Author Topic: plane on a conveyor belt? (Read 19873 times)

Mini D · « **Reply #210 on:** January 22, 2007, 09:20:21 PM »

Quote

Originally posted by hitech
Mini D: Picture a 10000 LB wheel suported by a bearing and none of it sides are touching. Picture your slef trying to turn the wheel. Obviously you would have to push fairly hard to get it turning. Now stop pushing, the wheel will very gradually slow to a stop. Where all your force went is into the rotational acceleration of the wheel. It is derived from F = m * A. (Force = Mass * Acceleration). Sorry can't pull the rotational version out of my head at the moment. (no pun intended)

I don't have a problem understanding this. No need to explain.

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In the airplanes case, this force would be transmitted to the airplane, and if the force of the conveyor equaled the thrust of the plane. The plane would not move.

This is where we drastically depart. The friction would be all that prevented the aircraft from moving. In the absence of friction, it will move.

The counter force would only cause the wheel to spin faster. It is effectively operating in the same direction as the aircraft's thrust by spinning the wheel in the same direction. The only real drag is created between the wheel and the bearings. This is the only drag that can stop the aircraft. Normally... it would be between the brakes and the wheel... but not with the breaks off.

kamilyun · « **Reply #211 on:** January 22, 2007, 11:23:28 PM »

If we simply consider the wheels, the plane will not take off. I think someone mentioned the wheels will move twice as fast. However, the conveyor belt will not allow this as it matches the speed exactly.

Quote

Originally posted by hitech
mijac: Note the Frictional force is independent of speed. Power required changes with speed, but the force remains the same.

1. Friction force at high speeds IS dependent on the speed.

From Wikipedia :

Now this is in fluids...could be the axle grease, or in it's absence, the air between the bearings. Either way, it's a fluid.

2. Golfer's argument:

"Turn on the engines. Lets say they're jet engines. Power up. gently...even though the wheels are spinning the engines are taking air from in front of the airplane and squirting it out the back of the airplane. The plane is moving in relation to the fluid (air) around it."

...I'm pretty sure is the only way to remove the wheel argument from the problem.

3. The original question describes an impossible situation as, um, eagl (?) pointed out:

The point is that the second ANY force is applied to the plane, the wheel speed jumps to infinity. If there is any delay in the spin-up of the treadmill and wheels, the plane will move which violates the premise that the treadmill will accelerate to match the wheelspin. If the plane is moving, then the treadmill must be moving slower than the wheels are spinning, which violates the whole premise behind the question. And it still results in the wheels and treadmill moving at an infinite speed. Which isn't possible.

The situation described in the question is impossible.

So we are all wrong, and all right

hitech · « **Reply #212 on:** January 23, 2007, 11:13:13 AM »

kamilyun: That equation you posted is drag, not friction. They are 2 completely different equation forms and concepts.

Surface friction does not have a Velocity component.

Mini D:

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he only real drag is created between the wheel and the bearings.

Correct in the Drag piece, but drag is not the only force. You are not quite seeing the force created by the acceleration of the wheel.

Wish eskimo2 sander had a variable speed control so you could see the rubber band stretch at constant speed, see it stretch more during the 2nd acceleration,and then return to it's steady state stretch at the new higher speed.

HiTech

RATTFINK · « **Reply #213 on:** January 23, 2007, 11:39:16 AM »

B@tfinkV · « **Reply #214 on:** January 23, 2007, 02:07:11 PM »

ok now that we reached page 5, if there is anyone who still doesnt get it i think its about time you went out back and removed yourself from the gene pool

Terror · « **Reply #215 on:** January 23, 2007, 02:14:03 PM »

Quote

Originally posted by hitech

In the airplanes case, this force would be transmitted to the airplane, and if the force of the conveyor equaled the thrust of the plane. The plane would not move.

HiTech

But in this example, the conveyor is only matching the speed of the wheels. So the energy added by the conveyor to the wheel/plane from inertial forces would only be about double the normal acceleration forces on the wheel. So probably something similar to the friction from a semi-flat tire. The plane will still accellerate and will still take off.

Terror

Terror · « **Reply #216 on:** January 23, 2007, 02:24:48 PM »

Quote

Originally posted by hitech

Wish eskimo2 sander had a variable speed control so you could see the rubber band stretch at constant speed, see it stretch more during the 2nd acceleration,and then return to it's steady state stretch at the new higher speed.

HiTech

I would like to see a slow steady rate of accelleration. If the forces are added incrementally (ie. like an airplanes acceleration), the inertial forces would be easily overcome.

And in the end, the plane still takes off. The rolling friction and inertial forces from the wheels would not be enough to overcome the theoretically limitless power of the thrust from the airplane's engine.

I agree that a RAPID accelleration will produce some huge peak inertial forces, but a slow progressive accelleration will allow for the plane to reach take off speed and fly!!

Terror

PS. And did you notice in eskimo2's movie that the "spring loading" of the wheel overcame the wheel friction as soon as it was up to speed. Which would mean for a time it actually ACCELLERATED on the belt.

lukster · « **Reply #217 on:** January 23, 2007, 04:36:28 PM »

If the belt tried to match the rotational speed of the wheel (as measured like a speedometer connected to the wheel), the belt would continue to increase in speed so long as the wheel was not stationary or moving backwards relative to me standing beside the belt and plane. This speed would extend to infinity unless you put a limit on how fast the belt was allowed to turn.

I'm not sure everyone believes this. To illustrate: the plane engine starts and both the belt and wheel are stationary. The throttle is applied and the plane begins to move forward. For the sake of argument let's say the belt does not engage until there is a one mile an hour difference between it's speed and that of the wheel. At 1 mph the belt then rotates backward at 1 mph. Assuming enough power is applied to maintain the plane's position relative to me the wheel is now rotating at 2 mph. The belt senses this and speeds up to 2 mph. This causes the wheel to rotate at 4 mph causing the belt to increase to 4 mph which in turn makes the wheel spin at 8mph. If enough power is applied to cause the plane to accelerate relative to me it will cause to belt to accelerate.

Realistically? If the belt's response time were sufficient and it's speed capable of freezing the bearing the plane would not take off.

hitech · « **Reply #218 on:** January 23, 2007, 04:55:42 PM »

Terror:Im not in disagreement with your 2nd post.

lukster: As we said earlier , the posted case is not solvable. Because with out your special case delays, you reach infinity as soon as the wheel turns at all.
But your example does illustrate the issue fairly well

Golfer · « **Reply #219 on:** January 23, 2007, 05:17:08 PM »

What's wrong with saying this:

Airplane ready to go at the end of a huge conveyor. The wheels aren't going to move at all if the airplane isn't moving to begin with. No power is transferred through the wheels to the ground so the wheels are simply along for the ride. The airplane starts moving. From power application you accelerate (we'll pretend that this is a constant rate of acceleration) to rotation speed for the airplane. If the airplane rotates at 100kts then it would have constantly accelerated from 0 to 100kts. The belt would have accelerated in the opposite direction from 0 to 100kts in opposition of the wheels.

The wheels are rolling along at 200kts because the airplane is moving 100kts along a 100kt conveyor moving in the opposite direction.

The airplane is at 100kts anyway so the airplane takes off normally.

Where's the fault in that which lacks fancy drawings, illustrations, soundbytes and videos?

eskimo2 · « **Reply #220 on:** January 23, 2007, 05:29:43 PM »

Golfer,

One thing that I discovered on the physics board (had pointed out to me) is that their question has the conveyer moving opposite of the plane at the same speed. What you have stated is the correct answer for their question (plane takes off at 200 mph, wheels are spinning at 200).

This question, however, has the conveyer matching the wheel speed. When the plane moves forward 1 inch, its wheel is going faster than the conveyor. This cannot be allowed so the conveyor must speed up like mad trying to move it back. By dumping enough rotational energy into the wheel, it can and will keep the plane in place.

eskimo2 · « **Reply #221 on:** January 23, 2007, 05:39:28 PM »

More movies;

I dumped a flood light of the sander and brought the shutter speed from 1/30th second to 1/250th. I also hooked a crappy variable speed Dremel motor control to the sander. I sort of got the 2 speed effect. Both movies are available in AVI and QuickTime. The QuickTime ones are in the original Nikon format and are a bit sharper and are easier to move frame by frame.

1/250th exposure wheel on sander:
http://hallbuzz.com/movies/wheel_on_sander_250th.AVI
http://hallbuzz.com/movies/wheel_on_sander_250th.MOV

1/250th exposure 2-speed wheel on sander:
http://hallbuzz.com/movies/wheel_on_sander_2_speed.AVI
http://hallbuzz.com/movies/wheel_on_sander_2_speed.MOV

lukster · « **Reply #222 on:** January 23, 2007, 05:52:30 PM »

Ok, let's say this plane has very strong landing gear with a nose wheel. All you need to do is nudge it backwards a bit, the belt rotates forward instantly launching the plane due to the energy imparted to the wheels. Problem solved.

Mini D · « **Reply #223 on:** January 23, 2007, 07:51:35 PM »

Quote

Originally posted by hitech
Mini D:

Correct in the Drag piece, but drag is not the only force. You are not quite seeing the force created by the acceleration of the wheel.

Yes, I am. But that acceleration needs to be transfered to drag on the airframe just as friction is required to transfer the energy from the jets to the rotating wheel. Ask yourself this: what requires more work, pushing a airplane or spinning a suspended wheel. You're ignoring the primary energy source and focussing on the less significant source.

Wes14 · « **Reply #224 on:** January 23, 2007, 08:37:07 PM »

Quote

Originally posted by lukster
Ok, let's say this plane has very strong landing gear with a nose wheel. All you need to do is nudge it backwards a bit, the belt rotates forward instantly launching the plane due to the energy imparted to the wheels. Problem solved.

but as soon as it launches forward wouldnt the belt catch it and fling it back,then forward,then back, like a swingset or sumthing?