If the wheel accelerates, it gains angular momentum. That means force is applied to the edge, and therefore to the axle. That means the plane will move.
It won’t move a lot because the weight of the wheel is small compared to the weight of the plane. But it will move.
Treis has made a point several times but maybe it got buried in the math.
The belts reverse motion energy can only be applied to the plane through the wheel contact. That is too small and tenuous a link to transfer a force capable of countering the engine thrust.
OK, I was able to find the answer the OP gave in the other forum. The thread wasn’t deleted, I jsut wasn’t searching for it correctly. :smack:
Like others have said, the conveyor belt realyl doesn’t figure into the equations at all, all itdoes is force the wheels to spin faster, but doesn’t realyl provide any more or less friction that has to be overcome for the plane to move and take off.
The big sticking point is, since the treadmill is moving backwards againt the desired movement of the plane, it would be kinda like trying to launch that same plane off the back of that carrier running full speed, losing the airspeed generated by the movement of the carrier. Throw in a stiff tailwind and our C1 goes splash, because although it may be moving 60-70 mph across the carrier deck, its speed relative to the air around it could be pretty much zero. Without that airspeed, no lift.
zut, I really think you did not. Well done!
Yes, but we * long * ago established that the original statement of the problem contains a logical and physical impossibility. And there’s very little chance that it was deliberately phrased that way as a subtle test of logic. The original problem was asking whether a plane could take off from a conveyor belt moving rapidly in the opposite direction of the plane’s flight and the person posing the problem tried (incorrectly) to nail down the velocity of the conveyor belt.
A better phrasing might have been, “A plane is on a conveyor belt that can move at any desired speed in the reverse direction. Is there any way that this conveyor belt can stop the plane from taking off?” Phrased like that, the answer is “no, the plane is going to take off”.
Anyone who says “the conveyor can’t match the speed of the wheels and therefore the plane must be stationary” is just playing silly buggers with the word problem.
As most pilots would agree, you can zoom around at full thrust on the runway as long as you like, but until you pull back on the stick you aren’t going to take off. What does pulling back on the stick do? Activate flaps to redirect the flow of air over the wings… flow of air you don’t have if you’re sitting on a giant magical conveyor belt and going nowhere.
Sorry, Dead Battery, but no, that’s not right. Have you ever seen a 747? The engines hang under the wings and do not blow air over the wings. They push the plane forward. The movement of the wings through the air is what generates airflow over the wings.
The only reason is that it takes time (and deck space) to first cancel the movement of the carrier, and then accelerate to takeoff speed. But on an infinitely long aircraft carrier (which is analogous to a treadmill), an aircraft should have no problem taking off backwards agains the motion of the carrier.
I thought we went through this.
Q: If the treadmill could prevent the airplane from moving, will it take off?
A: No.
Q: If the treadmill cannot stop the plane from moving forward, will it take off?
A: Yes.
Q: In an idealized situation (frictionless bearings and no failures), can a treadmill prevent the plane from moving forward?
A: Yes, but the treadmill must continue to accelerate. The wheels would spin faster and faster.
Q: Can a real-life treadmill prevent the aircraft from moving?
A: Yes, but only if it can move fast enough to cause the wheel bearings or tires to fail, or generate enough friction in the bearings to counteract engine thrust.
Disagree. With frictionless bearings, the treadmill will not have any affect on the plane and the plane will take off. The treadmill might as well not exist at all.
If there’s no friction, then there is nothing to keep the thrust of the engines from pushing the plane forward. If the system is frictionless, then it’s not impeding the movement of the plane to use it’s thrust to take off. Frictionless. Like on ice, but planes can take off of ice.
Go back to walking on the treadmill at the gym.
Start off with the treadmill off. Stand on it. Spit. The spit goes forward, propelled by your mouth.
Now set the treadmill to 3. Repeat. The spit still goes forward.
Set it on 10. No change. No matter how fast the treadmill is going backwards, it has no effect on how far the spit travels.
Same thing with throwing a paper airplane while on a treadmill. Or taking a plane off of ice. Or off a frictionless treadmill running backwards.
Thanks for that post, it cleared up all the confusion in my head from reading this thread.
Let’s try a bowling analogy. The ball speed of a pro bowler is about 22 MPH. If we
have a conveyor belt replacing the lane between the front of the pins to the foul line,
moving at 22 MPH toward the bowler, and the bowler throws the ball. Will it reach
the pins?
No, for the same reason that the aircraft won’t move over the ground, the ball and
the
airplane wheels are connected to the belt by friction. The acceleration of the airplane
is limited by the maximum output of the engine, just as the ball is limited by the
power
of the bowlers arm. The forward movement of both will be dissipated by the friction
of contact w/ the belt.
There is no infinite acceleration. There have been land vehicles that have exceeded
700 MPH, so there are wheels that would withstand the speed generated by a jet
aircraft engine, and the wheels would turn at the same speed as the belt, not twice as
fast.
The power source driving the airplane does not have to be transmitted mechanically
to the belt, the fact that the belt cancels out forward movement of the wheels through
friction, is the same.
The analogy of the aircraft carrier launching planes, while steaming into the prevailing
wings, is the reverse of the OP. The belt/runway/carrier deck is moving in the
direction of flight, adding to the relative speed of the airplane, rather than subtracting
from it. This is not critical on landing because the arresting cable are used to
dissipate the momentum and engine power of the airplane.
Just as the reverse acting conveyor in the OP, an aircraft carrier cannot launch planes
while steaming with the prevailing wing.
This is wrong. The ball is like the wheels on the plane, but for the analogy to work the bowler would need to hop onto the rolling ball and ride it like a log rolling, then throw a baseball at the pins and knock them over. The bowling ball on the lane and the throwing of the baseball are 2 distinct forces, just as the tires on a plane are distinct from the thrust of the engine.
I really don’t thing that’s a good analogy. Try this.
Set the bowling ball on the conveyer belt. Or better yet, a little red radio flyer wagon. Stand to the side of the conveyer with a broom or the like. Something that you can push the wagon with (this represents the engines of the plane)
Now start up the conveyer. Can you (the engines) prevent the wagon from moving? Sure ya can.
In fact you (again, representing the engines) can push the wagon against the conveyer to the pins. Push it fast enough, and put wings on it and you have an airplane.
Sorry for the double, but we are going around and around.
Say the bowler tosses not a bowling ball onto the 22mph reverse lane, but a skateboard. A skateboard with an Estes rocket mounted on it. As soon as the skateboard hits the lane, it doesn’t move, just as predicted by you. Then I fire the Estes rocket. The skateboard will move. The lane can speed up all it needs to, but the skateboard will still move forward.
The thing you have to remember is that it is a frictionless system. Think about that. Frictionless. Meaning that no matter what is going on with the wheels or conveyer belt, it is equivalent to being on a perfect sheet of ice. Frictionless.
Now picture a rocket sled on an ice lake. Do you think that the sled won’t move when fired because the ice it is setting on is frictionless??
Come on guys, several people have posted the correct answer. The plane will take off.
Case 1:
With frictionless bearings, the wheels will rotate with infinite speed without exerting a horizontal force on the airplane. The only force applied by the wheels on the airplane will be vertical and will exactly counter act gravity.
Case 2:
Normal bearings that do not fail/seize. In this case the rotating wheel will exert a horizontal friction force on the plane proportional to the planes weight. The force of friction is NOT proportional to velocity and thus the speed at which the wheels rotate will NOT have an effect on the magnitude of the friction force (Google kinetic friction and look at the equation). As long as the force of the engines is greater in magnitude than the friction force (which obviously it is or planes would never move), the plane will accelerate and take off.
Case 3:
Normal bearing that fail/seize. The issue is the work being done by the conveyor. Remember work can be defined as the integral of force over a distance that the force is applied. The conveyor spinning the wheels faster and faster will be impeded by the constant friction force. Integrating the frictional force over the circumference of the bearing multiplied by the number of rotations and you will have put a LOT of energy into the bearings, which of course will sooner or later melt and seize.
The whole confusion here seems to be regarding the wording of the OP. The conveyor spins at the speed needed to match the speed of the wheels. By definition this can be any speed. The conveyor could be moving forward at take off speed with completely still wheels and the plane would take off and the condition would be met. The conveyor could be moving backwards at 6000 mph with the wheels rotating at the same speed and the only force on the plane would be the CONSTANT rolling friction that is proportional to the planes mass.
My guess is that the wheels would stay motionless and the conveyor would move the plane forward until takeoff speed was reached.
Try this: The plane is motionless on the motionless conveyor and turns on it engines. The engines starts to nudge the plane forward due to the thrust applied. The wheels start to spin. At this moment, the conveyor starts to counteract the spin of the wheels and moves forward so the way remains motionless. The engine continues applying thrust to the plane (by pushing on the air), the wheels continue to try to turn and the conveyor continues to compensate and keep the wheels still. Sooner or later, airflow over the wings will be fast enough to generate lift and the plane will take off.
Well played, sir.
Um, yes it will just fine - and it will only be slowed a tiny bit. Actually this analogy is greatly complicated by angular momentun of the rotating ball, but if we go with a real world situation (oiled lane), then what we find is that there is only a small amount of friction. You’ll notice that a pro bowler’s ball does not rotate in the direction of travel during most, if not all, of its path to the pins. This makes it a great analogy for the plane, as there is also very little friction in the plane’s wheel bearings. The ball will reach the pins and the plane will take off just fine.
I think zut did the best job pointing out that the original statement of the problem makes little sense, but if anyone’s trying to figure out details, simplifying and looking at similar cases may help.
We have either a treadmill or an infinite and movable strip, which I’ll call “the belt”. The part we want to move relative to will be “the ground”.
Since we don’t really care about lift so much as whether we can move a certain speed (or at all) relative to the ground, these may as well be carts. Simple vehicles moving in a straight line.
Consider these cases :
(A) Rocket Sled : No wheels; has some means of thrust controlled by the pilot (e.g. jet engine, tow rope, child pushing it).
(B) Auto Cart : Has wheels; moves by turning its own wheels (e.g. bicycle, car, locomotive).
© Rocket Car : Has wheels, but moves by some other force as in (A).
Think about these questions for each vehicle. Start with (A), it’s easiest. Consider how much © is like (A).
What happens if there is no friction on the belt?
Now add friction (to the belt). What happens when the belt moves at a constant, low speed (no slippage) in any direction? Why?
Imagine the vehicle is moving, applying just enough throttle to keep a constant forward speed v[sub]0[/sub].
What happens to the vehicle’s speed if the belt moves at constant speed in the opposite direction (-v[sub]0[/sub] )
-relative to the belt?
-relative to the ground?
What can the belt do to slow or stop the vehicle relative to the ground?
When you are finished, please return your blue books to the proctor. If you need to cheat, look off treis’s paper.