@vortexau

Actually, your fifth pic, the "flying pancake" , is a conventional plane with an unconventional wing. It still needs to go forward to take off.

Here's a better photo:
click me

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People who generalize are always wrong.


1989 - 500 / 1991 - 3000 / 1997 - Genesis Flyer 1200T / 2003 - A1XE

@A1200

I haven't read this thread but the answer is pretty simple. The rate of the speed needed for lift is the rate of speed vs thewind not vs the conveyer belt. The wheels don't create the rate of speed the engines on the wings do. As such the airplane would appear to stand in one spot then lift off of the conveyer belt and move forward. Physics is so boring sometimes.

Last edited by BrianK on 04-Mar-2006 at 06:14 PM.

@all

Well, earlier someone mentioned getting a physicist to talk about it. As it happens, I teach physics and engineering at the University of Washington in Seattle, so I'll have a go at it.

First my conclusion: I am firmly in the camp that says the plane will fly and that the wheels will spin twice as fast. This is just an approximation to the truth though, and there are logical considerations to be addressed, as well as physical considerations and matters of interpretation.

1: The question uses the word "speed" very loosely. There is no such thing as absolute speed, there is only speed relative to some other object or coordinate system. There are at least 4 relevant speeds in the question, only two of which are mentioned: speed of plane relative to air (called "airspeed" by aviators), speed of plane relative to ground ("groundspeed") and speed of the conveyor belt relative to the ground (which I will call "beltspeed"), and speed of the plane relative to the belt, which relates to how fast the wheels spin, and which I will call "wheelspeed".

2: The different speeds have different physical effects. Airspeed controls the lift on the plane's wings, which determines whether it can sustain flight. Wheelspeed determines how fast the wheels will turn. Groundspeed has some effect on the plane's ability to take off because it influences the strength of the gound effect, which partially supports the plane's weight during takeoff. Beltspeed may make a slight difference in airspeed by frictionally dragging air backwards along the belt, creating a slight headwind for the plane to take off into. This would actually make it very slightly easier to take off, not harder.

3: Because of 1 and 2, it is very important to define exactly which speeds the question is talking about. The question says that the conveyor senses the plane speed and adjusts the conveyor to move in the opposite direction at the same speed. The conveyor motor must be mounted to the ground somewhere, so the conveyor speed in question is obviously relative to the ground, i.e. it is the beltspeed. However, there are several possibilities for which plane speed the conveyor is sensing.

Is it the airspeed? If that were true, there would be a logical contradiction: if you assume that the belt is capable of stopping the plane's forward motion, then the airspeed would be zero. But in that case, the sensor will tell the belt that the plane's speed is zero, so the belt will STOP MOVING. Therefore, if you assume beltspeed > 0 you can prove beltspeed = 0. This is a direct logical contradiction, so this interpretation cannot be correct.

Is it the groundspeed? If there is no wind, airspeed and groundspeed are the same, and so this interpretation suffers from the same logical contradiction as the airspeed interpretation. Even if there is wind, you can still get the same contradiction if you assume that the conveyor belt is capable of stopping the plane's forward motion relative to the ground. Therefore, this interpretation is not correct.

Is it the wheelspeed? Under this interpretation, the plane must stand still relative to the ground, because of the way relative velocities work: wheelspeed = groundspeed - beltspeed, so if beltspeed is adjusted to be the opposite of wheelspeed, groundspeed is forced to be zero. In other words, this interpretation only makes sense if you already know that the groundspeed is zero, which is what the whole question is about. If the groundspeed is not zero, this interpretation is impossible because the equation can never be satisfied. Therefore, you must already have answered the question about groundspeed before you can know whether this interpretation is even possible, and so you can't use this interpretation to try to answer the question without going in a logical circle.

4: Because of 3, if you assume the belt has the power to stop the plane, only the wheelspeed interpretation makes sense, and if you assume that it does not have that power, then only the airspeed or groundspeed interpretations make sense. Therefore, the real question is whether the belt does or does not have the power to stop the plane. The case of a plane and a car are quite different here, because a car gets its thrust by pushing against the ground with its wheels, and a plane gets its thrust by forcing air backwards with its propellor or jets.

(The ONLY way to get a forward force is to push backwards on something else and let Newton's 3rd Law produce a forward reaction force on you. The plane pushes air backwards, the car pushes the ground backwards, a boat pushes water backwards, and so on. The easy way to convince yourself of this is to imagine what would happen on a muddy road: if you tried to take a step forwards, your foot would slip and kick mud backwards; if a car tried to start forwards, the wheel would spin and throw mud backwards. So the car is definitely pushing something backwards, and if there were no mud, the wheel would be pushing the ground backwards.)

In the case of a car, the conveyor could move backwards fast enough that the car wheel was unable to push against it. In that case the car wheel is trying to push backwards on the conveyor belt, but the conveyor belt motor is moving the belt backwards already at the same speed the wheel is turning, so there is nothing for the motor to do. To see why this is true, imagine that the car was raised up off the ground so the wheels didn't touch anything. Then the engine would spin the wheels very fast, until the motor overheated, but the wheels wouldn't exert any FORCE on anything. Now set the conveyor belt moving backwards to that it is moving the same speed as the bottoms of the car's wheels, and gently lower the car onto the belt. Since the wheels and belt are already moving at exactly the same speed when they touch, there will be no relative speed at all, and so the force will be the same as if the wheels and belt were standing still. But that is no force at all in the forward direction (of course, there is the pressure of the wheel on the belt, but that is a vertical force, and doesn't affect the horizontal motion in any way).

In the case of a plane, the force which moves the plane forward comes from pushing air backwards, not pushing the ground backwards, so making the ground move will not affect this force at all. To prevent the plane from moving, the conveyor belt will need to pull backwards on the plane just as hard as the engines are pushing it forward, so the belt must exert a force on the plane. The only place the plane touches the belt is at its wheels, so the force must come through them. However, the wheels of a plane are free to turn (except for a small amount of friction), so the belt CANNOT exert a horizontal force on the plane through the wheels. In fact, that is the whole point of wheels in the first place. Why did people put wagons on wheels, instead of just making horses drag boxes along on the ground? Because wheels remove the ground's ability to drag backwards on the box, making things much easier for the horse. The only way the conveyor belt could exert a force on the plane is if the brakes were on. If the wheels are strong enough not to break, in this case the conveyor could stop the plane.

5: So in conclusion, if the brakes are on, the conveyor CAN stop the plane, the wheelspeed interpretation is correct, and the plane cannot take off. If the brakes are not on, the conveyor CANNOT stop the plane, the airspeed interpretation is correct, and the plane can take off. So what the whole argument boils down to is:

Can a plane take off with its brakes on? No. Duh.
Can a plane take off with its brakes off? Yes. Duh.

6: As I mentioned before, the wheels won't turn exactly twice as fast but pretty close, because the conveyor's motion may affect the ground effect (I don't know how to compute that -- it would require an experiment, I think, to see how groundspeed affects the strength of ground effect), and because the air drag of the backwards conveyor motion will produce a slight headwind. I think the plane might take off a little easier because of the headwind, so the wheels would turn slightly less than twice their normal rate, as the plane would need slightly less goundspeed to take off with a headwind. However, I am unable to assess the strength of the ground effect, so it is possible that this might change things slightly, and the takeoff groundspeed might me slightly greater than normal, instead of slightly less.

If anyone has read all the way to the end of this, thank you for your attention. I originally came to amigaworld.net today to look for hints on getting my DVD drive to work, and got distracted by this thread. See what you've done! Now, back to my DVD search....

--Stuart Anderson

I think everyone's blinding themselves with science and pseudo-science. The effect of the moving runway is irrelevent to flight. A plane can take off from land or water in exactly the same distance. It will also take off from a runway made of ice in the same distance. It would take of from a 'super' teflon coated runway where the coefficient of friction is zero. And it will take off from the conveyor belt too. As noted by many, the wheels will spin faster (assuming normal friction applies), but that's irrelevant to flight.

Everyone's sussed the need for air flow over the wings and that it's created by forward motion. Well even forward motion isn't actually necessary. You simply need air flow relative to the wings. Hence the aircraft carrier effect. But you get this effect in a gale or in a wind tunnel.

Tie a chain to the nose of a plane and face it into a strong gale and it will take off and 'fly'. It will fly more like a kite than a plane, but it will fly. It will also fly if tethered in a wind tunnel, without moving relative to the 'ground'.

The plane will take off from the conveyor belt in exactly the same distance it would from a normal runway or any other surface you care to invent. Wheels, floats, skids, whatever. The plane will fly.

[EDIT] The wheels/conveyor belt don't figure in it because they aren't creating the forward motion. That's due to the propellor or jet engine. If the 'plane' was a car with wings and no propellor, it wouldn't fly. The conveyor would prevent forward motion via the wheels.

JaX

Last edited by WaveGuide on 04-Mar-2006 at 11:49 PM.

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@mr_homm

The conveyor belt runway is most amusing since people seem to attribute to it properties the question does not say it has. It simply says that the runway goes at the same speed as the plane but in the opposite direction. Since both plane speed and runway speed must be relative to something, the ground seems to be the most logical thing to choose. (Of course we could choose an arbitrary moving reference but the we still don't really change the answer).

The conveyor is most amusing simply for the fact that so many people interpret the question in a way that it cannot possibly make sense. If the planes speed is vp and the conveyor is vc then vp = -vc because vp is equal and opposite to vc. If the plane was propelled by its wheels then vp would be related to the conveyor speed in that vp = vp +vc which has only a single solution, i.e.

vp-vp = vc
0 = vc
and vp = -0 = 0

So if the plane was driven by the wheels the only condition that will satisfy the question is that the plane and the conveyor are both stationary.

People who claim that the conveyor may be able to move backwards fast enough to apply enough friction to hold the plane still neglect the stipulation about the conveyors speed being equal to the planes speed but opposite. If the conveyor is whipping backwards at 80% of the speed of light then we would rightly be concerned for the safety of the bearings (on the wheels and the conveyor) but the conveyor would only be going -0.8c if the plane was travelling at 0.8c, a velocity quite likely to result in flight for even unplanelike objects such as rocks if they could survive their brief encounter with the atmosphere.

If it's a plane, it flies. If it's a car it doesn't. In fact, if it's a car, nothing moves or the question blows up.

The most amazing thing about this question is the length of the threads it has spawned.

@FluffyMcDeath

Yes, I agree 100%. The problem itself is not really hard; what makes the threads so long is lots of people struggling to interpret it. I see that you went straight for the "all speeds are relative to the ground" interpretation. This one is the most logical, of course, although in my post I wanted to address other possible interpretations that people might be unconsciously making.

The trouble with that is, one ends up talking more about the wrong interpretations than the right one, because that's where all the confusion is. The clearest explanation of the problem would be to just say, "No, I'm not even going to talk about your weird interpretation, here's the truth," but people would probably think that was rude. Still, it's tempting.

Thank you, by the way, for stating that many people's interpretation of the problem cannot make any sense. Your explanation of this was briefer and clearer than mine.

--Stuart Anderson

@mr_homm

Numbers are a razor.
Poetry is a brush.
Pick your tool with intent
to sharpen or to blur.

@syrtran
Quote:

@vortexau Actually, your fifth pic, the "flying pancake" , is a conventional plane with an unconventional wing. It still needs to go forward to take off.

Bzzz! Wrong! The Chance-Vought V-173 is, by no means, a "conventional plane":
See Chance-Vought XF5U Skimmer
carrier-borne STOL aircraft
1945 Both the V-173 & its unfinished sucessor, the XF5U, fit into the category of STOL aircraft.


From Vought-Sikorsky and Chance Vought Aircraft (V-173 Flying Flapjack and XF5U-1 (V-315) STOL Fighter -) halfway down the page:
Quote:

The aircraft was to take off nearly vertically, with the large propellers providing thrust and lift from the airflow over the upper surface. As it moved forward in the air, it would rotate to the horizontal and accelerate to flight speeds over 500 knots. In forward flight, propwash past the wingtips countered tip vortices, to fool the wing into thinking it had a much higher, more efficient, aspect ratio. In theory, the wing was stallproof . . . Test pilots, admirals, even Charles Lindbergh, all checked out the V-173\s astounding near-vertical performance; . . .

Actually, I did chuck in a ringer to see who was awake; but it was the NEXT aircraft below that with the extremely-wide fusilarge!

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A2000HD (from 1991) 060 64Mb PicassoII with OS3.5 . . . still working.

Quote:

by BrianK on 4-Mar-2006 18:14:11 @A1200 I haven't read this thread but the answer is pretty simple. The rate of the speed needed for lift is the rate of speed vs thewind not vs the conveyer belt. The wheels don't create the rate of speed the engines on the wings do. As such the airplane would appear to stand in one spot then lift off of the conveyer belt and move forward. Physics is so boring sometimes.

The explanation clarifies that an aircraft’s takeoff depends on its engine speed relative to wind, not a moving surface like a conveyor belt. The wheels merely support stationary positioning until lift-off occurs due to aerodynamic forces from the engines and wings. Physics is indeed intriguing!

Quote:

by Seer on 24-Feb-2006 21:24:18 @minator Have you read the link http://www.straightdope.com/columns/060203.html ? What's you're take on that one ? And the http://www.pprune.org/ forum links has some rather good points, in both it will fly and wil not fly "camps". Good discusion on that forum. As the original question is flawed allready , how fast the conveyor belt and the wheels are moving (a=a+5 ??). After reading pprune I think it will fly but still have my doubts.. /edit After looking at that movie link, that one is flawed as well I think, isn't the paper pulled in the wrong direction ? /edit 2 No it isn't.... Right ?

The conveyor belt and wheel speeds are not clearly defined. The question about whether a piece of paper will fly based on these variables seems flawed, as both sites present arguments suggesting the possibility but with differing conclusions. After reviewing content from Pprune.org, it's clear that opinions vary; some believe the concept can work while others are skeptical due to various reasons such as insufficient speed and unrealistic expectations of efficiency. The movie in question might also contain misconceptions or oversimplifications regarding this principle for entertainment purposes rather than scientific accuracy, which could lead viewers to incorrect conclusions about the feasibility of a paper airplane-like device powered by