# Flight and the Conveyor Belt

**URL:** <https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759>\
**Category:** Cecil's Columns/Staff Reports\
**Created:** [February 3, 2006, 12:25am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759 "2006-02-03T00:25:10Z")\
**Posts on this page:** 20\
**Page:** 9

<div class="post-metadata">

**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\
**Post date:** [February 4, 2006, 4:50pm UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/161 "2006-02-04T16:50:56Z")

</div>

All right, then, I’m going to repost something from the _other_ thread about force transferrence. First of all, let me point out again that the answer to this question **depends on the assumptions you’re making** about what’s happening in the problem.

There’s nothing wrong with interpreting “wheel speed” as “hub speed relative to the ground” or “tire diameter speed.” There’s nothing wrong with assuming no friction or massless tires (or high friction or high mass). There’s nothing wrong with pointing out that you doubt a _physical_ system like this could be fabricated, for a 747 at full thrust. But for heaven’s sake, _state your assumptions_.

Now, with that over. I see that a number of people (including **Cecil** , I might add) are forgetting that rotational acceleration of the tires will produce a force on the airplane. Nothing wrong with assuming massless wheels, but you’ve gotta _say so._ So let’s go to the basics and talk about forces and force transfer. Let’s talk about forces in the context of, say, a wheel:

```auto

        *******
     ****
   ****
  * *
 * *
 * *
 * O *
 * *
 * *
  * *
   ****
     ****
        *******

```

The wheel is round, and it has some mass, m, with a center of mass in the center of the wheel at “O”. It’s also got rotational inertia, I. One way to think of mass is as _the resistance of the wheel to motion when a force is applied._ In the same way, rotational inertia can be thought of as _the resistance of the wheel to rotation when a torque is applied._ With me so far?

In addition, let’s assume that the wheel has a bearing in the center, at the “O”. The other side of the bearing is connected to Something. We haven’t defined what Something is, yet, but we will. Be patient. Let’s make this simple and assume the bearing is _frictionless_. We can add friction in later if we want, but let’s keep it simple for now. Now, the bearing is a pin joint–it allows both horizontal and vertical forces between the wheel and the Something that it’s connected to, but does not allow torques to be transferred.

One last thing. Let’s make this wheel and the associated forces as simple as possible. So let’s ignore gravity and everything else. No gravity, no treadmill, no Earth, no nothing. This is, right now, just a wheel in space connected to Something through the bearing. OK. Got it?

Now let’s change the story.

```auto

        *******
     ****
   ****
  * *
 * *
 * *
 * O *<----F
 * *
 * *
  * *
   ****
     ****
        *******

```

I’ve added a force F on the wheel; this force F passes through the center of mass. This force is, as drawn, _unbalanced_, and it isn’t yet the whole story. From here on out, a few different things could happen.

Suppose the wheel isn’t connected to _anything_ at the bearing (the Something is Nothing, in other words). In this case, there’s no way the force F can be resisted, and the entire wheel will accelerate to the left. The acceleration, in fact, will obey Newton’s law, F = ma.

OK, but what if the wheel is actually connected to Something? What if that Something was the ground, and the wheel is prevented from actually moving to the left? In that case, there will be a _reaction force_ at the bearing. The wheel will push on the ground, through the bearing, and _the ground will push back:_

```auto

        *******
     ****
   ****
  * *
 * *
 * *
 * R---->O *<----F
 * *
 * *
  * *
   ****
     ****
        *******

```

The ground will push back, in fact, so that **R exactly equals F**. This is the key: _because the wheel does not move, the forces **must** be add to zero._ If they didn’t add to zero, the wheel would accelerate to the left or right. But it doesn’t. So the forces must be balanced, and the force F is transmitted to the ground.

Another possible thing that could happen would be that the Something that the wheel is connected to is something very massive, but moveable, which has a mass M. In that case, as soon as the force F is applied, _everything_ accelerates–both the wheel and the Something–at an acceleration of F = (M+m)a. In this case, there will still be a reaction R on the bearing, but the reaction R will be _less_ than F. How much less is left as an exercise to the reader.

All right, got all that? Now let’s do something a little different. Let’s move the force:

```auto

        *******
     ****
   ****
  * *
 * *
 * *
 * O *
 * *
 * *
  * *
   ****
     ****
        ******* <----F

```

Now the force F is _no longer a the center of mass_. How does that change things?

First or all, let’s go back to the assumption that the wheel is just free in space–nothing is connected to the bearing. In this case, the wheel will _still_ accelerate to the left in accordance with F = Ma. The force F is _still_ unbalanced, and the unbalanced force must result in an acceleration. However, the wheel will also _rotationally accelerate_. The force F is not through the center of mass, and that creates a torque T = Fr. This torque rotationally accelerates the wheel through the rotational equivalent of Newton’s law: T = I[symbol]a[/symbol] ([symbol]a[/symbol] being rotational acceleration). So the wheel will begin to move to the left, _and_ spin clockwise.

Now let’s assume, instead, that the wheel is connected to the ground at the bearing–the Something is the ground again. This gives a case like so:

```auto

        *******
     ****
   ****
  * *
 * *
 * *
 * R---->O *
 * *
 * *
  * *
   ****
     ****
        ******* <----F

```

Here’s the key question: does the center of mass of the wheel accelerate to the left? No! it’s connected to the ground! It _can’t_ move to the left. And because it can’t move to the left, the forces _must_ add to zero, and the force R equals the force F.

Of course, the difference between this case and the one above where the force F was pointed toward the center of mass is that now _the wheel will spin_. And we can calculate exactly how much it will spin: the two forces set up a torque T = Fr, which rotationally accelerates the wheel through the rotational equivalent of Newton’s law: T = I[symbol]a[/symbol].

So all that leads to the real question: how does this apply to an airplane? The point is, to keep an airplane from moving, you need to apply a force F to the plane that is equal and opposite the engine thrust. Assuming the plane won’t flip end-for-end or anything silly like that (adding back gravity and so forth), it _doesn’t matter_ if that force is applied to the nose of the airplane, or the tail, or the landing gear.

It doesn’t even matter if the force is applied _at the bottom of the tires_. That force will still be transmitted to the plane and oppose the engine force. Given that this is a thought experiment, it _is_ possible to apply an opposing force to keep the plane in place via the tires. An accelerating treadmill will accelerate the wheels, which will **transmit the force to the plane**. And, to counteract a 747 at full thrust, that acceleration is apt to be very large. A rubber-band powered toy? Not so large.

---

<div class="post-metadata">

**Author:** ![GlacialMaximum](https://avatars.discourse-cdn.com/v4/letter/g/e8c25b/32.png) [@GlacialMaximum](https://boards.straightdope.com/u/GlacialMaximum)\
**Post date:** [February 4, 2006, 5:31pm UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/162 "2006-02-04T17:31:00Z")

</div>

> [@zut](#):
>
> The gist of these comments being that the conveyor belt **cannot** impart enough force to the plane to counteract the thrust of the plane’s engine. This _could_ be true, if you assume either (a) some real-world limitations on the acceleration of the belt, or (b) that the wheels are massless. Either of these is a perfectly fine assumption.
> 
> However, _without_ those assumptions, there is a coupling betwee the belt and the plane through the acceleration of the wheels. If the belt accelerates, it will impart a force on the wheel, accelerating the wheel. The wheel will in turn impart this force on the plane. If the acceleration is high enough, **the force will counteract the force of the engine thrust.**

But the wheels aren’t what’s moving the plane forward! They just roll along as the plane moves! Spinning the wheel is not the same as moving the plane forward - if it were, we would be discussing a wheel-driven plane, which is an absurdity.

---

<div class="post-metadata">

**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\
**Post date:** [February 4, 2006, 5:46pm UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/163 "2006-02-04T17:46:05Z")

</div>

You are making two different statements:

1. “the wheels aren’t what’s moving the plane forward”: competely true.

2. “wheels have no impact on the plane’s acceleration”: not true.

Force _from the conveyor_ is transmitted _through_ the wheels _to_ the plane. If the force is high enough, it will counteract the engine thrust. SImple as that.

---

<div class="post-metadata">

**Author:** ![Christi7df](https://avatars.discourse-cdn.com/v4/letter/c/57b2e6/32.png) [@Christi7df](https://boards.straightdope.com/u/Christi7df)\
**Post date:** [February 4, 2006, 5:55pm UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/164 "2006-02-04T17:55:56Z")

</div>

> [@zut](#):
>
> If the force is high enough, it will counteract the engine thrust. SImple as that.

It is impossible to build a belt that can counteract the force of the airplanes engines through the free spinning wheels alone. The speed of the belt in reverse would have to be many orders of magnitude greater than the takeoff speed of the airplane to accomplish this.

Read my post on the previous page.

According to the way the puzzle is usually written, the belt is not even trying to hold the airplane still.

---

<div class="post-metadata">

**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\
**Post date:** [February 4, 2006, 6:26pm UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/165 "2006-02-04T18:26:42Z")

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> [@mpladd](#):
>
> The best description I have seen so far is the rollerskates on a treadmill. You stand on the treadmill with rollerskates, and what happens, if you do absolutely nothing but stand there? You’ll stay in the same place. Granted, enough friction can be built up against the wheels to propell you backwards.

Real life results with a small car and a hand pulled piece of paper:  
Paper pulled very very very slowly:  
Wheels don’t spin at all, car moves backwards at same speed of paper.

Paper pulled at moderate pace:  
Wheels spin and car moves backwards at about 1/2 the speed of the paper.

Paper pulled very quickly:  
Wheels spin, car does not move backward at all.  
While I agree the rollerskater would not move backward at the same rate as the conveyor belt, I think you are underestimating friction, you will not just stay in one place.

---

<div class="post-metadata">

**Author:** ![robby](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/robby/32/11048_2.png) [@robby](https://boards.straightdope.com/u/robby)\
**Post date:** [February 4, 2006, 10:13pm UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/166 "2006-02-04T22:13:46Z")

</div>

> [@Christi7df](#):
>
> It is impossible to build a belt that can counteract the force of the airplanes engines through the free spinning wheels alone…

I’m going to stay away from whether or not it’s actually possible to _build_ such a belt for a full-size airplane. Let’s consider this as a thought experiment.

That being said, your statement is simply not true, depending on your assumptions about the mass of the wheels, mass of the plane, the amount of bearing friction, the amount of engine thrust, and the speed and acceleration of the belt in the reverse direction.

The **speed** of the belt is somewhat less relevant than the **acceleration** of the belt in the reverse direction. If the wheel bearings are frictionless, the belt speed is actually irrelevant.

> [@Christi7df](#):
>
> …Interestingly enough, I have read through this thread and other threads in other forums about this. I have seen several people convert from “it won’t fly” to “it will fly” but I have never seen anyone converted the other way.

In our last thread, I went from “it will definitely fly” to “it depends on your assumptions.” I had neglected to consider the rotational inertia of the wheels in a situation where the belt is accelerating backwards.

Read **zut** ’s posts.

---

<div class="post-metadata">

**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\
**Post date:** [February 4, 2006, 11:41pm UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/167 "2006-02-04T23:41:39Z")

</div>

> [@Christi7df](#):
>
> Read my post on the previous page.
> 
> According to the way the puzzle is usually written, the belt is not even trying to hold the airplane still.

I did read it. For the most part, your post is correct. I think, in fact, that pretty much everyone agrees that _if belt is not even trying to hold the airplane still_ (i.e. the belt just matches the plane fuselage’s speed), the airplane will take off without much problem. I’m not sure why that’s even a question; why _wouldn’t_ it take off? However, if you examine the more interesting case where the belt _does_ try to keep the plane stationary, the answer _depends on the other assumptions you make._

> [@Christi7df](#):
>
> It is impossible to build a belt that can counteract the force of the airplanes engines through the free spinning wheels alone. The speed of the belt in reverse would have to be many orders of magnitude greater than the takeoff speed of the airplane to accomplish this.

Yes and no. If you mean, “Assuming that we’re talking about a large plane, it is technologically impossible to physically build a belt that would prevent the plane from taking off,” then I’m inclined to agree.

However, the problem is more fun if you assume it’s a thought experiment. Allow the belt to do whatever it wants to do. Infinitely strong, capable of prodigous acceleration, etc. In this case, the belt will accelerate the wheels and transmit a force to the plane. (The acceleration’s the key here, not the speed, although a real wheel bearing would have some frictional effects, etc, ect, as **robby** says.) Higher acceleration, higher force. High enough acceleration, and the force balances out the engine thrust.

---

<div class="post-metadata">

**Author:** ![Christi7df](https://avatars.discourse-cdn.com/v4/letter/c/57b2e6/32.png) [@Christi7df](https://boards.straightdope.com/u/Christi7df)\
**Post date:** [February 5, 2006, 2:17am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/168 "2006-02-05T02:17:45Z")

</div>

> [@zut](#):
>
> However, the problem is more fun if you assume it’s a thought experiment. Allow the belt to do whatever it wants to do. Infinitely strong, capable of prodigous acceleration, etc. In this case, the belt will accelerate the wheels and transmit a force to the plane. (The acceleration’s the key here, not the speed, although a real wheel bearing would have some frictional effects, etc, ect, as **robby** says.) Higher acceleration, higher force. High enough acceleration, and the force balances out the engine thrust.

That does not work either. Because if you can give the belt infinite capability to hold back the airplane, I can give the airplane infinite capability to overcome any resistance.

Then you just have a paradox and are not living in the real world.

---

<div class="post-metadata">

**Author:** ![Christi7df](https://avatars.discourse-cdn.com/v4/letter/c/57b2e6/32.png) [@Christi7df](https://boards.straightdope.com/u/Christi7df)\
**Post date:** [February 5, 2006, 2:31am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/169 "2006-02-05T02:31:40Z")

</div>

> [@robby](#):
>
> In our last thread, I went from “it will definitely fly” to “it depends on your assumptions.” I had neglected to consider the rotational inertia of the wheels in a situation where the belt is accelerating backwards.

You are the first I have seen going from it will definately fly to even being doubtful.

The wheels will only rotate twice as fast and the rolling resistance will actually reduce as the wheels spin faster.

If you want to restrict it to being a problem for a large jet, then you don’t comprehend just how powerful those big jet engines are.

It is really a simple thing to understand that the wheels don’t matter. You just have to look at it correctly.

I think that I have done all that I can do to enlighten here.

The bottom line is that Cecil is correct.

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<div class="post-metadata">

**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\
**Post date:** [February 5, 2006, 2:45am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/170 "2006-02-05T02:45:49Z")

</div>

I don’t have to give the belt “infinite capability to hold back the airplane.” It just needs to be _strong enough_ to withstand the forces required. I’m using “infinitely strong, etc.” as a shorthand notation so I don’t have to calculate exactly how strong it would have to be.

And sure you could “give the airplane infinite capability to overcome any resistance,” if you wanted to. But this isn’t a contest, it’s a thought experiment. Given one set of assumptions, the airplane stays in place. Given another set of assumptions, it takes off.

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<div class="post-metadata">

**Author:** ![Christi7df](https://avatars.discourse-cdn.com/v4/letter/c/57b2e6/32.png) [@Christi7df](https://boards.straightdope.com/u/Christi7df)\
**Post date:** [February 5, 2006, 3:39am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/171 "2006-02-05T03:39:43Z")

</div>

You have to give the belt capability beyond any practical reason.

The plane already exists with the capability to overcome any belt that anyone can practically build.

So, if you want to give the belt capability beyond any practical reason then I give the plane power beyond any practical reason.

That is still a magical world and you still have a paradox.

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<div class="post-metadata">

**Author:** ![Christi7df](https://avatars.discourse-cdn.com/v4/letter/c/57b2e6/32.png) [@Christi7df](https://boards.straightdope.com/u/Christi7df)\
**Post date:** [February 5, 2006, 3:57am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/172 "2006-02-05T03:57:07Z")

</div>

Anyway, in the puzzle as it is usually stated, the belt is not even trying to hold the airplane still. So, the belt (no matter how powerful) does not prevent the plane from taking off.

---

<div class="post-metadata">

**Author:** ![zut](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zut/32/2875_2.png) [@zut](https://boards.straightdope.com/u/zut)\
**Post date:** [February 5, 2006, 4:09am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/173 "2006-02-05T04:09:23Z")

</div>

Jiminy Christmas.

1. This ain’t a contest. We’re exploring what happens in a thought experiment given different starting assumptions. There’s no need to counter with bigger engines and more massive planes just to win. There’s nothing _to_ win.

2. You are _completely correct_ that an acceptable answer to this problem is: “Assuming that we’re talking about a large plane, it is technologically impossible to physically build a belt that would prevent the plane from taking off.” There is nothing wrong with that answer, and it implicitly includes the assumptions that a) we’re talking about a large plane, and b) we’re limiting the question to physically available materials.

3. Nonetheless, there are other interpretations of the question, which to my mind are more interesting. Hypothetical thought experiments: let’s assume the treadmill can accelerate as fast as we want. Let’s assume the tires won’t blow from the heat. Let’s assume the jet has an infinite supply of fuel. What happens in these cases? One more time: _The answer depends on your assumptions._

4. There is no paradox, and despite what Cecil says, there never was any. There’s nothing paradoxical about any interpretation of the question I can come up with.

(and, on preview)

1. Sure, if the belt is _not_ trying to hold the airplane still, it’ll take off. Completely correct. But, seriously, how is that situation even a “puzzle”? Why would anyone think the plane _wouldn’t_ take off? That might be the most usual statement (or interpretation, if you prefer) of the puzzle, but it’s not very interesting.

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<div class="post-metadata">

**Author:** ![frankenberrycat](https://avatars.discourse-cdn.com/v4/letter/f/eada6e/32.png) [@frankenberrycat](https://boards.straightdope.com/u/frankenberrycat)\
**Post date:** [February 5, 2006, 4:33am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/174 "2006-02-05T04:33:10Z")

</div>

The problem with some of these arguments about a “super” treadmill is that the original questions said it moved at the same speed as the airplane in the opposite direction. Since the thing would probably carry the airplane backwards if the engines weren’t started, slowly at first than accelerating, the engines must be running. Could you throttle the engines down and prevent the airplane from moving? Sure.

But here’s the point everyone has missed: “There are some difficulties with the wording of the problem, specifically regarding how we define speed, but the spirit of the situation is clear.”

The wording has some problems, since a treadmill can’t move at 150 MPH unless you turn it upside down. If the plane is moving forward on the treadmill that is moving at 150 MPH, it’s still moving foward.

I other words, you can create a conundrum such as “Can God create a rock so big that He can’t move it?” as an excersize if futility, or you can look at the realistic logic that is being stated. Obviously, the wording is the way it is to trip up anyone answering the question.

So, to further the discussion, let’s throw away the treadmill.

Suppose a seaplane was taking off into a 100 MPH wind, would the water current, also at 100 MPH, in the opposite direction slow the airplane down enough so that it couldn’t take off?

CPL

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<div class="post-metadata">

**Author:** ![Coastal\_Ron](https://avatars.discourse-cdn.com/v4/letter/c/67e7ee/32.png) [@Coastal\_Ron](https://boards.straightdope.com/u/Coastal_Ron)\
**Post date:** [February 5, 2006, 4:48am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/175 "2006-02-05T04:48:13Z")

</div>

> [@mpladd](#):
>
> I’m sorry, but you are incorrect. For any vehicle to move forward it must overcome the force, if any, opposing it. There is no force directly opposing the plane itself, only the freely rotating weels. start the engine and the plane will move forward.
> 
> Period.

Go to your nearest airport, and ask someone if you can drag around their small plane. There is a lot of mass to an airplane, and this is applied to small diameter wheels that are packed in grease.

Taking into account real-world physics (no frictionless bearing or other nonsense stuff), and taking into account what the original question states - “This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)”, I say the plane will not take off, but will instead suffer a tire blow-out and cause some kind of bad calamity. This will happen if the pilot continues to add power past the point of the safe rotationaly speed of the wheels. Why?

If the conveyory belt speeds up to counteract any forward movement of the airplane, and the airplane is not moving relative to the ground, then it will not take off. What’s causing the plane to be held back is the friction of the wheels against the conveyor belt. I can imagine the pilot smoothly moving the throttles forward, and the net effect (because the conveyor keeps picking up speed to keep the plane in the same spot on the conveyor) is that the airplanes wheels keep spinning faster and faster.

Remember, the full weight of the airplane is still on the wheels (it has not transferred to the wings because there is no wind moving over the wings), so if you have a Cessna 172 on the conveyor, then the wheels are carrying ~2,000lbs of weight. These wheels are not made for continuous high-speed use, and the friction will increase to some degree the faster the wheels spin (not to mention heat build-up over time). At some point too, the rubber tires will spin too fast and fail. The only question is which will fail first - the bearings or the tires…this can only end in tears…

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<div class="post-metadata">

**Author:** ![Christi7df](https://avatars.discourse-cdn.com/v4/letter/c/57b2e6/32.png) [@Christi7df](https://boards.straightdope.com/u/Christi7df)\
**Post date:** [February 5, 2006, 4:56am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/176 "2006-02-05T04:56:30Z")

</div>

> [@frankenberrycat](#):
>
> Suppose a seaplane was taking off into a 100 MPH wind, would the water current, also at 100 MPH, in the opposite direction slow the airplane down enough so that it couldn’t take off?

Actually that is easy. But I’m not sure that what you said is what you meant.

Taken as stated, that means that the water current is pushing on the airplane floats from behind. So, in this case the water current would actually assist the airplane in taking off.

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<div class="post-metadata">

**Author:** ![mconner](https://avatars.discourse-cdn.com/v4/letter/m/e8c25b/32.png) [@mconner](https://boards.straightdope.com/u/mconner)\
**Post date:** [February 5, 2006, 6:15am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/177 "2006-02-05T06:15:55Z")

</div>

> [@zut](#):
>
> 1. You are _completely correct_ that an acceptable answer to this problem is: “Assuming that we’re talking about a large plane, it is technologically impossible to physically build a belt that would prevent the plane from taking off.”.

Well, the conveyor could simply be covered with some really sticky goo. That would increase the rolling resistance significantly. But I suppose that’s not in the spirit of the thing.

So if we are to be practical, let’s be practical: The original question stated: _“This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).”_

Assuming “plane speed” to be relative to a stationary observer, the wheels will be spinning twice as fast as normal at any point during takeoff. Being practical, we need to consider what the conveyor belt is made of. If the material is flexible – as would be required for any belt – its needs to be held up by something. I’m imagininge a lot of little rollers underneath the belt, just like the illustration for the article, only for the entire length of a runway. Given a heavy plane, I would think the belt would deform between the rollers. This would increase resistance, probably considerably, unless the rollers were small, relative to the belt thickness. So we have a heavy plane with wheels spinning twice as fast as normal over a relatively bumpy runway. Oh, and presumably, the runway would be a source of heat for the tires, rather than a sink, since it would heat up from friction with its rollers. This would make the tires stickier as they heat up. Doesn’t sound much better than the goo. My point is, if you are going to be practical about the belts capabilities (like speed), you also have to be practical about its other properties.

Or we could take the question in the spirit in which it was meant, a thought experiment. My take: assuming a typical jet (albeit one with indistructible landing gear and tires), and given an ideal conveyor, and assuming that the conveyor was supposed to run fast enough to impart a backward force on the plane (by way of the tires) equal but opposite to that of the jet’s engines (the original intent of the question, I suspect, if not the wording in this case), then the plane could not take off, because it would not move, and there would therefore be no lift. On the other hand, assuming all of the above save for an ideal but same-speed-as-plane conveyor, I would imagine the plane would take off just fine.

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<div class="post-metadata">

**Author:** ![frankenberrycat](https://avatars.discourse-cdn.com/v4/letter/f/eada6e/32.png) [@frankenberrycat](https://boards.straightdope.com/u/frankenberrycat)\
**Post date:** [February 5, 2006, 7:01am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/178 "2006-02-05T07:01:52Z")

</div>

> [@Christi7df](#):
>
> Actually that is easy. But I’m not sure that what you said is what you meant.
> 
> Taken as stated, that means that the water current is pushing on the airplane floats from behind. So, in this case the water current would actually assist the airplane in taking off.

Umm, no, what I actually meant is that the wind is causing the current, of course, and the current is against the airplane. In other words, if your going _into_ a 100 MPH wind, you’re also going _against_ a 100 MPH current, correct?

The problem I see is that people are either over-thinking this or trying to rationalize their wrong answer…

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<div class="post-metadata">

**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\
**Post date:** [February 5, 2006, 7:37am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/179 "2006-02-05T07:37:42Z")

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I haven’t the time nor the inclination to read through and correct all the physics mistakes that are undoubtably in this thread. I am certain that some are claiming or believe that no force can be transimitted from the treadmill to the plane with frictionless bearings. This is 100% undoubtably WRONG. Friction between a surface and a rolling object does slow down the forward motion of the rolling object. If you don’t believe me perform the following experiment:

Acquire two different cans. Suggestions are soup cans with one being a water base soup (i.e. chicken noodle, vegetable, tomato etc.) and one being a cream based soup (cream of potato, clam chowder, cream of brocolli etc.). Those are the best ones to use becuase they are the same shape of can and have similar masses thus equalizing air resistance. If you don’t have those on hand two soda cans, one empty and one full, two water bottles, one empy and one full will do.

Once you have the cans get some books or something to prop up one end of a coffee table so that it has an inclined surface. Hold your cans at the top of the table and release at the same time. You should see that the empy can, bottle or water based soup will easily beat the full can, bottle or cream based soup. Why? Becuase the friction force between the table and the cans resist the linear motion of the cans.

Note: Ensure that the cans are actually rolling down the table not sliding.

If you have access to a treadmill put a cylinder, ball or anything that can roll on a motionless treadmill. Start up the treadmill and watch it go flying off of the back. It goes flying off the back becuase of the frictional force between the treadmill and the base of the can.

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<div class="post-metadata">

**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\
**Post date:** [February 5, 2006, 7:51am UTC](https://boards.straightdope.com/t/flight-and-the-conveyor-belt/342759/180 "2006-02-05T07:51:38Z")

</div>

> [@treis](#):
>
> Once you have the cans get some books or something to prop up one end of a coffee table so that it has an inclined surface. Hold your cans at the top of the table and release at the same time. You should see that the empy can, bottle or water based soup will easily beat the full can, bottle or cream based soup. Why? Becuase the friction force between the table and the cans resist the linear motion of the cans.

Whoops I wrote this backwards. The full can, bottle or cream soup will beat the empy can, bottle or water based soup. See [this page](http://solomon.physics.sc.edu/~tedeschi/demo/demo12.html) for an explanation and a video of the experiment.

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