# Will a plane on a treadmill take off? **URL:** \ **Category:** Factual Questions\ **Created:** [December 7, 2005, 9:19pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567 "2005-12-07T21:19:53Z")\ **Posts on this page:** 20\ **Page:** 16
**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:** [December 13, 2005, 4:21pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/301 "2005-12-13T16:21:42Z")
> [@Sage Rat](#): > > Backwards at the same speed as the wheels. If the wheels do not turn, the conveyor belt does not turn. But, the conveyor does have to move with the plane, which is separate from the wheels. Er, what? The conveyor does not move, yet it does? You’re not saying that the entire conveyor is uprooted and dragged down the runway, stuck to the plane, are you? That’s an interesting take on the problem. Posit a stake connecting the treadmill frame (not belt) to the Earth. > [@UncleRojelio](#): > > The thrust from the engines pushes the entire aircraft forward through the air, regardless of whether the wheels spin clockwise, anti-clockwise, or not at all. When the air over the wings reaches the appropriate speed, the aircraft lifts upward. QED If you assume massless wheels and limited friction. Or limitations on the treadmill. Or that “matching wheel speed” means “matching hub speed” as opposed to “matching tire circumference speed.” It’s all about the assumptions. > [@Sage Rat](#): > > But if the plane moved, then the conveyor belt did not work to keep it in place. And if the plane didn’t move, then the wheels have no reason to roll–so the conveyor belt doesn’t move. The plane _experiences forward thrust._ Not the same as _moving._ And posit some sort of sensor/feedback system that reacts when the plane moves a small distance epsilon, for whatever small distance you like, down to infinitesimally small. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [December 13, 2005, 4:24pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/302 "2005-12-13T16:24:02Z")
> [@UncleRojelio](#): > > Say the aircraft needs to have an airspeed of 200mph to achieve lift, and this aircraft is on this treadmill and the treadmill is actively trying to roll backwards at the same rate the aircraft is rolling forwards. That just means that, at liftoff, the wheels are spinning as if the aircraft were going 400 mph. No big deal to the axles. The wheels would have to be spinning fast enough that just the friction between the wheels and the axle would be enough to counter the jet engines. I suspect it would be much greater than 400mph. Again, I feel that this answer goes more against the OP than mine does. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [December 13, 2005, 4:32pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/303 "2005-12-13T16:32:31Z")
> [@zut](#): > > Er, what? The conveyor does not move, yet it does? You’re not saying that the entire conveyor is uprooted and dragged down the runway, stuck to the plane, are you? No, that the belt will rotate forward with the plane. The wheels will not rotate and the conveyor will not be rotating compared to the wheels. > [@](#): > > And posit some sort of sensor/feedback system that reacts when the plane moves a small distance epsilon, for whatever small distance you like, down to infinitesimally small. The sensor/feedback system is only possible if you have friction at the axle. Minus that, which I take to be the implication, and you are in a catch-22 situation. The plane can’t move without the wheels moving, but there is no friction to apply anywhere to hold the plane in place on the conveyor. ---
**Author:** ![spingears](https://avatars.discourse-cdn.com/v4/letter/s/ebca7d/32.png) [@spingears](https://boards.straightdope.com/u/spingears)\ **Post date:** [December 13, 2005, 4:43pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/304 "2005-12-13T16:43:18Z")
301 unnecessary reply posts to argue about the OP and the answer in Post #2. :rolleyes: repeated 300 times ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [December 13, 2005, 4:47pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/305 "2005-12-13T16:47:20Z")
If the plane moves forward then the treadmill has stopped doing its job. The only way for the plane to move forward is if the wheels are turning faster than the treadmill is. Therefore, one of either two things happens. The plane generates a heap of thrust but doesn’t move forwards because the treadmill and wheels are spinning so incredibly fast that they actually create enough rearward force via friction to counterbalance the thrust. Or, we say that there is no friction in the system in which case the treadmill and wheels end up spinning infinitely fast, the plane moves forwards anyway, and the universe implodes destroying the plane, the treadmill, and the wheels. ---
**Author:** ![HMS\_Irruncible](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hms_irruncible/32/7394_2.png) [@HMS\_Irruncible](https://boards.straightdope.com/u/HMS_Irruncible)\ **Post date:** [December 13, 2005, 4:51pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/306 "2005-12-13T16:51:26Z")
> [@Sage Rat](#): > > But if the plane moved, then the conveyor belt did not work to keep it in place. Nothing in the OP says that the conveyor belt has to keep the plane in place. It just says that the belt moves at a retrograde speed equal to the forward motion of the wheel. The wheels are totally passive and unpowered, therefore their behavior is dictated by traction. You do realize that aircraft wheels aren’t powered, right? ---
**Author:** ![HMS\_Irruncible](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hms_irruncible/32/7394_2.png) [@HMS\_Irruncible](https://boards.straightdope.com/u/HMS_Irruncible)\ **Post date:** [December 13, 2005, 4:58pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/307 "2005-12-13T16:58:41Z")
> [@1920s Style "Death Ray"](#): > > If the plane moves forward then the treadmill has stopped doing its job. The only way for the plane to move forward is if the wheels are turning faster than the treadmill is. You have just become person number #101 laboring under the misconception that planes work like cars. Aircraft wheels are not powered. Airplanes don’t have transmissions. The wheels turn passively, let’s all chant it together… ---
**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:** [December 13, 2005, 5:22pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/308 "2005-12-13T17:22:08Z")
> [@Sage Rat](#): > > No, that the belt will rotate forward with the plane. The wheels will not rotate and the conveyor will not be rotating compared to the wheels. Ah. You’re interpeting “conveyor speed” as “speed with respect to the wheels.” I don’t think anyone else is doing that; they’re using “speed with respect to the ground.” Under your interpretation, the conveyor seeks to hold the wheel rotation to zero, yes? Yet another interpretation. > [@spingears](#): > > 301 unnecessary reply posts to argue about the OP and the answer in Post #2. > :rolleyes: repeated 300 times Not exactly true. The “answer” depends on what assumptions you make. I should point out that there’s nothing inherently wrong with deep and profound ignorance; that’s what the whole educational system is here for. Personally, though, I find _aggressive_ ignorance to be counterproductive. You obviously have a different perception. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [December 13, 2005, 5:34pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/309 "2005-12-13T17:34:40Z")
> [@zut](#): > > Ah. You’re interpeting “conveyor speed” as “speed with respect to the wheels.” I don’t think anyone else is doing that; they’re using “speed with respect to the ground.” Under your interpretation, the conveyor seeks to hold the wheel rotation to zero, yes? Yet another interpretation. Only in a sense. Rather I am viewing the conveyor belt as **not being** a mechanized belt that moves itself to stay in synch, but rather it is like one of the jogging in place ones where it is **your inertia** forcing it to move backwards. For real life ones, we need to slant the belts upwards in order for this to work as the belt has intertia and friction about its tumblers. But if you removed that inertia and friction, you could have it perfectly horizontal and if you ran on it, you would stay in place: as the OP requested. But when you are running on it, you are trying to force yourself forward by pushing on the belt. When you put a plane on it, you are pushing against the air. Since the plane starts at rest, its wheels are not initially moving. When you push it forward, the belt has no inertia nor friction to fight itself being drawn forward with the plane. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [December 13, 2005, 5:52pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/310 "2005-12-13T17:52:58Z")
> [@Brain Wreck](#): > > Nothing in the OP says that the conveyor belt has to keep the plane in place. It just says that the belt moves at a retrograde speed equal to the forward motion of the wheel. The wheels are totally passive and unpowered, therefore their behavior is dictated by traction. Alright well let’s try that. The wheel moves to the left at 1 mph and the top of the conveyor belt moves to the right at 1 mph. Sum total, 0, the wheel did not move. If the wheel did not move, how could traction start it moving? So the conveyor belt unilaterally moved itself backwards, turning the wheel. Fine, but no matter how fast you turn the wheel, if the conveyor is going to move backwords at the exact speed the plane _would have_ moved forward then the plane cannot move. Given friction between the wheel and the plane, this is a possible scenario, but requires that friction. If you remove it, there is no speed at which the conveyor could go to equal the forward movement of the plane. If the wheel does physically move to the left it **is** moving faster to the left than the conveyor belt is moving to the right. ---
**Author:** ![HMS\_Irruncible](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hms_irruncible/32/7394_2.png) [@HMS\_Irruncible](https://boards.straightdope.com/u/HMS_Irruncible)\ **Post date:** [December 13, 2005, 6:07pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/311 "2005-12-13T18:07:02Z")
> [@Sage Rat](#): > > Alright well let’s try that. > > The wheel moves to the left at 1 mph and the top of the conveyor belt moves to the right at 1 mph. Sum total, 0, the wheel did not move. If the wheel did not move, how could traction start it moving? If the wheel is free to rotate, and traction exists, then the wheel will turn against the treadmill. The force of the treadmill is translated to the rotational energy of the wheel, instead of moving the plane backward. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [December 13, 2005, 6:10pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/312 "2005-12-13T18:10:52Z")
> [@Brain Wreck](#): > > If the wheel is free to rotate, and traction exists, then the wheel will turn against the treadmill. The force of the treadmill is translated to the rotational energy of the wheel, instead of moving the plane backward. If the wheel does physically move to the left it is moving faster to the left than the conveyor belt is moving to the right. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [December 13, 2005, 6:21pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/313 "2005-12-13T18:21:32Z")
Or it’s skidding. But that’s not magical! I want…I want dancing fairies in thongs!! ---
**Author:** ![HMS\_Irruncible](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hms_irruncible/32/7394_2.png) [@HMS\_Irruncible](https://boards.straightdope.com/u/HMS_Irruncible)\ **Post date:** [December 13, 2005, 7:08pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/314 "2005-12-13T19:08:15Z")
> [@Sage Rat](#): > > If the wheel does physically move to the left it is moving faster to the left than the conveyor belt is moving to the right. No, it isn’t. The wheel and the belt would diverge from a fixed point at the same speed. The wheel spins twice as fast as it would if the belt weren’t stationary. I’m still not sure you get that the wheel is a passive agent in this case. Or maybe you’re using the terms “moving” and “spinning” interchangeably, in which case it’s impossible to understand what you mean. ---
**Author:** ![The\_Controvert](https://avatars.discourse-cdn.com/v4/letter/t/dec6dc/32.png) [@The\_Controvert](https://boards.straightdope.com/u/The_Controvert)\ **Post date:** [December 13, 2005, 7:16pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/315 "2005-12-13T19:16:44Z")
> [@Brain Wreck](#): > > You have just become person number #101 laboring under the misconception that planes work like cars. Aircraft wheels are not powered. Airplanes don’t have transmissions. The wheels turn passively, let’s all chant it together… While you’re chanting, let’s strap you to some roller skates and put you on a treadmill. You are offered a helmet, but you refuse it since the wheels turn passively. We’re gonna turn this treadmill on… aren’t you worried about friction? Your response: “Wheels turn passively! Wheels turn passively! Let’s all chant it together! Wheels turn passively! Hey, why am I moving?” 😃😃 ---
**Author:** ![HMS\_Irruncible](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hms_irruncible/32/7394_2.png) [@HMS\_Irruncible](https://boards.straightdope.com/u/HMS_Irruncible)\ **Post date:** [December 13, 2005, 7:24pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/316 "2005-12-13T19:24:31Z")
> [@The Controvert](#): > > While you’re chanting, let’s strap you to some roller skates and put you on a treadmill. You are offered a helmet, but you refuse it since the wheels turn passively. We’re gonna turn this treadmill on… aren’t you worried about friction? Your response: “Wheels turn passively! Wheels turn passively! Let’s all chant it together! Wheels turn passively! Hey, why am I moving?” 😃😃 Errrr… you forgot about the thrust from the jet engine strapped to my butt. Wheels still turn passively, a lot faster, and I don’t move forward. However, I do accept the helmet, because if I’m not coordinated enough to keep my butt pointed precisely against the direction of the treadmill then it’s all going to end in tears. ---
**Author:** ![HMS\_Irruncible](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hms_irruncible/32/7394_2.png) [@HMS\_Irruncible](https://boards.straightdope.com/u/HMS_Irruncible)\ **Post date:** [December 13, 2005, 7:29pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/317 "2005-12-13T19:29:04Z")
Gar… typed too soon. :smack: Correction to previous: > [@Brain Wreck](#): > > Errrr… you forgot about the thrust from the jet engine strapped to my butt. Wheels still turn passively, a lot faster, and I don’t move **backward if the engine is engaged. And I can move forward if I increase thrust.** ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [December 13, 2005, 7:36pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/318 "2005-12-13T19:36:08Z")
> [@Brain Wreck](#): > > You have just become person number #101 laboring under the misconception that planes work like cars. Aircraft wheels are not powered. Airplanes don’t have transmissions. The wheels turn passively, let’s all chant it together… Yes I know how they work, I fly them for a living. If you read my post more thoroughly you’ll see that I allow for two possibilities. 1. We allow for friction in which case, the treadmill ends up going fast enough that the friction is enough to counter the several thousand pounds of thrust coming from the engine. 2. We say that the system has no friction in which case the plane accelerates down the treadmill and takes off. The second option is the one that I think of as the “obviously correct” answer in that it is probably the one the poser of the question is looking for. However, the “obviously correct” answer requires that one of the conditions of the experiment not be met, i.e., the moment the plane moves forwards the treadmill is no longer matching the speed of the wheels. This means that the thought experiment, as posed, is seriously flawed and not really worth thinking too hard about. There is another possibility. IF you could get a treadmill to accelerate fast enough, then once the wheels were turning at a couple of hundred knots, the tires would fail, and the plane would collapse onto its undercarriage struts. Now that it is no longer on wheels it will lose control and turn into a mangled wreck. ---
**Author:** ![brossa](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/brossa/32/3040_2.png) [@brossa](https://boards.straightdope.com/u/brossa)\ **Post date:** [December 13, 2005, 7:45pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/319 "2005-12-13T19:45:18Z")
> [@](#): > > Originally posted by **Sage Rat** > If the wheel does physically move to the left it is moving faster to the left than the conveyor belt is moving to the right. Picture a wheel freely rolling down the road at (hub velocity) 4mph - I dunno, maybe it fell off a truck or something. It approaches the back end of the treadmill which is running 2mph (surface velocity) in the opposite direction. The wheel runs up onto the treadmill. Now the wheel is running at 2mph (hub velocity) in its original direction, and the treadmill surface is moving at 2mph in the opposite direction. But the wheel still moves forward, relative to both the ground and the treadmill. Or are you arguing that the wheel is then moving at 4mph (hub speed) \* relative to the surface of the conveyor belt\* so the belt should speed up (assuming a powered belt) to 4mph; that would hold the wheel still with respect to the ground, _provided that there were no other forces on the wheel._ But the engine applies a force to the wheel that will accelerate the wheel hub forward barring an equal opposing force. ---
**Author:** ![Richard\_Pearse](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/richard_pearse/32/13144_2.png) [@Richard\_Pearse](https://boards.straightdope.com/u/Richard_Pearse)\ **Post date:** [December 13, 2005, 7:55pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/320 "2005-12-13T19:55:06Z")
> [@1920s Style "Death Ray"](#): > > Yes I know how they work, I fly them for a living. > > If you read my post more thoroughly you’ll see that I allow for two possibilities. > > 1. We allow for friction in which case, the treadmill ends up going fast enough that the friction is enough to counter the several thousand pounds of thrust coming from the engine. > > 2. We say that the system has no friction in which case the plane accelerates down the treadmill and takes off. > > The second option is the one that I think of as the “obviously correct” answer in that it is probably the one the poser of the question is looking for. However, the “obviously correct” answer requires that one of the conditions of the experiment not be met, i.e., the moment the plane moves forwards the treadmill is no longer matching the speed of the wheels. This means that the thought experiment, as posed, is seriously flawed and not really worth thinking too hard about. > > There is another possibility. IF you could get a treadmill to accelerate fast enough, then once the wheels were turning at a couple of hundred knots, the tires would fail, and the plane would collapse onto its undercarriage struts. Now that it is no longer on wheels it will lose control and turn into a mangled wreck. All of which has been more than adequately tackled by other posters I see (I missed all those middle pages:).) [Previous page](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567.md?page=15) [Next page](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567.md?page=17)