# If a plane can take off on a conveyer belt, then why not use conveyer belts? **URL:** \ **Category:** Cecil's Columns/Staff Reports\ **Created:** [March 27, 2018, 3:33pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279 "2018-03-27T15:33:10Z")\ **Posts on this page:** 20\ **Page:** 4
**Author:** ![jz78817](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jz78817/32/1028_2.png) [@jz78817](https://boards.straightdope.com/u/jz78817)\ **Post date:** [March 29, 2018, 11:52am UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/61 "2018-03-29T11:52:40Z")
> [@nate](#): > > So how does the plane ever move forward? for the 5 millionth time, the thrust from the engines. ---
**Author:** ![RitterSport](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rittersport/32/6326_2.png) [@RitterSport](https://boards.straightdope.com/u/RitterSport)\ **Post date:** [March 29, 2018, 12:25pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/62 "2018-03-29T12:25:25Z")
> [@jz78817](#): > > for the 5 millionth time, the thrust from the engines. I predict this will satisfy all readers and this thread will quickly die. ---
**Author:** ![Morgenstern](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@Morgenstern](https://boards.straightdope.com/u/Morgenstern)\ **Post date:** [March 29, 2018, 1:47pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/63 "2018-03-29T13:47:43Z")
> [@jz78817](#): > > for the 5 millionth time, the thrust from the engines. Propeller. 🙂 But yeah, you’re right. ---
**Author:** ![jz78817](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jz78817/32/1028_2.png) [@jz78817](https://boards.straightdope.com/u/jz78817)\ **Post date:** [March 29, 2018, 1:51pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/64 "2018-03-29T13:51:19Z")
> [@nate](#): > > So how does the plane ever move forward? The only way is for the wheel’s circumference to cover more “ground” per unit time then the conveyor belt’s backward speed. So if the wheel circumference is c, and the distance the belt moves is d, and d/sec always equals -c/sec. This, in its ideal form, keeps the plane from moving forward w.r.t. ground. The only way the plane moves wrt ground is if d/sec != c/sec. If this is wrong, I’d like to see why. This is the more interesting problem, in my opinion. I’d like to know what the imaginary plane would do in this scenario even though it obviously can not be created in the real world. in the ideal world the plane’s wheel bearings have no drag or friction, and the tires have no rolling resistance. in which case the wheels are irrelevant. the treadmill could be going eleventy billion miles per hour and it would have no effect on the plane. ---
**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:** [March 29, 2018, 2:26pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/65 "2018-03-29T14:26:58Z")
This is the pattern for a lot of thought experiments. You start from some set of circumstances which naively seem possible, and ask what would happen. You follow through on that, and reach a contradiction. Therefore, you conclude that that that set of circumstances isn’t possible after all, even though it seemed like it at first. And then you stop. You don’t keep on saying “but what if it happens anyway, even though it’s impossible?”. Once you ask that question, you’re talking about magic, not science, and literally any answer is possible. You can literally logically conclude “then the sky turns green, and Santa Clause takes back all of the presents he’s given away over the years”. ---
**Author:** ![nate](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nate/32/13085_2.png) [@nate](https://boards.straightdope.com/u/nate)\ **Post date:** [March 29, 2018, 4:26pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/66 "2018-03-29T16:26:10Z")
…sigh… I feel like at least one of you could actually answer the question but maybe you are unsure yourselves. There could be a real-world experiment where the treadmill always moves faster than the plane’s wheels. For example, in the real world the plane has limited thrust, so the speed of treadmill is always at the plane’s maximum ground speed + 1 ft/sec. How does the wheels’ axles move forward referenced to ground? Even if there is zero rolling resistance, infinite friction between the wheel and belt what force prevents the plane from moving forward? I can’t think of any, but at the same time it doesn’t make mechanical sense to me that the plane, with all of its weight on the wheels, the wheels have to turn for the plane to move forward, and they do, but for all the distance 1 revolution covers, the new starting point for the next revolution is actually behind this initial starting point (w.r.t. ground) due to the belt moving backward at a higher speed. Just saying the plane moves due to thrust from the jets is not explaining the above. Like me wearing roller skates on a treadmill, if my wheels are not allowed to turn as fast as the treadmill is moving, I’d quickly fall off the back, regardless of my arms (the jets) pulling myself forward. ---
**Author:** ![DrCube](https://avatars.discourse-cdn.com/v4/letter/d/a3d4f5/32.png) [@DrCube](https://boards.straightdope.com/u/DrCube)\ **Post date:** [March 29, 2018, 4:30pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/67 "2018-03-29T16:30:27Z")
Yeah, imagine the roller skates have brakes. They can’t turn as fast as they need to to keep up with the treadmill. But if you’re pulling yourself forward by a rope attached to the wall, you’ll still move forward, and the wheels will just skid. It will require a little more force to pull yourself forward, but not an infinite or insurmountable force. ---
**Author:** ![k9bfriender](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k9bfriender/32/3283_2.png) [@k9bfriender](https://boards.straightdope.com/u/k9bfriender)\ **Post date:** [March 29, 2018, 4:30pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/68 "2018-03-29T16:30:35Z")
> [@nate](#): > > …sigh… I feel like at least one of you could actually answer the question but maybe you are unsure yourselves. There could be a real-world experiment where the treadmill always moves faster than the plane’s wheels. For example, in the real world the plane has limited thrust, so the speed of treadmill is always at the plane’s maximum ground speed + 1 ft/sec. How does the wheels’ axles move forward referenced to ground? Even if there is zero rolling resistance, infinite friction between the wheel and belt what force prevents the plane from moving forward? I can’t think of any, but at the same time it doesn’t make mechanical sense to me that the plane, with all of its weight on the wheels, the wheels have to turn for the plane to move forward, and they do, but for all the distance 1 revolution covers, the new starting point for the next revolution is actually behind this initial starting point (w.r.t. ground) due to the belt moving backward at a higher speed. > > Just saying the plane moves due to thrust from the jets is not explaining the above. Like me wearing roller skates on a treadmill, if my wheels are not allowed to turn as fast as the treadmill is moving, I’d quickly fall off the back, regardless of my arms (the jets) pulling myself forward. If that is the case, then the wheels will skid until the plane either lifts off, or they explode. ---
**Author:** ![Sparky812](https://avatars.discourse-cdn.com/v4/letter/s/eb9ed0/32.png) [@Sparky812](https://boards.straightdope.com/u/Sparky812)\ **Post date:** [March 29, 2018, 4:33pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/69 "2018-03-29T16:33:07Z")
> [@nate](#): > > So how does the plane ever move forward? Forget about the wheels and treadmill, they do not act of the plane. The plane propels itself through the air without friction with the ground like a boat in water. The wheels only support the plane off the ground long enough to achieve enough lift to take-off. ---
**Author:** ![jz78817](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jz78817/32/1028_2.png) [@jz78817](https://boards.straightdope.com/u/jz78817)\ **Post date:** [March 29, 2018, 4:40pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/70 "2018-03-29T16:40:57Z")
> [@nate](#): > > …sigh… I feel like at least one of you could actually answer the question but maybe you are unsure yourselves. we’ve answered it multiple times. You not liking the answer you were given doesn’t change that. > [@](#): > > There could be a real-world experiment where the treadmill always moves faster than the plane’s wheels. For example, in the real world the plane has limited thrust, so the speed of treadmill is always at the plane’s maximum ground speed + 1 ft/sec. How does the wheels’ axles move forward referenced to ground? the force pushing the plane forward (thrust) is far greater than whatever force the treadmill can apply to the wheels to try to hold the plane still. ---
**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:** [March 29, 2018, 4:49pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/71 "2018-03-29T16:49:29Z")
The plane doesn’t have a maximum groundspeed. It has a maximum airspeed. And if you set the treadmill to a speed greater than the plane’s maximum airspeed, then when the plane reaches that airspeed, the wheels are turning twice as fast. ---
**Author:** ![AlsoNamedBort](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alsonamedbort/32/3213_2.png) [@AlsoNamedBort](https://boards.straightdope.com/u/AlsoNamedBort)\ **Post date:** [March 29, 2018, 4:58pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/72 "2018-03-29T16:58:09Z")
> [@nate](#): > > …sigh… I feel like at least one of you could actually answer the question but maybe you are unsure yourselves. There could be a real-world experiment where the treadmill always moves faster than the plane’s wheels. For example, in the real world the plane has limited thrust, so the speed of treadmill is always at the plane’s maximum ground speed + 1 ft/sec. How does the wheels’ axles move forward referenced to ground? Even if there is zero rolling resistance, infinite friction between the wheel and belt what force prevents the plane from moving forward? I can’t think of any, but at the same time it doesn’t make mechanical sense to me that the plane, with all of its weight on the wheels, the wheels have to turn for the plane to move forward, and they do, but for all the distance 1 revolution covers, the new starting point for the next revolution is actually behind this initial starting point (w.r.t. ground) due to the belt moving backward at a higher speed. > > Just saying the plane moves due to thrust from the jets is not explaining the above. Like me wearing roller skates on a treadmill, if my wheels are not allowed to turn as fast as the treadmill is moving, I’d quickly fall off the back, regardless of my arms (the jets) pulling myself forward. Cecil answered this question as well: > [@](#): > > As you point out, one problem here is the wording of the question. Your version straightforwardly states that the conveyor moves backward at the same rate that the plane moves forward. If the plane’s forward speed is 100 miles per hour, the conveyor rolls 100 MPH backward, and the wheels rotate at 200 MPH. Assuming you’ve got Indy-car-quality tires and wheel bearings, no problem. However, some versions put matters this way: “The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.” This language leads to a paradox: If the plane moves forward at 5 MPH, then its wheels will do likewise, and the treadmill will go 5 MPH backward. But if the treadmill is going 5 MPH backward, then the wheels are really turning 10 MPH forward. But if the wheels are going 10 MPH forward . . . Soon the foolish have persuaded themselves that the treadmill must operate at infinite speed. \*\*Nonsense. The question thus stated asks the impossible — simply put, that A = A + 5 — and so cannot be framed in this way. \*\*Everything clear now? Maybe not. But believe this: The plane takes off. ---
**Author:** ![nate](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nate/32/13085_2.png) [@nate](https://boards.straightdope.com/u/nate)\ **Post date:** [March 29, 2018, 5:39pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/73 "2018-03-29T17:39:23Z")
> [@k9bfriender](#): > > If that is the case, then the wheels will skid until the plane either lifts off, or they explode. Alright, this is what I would imagine would happen. I feel like I’m getting somewhere with understanding this. The skidding part is left out of the common explanations I’ve seen. But if there is no slippage allowed, the plane would never move forward, right? The force that is enforcing the no slippage policy obviously would be much greater than the plane’s thrust. ---
**Author:** ![nate](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nate/32/13085_2.png) [@nate](https://boards.straightdope.com/u/nate)\ **Post date:** [March 29, 2018, 5:47pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/74 "2018-03-29T17:47:33Z")
> [@AlsoNamedBort](#): > > Cecil answered this question as well: Wait, why would the wheels need to travel @ 2x the treadmill speed for the axle to remain stationary? If the “treadmill” was just a copy of the wheel rotating in the opposite direction, they would rotate at the same speed to keep the axle stationary, right? Like a 1:1 gear? ---
**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:** [March 29, 2018, 5:48pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/75 "2018-03-29T17:48:37Z")
> [@nate](#): > > But if there is no slippage allowed, the plane would never move forward, right? The force that is enforcing the no slippage policy obviously would be much greater than the plane’s thrust. Sure. But that force doesn’t exist. So the plane still takes off. ---
**Author:** ![AlsoNamedBort](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/alsonamedbort/32/3213_2.png) [@AlsoNamedBort](https://boards.straightdope.com/u/AlsoNamedBort)\ **Post date:** [March 29, 2018, 5:52pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/76 "2018-03-29T17:52:42Z")
> [@nate](#): > > Wait, why would the wheels need to travel @ 2x the treadmill speed for the axle to remain stationary? If the “treadmill” was just a copy of the wheel rotating in the opposite direction, they would rotate at the same speed to keep the axle stationary, right? Like a 1:1 gear? Because the axle isn’t remaining stationary. The plane is moving forward, the treadmill moving backward, the wheels are spinning faster. ---
**Author:** ![nate](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nate/32/13085_2.png) [@nate](https://boards.straightdope.com/u/nate)\ **Post date:** [March 29, 2018, 6:07pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/77 "2018-03-29T18:07:33Z")
Again, I’m aware this topic has been beat to death, and I swear I’m not trying to assert that I’m right, I’m genuinely trying to understand where my logic is wrong. Sorry that it’s taking so much effort. ---
**Author:** ![RitterSport](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rittersport/32/6326_2.png) [@RitterSport](https://boards.straightdope.com/u/RitterSport)\ **Post date:** [March 29, 2018, 6:16pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/78 "2018-03-29T18:16:31Z")
> [@nate](#): > > Again, I’m aware this topic has been beat to death, and I swear I’m not trying to assert that I’m right, I’m genuinely trying to understand where my logic is wrong. Sorry that it’s taking so much effort. Can you describe how you think this works? The plane starts, so the wheels are moving at 0.001 m/s. So, the treadmill immediately moves to 0.001 m/s in the other direction, causing the wheels to move at 0.002 m/s. Now what? Does it go to infinity immediately? Did you see the last paragraph of Cecil’s explanation where he says that A cannot equal A+5? Are you positing a world where there are frictionless bearings but treadmill surfaces with infinite friction? ---
**Author:** ![jz78817](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jz78817/32/1028_2.png) [@jz78817](https://boards.straightdope.com/u/jz78817)\ **Post date:** [March 29, 2018, 6:26pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/79 "2018-03-29T18:26:04Z")
> [@nate](#): > > Again, I’m aware this topic has been beat to death, and I swear I’m not trying to assert that I’m right, I’m genuinely trying to understand where my logic is wrong. Sorry that it’s taking so much effort. wheels convert rotational/angular velocity to linear velocity (and vice versa.) All you are doing by increasing the linear velocity they’re experiencing (by speeding up the ground surface e.g. treadmill) is increasing their angular velocity (e.g. making them spin faster.) that doesn’t translate directly to a linear force capable of counteracting the engine thrust. ---
**Author:** ![Mithras](https://avatars.discourse-cdn.com/v4/letter/m/f04885/32.png) [@Mithras](https://boards.straightdope.com/u/Mithras)\ **Post date:** [March 29, 2018, 6:31pm UTC](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279/80 "2018-03-29T18:31:55Z")
Toys on a real treadmill have been mentioned before, but I think thinking about that is the best way to understand this intuitively. If you put a toy car on a treadmill with your finger against the back of it and set the treadmill speed to 1 mph, the car stays in place and presses against your finger with a minimal force. Crank up the treadmill’s speed as high as you can and the car becomes no harder to hold in place. And it takes the same amount of effort in both cases to push the car forward. Your finger is the plane’s engine. [Previous page](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279.md?page=3) [Next page](https://boards.straightdope.com/t/if-a-plane-can-take-off-on-a-conveyer-belt-then-why-not-use-conveyer-belts/811279.md?page=5)