# error in the "will the plane take off" **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [August 14, 2007, 11:05am UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537 "2007-08-14T11:05:17Z")\ **Posts on this page:** 10\ **Page:** 3
**Author:** ![Alexis\_Brooke](https://avatars.discourse-cdn.com/v4/letter/a/58956e/32.png) [@Alexis\_Brooke](https://boards.straightdope.com/u/Alexis_Brooke)\ **Post date:** [November 2, 2007, 7:25am UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/41 "2007-11-02T07:25:23Z")
> [@](#): > > _ **A.** Suppose we actually built a treadmill and put a 747 on it, and had the treadmill match the speed of the **plane**. Would the 747 take off?_ If the treadmill matches the plane _fuselage speed_, then yes. The treadmill simply accelerates in the opposite direction that the plane does; the plane moves in one direction relative to the ground and the treadmill moves in the other. The wheels wind up _rotating_ twice as fast as they normally would, but the plane will take off, leaving a treadmill behind that’s rotating in the opposite direction. The plane’s wheels will only rotate twice as fast if the plane is moving at twice the speed of the treadmill, or simply the speed it would move if the treadmill was not in motion. In order for the wheels to rotate, some force must be imparted upon the plane in the direction opposite the treadmill. Being tied to something in front of it will cause the plane to remain stationary. However, without the restraint, or thrust from the engines, the wheels will not rotate at all, and the plane will simply move backwards. ---
**Author:** ![Terminus\_Est](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/terminus_est/32/3087_2.png) [@Terminus\_Est](https://boards.straightdope.com/u/Terminus_Est)\ **Post date:** [November 3, 2007, 5:56pm UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/42 "2007-11-03T17:56:19Z")
[QUOTE=zut] Knowing Mythbusters, I suspect the plane revved up, lurched forward, slewed off the runway, careened wildly toward the camera crew, tipped onto its nose, and exploded in a ball of flame. [/QUOTE] So that’s what [this picture](http://www.snopes.com/photos/airplane/flightschool.asp) was about! ---
**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:** [November 4, 2007, 2:04pm UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/43 "2007-11-04T14:04:10Z")
[QUOTE=Alexis Brooke] The plane’s wheels will only rotate twice as fast if the plane is moving at twice the speed of the treadmill, or simply the speed it would move if the treadmill was not in motion. [/QUOTE] You’re getting confused by the reference point for relative velocity. In the quoted case, I’m talking about plane fuselage speed relative to the _ground_, as well as treadmill speed relative to the ground. The treadmill runs in one direction at the same speed (relative to ground) as the plane speed (relative to ground) does in the other–and thus the wheels must rotate twice as fast. You could, of course, talk about plane fuselage speed relative to the _treadmill_, but that reduces the problem to one of four cases: a) If the plane fuselage speed _relative to the treadmill_ matches the treadmill speed _relative to the ground_ in the _opposite_ direction, then the plane doesn’t move at all relative to the _ground_ (and turns into the same problem as wheel-speed-matching, covered by my above post). b) If the plane fuselage speed _relative to the treadmill_ matches the treadmill speed _relative to the ground_ in the _same_ direction, then the plane travels at twice the speed of the treadmill _relative to the ground_ (and takes off with its wheels turning at _half_-speed). c) If the plane fuselage speed _relative to the treadmill_ matches the treadmill speed _relative to the plane_ in the _opposite_ direction, then that’s no restriction at all (the plane and treadmill can do anything at all and the condition will be satisfied). d) If the plane fuselage speed _relative to the treadmill_ matches the treadmill speed _relative to the plane_ in the _same_ direction, then that’s an over-constraint, and can only be satisfied if both speeds are zero. [QUOTE=Alexis Brooke] In order for the wheels to rotate, some force must be imparted upon the plane in the direction opposite the treadmill. Being tied to something in front of it will cause the plane to remain stationary. However, without the restraint, or thrust from the engines, the wheels will not rotate at all, and the plane will simply move backwards. [/QUOTE] Well, yes and no. First of all, I don’t think anyone anyone interpreted the problem as asking what would happen with the engines _off_ (certainly I didn’t). However, I suppose there’s nothing wrong with that assumption. Clearly, in this case the plane will move in the direction the treadmill moves. However, exactly what happens depends on the acceleration of the treadmill. Three things can happen: a) If the treadmill acceleration is _small_ (i.e., not enough to overcome friction in the wheel bearings), the plane will move at the same speed as the treadmill (with no wheel rotation). b) If the treadmill acceleration is _medium_ (i.e., big enough to overcome friction in the wheel bearings, but not large enough to overcome friction between the tire and treadmill), the wheels will begin to rotate with acceleration that depends on its mass and mass moment of inertia. However, some force is still transmitted to the plane, so the plane will also move, but at a speed much less than that of the treadmill. c) If the treadmill acceleration is _large_ (i.e., big enough to overcome friction between the tire and treadmill), the result is similar to case (b), but the force transmitted to the wheel is no longer a function of treadmill motion. ---
**Author:** ![PinzEOD](https://avatars.discourse-cdn.com/v4/letter/p/f19dbf/32.png) [@PinzEOD](https://boards.straightdope.com/u/PinzEOD)\ **Post date:** [November 9, 2007, 6:51pm UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/44 "2007-11-09T18:51:00Z")
I might be thinking too far outside the box here, but the answer to me seems obvious. At the onset of the problem, the force pushing/pulling the plane (jet or prop, doesn’t matter) equals the force applied by the moving conveyor (the belt against the rotating tires), so the plane is stationary. If power is added to the force against the plane, and an equal increase in power is applied to the conveyor’s force in the opposite direction, the plane remains stationary. I.E: 100 units of ‘force x’ push the plane east, a corresponding 100 units of ‘force y’ move the conveyor belt west, no movement. Both forces increase equally, the plane still will not move. The cause of the force doesn’t matter. The plane is trying to move ahead, the spinning belt stops it. MPH has no bearing, wind speed and ground speed too. An object at rest has zero velocity - and (in the absence of an unbalanced force) will remain with a zero velocity. Such an object will not change its state of motion (i.e., velocity) unless acted upon by an unbalanced force. An object in motion with a velocity of 2 m/s, East will (in the absence of an unbalanced force) remain in motion with a velocity of 2 m/s, East. Such an object will not change its state of motion (i.e., velocity) unless acted upon by an unbalanced force. Objects resist changes in their velocity. More fuel for the fire I guess. ---
**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:** [November 9, 2007, 6:56pm UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/45 "2007-11-09T18:56:04Z")
[QUOTE=PinzEOD] The plane is trying to move ahead, the spinning belt stops it. [/QUOTE] If you can explain how the free spinning airplane wheel allows the belt to apply force to the plane you might have something. 🆒 ---
**Author:** ![Sapo](https://avatars.discourse-cdn.com/v4/letter/s/ec9cab/32.png) [@Sapo](https://boards.straightdope.com/u/Sapo)\ **Post date:** [November 9, 2007, 7:02pm UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/46 "2007-11-09T19:02:17Z")
[QUOTE=zut] Knowing Mythbusters, I suspect the plane revved up, lurched forward, slewed off the runway, careened wildly toward the camera crew, tipped onto its nose, and exploded in a ball of flame. [/QUOTE] Ooh! missed this the first time around. This deserves its own thread. They will put someone that has never before flown on conveyor made of supermarket plastic bags. It will fail and they will declare it busted. ---
**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:** [November 9, 2007, 8:43pm UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/47 "2007-11-09T20:43:03Z")
[QUOTE=PinzEOD] At the onset of the problem, the force pushing/pulling the plane (jet or prop, doesn’t matter) equals the force applied by the moving conveyor (the belt against the rotating tires), so the plane is stationary. [/QUOTE] How? Airplane wheels spin freely. They don’t transmit force like a car. Go back up and read **zut** ’s post again, carefully. ---
**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:** [November 9, 2007, 8:51pm UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/48 "2007-11-09T20:51:12Z")
[QUOTE=Telemark] If you can explain how the free spinning airplane wheel allows the belt to apply force to the plane you might have something. 🆒 [/QUOTE] Covered above, post 3, case E (and explained further in case J). Also rather exhaustively discussed in one or 'nother of those old ten-page threads, which I’m too lazy to look up. > [@Sapo](#): > > Ooh! missed this the first time around. This deserves its own thread. > > They will put someone that has never before flown on conveyor made of supermarket plastic bags. It will fail and they will declare it busted. Mmph. It has been my observation that Mythbusters is very good at putting together apparatus to perform an experiment, but less good at actually designing an experiment to demonstrate a particular problem. Which I believe is your point. ---
**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:** [November 9, 2007, 9:47pm UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/49 "2007-11-09T21:47:56Z")
[QUOTE=zut] Covered above, post 3, case E (and explained further in case J). Also rather exhaustively discussed in one or 'nother of those old ten-page threads, which I’m too lazy to look up. [/QUOTE] I know, but I was reading between the lines of the post. 🙂 ---
**Author:** ![Sapo](https://avatars.discourse-cdn.com/v4/letter/s/ec9cab/32.png) [@Sapo](https://boards.straightdope.com/u/Sapo)\ **Post date:** [November 10, 2007, 10:00am UTC](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537/50 "2007-11-10T10:00:43Z")
[QUOTE=zut] Covered above, post 3, case E (and explained further in case J). Also rather exhaustively discussed in one or 'nother of those old ten-page threads, which I’m too lazy to look up. Mmph. It has been my observation that Mythbusters is very good at putting together apparatus to perform an experiment, but less good at actually designing an experiment to demonstrate a particular problem. Which I believe is your point. [/QUOTE] My complaint is that they always assume that if they can’t do something themselves on their first try, then it is impossible. I almost stopped watching the show altogether with the stamp on a helicopter blade episode. Except that I keep coming back for the explosions. [Previous page](https://boards.straightdope.com/t/error-in-the-will-the-plane-take-off/415537.md?page=2)