# 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:** 13
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [December 9, 2005, 10:40pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/241 "2005-12-09T22:40:42Z")
> [@GusNSpot](#): > > It is a post count thread – nothing more… Not one thing worth while was learned except for those poor folks that thought aircraft wheels were driven by the engines like a car. Actually I learned something useful: that some people have an irrational hatred of discussions that do not have a clear YES or NO answer. As for aircraft carriers, that’s not really analogous to tradmills. Aircraft on carriers start out being anchored to the deck, moving with the speed of the carrier. So if the carrier is moving forward, the aircraft needs less relative speed to take off. If an aircraft on a treadmill starts out at rest relative to the ground, a moving treadmill under it does not assist takeoff at all. ---
**Author:** ![Thinktank](https://avatars.discourse-cdn.com/v4/letter/t/6a8cbe/32.png) [@Thinktank](https://boards.straightdope.com/u/Thinktank)\ **Post date:** [December 9, 2005, 10:44pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/242 "2005-12-09T22:44:40Z")
pick,pick,piiick… I ready to let this one die. Ladies and Gentlemen, a vow of silence for the airplane on a treadmill thread… please ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [December 9, 2005, 10:56pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/243 "2005-12-09T22:56:25Z")
> [@scr4](#): > > As for aircraft carriers, that’s not really analogous to tradmills. Aircraft on carriers start out being anchored to the deck, moving with the speed of the carrier. So if the carrier is moving forward, the aircraft needs less relative speed to take off. If an aircraft on a treadmill starts out at rest relative to the ground, a moving treadmill under it does not assist takeoff at all. Actually its a pretty good analogy. The difference is that if you wanted to use a treadmill on an aircraft carrier you would have to accelerate the treadmill to ridiculous speeds to make it work (thousands and thousands of MPHs). If you did that you would either have to have ridiculously strong and massive tires or you would rip them to shreads. The advantage of using a physical link between the launching deelie is that you can (more or less) apply as much force through that link as you want. Theoretically you could launch a plane and get it airborn with both apparatuses (treadmill or steam piston launcher) but if you use a treadmill the tires on the plane would be spinning at an extremely high rate (like 50 million RPM high). ---
**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 9, 2005, 11:17pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/244 "2005-12-09T23:17:36Z")
> [@Lemur866](#): > > No, the energy to accelerate the wheels has to come from the belt. Whoops; you’re right, of course. The forces from the jet and from the belt are equal and opposite, but energy flow is from the belt into the wheel. Damn magic conveyors. > [@UncleRojelio](#): > > Once the plane is airborne, who gives a flying fuck about the wheels? > > This is the most absurd thread I have ever had the misfortune of reading on the Dope. Simply a travesty. You people should be ashamed of yourselves! Eh. Thought experiments and the exploration of limiting conditions of physical systems can often provide some interesting insights into How Stuff Works. They’re good teaching tools, too. That is, they’re good teaching tools when directed at those who are interested and willing to learn. I would suggest that those people who aggressively flaunt their ignorance, to the extent of not even bothering to read the OP and making what can be charitably described as misguided comments, will probably get less out of these kinds of discussions than others. You obviously disagree. ---
**Author:** ![Hombre](https://avatars.discourse-cdn.com/v4/letter/h/ecb155/32.png) [@Hombre](https://boards.straightdope.com/u/Hombre)\ **Post date:** [December 9, 2005, 11:28pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/245 "2005-12-09T23:28:46Z")
> [@treis](#): > > Actually its a pretty good analogy. The difference is that if you wanted to use a treadmill on an aircraft carrier you would have to accelerate the treadmill to ridiculous speeds to make it work (thousands and thousands of MPHs). If you did that you would either have to have ridiculously strong and massive tires or you would rip them to shreads. The advantage of using a physical link between the launching deelie is that you can (more or less) apply as much force through that link as you want. Theoretically you could launch a plane and get it airborn with both apparatuses (treadmill or steam piston launcher) but if you use a treadmill the tires on the plane would be spinning at an extremely high rate (like 50 million RPM high). How would spinning the wheels of a jet help it launch? ---
**Author:** ![Ike\_Witt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ike_witt/32/283_2.png) [@Ike\_Witt](https://boards.straightdope.com/u/Ike_Witt)\ **Post date:** [December 9, 2005, 11:35pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/246 "2005-12-09T23:35:36Z")
I’m the first to admit that my knowledge of physics is very limited. Limited to a few astronomy courses and one intro level course. Can somebody please draw a diagram with arrows that represent the forces involved? ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [December 10, 2005, 12:52am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/247 "2005-12-10T00:52:46Z")
> [@adam yax](#): > > I’m the first to admit that my knowledge of physics is very limited. Limited to a few astronomy courses and one intro level course. > > Can somebody please draw a diagram with arrows that represent the forces involved? [http://rapidshare.de/files/8898730/forces.pdf.html](http://rapidshare.de/files/8898730/forces.pdf.html) > [@Hombre](#): > > How would spinning the wheels of a jet help it launch? Basically what happens is that the treadmill accelerates the tires and by action/reaction it in turn accelerates the airplane. With a few simplifying assumptions (mainly that the angular acceleration of the tires is \>\>\> acceleration of the plane along with the normal frictionless bearings, air resistance etc. etc.) you find that the angular acceleration of the tire is radius of the wheels_mass of plane/I wheels times the acceleration of the plane. After integration we find that the angular velocity is R_M/I times the acceleration of the plane. For practical numbers here R is on the order of .5 meters, I is on the order of 50 Kg_m^2 and M is 14000 Kg. Basically that means the tires rotate at 1400_Speed of the plane (RPMs and m/s for units). For a take off speed of approximately 500 miles per hour your tires are rotating at 315,000 RPM. [http://rapidshare.de/files/8900092/aircraft\_carrier.pdf.html](http://rapidshare.de/files/8900092/aircraft_carrier.pdf.html) ---
**Author:** ![Ike\_Witt](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ike_witt/32/283_2.png) [@Ike\_Witt](https://boards.straightdope.com/u/Ike_Witt)\ **Post date:** [December 10, 2005, 12:57am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/248 "2005-12-10T00:57:56Z")
Thanks **treis**. ---
**Author:** ![Hombre](https://avatars.discourse-cdn.com/v4/letter/h/ecb155/32.png) [@Hombre](https://boards.straightdope.com/u/Hombre)\ **Post date:** [December 10, 2005, 1:09am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/249 "2005-12-10T01:09:15Z")
> [@treis](#): > > Basically what happens is that the treadmill accelerates the tires and by action/reaction it in turn accelerates the airplane. With a few simplifying assumptions (mainly that the angular acceleration of the tires is \>\>\> acceleration of the plane along with the normal frictionless bearings, air resistance etc. etc.) you find that the angular acceleration of the tire is radius of the wheels_mass of plane/I wheels times the acceleration of the plane. After integration we find that the angular velocity is R_M/I times the acceleration of the plane. For practical numbers here R is on the order of .5 meters, I is on the order of 50 Kg_m^2 and M is 14000 Kg. Basically that means the tires rotate at 1400_Speed of the plane (RPMs and m/s for units). For a take off speed of approximately 500 miles per hour your tires are rotating at 315,000 RPM. > > [http://rapidshare.de/files/8900092/aircraft\_carrier.pdf.html](http://rapidshare.de/files/8900092/aircraft_carrier.pdf.html) Thanks! ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [December 10, 2005, 2:02am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/250 "2005-12-10T02:02:04Z")
> [@GusNSpot](#): > > There isn’t one, it is a thought experiment… Inherently unsolvable because you can’t keep some duffus from saying ‘what if’ because we voted that we can’t shoot folks just cause they need it so the whole thing collapses because you did not vote to make it mandatory that everyone become a Republican who hates Bush and blames him for everything and throwing Einstein through the window willy nilly so you can say once again, “What if?” > > It is a post count thread – nothing more… Not one thing worth while was learned except for those poor folks that thought aircraft wheels were driven by the engines like a car. Some of them may have learned something if they read this whole thing. ( doubtful ) Actually, I thought this was one of the better threads I’ve read in a while. It took alot of work for me to mentally figure out where the problem really was. I knew the air-speed over the wings was all that mattered to get in the air. I knew the thrust of the engines was sure as heck going to move that thing forward. But I also knew that the wheel speed/belt speed (based on my assumptions about wheel speed) meant no forward progress was possible. What I couldn’t figure out was, what was I missing in this contradiction? As I read posts, thought about other arguments, etc. I was forced to really dive down to a level of detail I didn’t expect after first reading the OP, and ultimately the answer becomes, not one of physics, but one of language in the OP. ---
**Author:** ![devilsknew](https://avatars.discourse-cdn.com/v4/letter/d/4da419/32.png) [@devilsknew](https://boards.straightdope.com/u/devilsknew)\ **Post date:** [December 10, 2005, 3:01am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/251 "2005-12-10T03:01:30Z")
I don’t know if this has been mentioned yet in the 6 pages of posts (I only had time to read the first page.), but I know for a fact that it is physically impossible for a plane to achieve lift off on a treadmill for the simple fact that there are no treadmill runways on any aircraft carriers or on military airbases. If this was possible there would be no Harrier jet and there would be very tiny airports. ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [December 10, 2005, 3:04am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/252 "2005-12-10T03:04:17Z")
> [@devilsknew](#): > > I don’t know if this has been mentioned yet in the 6 pages of posts (I only had time to read the first page.), but I know for a fact that it is physically impossible for a plane to achieve lift off on a treadmill for the simple fact that there are no treadmill runways on any aircraft carriers or on military airbases. If this was possible there would be no Harrier jet and there would be very tiny airports. Its too bad that you didn’t read the entire thread becuase I just proved that is in fact possible to launch a jet from a treadmill albeit extremely impracticle. ---
**Author:** ![astro](https://avatars.discourse-cdn.com/v4/letter/a/9dc877/32.png) [@astro](https://boards.straightdope.com/u/astro)\ **Post date:** [December 10, 2005, 3:07am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/253 "2005-12-10T03:07:56Z")
Not that I don’t appreciate the efforts in this thread, but in order to cut to the chase in this lengthy dissertation which post # got it right re the answer? ---
**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:** [December 10, 2005, 3:26am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/254 "2005-12-10T03:26:33Z")
> [@scr4](#): > > If the tire and treadmill surfaces are not frictionless (i.e. tire is not slipping across the treadmill), then there _will_ be horizontal force, even if the bearing is frictionless. Because a bearing does not need friction to transmit horizontal force. > [@scr4](#): > > As I wrote earlier, a frictionless bearing can still transmit horizontal force. If the treadmill is in good contact (not frictionless) with the tire, and if the treadmill is accelerating, then it is exerting horizontal force on the tire. This horizontal force is not counter-acted by anything, so it is transmitted to the rest of the plane. This is the point that I missed in the beginning, by the way, as I noted back in post #103. Oh well, nobody’s perfect. ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [December 10, 2005, 3:33am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/255 "2005-12-10T03:33:34Z")
> [@astro](#): > > Not that I don’t appreciate the efforts in this thread, but in order to cut to the chase in this lengthy dissertation which post # got it right re the answer? There are two possible interpetations for what is meant by the problem. The first is that the treadmill goes backwards with a speed equal to the forward linear speed of the plane. In that case the plane takes off requiring slightly more energy and a slightly longer distance. The second case is that the treadmill speed is equal and opposite to the linear speed on the edge of the tire. In that case the plane does not take off but spins its wheels faster and faster. Eventually the tires will fail and your plane goes shooting off the back of the treadmill. If we assume indestructable tires eventually relativistic effects take over and the tires become more and more massive but the plane still doesn’t take off. See my pdf will pretty pictures and the math: [http://rapidshare.de/files/8904504/answer.pdf.html](http://rapidshare.de/files/8904504/answer.pdf.html) ---
**Author:** ![A.R.Cane](https://avatars.discourse-cdn.com/v4/letter/a/ee7513/32.png) [@A.R.Cane](https://boards.straightdope.com/u/A.R.Cane)\ **Post date:** [December 10, 2005, 3:35am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/256 "2005-12-10T03:35:31Z")
> [@robby](#): > > This is the point that I missed in the beginning, by the way, as I noted back in post #103. > > Oh well, nobody’s perfect. So are you now convinced that the plane cannot achieve flight? ---
**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:** [December 10, 2005, 4:52am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/257 "2005-12-10T04:52:27Z")
> [@A.R. Cane](#): > > So are you now convinced that the plane cannot achieve flight? I think **zut** ’s post #224 and **treis** ’s post #255 both summed things up pretty well. It depends on the assumptions made about the problem. However, I now believe I was wrong to flatly state that the plane would take off under all conditions, as if the plane was taking off from a frictionless surface. ---
**Author:** ![Uncommon\_Sense](https://avatars.discourse-cdn.com/v4/letter/u/f9ae1b/32.png) [@Uncommon\_Sense](https://boards.straightdope.com/u/Uncommon_Sense)\ **Post date:** [December 10, 2005, 7:29am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/258 "2005-12-10T07:29:42Z")
> [@treis](#): > > This is wrong, the friction between the wheel and the conveyor belt provide a force opposite to the thrust. I wasn’t wrong, I just wasn’t totally correct. you are right the friction between the conveyor and the wheel must be dealt with, as negligible as it may be. ---
**Author:** ![Uncommon\_Sense](https://avatars.discourse-cdn.com/v4/letter/u/f9ae1b/32.png) [@Uncommon\_Sense](https://boards.straightdope.com/u/Uncommon_Sense)\ **Post date:** [December 10, 2005, 7:38am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/259 "2005-12-10T07:38:54Z")
Am I correct to assume that in a frictionless environment that as soon as the plane started to move the conveyor would have to reach infinite speed? Any movement of the plane at all relavent to the ground (sans conveyor) would elicite a reaction that would destroy all physical properties as we know them. Hence, the problem cannot be solved in the frictionless environment. We can only solve this problem in the practical reference. That of which the conveyor reacts to the speed opposite the tires. ---
**Author:** ![Brutal\_Tokyo](https://avatars.discourse-cdn.com/v4/letter/b/278dde/32.png) [@Brutal\_Tokyo](https://boards.straightdope.com/u/Brutal_Tokyo)\ **Post date:** [December 12, 2005, 9:16am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/260 "2005-12-12T09:16:36Z")
[QUOTE=bouv] Can the plane take off? The fact that the plane has wheels that spin is irrelevant. The fact that people are confusing the wording of the problem is completely relevant as well as the minor logical imperfections and areas open to interpretation of the original poster’s question, so here are few thoughts I’d like to add without digressing into any particularly confusing or cryptic examples. The most common interpretation is that the tires are spinning as the treadmill is spinning, and there is the assumption that applying forward thrust to the airplane makes the tires spin, which makes the treadmill spin under them at the same speed. We can make different assumptions for a powered treadmill, and intelligent treadmill that adjusts itself to the speed of the wheels automatically (take speed of zero for instance, as another posted suggested, and play with that for a bit). The real problem here is that some don’t grasp is that the wheels have nothing to do with the power source of the airplane, so let’s try this: Put a glider with wheels on a treadmill. Put Jim and Larry and Bob and Fran on the treadmill. Jim, Bob and Larry and Fran push on the glider from behind…what happens to the glider as the ground speed of the treadmill increases? The glider wheels move and so do Jim, Bob, Larry and Fran until they get tired and can’t push anymore. The glider will stay there as long as the wheels continue to spin under the glider. With the Jet airplane, the thrust is external to the treadmill/wheel system, so pushing with a stick at the back of the airplane will move the airplane. pushing with a stick while on the treadmill yourself and while attached to the airplane will have no affect. If you are on the treadmill and on rollerblades and push on the airplane with a stick, the opposing forces equal about zero (given friction, etc.) and you will be propelled backward because you weight much less than the airplane you pushed on. With the jet airplane, the only thing that matters is that the jet is pushing on the plane. The wheels can do whatever they want and spin as fast as they want, but it won’t make the plane go any slower or stay still unless the jet engine had absolutely no thrust and was instead used to drive a belt or shaft that drove the wheels. This would be a huge problem because as soon as the plane hit take-off speed, the wheels would not have anything to accelerate against (the ground or treadmill) and the plane would crash after briefly taking flight. So of the plane were driven only by wheels, it would not fly, and a plane of this type would never be designed in the first place, except for an hang glider, a kite, or a parasail. Now, you could fly a kite while sitting in a wagon on a treadmill, but you would have a hard time launching a hang gliding. If we clamp the plane to the tarmac or the base assembly of the treadmill will the plane take off? No. It has all the additional weight of the treadmill to try to push forward and we assume the thrust of the engines is not that great? This will also pose some serious aerodynamic problems if the plane were eventually able to drage the entire treadmill assembly down the runway until it achieved take-off speed. Will the ropes holding the plane to the base of the treadmill be pulled taught? Yes. What will happen if the ropes are released? The plane will take off. For those that are so certain that the plane will not take, off try this: stand behind the airplane with a rope tied to it and tied to your waist (or neck or arms for the more disgusting among you) while your feet are tied to the tarmac. Is this something you are willing to do try to prove your point as the engines go to max thrust? What would happen if we put another treadmill on the top of the plane attached to another set of wheels protruding from the top of the plane and the bottom treadmill and top treadmill were operated in opposite directions thereby cancelling each other out? The wheels will just spin under the friction of the airplane and the airplane will stand still. When the engines are lit and the air is blown out the back of them at high speed, the plane will then move and will take off after the plane overcomes the friction of the wheels against the treadmills, which is very small. [Previous page](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567.md?page=12) [Next page](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567.md?page=14)