# Plane on a Treadmill - SOLUTION **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [March 3, 2006, 8:26pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954 "2006-03-03T20:26:14Z")\ **Posts on this page:** 20\ **Page:** 11
**Author:** ![Powers](https://avatars.discourse-cdn.com/v4/letter/p/edb3f5/32.png) [@Powers](https://boards.straightdope.com/u/Powers)\ **Post date:** [July 18, 2009, 2:49am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/201 "2009-07-18T02:49:14Z")
> [@SkylerHart](#): > > In the experiment, we are told that the conveyor belt is moving fast enough to keep the plane stationary. Thus, any live experiment in which the plane is not held stationary (you could simply set the brakes) is not valid as a “solution” to the original thought experiment. There is no such thing as a conveyor belt moving fast enough to keep a plane at full thrust stationary. As pointed out, a “magic” conveyor belt could accelerate fast enough to counteract the thrust, but that acceleration would very quickly lead to unrealistic speeds. The thought experiment, as normally worded, specifies a treadmill moving backward at the same speed the plane is moving forward. _This_ is the experiment Cecil addressed, and the experiment the Mythbusters carried out. As **zut** pointed out, the thought experiment could be worded as you suggest – that a treadmill is somehow magically empowered to perfectly counteract the forward thrust of the plane. But in that case we don’t need a treadmill – we might as well say “can a plane _with its brakes on_ take off?” It’s a trivial question and answer (“no”) and not at all interesting. That’s why the vast majority of experimenters take on the much more interesting question of whether the plane will move forward or not on a treadmill moving backwards. But you were not happy with simply positing and answering the trivial question. You had to go and say that Cecil was wrong, and that the Mythbusters were wrong, and that everyone else was wrong, when really – they’re just busy answering the _interesting_ question while you’re still wondering about a plane with its brakes on. Powers &8^] ---
**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:** [July 18, 2009, 2:52am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/202 "2009-07-18T02:52:03Z")
> [@DSYoungEsq](#): > > But I raised objection mostly to the jet engine theory. HOW are you positioning the jet engine so that it’s intake is coming in via the underside of the wing??? The intake isn’t the only factor. The exhaust (which will necessarily be greater than the intake) will drag surrounding air back with it, and air will rush in from the front (and sides) to replace it. ---
**Author:** ![straggler](https://avatars.discourse-cdn.com/v4/letter/s/3d9bf3/32.png) [@straggler](https://boards.straightdope.com/u/straggler)\ **Post date:** [July 18, 2009, 3:34am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/203 "2009-07-18T03:34:25Z")
Let’s say I am Superman, and I fly up to plane that is cruising along in the air at whatever speed at whatever altitude. I fly to the front of the plane and start pushing against it, slowing it right down to the point that it is now stationery. 1. Does the plane start falling down? 2. If I let go of the plane, will it slowly pick up speed again without falling? ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [July 18, 2009, 3:55am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/204 "2009-07-18T03:55:55Z")
> [@straggler](#): > > Let’s say I am Superman, and I fly up to plane that is cruising along in the air at whatever speed at whatever altitude. > I fly to the front of the plane and start pushing against it, slowing it right down to the point that it is now stationery. No need to invoke a magical Superman (and all the strange possibilities thereby possible) for this thought experiment - simply posit an aircraft hauled aloft by a blimp and then cut loose at zero airspeed. > [@](#): > > 1. Does the plane start falling down? Yes, of course - without some force such as aerodynamic lift to oppose gravity, any object falls. > [@](#): > > 1. If I let go of the plane, will it slowly pick up speed again without falling? No - it will fall, gain speed, and stop falling when lift equals weight. ---
**Author:** ![straggler](https://avatars.discourse-cdn.com/v4/letter/s/3d9bf3/32.png) [@straggler](https://boards.straightdope.com/u/straggler)\ **Post date:** [July 18, 2009, 4:05am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/205 "2009-07-18T04:05:35Z")
Cool, thanks. Does this help us get closer to an answer? ---
**Author:** ![JimOfAllTrades](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@JimOfAllTrades](https://boards.straightdope.com/u/JimOfAllTrades)\ **Post date:** [July 18, 2009, 4:18am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/206 "2009-07-18T04:18:10Z")
> [@SkylerHart](#): > > Of course a treadmill could prevent the plane from moving. Nothing magical about it. Loathe though I am to encourage this anymore, how do you think a non-magical treadmill could stop a plane? ---
**Author:** ![Xema](https://avatars.discourse-cdn.com/v4/letter/x/9de053/32.png) [@Xema](https://boards.straightdope.com/u/Xema)\ **Post date:** [July 18, 2009, 4:46am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/207 "2009-07-18T04:46:25Z")
> [@RJKUgly](#): > > … how do you think a non-magical treadmill could stop a plane? I think it’s common that the statement in the original problem that the treadmill moves at a speed equal to the plane’s gets interpreted to mean that the plane is held stationary with respect to the earth. This is, of course, quite false - but it’s often taken to be obviously true. So the question then gets interpreted as “Can a plane with no airspeed take off?” Unsurprisingly, confusion ensues. ---
**Author:** ![DiggitCamara](https://avatars.discourse-cdn.com/v4/letter/d/df788c/32.png) [@DiggitCamara](https://boards.straightdope.com/u/DiggitCamara)\ **Post date:** [July 18, 2009, 5:09am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/208 "2009-07-18T05:09:46Z")
> [@RJKUgly](#): > > Loathe though I am to encourage this anymore, how do you think a non-magical treadmill could stop a plane? - 1 Really, I thought that zut’s post was fool-proof. It’s obvious the old adage about fool-proof plans still holds true. ---
**Author:** ![JimOfAllTrades](https://avatars.discourse-cdn.com/v4/letter/j/ba8739/32.png) [@JimOfAllTrades](https://boards.straightdope.com/u/JimOfAllTrades)\ **Post date:** [July 18, 2009, 5:12am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/209 "2009-07-18T05:12:23Z")
> [@Xema](#): > > I think it’s common that the statement in the original problem that the treadmill moves at a speed equal to the plane’s gets interpreted to mean that the plane is held stationary with respect to the earth. > > This is, of course, quite false - but it’s often taken to be obviously true. So the question then gets interpreted as “Can a plane with no airspeed take off?” Unsurprisingly, confusion ensues. Oh, I agree, assumptions are everything here, as **zut** ’s post shows. But **SkylerHart** seems to be saying that a non-magical treadmill could somehow keep a plane from moving with respect to the ground (and the air), so that the plane would have no airspeed. If I’ve interpreted his remark correctly, I’m wondering how he thinks anything like a real world treadmill could impart that much force to a plane. ---
**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:** [July 18, 2009, 12:13pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/210 "2009-07-18T12:13:27Z")
> [@garygnu](#): > > ONLY a magical treadmill could prevent an airplane from taking off. > [@RJKUgly](#): > > Loathe though I am to encourage this anymore, how do you think a non-magical treadmill could stop a plane? > [@DiggitCamara](#): > > - 1 > Really, I thought that zut’s post was fool-proof. > [@RJKUgly](#): > > Oh, I agree, assumptions are everything here, as **zut** ’s post shows. > > But **SkylerHart** seems to be saying that a non-magical treadmill could somehow keep a plane from moving with respect to the ground (and the air), so that the plane would have no airspeed. If I’ve interpreted his remark correctly, I’m wondering how he thinks anything like a real world treadmill could impart that much force to a plane. The key here are your assumptions. I’m absolutely positive that you can’t build a treadmill that will keep a 747 stationary. It’s _possible_ you could build a treadmill that will keep an overloaded Cessna stationary for a second or so, but even that seems like a stretch. However, if you’re not fussy, it seems to me that you could design a \*plane \*specifically to be \*able \*to be stopped by a treadmill. Imagine, for example, a scale model RC plane with large diameter (high inertia) wheels and oversized, heat-dissipating disk brakes that are pre-loaded. Of course they can’t be _too_ big, else the plane will never fly because of the weight (and that certainly violates the spirit of the question), but I think that, in this specialized circumstance, an appropriately designed treadmill has a decent chance of holding the plane stationary for a reasonable period of time. As far as I know, no one really interprets the “original” question (whatever that is) as requiring a specially designed plane, but as long as we’re willing to treat it as a thought experiment, I think it’s possible to actually build a “plane-treadmill system” that keeps the plane stationary. You might reasonably argue that intentionally “crippling” the plane so it’s difficult to take off violates the spirit of the question, and that’s fine–but it’s also an assumption. 🙂 ---
**Author:** ![AskNott](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/asknott/32/5790_2.png) [@AskNott](https://boards.straightdope.com/u/AskNott)\ **Post date:** [July 18, 2009, 6:50pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/211 "2009-07-18T18:50:04Z")
> [@DSYoungEsq](#): > > Stop. Think. > > I’ve already addressed the issue of propellers, and others can do the math for you to establish that the inflow wouldn’t be enough to lift the plane. > > But I raised objection mostly to the jet engine theory. HOW are you positioning the jet engine so that it’s intake is coming in via the underside of the wing??? > > Oh, right, that’s not where jet engines are located (directly behind the wings). 😉 Although many jet planes have tail-mounted engines, or engines within the fuselage, it’s not hard to find planes with jet engines in nacelles hung on struts right under, and slightly behind, the wing. [QUOTE=John W. Kennedy] The intake isn’t the only factor. The exhaust (which will necessarily be greater than the intake) will drag surrounding air back with it, and air will rush in from the front (and sides) to replace it. [/QUOTE] Yes. Unlike cells in a spreadsheet, large masses of air cannot be shoved around without dragging other large masses of air along. Air is like that. Mindlessly, mooingly, it follows other air. _At this point, the main point has been laid to rest, and we are throwing spitwads. It’s amusing, but it doesn’t mean anything._ If you strain at a gnat on a treadmill in a forest, can a bear fly? I think that’s too many quick turns. I’m sorry.:smack: ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [July 18, 2009, 8:35pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/212 "2009-07-18T20:35:53Z")
> [@Xema](#): > > No need to invoke a magical Superman (and all the strange possibilities thereby possible) for this thought experiment - simply posit an aircraft hauled aloft by a blimp and then cut loose at zero airspeed. > > Yes, of course - without some force such as aerodynamic lift to oppose gravity, any object falls. > > No - it will fall, gain speed, and stop falling when lift equals weight. Well, that or when altitude equals zero… ---
**Author:** ![Ruken](https://avatars.discourse-cdn.com/v4/letter/r/f475e1/32.png) [@Ruken](https://boards.straightdope.com/u/Ruken)\ **Post date:** [July 18, 2009, 10:07pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/213 "2009-07-18T22:07:06Z")
> [@straggler](#): > > Let’s say I am Superman, and I fly up to plane that is cruising along in the air at whatever speed at whatever altitude. > > I fly to the front of the plane and start pushing against it, slowing it right down to the point that it is now stationery. > > 1. Does the plane start falling down? > 2. If I let go of the plane, will it slowly pick up speed again without falling? **Xema** answered your questions, but this has little to do with treadmills. The plane is flying with it’s landing gear down. Superman flies up to it and spins its wheels quickly. Does the plane start falling down? ---
**Author:** ![DSYoungEsq](https://avatars.discourse-cdn.com/v4/letter/d/c6cbf5/32.png) [@DSYoungEsq](https://boards.straightdope.com/u/DSYoungEsq)\ **Post date:** [July 19, 2009, 4:35am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/214 "2009-07-19T04:35:34Z")
> [@AskNott](#): > > Although many jet planes have tail-mounted engines, or engines within the fuselage, it’s not hard to find planes with jet engines in nacelles hung on struts right under, and slightly behind, the wing. I am quite familiar with where intakes on jets are likely to be found. And I defy you to demonstrate how the placement of a jet engine intake below (and even possibly slightly behind the leading edge of a wing, though in most cases not) would result in any significant, or really insignificant amount of air being pulled up against the bottom of the wing! That’s what creates lift, and that ain’t gonna happen in the situation you postulate, unless you have an example I’m not thinking of… ---
**Author:** ![DanBlather](https://avatars.discourse-cdn.com/v4/letter/d/f4b2a3/32.png) [@DanBlather](https://boards.straightdope.com/u/DanBlather)\ **Post date:** [July 19, 2009, 5:17am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/215 "2009-07-19T05:17:12Z")
> [@SkylerHart](#): > > The idea that the conveyor’s speed will somehow have to ramp to infinity to keep the plane stationary is ludicrous. You can walk backwards up the escalator and maintain the same position… You seem to have an utter lack of insight into the problem. Here is a question for you to think about: what moves you forward relative to the escalator and how is it different than what moves a plane forward? Now replace the escalator with an inclined treadmill and put yourself on rollerskates. There is not necessarily a right answer to the badly worded problem, but there are some wrong answers and you have one of them. ---
**Author:** ![Askance](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/askance/32/8281_2.png) [@Askance](https://boards.straightdope.com/u/Askance)\ **Post date:** [July 20, 2009, 4:21am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/216 "2009-07-20T04:21:22Z")
> [@SkylerHart](#): > > Go look at some dimensional layouts. Many aircraft do not have wings with a positive angle of attack during level flight. How do they stay aloft? Show us some. I bet they do, in flight. > [@](#): > > Unless the Federal Aviation Administration and all of the licensed aviation schools in this country are wrong? As it wouldn’t affect them in the slightest if they were wrong in this matter, yes, they are if they all truly say that. Are you saying NASA is wrong?. > [@](#): > > But let’s say for a second that lift is generated solely by a positive angle of attack. In the thought experiment, the aircraft is stationary on the conveyor belt. If you hold your hand outside the car window, but you’re not moving, is your hand still lifted in to the air? You’ve not addressed my main point. The engines throwing air backwards moves the plane forwards, irrelevant of what the wheels are doing (assuming the brakes are off, of course). As the plane moves forward due to Newton’s law of action and reaction, the underside of the wing moves forward, hitting until-then stationary air, generating lift. The plane may _start_ stationary but it doesn’t _stay_ stationary. ---
**Author:** ![DiggitCamara](https://avatars.discourse-cdn.com/v4/letter/d/df788c/32.png) [@DiggitCamara](https://boards.straightdope.com/u/DiggitCamara)\ **Post date:** [July 20, 2009, 5:55am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/217 "2009-07-20T05:55:04Z")
> [@SkylerHart](#): > > Oh, well, I’m sorry. What were your credentials again? [Appeal to authority](http://en.wikipedia.org/wiki/Argument_from_authority). And, actually, not even that (Hint: on the interwebs? No one knows your credentials. Even when you write them down.;)) ---
**Author:** ![Irishman](https://avatars.discourse-cdn.com/v4/letter/i/b487fb/32.png) [@Irishman](https://boards.straightdope.com/u/Irishman)\ **Post date:** [July 20, 2009, 4:46pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/218 "2009-07-20T16:46:02Z")
**SkylerHart** said: > [@](#): > > The problem, sir, is that it’s a thought experiment. In the experiment, we are told that the conveyor belt is moving fast enough to keep the plane stationary. The thought experiment is poorly worded. But **Powers** has addressed this statement. You are **assuming** an interpretation of the poorly worded statement. Your assumption is a trivial case. Everyone seems willing to concede that if the plane has no speed relative to the ground (as opposed to the treadmill belt), that barring strange wind conditions (running the experiment in a hurricane), the plane will not take off. But the thing is, the original problem can have other interpretations, interpretations that do not define the interesting part of the problem away. > [@](#): > > The idea that the conveyor’s speed will somehow have to ramp to infinity to keep the plane stationary is ludicrous. You can walk backwards up the escalator and maintain the same position… This suggests that part of the problem is your basic misunderstanding of how a plane works vs how a car works (or a person walks). Cars get their thrust by the interplay between the tires and the road. Put a car on a treadmill (dynamometer), and the interplay remains the same, but the “road” surface rotates, so the car remains stationary. Similarly, people get their forward motion by the interplay between their feet and the street. That is why a treadmill works - the interplay remains the same, but the surface moves, so the person does not. But planes do **not** get their forward motion from their wheels. It comes from the engines pushing on air. The wheels just provide a reduction in traction between the mass of the plane and the ground. The wheels roll, and thus the plane moves forward. That’s why seaplanes don’t need wheels, and snow planes use skids. As long as the friction between the plane and the ground is overcome by the engine thrust, the plane moves forward. Try this thought experiment. Put the plane on skids instead of wheels, then cover the treadmill with shaving cream. Now try to make the plane take off, while turning the treadmill in reverse. HINT: once the thrust overcomes the friction enough for the the plane to remain stationary while the treadmill goes in reverse, it has overcome the friction enough to not sit still, but rather move forward. > [@](#): > > Of course a treadmill could prevent the plane from moving. Nothing magical about it. Please explain in detail how the treadmill prevents the plane from moving. ---
**Author:** ![joesixpack](https://avatars.discourse-cdn.com/v4/letter/j/839c29/32.png) [@joesixpack](https://boards.straightdope.com/u/joesixpack)\ **Post date:** [July 25, 2009, 4:15pm UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/219 "2009-07-25T16:15:19Z")
I believe the question was meant to be a thought experiment and in the thought experiment the answer is: No the plane will not fly. To visualize this, put a 747 or any size plane that can not generate air flow on an imaginary tread mill. Start the tread mill running backwards. The plane moves backwards. Now fire up the jets until the plane reaches parity keeping it in place. Increase the speed of the tread mill and the plane will begin moving backwards again. Increase the thrust to achieve parity. Continue this and the plane could never fly. No air flow. In our reality, to the best of my knowledge, the materials and technology needed to build this contraption do not exist. The final answer to the question is: Yes the plane can be kept from taking off but the apparatus to keep it from taking off can not be constructed. Only in the mind.:smack: ---
**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:** [July 26, 2009, 3:45am UTC](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954/220 "2009-07-26T03:45:49Z")
Only if the damn treadmill is moving fast enough to fuse the bearings in the landing-gear axles. (Actually, the tires will probably burst before that.) Let’s try it one more time. Landing-gear wheels are free-wheeling. [Previous page](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954.md?page=10) [Next page](https://boards.straightdope.com/t/plane-on-a-treadmill-solution/346954.md?page=12)