# Plane on a treadmill **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [September 6, 2008, 8:09pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380 "2008-09-06T20:09:18Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![sturmhauke](https://avatars.discourse-cdn.com/v4/letter/s/e47c2d/32.png) [@sturmhauke](https://boards.straightdope.com/u/sturmhauke)\ **Post date:** [September 7, 2008, 8:08am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/21 "2008-09-07T08:08:40Z")
> [@Zhing](#): > > If the plane is still, the treadmill won’t move at all. If the plane is still, and we’re assuming there’s no headwind, then nothing at all interesting is happening anyway. What does this have to do with anything? ---
**Author:** ![Hilarity\_N.Suze](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hilarity_n.suze/32/6223_2.png) [@Hilarity\_N.Suze](https://boards.straightdope.com/u/Hilarity_N.Suze)\ **Post date:** [September 7, 2008, 8:49am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/22 "2008-09-07T08:49:56Z")
This will not end [del]well[/del] ever. ---
**Author:** ![DSYoungEsq](https://avatars.discourse-cdn.com/v4/letter/d/c6cbf5/32.png) [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)\ **Post date:** [September 7, 2008, 12:59pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/23 "2008-09-07T12:59:09Z")
> [@Johnny\_L.A](#): > > I disagree. As soon as the airplane tries to move forward, the treadmill will speed up to match the speed of the wheels. But the airplane isn’t connected to the treadmill except by a couple inches of rubber. There is no connection between the engine and the wheels. The wheels are unpowered. Since the propeller is moving the airplane through the air and not providing thrust against the treadmill, the aircraft will move forward and take off. The wheels will spin at twice the speed they would in a normal takeoff. Johnny, PLEASE read the multiple threads on this. DFTH is correct, IF you make an assumption about what the thought problem is asking. This is covered in an excellent compilation of the various possibilities posted by Zut(?) in several of the threads on this subject. Zhing, the trouble with your approach is this: at the moment the plane begins to apply power, it tries to move forward. When it does, the treadmill has to try to move backward to counteract that effort. Once that happens, the plane and the treadmill are off and running. It’s similar to an issue of limits, though what Zeno would make of the question, goodness knows. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [September 7, 2008, 3:19pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/24 "2008-09-07T15:19:46Z")
> [@DSYoungEsq](#): > > DFTH is correct, IF you make an assumption about what the thought problem is asking. This is covered in an excellent compilation of the various possibilities posted by Zut(?) in several of the threads on this subject. I assume you mean [this post](http://boards.straightdope.com/sdmb/showpost.php?p=7179005&postcount=138). It all depends on the assumptions you make. In **zut** ’s post each argument is countered by yet another assumption. In the end, the question can be reworded to ‘If you could build a treadmill such that it is impossible for an airplane to take off from it, will the airplane take off?’ ---
**Author:** ![Don\_t\_fight\_the\_hypothetical](https://avatars.discourse-cdn.com/v4/letter/d/59ef9b/32.png) [@Don\_t\_fight\_the\_hypothetical](https://boards.straightdope.com/u/Don_t_fight_the_hypothetical)\ **Post date:** [September 7, 2008, 3:29pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/25 "2008-09-07T15:29:19Z")
> [@Johnny\_L.A](#): > > There is no connection between the engine and the wheels. Yes there is. It is the aircraft itself. Think of it this way, would your above statement work if the wheels were tied to the tarmac? Of course not. The wheels are connected to the engine by the airframe, if the wheels can’t move forward in relationship to the ground the treadmill is resting on, neither can the plane. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [September 7, 2008, 3:40pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/26 "2008-09-07T15:40:50Z")
> [@Don\_t\_fight\_the\_hypothetical](#): > > Yes there is. It is the aircraft itself. Think of it this way, would your above statement work if the wheels were tied to the tarmac? Of course not. The wheels are connected to the engine by the airframe, if the wheels can’t move forward in relationship to the ground the treadmill is resting on, neither can the plane. But the wheels don’t do anything. They just roll around an axle. They have nothing to do with the thrust of the aircraft. All they’ll do is spin twice as fast as they normally would and the airplane would fly. ---
**Author:** ![Telemark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/telemark/32/372_2.png) [@Telemark](https://boards.straightdope.com/u/Telemark)\ **Post date:** [September 7, 2008, 3:45pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/27 "2008-09-07T15:45:05Z")
> [@Johnny\_L.A](#): > > But the wheels don’t do anything. They just roll around an axle. They have nothing to do with the thrust of the aircraft. All they’ll do is spin twice as fast as they normally would and the airplane would fly. That’s only in a perfect world with frictionless bearings. In our world, you can indeed impart some force to the plane through the wheels. Which world you choose to set the problem in will determine which answer is correct. ---
**Author:** ![Cervaise](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cervaise/32/16693_2.png) [@Cervaise](https://boards.straightdope.com/u/Cervaise)\ **Post date:** [September 7, 2008, 3:46pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/28 "2008-09-07T15:46:49Z")
The wheels spin freely. They are connected physically but they are not tied to its movement. The movement of the aircraft is tied to the surrounding airspace via the propellers. Metaphor: You put on a pair of roller skates. You put a long conveyor belt in the middle of a room. You tie a rope to the wall of the room. You take hold of the rope, stand on the conveyor belt, and turn it on. Follow so far? You are standing on the conveyor, holding the rope. The rope holds you in place while the conveyor belt turns below you and your wheels spin on the belt. Now you begin pulling yourself forward on the rope. What happens? This is analogous to the airplane’s propellers pushing against the air. You move forward. So does the plane. The conveyor moving beneath you does not, and can not, have any effect on your pulling on the rope. Likewise, the conveyor under the airplane does not, and can not, have any effect on the propellers (or the jet engine, or whatever) pushing against the air. The plane moves forward. It takes off. Period. Yes, as covered in previous threads, there are potential complications depending on how the question is framed; if you allow a hypothetical conveyor that spins at an infinite rate, and an idealized aircraft whose frame and carriage will not be burned out by ludicrously high forces, it is possible to impart angular momentum that holds the aircraft in place. But that’s not how the question is commonly understood, and it takes high-level physics even to discuss the situation. As far as the problem is generally defined and understood, my rope-and-roller-skates analogy above demonstrates how and why the airplane moves on the belt, and how and why it takes off. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [September 7, 2008, 4:05pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/29 "2008-09-07T16:05:16Z")
> [@Telemark](#): > > That’s only in a perfect world with frictionless bearings. In our world, you can indeed impart some force to the plane through the wheels. Which world you choose to set the problem in will determine which answer is correct. But one of the common assumptions is that there is no friction, so that the wheels can spin as fast as they have to without melting or blowing up. It’s like saying, ‘All friction that would tend to prevent an airplane from taking off is allowed. All friction that would tend to allow an airplane to take off is not permitted.’ We’re back to ‘If you could build a treadmill such that it is impossible for an airplane to take off from it, will the airplane take off?’. ---
**Author:** ![Don\_t\_fight\_the\_hypothetical](https://avatars.discourse-cdn.com/v4/letter/d/59ef9b/32.png) [@Don\_t\_fight\_the\_hypothetical](https://boards.straightdope.com/u/Don_t_fight_the_hypothetical)\ **Post date:** [September 7, 2008, 4:33pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/30 "2008-09-07T16:33:52Z")
> [@Johnny\_L.A](#): > > But one of the common assumptions is that there is no friction, so that the wheels can spin as fast as they have to without melting or blowing up. It’s like saying, ‘All friction that would tend to prevent an airplane from taking off is allowed. All friction that would tend to allow an airplane to take off is not permitted.’ We’re back to ‘If you could build a treadmill such that it is impossible for an airplane to take off from it, will the airplane take off?’. This hill isn’t worth dying on so I’m probably not long for this thread, but… You have it backward. It is you who is introducing factors (not in the original question) that _allow_ the plane to take off. Why would you allow assumptions that are not part of our physical world? As I stated above, the introduction of “frictionless bearings” in the original thread was to facilitate the ‘It Can Take Off’ crowd. There was no bias in the query, no expectation to be met. The question was not, _“If you could build a treadmill such that it is impossible for an airplane to take off from it, will the airplane take off?”_ The question was ‘if a real plane was put on real treadmill such that the treadmill could counter the forward motion of the wheels, could the plane take off?’ I respect you **Johnny** , but in this instance you are trying to shoehorn the question to fit your answer. Friction is a way of the world. ---
**Author:** ![Don\_t\_fight\_the\_hypothetical](https://avatars.discourse-cdn.com/v4/letter/d/59ef9b/32.png) [@Don\_t\_fight\_the\_hypothetical](https://boards.straightdope.com/u/Don_t_fight_the_hypothetical)\ **Post date:** [September 7, 2008, 4:48pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/31 "2008-09-07T16:48:59Z")
> [@Cervaise](#): > > You put on a pair of roller skates. You put a long conveyor belt in the middle of a room. You tie a rope to the wall of the room. You take hold of the rope, stand on the conveyor belt, and turn it on. Follow so far? > > You are standing on the conveyor, holding the rope. The rope holds you in place while the conveyor belt turns below you and your wheels spin on the belt. > > Now you begin pulling yourself forward on the rope. What happens? Here is why your metaphor is not analogous, you have left out the most important part of the puzzle. You do not provide for the treadmill being able to match the forward motion of the skates. The whole reason for the question must surely have been this part. Your metaphor assumes (incorrectly) a constant conveyor speed - the same mistake the Mythbusters made. If you take your above analogy and speed the treadmill up to the point where the force of the friction is more than the force the skaters muscles can overcome, when he pulls nothing will happen. ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [September 7, 2008, 5:00pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/32 "2008-09-07T17:00:35Z")
> [@Don\_t\_fight\_the\_hypothetical](#): > > This hill isn’t worth dying on so I’m probably not long for this thread, but… On this we agree. [QUOTE=Don’t fight the hypothetical] You have it backward. It is you who is introducing factors (not in the original question) that _allow_ the plane to take off. [/quote] You may be right. It seems people modify the question to fit their agendas. As I understand it, the argument is this: Pro-Takeoff: The wheels are freewheeling. Thus, it makes no difference how fast the treadmill runs since the thrust is against the air and not the treadmill. Anti-Takeoff: But there is friction in the bearings, so the wheels are virtually connected to the engine. PT: Doesn’t matter. In the real world there’s no way the treadmill can spin fast enough to counter the airplane’s thrust against the air. At some point the bearings will fail and the airplane will simply skid along to take-off speed. AT: But what if the bearings were made of unobtanium so that they wouldn’t fail? It’s a thought experiment, after all. PT: Then you have what amounts to frictionless bearings. [QUOTE=Don’t fight the hypothetical] The question was not, _“If you could build a treadmill such that it is impossible for an airplane to take off from it, will the airplane take off?”_ The question was ‘if a real plane was put on real treadmill such that the treadmill could counter the forward motion of the wheels, could the plane take off?’ [/quote] In the real world the airplane would take off. This is how it works theoretically, and how it was demonstrated in the _Mythbusters_ experiments. But when assertions are made that the plane will take off, the AT side introduces unobtainium and infinite speeds. [QUOTE=Don’t fight the hypothetical] I respect you **Johnny** , but in this instance you are trying to shoehorn the question to fit your answer. Friction is a way of the world. [/QUOTE] Thank you. But I don’t think the PT side is the one doing the shoehorning. In the real world friction exists, as you say. This means that given a magical treadmill, the bearings will fail. There’s just no way there would be enough friction on the axle to prevent the airplane from taking off. Let’s look at it another way: You’re flying along in your Bugsmasher 150 at 100kts. You see an enormous Magical Treadmill whose belt is running at 100kts in a direction opposite to yours. Since it’s magical, the treadmill instantly adjusts to the airplane’s speed. The Bugsmasher 150 has a stall speed of 50kts, and you always make full-stall landings. At the instant you touch down your airspeed is 50kts and the treadmill is running at 50kts the other direction. What happens? A) Your Bugsmasher 150 comes to an immediate halt over a fixed point on the ground. B) Your Bugsmasher 150 shoots forward to 100kts. C) Your Bugsmasher 150 lands normally, but the wheels are rolling at 100kts. Obviously the answer is C. So on takeoff the wheels will simply be spinning twice as fast but the airplane will still take off. ---
**Author:** ![Don\_t\_fight\_the\_hypothetical](https://avatars.discourse-cdn.com/v4/letter/d/59ef9b/32.png) [@Don\_t\_fight\_the\_hypothetical](https://boards.straightdope.com/u/Don_t_fight_the_hypothetical)\ **Post date:** [September 7, 2008, 5:55pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/33 "2008-09-07T17:55:41Z")
> [@Johnny\_L.A](#): > > Thank you. But I don’t think the PT side is the one doing the shoehorning. In the real world friction exists, as you say. This means that given a magical treadmill, the bearings will fail. There’s just no way there would be enough friction on the axle to prevent the airplane from taking off. This really is the crux of it. I agree that even if we could make a treadmill that could make the hypothetical adjustments, in the ‘real’ world the bearings would explode almost instantly. I am working under the assumption that because it is a thought experiment that we could ignore our lack of technology that prevented the experiment. Sort of like Einstein’s elevators in space. The calculations of how much drag plane wheel bearings exert and how fast they would need to spin (hypothetically) to counter the force of the prop can be made. I postulated in the original thread that the question was posed in such a way as to be unanswerable. I suspect it’s true. ---
**Author:** ![John\_W.Kennedy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_w.kennedy/32/1031_2.png) [@John\_W.Kennedy](https://boards.straightdope.com/u/John_W.Kennedy)\ **Post date:** [September 7, 2008, 6:29pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/34 "2008-09-07T18:29:12Z")
> [@DiggitCamara](#): > > If the plane is jet-powered, the actual thrust comes from those engines. They push against air. ARRGGGHHHH! Now we’re back to the article in the _New York Times_ that claimed that Robert Goddard was wasting his time, because rockets couldn’t work in space. ---
**Author:** ![John\_W.Kennedy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_w.kennedy/32/1031_2.png) [@John\_W.Kennedy](https://boards.straightdope.com/u/John_W.Kennedy)\ **Post date:** [September 7, 2008, 6:41pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/35 "2008-09-07T18:41:56Z")
> [@Don\_t\_fight\_the\_hypothetical](#): > > It is you who is introducing factors (not in the original question) that _allow_ the plane to take off. Why would you allow assumptions that are not part of our physical world? As I stated above, the introduction of “frictionless bearings” in the original thread was to facilitate the ‘It Can Take Off’ crowd. Not so. It is only necessary to assume that the bearings are near enough to frictionless to behave like real bearings on real aircraft wheels. The only way to stop the aircraft from taking off in this case is to have the treadmill getting up to a perfectly ridiculous speed – probably about Mach 5 or so – where, frankly, I’d bet that either the treadmill or the wheel bearings would break down, or the tires would burst, anyway. And that is certainly not what the original wording seems to be suggesting. In any case, if the problem is to be analyzed at this level, then [ul] [li]the friction in the wheel bearings[/li][li]the friction between the tires and the treadmill,[/li][li]the speed at which the tires will burst,[/li][li]the speed at which the bearings will freeze up,[/li][li]the speed at which the bearings in the treadmill will freeze up,[/li][li]the speed at which the treadmill material will break down, and[/li][li]a different wording of the specification of the treadmill feedback[/li][/ul]_all_ have to be supplied before any answer can be given. ---
**Author:** ![DiggitCamara](https://avatars.discourse-cdn.com/v4/letter/d/df788c/32.png) [@DiggitCamara](https://boards.straightdope.com/u/DiggitCamara)\ **Post date:** [September 9, 2008, 3:18am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/36 "2008-09-09T03:18:09Z")
> [@John\_W.Kennedy](#): > > ARRGGGHHHH! > > Now we’re back to the article in the _New York Times_ that claimed that Robert Goddard was wasting his time, because rockets couldn’t work in space. Sorry. Didn’t phrase it right. I meant the turbines produce the action force that produce a reaction force on the plane’s body which propels it forward. Air doesn’t need to be pushed against. Though, in all justice, without the air the turbines wouldn’t work either… ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [September 9, 2008, 4:58am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/37 "2008-09-09T04:58:20Z")
> [@](#): > > If you take your above analogy and speed the treadmill up to the point where the force of the friction is more than the force the skaters muscles can overcome, when he pulls nothing will happen. Except that there is no such speed. Sure, there’s friction in the bearings. But when the treadmill speeds up, do you know what happens to that friction? Absolutely nothing. Dry friction doesn’t really depend on speed. So if the plane is able to overcome the friction on a normal runway, it’ll also be able to overcome the friction on a conveyor belt, _no matter how fast the conveyor belt is moving_. Now, assuming that everything’s textbook-standard, it is possible for the treadmill to keep the plane stopped, but it has to be continually accelerating, and at a truly ludicrous rate (many thousands of gees, depending on the exact design of the airplane). Which still doesn’t change the ultimate result: Such a treadmill would quickly reach a speed where it’s entraining the air to it, and the wind blowing over the stationary plane’s wings would be enough for it to take off anyway. ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [September 9, 2008, 5:46am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/38 "2008-09-09T05:46:44Z")
> [@Chronos](#): > > Except that there is no such speed. Sure, there’s friction in the bearings. But when the treadmill speeds up, do you know what happens to that friction? Absolutely nothing. Dry friction doesn’t really depend on speed. So if the plane is able to overcome the friction on a normal runway, it’ll also be able to overcome the friction on a conveyor belt, _no matter how fast the conveyor belt is moving_. This statement appears to be saying that a treadmill carrying an un-powered airplane with the treadmill (belt) traveling at 5mph would accelerate the plane at the same rate as a treadmill (belt) traveling at 1,000,000,000 miles per hour. Don’t get me wrong, I’m not making any statement about whether a plan would take off or not, merely that a faster moving treadmill should accelerate the plane backwards more than a slower moving treadmill. Shouldn’t it? ---
**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:** [September 9, 2008, 11:31am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/39 "2008-09-09T11:31:23Z")
> [@Chronos](#): > > Except that there is no such speed. Sure, there’s friction in the bearings. But when the treadmill speeds up, do you know what happens to that friction? Absolutely nothing. Dry friction doesn’t really depend on speed. So if the plane is able to overcome the friction on a normal runway, it’ll also be able to overcome the friction on a conveyor belt, _no matter how fast the conveyor belt is moving_. Not true. Roller bearing friction increases with speed. The increase isn’t large, and the speed dependency is close to a square root fuction, so often _approximating_ the frictional moment as constant is reasonable. But that’s just an approximation. The actual frictional moment can double or triple across the bearing’s rated speed range. (Of course, as should be intuitively obvious, dissipating full power of a large jet engine in bearing friction would quite quickly slag a bearing. But thought experiment, etc etc.) > [@RaftPeople](#): > > This statement appears to be saying that a treadmill carrying an un-powered airplane with the treadmill (belt) traveling at 5mph would accelerate the plane at the same rate as a treadmill (belt) traveling at 1,000,000,000 miles per hour. > > Don’t get me wrong, I’m not making any statement about whether a plan would take off or not, merely that a faster moving treadmill should accelerate the plane backwards more than a slower moving treadmill. Shouldn’t it? Sort of. In addition to the friction in the bearing, there’s an inertial coupling between the treadmill and the plane, which means if the treadmill and the wheel are _accelerating_, the force is passed to the body of the plane. Note this is based on the _acceleration_, not the _velocity_, so you would see the effect as you accelerated up to 1,000,000,000 mph, and not at a constant 1,000,000,000 mph. (This assumes the acceleration isn’t enough to skid the tires.) You can demonstrate this to yourself with a tablecloth and a roll of masking tape. ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [September 9, 2008, 3:11pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill/462380/40 "2008-09-09T15:11:27Z")
> [@zut](#): > > Note this is based on the _acceleration_, not the _velocity_, so you would see the effect as you accelerated up to 1,000,000,000 mph, and not at a constant 1,000,000,000 mph. (This assumes the acceleration isn’t enough to skid the tires.). If I place a rollable object on an already moving conveyor that is at a constant speed, the rollable object will be accelerated backwards. Your statement appears to say this is not the case. [Previous page](https://boards.straightdope.com/t/plane-on-a-treadmill/462380.md?page=1) [Next page](https://boards.straightdope.com/t/plane-on-a-treadmill/462380.md?page=3)