are basing that on reading the problem as defining the plane to be stationary. Since the question is poorly worded and barring a clarification from the writer, it is possible to interpret the question that way. However, the problem with doing that is two-fold: First, if the problem simply reduces to: "If a plane is stationary, will it take off?", why even bother asking the question? It's so basic that it's pointless. Second, just defining that the plane is stationary does not address the question of whether such a thing is physically possible. And while we engineers are arguing about what is physically possible, those who are saying the plane is stationary are simply assuming it without basis in physical reality. I think if you analyze the problem - think through the steps of how it would work - you'd find that it would be useless to ask the question you are describing for the two reasons above.

However, if you guys do think that your position is physically possible, please follow the steps of how it would happen and explain it. If you do that, I think you will find the scenario falls apart. Let me start it:

Step 1: A plane is sitting stationary on a stationary treadmill.

Step 2: The plane fires up it's engine and begins to accelerate.

Step 3: The treadmill senses the motion/acceleration.
-------Step 3 is a toughie: how can the treadmill sense the acceleration? Unlike a car, which exerts a direct force on the treadmill in order to accelerate, the plane does not. About all you could do is sense the motion with sensors along the surface of the treadmill.

Step 4: The treadmill responds to the motion of the plane and begins to move...how fast?
-----Step 4 is where the scenario completely falls apart. Since the treadmill is not capable of exerting a direct force on the plane in the way that it can on a car, it is not possible for the treadmill to instantly react to it's motion and keep it stationary like it can a car. It could keep a car stationary regardless of what the car does - accelerate, decelerate, whatever. With the plane, the only way the treadmill can react is by speeding up - and while the treadmill accelerates, the plane is still accelerating with respect to the ground. The treadmill can't stop the plane and keep it stationary in a stable situation like it can with the car.

The only physically possible way to stop the plane is to accelerate the wheels until the wheels actually fail - heat up, burn up, disintegrate, ripping the landing gear off the plane. If the problem was meant to allow that, fine - you could always make higher speed wheels and then the problem becomes a battle between the engineering of the wheels and the acceleration capability of the treadmill. But again, that's not a very useful discussion. Plus, the scenario is uncontrolled - the treadmill is not under any sort of active control - it's not reacting to anything the plane is doing, you just turn on the treadmill when the plane fires up it's engine and see who wins the battle.

 

[jackie_nkm]

hi,
On ground, the force of the propeller makes the plane go forward irrespective of the wheels being present. wheels mere act as ion reducers( not as in car where the are the driving force generators)

this riddle can be solved by this:

Normally,
if the plane were moving with 150knts on runway w.r.t. ground , at that moment ground is also moving at 150knts w.r.t. to plane. the plane is lifted up bcos of the wind also moving at nearly same speed opposite to it and due to all that Bernoulli stuff.

Here,
when the plane is moving with 150knts, and the belt is moving at 150 knts the plane cannot move forward bcos it is already at 150knts speed w.r.t. belt(just as above case) since the plane is on belt. and belt is at 150knts w.r.t. plane (just as above case). so plane wouldn't move w.r.t. stationary ground on which the belt is kept.
Same is case with the air, which is staionary w.r.t. plane since air is not in frame of belt but in frame of ground. and so plane cannot take off.NO opposing force on the wings same from bernoulli eqns.

 

[jackie_nkm]

sorry spelling mistake
hi,
On ground, the force of the propeller makes the plane go forward irrespective of the wheels being present. wheels mere act as FRICTION reducers( not as in car where the are the driving force generators)

 

[krab]

Russ is right. The thing that everyone forgets is that the jet is pulling on the AIR, not the runway. With the brakes off, the wheels and the runway are not going to apply any force to the plane and so whatever they are doing is entirely irrelevant to whether the plane takes off.

 

[russ_watters]

when the plane is moving with 150knts, and the belt is moving at 150 knts the plane cannot move forward bcos it is already at 150knts speed w.r.t. belt(just as above case) since the plane is on belt. and belt is at 150knts w.r.t. plane (just as above case). so plane wouldn't move w.r.t. stationary ground on which the belt is kept.

How is such a situation physically possible? Ie, answer the question implied under step 4 of my previous post: how can the conveyor impose a force on the plane equal to and opposite of its acceleration force?

 

[w_benjamin]

As I posted earlier, there are two different versions of this; one that's tracks plane speed, and one that tracks wheel speed. The first one is easily answerable, yes it will fly. The second one is the one I am intrigued with.

 

[FredGarvin]

However we are dealing with a plane which is not flying but standing still with its engine on full power, pulling in and pushing out large quntaties of the surrounding air. so to say there will be no vorticies created around the wing is madness

LOL! OK. I'll stick with my madness.

 

[FredGarvin]

May I humbly request that this thread be locked before I'm forced to wriggle my fingers through the ADSL line and choke someone?

You just got my vote if there is ever an election for PF Prime Minister.

 

[w_benjamin]

I emailed the author of that link with the version of the question I have and got this response:

That's a very good question and you are correct, different than the one
I
looked at.

I guess I'm troubled by the "match the speed of the wheels" language
because the feedback loop gets kind of strange. The propeller will
pull
the airplane forward, causing the wheels to begin to turn. Does that
then
mean the conveyor will begin to turn in the opposite direction at the
same
speed the wheels are turning? If so, then it causes the wheels to turn
faster. It sounds like a feedback loop that would very rapidly
accelerate
the wheel to exceed the tire speed of the airplane, blowing the tires
and
thus possibly preventing the takeoff. Sort of a feedback loop of "the
faster it goes, the faster it goes".

Having taken off upwind, crosswind and downwind and in seaplanes on
moving
water, I suspect I'll never make a takeoff on a conveyor belt.

All the best,
Rick

 

[Danger]

One problem with that: there's a tremendous amount of hydrodynamic (right term?) drag on the floats of a seaplane until it gains lift. That would be equivalent to having partial brakes applied to one on the conveyor, and is thus irrelevant to this discussion.
PS: Thanks for the vote, Fred... and for using the right title.

 

[russ_watters]

As I posted earlier, there are two different versions of this; one that's tracks plane speed, and one that tracks wheel speed. The first one is easily answerable, yes it will fly. The second one is the one I am intrigued with.

Yes, I know - and you haven't answered the question about how the second one is possible.

I emailed the author of that link with the version of the question I have and got this response:

That's a very good question and you are correct, different than the one
I looked at.

So the author says that your interpretation of the question isn't what was meant. Great! So the answer become a simple "yes" again!

 

[KingNothing]

This thread's dragged on for far too long.

 

[ukmicky]

Some of us are being too clever for our own good and assuming that the treadmill is more than your basic treadmill which moves by a external force being applied to it, but rather a more advanced system which is able to accurately sense the forward motion of the plane and is able to compensate and adjust its own speed of movement in the opposite direction. but then we're still not taking into account that the wheels on the plane can move independently to the motion of the plane.


However an advanced system with motion detectors could attempt to prevent the plane from taking off if in response to the forward motion of the plane the front of the treadmill could lift up allowing the plane itself to halt its forward motion and fall backwards due to it own weight, but even then if the engines were powerful enough it would still be able to take off vertically.

 

[Danger]

While that's an unnecessary complication to the picture, ukmicky, it does serve to illustrate another aspect of it. Given enough thrust (or wind) the plane could have zero ground speed and still take off.
I remember once seeing a German Stork aeroplane, which has just about the lowest take-off and landing speeds that you can find, flying backward over the runway. The wind was about 5 knots faster than its airspeed.

 

[w_benjamin]

My response was to show that the article linked to had no bearing on the version of the question I asked, and that the author indicated the in my version he probably wouldn't be able to take off, given his experience in taking off on moving terrain(ie:a river) "So the author says that your interpretation of the question isn't what was meant. Great! So the answer become a simple "yes" again!" No, that was an observation, not a statement. As I said, there are two versions of this, one which was easy to answer and one which is not. If the conveyor is tracking wheel speed, then I don't think the plane will take off. The conveyor is reacting to the force being applied to the wheels from the thrust of the plane. As for "Given enough thrust (or wind) the plane could have zero ground speed and still take off.", I reject that statement. The thrust is used for forward momentum which the conveyor is cancelling out, similar(but not exactly) to when brakes are being applied to the wheels.

 

[ukmicky]

Place a shopping trolley on a conveyer, stand behind it and hold on to the handle so it can't move backwards or forwards .
Now get someone to turn on the conveyor so it moves backward at 5 mph.
WHAT WILL HAPPEN
The wheels will turn on the trolley and you will feel a slight strain on your arms as they fight against the friction created in the wheel bearings.

Now turn the conveyer speed up to 200 mph
WHAT WILL HAPPEN
Not much ,you will still be able to hold on to the trolley and prevent it from moving.

Now increase the speed of the conveyer to 1000 mph
WHAT WILL HAPPEN
once again not much ,the force required to hold the trolley still hasn't increased by any significant amount and if you could prevent the bearings from getting hot causing extra friction the amount of strength required to hold to trolley at 5 mph would basically still be the same as it is at 1000 mph.

Now apply that to the plane, once the engines have overcome the friction in the wheel bearings, you would still have more than 90 percent of your engine power to move the plane forward to take off speed. All the conveyer does is cause the wheels to rotate faster and nethier the wheels or conveyer have any bearing on how fast or slow the plane moves once the friction in the wheel bearings is overcome.

Its not a car the wheels are not connected to a drivetrain

 

[w_benjamin]

Ah, the classic trap. In your trolley example, the conveyor is the actor, and the wheels are the reactor. In the question, it is the other way around, and it does make a difference. Use this analogy instead: Get a little cart with wheels on it, and mount an electric fan onto it that's big enough to move the cart maybe 2-3 mph. Start up the treadmill and set it for maybe 10 mph?(arbitrary number) Start up your fan cart, and place it on the treadmill, holding it so the wheels get up to speed with the treadmill, then let go. If the 'it will fly' crowd is right, the cart will move forward at the 2-3mph it did on solid ground. If the 'it won't fly' people are right, the treadmill will move the cart backwards until it falls off the back of the treadmill. This treadmill doesn't have the precision of the one in the question, but the principle elements are there.

 

[Danger]

"Given enough thrust (or wind) the plane could have zero ground speed and still take off.", I reject that statement. The thrust is used for forward momentum which the conveyor is cancelling out, similar(but not exactly) to when brakes are being applied to the wheels.

You can reject it until you're blue in the face, but it's a fact. If a 152 with a take-off speed of approximately 80 knots is facing into a 90 knot wind, it will take off without even starting the engine. Assume that there's a cable from it to the ground to prevent rearward motion, and it will continue to fly like a kite. If you replace the 152 with a Harrier, it will take off vertically with zero ground speed because it has enough thrust to overcome gravity.

Get a little cart with wheels on it, and mount an electric fan onto it that's big enough to move the cart maybe 2-3 mph. Start up the treadmill and set it for maybe 10 mph?(arbitrary number) Start up your fan cart, and place it on the treadmill, holding it so the wheels get up to speed with the treadmill, then let go. If the 'it will fly' crowd is right, the cart will move forward at the 2-3mph it did on solid ground.

Which it will, assuming no friction in the wheel/axle system. That's what we've been trying to tell you all along.

 

[w_benjamin]

"You can reject it until you're blue in the face, but it's a fact. If a 152 with a take-off speed of approximately 80 knots is facing into a 90 knot wind, it will take off without even starting the engine. " You are absolutely right. However, it has no bearing on the question as there is no wind. As such all you have left is thrust. At zero ground speed, thrust will not lift the plane. If that were true, you could put the brakes on full on a plane, load up with thrust, and just take off with no wind to aid you. Unless you have a Harrier (which you did mention), I don't think you're going to be doing that anytime soon. As for the second part, well, this is where we disagree. You believe the cart will move forwards, and I believe it will move backwards.

 

[w_benjamin]

Using the same analogy against ground speed, try this: Take a cart with wheels and set it on the ground. 0 mph, right? No movement? Take the cart and once again put in on the treadmill going 10 mph, holding it until the wheels get up to speed. If you let it go, using your logic, it should stay at 0 mph. In other words, it won't move on the treadmill, the wheels will just spin underneath and it will sit in the same spot indefinately. That's an experiment you can try very easily.

 

[f91jsw]

This thread has definately dragged on for way too long for a physics forum. The simple answer is:

The plane will take ALWAYS take off NO MATTER WHAT SPEED the conveyor belt moves with.

For those who can't see it intuitively it's simple Newtonian physics: The engines produce thrust, which means a large force on the aircraft. Barring another force that counteracts this large force there's nothing stopping the aircraft accelerating according to F=ma. In the given problem there is no such counteracting force except for the very small friction force from the wheels. As the aircraft accelerates it will gain speed in the reference frame defined by the airmass and the surrounding landscape, and it will take off. This will happen in all the discussed cases, no matter what feedback loop exists between the aircraft/wheel speed etc. and the conveyor belt.

It's a fun problem by the way, I will remember it and try it on my first year physics students in the future.

Johannes

 

[Danger]

Thanks for weighing in, Johannes. I'm seriously at my wits' end trying to figure out how to make him understand. (And I suspect that you soon will be as well.)

 

[w_benjamin]

Johannes, if you're a physics teacher, then I weep for the future of our country. You're dismissing the wheels as a small frictional force, and your agreement with him Danger, shows that it is YOU who lack the understanding. You're saying that just because the wheels only need a small amount of energy under normal circumstances, that they will need no more in this one? Different circumstances do indeed require different amount of energy to the wheels. (and if you think that the wheels have no energy being transferred to them, you're sadder than I thought-- see "Newtons Cradle"). What if the wheels weren't exactly round? More energy would be needed. What if the wheels are not on a smooth surface, such as sand? More energy would be needed. And what if the wheels have a counteracting force being applied to them? More energy would be needed. The more counteracting force, the more energy is needed. If the conveyor provides such a force (and yes, it can be done through the wheels) then it is theoretically possible to hold the plane in place using that force. The plane only moves forward after all objects that hold it back have been overcome. The energy for that ability to overcome is the thrust. If you use all the energy from the thrust to overcome the energy holding back the plane, there's none left to move the plane forward. What if you put a two foot high lump in front of the tires? The wheels roll just as freely as before, will they still need the same amount of energy to turn as on flat ground?

 

[f91jsw]

I'm not a physics teacher, I just teach physics between doing physics research (in the UK).

The problem formulation did not state that the plane was starting from a sand trap or that the wheels were locked. You can't invent new circumstances to save your theory.

BTW, hint: look up a physics textbook for the distinction between "energy" and "force."

Johannes

 

[w_benjamin]

You're right, those were just other examples of how more "force" might be needed to move the plane forward. And you're right in that I used the term energy in place of force. I will give you the question again, and let you read it carefully:

Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.

Can the plane take off?

Note that this version says "wheel speed". That means the wheel speed cannot exceed the conveyors speed no matter how much "force" you convert the thrust into as the conveyor always corrects itself to match the speed of the wheels. Also note that the conveyor is acting as a reactor to the "force" applied to the wheels.

 

[ukmicky]

Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.
Can the plane take off?
Note that this version says "wheel speed". That means the wheel speed cannot exceed the conveyors speed no matter how much "force" you convert the thrust into as the conveyor always corrects itself to match the speed of the wheels. Also note that the conveyor is acting as a reactor to the "force" applied to the wheels.

How can the conveyer match the speed of the wheels ,when any change to the speed of the conveyer will affect the speed that the wheels are moving.

Also the wheels can still move without affecting the motion of the plane as the wheels on the plane are not connected to any drive train .


And by moving the conveyer in the opposite direction of rotation of the wheels .( I am trying to visualise which way the wheels turn on a forward moving plane) wouldn't the conveyer be moving in the same direction as the plane is moving, pushing it through the air slightly faster than it would have gone with just the engines as it would help combat the frictional forces of the wheel bearings

 

[russ_watters]

You're dismissing the wheels as a small frictional force, and your agreement with him Danger, shows that it is YOU who lack the understanding... [bla, bla, bla...]

benjamin, how much friction do you think there is in an airplane wheel? I'll help you: the engines exert hundreds, even thousands of times the force of the friction on the wheels. So yeah, that qualifies it as "a small frictional force".

Also, you are aware that friction is not dependent on speed, right? Increasing the speed of the wheels does not increase the force of friction. If the friction force in the wheels is 1/1000th the force of the engine at 10mph, it is still 1/1000th the force of the engine at 100mph. So again, the only way for the conveyor to halt the acceleration of the plane (the plane does accelerate with respect to the ground, no matter how you slice the question) is for the conveyor to quickly speed up to the point where the wheels melt and come apart before the plane becomes airborne.

But again - that's a pretty useless way to view this issue.

The more counteracting force, the more energy is needed. If the conveyor provides such a force (and yes, it can be done through the wheels) then it is theoretically possible to hold the plane in place using that force.

That's nonsense. The only way the conveyor is capable of exerting a force is through the friction in the wheels and that force is constant. Nothing the conveyor does can increase that force. [caveat: there is viscous friction due to the lubricant, but just as the regular dynamic friction is much less than the thrust, the viscous friction is less still.]

So is that all the problem is here: you think friction is dependent on speed? That's a common mistake due to the heating of the wheels. People think that since faster=hotter, faster also equals more force. Nope. I think you may need to review your Newtonian physics.

 

[krab]

Man, I've seen some pretty lame threads. This one is right up there with questioning 0.999...=1.

 

[Doc Al]

krab's right. I think we've had enough.

 

[ice87]

would the plane take off?

Someone sent this to me, and apparently it caused quite a ruckus on another forum. I couldn't make any sense out of their responses, so I decided to put it to the great minds of NeoWin. I didn't find it anywhere, so sorry if this is already on here. The Question:

A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

Please post a reason.

Can this plane take off given no winds?

Theres a quite a bit of discussion on this over at neowin. http://www.neowin.net/forum/index.php?showtopic=413477

 

[Pengwuino]

Screw this, I can't figure this out yet, I need to think about it.

I have a feeling it will take off as long as its engines are capable of producing enough thrust to reach take-off speed while having to deal with the frictional force created by the tires going twice as fast.