# B Can this plane take off?

1. Aug 14, 2017

### RandyD123

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?

2. Aug 14, 2017

### Staff: Mentor

If the airplane was on a frictionless surface, do you think it would be able to take off?

3. Aug 14, 2017

### phinds

This exact question was answered fairly recently. I suggest a forum search.

4. Aug 14, 2017

### RandyD123

I tried that first, but unfortunately I didn't find that thread. Sorry

5. Aug 14, 2017

### phinds

Hm ... I don't have a link. Maybe someone else will remember it or know what search term to use.

6. Aug 14, 2017

### Bandersnatch

Or... the OP could try and work it out himself instead. Why not start by answering DrClaude's question?

(By the way there's an issue with the wording of this version of the problem - the conveyor belt should be matching plane speed w/r to the ground, otherwise the proposition is faulty and results in infinities)

7. Aug 14, 2017

### phinds

Good point
Another good point. I missed that by dismissing the question too quickly.

8. Aug 14, 2017

### Staff: Mentor

This "riddle" went around the internet a few years ago and we have a few old threads on it. Mythbusters actually tested it with a Cessna. As you worded it, there is no reason the plane wouldn't be able to take off, but "exactly match the speed of the wheels, but run in the opposite direction" doesn't actually make any sense because the wheels are already rolling when the runway is stationary and the contact patch is always stationary - so as worded, either the conveyor isn't moving or the plane has to be tethered to prevent it from moving while the conveyor rolls at any random speed under it. And that's the only thing difficult about the various incarnations of the "riddle": they are badly or impossibly worded, which triggers arguments about trying to reconcile the wording with reality.

9. Aug 14, 2017

### Clausen

The plane will take off. Wheel speed is not even relevant as long as there is sufficient engine thrust to push the plane forward with respect to the air. The plane doesn't even need wheels, pontoons will do just as well.

10. Aug 14, 2017

### RandyD123

Wheels have nothing to do with solving this question....more of less. Think of this, let's use a SEA PLANE....NO WHEELS and let's put that plane in water, near the edge of a waterfall. There is a point of no return for any object in the water. Now lets put power to the plane weather it's jet power or propeller power. The water going over the edge of the waterfall is the "conveyor" belt. The plane, in that water has a point of no return. That point will change based on the THRUST of the engines. But if the THRUST MATCHES the force of the water going over the falls, the PLANE DOES NOT MOVE. Therefore it creates NO LIFT. NO LIFT.... NO FLY.

11. Aug 14, 2017

### A.T.

Even given the already mentioned ambiguity of the original formulation, this is a completely different one.

12. Aug 14, 2017

### Clausen

Yes, that is what I said. Pontoons will do just as well

Yes, and that thrust must be able to push the plane with respect to the air, in order to create lift on the wings.

The force of the water going over the falls has nothing to do with the plane taking off. The engine thrust only needs to be greater than the force of the water on the pontoons. The engine thrust will most certainly be sufficient to overcome that frictional resistance as that resistance is approximately constant over a large range of velocities.

13. Aug 14, 2017

### RandyD123

Not sure if the "wheels" make the difference. If it's a waterfall or black hole, in both cases there is a point of no return, no matter what the thrust is. If the plane is on the "edge" of the point of no return then the plane can't fly. Why would a conveyor belt mean any less than the other 2?

14. Aug 14, 2017

### A.T.

Nothing is sure if the assumptions are not clear. What horizontal force are the wheels assumed to produce? How does this force depend on the relative speed between plane and surface? How is the belt speed defined exactly? That determines if the plane can take off, or not.

15. Aug 14, 2017

### RandyD123

I say the plane can't fly, if it could then conveyors would be on all aircraft carriers.

16. Aug 14, 2017

### Staff: Mentor

The conveyor belt applies virtually no force to the plane because the plane is on wheels. If you think otherwise, that is your error.
That makes no sense at all, however aircraft carriers do have catapaults...and also conduct flight operations while in motion...

It is starting to feel like you are going to keep altering the scenario until you figure out a way to keep the plane from flying. Certainly you can, but why do that except to be argumentative?

17. Aug 14, 2017

I would like to contend that there is a difference (in practice) between wheels and pontoons, though it's a difference in magnitude rather than in kind. That difference has to do with the type and amount of "friction" opposing motion.

I think the fundamental issue that @RandyD123 is missing here is that the plane's motion has everything to do with the thrust, which is completely decoupled from the motion of the treadmill underneath. It has little to do with that friction force from wheels since that will be many, many orders of magnitude less than the thrust. The treadmill could tend to drag the plane along with it a little bit, but it won't be much, and, depending on the situation, it's possible the conveyor could simply spin the wheels without moving the plane. So relative to the moving treadmill, the plane could have some motion, but this motion is irrelevant when it comes to lift. The motion relative to the air is what matters, and that is going to depends pretty much entirely on the thrust in this case. In other words, once that engine starts, that plane is going to move forward nearly identically whether it is on a runway or a treadmill. The only difference will be the rotation rate of the wheels, not the speed of the plane relative to the air.

With pontoons it is slightly different because the drag of the water moving over pontoons will be much larger (probably several orders of magnitude) than rolling friction on wheels. In that case, there may be a noticeable difference between a boat with pontoons taking off, say, upstream on a river, compared to a plane with wheels on a treadmill. In that case, for a given engine thrust, there could be some water velocity that would result in the drag exactly matching the thrust and the plane not going anywhere, but the water would have to be moving pretty quickly to do that.

At any rate, here's a video of a plane taking off on a treadmill:

18. Aug 14, 2017

### Staff: Mentor

What is the net force on the plane? If it is positive the plane will accelerate until it reaches a speed sufficient to take off. If it is negative, the plane will be dragged backwards against the best efforts of its howling engines. If it is zero, the plane will sit there until runs out of fuel.

As this problem is most often presented (it is all over the Internet, although I'd trust the explanations you're getting here more than some of what's out there) the conveyor belt and wheels are frictionless so apply no backwards force; the net force is the engine thrust as on a normal takeoff. A pontoon system applies a significant backwards force acting against the engine thrust so will delay (normal float plane takeoff) or prevent (absurd hypothetical in which the plane takes off against an absurd current) the takeoff. The catapult on an aircraft carrier applies a significant force in the same direction as the engine and assists the takeoff - that's why aircraft carriers use catapults instead of conveyor belts.

So bottom line: yes, the mechanism matters, if different mechanisms apply different forces to the plane. And yes, the plane will take off.

19. Aug 14, 2017

### RandyD123

That whole video is bogus. Does not even come close to the physics of the real question.

20. Aug 14, 2017

### RandyD123

Probably only until someone can provide real world physics to this question. Maybe someone already has and I just don't understand it. Can we all at least agree that in a waterfall or black hole scenario, the plane won't EVER fly?