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A question of physics.....

a simple little question, or is it?

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Nigel R14/10/2016 09:20:02
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Still going? The question has achieved its aims!

The Wright Stuff14/10/2016 09:35:09
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Posted by SuperNash on 14/10/2016 09:20:02:

Still going? The question has achieved its aims!

Indeed! And discussing physics is infinitely more interesting than Brexit or Trump!!!

The Wright Stuff14/10/2016 09:43:57
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Posted by Bob Burton on 14/10/2016 08:50:00:
Posted by The Wright Stuff on 14/10/2016 08:40:55:

Provided the wheels and tyres could withstand travelling at twice the take off speed, the 747 COULD take off.

But as the plane will never move forward on the conveyor belt due to it matching the speed of the wheels how could it ?

I understand the confusion, but that logic breaks down because that part of the initial question violates the concept of 'cause and effect'. The wheels rotate in response to the relative speed between the conveyor and the aircraft, not the other way around.

Physics says the aircraft will accelerate and take off. Physics has no answer for the speed of either the conveyor or the wheels because the laws of physics have already been violated.

If you insist, you could resolve with mathematical or engineering arguments.

Mathematically, the conveyor speed and wheel speed would diverge to infinity, in which case it is simultaneously possible for them to be travelling at the same speed and different speeds.

Engineering would argue that there exists a speed, taking into account friction, by which the wheel would start to slide, meaning that it's rotation speed (and hence conveyor speed) can be different from the aircraft speed.

Harry Twist14/10/2016 10:04:31
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All good fun.. i'm amazed its gone on for 9 pages .. good to exercise our grey matter in a fun way...

So ...All discussion about bearings, axles, shafts wheel centres, brakes - etc with respect -is irrelevant.

All the mass of the aircraft acts through the few square centimetres of contact between the tyres and conveyor belt. So the only point of interest is this location.

In addition friction is not negligible - in fact it is considerable! ( if you did 100miles on a running machine you would wear out your shoes and you would also have worn out the conveyer belt a bit).

The only way in which a normal aircraft can taxi around any airfield or start a take off role is by applying thrust to a level which is greater than the combined effect of rolling friction and air resistance - otherwise you dont move anywhere. (To accelerate the forces must be unbalanced).

In our problem the friction is still present - it has not simply disappeared. The aircraft wheels are still wearing away due to turning and contact with the conveyor - which is also wearing away.

The runway is moving along underneath us at the same rate that our wheels are turning - all the thrust is doing is making the wheels turn faster - which makes the belt turn faster with it! So no amount of thrust will move us forwards - and we will not move any where.

(Sort of analogy - imagine trying to drive a car off a muddy/wet field - however much revs you put on - the wheels spin and the back of your car and wheel arches get covered in muck - as you push the ground away from you - but you dont go anywhere!)

So no we cant take off!

Edited By Harry Twist on 14/10/2016 10:08:04

Edited By Harry Twist on 14/10/2016 10:09:11

Edited By Harry Twist on 14/10/2016 10:10:15

The Wright Stuff14/10/2016 10:26:37
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Posted by Harry Twist on 14/10/2016 10:04:31:

(Sort of analogy - imagine trying to drive a car off a muddy/wet field - however much revs you put on - the wheels spin and the back of your car and wheel arches get covered in muck - as you push the ground away from you - but you dont go anywhere!)

But that is a fundamentally different situation because the drive is through the wheels. Stick a jet engine on the back and I guarantee the car will move, regardless of how muddy, icy, or hypothetically-magically-conveyor-belty the ground happens to be.

WolstonFlyer14/10/2016 10:37:33
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Try this.

Put a toy plane on a treadmill that's set to 5MPH and hold it still with your hand to simulate the thrust from the jet engine holding it steady. How fast are the wheels rotating? At 5MPH right? Because they are rotating freely.

So here the planes wheels and the treadmill are matched in speed. Is the plane moving anywhere with you not pushing it harder?
No

Are the wheels/treadmill matched at 5MPH?
Yes!

Ok, now turn up the thrust of the engines. Which for this example is your hand.

Notice how just like the real plane, the forward force comes from your hand and not the wheels (like the forward force comes from the jet engines and not the wheels).

What happens?

The plane moves forward. Ok, the treadmill is still going at 5MPH and the wheels are going at what speed? Well, since the plane is moving forward its wheels are moving at a speed higher than 5MPH because it needs to overcome the treadmill speed.

Speed of the wheel > than the treadmill speed so speeds are no longer matched, as stated in the question.

If the speed of the wheels touching the ground is always the same as the speed of the belt then the plane has no forwards motion relative to the belt, generates no lift and does not take off, or does it??

It is more fun than talking politics or Brexit or whatever!

 

Edited By WolstonFlyer on 14/10/2016 10:37:58

Martin Harris14/10/2016 10:42:21
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One last try...

NEITHER ANSWER IS CORRECT!

There are two conditions to satisfy:

One is that at any belt speed, the aircraft can take off due (real world mechanical failures excluded) to the reasons so ably stated in many posts.

The other is that the wheel and belt always run at the same speed.

Neither of these two can exist at the same time.

The question is invalid.

Bob Burton14/10/2016 10:42:55
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Posted by Harry Twist on 14/10/2016 10:04:31:

The runway is moving along underneath us at the same rate that our wheels are turning - all the thrust is doing is making the wheels turn faster - which makes the belt turn faster with it! So no amount of thrust will move us forwards - and we will not move any where.

So no we cant take off!

Agreed wholeheartedly

Gary Manuel14/10/2016 10:48:00
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Morning all.

Glad to see this thread is still going strong. I think it's got a few more miles in it yet smiley

Nice to see we have a professional physicist on board. I agree with your initial assessment and conclusion. I don't agree with you however, that physics has no answer for the speed of either the conveyor or the wheels. I also don't agree that any laws of physics have been violated. I see no parodox in the scenario. It would just be difficult to construct.

I also disagree with your mathematical and engineering argument. There is no need for infinite speeds or consideration of friction. The wheels will simply rotate at twice the speed they normally would.

Posted by The Wright Stuff on 14/10/2016 09:43:57:

Physics says the aircraft will accelerate and take off. Physics has no answer for the speed of either the conveyor or the wheels because the laws of physics have already been violated.

If you insist, you could resolve with mathematical or engineering arguments.

Mathematically, the conveyor speed and wheel speed would diverge to infinity, in which case it is simultaneously possible for them to be travelling at the same speed and different speeds.

Engineering would argue that there exists a speed, taking into account friction, by which the wheel would start to slide, meaning that it's rotation speed (and hence conveyor speed) can be different from the aircraft speed.

It would be a simple matter to draw a vector diagram for the speed of the wheels and the conveyor relative to the ground and see that the plane produces a vector in one direction and the conveyor produces a vector in the other direction. If you want to produce a vector line relative to the plane (as would be measured by it's wheel driven speedometer), it would be the sum of the two separate vectors - i.e. twice the normal take off speed. Similarly a vector line relative to the belt would be the same length but in the opposite direction.

Physics requires you to make all measurements relative to the same fixed reference. It doesn't matter which reference point it is, the end result will be the same.

Gary Manuel14/10/2016 10:57:36
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Posted by WolstonFlyer on 14/10/2016 10:37:33:

Try this.

Put a toy plane on a treadmill that's set to 5MPH and hold it still with your hand to simulate the thrust from the jet engine holding it steady. How fast are the wheels rotating? At 5MPH right? Because they are rotating freely.

Are the wheels/treadmill matched at 5MPH?
Yes!

Sorry Andy but that's not quite right. While your hand is holding the toy plane stationary, it's speed is not matching the treadmill. The treadmill is moving backwards at 5mph and the toy plane is moving at 0 mph.

Also, wheel rotation is not measured in MPH, it's measured in RPM. The actual RPM is dependant upon the radius of the wheel. Only the centre of the wheel can be measured in RPM, which will be the same as the plane = 0mph.

Edited By Gary Manuel on 14/10/2016 10:58:41

The Wright Stuff14/10/2016 11:03:59
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Martin is correct that there is no complete answer: hence physics violation.

Gary, I don't agree that there is no paradox. There are lots of issues with the problem that we haven't even got to yet.

For a start, for the conveyor to affect the motion of the aircraft exclusively, it must be overwhelmingly more massive than the aircraft (otherwise the conveyor would push itself forward relative to the aircraft and the ground on which it is laid). But then the belt couldn't be accelerated using the energy provided by the aircraft via a pulley or whatever.

You could rig a digital sensor to the wheel, and use a nuclear power station next to the runway as a power source, but then the speed of light would delay the increase in speed of the conveyor from happening soon enough to exactly cancel the increase in wheel speed. I could go on and on...

[At this point I will confess my area of expertise is semiconductor physics, not mechanics!]

Gary Manuel14/10/2016 11:07:45
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Posted by john stones 1 on 14/10/2016 08:26:25:

Beginning to look like folk are mocking one another, but that just my opinion, no physics involved.

Plenty of physics involved John, and maybe a little mocking for which I apologise, but that's what the question is designed to evoke. It's because different people see the problem from different perspectives. I see it from a purely physical perspective and see no paradoxes.

Gary Manuel14/10/2016 11:18:58
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Posted by The Wright Stuff on 14/10/2016 11:03:59:

For a start, for the conveyor to affect the motion of the aircraft exclusively, it must be overwhelmingly more massive than the aircraft (otherwise the conveyor would push itself forward relative to the aircraft and the ground on which it is laid). But then the belt couldn't be accelerated using the energy provided by the aircraft via a pulley or whatever.

The conveyor doesn't need to affect the motion of the aircraft. All it needs to do is rotate the aircraft wheels.

The belt could indeed be accelerated using the aircraft via a pully system but would obviously need additional thrust to overcome the friction of turning the belt, pully and wheels by the additional component. Now if the pully included a sensor for the speed of the rope and a mechanism for applying the required amount of power to drive the belt, we would have a working system. The system used on old reel to reel tape decks where the position of a loop of slack was used to either accelerate of decelerate the motor would work just fine.

Edited By Gary Manuel on 14/10/2016 11:21:15

The Wright Stuff14/10/2016 11:27:55
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Posted by Gary Manuel on 14/10/2016 11:18:58:

The conveyor doesn't need to affect the motion of the aircraft. All it needs to do is rotate the aircraft wheels.

The belt could indeed be accelerated using the aircraft via a pully system but would obviously need additional thrust to overcome the friction of turning the belt, pully and wheels by the additional component. Now if the pully included a sensor for the speed of the rope and a mechanism for applying the required amount of power to drive the belt, we would have a working system. The system used on old reel to reel tape decks where the position of a loop of slack was used to either accelerate of decelerate the motor would work just fine.

Edited By Gary Manuel on 14/10/2016 11:21:15

I still don't agree - however I am enjoying debating it so all in good nature!

I think there will always be a time delay, between the sensor detecting a speed increase, and the mechanism adding power, however small. This might be milliseconds, microseconds, or nanoseconds. As the speed of the wheels goes ever faster, and the conveyor goes ever faster, eventually you would reach a point where either the top of the wheel tread reached the speed of light, or the delay was sufficient for the speed differential to be big enough for the aircraft to take off.

Gordon Nicol14/10/2016 11:28:01
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If this worked would they not be cheaper putting a rotating (conveyor belt) deck onto the new aircraft carriers.. I'm sure I could liberate a few million pounds from the government to do a feasibility study, like they wasted on the study into cats and traps on the ships

WolstonFlyer14/10/2016 11:39:26
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Posted by Gary Manuel on 14/10/2016 10:57:36:

"Sorry Andy but that's not quite right. While your hand is holding the toy plane stationary, it's speed is not matching the treadmill. The treadmill is moving backwards at 5mph and the toy plane is moving at 0 mph."

Also, wheel rotation is not measured in MPH, it's measured in RPM. The actual RPM is dependant upon the radius of the wheel. Only the centre of the wheel can be measured in RPM, which will be the same as the plane = 0mph."

 

It's James not Andy but that doesn't matter..

You are correct Gary - the plane is stationary moving at 0mph, but the surface of the tyre on the wheel (the speed of the wheel you could say) is the same as the conveyor belt - 5MPH , it cannot be different unless the tyre is slipping on the belt.

We are not talking about the speed of the plane, the question does not mention the speed of the plane.

Ahhh, we are getting somewhere, it's all about how you define 'the speed of the wheel' ?

What does a speedometer measure - well yes it measures RPM, but the dashboard of your car does not tell you the RPM of your car, it tells you the speed in MPH, the 'Speed' of the car is the speed of the surface of the tyre covering X distance in time T

Edited By WolstonFlyer on 14/10/2016 11:42:07

Gary Manuel14/10/2016 11:39:35
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TWS - thats what the tape deck sensors do. They maintain a loop of slack between 2 sensors. If the loop gets to long, more power is applied. If it gets too short, less power is applied.

GN. It wouldn't work. The whole point of this is that the plane takes off as normal, using the full runway length.

An aircraft carrier would be too short. Hence the need for the aircraft catapult.

Gary Manuel14/10/2016 11:43:20
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Posted by WolstonFlyer on 14/10/2016 11:39:26:
Posted by Gary Manuel on 14/10/2016 10:57:36:

"Sorry Andy but that's not quite right. While your hand is holding the toy plane stationary, it's speed is not matching the treadmill. The treadmill is moving backwards at 5mph and the toy plane is moving at 0 mph."

Also, wheel rotation is not measured in MPH, it's measured in RPM. The actual RPM is dependant upon the radius of the wheel. Only the centre of the wheel can be measured in RPM, which will be the same as the plane = 0mph."

 

It's James not Andy but that doesn't matter..

You are correct Gary - the plane is stationary moving at 0mph, but the surface of the tyre on the wheel (the speed of the wheel you could say) is the same as the conveyor belt - 5MPH , it cannot be different unless the tyre is slipping on the belt.

We are not talking about the speed of the plane, the question does not mention the speed of the plane.

Ahhh, we are getting somewhere, it's all about how you define 'the speed of the wheel' ?

What does a speedometer measure - well yes it measures RPM, but the dashboard of you car does not tell you the RPM of your car, it tells you the speed in MPH, the 'Speed' of the car is the speed of the surface of the tyre.

Edited By WolstonFlyer on 14/10/2016 11:39:42

Lightbulb moment - yes it's all about how people interpret wheel speed!

Yes and the speedometer is calibrated for a certain wheel radius. As the tire wears, the speedometer accuracy varies.

Thats also how tyre pressure sensers work (on my car anyway). They compare the rotational speed of all 4 wheels and if one of them suddenly changes, it gives a tyre pressure warning.

Edited By Gary Manuel on 14/10/2016 11:44:09

WolstonFlyer14/10/2016 11:45:24
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So can the plane take off?

Gary Manuel14/10/2016 11:45:45
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Love to carry on, but I've got some work to do.

Hopefully the debate will continue in my absence.

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