# 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:** 18
**Author:** ![David\_Simmons](https://avatars.discourse-cdn.com/v4/letter/d/9de053/32.png) [@David\_Simmons](https://boards.straightdope.com/u/David_Simmons)\ **Post date:** [December 18, 2005, 2:11am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/341 "2005-12-18T02:11:18Z")
> [@yoyodyne](#): > > Imagine that the plane has 25 foot high and 10 foot wide wheels that weigh 100 tons each. It has frictionless bearings and is sitting on a stopped belt. When the belt starts spinning, do you think the plane will just sit there in place relative to the ground? Yes. Draw us a picture of the forces on the wheel and how a backward force gets transmitted to the plane. The treadmill’s force on the wheel results in a torque that spins the wheel With a frictionless bearing that’s as far as it goes. ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [December 18, 2005, 2:26am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/342 "2005-12-18T02:26:54Z")
> [@David Simmons](#): > > Yes. Draw us a picture of the forces on the wheel and how a backward force gets transmitted to the plane. The treadmill’s force on the wheel results in a torque that spins the wheel With a frictionless bearing that’s as far as it goes. Lets say you are on a bike with big heavy wheels sliding on some ice at 10 m/s. You slide off of the ice and onto some pavement that the tires do not slip on. Remembering that the mass of the tires makes up a significant portion of the overall mass, will you slow down or remain at the same speed. If you answer that you remain at the same speed please include where the energy comes from to spin the tires. If you answer that you slow down please include what force is responsible for your negative acceleration. ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [December 18, 2005, 2:28am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/343 "2005-12-18T02:28:10Z")
> [@treis](#): > > Lets say you are on a bike with big heavy wheels sliding on some ice at 10 m/s. You slide off of the ice and onto some pavement that the tires do not slip on. Remembering that the mass of the tires makes up a significant portion of the overall mass, will you slow down or remain at the same speed. If you answer that you remain at the same speed please include where the energy comes from to spin the tires. If you answer that you slow down please include what force is responsible for your negative acceleration. I should clarify, the wheels are not rotating when you are on the ice and do rotate when you move to the pavement. ---
**Author:** ![yoyodyne](https://avatars.discourse-cdn.com/v4/letter/y/a9a28c/32.png) [@yoyodyne](https://boards.straightdope.com/u/yoyodyne)\ **Post date:** [December 18, 2005, 2:53am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/344 "2005-12-18T02:53:09Z")
How about this: suppose there is no airplane at all, just a big wheel not attached to anything sitting on the stopped belt. When the belt starts to move, does the wheel move with the belt or just stay in place and spin? ---
**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 18, 2005, 3:10am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/345 "2005-12-18T03:10:17Z")
> [@David Simmons](#): > > No doubt about that. But the fucking wheels are decoupled from the fucking plane by the bearings and that force backwards on the wheels can’t be transmitted to the fucking plane. That is simply wrong. Neglecting acceleration for a moment, all the frictional force between the rubber tire and the pavement is transmitted through the hub to the plane. How else would automobile tires transmit force to keep a car going at constant speed? Even with acceleration, some proportion of the force must be transferred. And, by the way, you’re neglecting wheel inertia, which I assume is what **yoyodyne** and **treis** are referring to. That’s another way forces can be transferred. ---
**Author:** ![Sam\_Stone](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Sam\_Stone](https://boards.straightdope.com/u/Sam_Stone)\ **Post date:** [December 18, 2005, 3:37am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/346 "2005-12-18T03:37:56Z")
> [@treis](#): > > Lets say you are on a bike with big heavy wheels sliding on some ice at 10 m/s. You slide off of the ice and onto some pavement that the tires do not slip on. Remembering that the mass of the tires makes up a significant portion of the overall mass, will you slow down or remain at the same speed. If you answer that you remain at the same speed please include where the energy comes from to spin the tires. If you answer that you slow down please include what force is responsible for your negative acceleration. Okay, I never read your PDFs because I didn’t thread my way through the free download thing, but I see what you’ve been getting at. However… Aren’t you assuming that the force to spin the wheels must be coming from the airplane’s engines? If the bearings are frictionless, then the force required to overcome the inertia of the wheels is coming from the treadmill, not the airplane’s engines. As the airplane’s engines spool up and thrust it forward, the treadmill will accelerate - but the additional force on the wheels is coming from the treadmill, isn’t it? The airplane’s engines aren’t contributing to that at all. Thus, the thrust from the engines is left to move the aircraft forward. In your example above, there is no other force involved, so yes, the bicycle will slow down when it hits the dry pavement. To make the analogy more accurate, imagine the bike sliding onto a moving conveyer belt that will accelerate fast enough to absorb the force from the wheels. In that case, the bike won’t slow down because all the work is coming from the treadmill. In any case, you’ve built a complicated scenario, whereas I read the OP to be quite simple - the OP was thinking of a treadmill just like one would walk on. He’s thinking about a situation where the faster you walk, the faster the treadmill goes to keep you in place. He’s asking what would happen if an airplane were on such a treadmill. The answer is - the airplane would accelerate anyway, and would still take off, but it would take slightly longer because the force from bearing friction would have to be overcome, and at rotation the wheels would be turning twice as fast as they normally would, and the treadmill would be going the same speed as the airplane, except in the opposite direction. As I understand your scenario, the treadmill is simply trying to keep the airplane in place, by accelerating fast enough to always apply enough force to the axles to keep the airplane stationary. Is that correct? ---
**Author:** ![yoyodyne](https://avatars.discourse-cdn.com/v4/letter/y/a9a28c/32.png) [@yoyodyne](https://boards.straightdope.com/u/yoyodyne)\ **Post date:** [December 18, 2005, 4:15am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/347 "2005-12-18T04:15:39Z")
The treadmill would supply the energy to spin the wheels and the force from the engines would be holding the plane motionless against the acceleration of the treadmill. The problem is that the OP can be read two ways. If you read it as the treadmill will move to counteract any forward motion of the wheels, it would have to have an acceleration that would counter any and all thrust from the engine. Thus it would either reach infinite speed or something would break, and the conditions of the OP would be broken. ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [December 18, 2005, 4:21am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/348 "2005-12-18T04:21:22Z")
> [@Sam Stone](#): > > Okay, I never read your PDFs because I didn’t thread my way through the free download thing, but I see what you’ve been getting at. However… Aren’t you assuming that the force to spin the wheels must be coming from the airplane’s engines? I am not sure I understand the question here. The force from the airplane engines is to prevent the wheel from accelerating backwards. It can’t cause rotation becuase it acts on the axle through the center of mass of the wheel. > [@Sam Stone](#): > > If the bearings are frictionless, then the force required to overcome the inertia of the wheels is coming from the treadmill, not the airplane’s engines. As the airplane’s engines spool up and thrust it forward, the treadmill will accelerate - but the additional force on the wheels is coming from the treadmill, isn’t it? The airplane’s engines aren’t contributing to that at all. Thus, the thrust from the engines is left to move the aircraft forward. The force from the treadmill opposes the force from the engines. If its of equal magnitude as the force from the engines the plane will not move. Just to be clear here we have two forces of friction. We have the bearing friction which occurs between the axle and the wheel. This doesn’t cause linear acceleration but acts against the rotation of the wheel. Then there is friction between the treadmill and the point of contact on the wheels. This is a linear force that acts at that point. It both causes the wheel to accelerate backwards and causes the wheels to rotate. The force from the engine and the force from the treadmill are independent of eachother. One does not cause the other in the second case. > [@Sam Stone](#): > > In your example above, there is no other force involved, so yes, the bicycle will slow down when it hits the dry pavement. To make the analogy more accurate, imagine the bike sliding onto a moving conveyer belt that will accelerate fast enough to absorb the force from the wheels. In that case, the bike won’t slow down because all the work is coming from the treadmill. This isn’t physically possible. If the wheel starts spinning and the only force is the friction between the wheel and the road the bike has to slow down or speed up. The only way you could maintain the speed of the bike is to match the treadmill velocity with the linear forward velocity of the bike. If that happens there would be no force from friction and no wheel rotation. > [@Sam Stone](#): > > In any case, you’ve built a complicated scenario, whereas I read the OP to be quite simple - the OP was thinking of a treadmill just like one would walk on. He’s thinking about a situation where the faster you walk, the faster the treadmill goes to keep you in place. He’s asking what would happen if an airplane were on such a treadmill. The answer is - the airplane would accelerate anyway, and would still take off, but it would take slightly longer because the force from bearing friction would have to be overcome, and at rotation the wheels would be turning twice as fast as they normally would, and the treadmill would be going the same speed as the airplane, except in the opposite direction. Right, thats how I read it too but its not clear. The other interpetation is valid too. > [@Sam Stone](#): > > As I understand your scenario, the treadmill is simply trying to keep the airplane in place, by accelerating fast enough to always apply enough force to the axles to keep the airplane stationary. Is that correct? It applies enough force to the point of contact between the wheel and the treadmill. That is transferred through the axle to the body of the plane and counteracts the engines. ---
**Author:** ![Sam\_Stone](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Sam\_Stone](https://boards.straightdope.com/u/Sam_Stone)\ **Post date:** [December 18, 2005, 4:50am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/349 "2005-12-18T04:50:04Z")
Yep. I understand what you’re saying now. I was assuming a different problem. Although I still think your scenario doesn’t answer the OP. You’ve simply worked the problem backwards, saying, “okay, what would a treadmill have to do to keep an airplane standing still?” Anyway, it’s a much more interesting problem your way. ---
**Author:** ![lissener](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lissener/32/6139_2.png) [@lissener](https://boards.straightdope.com/u/lissener)\ **Post date:** [December 18, 2005, 5:32am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/350 "2005-12-18T05:32:30Z")
This cracks me up. The treadmill is 100% irrelevant to the airplane. It’s airspeed, not ground speed, that provides lift. How simple is this? This thread should go down in some kind of hall of fame for the most ridiculous argument ever. ---
**Author:** ![cainxinth](https://avatars.discourse-cdn.com/v4/letter/c/7bcc69/32.png) [@cainxinth](https://boards.straightdope.com/u/cainxinth)\ **Post date:** [December 18, 2005, 5:42am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/351 "2005-12-18T05:42:23Z")
Forget all this nonsense… now can someone please tell me if a submarine will dive in a tank of Jell-o? ---
**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\ **Post date:** [December 18, 2005, 5:42am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/352 "2005-12-18T05:42:41Z")
> [@lissener](#): > > This cracks me up. The treadmill is 100% irrelevant to the airplane. It’s airspeed, not ground speed, that provides lift. > > How simple is this? This thread should go down in some kind of hall of fame for the most ridiculous argument ever. And your post should be right up next to it with the most ridiculous argument in the most ridiculous thread. ---
**Author:** ![Sam\_Stone](https://avatars.discourse-cdn.com/v4/letter/s/ecccb3/32.png) [@Sam\_Stone](https://boards.straightdope.com/u/Sam_Stone)\ **Post date:** [December 18, 2005, 5:51am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/353 "2005-12-18T05:51:12Z")
> [@cainxinth](#): > > Forget all this nonsense… now can someone please tell me if a submarine will dive in a tank of Jell-o? Only if it’s made of lead. ---
**Author:** ![lissener](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lissener/32/6139_2.png) [@lissener](https://boards.straightdope.com/u/lissener)\ **Post date:** [December 18, 2005, 5:56am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/354 "2005-12-18T05:56:55Z")
> [@Sam Stone](#): > > Only if it’s made of lead. lead jello? sounds yucky. ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [December 18, 2005, 7:59am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/355 "2005-12-18T07:59:35Z")
> [@Sam Stone](#): > > So what? **This makes almost no difference**. This makes ALL the difference (if you interpret “speed” as circumference etc. etc.) Here is a simple example: Circumference of wheel=1 foot Length of belt=1 foot Place a mark on the wheel where it contacts the belt. Place a mark on the belt where it contacts the wheel. Place a 3rd mark on the ground directly below the wheel and the belt marks. Now spin wheel and belt **at exactly the same speed at all times** , let’s start with 1 foot per second. At time 0 seconds, both wheel and belt marks are touching, and lined up with ground mark. At time 1 second, same thing. At time 2 seconds, same thing. Now we instantaneously double wheel and belt speed. At time 3 seconds and new speed, all marks are still lined up. No forward progress relative to the ground. If you interpret “speed” as stated, you could leave the airplane out of the equation entirely and restate the OP as follows: “Consider a wheel and belt such that no forward movement is mathematically possible, will there ever be forward movement?” ---
**Author:** ![matt](https://avatars.discourse-cdn.com/v4/letter/m/a6a055/32.png) [@matt](https://boards.straightdope.com/u/matt)\ **Post date:** [December 18, 2005, 8:13am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/356 "2005-12-18T08:13:39Z")
> [@lissener](#): > > This cracks me up. The treadmill is 100% irrelevant to the airplane. It’s airspeed, not ground speed, that provides lift. > > How simple is this? This thread should go down in some kind of hall of fame for the most ridiculous argument ever. Disagree. It has brought up an interesting subtlety of physics that hadn’t occurred to me, so it has decreased the ignorance of at least one person… > [@David Simmons](#): > > No doubt about that. But the fucking wheels are decoupled from the fucking plane by the bearings and that force backwards on the wheels can’t be transmitted to the fucking plane. > [@David Simmons](#): > > Yes. Draw us a picture of the forces on the wheel and how a backward force gets transmitted to the plane. The treadmill’s force on the wheel results in a torque that spins the wheel With a frictionless bearing that’s as far as it goes. I thought that too. First time it was brought up, I thought “Nonsense! This guy **treis** doesn’t know what he’s talking about!” Lucky I didn’t post that, because he was right and I was wrong. The wheels have mass, yes? They have a rotational moment of inertia. If the treadmill is _continuously accelerating_ backwards, the wheels are building up more and more speed on their frictionless bearings. And they are building up energy, acting as flywheels. Now, because of the rotational inertia of the wheels, the treadmill is exerting a force on the wheels. At constant velocity it will not, but when accelerating, it must, or where is the energy building up in the wheels coming from? And that force is transmitted to the plane through the line of the axle, frictionless bearings be damned. This is the subtle effect I was referring to in my response to **lissener** - it was not at all obvious to me and I had to think about it for a while. It’s also one of the reasons why this thread is so long! If the plane is on frictionless _skids_, then it is truly decoupled from the treadmill and can ignore it whatever it does. But wheels with frictionless bearings only decouple at constant speed. When accelerations take place, they don’t decouple completely unless they are also massless. (Another way to look at it - scrap the treadmill. Have the plane take off on a normal runway, with frictionless bearings on its wheels. The energy required is the KE of the plane at take-off speed, plus the rotational energy stored in the spinning wheels at take-off speed, yes? (Neglecting drag and rolling resistance and all that real-world crap.) Now, replace the wheels with new ones of twice the density, and kick off some passengers so the total weight remains unchanged. The energy required to take off is greater, because the wheels have more rotational energy at take-off speed due to their greater mass. The engines would have to push harder over the same take-off distance. So accelerating the wheels requires additional engine force, and continuously accelerating the wheels backwards with a treadmill will create a force that opposes the thrust of the engines.) ---
**Author:** ![RaftPeople](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@RaftPeople](https://boards.straightdope.com/u/RaftPeople)\ **Post date:** [December 18, 2005, 8:22am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/357 "2005-12-18T08:22:03Z")
> [@lissener](#): > > This cracks me up. The treadmill is 100% irrelevant to the airplane. It’s airspeed, not ground speed, that provides lift. The treadmill does change the situation. Consider if the OP said “Imagine an airplane on a treadmill, no wait, imagine an airplane on a concrete runway…”, I think this would have died on page 1. > [@](#): > > **How simple is this?** You’ve grasped the easy part, that airspeed is required for lift, but I don’t really think anyone here didn’t know that already. This problem has been about “will the airplane move forward so that it can get airspeed?” > [@](#): > > This thread should go down in some kind of hall of fame for the most ridiculous argument ever. I think that when you grasp the various issues people have been trying to work out to determine the answer to the harder question, you will probably be either amused or unhappy with the fact you posted this. ---
**Author:** ![matt](https://avatars.discourse-cdn.com/v4/letter/m/a6a055/32.png) [@matt](https://boards.straightdope.com/u/matt)\ **Post date:** [December 18, 2005, 8:37am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/358 "2005-12-18T08:37:28Z")
> [@RaftPeople](#): > > Now spin wheel and belt **at exactly the same speed at all times** , let’s start with 1 foot per second. All you’ve shown is that there’s no slipping between the wheel and the belt. If in your example you push the wheel forward on the rolling belt, the marks will still line up even as the wheel rolls off the belt. ---
**Author:** ![Seven](https://avatars.discourse-cdn.com/v4/letter/s/3d9bf3/32.png) [@Seven](https://boards.straightdope.com/u/Seven)\ **Post date:** [December 18, 2005, 9:57am UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/359 "2005-12-18T09:57:58Z")
You guys are thinking about wheels and treadmills way too much. I’m going to pull some numbers out of my ass because I don’t know what the true numbers are, but it doesn’t really matter at the end of the day. Let’s say a jet airplane needs to be moving at 100 kph to take off. That means it needs 100 kph of wind going over it’s wings to get lift. It gets this wind from jet engines pushing the plane forward. Now, put this plane on a treadmill. The plane starts it’s engine and begins to move forward - the treadmill matches the forward movement (how it does this is of no matter). Let’s say on a normal runway it takes 75% of full power to get the plane up to 100 kph. Put the plane on the magic treadmill and crank the engines to 75%. The plane makes lots of noise by isn’t taking off? Why is that? Why not walk out on the wing and take a wind reading? Hey? how come you aren’t being blown off the top of the wing? Because there isn’t 100 kph of wind going over it. There is zero air flow. The airplace needs the airflow over the wing to get lift. The engines do not provide enough thrust to lift the plane alone. They provide enough thrust to get enough wind over the wing and the wing shape provides the lift. If the engine DID have enough thrust to lift the airplace without wings it would be called a rocket. For those of you having a hard time understanding this, let’s set up a slightly different situation. Put on the magic, no friction rollerblades (mentioned a few pages back) and head to the gym. Rewire the treadmill to go 100 kph. Hop on. Now, take out your kite (which you just happened to have in a large oversized pocket) and see if you can get it to fly. ---
**Author:** ![matt](https://avatars.discourse-cdn.com/v4/letter/m/a6a055/32.png) [@matt](https://boards.straightdope.com/u/matt)\ **Post date:** [December 18, 2005, 12:16pm UTC](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567/360 "2005-12-18T12:16:04Z")
> [@Seven](#): > > You guys are thinking about wheels and treadmills way too much. No we are not. > [@Seven](#): > > Let’s say a jet airplane needs to be moving at 100 kph to take off. That means it needs 100 kph of wind going over it’s wings to get lift. It gets this wind from jet engines pushing the plane forward. True. > [@Seven](#): > > Now, put this plane on a treadmill. The plane starts it’s engine and begins to move forward - the treadmill matches the forward movement (how it does this is of no matter). I think you mean the treadmill _cancels_ the forward movement of the plane. And how it does this is certainly not of “no matter”, because it simply can’t do it in real life. > [@Seven](#): > > Let’s say on a normal runway it takes 75% of full power to get the plane up to 100 kph. Put the plane on the magic treadmill and crank the engines to 75%. The plane makes lots of noise by isn’t taking off? Why is that? Why not walk out on the wing and take a wind reading? Hey? how come you aren’t being blown off the top of the wing? Because there isn’t 100 kph of wind going over it. There is zero air flow. Everyone understands this. But your treadmill really is magic, and so are your plane wheels, since the they both have to be going insanely fast to cancel the thrust of the engines. > [@Seven](#): > > The airplace needs the airflow over the wing to get lift. The engines do not provide enough thrust to lift the plane alone. They provide enough thrust to get enough wind over the wing and the wing shape provides the lift. WE KNOW. > [@Seven](#): > > If the engine DID have enough thrust to lift the airplace without wings it would be called a rocket. No it wouldn’t. A harrier jump jet can do it. A fair few military fighters can do a vertical climb. > [@Seven](#): > > For those of you having a hard time understanding this, let’s set up a slightly different situation. > > Put on the magic, no friction rollerblades (mentioned a few pages back) and head to the gym. Rewire the treadmill to go 100 kph. Hop on. Now, take out your kite (which you just happened to have in a large oversized pocket) and see if you can get it to fly. Nothing to do with the situation. EVERYBODY UNDERSTANDS that if the plane doesn’t move relative to the air, there’s no lift. YOU don’t understand that it’s really, really difficult for a treadmill to stop the plane from moving. Stand at one end of your gym treadmill on your no friction rollerblades and get someone else NOT on the treadmill to push you along it to the other end. That’s what the plane’s engines are doing. [Previous page](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567.md?page=17) [Next page](https://boards.straightdope.com/t/will-a-plane-on-a-treadmill-take-off/334567.md?page=19)