Physics Question

[Armitage]

Originally posted by: KillerCharlie

Originally posted by: Evadman

Unless the wheels were bolted to the conveyor, and a speed differential between the conveyor and the air is impossible, the plane will fly. The plane only havs to make slightly more power than a regular take off to make up for the friction loss of the bearings.

Interestingly, the resistance from the wheels (to a high order of accuracy) depends just on the normal force (weight) of the aircraft, not the speed of the wheels. Given that the aircraft is not constrained in the fixed reference frame, then the conveyor speed actually has 0 effect on the airplane.

This means the ODE governing the aircraft velocity is:

m(dv/dt)=T-D-mu*(W-L)

T=thrust
D=drag
mu=coefficient of rolling friction
W=weight
L=lift

Of course thrust, drag, and lift are functions of velocity. Drag is also a function of lift, but because of ground effect the induced drag changes quite a bit, meaning you'd need a simple numerical ODE solver for this.

The wheel resistance does not depend on the speed, so the conveyor speed is irrelevant (once again, only if the airplane is not constrained in the fixed reference frame). If the aircraft is fixed in the reference frame as per some interpretations, then the thrust needed to cancel out the wheel resistance and keep the plane stationary is constant.

Where does anything in the OP imply that the aircraft is "constrained in the fixed reference frame"? There is just the airplane, and the conveyer. How can the conveyer possibly prevent the plane from taking off?

 

[myusername]

Originally posted by: Mo0o
No. the "lift" comes from the air passing through the wings and creating a pressure difference . If the plane is not cutting through the air it will NOT lift off. Another question can be, if you're running on a treadmill holding one of thoes 50c glittering foil fans like 6 year old girls like, will that fan spin?

This is based on the assumption the plane is stationary to begin with and any acceleration attempt forward is countered completely by the coveyer belt carrying it back

Really this is a great analogy! I like the glitter fan.

Except for the fact that the Assumption that is made IS NOT VALID IN PRACTICE.

In real life, if you placed an airplane on a conveyor belt, the airplane would accelerate right off the belt.

 

[91TTZ]

Originally posted by: mugs

Originally posted by: 91TTZ
No. Unless it's a Harrier. Wheel speed doesn't matter, it's air over the wings which make it fly.

:frown:

The wording of the question is puzzling people, so the two different camps are envisioning two different things.

One camp pictures the plane not moving forward but the tires are spinning due to the conveyor belt moving. The other camp pictures the plane moving forward but the tires are going twice the speed.

 

[Armitage]

Originally posted by: 91TTZ

Originally posted by: mugs

Originally posted by: 91TTZ
No. Unless it's a Harrier. Wheel speed doesn't matter, it's air over the wings which make it fly.

:frown:

The wording of the question is puzzling people, so the two different camps are envisioning two different things.

One camp pictures the plane not moving forward but the tires are spinning due to the conveyor belt moving. The other camp pictures the plane moving forward but the tires are going twice the speed.

Except the first camp hasn't explained why the plane isn't moving yet. What is counteracting the thrust?

 

[FallenHero]

planes cant stand. Next.

 

[91TTZ]

Originally posted by: Armitage

Except the first camp hasn't explained why the plane isn't moving yet. What is counteracting the thrust?

Just wheel resistance, really. It could probaby do that at idle.

 

[mugs]

Originally posted by: Armitage

Originally posted by: 91TTZ

Originally posted by: mugs

Originally posted by: 91TTZ
No. Unless it's a Harrier. Wheel speed doesn't matter, it's air over the wings which make it fly.

:frown:

The wording of the question is puzzling people, so the two different camps are envisioning two different things.

One camp pictures the plane not moving forward but the tires are spinning due to the conveyor belt moving. The other camp pictures the plane moving forward but the tires are going twice the speed.

Except the first camp hasn't explained why the plane isn't moving yet. What is counteracting the thrust?

Exactly! The question is intended to make you *think* the plane is not moving, but there's nothing in the question that actually indicates that it can't or won't move. Physics indicates that it can and will with enough thrust!

 

[Mo0o]

Originally posted by: 91TTZ

Originally posted by: Armitage

Except the first camp hasn't explained why the plane isn't moving yet. What is counteracting the thrust?

Just wheel resistance, really.

If you have a belt that's accelerating the opposite direction as your direction of acceleration, how do u beat it? This a genuine question

 

[Armitage]

Originally posted by: 91TTZ

Originally posted by: Armitage

Except the first camp hasn't explained why the plane isn't moving yet. What is counteracting the thrust?

Just wheel resistance, really.

Which isn't significantly different then the rolling resistane of the wheels on a normal takeoff run. And which is much less then the aerodynamic drag an aircraft experieces at takeoff speed.

In simpler terms, he engines have more then enough thrust to overcome the rolling resistance of the wheels. They have to if the plane can ever takeoff in a normal situation.

 

[91TTZ]

Originally posted by: mugs

Exactly! The question is intended to make you *think* the plane is not moving, but there's nothing in the question that actually indicates that it can't or won't move. Physics indicates that it can and will with enough thrust!

Yeah, it's worded poorly.

Imaging sitting on a bike coasting on one of those people movers at the airport. The rolling resistance would still make you slow down a bit and eventually you'd be going in the same direction and speed as the conveyor if you didn't apply a little bit of power to overcome the rolling resistance.

 

[mugs]

Originally posted by: Mo0o

Originally posted by: 91TTZ

Originally posted by: Armitage

Except the first camp hasn't explained why the plane isn't moving yet. What is counteracting the thrust?

Just wheel resistance, really.

If you have a belt that's accelerating the opposite direction as your direction of acceleration, how do u beat it? This a genuine question

The wheels on a plane rotate freely. The conveyor belt will affect it minimally. Take my car analogy from way back in the thread. Put only the rear wheels of a FWD car on the conveyor belt. The car can still move, because it's drive wheels are not affected by the conveyor belt. Now apply that to plane - the plane moves forward with thrust, not by rotating its wheels. The conveyor belt does not counteract the thrust.

 

[91TTZ]

Originally posted by: Armitage

Which isn't significantly different then the rolling resistane of the wheels on a normal takeoff run. And which is much less then the aerodynamic drag an aircraft experieces at takeoff speed.

In simpler terms, he engines have more then enough thrust to overcome the rolling resistance of the wheels. They have to if the plane can ever takeoff in a normal situation.

I agree. It wouldn't amount to much at all.

The question just seems to be worded to make you take for granted that for whatever reason, the plane isn't allowed to move forward.

 

[Mo0o]

Originally posted by: mugs

Originally posted by: Mo0o

Originally posted by: 91TTZ

Originally posted by: Armitage

Except the first camp hasn't explained why the plane isn't moving yet. What is counteracting the thrust?

Just wheel resistance, really.

If you have a belt that's accelerating the opposite direction as your direction of acceleration, how do u beat it? This a genuine question

The wheels on a plane rotate freely. The conveyor belt will affect it minimally. Take my car analogy from way back in the thread. Put only the rear wheels of a FWD car on the conveyor belt. The car can still move, because it's drive wheels are not affected by the conveyor belt. Now apply that to plane - the plane moves forward with thrust, not by rotating its wheels. The conveyor belt does not counteract the thrust.

Ouuuuuuuuuuu, that's right.

Ok so new question. What if the plane is moved by the wheels, not jet engines. Can teh plane take off then?

 

[91TTZ]

Originally posted by: Mo0o

If you have a belt that's accelerating the opposite direction as your direction of acceleration, how do u beat it? This a genuine question

It doesn't take much at all to overcome a wheel's rolling resistance. If the plane's engines couldn't do that, it would never be able to take off in any situation, conveyor or not.

 

[Armitage]

Originally posted by: Mo0o

Originally posted by: mugs

Originally posted by: Mo0o

Originally posted by: 91TTZ

Originally posted by: Armitage

Except the first camp hasn't explained why the plane isn't moving yet. What is counteracting the thrust?

Just wheel resistance, really.

If you have a belt that's accelerating the opposite direction as your direction of acceleration, how do u beat it? This a genuine question

The wheels on a plane rotate freely. The conveyor belt will affect it minimally. Take my car analogy from way back in the thread. Put only the rear wheels of a FWD car on the conveyor belt. The car can still move, because it's drive wheels are not affected by the conveyor belt. Now apply that to plane - the plane moves forward with thrust, not by rotating its wheels. The conveyor belt does not counteract the thrust.

Ouuuuuuuuuuu, that's right.

Ok so new question. What if the plane is moved by the wheels, not jet engines. Can teh plane take off then?

It couldnt take off on a normal runway, much less the conveyer. As soon as the plane has enough speed to lift off, it loses all thrust and slows down, so now it doesn't have enough speed to lift off.

That's a bit of a simplification - you could get a hop into the air, but not sustained flight.

 

[91TTZ]

Actually, I just thought of another scenario:

If the conveyor had limitless power/speed and could accelerate to whatever speed was necessary to stop the plane from moving (airspeed), it technically COULD stop the plane from taking off. As the plane tried to take off, the belt would just keep accelerating until the rolling resistance reached a point of equilibrium with the engine's power, and 100% of the engine's power would be devoted to overcome that rolling resistance.

Of course the tires would blow out long before that, but it's something to ponder.

 

[Mo0o]

Originally posted by: Armitage

Originally posted by: Mo0o

Originally posted by: mugs

Originally posted by: Mo0o

Originally posted by: 91TTZ

Originally posted by: Armitage

Except the first camp hasn't explained why the plane isn't moving yet. What is counteracting the thrust?

Just wheel resistance, really.

If you have a belt that's accelerating the opposite direction as your direction of acceleration, how do u beat it? This a genuine question

The wheels on a plane rotate freely. The conveyor belt will affect it minimally. Take my car analogy from way back in the thread. Put only the rear wheels of a FWD car on the conveyor belt. The car can still move, because it's drive wheels are not affected by the conveyor belt. Now apply that to plane - the plane moves forward with thrust, not by rotating its wheels. The conveyor belt does not counteract the thrust.

Ouuuuuuuuuuu, that's right.

Ok so new question. What if the plane is moved by the wheels, not jet engines. Can teh plane take off then?

It couldnt take off on a normal runway, much less the conveyer. As soon as the plane has enough speed to lift off, it loses all thrust and slows down, so now it doesn't have enough speed to lift off.

That's a bit of a simplification - you could get a hop into the air, but not sustained flight.

Hmm... true true. Let's say it's a car, would it roll in place

 

[mugs]

Originally posted by: Mo0o

Ok so new question. What if the plane is moved by the wheels, not jet engines. Can teh plane take off then?

Only with a big gust of wind

But it'd have a hard time staying aloft with its wheels spinning in the air.

 

[Chode Messiah]

it's a vtol aircraft that can take off without foward thrust.

 

[Armitage]

Originally posted by: 91TTZ
Actually, I just thought of another scenario:

If the conveyor had limitless speed and would accelerate to whatever speed was necessary to match the wheel speed and stop it from moving, it technically COULD stop the plane from taking off. It would just keep accelerating until the rolling resistance reached a point of equilibrium with the engine's power, and 100% of the engine's power would be devoted to overcome that rolling resistance.

You'd slag the bearings first Which would add quite a bit of drag. But in any case, te OP says the conveyer just matches the speed of the aircraft.

 

[mugs]

Originally posted by: Mo0o
Hmm... true true. Let's say it's a car, would it roll in place

Yes

 

[91TTZ]

Originally posted by: mugs

Originally posted by: Mo0o
Hmm... true true. Let's say it's a car, would it roll in place

Yes

Mathematically speaking, the car would actually face the same problem that the plane would. If the car had unlimited gearing, it would spin the wheels faster and faster until the rolling resistance sapped 100% of the engine's power.

Without air resistance being a factor, it would be all about rolling resistance.

In either case, regardless of if the vehicle's power is transferred to the belt or through jet propulsion, if that conveyor had unlimited power and speed it would just keep going faster and faster as required until no vehicle can achieve any forward motion (airspeed) due to rolling resistance. Since any object on that converyor will have rolling resistance, THAT will that vehicle's fate against the conveyor.

The all-powerful conveyor will always win against a vehicle with finite power and rolling resistance.

 

[cubalis]

Originally posted by: 911paramedic

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off?"

Thanks in advance. (no, its not homework, you guys know me...duh)

I am in the theoretical 'yes' camp.

The arguments stating that the wheels would be moving 2x as fast seem to be correct.

I thought of it like this:

If you were wearing rollerblades, standing on a treadmill, and had a rope tied around your waist. The rope is being 'held' by some force infront of you, independant of the track. Assuming my blades are perfect, and the wheel bearings have 0 friction, it would only take a minute force from the rope to keep me stationary, no matter how fast the treadmill is running. If that rope force increases, I will be pulled forward. The wheels will spin faster.

The propulsion in a plane is from the air (or rope), not the ground. A planes wheels on take off act as a means to lessen the friction to the ground, not to accelerate the craft like a car.

meh. maybe I'm wrong.

 

[Chode Messiah]

im still sticking to my guns on the vtol idea.

 

[91TTZ]

Infinite power conveyor > finite power vehicle with rolling resistance


The conveyor will just keep accelerating until the rolling resistance consumes all of the vehicle's power. As long as there is at least some friction between the belt and the vehicle, the vehicle has no chance against the all-powerful conveyor.