Aircraft carriers - ramps - makes less than zero sense to me

[Sarkus]

The goal is to prevent an airplane from taking off (to the right) from a moving conveyor belt.
Initially the wheel of the plane is at conveyor position 0 (red line) which is also ground position 0.
The conveyor drive system is only capable of motion to the left.
One method of control could use a photo sensor on the belt to detect the presence of the wheel.
With synchronized motions, the tire moves a distance dw to the right while the conveyor belt moves a distance db to the left, with a net movement of 0.

The flaw in your thinking is "With synchronized motions". There can be no synchronised motions in the scenario you put forth. There can be for cars, but not for aircraft.

Look at in terms of forces.
When the aircraft switches on its engines it produces thrust in the forward direction. F = ma, so in the absence of any other forces, the aircraft starts to accelerate forward.
For the conveyor belt to prevent this, and to stop the aircraft moving forward, it must produce a force in the opposite direction so that the net force on the aircraft is zero. F = ma, so zero force = zero acceleration.
So how can the conveyor belt do this? Simply by moving quicker and quicker under the aircraft doesn't do that, as that will just turn the aircraft tyres (assuming friction between the two) quicker and quicker. The only way would be if the conveyor belt physically prevented the aircraft from moving forward, by holding on to it like a vice, such that as the aircraft increased its thrust, the reaction force on the vice was equal and opposite this. Much like if you tried to push your house... the more force you push the house with, the greater (always equal and opposite) the reaction force of the house acting on you.
But this results in the tyres never rotating, and the aircraft engine eventually burning itself out. And it's not really a conveyor belt but a sort of locking mechanism.

In terms of an actual conveyor belt, one that turns, etc, it can not apply a force on the aircraft that will negate the thrust of the aircraft engines. So there will be a net Force in the forward motion, F = ma and therefore the aircraft accelerates.

But, you say, how can this be if the conveyor belt matches the forward motion of the aircraft's tyres?
The answer is in your "if". There is no "IF", as it is simply not possible (for net forces in the forward direction) for such a set-up to stop the aircraft from moving forward.

If you can explain how the conveyor belt, simply by trying to match the rotation of the aircraft tyres, can provide an equal and opposite force on the aircraft compared to the thrust of the engines (i.e. so net force forward = zero) then please do so.


Another way to look at it is with a shopping-trolley analogy.
If you stand on a conveyor belt and push it, with the conveyor belt matching the forward motion of the wheels but in the opposite direction, you will stay stationary relative to an external observer. This is analogous to a car, because the force pushing the trolley forward ise also on the conveyorbelt.
If you now stand off the conveyor belt, but the trolley still on it with a handle protruding out so that you can push on it, and now you push, it doesn't matter how fast the conveyorbelt is going, the trolley will move forward based on the force that you apply to it. This is analogous to the aircraft, because the force pushing the trolley forward is now not on the conveyorbelt (and aircraft pushes against air, not the conveyorbelt).

 

[exchemist]

Oh Christ. Someone should summon up Motor Daddy and then we can keep this going round in circles for 20 pages.

(There have been occasions when planes have had to be strapped down to stop them taking off by themselves in gales, even though they are stationary on the ground:-

)

 

[Michael 345]

Oh Christ. Someone should summon up Motor Daddy and then we can keep this going round in circles for 20 pages.

(There have been occasions when planes have had to be strapped down to stop them taking off by themselves in gales, even though they are stationary on the ground:-

)

Caused by microtubules

Wind just happened to be blowing

 

[phyti]

Sarkus;

In 1870, sending someone to the moon was fantasy.
In 1970, it happened after all the technical issues were solved.
The plane/conveyor problem is another thought experiment which depends on solving the technical issues associated with it.

If you are running on a treadmill, and your speed forward equals the belt speed backward, you are running in place. You do not move relative to the floor.

Starting in reverse with a small Cessna class plane (speed approx. 70 mph),
if the plane is on a conveyor belt with the engine off, as the belt moves to the left, the plane moves with it (friction of tire to surface or brakes on), away from ground zero.
If the engine is on and simultaneously accelerates the plane at the same rate as the belt to the right, the plane remains at ground zero.
The thrust of the engine is cancelled by the thrust of the conveyor drive.

It all reduces to relative motion.

 

[DaveC426913]

The thrust of the engine is cancelled by the thrust of the conveyor drive.

No it isn't.
This is the mistake you make.

The wheels are free spinning. They can spin at any rate: forward - or backwards - without impeding the motion of the plane at all. The whole point of having wheels on a plane is so that it can move under power of its prop, unimpeded by contact with the ground - and, in this case - the conveyor.


I would ask that before you respond with another explanation of how you think it should work, please address the following question:

Since the wheels are free-spinning by design, how can any significant movement be imparted from the conveyor to the plane through them?

 

[billvon]

If you are running on a treadmill, and your speed forward equals the belt speed backward, you are running in place. You do not move relative to the floor.

Correct! But if you are running on a treadmill and you have a rocket on your back, it will shoot you right off that treadmill, no matter how fast it moves, and no matter what your feet do.

Starting in reverse with a small Cessna class plane (speed approx. 70 mph),
if the plane is on a conveyor belt with the engine off, as the belt moves to the left, the plane moves with it (friction of tire to surface or brakes on), away from ground zero.

Also correct.

If the engine is on and simultaneously accelerates the plane at the same rate as the belt to the right, the plane remains at ground zero.

If the brakes are on - the plane moves with the conveyor belt.

If the brakes are off - the wheels start turning, the aircraft accelerates, and eventually takes off. Quite simple!

It all reduces to relative motion.

Yes, it does. But you are completely missing which relative motions to look at.

 

[Sarkus]

Sarkus;

In 1870, sending someone to the moon was fantasy.
In 1970, it happened after all the technical issues were solved.
The plane/conveyor problem is another thought experiment which depends on solving the technical issues associated with it.

No, it isn't. There is no technical issue to overcome, just an impossible scenario. Just as we can string the words "perpetual" and "motion" together to come up with a concept that can be understood but is actually impossible, we are also doing the same in this scenario: "a conveyor belt that exactly matches the speed of the aircraft's tyres". It sounds like an understandable concept but is actually impossible for non-zero speeds, due to how the aircraft generates thrust (i.e. nothing to do with the conveyor belt, unlike a car).

Look, give this website a visit: http://c-aviation.net/plane-conveyor-belt-explained-debunked/
It hopefully explains it in a manner that you can understand.

There are plenty of others out there, I have no doubt, and they should all give the same answer to the same question: the wording of the question creates an impossible scenario. The conveyor belt can never match the motion of the tyres (other than at zero speed).

 

[DaveC426913]

...actually impossible...

...the conveyor belt can never match the motion of the tyres (other than at zero speed).

Elegantly spoken.

The riddle's solution is more than won't; it's can't.

 

[exchemist]

I sense the mantle of Motor Daddy descending on phyti's shoulders.....................

 

[Neddy Bate]

Oh Christ. Someone should summon up Motor Daddy and then we can keep this going round in circles for 20 pages.

Motor Daddy!! Thanks for the memories, lol. Yeah, phyti has a similar thing going on.

 

[Yazata]

Sarkus;

In 1870, sending someone to the moon was fantasy.
In 1970, it happened after all the technical issues were solved.
The plane/conveyor problem is another thought experiment which depends on solving the technical issues associated with it.

I'm inclined to agree with Sarkus on this one. It isn't an engineering problem, it's more fundamental than that, more of a physics problem.

If you are running on a treadmill, and your speed forward equals the belt speed backward, you are running in place. You do not move relative to the floor.

When you are running, you are exerting force on what's beneath you to propel yourself forward. If what is beneath you is moving in the opposite direction at an equal velocity, you don't move in relation to the surrounding reference frame. The same thing is happening with a car, It forceably turns its wheels and propels itself by exerting force against the road (newtons 3'd law). If the road were moving in the opposite direction, then the car wouldn't move relative to the surroundings.

Starting in reverse with a small Cessna class plane (speed approx. 70 mph),
if the plane is on a conveyor belt with the engine off, as the belt moves to the left, the plane moves with it (friction of tire to surface or brakes on), away from ground zero.

Ok, if the plane is fixed to the belt, the belt is essentially a catapult in reverse. (Except that planes can't fly backwards.)

If the engine is on and simultaneously accelerates the plane at the same rate as the belt to the right, the plane remains at ground zero.

Weren't we assuming that the plane had wheel brakes on or chocks under the wheels? Suppose that the wheels were free to roll. The engine would exert force on the airframe and accelerate it. The wheels would exert far less force in the opposite direction, since wheels are designed to roll freely. So the belt would just be spinning the wheels while the engine would be pulling/pushing the entire plane. All the belt would end up accomplishing is making the wheels spin faster at takeoff velocity.

The thrust of the engine is cancelled by the thrust of the conveyor drive.

That's the difficulty I think. If the wheels are turning freely, they would be transferring little force from the belt to the airframe. Meanwhile the engine is attached to the airframe and is transferring all of its thrust to the plane. So the net force would be much greater in the direction of the engine vs the direction of the belt.

It all reduces to relative motion.

The way I picture it, it all reduces to the forces imparted to the airframe.

 

[Michael 345]

If the wheels are turning freely, they would be transferring little force from the belt to the airframe

In practice ZERO

 

[Sarkus]

In practice ZERO

In practice, you forgot friction.
Tyres and ground have friction between them. Albeit almost insignificant. The friction reduces the net forward thrust from the engines... so F(thrust) - F(friction) = F(net).
F(thrust) >>>>>>> F(friction), but F(friction) is non-zero... in practice.

 

[DaveC426913]

All the belt would end up accomplishing is making the wheels spin faster at takeoff velocity.

Worse than merely "faster".

The moment the plane starts to move, the belt immediately accelerates to the maximum speed it is capable of and remains at top speed until it is shut down or fails.

Think about the first inch of roll.
How fast does the conveyor have to move in reverse to cancel that first inch?
Even infinitely fast is insufficient. There is no speed the conveyor can move that is sufficient to cancel that forward movement.
The feedback mechanism of this device will tell it to keep accelerating "until the plane's movement is cancelled". That never happens - even in that first inch of roll.

Thus, the problem statement is poorly formed. It contains a faulty assumption. It assumes the construction of a feedback mechanism that cannot be built to do what it is presumed to do. It's a physically and logically impossible goal to meet.

 

[billvon]

I am really curious as to whether the original poster now understands this a bit better.

 

[DaveC426913]

I am really curious as to whether the original poster now understands this a bit better.

It certainly appears like he lost interest as soon as his assumptions were corrected.

 

[phyti]

Sarkus;

After watching a demonstration of the experiment with a small aircraft on a portable surface, the mistake in interpretation is obvious. Was impressed by their low tech method. The force of the accelerating 'runway' transforms the wheel into a powered one, boosting the acceleration of the plane, (and why I prefer pictures which can convey more information than a page of math). Way before I interacted with forums (2006), I knew some of my answers would be wrong, but it's the challenge.

There was another article by a pilot who used some good graphics in his explanation.
The article written by Wojciech Przybylski wasn't as clear.

If a powered belt can't prevent a small plane from taking off, how about an un powered belt that is free to move? The wheels have traction via f=mg, and would push the belt in the opposite direction, with the plane standing still. You might see this in the wintertime, where a mat is placed under a tire for traction, but goes flying to the rear without the car moving.

The friction reduces the net forward thrust from the engines... so F(thrust) - F(friction) = F(net).

The purpose of a 'runway' is to allow an aircraft time and space to accelerate to flying speed.
The friction f=mg is constant until lift off. The bearings on the axle allow the wheels to rotate, along the runway surface, minimizing drag. The engines are rated to provide adequate thrust for safe performance, so there is no significant loss of power, especially at takeoff (or landing), the worst time for such an event.
In the 1950's jet engine development was not advancing as fast as airframe design, and most military aircraft were underpowered, as measured by thrust to weight ratios of <1.
Today most are >1 allowing vertical acceleration, and aircraft meeting their design potential

 

[DaveC426913]

If a powered belt can't prevent a small plane from taking off, how about an un powered belt that is free to move? The wheels have traction via f=mg, and would push the belt in the opposite direction, with the plane standing still. You might see this in the wintertime, where a mat is placed under a tire for traction, but goes flying to the rear without the car moving.

STILL NO!! (fer cryin out loud)

 

[Sarkus]

After watching a demonstration of the experiment with a small aircraft on a portable surface, the mistake in interpretation is obvious.

Whose mistake? I'm not clear if you're admitting your error, or still trying to claim reality is wrong?

If a powered belt can't prevent a small plane from taking off, how about an un powered belt that is free to move? The wheels have traction via f=mg, and would push the belt in the opposite direction, with the plane standing still. You might see this in the wintertime, where a mat is placed under a tire for traction, but goes flying to the rear without the car moving.

An unpowered belt will only go backward as a result of the friction between it and the wheels. With an aircraft, however, that friction is minimal compared to the force provided by the engine.
The result will be the same: aircraft will move forward, and eventually hit take-off speed, rotate, and fly.

So let's remove friction - as it is a complexity you seem to be struggling with.
Let's take an entirely frictionless surface.
The aircraft is at rest.
It turns its engines on. No friction between tyres and ground. The aircraft pushes against the air (not the ground) and moves forward. Because of no friction between ground and tyres, the tyres don't even rotate. The aircraft glides over the surface until it reaches take-off speed, etc.

Friction is what causes the tyres to rotate on an aircraft.
And in normal circumstances, including on a conveyor belt, friction is tiny compared to the forces the engine exerts on the aircraft.

All a conveyor belt can do is affect the speed of the tyre rotation, not the forward motion of the plane itself. In normal operation, the speed the tyre rotates at is an indication of the speed the aircraft is travelling along the ground at, but being on a conveyor belt is not normal operation, and that normal link between aircraft speed and wheel speed is broken when the conveyor belt is turning while the aircraft has its engines on.


Now imagine a car on a frictionless surface... its wheels spin but no forward motion. Why not? Because it generates its forward motion from the interaction of tyre and ground. It relies on friction (to grip the wheel, the wheel turns without sliding, thus creating forward motion). If there was no friction, a car would not move by rotating its tyres.

Hopefully you can now accept / see that the car and the aircraft generate their forward motion (force) by to different mechanisms. Unfortunately you are continuing to analyse the aircraft as if it operates like a car, as if its tyres (and friction) are the means of generating the forward motion. Hence you are arriving at incorrect conclusions.

 

[billvon]

If a powered belt can't prevent a small plane from taking off, how about an un powered belt that is free to move?

Same thing. Plane doesn't care.

If the wheels have more friction than the belt, then the belt will accelerate to takeoff speed along with the plane. If the belt has more friction than the wheels, then the belt will remain stationary.

In the 1950's jet engine development was not advancing as fast as airframe design, and most military aircraft were underpowered, as measured by thrust to weight ratios of <1.
Today most are >1 allowing vertical acceleration, and aircraft meeting their design potential

The vast majority of military aircraft have thrust to weight ratios well below 1:1.