# Will a conveyor belt push a hovercraft along?

#### Izzard

Hi. This forum seems to be just what I'm looking for!

My friend and I have just been having one of those drawn out debates over a hypothetical physics model and I guess (although it was an animated discussion) neither of us was 100% convinced we were correct what we were saying. We were both pretty adamant the other person was wrong though ;)

The basic hypothetical situation is a hovercraft hovering over a moving conveyor belt. Does the hovercraft move in the direction of the belt, or does it remain stationary (relative to everything else in the universe)?

We tried thinking of it as a mathematically perfect model. Or at least with these constraints: The workings of the ‘hovercraft’ are unspecified, but you can assume it pushes air downwards from a skirt and is completely stable.. ..on unmoving ground it would appear completely stationary. The conveyor belt is a huge (maybe even infinite) plane, moving at a constant velocity. The ‘craft’ has just magically popped into existence above it at a stable altitude. Actually, feel free to toy around with the restraints all you like if you have any comment to make :)

This came about because my friend was playing a console game where his character, riding a ‘hoverboard’ glides onto a conveyor belt for a few moments. The character is pushed along as though he had stepped onto the belt. Obviously wrong. My friend said that the belt should not affect the board at all. I said I thought it would, a bit, after a fashion. He said it never would.

Well my thinking was that if the board is *hovering* over the belt then it is using thrust to overcome the effect of gravity on its mass. I.e. there are forces acting directly upwards and directly downwards which are equal and opposite, so the hoverboard remains in place. I thought that this made the two things connected, albeit loosely (the conveyor belt isn’t frictionless, after all), so eventually the relentless motion of the belt would be transferred through the column of air to the board. Now my brain hurts. Please help!

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#### chroot

Staff Emeritus
Science Advisor
Gold Member
Originally posted by Izzard
Please help!
Draw a free-body diagram of the stationary hovercraft. The only force on it, ideally, is its lift.

Now turn on the conveyor belt. What happens? In a vacuum, nothing would happen at all. The two objects (belt and hovercraft) are not touching, and therefore the hovercraft stays exactly where it is.

In the real world, the conveyor belt exerts some friction on the air above it, and the air between the belt and hovercraft moves slightly along with the belt. The air then pushes on the hovercraft, and exerts a teeny-tiny force on it. It's essentially the drag force caused by the "wind" which is (only slightly) moving along with the conveyor. The force is negligible for a reasonably massive hovercraft, and probably completely immeasurable in practice.

You can safely say that your hovercraft would stay exactly as it is, regardless of what the conveyor belt is doing under it.

- Warren

#### LURCH

Science Advisor
Re: Re: Will a conveyor belt push a hovercraft along?

Originally posted by chroot
Draw a free-body diagram of the stationary hovercraft. The only force on it, ideally, is its lift.

Now turn on the conveyor belt. What happens? In a vacuum, nothing would happen at all. The two objects (belt and hovercraft) are not touching, and therefore the hovercraft stays exactly where it is.

In the real world, the conveyor belt exerts some friction on the air above it, and the air between the belt and hovercraft moves slightly along with the belt. The air then pushes on the hovercraft, and exerts a teeny-tiny force on it. It's essentially the drag force caused by the "wind" which is (only slightly) moving along with the conveyor. The force is negligible for a reasonably massive hovercraft, and probably completely immeasurable in practice.

You can safely say that your hovercraft would stay exactly as it is, regardless of what the conveyor belt is doing under it.

- Warren
I dissagree (though I am not "adamant that [you are] wrong"!). Althought hovercraft have a very low drag coefficient with the ground, it is not zero. The air trapped under the skirt is escaping around the edges. As it escapes, it interacts with whatever surface it is "hovering" itself above. The air trying to escape out the leading edge of the skirt (or the edge that is facing in the direction from which the conveyer surface is aproaching) will encounter slightly more resistance when trying to escape. Likewise, the air on the trailing edge (in the direction the belt is moving towards) will secape with less resistance. So the hovercraft will experience some slight drag in the direction of surface movement.

Of course, your friends "hoverboard" being of video-game design, it might be hovering magnetically, or antigravitationally, ni which case the specifics of the mechanism would make all the difference.

#### chroot

Staff Emeritus
Science Advisor
Gold Member
Re: Re: Re: Will a conveyor belt push a hovercraft along?

Originally posted by LURCH
So the hovercraft will experience some slight drag in the direction of surface movement.
I believe I explicitly said that!

- Warren

#### Izzard

Re: Re: Re: Will a conveyor belt push a hovercraft along?

Thank you for these comments, you two.

Originally posted by LURCH
Of course, your friends "hoverboard" being of video-game design, it might be hovering magnetically, or antigravitationally, ni which case the specifics of the mechanism would make all the difference.
Right! So is there a situation where you can be fairly sure that moving the 'ground' will also move the hovercraft?

For example, if I have a 'large', traditional hovercraft, big enough to carry a few people, hovering over a wooden area which is, say, 100m x 100m and no part of the craft is touching that surface. If we then slowly push the wooden area along, can we affect the craft enough to move it along too? If we move the wood too briefly and or/quickly, inertia negates movement of the craft (tablecloth/crockery style). Perhaps moving it too slowly allows the wood to creep past underneath without moving the hovercraft...? Is there a sweet spot where the speed of the 'conveyor' would eventually move the hovercraft or will the other forces in the real world always prevent the craft moving by an appreciable amount?

#### LURCH

Science Advisor
Re: Re: Re: Re: Will a conveyor belt push a hovercraft along?

Originally posted by chroot
I believe I explicitly said that!

- Warren
I'm sorry chroot, I thought you were talking only about the ambient air in the room (especially that right close to the conveyor) being moved along, and that would move the hovercraft. What then did you mean by, "In a vacuum, nothing would happen at all"?

Izzard, in the scenario you propose, the hovercraft would move when the board is moved, and in the same direction, too. It just wouldn't move very much. I can't think of a stuation ni which the force you apply to the board would be transferred to the craft with enough efficiency so that the two become synchronised, but I'll let my subconscious gnaw at it for a while and see what it regurgitates.

#### chroot

Staff Emeritus
Science Advisor
Gold Member
Well, I guess you're right LURCH -- a hovercraft in a vacuum wouldn't even make much sense!

The hovercraft will move along with the underlying surface best when it's moved more slowly. That's why you're not arriving at a clear answer, LURCH: the only time when the hovercraft will have the same velocity as the underlying surface is when the underlying surface is not moving!

- Warren

#### Izzard

I'm delighted it's making other people have to thing hard too! Very interesting.

#### LURCH

Science Advisor
Originally posted by chroot
Well, I guess you're right LURCH -- a hovercraft in a vacuum wouldn't even make much sense!

- Warren
Now that's the question that's puzzling me; exactly what would a hovercraft do in a vacuum? Obviously, ducted fans pointed inward would give no lift at all. The air for the "air cusion" would have to be supplied by a tank of compressed gas of some sort being slowly released into the hoverskirt. Or maybe a heating coil is boiling water under there, or a hose running in from outside the vacuum chamber supplies the air. Either way, what would the vehicles behavioral characteristics be?

On the one hand, I can see that zero pressure outside the hoverskirt would mean that you need very little air inside to keep it inflated. But on the other hand, it would also seem that having zero pressure outside would mean that the air would get sucked out around the bottom faster than you could replace it. I wonder which would be the dominant factor?

#### Izzard

My own hunch is that any air you release/expand will just go towards filling the void and that the craft can't rise until there is a certain pressure of air in the 'room' for it to rise in. Don't know what that pressure threshold would be. ..maybe a function of the mass of the aircraft? Anybody got a bell jar, pump and tiny model hovercraft? :)

#### NateTG

Science Advisor
Homework Helper
It also depends on the belt.

If the belt is somewhat strechy, then you could get a situation where the hovercraft makes a dent in the belt which would allow for significantly stronger interaction between the sub and the hovercraft.

If the belt is made of mesh then the hovercraft would come to rest on it, and be affected by the belt's movement.

#### chroot

Staff Emeritus
Science Advisor
Gold Member
Re: It also depends on the belt.

Originally posted by NateTG
If the belt is somewhat strechy, then you could get a situation where the hovercraft makes a dent in the belt which would allow for significantly stronger interaction between the sub and the hovercraft.

If the belt is made of mesh then the hovercraft would come to rest on it, and be affected by the belt's movement.
Those are both very good points!

- Warren

#### Njorl

Science Advisor
OK, just to be irritating - a stretchy belt would cause the craft to move in the opposite direction of the belt.

Call the end from which the belt emerges the front, and the other end the back.

The whole area of the belt under the craft is depressed. As the belt exits from the front, it remains depressed for some brief period of time. The area at the back of the craft is less depressed as it begins passing under the craft. The larger gap at the front allows more air to escape. Conservation of momentum demands that the craft move in the opposite direction of the belt.

Njorl

#### NateTG

Science Advisor
Homework Helper
Note that I didn't claim that the dent would cause the hovercraft to move forward. ;)

But there would be more pressure on the side where the belt is closer to the hovercraft which indicate that the hovercraft should move with the belt.

Ugh. This would be a *really* ugly problem to do on paper. Fluid dynamics for the air, the streching of the belt in two dimensions, and they're all moving. Also not the kind of experiment that's likely to get you funding.

#### Mad_Gouki

the hovercraft is displacing air beneath it... kind of like the bernouli effect but not exactly...
no, the hovercraft will stay stationary with something moving under it... thats how they can float on water... the hovercraft makes an air pocket of sorts... which cushiones the craft from the ground, but because the actual air isnt moving with the conveyor belt, the hovercraft wouldnt move... or if you want to get really detailed, yes, the hoverraft will move on the coonveyor belt, but it will be so minute that it wont be noticeable...

now if the skirt of the hovercraft is TOUCHING the conveyor belt... yeah, that would make it move...

but the reason it does that in that game is because they tried to take a shortcut and leave some physics stuff out, so they made the model higher off the ground... which means if you put the hovercraft on a conveyor belt, it will move with it... simple solution to making a hovercraft....

if you think about th3 fundamental parts... the air being pushed downwards by the hovercraft, the hovercraft itself, and the conveyor... the air being pushed down doesnt have any treal physical link between the hover craft and the conveyor belt... its simple, no, it shouldnt be moving

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