a simple little question, or is it?
|1344 forum posts|
The forward speed of the aircraft is NOT negated by the reverse effect of the treadmill.
The forward speed is provided by the jet engines and the plane will take off.
Actually this is not a theoretical problem but one that happens every day any plane takes off. Let's not forget the speed of rotation of the Earth. If John F's theory is right, then every plane taking off against the direction of rotation of the Earth would get nowhere. The Earth's rotation is doing exactly what the conveyor belt is doing. The only difference is that the plane's wheels are not rotating to match the speed of the Earth.
Another way to look at it is this. Imagine a plane where the power to take off was actually provided by the wheels. The plane would accelerate enough to take off, but once contact is lost with the ground, the plane would slow down and return to the ground. The plane would in effect stay on the runway at take-off speed.
|Bob Cotsford||13/10/2016 10:28:32|
7829 forum posts
The simple empirical answer is yes, it will take off. Mythbusters proved this on tv, admittedly not with a 747 but with a lightplane. Unless the brakes are left on the plane doesn't care about the wheel speed, it only cares about airspeed, which the conveyor cannot affect.
|Barrie Dav 2||13/10/2016 10:30:14|
|1012 forum posts|
I think that I'll go back to bed...............
|Robert Welford||13/10/2016 11:16:20|
|154 forum posts|
Mention this on the RCMF forum and there will be a riot! I dare you ...
2104 forum posts
Ahh Bob found the Mythbusters video, does that answer this specific question, they used a prop driven plane, not a jet, and does the speed of the 'belt' exactly match the speed of the wheels all the time, do they measure the speed of ether?
Go on Robert, you cannot say a dare like that and then not do it.
Of course this is a question that is designed to cause contradiction.
Back in the real world the plane would simply power forwards with thrust from the engines, the wheels would rotate forwards faster than the belt is moving backwards (they freewheel) and the plane would take off . The illogical part is when you try and explain how the belt speed can "always equal" the speed of the wheels, the result would be the treadmill quickly spinning up to infinity.
If you missed the earlier link, have a look here
It is a bit of fun to get you thinking, there is no correct answer that matches the rules of the specific question as it is written.
Edited By WolstonFlyer on 13/10/2016 11:45:16
|512 forum posts||
They argued about this one several years ago!
|Nigel R||13/10/2016 12:17:07|
2849 forum posts
In an equally stupid modification to this ridiculous scenario, my 747 is facing into a 200mph hurricane.
So it doesn't need to move anywhere.
|Biggles' Elder Brother - Moderator||13/10/2016 12:32:30|
15748 forum posts
Newton's third law!
Jet engines work by creating a reactive force against the air - not the ground!!
This resultant force means they will accelerate relative to the air. (F=ma)
The aeroplane is firmly attached to the engines so it will accelerate through the air as well.
The airspeed will increase over the wings, lift will result and the aircraft will take off!!!!!
Its all about the air - what the ground is doing is utterly immaterial! It could be still, it could be moving, it could be doing the bosa-nove - it matters not one jot!
PS Got to stop here - about to suffer a serious, frustration driven, sense of humour failure!!!
|Martin Harris||13/10/2016 12:46:35|
8540 forum posts
Sorry BEB - just take deep breaths!
I'm sure this is a real world versus theoretical poser. You and I know that if the aircraft was on a moving road, the only effect would be that the wheels would spin faster than the road is moving but the terms of the question don't allow this.
|Richard Wills 2||13/10/2016 12:49:26|
165 forum posts
Speed is always relative to something, in this case a wheels speed is relative to the aircraft. If you assume that the belt is stationary at the start this speed is zero. So the belt is designed to match this speed relative to the wheels and aircraft of zero. What would happen is the thrust moves the aircraft forward, and to maintain zero speed relative to the wheel, the belt moves forward relative to the ground at the same rate as the aircraft, The wheels never actually turn, and the aircraft takes off normally.
|Peter Beeney||13/10/2016 12:53:28|
|1554 forum posts|
It seems to me there is not very much trickery about the question, is it not a case of just considering the drive medium, flexible or solid?
If the brakes were full on and the engines run up to full power the plane wouldn’t move, the braking force exceeding that of the engines but all the ‘motion slip’, being taken up in moving the air, or ‘flexible drive medium’, through the engines rather than moving the plane forwards.
If the brakes were then slightly released the plane starts to move forward and instantly pushes against a pressure switch which applies enough power to start the belt moving backwards sufficiently fast enough to match the force moving the plane forward; the whole mass of the plane is now being moved backward at exactly the same speed as the wheels are taking it forward; nett result: the pane remains stationary. The brakes are released further and the same thing happens until the power applied to the belt ultimately equals that applied by the full power of the engines. Two forces acting in opposition just moving vast quantities of air.
The power required to drive the belt backwards has to be in excess of 4 jet engine thrusts in parallel. It is after all effectively holding the dead weight of the plane against the engines.
If the drive medium were solid, i.e. an externally driven winch rope pulling the plane forward against the pressure switch the rearwards moving belt would again prevent the plane moving forward and if the belt drive power exceeded the winch motor power unless there were some form of slipping clutch the winch motor would not be able to move and thus stall. Or something else would break!
If the wheels were being driven by a solid prop shaft from the engines the plane would still not move, two power sources again acting in opposition, but with the ‘ flexible slip’ now being the relatively increased movement between the belt and the wheels; the power requirements very considerable again.
I would hazard a guess after all this and say that because the plane is never going to move forward it’s never going to take off.
Maybe the real question should be is what happens to the wheels in amongst all of this? The force required to overcome the natural inertia of the wheels must increase on some sort of exponential curve and in the end they simply refuse to turn any faster. I suspect they will then cry ‘enough is enough’.
In practise it might be difficult to try this, but with enough determination it might be possible to scale it down sufficiently to try it. I certainly won’t be doing it though…
I agree with entirely with John F, if you consider anything other than the question exactly as stated then it does become meaningless and any answer might cover any situation.
Rehashing the question slightly, let’s say we have an object, on wheels, standing stationary on a road with a casual observer to one side. Then the object is moved forward with any means of propulsion, the observer sees this at say 10 mph. Then the road moves in a rearward direction at the same 10 mph. What does the observer see then? It surely cannot be the same 10 mph forward, I think it would be zero mph forward, the two motions are now balancing each other out. The forward motion is zero but the power is translated into increased motion between the wheels and the road. If the forward motion were created by means of a winch the coefficient of friction might play a part and the wheels simply dragged across the surface; but if the mass downward of the object and the power applied to the rolling road were more than sufficient I think the winch would eventually be stalled again.
I’ll stick with this one until I change my mind…
|Don Fry||13/10/2016 13:00:30|
3615 forum posts
BEB, yes you are right, but the belt is moving at a speed causing the wheels not to move. The energy being put into the system by the engines is negated by losses in the wheel system, and hence failure occurs in the undercarriage, It is designed for a couple of hundred kph, not the many thousands that belt has to travel at to cause so much energy to be put into destroying the undercarriage.
Irrelevant whether a prop or a turbine doing the energy thansfer.
Someone said above that rotation of the earth replaced this hyperthetical belt, not so, the earth moves the air at the same pace, allowing the plane to move through the air, and fly.
This plane don't move, hence don't fly. The undercarriage fails.
Edited By Donald Fry on 13/10/2016 13:01:57
|Gary Manuel||13/10/2016 13:11:21|
1844 forum posts
This thread will go round in circles even faster than the wheels!
That's what the question is designed to do.
|Nigel R||13/10/2016 13:15:28|
2849 forum posts
speed of wheels exceeds maximum design rating of conveyor belt
conveyor belt stops
takeoff occurs as normal
2104 forum posts
Everybody having fun? It is a brain twister after all
|Biggles' Elder Brother - Moderator||13/10/2016 13:24:42|
15748 forum posts
What losses in the wheels - where are they mentioned?
PS I must stop opening this ttrhread!!!
|john stones 1||13/10/2016 13:41:23|
10381 forum posts
I'm enjoying googling the various laws of Physics that get mentioned, keep going for me.
|Martin Harris||13/10/2016 13:50:26|
8540 forum posts
The question is just as relevant as the "chicken and egg" poser. The conditions stated cannot exist in the real world, just as evolution means that the chicken didn't suddenly appear as we know it.
|john stones 1||13/10/2016 13:56:03|
10381 forum posts
Chickens originally gave birth same as humans, they saw a market opportunity and evolved the egg laying to meet a need in the market " Ferenghi 49th rule of acquisition"
|1344 forum posts|
People, I think you are looking in the wrong place for the answer. Of course the plane will fly, but there is an obvious flaw in the argument about the treadmill.
Going to the third option where a speedometer measures the wheel speed. The "answer" says vC=vW+vC and the conveyor belt would have an infinite speed.
However, all this answer says is that it is impossible to build a frictionless treadmill/ wheel system which will always match the speed of the wheels, not that the plane won't take off. In practical terms you cannot have a frictionless system which would allow the above equation to be true.
This thread is closed.
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