The moving runway thought puzzle

[paul devereux]

2 hours ago, J D 8 said:

                  The thrust from prop has no connection to the conveyor. The plane wheels are not driven and are free to turn at whatever rate they need until plane reaches flying speed and lifts off.

But it has! Since the wheels are not powered, it is only prop thrust that is providing forward motion, causing the wheels to turn.

[paul devereux]

24 minutes ago, Andy Stephenson said:

There's a lot more common-sense talked about this ridiculous conundrum here than there was over on RCG. It even came to a point where the mods had to step in and suspend members for attacking each other.

I haven't seen that. Did they come to a consensus or a conclusion?

[Andy Stephenson]

38 minutes ago, paul devereux said:

I haven't seen that. Did they come to a consensus or a conclusion?

The whole thread was far too tedious to follow and no there was no conclusion and as far as I remember they were still arguing about it when gave up with it due to all the stupidity there.

[Steven Curry]

To quote Mr Gumby, (Monty Python), "my brain hurts" 🤔😀

[Martin Harris - Moderator]

54 minutes ago, paul devereux said:

But it has! Since the wheels are not powered, it is only prop thrust that is providing forward motion, causing the wheels to turn.

Except that the wheels cannot move forward from their starting position within the terms of the question.  To move forward from the aircraft’s thrust requires the wheels to move faster than the conveyor belt which contravenes the conditions stated in the question. 
 

It’s an unreal situation - we know that we need forward speed relative to the air mass we’re in and that our wheels would be rotating faster than normal in the case of a conveyor belt running in the opposite direction - the wheels turning at air speed plus conveyor belt speed but it’s not a frictionless system so we need to compensate for wheel bearing and tyre drag meaning that the wheels need to turn faster than the belt  speed in order to accelerate in relation to the air mass that the system is in. 

[J D 8]

The wheels will easly rotate fast enough and overcome any extra drag friction in the system as most aircraft have a fair reserve of power

[Martin Harris - Moderator]

But then the wheel rotation must exceed the belt speed to compensate for the tyre/wheel friction drag which is tending to move the aircraft backwards. Yes, it would happen on a “real world” system roughly matching the wheel speed but it doesn’t comply with the conditions of the question. 
 

I think that what would happen in a compliant theoretical system is that in order to move forward, any increase in forward velocity would need to increase the belt speed by a slightly larger speed to compensate for the wheel drag. At this point the required wheel speed would need to be slightly higher than the belt speed so the theoretical system would increase the belt speed instantaneously. This would then require a higher wheel speed to maintain acceleration which would require a further instantaneous increase in belt speed. This process would repeat in a very small timeframe until thrust was equal to wheel drag although the tyres would have destroyed themselves long before due to centrifugal effects. 

[Paul De Tourtoulon]

11 hours ago, Alan Hilton said:

Yes because the motorbike is driven by its wheels

Not mine, I drive them,,,🤩

[paul devereux]

On 31/03/2023 at 13:04, Christopher Wolfe said:

 

This is sounding a bit like the dreaded 'Downwind Turns' debate that raises it's head on a regular basis 🙃

 

 

Chris

Now, I understand the argument that the plane doesn't 'know' it is in a wind, it is only the observer on the ground who appears to be affected because of the change in groundspeed, and that the impression we get that a plane zooms in upwind turns and dives in a downwind turn is caused by us unconsciously applying or reducing throttle, but since you mentioned this I Googled it and it seems full-size pilots experience the same illusion! And they are actually sitting in the cockpit! Strange.

Downwind turns equal disaster?? [Archive] - PPRuNe Forums

[J D 8]

         Problem comes for the full size pilots when they start judging their air speed by the rate the ground is going past and not watching the airspeed indicator. Been there, but lucky in an open wire braced microlight on the glide [ engine had failed ] the lack of wind noise in the wires gives warning of lack of air speed.

[Ron Gray]

11 hours ago, paul devereux said:

But it has! Since the wheels are not powered, it is only prop thrust that is providing forward motion, causing the wheels to turn.

The wheels turning is only due to the friction between the wheels and the surface they are on, no friction and the wheels would skid, therefore the prop thrust has, in itself, nothing to do with the wheels turning. And therein is the answer, on take off we initially need thrust to overcome friction to allow the model to move forward thus generating lift. Without friction the model still needs to move forward but is using less thrust (at take off) to do that. As long as the conveyor belt doesn't produce more friction than the thrust produced by the prop then the model will move forward and it will gain lift.

[Martin Harris - Moderator]

1 hour ago, J D 8 said:

         Problem comes for the full size pilots when they start judging their air speed by the rate the ground is going past and not watching the airspeed indicator. Been there, but lucky in an open wire braced microlight on the glide [ engine had failed ] the lack of wind noise in the wires gives warning of lack of air speed.

Yes - it’s killed or severely scared many a glider pilot scratching for lift at low altitude. Funnily enough, the wind has no effect once high enough to nullify the visual effects of relative ground movement…
 

[Christopher Wolfe]

About 20 years ago I took a flight in a hot air balloon at Jerilderie (NSW Australia) and as we drifted slowly along I was permitted to launch a small free flight balsa glider just when the balloon hit a thermal bump. (Altitude about 2000')

 

The tiny glider performed perfect circles around the balloon and eventually was lost above us as the operator modulated the burners to reduce altitude.

 

My point is that my glider did not know or care about the gentle breeze although from the ground it's path may have probably looked like a series of elliptical circles.

 

Glider was found by a farmer who was kind enough to phone me a few months later (always put your name and contact details on a free flight model) so I asked him to donate it to his grand-kids.

 

I agree that downwind turns are only a problem if people use the ground as a reference.

 

Just the same if the ground is a moving converter belt.

 

The aircraft does not know this and until it lands and the wheel brakes are applied it is purely the airspeed over the wing that determines how gentle the landing is.

 

Chris

 

 

 

[Dickw]

I see you lot are still playing with this relatively simple problem, so why not just look at the laws of physics, especially those explained in the theory of relativity.

There is no such thing as absolute motion, everything is moving relative to something else – particularly the observer of that motion.

We usually measure speed relative to the ground because that is where we are, but for an aircraft speed relative to the air mass is the relevant speed. Indeed, a plane flying in a high wind can have a positive airspeed but a negative ground speed

If we watch an aircraft taking off, we see it moving relative to the runway, but to anyone in the plane they are stationery and it is the runway and air mass that is moving relative to them.

 

So:-

a)       Relatively speaking all we can say is that for a normal take off the plane moves in the opposite direction to the runway and the air mass.

b)      The question states that the runway/conveyor belt (but not the air mass) moves backwards, so that must be backwards relative to its normal direction – i.e. it is now moving in the same direction as the aircraft.

c)       If the conveyor belt/runway moves in the same relative direction and speed as the aircraft the wheels will not rotate but the aircraft will still take off.

 

That’s me finished, and I must sign off now as I have some relatives coming round relatively soon.

 

Dick

[john stones 1 - Moderator]

Nice Chianti ?

 

[Don Fry]

5 minutes ago, john stones 1 - Moderator said:

Nice Chianti ?

 

Nah, one of they Tequila with worm oles init. 

[Peter Beeney]

Another attempt at an answer to this conundrum and to be fair all round I’ve considered the original question. Reproduced below. But to be honest I think Paul's O/P is near enough to make no difference anyway so this is an answer to that as well. If indeed this is an answer, though, it may well be just rubbish..

Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction.
                                                      
                                                                                             Can the plane take off?

 

                                And now imagine this sentence is a free hand sketch of a 747 standing on the conveyor belt!!

I would agree with Martin, providing we keep absolutely to the spec. in the statement above then the plane cannot move forward. With regard to the timing would say a picosecond lead/lag time be sufficient and would this actually be obtainable in practice? In today's technical world I think it may well be yes to both…

 

The plane is standing on the conveyor belt. We make a chalk mark on the side of the tyre on the bottom of the wheel and another one to match this on the the conveyor belt. Then a 3rd at the side of the conveyor belt on the ground to mark the position of the axle in the centre of the wheel in relation to the ground. At this stage the wheel is held firmly in contact with the conveyor belt by the weight of the plane bearing down vertically through the axle. The pilot opens the throttle, the thrust increases and the plane starts to move slowly forward due to the pressure of the axle moving at right angles to the vertical forcing the wheel to turn forwards against the friction of the belt. One picosecond later said belt starts to move backwards and from then on in keeping strictly with the spec. it's speed is inexorably linked exactly with the speed of the accelerating wheel. Normally the wheel would of course move forward on a stationary runway but now the wheel’s point of contact moving forward is meeting the belt’s point of contact moving backwards at exactly the same speed, the nett result causing the wheel to revolve around the axle but keeping it in a stationary position relative to the ground beneath the belt. If the circumference of the wheel is 15 feet after the first revolution we note the chalk mark on the belt is 15 feet behind the wheel but the chalk mark on the ground is still exactly in line with the axle…. and probably much more obvious, the plane itself has not gone anywhere either!

 

The second revolution is the same as the first except that the speed of the whole process is accelerating due to the forward pressure on the wheel’s axle and will continue to do so. Therefore, again like Martin, I think this is going to  eventually end in one almighty tangle. Also I think crucially not only does the speed of both items have to match but also the power output as well, it seems to me that the two forces have to equalise. Maybe the power supplied to the belt would need to be in excess to that of the jet! So now is it possible that before the wheels start to come off the wagon natural inertia becomes great enough to keep the process at a steady speed at some point? I've no idea, maybe it’s the next silly question perhaps…

 

I would consider that as long as the belt speed stays in exact sync. with the speed of the wheel then the axle and thus the plane is never ever going to move. If the pilot shuts the throttle, say to around half, maybe that would still be enough force to keep the wheel turning and then if the belt stayed in sync going backwards too you could sit and watch the wheels going round with the plane going nowhere. But it sure would cost a bob or three I reckon.

 

PB

[David Holland 2]

Peter, that cannot be right. The thrust from the aircraft’s engine is independent of the conveyor belt and will accelerate the aircraft up to tale-off speed irrespective off the speed of the belt. The rotational speed of the wheels will be belt speed plus aircraft speed, everything being relative to the position of the observer. I think……..

[Ron Gray]

The only thing the conveyor belt does is provide friction acting upon the wheel which the 'plane's thrust needs to overcome. the other thing the conveyor belt does is provide one hell of a lot of confusion, which is exactly what was planned with the question!

[Don Fry]

In the case of a 747, the only worry, is the wheel, tyre, bearing assembly capable of doing twice the max take off speed. I suspect not, but that’s just a minor design modification, or just more careful balancing. 

[john stones 1 - Moderator]

Much fuel on this Jet ? 😉

[Don Fry]

10 minutes ago, john stones 1 - Moderator said:

Much fuel on this Jet ? 😉

Well I admit, minor the second time they try it, if we are being pedantic.

[paul devereux]

1 hour ago, john stones 1 - Moderator said:

Much fuel on this Jet ? 😉

It might have to run for ever?

[Andy48]

Can I explain this another way? Instead of a conveyor belt, consider that when your model is sat there waiting to take off, it is already travelling at 1000 mph. - the speed of the Earth's rotation. None of us has ever noticed the difference in taking off with or against the Earths rotational speed. In order to take off all that is needed is sufficient airflow under the wings which is partly provided by the propeller moving the plane forward on the runway, partly by the airflow created by the propeller itself, and partly by the actual wind speed. Indeed with a sufficiently powerful motor, and a strong wind, one should be able to take off into the wind without actually gaining any forward momentum.

 

It is no different for a conveyor belt system. The conveyor belt is irrelevant, all that matters is the airflow across the wings, as is apparent every time we land.

[Brian Cooper]

I must confess to being very amused with this thread.

 

Okay, chaps, imagine this conveyor belt is on an aircraft carrier. 

It doesn't matter if the belt is running forwards or backwards, the aeroplane will still get airborne in exactly the same time/distance. . . . . Because the aeroplane isn't  attached to the runway.