Airplane physics question

Add me in the camp where the plane won't take off, based on the premise of the puzzle, physics, and the idea of infinity.

1) Premise, conveyor keeps up EXACTLY with the planes wheel speed.
2) Premise: Plane needs forward wind speed to take off.
3) Premise: Plane thrust is via the turbines, not wheel driven.
4) Premise: Threadmill has infinite speed potential, and AT ALL TIMES KEEPS UP EXACTLY WITH THE PLANE WHEELS.

Assumption based on above:

The ONLY WAY the plane won't move forward, is if there is a force keeping it from moving forward and gaining airspeed. By definition THERE IS SUCH A FORCE HERE, no matter how preposterous it sounds: wheel bearing friction (someone else mentioned it before).

If the threadmill keeps up exactly with tire speed, then the plane can't move forward. Simple as that. The speeds we are talking about here are fictional, and unattainable.

Think back to algebra and asymptote (?spelling) type graphs.

As the plane thrust tries to push it forward, IT CAN'T, because the threadmill would immediately counter it in the opposite direction. THAT is a presumed premise of the puzzle. Basically the plane speed and threadmill speed would head towards infinity, and the speed would stop progressing once engine thrust were matched with wheelbearing/rolling friction.

Thats that.

 

You need wind. That creates the up draft to keep the airplane suspended off the ground. If you have enough wind, you don't need the airplane to move. In hurricane winds, small airplanes not tied down will lift off when the engines are not even running. In wind tunnels, airplanes get lift when they are actually stationary. Wind creates the lift. The fact that an airplane taxis down the runway only acts to increase the speed of the wind at the leading edge of the wing.

Viper

 

Ok, I have thought it through some more. Plane still wouldn't fly, but for more simple reasons. These are more realistic and easier to follow:


1) Engine would blow within 30 seconds, because some mechanic used speed tape to hold the impeller blades on...

2) Wouldn't fly because airline would file for bankruptcy before threadmill got going...

3) Pilot would go on strike, because he didn't make as much as the threadmill operator...

4) Threadmill would have to be turned off because of neighborhood complaints...

5) Wouldn't fly because terrorists would use a nail clipper to jamb the threadmill...

 

Hi Viper/Dr J and bpu699/bo,

Thanks for your well-considered responses.

I do understand that the plane needs airflow over its wings to generate lift to take off. I have been stating all along that the conveyor belt can't 'grab' the plane and drag it backwards because:

1) the plane's wheels are free wheeling under it
2) the plane derives its forward motion as a result of the thrust of the engines, which is generated by the exhaust gases being pushed out the back of a jet or the action of a propellor on the air.

I hope you agree that if we disregard (just for a moment) the 'conveyor belt matches the wheels' speed' bit and generalise it to 'the conveyor belt is just going backwards quite fast' that the plane can drag itself forwards (with faster than usual rotation of the wheels).

My earlier post was aimed at also showing that the constraint stated in the problem (the conveyor belt moves backwards to match the speed of the wheels) that the plane can still move forwards.

How can this be? There would appear to be TWO sets of speeds, which are different - isn't that a paradox? No...

When specifying a speed, you have to specify what it is in relation to, which is a crucial point that I'll get back to a bit lower down.

Note that the problem states that the conveyor belt is designed to 'exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation'. This clearly makes it obvious that the conveyor belt WILL move.

The only way the static, plane at 0mph, conveyor at 0mph start point can be broken and the conveyor belt start to move is if the plane starts to move forward. It's very important to realise here that the actual, real forward motion of the plane is the only way you can get the wheels to turn at all.

If the plane can move forwards at say, 0.1mph in relation to the Earth, then the conveyor belt starts to moves backwards at 0.1mph in relation to the Earth (and the still wind). The constraint is still in place as far as the reference point of the Earth is concerned, so that's good.

Now - what about the *rotational* speed of the plane's wheels and the speed of the conveyor underneath them?

The plane's wheels (unlike those of a conventional car) are not geared/connected to the plane's engines but are free to rotate to match the surface on which they sit. As far as the wheels are concerned, they are moving at 0.1mph forwards in relation to the Earth and wind, but in relation to the conveyor belt (which is moving backwards at 0.1mph in relation to Earth) they see a surface travelling at 0.2mph away from them. So we can conclude that the speed of the wheels in relation to the speed of the conveyor belt is *still* equal and opposite - which is as stated in the problem.

This situation is analogous to the, er, analogy I posted earlier about the guy walking down the aisle of a moving train.
The train is doing 100mph forwards, he is walking backwards at 5mph in relation to the train. What is his speed? Well, he is doing 95mph compared to the train track under the train, yet 5mph compared to the train. Likewise the train is doing 5mph in relation to him and 100mph in relation to the track underneath it. None of these situations is a paradox that 'can't happen', and none of these situations involve a speed suddenly zooming up to infinity.

Debunking the 'plane sits still is the only way to maintain the constraint' argument:
So now that I've promoted my thinking as to why my solution is OK, what about 'shooting down' (sorry ) the premise that the plane sits still on full throttle with the conveyor belt frantically shooting backwards under it:

If the plane is sitting still, the wheels are rotating, yes, but the conveyor belt is ALSO moving in relation to the Earth and the plane ISN'T. Although that does satisfy the rotational part of the constraint, it absolutely, totally, does **not** adhere to the constraint that the conveyor belt is designed to 'match the speed of the wheels', because the wheels aren't going anywhere and the conveyor belt is going hell for leather backwards. That isn't equal and opposite.

I hope that adequately describes how I see no problem with the plane taking off, with the wheels underneath spinning twice as fast as they normally would if it was using a fixed (in relation to the ground ) runway.

Best regards,

Rich.

Edit: typo in the debunking paragraph, said 'are' when I meant 'aren't' - I'm a dumbass!

 

please, peusdo ground effects making the plane lift off.......


first to get ground effects working (like the russian bomber the cruised above the ocean for max thrust, etc) you have to be moving, ie there has to be air flow (creating a downward flow of air etc...).

and now you may say, "the enzo uses ground effects to create downforce, and downforce is the inverse of lift"

funny thing, the enzo is like 3 inches off the ground, a plane's wing is like 20 feet. we will use an anology here. take a vacuum and put it to the floor. see all the suction it creates? now hold it .2 inches above the floor, see that suction? considerably less huh? now hold it 20 feet (the height of our airplane's wing) negligable huh?

same principle, different aparatuses.

also may it be noted, the conveyor belt will create a very low V airstream, because its friction (drag) coefficient is very little a parallel (to airstream) plane. now if you put bumps/slat things on it to catch wind that would be a differet story. but then the tires would run over it (problems associated with that) and imagine the force on a finate flat plane (Cd = 1.05(ish)) with freestream velocity of infinity? well the force is infinity, then multiplied by the lever arm, and the moment at the joint of the slat and the belt would be an even higher form of infinity. which brings me back to the point that YOU CANNOT BUILD THIS MACHINE WITHIN THE CONFINES OF PHYSICS to perform as it theoretically would have to to produce a solution.


although this thread should distinguish: the engineers (thinking realistically), scientists (thinking theoretically), and neither of the aforementioned (thinking [or not because they dont care])

 

Hi bo,

regarding your last post - I like it!

Except, if terrorists jammed the conveyor, it'd just be like an ordinary runway

Good debate, I'm enjoying this (can't drive the F-car with all that salt on the roads, need a diversion!)

Cheers!

R.

 

Hi RammsteinMatt,

I'm with you on the ground effect/air stirred up by the conveyor concept - the effect would be no more than a small part of virtually nothing.

But I still don't think the wheel bearings of the plane would seize - no infinite speeds involved, just a doubling of the rotational wheel speed a plane would normally experience on a fixed, conventional runway.

Anyway - that's not important - which Rammstein album should I buy my mate for Christmas - which is heaviest, Mutter or Rosenrot?

Best regards,

Rich.

 

This one will take off and it HAS a conveyor belt......
Image Unavailable, Please Login
Image Unavailable, Please Login

 

but that is not an anagolous situation. because the legs are contacting the train, and they are also providing the foreward movement.

in this problem, the wheels are independant of the movement (they could be stopped with plane motion, or they could assumedly be moving with a static plane)

this goes back to my original post on like page 5. the conveyor would have to zoom up to infinity instantaneously. i'll try and explain it better.

remember this is theoretical writing, therefore no friction, speed constraints, C >> infinity , etc...

ok you throttle up the engines (we'll say 5% so its not durastic, and the process would take miliseconds instead of instantaneously) the throttling of the engines WILL cause a movement regardless of the wheels right? (think of a boat, same principle, displacing a fluid to move. if a boat had wheels attached to it, would they have to move for the boat to move, no) so off the basic principle of thrust, the airplane would have to move, becasue there is a force applied to a mass, and that would produce an acceleration.

now the wheel situation. the conveyor exactly matches the speed of the wheels. (namely the conveyor is going to resist all movement of the body)
so the plane just is bearly starting to creep foreward (lets 1 inch/hr) well the conveyor will move in the opposite direction at 1 inch/hr to resist vehicle movement, but since the engines dont care what the conveyor is doing, they continue to produce thrust, and now they are producing thrust to produce a speed of 1 in/sec (from a static location) (now the plane has a relative speed of 1in/sec becasue the conveyor is cancling out the first 1in/sec and the engines continue to produce 1in/sec of thrust. and just leaving the throttle at 5% (or whatever it takes to start movement) the conveyor will zoom to infinity because the engines continue to force the plane foreward producing a wheel movement (or angular velocity if you must) but the conveyor sees this and makes a corrective speed (and assuming the corrections are instantaneous) the plane will not move foreward.

which brings us to the infinity thing. theoretically you could have greater amounts of infinity and never take off whether the throttle is at 5% or 100%, or infinity could somehow be overcome (not quite sure how) and the plane would start to roll down the conveyor runway (but planes weight like 600k lbs, so thats a pretty heavy duty conveyor)


also some considerations (since we are speaking theoretically). the engines sucking in air are creating an airflow. so theoretically if you had large enough engines, you could theoretically create and airflow over the wings (but realistically speaking the engines would have to produce like 10^15 lbs thrust to intake that much air.

 

sent you a PM so i dont get slapped but the Fchat air marshalls on OT deviations

 

Hi RammsteinMatt,

First up - many thanks for the PMs, I promise not to hijack the thread but was getting stressed about choices for presents!!

Thanks for reading the guy walking in the train analogy - I should have pointed out more strenuously that this is just to show that the same guy can have more than one speed, depending what the speed is in relation to, and also to show that if the you take the reference point and ask how fast it appears to be going in relation to him, you get an equal and opposite figure. This must *always* be true (the distance between you and me may be changing because we're moving in relation to each other, but that distance is the SAME whether you measure it from you to me or me to you).

I like your post - it's nice and clear, but of course there's a bit I don't agree with ...

I'll have to go to bed soon, it's already late here, so I'll try to make this short.

Let's try to agree on some parts of the problem first.

Do you agree that the conveyor belt has no purchase on the wheels (by this I mean that if the plane was parked, non moving in relation to the Earth and the static conveyor with the plane's brakes OFF, and then you whizzed the conveyor up to a high speed under it, the plane wouldn't move? I'm working to your rules of the situation of no friction, no restrictions on speed etc (but even in real life the wheel friction would be TINY and only move the plane a tiny little bit). So, basically, the conveyor can't 'grab' the plane.

So, following on from that, even if the conveyor belt suddenly did zoom up to a high speed (which I believe it doesn't, but I'll go with your belief that it does, for a moment) that it wouldn't actually move the plane back (zero wheel bearing friction - the plane MUST have moved forward and there's no way the conveyor can actually drag it back? I hope you agree with that. Because it doesn't and can't move the plane back, the plane's engine's thrust can and does result in forward motion of the plane.

There are two problems with the concept of the conveyor whizzing up to infinity. If it does so in a few milliseconds, but fails to move the plane back what happens a few more milliseconds later - is the belt going at 2 x Infinity, or maybe the acceleration of the conveyor is such that it now doing Infinity Squared? How big is that? Bigger than Infinity, it would appear, which you did admit you had trouble with (as do I! let's call it Bigfinity!!)

The other problem is that the constraint would be broken if the conveyor belt was moving backwards at infinity speed (in relation to the plane and also in relation to the Earth) but the plane was *not* moving in relation to the Earth? It wouldn't be possible for the constraint to still stay true if the plane-earth/air speed was zero and the conveyor belt-earth speed was infinity. If the plane is not going anywhere, you could point a stick at the wheel position, go shopping, visit your Gran, re-read all of this thread, come back and the stick would still be pointing at the wheel. Yep, the wheel would be spinning, but the relative speeds of the belt and the wheel would be *different* in relation to the same reference point (whatever that point is, even if its moving)

You started with the plane being allowed to move forward at 1 inch/hour and the conveyor going backwards at 1 inch/hour (and you do relate these speeds to a static location) but all of a sudden you're saying the conveyor MUST zoom up to high speed. If that happened, compared to that static location (observation bar in Terminal, with you and me having a beer listening to Rammstein ) the constraint gets broken, because the plane is doing 1 inch/hour and the conveyor is a blur in the other direction.

I agree that the conveyor *tries* to counteract the movement of the plane, by moving backwards as the wheels turn forwards, but if you don't mind me saying, I think you're being TOO intelligent with the way you would manipulate the conveyor belt - it seems as though you're deciding to make the conveyor belt go faster because the first attempt at slowing the plane down didn't work. If I was a human operator with a throttle/speed control for the conveyor and were dead set on stopping the plane, this is what I'd do, too. But that simply isn't within the constraints of the problem, which says the same conveyor backward speed as the plane's forward speed.

Anyway - as always, good debating this with you. Off to bed now.

Du hast mich gefragt und Ich hass jetzt gesagt!!

Night,

Rich

 

Unfortunately, I’ve arrived late to this party, so I award points to teak360 for great explanation in Post 326 and overall excellent understanding of Newtonian mechanics, as well as points for smg2 and Steve R for being the first to post correctly and for remaining persistent. You three would get an A+ in the mechanics class for which I am teaching assistant.

Since I’m about to graduate university with a BS in Physics, I’d like to offer my opinion. Anyone who understands and agrees with what teak360, smg2, and Steve R wrote should just skip everything else I’m including in this post should turn off their computer and go drive their Ferrari, because I sure as heck would rather be doing that than reading physics arguments on the internet. Everyone else, maybe I can offer a slightly different explanation than other posts, it's up to you.

This problem does not require any numbers or complex math (a relief after some of the exams I’ve taken this week), just some simple principles. The MAIN thing to consider in this situation is that the rotational wheel speed of an aircraft has, for all intents and purposes, nothing to do with the aircraft's velocity relative to the air/ground. It is also important to understand classical (Galilean) relativity.

In pure theory, there is absolutely no question that the plane would become airborne. Remember inertia: it is the tendency of any object to remain in its current [kinetic] state unless acted upon by an external force. Assuming that the wheel bearings are perfect (no friction) it doesn’t matter what speed the belt is moving; there is zero force transmitted to the fuselage via the wheels so the plane will remain still. All of the conveyor’s energy is transmitted to the airplane in the form of rotational energy contained solely within the wheels and tires. Translational motion relative to the stationary ground will occur only when an external force (aka thrust) is applied to the aircraft.

In the real world, the bearings do experience friction. This should not change the situation dramatically, just a couple F=ma arguments to consider (we’ll say that positive F is thrust and a is a requirement for take-off, and negative F is bearing friction and negative a represents moving backwards). With respect to the airplane, bearing friction would simply be seen as a force pushing slightly backwards and the plane would accelerate in that direction (F<0, a<0). [Will the force vary with wheel speed? Possibly, but then we’re opening a whole other can of worms.] When an amount of thrust equal to the bearing-friction force is applied, the plane would become stationary since all forces would be in equilibrium (F=0, a=0). Upon applying a greater amount of thrust than the wheel bearing friction is producing, forward motion would occur relative to the ground (F>0, a>0).

I tend to dislike analogies as they aren’t very good at showing all aspects of the problem, but here we go: next time your wife/girlfriend is jogging on the treadmill, give her a nice shove. If you sleep on the sofa that night because she’s ticked at you for making her face-plant on the treadmill, then the airplane will take off….

Some people are reading into this problem way too deep. Could the bearings burn up? Sure. Could the tires disintegrate? Absolutely. But those have no influence on the basic physical principles that this questions is designed to exploit.

Also, some random observations:

XR4Tim: “This is just like if you had a car on a treadmill going 70 mph. The car isn't going anywhere, right? Lock up the brakes (the treadmill will do the same), and your car will slide forward at 140 mph off the edge of the treadmill.”

The only energy in the car in that situation is the rotational energy of the wheels. Upon lockup, that rotational energy is dissipated as heat energy by the brakes. While the car is moving 140mph relative to the conveyor belt, remember the conveyor belt is moving -140mph relative to the ground, so the car’s net relative velocity is zero. The actual automobile has zero kinetic energy relative to the ground, so no momentum. Without any momentum or external forces, it’s not going to move.

As far as jet engines, or rocket engines for that matter, they are not “pushing” against anything. It is simply conservation of momentum (or more popularly, Newton’s 3rd law): the mass and velocity of the spent fuel exiting the rear of the engine must be conserved by having the source/engine/body move forward. Imagine standing on ice-skates on a frozen pond with a bowling ball in hand. Upon throwing the bowling ball (fuel), you will move the opposite direction in order to conserve momentum. The momentum of the thrown bowling ball will equal your momentum since the velocity of the initial system was zero.

Anyway, that's my first post. Time to go study so one day I can own a Ferrari.

 

see, now thats a nice little nutshell.
Chris, wait till grad school the subject of physics and my favorite astrophysics get real juicy. still have my 10lb Gravitation text book. Kip Thorne has a real knack for making it simple, to me at least.

For those in the it won't fly camp, what are they teaching you physics class?

off to read up on superstrings....

 

This is one of those times when some people are either too smart, or not smart enough. If the conveyor is simply going to go opposite the direction of the wheels and match thier speed, the most that could happen is the wheels would be spun up to twice the speed of takeoff. Since most aircraft tires are tested to withstand something like 1 and a half times thier standard rotational speed, this shouldnt be any trouble. For anyone having trouble disconnecting the plane from its wheels, go try holding back your neighbors car while you wear roller blades on your feet. Yeah, you would probably burn up your rollerblades, but I doubt youll effect his car much. Except the damage caused when you fall under it. The neat thing about a airplane is that it doesnt need any wheels to fly. They dont really need any to land either. That this took this many pages seems utterly retarded considering how smart everyone here seems to be.

 

I'm truely and honestly baffled this is still being discussed. Those who don't get it (think the plane won't fly) will try to nit pick and over analize this till they are blue in the face and we all finally quit caring. . . Oh thats right, I now remember why I quit postin on this 2 pages ago...

ciao

 

Sorry. In your case if the tires are spinning at 200mph, then the conveyor is only going 100 mph.

You said it....

 

I’m agog. Why? Because this is still limping along (now helped by me).

Ok, if you want to be accurate here’s what can happen:

The conveyor belt, in attempting to play catch-up, speeds up like mad and goes several hundred miles an hour while continuing to accelerate.

The plane’s tires blow up and the plane crashes.

Now shod with unburstable tires, we try again with our next plane - and we have bearing failure.

But where?

The runway sized conveyor belt also runs on bearing. Which has more? Which is more likely to seize? The large diameter of the plane wheels would be an advantage to the aircraft - the runway bearings would seize first, at which point the plane would take off.

Now the conveyor belt has been fitted with friction free unburstable bearings:

The plane’s bearings seize. It doesn’t fly. Everyone on board gets a soft drink voucher and is shifted back to the departure gate.

Bring on the third plane, this one with friction free bearings.

The throttle is firewalled.

The runway/conveyor belt moves in perfect time to the plane’s wheels, and suddenly the wheel speed is several hundred mph and climbing. At about 750 mph the wheels and the conveyor belt exceed the speed of sound. As the cross sectional area of both objects is unchanged with respect to the air they are moving through, so sadly not a lot happens. The same is true for Mach 2 and upwards.

As things accelerate towards the speed of light stuff happens. At (and I’m working from memory here) about 99.98% the speed of light both the conveyor belt and the plane’s wheels start to gather mass. This makes the plane heavier, but it also limits the conveyor belt speed. Mind you, the plane still can’t roll forward - why? It’s wheels can’t turn any faster, they just grow heavier and, ultimately, if more energy goes into the system, larger. At this point an equilibrium will be reached - the plane cannot move forward because the tire’s outside diameter cannot roll any faster, and thus the conveyor belt will not continue to accelerate. Were it to try and go faster then more mass would be added to both objects and, as far as the plane is concerned the outside diameter of the tires would grow and the wings would get further away from the runway, and yes, now the plane would be lifting off but not flying! This business would go on until the tire diameter reached up to the wings, at which point, acting like a buzz saw, it would chop off most of the flying surface cleaner than a laser could. The plane would continues to rise, and would do so until it ran out of fuel - which due a lack of wing tanks will be sooner rather than later.

However, interesting though that may be (!) in fact, once the wheels refused to spin any faster the system would reach equilibrium and the plane would not move, no matter what the engines did. Let’s face it, 99.98% the speed of light is a pretty good hand brake.

Either way the passengers and crew on the plane are doomed. Remember the friction free bearing? Even when the plane runs out of Jet A the system will keep on running, forever. I hope they have more than a bag of peanuts on board.


At the end of the day I’m with the conveyor belt bearings frying themselves first and the plane flying happily away to some airport with a normal runway. Why? I want to take off from this thread and not come back......

 

Hi Chaps,

Please, please, please stop over-analyzing the problem!

So far I think I've made the mistake of answering with loads of detail all the theories of the conveyor speeding up to infinity etc.

The plane can move forward because the wheels are freely spinning (good analogy: stand in front of your neigbours car wearing roller blades and try to hold it back). The plane is generating its thrust from the reaction of the exhaust gases/wind over the propeller - crucially, this has NOTHING to do with the conveyor belt.

The speed in relation to the ground of the conveyor is the same size (but opposite direction) as the speed of the plane in relation to the ground. Ergo, if the plane can get up to about 180mph, then the conveyor only gets to 180mph backwards.

I kind of agree with Alan saying that the tires might explode - in his real world example of a plane needing to get to 180 to take off, the tyres would be seeing 360 down at the conveyor belt and would probably disintegrate. However, when I was studying Physics these questions were always posed in a purely theoretical sense, so you could assume zero friction wheel bearings and non-exploding tyres.

Also, if you remember Thrust SSC (mentioned this before) was a wheel-borne car that exceeded the speed of sound, it clearly had wheels and wheel bearings that could handle in excess of 700mph, so the technology IS available, TODAY.

I think Napolis' answer was the best - he just said 'yes' and wisely left it at that!! [post 293]

Cheers!

Rich.

 

Boy were you optomistic with your prediction. Or was that pessimistic?

Discuss......

 

I thought the plane wouldn&#8217;t fly. I admit I have no aptitude for science, so for those who state it would fly, perhaps you can help me understand.
I see that just about every question has already been addressed, but maybe someone can give a simpler explanation to this:

Do the wings need air flowing around them to generate lift? If not, why not? If not, then I can see why it would take off.

As an aside, if such a conveyer belt would allow a stationery plane to take off, I wonder why such a thing could not be employed for emergencies and military purposes, rather than always building a long runway.

Thanks. Again, perhaps someone can explain in the most simplistic terms to match my intellect on such things

 

When your thought processing abilities are deteriorated to levels this low, it's really time to remove your heroin dealer's number from your cell phone.

Bill in Brooklyn

 

Yes. Relative motion between the air and the wing is required to generate lift.

The motion could occur because the plane moves forward or because of a hurricane force headwind.

The plane will fly. Why? Because what happens between the wheels and the conveyor is not important.
Focus on what happens between the plane and the stationary mass of air.

A propellor plane moves forward thru the air because the propeller "pulls" the plane. Actually the propellor is a wing and rotating it causes relative motion between air and propellor. That relative motion creates "lift" in the forward direction so the plane moves. but I digress.

Again, the air is not moving the propellor generates thrust against that air.
That thrust will cause the plane to accelerate relative to the air. When the plane reaches a high enough speed RELATIVE TO THE AIR it will take off.

Think about this another way.

The propellor is pulling on the body of the aircraft. What other forces could act on the aircraft that would keep it from moving forward?
Tying the plane to the ground with a rope would do it.
Could a conveyor under the tires going backwards generate enough drag to counter act the thrust generated by the propellor? As long as the bearings in the wheels are functioning that drag force will not offset the propellor thrust. That thrust will cause the plane to accelerate forward RELATIVE TO THE STATIONARY AIR until it is going fast enough for the lift created by the wings exceeds the weight of the plane and it flys.

Erich

 

Many thanks to Rich Rowe for helping me see the missing components in my logic. I now understand it--yes, the plane will take off.

Even though the plane is attached to the conveyor belt via the wheels, there are no forces acting on the plane because of the belt or wheels. The conveyor belt's motion and the wheels' equal and opposite motion result in a net force of zero on the plane.

The only forces acting on the plane are gravity pulling it down on to the conveyor belt and the engine's thrust pushing it forward. So it moves forward and accelerates.

As the plane accelerates, the airflow over and under the wing result in a lifting force acting on the plane.As the plane accelerates, the lifting force acting on it increases. When this lifting force exceeds the pull of gravity, the plane takes off.