Plane on a conveyor belt

Mkjackary

The only way I could see that it wouldn't take off is that the friction of the wheels causes enough back force onto the aircraft to equal the thrust created by the aircraft. For the aircraft to stay still the Thrust vector must have an equal and opposite vector in the form of friction and drag. Now as there is no wind speed and the aircraft isn't moving then there is no drag, so all of the counterforce must come from friction. The only place to get friction is from the wheels.

Feasible with say a small desk fan attached to a set of wheels right, small initial thrust, so the friction of a few wheels could easily match that.

But with 4 Rolls Royce engines at max output, I just couldn't imagine the wheels creating enough friction to, in a sense, pull back and match the thrust of those 4 engines. Each engine can produce around 200kN of thrust, so that is 800kN that the friction would have to match which it could simply not do, even if it could, it could not do so for any extended period of time as it would burn up from the heat.

So the plane would move forwards and accelerate because the thrust force exceeds the drag/friction force and eventually gain enough lift to take off.


And to those who say frictionless wheels, then how would the thrust vector be counteracted? There must be some force counteracting the engine thrust for the plane to stay motionless.

As far as I could see if you had a truly frictionless wheels, you could put a car with zero friction on top of a stationary conveyer belt, then increase the speed of the conveyer to say 100mph (could be any speed), and the car would not move. It would stay still whilst the ground moved underneath it because the only way for it to be moved by the conveyer is via friction. 
With frictionless wheels it would be much easier to take off from the conveyer belt than with normal wheels, as the aircraft would not have to overcome the friction force, creating greater acceleration to the take off speed needed.

I'll post a diagram to try and help explain my view

menamestom

CabbageCat said:

This is obviously not a real world situation, but if it were to be I think that the question would be thus:

If a plane applied thrust smoothly as it normally would to get up to 200mph over 60 seconds and the conveyor belt that it was on accelerated smoothly up to 200mph in the opposite direction over 60 seconds would the plane take off?

I think that the answer is "no" for the reasons Maynehead has explained.

I don't think this is correct, the conveyor belt would need to be going well over 200mph to stop the plane going forward.  Or put another way, the plane would not need as much thrust as it normally would to get to 200mph, just to counteract a 200mph treadmill.  It would have power in reserve because of the lack of wind resistance.  if the treadmill could not go over 200mph, the plane may still be able to take off depending on how much power it was using to keep stationary.  Power would need to be greater than the wind resistance plus additional drag of the increased wheel friction.

Mkjackary

If the 747 is stationary, for it to start moving (acceleration) the thrust force must be equalled the friction force. Once the aircraft has overcome the friction force and starts moving through the air, drag and lift forces are also applied to the aircraft. As long as the thrust force is greater than the friction force and the drag force, the aircraft will accelerate until it is eventually at take off speed where the lift force from the wings is greater than the gravitational force.

The conveyer is almost irrelevant, all the conveyer can do to the aircraft is cause friction, so yes there is no conveyer in this diagram, but there need not be, it is represented by the friction arrow.

Very basic Forces diagram:


The only way for the aircraft to not take off is if the wheels could withstand 800kN of friction for any amount of time without burning up, but even then, if we had wheels that could withstand infinite  friction, then we also have infinitely powerfull engines, that would suck enough air over the wings to cause enough lift to counteract gravity anyway.

I haven't done maths or physics for a good while now but that seems like it makes sense to me.
Excuse the location of the force arrows too, I didn't want it to be too jumbled up and complicated.


Again with frictionless wheels there is no way to counteract the thrust vector, so it would take off easily.

dtr

Oh c'mon... the converyor belt "is designed to" blah blah blah.  It doesn't matter a goddam what the conveyor belt is designed to do - it could be designed to spin fast or play showtunes, if there's a 747 opening its throttles on top of it the plane's going to take off.

And for all those who assume that something "designed to" do a job must therefore actually do a job, I have an amazing scheme designed to make you incredibly rich - just PPG me a fiver and you can have the details!

Ravenous

Mkjackary said:

The only way I could see that it wouldn't take off is that the friction of the wheels causes enough back force onto the aircraft to equal the thrust created by the aircraft

But as a few people have already said, the tyres on a 747 would fall to bits once the rolling speed gets high enough. This is the one practical limit everyone seems to be ignoring.

menamestom

Ravenous said:

Mkjackary said:

The only way I could see that it wouldn't take off is that the friction of the wheels causes enough back force onto the aircraft to equal the thrust created by the aircraft

But as a few people have already said, the tyres on a 747 would fall to bits once the rolling speed gets high enough. This is the one practical limit everyone seems to be ignoring.

I think if you are imagining a hypothetical high speed conveyor belt, you are also imagining a hypothetical aircraft with limitless rolling speed.

CabbageCat

menamestom said:

CabbageCat said:

This is obviously not a real world situation, but if it were to be I think that the question would be thus:

If a plane applied thrust smoothly as it normally would to get up to 200mph over 60 seconds and the conveyor belt that it was on accelerated smoothly up to 200mph in the opposite direction over 60 seconds would the plane take off?

I think that the answer is "no" for the reasons Maynehead has explained.

I don't think this is correct, the conveyor belt would need to be going well over 200mph to stop the plane going forward.  Or put another way, the plane would not need as much thrust as it normally would to get to 200mph, just to counteract a 200mph treadmill.  It would have power in reserve because of the lack of wind resistance.  if the treadmill could not go over 200mph, the plane may still be able to take off depending on how much power it was using to keep stationary.  Power would need to be greater than the wind resistance plus additional drag of the increased wheel friction.

Yeah, I guess the conveyor's acceleration would have to be chosen to model the speed of the plane with no air resistance. The point is that the conveyor and the plane are trying to real-world match speeds without having to worry about exploding. I guess it's starting to disappear out of practicality again.

Mkjackary

Ravenous said:

Mkjackary said:

The only way I could see that it wouldn't take off is that the friction of the wheels causes enough back force onto the aircraft to equal the thrust created by the aircraft

But as a few people have already said, the tyres on a 747 would fall to bits once the rolling speed gets high enough. This is the one practical limit everyone seems to be ignoring.

Well, as soon as the wheels fall apart then the whole idea of the question falls apart, as there are no wheels for the conveyor to match the speed of. Then it is a different question altogether.

CabbageCat

Mkjackary said:

If the 747 is stationary, for it to start moving (acceleration) the thrust force must be equalled the friction force. Once the aircraft has overcome the friction force and starts moving through the air, drag and lift forces are also applied to the aircraft. As long as the thrust force is greater than the friction force and the drag force, the aircraft will accelerate until it is eventually at take off speed where the lift force from the wings is greater than the gravitational force.

The conveyer is almost irrelevant, all the conveyer can do to the aircraft is cause friction, so yes there is no conveyer in this diagram, but there need not be, it is represented by the friction arrow.

Very basic Forces diagram:


The only way for the aircraft to not take off is if the wheels could withstand 800kN of friction for any amount of time without burning up, but even then, if we had wheels that could withstand infinite  friction, then we also have infinitely powerfull engines, that would suck enough air over the wings to cause enough lift to counteract gravity anyway.

I haven't done maths or physics for a good while now but that seems like it makes sense to me.
Excuse the location of the force arrows too, I didn't want it to be too jumbled up and complicated.


Again with frictionless wheels there is no way to counteract the thrust vector, so it would take off easily.

The plane would stay stationary until the wheels broke, and they would be the only thing holding it up. Friction would then massively increase (wheels being nice low-friction turny things), sending the plane backwards at massive speeds while jetting in the opposite direction. Fireball, not takeoff.

paul_c2

dtr said:

Oh c'mon... the converyor belt "is designed to" blah blah blah.  It doesn't matter a goddam what the conveyor belt is designed to do - it could be designed to spin fast or play showtunes, if there's a 747 opening its throttles on top of it the plane's going to take off.

And for all those who assume that something "designed to" do a job must therefore actually do a job, I have an amazing scheme designed to make you incredibly rich - just PPG me a fiver and you can have the details!

PM sent (for Paypal details).























Joking!

Mkjackary

dtr said:

And for all those who assume that something "designed to" do a job must therefore actually do a job, I have an amazing scheme designed to make you incredibly rich - just PPG me a fiver and you can have the details!

Do you accept paypal goods and services? I'll cover the fees

Maynehead

menamestom said:

CabbageCat said:

This is obviously not a real world situation, but if it were to be I think that the question would be thus:

If a plane applied thrust smoothly as it normally would to get up to 200mph over 60 seconds and the conveyor belt that it was on accelerated smoothly up to 200mph in the opposite direction over 60 seconds would the plane take off?

I think that the answer is "no" for the reasons Maynehead has explained.

I don't think this is correct, the conveyor belt would need to be going well over 200mph to stop the plane going forward.  Or put another way, the plane would not need as much thrust as it normally would to get to 200mph, just to counteract a 200mph treadmill.  It would have power in reserve because of the lack of wind resistance.  if the treadmill could not go over 200mph, the plane may still be able to take off depending on how much power it was using to keep stationary.  Power would need to be greater than the wind resistance plus additional drag of the increased wheel friction.

This is correct. The treadmill needs to be going as fast as it takes to generate enough friction to counteract the engine thrust, so the precise speed is determined by the resistance in the wheels.

As soon as the thrust overcomes the resistive forces generated by the belt, the plane would start to move forward with respect to a stationary observer, which implies that the plane's wheels are spinning faster than the belt is moving in the opposite direction, thus breaking the premise of the question. Therefore for the premise of the question to hold, the plane must be stationary to the observer, which implies not enough airflow over the wings to achieve take off.

Emp_Fab

ICBM said:

Maynehead said:

Whether the wheels are driven or not is irrelevant. For the plane to move in relation to the ground there must be a speed differential between the rotational speed of the wheels and the rotational speed of the conveyor belt in the opposite direction. This is ruled out by the definition of the question.

No. In the thought experiment, the conveyor is moving forward relative to the ground at the same speed as the plane, in order to keep the wheels stationary.

Are you on drugs or something ?  The initial post stated that the conveyor moves in the OPPOSITE direction to the wheels.  The drawing accompanying it confirms that.  Conveyor moves clockwise, wheels move anticlockwise.  Plane remains stationary.  Zero airflow over the wings.  Plane remains on the conveyor belt.

How can anyone get basic physics so wrong ?  @ICBM ;

hywelg

ICBM said:

Anyone who thinks it can't doesn't understand basic physics.

+10^n

Correct. The wheel play absolutely no part in it other than apply a small amount of rolling resistance, inconsequential compared with the thrust of the engines. When thrust is applied the plane moves forward irrespective of the speed of the conveyor as soon as the thrust >= drag of the wheels.

hywelg

Its rather like the age old philosophical conundrum.

If a tree falls in the forest and no-one hears it did it make a sound.

Sound is completely independant of a human witness. Laws of physics.......

ICBM

Emp_Fab said:

Are you on drugs or something ?  The initial post stated that the conveyor moves in the OPPOSITE direction to the wheels.  The drawing accompanying it confirms that.  Conveyor moves clockwise, wheels move anticlockwise.  Plane remains stationary.  Zero airflow over the wings.  Plane remains on the conveyor belt.

How can anyone get basic physics so wrong ?  @ICBM ;

Jesus christ. You of all people should understand how a plane flies, you wanted to be a pilot!

*The wheels are irrelevant.* The plane could be on a runway, a conveyor belt, a set of flatbed lorries, thirty thousand roller skates or a magic carpet - it doesn't matter. The engine thrust *alone* propels the plane forward relative to the air, and when the airspeed exceeds that necessary to provide lift for flight, the plane takes off. Period, the end.

Next time you're near an airport, watch the planes coming into land with the undercarriage down. Are the wheels turning? If no, why doesn't the plane fall out of the sky? Answer: because the wheels do not provide the thrust!

Or are you just winding me up?

Maynehead

hywelg said:

ICBM said:

Anyone who thinks it can't doesn't understand basic physics.

+10^n

Correct. The wheel play absolutely no part in it other than apply a small amount of rolling resistance, inconsequential compared with the thrust of the engines. When thrust is applied the plane moves forward irrespective of the speed of the conveyor as soon as the thrust >= drag of the wheels.

...and for the plane to move forwards, the wheels MUST be turning faster than the speed of the conveyor, which breaks the main premise of the question.

Wolfetone

The wheels and the conveyor are irrelevant in this scenario as all the wheels do is support the airframe and reduce the ground drag. The work is done by the thrust of the engines against the air and the plane will take off as normal.

If on the other hand there was a massive fan blowing air from behind at 160kts the plane would need to be travelling at a ground speed of 32okts to reach take off speed.
 

Wolfetone

Sambostar said:

Ah, but could a plane take off with a 570 mph tailwind?

yes but it's ground speed would be 570mph plus its take off speed. It needs a minimum forward airspeed to reach its take off speed.

paul_c2

I think that the question is more about how you analyse scenarios, than whether the plane will take off or not. Some people on here are quite happy to accept that the conveyor has magical properties which prevent the 747 from moving forwards when its engines are put at full thrust, then tie themselves in knots with what happens next. Basically, they are blindly accepting an impossible assumption made in the question.