B Can a 747 Take Off on a Conveyor Belt?

[willem2]

Actually, If you accelerate the conveyor fast enough, it can stop the plane!
A force is needed to make the wheels rotate, The wheels can only start to rotate by a force of the conveyor on the wheels.
We have \alpha = \frac {T} {I} where T is the torque from the conveyor on the wheels, I the moment of inertia of the wheels.
Substituting I = \frac {1}{2} m r^2 for the moment of inertia of a cylinder, where m is the mass of the wheels.
and T = F r where F is the thrust of the engines that the conveyor must balance.
and a = \alpha r where a is the linear acceleration, we get: <br /> a = \frac {2 F} {m}. m ~ 1500 kg. (8 tyres of 184 kg) F = 250 kN . so<br /> a ~ 333 m/s^2. So if we only keep on accelerating the conveyor at this rate, the plane can't take off.<br /> <br /> A problem might be that the conveyor might cause so much wind, that the plane can take off at 0 ground speed anyway.

 

[sophiecentaur]

Barring obvious physical constraints,

I am fully with you there. This is what I can't understand. The constraints are really obvious and seem to be blinding people to the basic Physics of the situation. We had a similar problem on the 'filling buckets' problem, where people also couldn't let themselves just deal with the basic logical Physi,cs. These problems can always be analysed and analysed to death and there's no fun or (more to the point) there is no ANSWER.
How could we ever teach Science to kids if we littered the curriculum with practical details from the start about Wire Resistance, Non-uniform Gravity on Earth, Friction, Heat loss / gain? The poor devils would never feel able to predict anything because some smart alec would introduce a footling reason why they will be wrong. We are Physicists (aren't we?) and - just like Engineers, we start on a problem in the simplest possible way.

 

[Janus]

I am fully with you there. This is what I can't understand. The constraints are really obvious and seem to be blinding people to the basic Physics of the situation. We had a similar problem on the 'filling buckets' problem, where people also couldn't let themselves just deal with the basic logical Physi,cs. These problems can always be analysed and analysed to death and there's no fun or (more to the point) there is no ANSWER.
How could we ever teach Science to kids if we littered the curriculum with practical details from the start about Wire Resistance, Non-uniform Gravity on Earth, Friction, Heat loss / gain? The poor devils would never feel able to predict anything because some smart alec would introduce a footling reason why they will be wrong. We are Physicists (aren't we?) and - just like Engineers, we start on a problem in the simplest possible way.

The problem is that there are scenarios that if they are reduced too far, lead to nonsense results.

 

[jbriggs444]

a = \frac {2 F} {m}. m ~ 1500 kg. (8 tyres of 184 kg) F = 250 kN . so
a ~ 333 m/s^2. So if we only keep on accelerating the conveyor at this rate, the plane can't take off.
.

A 747 has 16 tires (4 each on 4 pylons) and each of 4 engines has around 250 kN thrust. However, I agree that the result is in the right ballpark and results in the wheels reaching their rated max speed in a fraction of a second.

Edit: I like your figure for tire+wheel mass. It's better than the one I used up-thread.

 

[sophiecentaur]

From OP:

The conveyor best is designed to exactly match the speed of the wheels, but run in the opposite direction.

results in the wheels reaching their rated max speed in a fraction of a second.

How does that follow? The wording in the OP is a bit vague but I read it as meaning that "match" means the conveyor surface always goes backwards at the same speed as the wheels are going forward (i.e. the bearings and the rest of the plane). The acceleration is just twice that of the plane over the ground. Where does the "fraction of a second" come from? The plane takes many seconds to accelerate to takeoff speed.

 

[A.T.]

... but I read it as ...

The whole thread in five words.

 

[sophiecentaur]

But I, personally, have been declaring how I read it. I think many of the loopy contributions have not ever stated their full case. 'It stands to reason' is never a full case.
I think we should demand that answers should include how the OP has been actually understood by the contributor and, where appropriate, some reference of book work. Some of the assumptions in this thread have been so 'intuitive'.

 

[jbriggs444]

I think many of the loopy contributions have not ever stated their full case. 'It stands to reason' is never a full case.

If you chase back the sub-thread to which you responded, you will find.

Actually, If you accelerate the conveyor fast enough, it can stop the plane!

@willem2 proceeded to perform a computation containing actual physics and arrived at a figure for how fast the conveyor would need to accelerate rearward so that the friction required to spin up the wheels to match the conveyor speed would match the forward thrust of the aircraft engines.
I then responded with agreement that..

result is in the right ballpark and results in the wheels reaching their rated max speed in a fraction of a second.

To which you responded that you did not see how it followed.

Looks to me like it follows.Now @willem2 did not quote the post to which he was responding, but his post immediately followed one by @TurtleMeister:

Barring obvious physical constraints, such as tire maximum ratings, the conveyor direction and speed has no bearing on whether the plane can take off or not.

@willem2's post seems to be on-point in a rebuttal of this claim. [Arguably a rebuttal which was already accounted for under the "obvious physical constraints" exception].

Edit to add a final clarification:

None of this should be read as disagreement with your (@sophiecentaur) sound advice to state assumptions first and calculations after.

 

[sophiecentaur]

Looks to me like it follows.

We are clearly at cross purposes here. I realize you are not a total loony (just enough to want to contribute as regularly as I do on PF!) by the sentence:

The conveyor best is designed to exactly match the speed of the wheels, but run in the opposite direction

If you are suggesting that means to drag the wheels back so fast that they lock up and drag the plane backwards then what you are claiming will follow.
But I do not understand what 'matching' means, in your interpretation.
The way the original question uses 'matching', surely implies that the linear speed of the conveyor would be equal and opposite to what would be the tangential speed of the wheel if it were on the ground. That is actually equal and opposite to the instantaneous speed of the plane over the ground. I have made that clear more than once. Are you saying that is the wrong interpretation? The wheels are free to rotate - just as if it were on ice, in an ideal case. No force (lateral) is exerted on the plane, even if you move the ice backwards.

 

[A.T.]

But I do not understand what 'matching' means, in your interpretation.

I think that sub-thread you reply to is not about guessing what "matching" means anymore, but simply asking what would the belt have to do, in order to stop the plane based on rotational inertia of the wheels.

 

[sophiecentaur]

None of this should be read as disagreement with your (@sophiecentaur) sound advice to state assumptions first and calculations after.

Sorry, I missed this last line of the post.
But I still take issue with the requirement to accelerate things in a fraction of a second. The air speed of the plane is the variable that determines what the conveyor needs to be doing.

 

[sophiecentaur]

I think that sub-thread you reply to is not about guessing what "matching" means anymore, but simply asking what would the belt have to do to stop the plane, based on rotational inertia of the wheels.

That could be true but what a fruitless conversation, in the light of almost absolute ignorance of the values of all the variables involved. I would totally agree that the experiment is a nonsense but it is scaled down very easily with a low speed prop aircraft and the Physics point is proved.
Like I said earlier, how easy is it to stop a bicycle by back-pedalling with a freewheel hub?

 

[TurtleMeister]

I think we should demand that answers should include how the OP has been actually understood by the contributor

Here's the op:

Imagine a 747 sitting on a large conveyor belt, as long and as wide as the runway.
The conveyor best is designed to exactly match the speed of the wheels, but run in the opposite direction.

CAN THE PLANE TAKE OFF?

The op is not clear, and in my opinion, is the cause of the confusion. So here is my interpretation, the way I think it should be stated:

Imagine a 747 sitting on a large conveyor belt, as long and as wide as the runway. The conveyor belt is designed to match the normal takeoff speed of the aircraft but in the opposite direction. Can the plane take off?

I think this is the interpretation used in the Myth Busters video.

 

[Jake Miguel]

The tire wheel speed is not really related to what the plane needs to fly; over 100mph of wind to make the lift. The plane will have no care for tire wheel speed. If there was a gale of 160mph, then it would be possible for the 747 to hover over a fixed position with respect to the ground. Planes don't have care for ground speed, but rather air speed is what they crave.

 

[jbriggs444]

Sorry, I missed this last line of the post.
But I still take issue with the requirement to accelerate things in a fraction of a second. The air speed of the plane is the variable that determines what the conveyor needs to be doing.

Reductio Ad Absurdum.

You persist in arguing against the perceived conclusion (the absurd requirement) instead of the real conclusion (that the interpretation that led to that requirement was unintended or that the problem is badly posed).

 

[Janus]

From OP:
How does that follow? The wording in the OP is a bit vague but I read it as meaning that "match" means the conveyor surface always goes backwards at the same speed as the wheels are going forward (i.e. the bearings and the rest of the plane).

The problem I have with that interpretation of the intent of the question is the equivalent of asking that if you put a car on a treadmill that travels backwards at the same speed as the car is moving forward relative to the ground, can the car move forward? It is a bit nonsensical, because the car moves forward as one of the initial postulates of the problem. It just seems more reasonable that the problem is assuming that the treadmill moves backwards at the same speed as the tread of the wheels move relative to the car or plane. Now you can reasonably ask whether or not the car or plane can move forward.

 

[sophiecentaur]

The problem I have with that interpretation of the intent of the question is the equivalent of asking that if you put a car on a treadmill that travels backwards at the same speed as the car is moving forward relative to the ground, can the car move forward?

But it isn't th3e same thing at all. In the car scenario, the motion of the car is determined entirely by the power delivered via the wheels. Forces on the wheels are an essential part of the propulsion. If the 'road' moves backwards at the tangential speed of the wheels, the car goes nowhere. That is just not the case with an aeroplane.

the same speed as the tread of the wheels move relative to the car or plane.

You can't include them in the same model. What drives the car forward? What drives the plane forward?
I suggested earlier that people in doubt should draw a free body diagram. Is the force on the plane in any way dependent on the wheels (in the absence of friction losses)?
I was all ready to drop this and I read your post. It's just not right.

 

[Janus]

But it isn't th3e same thing at all. In the car scenario, the motion of the car is determined entirely by the power delivered via the wheels. Forces on the wheels are an essential part of the propulsion. If the 'road' moves backwards at the tangential speed of the wheels, the car goes nowhere. That is just not the case with an aeroplane.

You can't include them in the same model. What drives the car forward? What drives the plane forward?
I suggested earlier that people in doubt should draw a free body diagram. Is the force on the plane in any way dependent on the wheels (in the absence of friction losses)?
I was all ready to drop this and I read your post. It's just not right.

But isn't that point? In the case where the treadmill moves at the same speed as ground speed, the results are the same for car and plane. When it's the same speed as tangential speed of the wheel, then obviously the car doesn't move relative to the ground as it is propelled by the wheels. The plane is not propelled by its wheels and the problem becomes more reliant on the constraints applied. Since the intent of the question is to present a perceived conundrum. It does not seem likely that the scenario with the trivial answer is what was meant

 

[sophiecentaur]

the problem becomes more reliant on the constraints applied.

This is just more over analysis. You can keep changing the goalposts for another 119 posts but who will it help? The original question was obviously about the simplest case. Why not deal with just that?

 

[DaveC426913]

I can't believe this is still under discussion.

It doesn't matter what the wheels are doing - it's not a car.
A plane gets its forward motion via the air, using props or jets.
Once the thrust of the engines rises, the plane will accelerate with respect to the air - and eventually gain lift via air, as usual - no matter what the wheels are doing.

You can do whatever you want with the conveyor - move it as fast as you want - till the wheels blow, and the landing gear is worn down to nubs - the plane is still going to move forward, given sufficient thrust.

Full stop.

 

[boneh3ad]

I can't believe this is still under discussion.

It doesn't matter what the wheels are doing - it's not a car.
A plane gets its forward motion via the air, using props or jets.
Once the thrust of the engines rises, the plane will accelerate with respect to the air - and eventually gain lift via air, as usual - no matter what the wheels are doing.

You can do whatever you want with the conveyor - move it as fast as you want - till the wheels blow, and the landing gear is worn down to nubs - the plane is still going to move forward, given sufficient thrust.

Full stop.

To clarify, it would matter slightly if only because the faster the wheels are turning, the more rolling friction the plane would likely experience, but this would only affect the rate at which the plane accelerates and would be very small compared to the overall thrust. I'd imagine that the wheels would simply catch fire and melt long before they moved fast enough to provide enough frictional force to stop the plane moving forward.

So yes, I fully agree (as I stated like 5 pages ago) that the rotation of the wheels is largely irrelevant because the engines, and therefore the forward force, really don't care what the wheels are doing. They only care about the air.

I feel like this thread has jumped the shark.

 

[OCR]

Lol... all in fun...

Now...
Carry on.

[Edit to add a final clarification:]

"If you’re desperate to tell me that I’m wrong on the internet, don’t bother.

I’ve snuck onto the plane into first class with the #5 crowd and we’re busy finding out how many cocktails they’ll serve while we’re waiting for the treadmill to start.

God help us if, after the fourth round of drinks, someone brings up the two envelopes paradox." <sup>[1]

1</sup>[Source attribution]


Oh, and BTW... has anybody looked here ? ...

[End of edit to add a final clarification:]

Now...
Carry on.

 

[Nidum]

+25

Yes - it's that simple .

 

[A.T.]

...till the wheels blow, and the landing gear is worn down to nubs - the plane is still going to move forward, given sufficient thrust.

But... but... with a landing gear worn down to nubs, will the thrust be sufficient to reach take off speed within the length of a normal runway?

 

[sophiecentaur]

I can't believe this is still under discussion.

Yes you CAN! This is PF

 

[sophiecentaur]

But... but... with a landing gear worn down to nubs, will the thrust be sufficient to reach take off speed within the length of a normal runway?

Then we no longer have wheels and the question no longer applies.

 

[DaveC426913]

Oh, and BTW... has anybody looked here ?

Oh my stars & garters - XKCD has a forum??
Where have you been all my life?

 

[berkeman]

Oh, and BTW... has anybody looked here ? ...

And with that, I think we can call this thread done. Thanks for helping out, folks.