Airplane on a conveyor belt

[McGurk]

OK, now on to the real tough question. If you are on an airplane and fire two guns, one pointing forward and one pointing backwards. Assume the aircraft is flying at the exact speed equal to the muzzle velocity of the bullets.
What happens to the two bullets?

Not such a hard question (as I'm sure you know)... Lets not talk about guns though and rather, a projectile.

Where you to... project the projectiles their projected velocity would be what they normaly would be (ignoring airpressure at the... appature of the projecting tube...) relitive to the ground, the rearward projectile projectile would be stationary on leaving the projecting tube and the forward projected projectile would have twice the velocity it would normaly have. The best bit, however, is that even though they are traveling at massivly differant velocities, they'll both hit the ground at the same time! (ignoring drag, which might be might be missing the point when it comes to aircraft.)

Well, I think I can remember Physics... how did I do, Teach?

[The Wizard of BC]

Ever watch the old war movies of B-17's? The gunners are firing in all directions and there is no effect on the bullets other than the relative motion of the two planes causing the gunners to "Lead" their targets.

From a purely Physics stand point the bullet fired rearwards will go farther than the one fired forwards.

The thing you have to remember that while in the barrel a bullet don't know that the gun is mounted in a moving airplane. It acts the same as if it were bolted to the ground. It's only after it leaves the barrel that it is affected by different air velocities that change the friction caused drag.

[BonnieT100]

As a teacher of physics and a pilot I have been reading this with some interest.

It's amazing how this subject comes around every year or so on the internet. It also comes up each year with new students. This question and the one about firing a bullet from a moving vehicle are the classic misunderstandings of the laws of physics.

Let me give an example that may help the understanding.

If you are sitting on a bicycle on a conveyor belt and have a rope in your hands that is tied to a fixed point and the conveyor starts to move you can stay in the same spot relative to the outside world by simply holding on the the rope. The bicycles wheels will spin at the same speed as the conveyor but you remain motionless.
Now start to pull on the rope. You will start to move. You simply must overcome the friction of the wheels and the static mass of you and the bike.
If you don't hold onto the rope when the conveyor starts you will begin to move backwards. You can still overcome the movement by overcoming the friction and now the inertia of yourself as a moving body.
No matter how fast the conveyor moves you can stop yourself or move forward or back at will as long as your arms can overcome the small friction or inertia.

Now look at an airplane. If an airplane flies low over a moving conveyor with it's wheels up will it magically fall out of the air? No. The airplane does not care what is on the ground underneath it. It only cares that a certain velocity and density of air is passing over its wings. Even it the case where the conveyor is moving backwards taking the plane along with it the airplane must only start to move forward till it's speed is equal to its take-off speed. In fact it is easier for the airplane to start moving in this case because there is air now trying to push it from behind and helping it along.

If the airplane is moving backwards with the conveyor it will simply take more time for it to achieve take-off speed. Similar to an aircraft attempting to take off with a tail wind. The only factor is fuel.

OK, now on to the real tough question. If you are on an airplane and fire two guns, one pointing forward and one pointing backwards. Assume the aircraft is flying at the exact speed equal to the muzzle velocity of the bullets.
What happens to the two bullets?

I just want to point out that the aircraft would never get any air flowing over the wings until it's speed relative to the belt exceeds the belts speed relative to the airplane. To the outside observer, the airplane is standing still. We are assuming there is no wind. We have to be talking about ground speed since the belt is on the ground and, generally speaking, doesn't fly.
I think this is a question dreamed up by philosophy majors as payback to engineers for making the following joke: Q: What's an engineer say? A: How Does it work? Q: What's a scientist say? A: Why does it work? Q: What's a liberal arts major say? A: Do you want fries with that?

[ccga3359]

I just want to point out that the aircraft would never get any air flowing over the wings until it's speed relative to the belt exceeds the belts speed relative to the airplane. To the outside observer, the airplane is standing still. We are assuming there is no wind. We have to be talking about ground speed since the belt is on the ground and, generally speaking, doesn't fly.
I think this is a question dreamed up by philosophy majors as payback to engineers for making the following joke: Q: What's an engineer say? A: How Does it work? Q: What's a scientist say? A: Why does it work? Q: What's a liberal arts major say? A: Do you want fries with that?

But a belt rushing by and with air being pushed behind by prop/jet surely would cause a negative air pressure under the wings giving lift.

[Yaish]

I just want to point out that the aircraft would never get any air flowing over the wings until it's speed relative to the belt exceeds the belts speed relative to the airplane. To the outside observer, the airplane is standing still. We are assuming there is no wind. We have to be talking about ground speed since the belt is on the ground and, generally speaking, doesn't fly.
I think this is a question dreamed up by philosophy majors as payback to engineers for making the following joke: Q: What's an engineer say? A: How Does it work? Q: What's a scientist say? A: Why does it work? Q: What's a liberal arts major say? A: Do you want fries with that?

I want to point out again, that the speeding belt does nothing to slow the aircraft at all. The airplane is moving because of the propellers pushing against the air, not because of the wheels pushing against the ground. The wheels just spin faster as the plane moves at the same speed it always does. Therefore, air passes over the wings just like normal.

[hallmarktex]

The belt gives the aircraft movement in the negative direction (relative to the airfoil).
The thrust from the prop/turbine gives movement in the positive direction.
If the belt moves at the same rate that the thrust pushes forward then there is no relative movement in the airstream. The observer on the ground sees the aircraft standing still.
However, the kilted observer gets away with the girl while the first guy is busy with his math book.
Also; the thrust alone does not cause movement of air over the airfoil that is sufficient to induce lift.

[Yaish]

The belt gives the aircraft movement in the negative direction (relative to the airfoil).
The thrust from the prop/turbine gives movement in the positive direction.
If the belt moves at the same rate that the thrust pushes forward then there is no relative movement in the airstream. The observer on the ground sees the aircraft standing still.
However, the kilted observer gets away with the girl while the first guy is busy with his math book.
Also; the thrust alone does not cause movement of air over the airfoil that is sufficient to induce lift.

The belt does not provide any movement to the rear, as the wheels simply spin faster while the aircraft moves forward at the same speed as on stationary ground.

The aircraft never standstill while there is thrust from the engines. It moves forward, completely ignoring the state of the ground beneath it. (other than some slight resistance from the wheel bearings)

[hallmarktex]

The belt does not provide any movement to the rear, as the wheels simply spin faster while the aircraft moves forward at the same speed as on stationary ground.

The aircraft never standstill while there is thrust from the engines. It moves forward, completely ignoring the state of the ground beneath it. (other than some slight resistance from the wheel bearings)

You're giving the thrust credit for overcoming both the rearward movement of the belt and the forward motion required to induce lift. The wheels and bearings cannot be assumed to be so efficient that the inertia that tends to make things stay in one place remains perpetually.
If the plane is sitting on the belt with no thrust applied and the belt starts moving, then the plane will move with it. The thrust is applied as a balancing force (or visa versa). That was the point (as I took it) of the original question.

[Yaish]

There is a world of difference between NO thrust and any thrust, even a little.

The wheels and bearings do contribute some resistance, but very little. That very little bit of resistance is all that is needed to get the plane moving forward, regardless of what the treadmill below the airplane is doing.

To reverse the situation, if you have the treadmill moving such that it moves the plane forward, and the plane uses it's own engine it will still take off and at the same speed as before. The wheels will just remain stationary while the plane moves forward.

Think of it as vectors.

Thrust is a vector acting this way on the body of the plane

--------->

The treadmill is a vector acting this way on the WHEELS

<---------

The bearings and hubs of the wheels transform the linear motion of the treadmill vector into rotational motion of the wheels. The thrust of the engines is also translated into a rotational motion on the wheels, and in this case the two vectors add to cause the wheels to spin twice as fast.
The only force that the thrust needs to overcome is the frictional resistance to the wheels turning.

If the airplane was a small model that could be pushed by a human, and it was placed on the treadmill that same human could pull it forward against the treadmill by a rope attached to the nose. He could also prevent it from moving backwards simply by holding tight and remaining stationary.

[hallmarktex]

There is a world of difference between NO thrust and any thrust, even a little.

The wheels and bearings do contribute some resistance, but very little. That very little bit of resistance is all that is needed to get the plane moving forward, regardless of what the treadmill below the airplane is doing.

To reverse the situation, if you have the treadmill moving such that it moves the plane forward, and the plane uses it's own engine it will still take off and at the same speed as before. The wheels will just remain stationary while the plane moves forward.

Think of it as vectors.

Thrust is a vector acting this way on the body of the plane

--------->

The treadmill is a vector acting this way on the WHEELS

<---------

The bearings and hubs of the wheels transform the linear motion of the treadmill vector into rotational motion of the wheels. The thrust of the engines is also translated into a rotational motion on the wheels, and in this case the two vectors add to cause the wheels to spin twice as fast.
The only force that the thrust needs to overcome is the frictional resistance to the wheels turning.

If the airplane was a small model that could be pushed by a human, and it was placed on the treadmill that same human could pull it forward against the treadmill by a rope attached to the nose. He could also prevent it from moving backwards simply by holding tight and remaining stationary.

Your rope analogy proves the point. The rope (in vector analysis) is an ever increasing force that resists the increasing speed of the belt working to move the mass backward. The mass remains in place because the forces are in balance. In order to achieve forward motion the person must pull the rope (as opposed to holding it in place) or the engine must provide a thrust greater than the rearward motion induced through the wheels on the belt.