Plane on conveyor on a FE... Will it ever take off?

Quote

Man, looks like somebody shit in your cereal.

Nope, just like annoying idiots like you.

What's annoying about me?  Somebody presented the question, I presented my opinion as to what the answer would be, and then was presented with a counter opinion to which I expressed my argument against.  I did so in what I think was a reasonably mature manner.

You come along out of nowhere and start calling me a jackass for god knows what reason, and for some reason believe that this question has any correct answer without any sort of experimentation on any level whatsoever.

It's as if you suddenly decided that I was evil and had to be dealt with. 

I have to say,

The plane WOULD take off.

You have to think about it for a while, but it would.

I created an animation to demonstrate this (admittedly this was pretty sad of me):



The wheels on the jet are free rolling. In other words, should the jet engine be off, and the conveyor belt on, the plane WOULD move backwards, but only very little. If there was no friction on the wheels, the plane would not move at all. However, there is friction on the wheels (a little), so the plane moves back slightly.

When the jets come on, the thrust is caused by pushing against the air, not by pushing against the ground, therefore the slight drag induced by wheel friction will be overcome and the plane will take off.

You can get caught out easily if you think of the plane like a car. However it is not using the wheels, so it's different.

Imagine it's a car - if you sat the car on the conveyor belt, and left the car IN gear, it would move backwards rather fast (and the wheels wouldn't really move). However if you left it out of gear, the wheels would spin, and the force pushing the car backwards would be quite small.

Regards,

David F.

Quote from: kasroa

Quote from: Wolfwood

Quote from: kasroa

The idea is that no matter how fas you turn up the conveyor belt the wheels will ALWAYS match it's speed by default.

Right but the speed of the wheels would change as the jet attempts to accelerate the plane forward. The conveyor is actually applying negative velocity to the entire plane based solely on the rotation rate of the weels.

The Conveyor is only attmepting to match speed with the wheels, as the jets push the plane forward the wheels will have to accelerate which causes the conveyor to accelerate.

You're forgetting that the wheels are free-wheeling so whatever the speed of the conveyr (it could be moving at 1000 mph) the wheels will match it as long as they can hold together under the heat!

No no no.

Ok lets see if I can sumarize.

Lets say the jets accelerate the plane forward to 100mph. The wheels would normally turn at 100mph. The conveyor would then spin in the opposite direction at 100mph causing the wheels to turn 200mph.

The overall effect is that the jets move forward at 100mph and the conveyor moves backwards at 100mph and the wheels spin at 200mph.

Jet velocity = 100mph
Conveyor velocity = -100mph
Plane velocity = 0mph

Umm... Sorry, Woolfwood, but I think you're wrong on this one. Not that it really matters...

It very much depends on how much drag is created by the wheels.

And what is the point of this thread?

Very little drag ought to be created, as the wheels should spin freely. Unless they were jammed, or the brakes were applied.

The point of this thread, was probably that the OP wanted to see if he could trick us!

Regards,

David F.

Twice the RPM's of regular take-off speed? ...but it doesn't matter.  Why am I still posting this?  I don't know.  Am I going to ask myself more questions?  Mostly in my head. 

Throw a prop plane into the example.

Less power, easier to figure out what happens.

Quote from: kasroa

Quote from: Wolfwood

Quote from: kasroa

The idea is that no matter how fas you turn up the conveyor belt the wheels will ALWAYS match it's speed by default.

Right but the speed of the wheels would change as the jet attempts to accelerate the plane forward. The conveyor is actually applying negative velocity to the entire plane based solely on the rotation rate of the weels.

The Conveyor is only attmepting to match speed with the wheels, as the jets push the plane forward the wheels will have to accelerate which causes the conveyor to accelerate.

You're forgetting that the wheels are free-wheeling so whatever the speed of the conveyr (it could be moving at 1000 mph) the wheels will match it as long as they can hold together under the heat!

No no no.

Ok lets see if I can sumarize.

Lets say the jets accelerate the plane forward to 100mph. The wheels would normally turn at 100mph. The conveyor would then spin in the opposite direction at 100mph causing the wheels to turn 200mph.

The overall effect is that the jets move forward at 100mph and the conveyor moves backwards at 100mph and the wheels spin at 200mph.

Jet velocity = 100mph
Conveyor velocity = -100mph
Plane velocity = 0mph

It's better to look at the net forces on the plane. Let's say the engines provide 100 N of force. For the plane to stay still the ground would have to push back with 100 N of force but it can't because as the ground pushes against the rubber of the tyres, the tyres spin round so all the force of the ground just goes into spinning the tyres and not into working on the plane. There would be some force due to friction of the bearings in the wheels..etc but not (in this example) 100 N worth.

And sorry to bump this thread but the site went down last night just before I tried to post a reply and this is the first chance I've had to post again!

This is a pure mechanics problem, and we must examine it in terms of forces applied on the plane.
While still on the conveyor/runway, the plane is subjected to the following forces:

Gravity, oriented downwards, constant.
Lift, oriented upwards, function of airspeed.
Thrust, oriented forwards, assumed constant.
Drag, oriented backwards, superposition of air resistance and friction in the wheels.

Obviously the plane will not take off until the force due to lift overcomes the force due to gravity. For this to happen, the plane must achieve some minimum forward velocity relative to the air. Forward acceleration will only occur as long as the force of thrust overcomes the drag force.

Because the conveyor belt speed is the inverse of the plane's airspeed, we can say that the conveyor belt does not move until the plane begins to accelerate forward. Thus, rolling resistance has already been overcome by thrust when this problem really begins.

Initially, the engine thrust is considerably higher than the drag—this is what allows aircraft to take off on regular runways. So the question is, once we start moving and the conveyor belt starts up, does it impose some force on the aircraft that can overcome the force of thrust?

Certainly not initially. Consider the case where the aircraft has just begun to move through the air at, say, 1 m/s. The conveyor belt is then moving backwards at 1 m/s and therefore the speed of the aircraft relative to the conveyor is 2 m/s. If a 2 m/s rolling speed created enough friction to overcome the engines, then no aircraft could ever accelerate beyond this speed on a regular runway.

In fact, we know that at the moment of takeoff the wheels are still on the ground and rolling and the aircraft is still accelerating. So up to that rolling speed at least, the engines still win the thrust vs. friction competition. Would rolling at twice that speed cause sufficient friction?

Consider the thrust of an aircraft engine. I won't give you figures here because it depends widely on the type of engine. But... it's a lot of force. Now contrast this with rolling friction. I'm guessing here, but I think that before a wheel could provide enough friction (without using the brakes) to completely counteract an aircraft engine at full throttle, the wheel would be spinning so fast that it would come apart. At any rate, it certainly would not reach this tremendous amount of friction at a rolling rate twice that of a standard takeoff speed.

The airplane would take off normally, with the wheels spinning twice as fast as normal and a *slight* reduction in acceleration due to added friction.

I think where people get thrown off is the idea that if the conveyor is moving backwards and the plane is on the conveyor, then this must translate to some backwards momentum that has to be overcome by the thrust. But of course the conveyor doesn't start up until the plane is already moving forward. It is the conveyor that must overcome the forward momentum imparted by the engines—and the forces just aren't comparable.

http://mouser.org/log/archives/2006/02/001003.html

Well that was worth bumping for.

k

This is a pure mechanics problem, and we must examine it in terms of forces applied on the plane.
While still on the conveyor/runway, the plane is subjected to the following forces:

Gravity, oriented downwards, constant.
Lift, oriented upwards, function of airspeed.
Thrust, oriented forwards, assumed constant.
Drag, oriented backwards, superposition of air resistance and friction in the wheels.

Obviously the plane will not take off until the force due to lift overcomes the force due to gravity. For this to happen, the plane must achieve some minimum forward velocity relative to the air. Forward acceleration will only occur as long as the force of thrust overcomes the drag force.

Because the conveyor belt speed is the inverse of the plane's airspeed, we can say that the conveyor belt does not move until the plane begins to accelerate forward. Thus, rolling resistance has already been overcome by thrust when this problem really begins.

Initially, the engine thrust is considerably higher than the drag—this is what allows aircraft to take off on regular runways. So the question is, once we start moving and the conveyor belt starts up, does it impose some force on the aircraft that can overcome the force of thrust?

Certainly not initially. Consider the case where the aircraft has just begun to move through the air at, say, 1 m/s. The conveyor belt is then moving backwards at 1 m/s and therefore the speed of the aircraft relative to the conveyor is 2 m/s. If a 2 m/s rolling speed created enough friction to overcome the engines, then no aircraft could ever accelerate beyond this speed on a regular runway.

In fact, we know that at the moment of takeoff the wheels are still on the ground and rolling and the aircraft is still accelerating. So up to that rolling speed at least, the engines still win the thrust vs. friction competition. Would rolling at twice that speed cause sufficient friction?

Consider the thrust of an aircraft engine. I won't give you figures here because it depends widely on the type of engine. But... it's a lot of force. Now contrast this with rolling friction. I'm guessing here, but I think that before a wheel could provide enough friction (without using the brakes) to completely counteract an aircraft engine at full throttle, the wheel would be spinning so fast that it would come apart. At any rate, it certainly would not reach this tremendous amount of friction at a rolling rate twice that of a standard takeoff speed.

The airplane would take off normally, with the wheels spinning twice as fast as normal and a *slight* reduction in acceleration due to added friction.

I think where people get thrown off is the idea that if the conveyor is moving backwards and the plane is on the conveyor, then this must translate to some backwards momentum that has to be overcome by the thrust. But of course the conveyor doesn't start up until the plane is already moving forward. It is the conveyor that must overcome the forward momentum imparted by the engines—and the forces just aren't comparable.

http://mouser.org/log/archives/2006/02/001003.html

Did it take you this last...month to write that?

I thought we killed this thread!!! ZOMBIE THREAD!!!!!!!!!!!

I miss this thread! it was one of my favorites because it was suck an easy answer, yet it went on forever.

Agreed.

But now it's evil and wants brains. How come the best ones are always the ones to zombify?

But now it's evil and wants brains. How come the best ones are always the ones to zombify?

Because they don't like you.