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Dilemma to sort out

Alex Pisarev
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Joined: Apr 10, 2002
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Here is an interesting problem to stimulate your grey cells.
We have an air plane (doesn't matter jet or propeller-powered) parked on a runaway. The runaway has a special system which allows the runaway to move backwards when the plane moves forward - the runaway linear speed is changed instantly in order to fully correspond to the angular speed of airplane wheels' on a chassis - when airplane wheel rotates once, the runaways moves backward on pi*Diameter of the wheel meters backwards.
Will the plane be able to take off from this kind of runaway?
SJ Adnams
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erm, of course. the plane gains _air speed_ thru the jet/props not ground speed. qed
Alex Pisarev
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Originally posted by Simon Lee:
erm, of course. the plane gains _air speed_ thru the jet/props not ground speed. qed

What about friction then? I reckon the friction between axles and the wheels will compensate all the engine power.
Alex
SJ Adnams
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What about friction then

Not that I know much about aircraft wheel bearings, but I'd guess a plane will reach take off @ airspeed ~ 150MPH, so thats 300MPH groundspeed.
I'd say a plane's landing speed will probably be in the ~300MPH ballpark? sure there will be friction, but remember jet tyres have a larger radius so axle speed is probably similar to car axle speeds.
Rolling resistance (tyre-runway friction) could be higher, however the tyres run at over 100psi (like truck tyres) so that won't be huge either...
Jim Yingst
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but I'd guess a plane will reach take off @ airspeed ~ 150MPH, so thats 300MPH groundspeed.
Eh? The problem statement implies that if the plane's wheels are going at a groundspeed of 300 MPH, the runway is also traveling backwards at 300 MPH, so its airspeed would seem to be zero. Well, the speed relative to an outside observer would be zero. I suppose if the whole runway is moving at 300 MPH (I'm imagining it as a sort of giant treadmill) then the air above the runway will be "dragged along" to some extent. It's sort of like a big wind tunnel with a horrendously inefficient design. I suppose if the thing's big enough you might get the air moving fast enough that the plane might actually be able to take off, but the whole scenario is so implausible from an engineering standpoint that serious analysis would be a waste of time.
Going back to the relation between wheel rotation and runway speed: the statment that
"when airplane wheel rotates once, the runaways moves backward on pi*Diameter of the wheel meters backwards."
implies that the forward movement of the wheels is exactly canceled by the backward movement of the runway, and so the plane does'nt move forward. Now, assuming the plane's engines are able to generate some forward thrust through the moving air, this implies that there must be some force holding the plane back, since net movement is zero. The only apparent place this could be coming from is friction from the wheels, translating the runway's backward movement into a backwards force felt by the plane. Which implies either the wheels are very rusty, or the runway's moving very fast, or someone is applying the plane's brakes. (!) Or, maybe there's actually a cable that anchors the plane to a fixed point behind the runway, guaranteeing the the plane won't move, and someone just forgot to tell us about that. Whatever, my point is that the whole original assertion that runway speed matches wheel movement leads to scenarios that are either preposterous, or trivially simple (but not adequately described). It's like pondering "can an irresistable force move an unmovable object" - it leads nowhere useful, except to expose the fact that the initial premises were flawed.


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John Smith
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Well, the speed relative to an outside observer would be zero.
Indeed. Also, disregarding the possible "air tunnel" effect that Jim already mentioned, it is safe to assume that the airplane speed relative to the outside air will also be zero. Therefore, the plane will never take off, no matter how powerful its engines are.
Max Habibi
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Unless they hit the breaks. And even then, very briefly


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Michael Ernest
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You can just feel the surge in pocket-protector sales...
Alex Pisarev
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Can someone give physical elaborations why the ground speed of the airplane will be zero?
Basically, the only force which over reacts the force of plane engine is the force of friction between wheel axles and wheels themselves.
Considering the fact, that such friction is intended to be minimal (usually, there is some oil between axles and wheels), it may be implied that the powerful plane engine will finally cause the plane to move without taking into consideration the wheel rotation factors - on some stage the wheel angular speed will be slower then actual plane movement speed.
Alex
Richard Hawkes
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Originally posted by Alex Pisarev:
... Will the plane be able to take off from this kind of runaway?
Maybe a Harrier could.
Max Habibi
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Originally posted by Michael Ernest:
You can just feel the surge in pocket-protector sales...

LOFLMAO
SJ Adnams
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implies that the forward movement of the wheels is exactly canceled by the backward movement of the runway, and so the plane does'nt move forward. Now, assuming the plane's engines are able to generate some forward thrust through the moving air, this implies that there must be some force holding the plane back, since net movement is zero.

Ok, I kind of get your point, but I'm not one to back down..
Lift is generated by airflow over the wing. Given enough power plane will generate enough lift to get of the treadmill (vertical take off style)..
Eleison Zeitgeist
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Originally posted by Simon Lee:

Ok, I kind of get your point, but I'm not one to back down..
Lift is generated by airflow over the wing. Given enough power plane will generate enough lift to get of the treadmill (vertical take off style)..

I agree with Simon.. the key is airflow over the wing. Jet engines/props located behind the wing would not work. However, jet engines/ props located in front of the wing would -- given Enough power... obviously, it would be extermely inefficienct because you dont' have the use of thrust that would normally cause the entire wing to glide over stationary air...
Basically what you would try to do is imitate those birds you see on tv where they are not moving horizontal but veritical due to wind...
Thomas Paul
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Forget lift. A jet plane is like a rocket. The thrust of the engines creates a backward force that is countered by the forward force of the plane (Newton - action and reaction).
Think in terms of a car. We know we can put a car on a treadmill and run it and it goes nowhere. But the force of movement is coming from the tires. Planes do not move because the wheels are turning. The wheels turn because the plane is moving. Put a plane on an oil soaked runway and it can still move because the tires would slide along the runway. Put a car on that same runway and it won't go anywhere.


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Max Habibi
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Originally posted by Thomas Paul:
Forget lift. A jet plane is like a rocket. The thrust of the engines creates a backward force that is countered by the forward force of the plane (Newton - action and reaction).
Think in terms of a car. We know we can put a car on a treadmill and run it and it goes nowhere. But the force of movement is coming from the tires. Planes do not move because the wheels are turning. The wheels turn because the plane is moving. Put a plane on an oil soaked runway and it can still move because the tires would slide along the runway. Put a car on that same runway and it won't go anywhere.

Compete nonsense. Of course, the only way that a jet really travels anywhere is through the mind: after all, what is 'place'? Thus, it follows naturally and intuitively that a Jet's ability to fly(or not fly, as the case may be), is really just a function of it's State Of Being. Or Not Being, as the case may be.
seems obvious to me anyway....
Jim Yingst
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Forget lift. A jet plane is like a rocket. The thrust of the engines creates a backward force that is countered by the forward force of the plane (Newton - action and reaction).
Except that given the rather ludicrous problem statment, this is evidently being countered by some other force, such as brakes or an unmentioned tethering cable. Given the problem statement ("when airplane wheel rotates once, the runaways moves backward on pi*Diameter of the wheel meters backwards"), as long as the wheels are in contact with the runway, there is no forward motion, period. Richard's Harrier solution is the only remotely practical one I see - but Max's answer is good too.
Ernest Friedman-Hill
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  34

OK, guys, here's my take:
The crucial realization here is that the wheels at take-off are free-spinning. It's not like a car -- the wheels are not connected to the engine. The plane can move forward even if the wheels are moving backwards. You can replace the wheels with sticks of butter or ice cubes, as long as the friction is low, everything works.
Both propeller and jet planes propel themselves forward by pushing gas (hot or not) backwards. For every action, there's a reaction, so the plane moves forwards. In the moving runway scenario, is there any extra backwards force being applied to the plane? No, there isn't. The plane gains speed and takes off, just as normal.
This is easy to see if we make the standard physics approximations (zero friction in the wheel bearings.) The only reason the wheels are there is to get a low coefficient of friction. The runway could be moving twice as fast as the plane, so the wheels turn backwards: the plane doesn't care which way the wheels are turning!
[ July 31, 2003: Message edited by: Ernest Friedman-Hill ]

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jason adam
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Originally posted by Max Habibi:

Compete nonsense. Of course, the only way that a jet really travels anywhere is through the mind: after all, what is 'place'? Thus, it follows naturally and intuitively that a Jet's ability to fly(or not fly, as the case may be), is really just a function of it's State Of Being. Or Not Being, as the case may be.
seems obvious to me anyway....

Zen and the Art of Aerodynamics
Thomas Paul
mister krabs
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yeah, what Ernest said. That was what I was trying to say when I compared the plane to the car.
Jim Yingst
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EFH's interpretation makes sense if we simply ignore the line about "when airplane wheel rotates once, the runaways moves backward on pi*Diameter of the wheel meters backwards". Which is good since that line led to some pretty silly scenarios anyway. (Moreso than the rest of the problem statement, with is rather silly to begin with.) We could also just replace the runway with a completely frictionless surface I suppose. Though that would make taxiing in a particular direction more difficult.
[ July 31, 2003: Message edited by: Jim Yingst ]
Max Habibi
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Along more practical lines....
I wonder if this 'treadmill' idea(with breaking) could be used as way to allow, say, fighter jets to accelerate from 0 to say takeoff speed practically instantly, thus allowing them take off with very, very, very short runways?
Of course, they can already takeoff with very, very short runways, so I doubt it's a worthwhile investment. Still, it would be cool
M
Thomas Paul
mister krabs
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Aircraft carriers use steam powered catapults to toss jets of the deck.
jason adam
Chicken Farmer ()
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*giggles as the image of the Monty Python cow being tossed over the castle wall pops into his head*
Now a cow on a treadmill.... it has potential
Angela Poynton
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I just wish I knew some of the Engineers in my company, they'd have a ball with this problem I'm sure!


Pounding at a thick stone wall won't move it, sometimes, you need to step back to see the way around.
 
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subject: Dilemma to sort out
 
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