Plane

[RichA]

Imagine standing on a treadmill wearing roller skates, hold onto the hand rails for balance and have someone accelerate the treadmill, at the same time pull backwards with your arms. You would move forwards relative to the ground.

The wheels and treadmill are supposed to be perfectly speed-matched.
So any forward motion relative to the ground caused by pulling yourself forward (or having a jet engine on your back) would require some slippage/skid between the wheels and the treadmill. That would generate friction.
Now the question is whether a 300 ton jumbo jet's tyres can withstand the friction, heat and wear for which they weren't designed as their surface rubs against the surface of the treadmill for 2 miles at up to 180mph.

 

[Bobski]

Great post.

I need some help with the bit above.

In my perception the circumference of the wheel will always move over the same distance of the conveyor belt and that is always equal to one circumference of the wheel.
In this respect, the speed of the conveyor and the speed of the wheels is matched. The time for one circumference length is matched and the distance is always the same as well.

I need to change my perception to accommodate the bit in bold.

It's the matching of speed to the plane that is important in this particular scenario. The plane is moving at a certain speed right to left, the treadmill at the same speed left to right. The wheels would have been moving at the speed of the plane had the conveyor been stationary, but since it is moving backwards (and spinning the wheels with it) you then add the two speeds together. Since they are matched it is the same as just doubling the plane or conveyor speed.

 

[Deleted member 36735]

I think we should have a forum meet and team match:

The Takeoffers v The Notmovers

Then discuss it over a night of beers...

I've just checked the diary and I'm busy that weekend...

 

[Deleted member 35927]

The wheels and treadmill are supposed to be perfectly speed-matched.
So any forward motion relative to the ground caused by pulling yourself forward (or having a jet engine on your back) would require some slippage/skid between the wheels and the treadmill. That would generate friction.
Now the question is whether a 300 ton jumbo jet's tyres can withstand the friction, heat and wear for which they weren't designed as their surface rubs against the surface of the treadmill for 2 miles at up to 180mph.

The wheels and treadmill are supposed to be perfectly speed-matched.
So any forward motion relative to the ground caused by pulling yourself forward (or having a jet engine on your back) would require some slippage/skid between the wheels and the treadmill. That would generate friction.
Now the question is whether a 300 ton jumbo jet's tyres can withstand the friction, heat and wear for which they weren't designed as their surface rubs against the surface of the treadmill for 2 miles at up to 180mph.

It's fair to say I have absolutely no idea what youre talking about anymore

 

[Deleted member 36735]

It's the matching of speed to the plane that is important in this particular scenario.

Which is not what the puzzle says

 

[Voyager EMH]

The wheels and treadmill are supposed to be perfectly speed-matched.
So any forward motion relative to the ground caused by pulling yourself forward (or having a jet engine on your back) would require some slippage/skid between the wheels and the treadmill. That would generate friction.
Now the question is whether a 300 ton jumbo jet's tyres can withstand the friction, heat and wear for which they weren't designed as their surface rubs against the surface of the treadmill for 2 miles at up to 180mph.

No more friction than in a normal takeoff, so nothing to worry about there.
One circumference of the wheel moves over one-circumference-wheel-length on the conveyor just the same as a normal take off - no extra slippage/skid danger or increased friction.

Unless I'm wrong.

 

[Golf is fun]

Which is not what the puzzle says

Out of curiosity, apart from moving at the speed the plane would normally move for the given amount of thrust from it's engines, (so relative to the conveyor the plane is still, but relative to the rest of the world it's moving forward at normal take off speed) how do you explain how a conveyor belt would stop a free wheel from rotating?

 

[Bobski]

Which is not what the puzzle says

Exactly. The problem is setup (I believe) so that the plane and treadmill are moving in the same direction. In this case it all works fine and the plane takes off. It's easy to think of what might happen if the conveyor and the plane were moving in opposite directions - and this is where some people might get caught out thinking the plane behaves like a car. The problem is that in this scenario (which I agree is not how the question is worded in the OP) you have to specify that the conveyor must match the plane speed and not the wheel speed or you get into the difficulties described above. I was playing out those scenarios to hopefully help identify where some of the disagreements were coming from. I suspect if it had been made more explicit in the question that plane and conveyor were moving in the same direction, there wouldn't have been much discussion.

 

[Voyager EMH]

It's the matching of speed to the plane that is important in this particular scenario. The plane is moving at a certain speed right to left, the treadmill at the same speed left to right. The wheels would have been moving at the speed of the plane had the conveyor been stationary, but since it is moving backwards (and spinning the wheels with it) you then add the two speeds together. Since they are matched it is the same as just doubling the plane or conveyor speed.

Thanks.
No need for me to change my perception then.

Speed of wheels = speed of plane
at all times is obvious.

Definition: Speed of wheels: tangential speed of outer surface of wheels.
This is what I have been sticking to, because this is perfectly matched to the speed of the conveyor, in the opposite direction, at all times. Can not be anything else.

 

[Golf is fun]

Exactly. The problem is setup (I believe) so that the plane and treadmill are moving in the same direction. In this case it all works fine and the plane takes off. It's easy to think of what might happen if the conveyor and the plane were moving in opposite directions - and this is where some people might get caught out thinking the plane behaves like a car. The problem is that in this scenario (which I agree is not how the question is worded in the OP) you have to specify that the conveyor must match the plane speed and not the wheel speed or you get into the difficulties described above. I was playing out those scenarios to hopefully help identify where some of the disagreements were coming from. I suspect if it had been made more explicit in the question that plane and conveyor were moving in the same direction, there wouldn't have been much discussion.

The key part here is that the planes wheels are not driven, so are free wheels (except when using the wheel brakes which isn't relevant here), the conveyor could be going in the opposite direction at 100x the speed of the plane, as long as the planes engines are producing thrust it will still have it's normal airspeed forward and the wheels will spin 100x faster than normal (effectively 100x faster groundspeed as measured by the wheels) - again ignoring the pedantry as to whether the tyres, wheel bearings etc... can handle that and don't just get so hot they fail or burst into flames

 

[Bobski]

Thanks.
No need for me to change my perception then.

Speed of wheels = speed of plane
at all times is obvious.

Definition: Speed of wheels: tangential speed of outer surface of wheels.
This is what I have been sticking to, because this is perfectly matched to the speed of the conveyor, in the opposite direction, at all times. Can not be anything else.

Wheel speed can be faster than conveyor, when there is movement relative to the conveyor. Imagine holding a dinky toy on a moving travolator. Wheel speed will be matching the travolator. Now push the dinky toy along the travolator (in the opposite direction to travolator movement) and the wheel speed will increase to become travelator plus dinky toy speed.

 

[Bobski]

The key part here is that the planes wheels are not driven, so are free wheels (except when using the wheel brakes which isn't relevant here), the conveyor could be going in the opposite direction at 100x the speed of the plane, as long as the planes engines are producing thrust it will still have it's normal airspeed forward and the wheels will spin 100x faster than normal (effectively 100x faster groundspeed as measured by the wheels) - again ignoring the pedantry as to whether the tyres, wheel bearings etc... can handle that and don't just get so hot they fail or burst into flames

Agreed. If you specify any finite speed for the wheels/conveyor then it all works without issue. The problem only occurs in the scenario of the treadmill having to match the wheel speed when they are travelling in opposite directions. This isn't the scenario in the OP, but I think is where some of the confusion kicks in. If the jet is moving along the treadmill, then the treadmill speed can never match the wheel speed (which will always be higher). The conveyor is forced by the requirements of the problem to keep accelerating to try and match the wheel speed, which it can never do. This problem doesn't happen if the conveyor is specified to match the speed of the jet rather than its wheels. Whilst this strictly isn't an issue for the problem as outlined in the OP I think it is behind the difficulties some have visualising the problem. If the treadmill could actually match the wheelspeed in the opposite direction, the wheels would not rotate, the plane would not move and so could not take off. Of course the jet must move along the conveyor which can therefore never exactly match the wheelspeed and the logic of the problem breaks down...

 

[Deleted member 36735]

Now push the dinky toy along the travolator (in the opposite direction to travolator movement) and the wheel speed will increase to become travelator plus dinky toy speed.

That can't happen in this puzzle because the rule says the belt speed will always match the wheel speed.
You can't use movement of the plane being faster than the counter movement of the belt because that breaks the main rule.

 

[Voyager EMH]

Wheel speed can be faster than conveyor, when there is movement relative to the conveyor. Imagine holding a dinky toy on a moving travolator. Wheel speed will be matching the travolator. Now push the dinky toy along the travolator (in the opposite direction to travolator movement) and the wheel speed will increase to become travelator plus dinky toy speed.

Which definition of wheel speed are you using here?

With my definition
Hold the dinky toy still on the travellator and time one circumference turn.
Now move the travellator along at 5mph and time one circumference turn.
Then yes, the wheel edge moves faster.
But this is on a travellator with constant speed.

If at the time the dinky toy is pushed to 5mph, the travellator speed is increased by 5mph, then wheel speed remains the same, but the toy still moves forward at 5mph.
The push has to have some effect, and the increase in speed of travellator does not hurt your hand.

Unless I'm wrong.

 

[RichA]

No more friction than in a normal takeoff, so nothing to worry about there.
One circumference of the wheel moves over one-circumference-wheel-length on the conveyor just the same as a normal take off - no extra slippage/skid danger or increased friction.

Unless I'm wrong.

Normal take off involves the wheels covering 2 miles of runway with no skidding; there's nothing to cause any.
Like you say, 1 circumference of wheel covers the same length of runway.

On the imaginary perfectly speed matched conveyor belt, perfect traction with no friction would result in the plane remaining stationary (my earlier suggestion for which I was mocked). But in "reality" the thrust of the jets forces it forwards.

For the plane to get to takeoff speed it has to travel about 2 miles down the runway until it reaches ~180mph.
The plane has travelled 2 miles yet the wheels and conveyor belt were perfectly speed matched. That's essentially 2 miles of high speed skidding under 300 tons of load. Massively more friction than normal takeoff.

 

[Bobski]

Which definition of wheel speed are you using here?

With my definition
Hold the dinky toy still on the travellator and time one circumference turn.
Now move the travellator along at 5mph and time one circumference turn.
Then yes, the wheel edge moves faster.
But this is on a travellator with constant speed.

If at the time the dinky toy is pushed to 5mph, the travellator speed is increased by 5mph, then wheel speed remains the same, but the toy still moves forward at 5mph.
The push has to have some effect, and the increase in speed of travellator does not hurt your hand.

Unless I'm wrong.

(just to clarify, this is not relevant to the OP problem). The displacement is the difference here. After pushing your dinky toy along the travolator it has moved a certain distance in a certain time ie. it has gained velocity. In order for this displacement to occur, the wheels must have moved faster than the travolator belt (or else your dinky toy would still be in the same spot (relative to an outside observer).

 

[Deleted member 35927]

That can't happen in this puzzle because the rule says the belt speed will always match the wheel speed.
You can't use movement of the plane being faster than the counter movement of the belt because that breaks the main rule.

You keep repeating this, but all it means is if the plane moves the belt matches, plane will take off.
All you keep doing is trying to phrase your definition to match your answer.

 

[Deleted member 36735]

You keep repeating this, but all it means is if the plane moves the belt matches, plane will take off.
All you keep doing is trying to phrase your definition to match your answer.

No, I've given numerous lengthy posts over the past few days that have done my best to describe my thought process as best I can whilst also acknowledging the other point of the argument.

What you have done though is simply deny anyone else's point with absolutely no logic or cohesive points of your own.
You continue to use laughing emojis and reply along the lines of "I haven't got a clue what you're on about ".
Your own points are the least logical of everyone's, all you have done is criticise without offering any type of intelligent input.
Irrelevant of which point of view they have, Rich A, Swango, Voyager et al have all written their points logically and have tried to explain themselves rationally, unlike you.

"Because it's science" doesn't cut it.

 

[Deleted member 36735]

In order for this displacement to occur, the wheels must have moved faster than the travolator belt (or else your dinky toy would still be in the same spot (relative to an outside observer).

Yes, but you can't do this and stick to the rules of the puzzle.

 

[Bobski]

Yes, but you can't do this and stick to the rules of the puzzle.

Apologies - as stated, this was not relevant to the puzzle, but was a response to a question posed by Voyager EMH.

To sumarise the puzzle as I see it - assuming the puzzle is written so that jet and treadmill travel in the same direction (which I believe it is) then the jet takes off as normal, the only interesting thing being that the wheels don't rotate (effectively the runway is travelling at the same speed as the jet). A lot of the confusion I think comes from considering what happens if jet and conveyor travel in opposite direction. In almost all scenarios, the jet takes off normally. The only situation where there is an issue is if the wording of the problem forces the conveyor to exactly match wheelspeed. For the reasons explained, this is not feasible. The only scenario in which conveyor and wheelspeed are exactly matched is if the jet is stationary. Since there is nothing to stop the jet moving, the conveyor will always be slower than the wheels, which means it will always be accelerating, which means it will likely break very quickly - this is however not the scenario as layed out in the OP.