Plane vs. Treadmill Solved (free body diagram)

[whotaughtyou]

HIJACK

[subductionzone]

neodoc, the oldest known version of this problem is the one that you claimed no fly's invented. That is the one where the velocity as measured at the wheels is the same as the belt. By definition the plane stays in place. But is there a force that will keep the plane in place? It turns out there is. It is not friction, it is the resistance to rotational acceleration that keeps a plane in place. This is the same force that keeps a rolling cylinder from accelerating down a ramp at gsin.

[subductionzone]

@subductionzone Sorry. At g*sin(theta) where theta is the angle of the ramp. A solid cylinder will accelerate a (2/3)g*sin(t) and a hollow one will accelerate at (1/2)g*sin(t). Yes, I agree with your simplified constant speed treadmill that the plane will take off, but that was not the original question. The original was an untestable thought problem that was designed to make you think of the effect of the moment of inertia. It takes a huge acceleration to keep the plane in place.

[kasunagi123]

Simple but great explanation

[NakaTometugawa]

Nice video, thanks for wasting youtube bandwidth for this uneeded, logical SHIT.

[Peter1992t]

This is quite needed, you don't know what your talking about.

[macarion]

NO SMOKE AND MOYERS

[Mnementh2230]

as far as I can tell, the root of the original question comes from mistaking the way locomotion in a car works with the way locomotion in an airplane works. Since the plane's movement is not dependent on force generated via contact with the ground, the treadmill will only make the aircraft's time to liftoff slightly longer, as he's not starting from a stop. With frictionless landing gear, there is no theoretical limit to the treadmill's velocity - the plane will still lift off in time.

[Ananas85]

you're forgetting something: trust has a limit for the plane. The friction force is speed dependant

[neodocneodoc]

From SKF The rolling frictional moment is calculated from the equation Mrr = Grr (ν n)^0,6 where Mrr = rolling frictional moment, Nmm Grr = a variable that depends on -- the bearing type -- the bearing mean diameter dm = 0,5(d + D), mm -- the radial load Fr, N -- the axial load Fa, N n = rotational speed, r/min ν = kinematic viscosity of the lubricant at the operating temperature, mm2/s (for grease lubrication the base oil viscosity).

[neodocneodoc]

So it is not linear, squared, or cubed, but it is a function of the 1.67th root of the speed (at least for SKF bearings). This means that the frictional moment increases, but not as quickly as the speed. For example look at the 1.67th root of 10, 100, 1000

[pribeirom]

The far I know about aerodynamics allow me to say that the plane will only take off if there is enough air speed on its wings to provide sustentation. As this experiment is done with models, I think that the prop could make wind enough to sustain the flight... it's nothing about the speed of the conveyor, unless it helps the plane by making some extra wind.

that's my point of view, thanks and sorry 'bout my english. I'm from Brazil.

[existentialvoid]

The air needs to move to create lift for a wing. I seem to have missed the problem.

[1Rukee]

People have a problem with the plane being able to accelerate. To me it`s a no brain`r that the treadmill is going to have little to no effect at all on the free wheeling wheels of the plane. Once sufficient thrust is applied to overcome the resistance of the wheels the plane will accelerate away normally to it`s take off speed. The only way the treadmill would keep the plane stationary would be to do like a billion miles an hour and melt the landing gear out from underneath the plane.

[Stylensky]

A simple explanation is this.....If the plane produces enough thrust then it doesnt matter how fast the treadmill goes as its only spinning the wheels. If a plane had a trust to weight ratio of say 2/1 then it could take off straight up with no runway at all. I personally dont see what the all the hype is over this anyway...whos launching their plane from a treadmill to begin with?

[knoxjeff]

It's just a fun mind experiment to test our knowledge of physics.

[s70fixer]

The problem is indeed solved, by the "infinte loop" as stated in other posts. For the myth to be accurately busted, the treadmill will have to be capable of increasing its MPH as the plane continously overcomes it's frictional forces.

Flight is based on relative wind. It doesn't matter if the wing is moving at 120kts over the ground. What matters is that the wind moving over the wing is moving at 120kts. If the treadmill keeps pace with plane, relative wind will never be enough to create lift.

[robert0380]

Again you don't understand what's going on. It doesn't matter how fast you spin the treadmill, once the Force of thrust is greater than the frictional force in the bearings of the wheels, the plane will roll forward regardless of what the treadmill is doing. The treadmill can be going 1000 time faster than the plane and the plane would still take off (given the wheels themselves don't fail and the plane crashes and burns on the treadmill. You can't bust the myth.

[s70fixer]

Constant Velocity of Airplane=120kts(for ex).

Constant Opposite Velocity of Treadmill=-120kts.

Total velocity=0 kts which means no relative wind over the wings and thus no lift.

The mythbuster plane ACCELERATED to a velocity that was faster than the treadmill. This means that it's velocity relative to the treadmill was greater:

Increasing Velocity of Airplane=140kts.

Constant Opposite Velocity of Treadmill=-120kts.

Total Velocity=20kts relative wind over the wings and potentially lift.

[s70fixer]

As the plane overcomes its own frictional forces and begins to reach a velocity greater to the that of the treadmill it will move forward and eventually fly. The Mythbusters and this video's creator failed to increase the MPH of the treadmill relative to the increase of the plane's velocity.

[mitchio83]

The treadmill and the plane were going the same MPH. If you are saying the plane should have been stationary, (0 MPH) then the treadmill needs to be going 0 MPH. You actually think moving the treadmill a few MPH faster would have kept the airplane stationary?

[solidsnake123]

its less complex then you think,just really think about it

[shoopj]

seriously? I mean... seriously?

[shoopj]

^^ that is in re: to s70fixer..

[Rudmin]

The third version of the question is where the belt moves at such a speed that it equals the forward speed of the wheels. This would instantly accelerate the belt and the wheels beyond the speed of light at which the wheels melt and the plane disintegrates.

[neodocneodoc]

I'm not sure if I agree with the outcome of this scenario. Its been awhile since I designed a motor control system...maybe in the future.

[Rudmin]

The second version is where the belt moves backwards at such a speed that it holds the plane in one position. This would theoretically prevent the plane from flying, but the belt would quickly reach such a speed that it melts the wheel bearings. In reality, the plane would disintegrate itself.

[neodocneodoc]

Sounds like this bastardization was created by no-flyers. If the plane is held still (melted bearings, whatever) it won't fly :)

[Rudmin]

There are actually three questions out there. One original one, and two bastardized versions. The original question is where the belt moves at the same speed as the plane in the opposite direction. It is really simple, and everyone can see that the plane takes off.

[neodocneodoc]

I wish everyone could see it would take off. That's why I made these videos, because people argue this scenario to death, even after seeing the videos. This is also the one Mythbusters is testing.

[Technodynamic]

that's wonderful, now the real test...where the belt matches the speed of the tires (creating the infinite loop), not matching the plane speed. I want to see that test performed.

[neodocneodoc]

The original question is when the belt matches the plane speed in the opposite direction. That is what I am addressing, not these pseudo-experiments that have evolved, and that I am not going to argue for or against.

[Technodynamic]

Perhaps, but your experiment seems so obvious to me, its a no brainer that the plane will fly. It really is difficult to envision this experiement witht he wheels matching the belt speeds at any given time... that makes for a good debate. The original question is a basic IQ test that anyone with a functioning brain can agree the plane will fly.

[neodocneodoc]

Well, considering all the debating that goes on about the original question, there are alot of people without a functioning brain (In your opinion)...and I have read the exact same statement that anyone that has a functioning brain knows that it CANNOT fly.

Now, if the wheels don't slip, why would they NOT match the belt speed?

[neodocneodoc]

The wheels will always match the belt speed, unless they slip...I'm not sure where you are getting this infinite loop scenario from.

[sssssss27]

Well if the plane is traveling at 2 MPH and the belt is moving 2 MPH in the opposite direction, wouldn't the wheels be spinning at 4 MPH?

[neodocneodoc]

Gotchya...Still don't see how it is 'infinite loop', but regardless, treadmill speed within reason (under the specification for the wheels) will not have any affect on the plane.

[eleccy]

I believe the "infinite loop" he is proposing is akin to achilles and the tortoise problem. ie the tires speed up, so the conveyor speeds up, so the tires speed up and so on. This confusion was put to rest by using the mathematical tool of differentials.

[neodocneodoc]

Thank you.

[haunclesam]

I also cam across this problem, although I would not call it an infinite loop, but still, let me pose thise question you might have hear a thousand times before;

As I have seen it, there are two scenarios on the Web, one where the speed of the treadmill is matched to the plane speed, and one where it is matched to the speed of the spinning wheels, and as I see it, that does matter,

[haunclesam]

because if you for example, as seen above, let your plan roll with 1mp/h the wheels start turning, then the conveyor belt is activly (!) accelerated to the speed of the spinning wheels, so the plane again has a speed of zero, in comparison to the earth, shouldn't it?

[MacaqueMacaque]

one problem, ur not incorporating the most important force, DRAGONFORCE. lol

[gumbeau967]

Adding additional acceleration without counteracting it with additional conveyor speed changes the premise of the experiment.

If the conveyor accelerates to equal the acceleration of the aircraft thrust the aircraft remains stationary and doesn't take off.

Your experiment is correct but it doesn't address the original premise of the conveyor matching the acceleration of the aircraft.

[neodocneodoc]

I guess we will find out on Jan 30th

[gumbeau967]

The 'tape' overcoming the frictional forces is accelerating of the airplane. It is providing a force opposite the motion of the treadmill. That is the original premise of the problem. The airplane doesn't takeoff.

[ArrowHead83]

The airplane does take off. Long story short, it's because a plane's thrust comes from its turbines or propellers pushing the air, not the wheels rolling against the ground - the wheels are free-spinning. So all the conveyor will do is make the wheels spin twice as fast as normally.

[TakashiRamaru]

Actually, it depends on whether or not the jet engines are going, if the jets are working then the conveyor belt won't affect it's forward movement and it will move forward allowing it to get lift. If the jets are off however it will stay in place and not take off. I hope that helped.

[CrimsonVoid]

Ok, I'm not sure if anyone has realized this yet, but this debate is not about whether the plane can take off, but rather, if the treadmill keeps the plane from moving. First, let me say that I know that the treadmill would have trouble doing this because of the small amount of friction, but it's hypothetical, right?

So, if the plane is held still, then there is no lift, if the plane can move forward relative to the ground then it will take off.

[dongsynormus]

the whole idea is that the treadmill moves at a speed mathcing the wheels at all times, this NEGATES forward motion so there is NO lift!

[tminus997]

Did you go to school? You should.....

[dongsynormus]

you obviously dont know the original theory...or any physics beyond what they taught you in public highschool.

[Hyperonic]

Do you know anything about planes? The wheels do not give the plane thrust. If the plane used the wheels for forward thrust at all, the treadmill would cancel that out. However, because planes uses their engines for forward thrust and not it's wheels (which have very little friction against the treadmill), the plane will move forward on the treadmill regardless of how fast the treadmill is moving and take off.

[06jds377]

Absolutely correct. The problem with this, well, problem is that it states that the conveyor is to match the speed of the wheels. It should state that it matches the ground speed of the plane.

[06jds377]

There will be absolutely no forward motion, it will be counteracted by the conveyor. The best way to imagine this is a propeller with fuselage and wings that sits on stagnant in relation to the ground and air on poles instead of wheels, like a tripod, there will not be enough lift generated by airflow over the wings by the propeller alone for it to take off.

[06jds377]

If forward motion had no effect on lift planes would simply be able to run their engines to full power and instantaneously take off with no motion at all.

[FrapFreak]

Clearly you didn't watch/understand the original video... the fact is, there will be forward motion.

[dongsynormus]

you clearly dont understand the original question then. If the plane can overcome the treadmill OF COURSE it will take off and if that were the case its a STUPID QUESTION but in the origina, the treadmill matches the forward speed keeping the plane in place with no forward motion

[FrapFreak]

No... the actual question is that if the treadmill matches the forward speed the airplane would have had it been on stationary ground, would the plane move forward... and the answer to that is yes. The treadmill will pull the wheels back as you expect, however the wheels will not pull the plane back along with it. Watch the experiment he did! The plane moves forward at roughly the same rate with both treadmill speeds (which are greater than the plane speed).

[ArrowHead83]

True. And we know that the plane will have forward motion in this problem.

[ArrowHead83]

Wrong. The conveyor doesn't counteract the plane's forward motion, even though it matches it in reverse - because the plane's thrust comes from its jet engines or propellers pushing against the air, NOT from the wheels rolling against the ground.

[FrapFreak]

It's the same thing... the speed of the wheels on stationary ground is the same speed as the ground speed of the plane, otherwise the tires will slip... So, whether you match the treadmill speed to the wheels or the plane's ground speed doesn't matter...

[robert0380]

Once the plane gets rolling, the treadmill would not be able to match the speed of the wheels in the opposite direction....impossible. It would mean the wheels and treadmill are moving at a speed of infinity. I'd explain why but I'll leave it to you to figure out. There is more than enough info on this topic already.

[acarlisl]

of course the plane is going to move forward using thrust on a surface with little friction, therefore it will eventually accelerate to a speed where it WOULD take off. but i believe the situation is one where the plane is stationary relative to your viewpoint, still moving over the treadmill, accelerating, but it will not take off because there would be no point in time where the plane would move relative to the air.

[ArrowHead83]

The plane is moving relative to the air the whole time.

[WoodenSwordL]

actually nevermind I didn't watch your other video I get what you're getting at now with the whole tape thing, my bad.

[WoodenSwordL]

That made no sense to me. What the heck is the tape? When was that ever mentioned? Now you are introducing things into the problem that weren't originally there. Its not Plane + something holding it vs treadmill, its plane vs treadmill.