sao123
Lifer
- May 27, 2002
- 12,653
- 205
- 106
the inertia of the plane which has several million kilograms of mass, has far more inertia than a single wheel which has a mere few thousand kilograms.
Youll also take note that in your video, after the wheel was pushed backwards, that the wheel was able to return forward... something you are claiming should not be able to happen. you own video proves its possible for the plane to move forward.
Ah your very confused. The wheel goes back to the starting position because of friction and the rubber bands that it is connected to. But hey way to miss the point treadmill will move a free spinning wheel. And it will move the plane.
Of course they can. But not if the treadmill is configured to match the speed of the aircraft which it wasn't in the video. That video is just to show that a treadmill will act on a free spinning wheel which a few post ago you claimed would not happen.
Jeff7
Lifer
- Jan 4, 2001
- 41,596
- 20
- 81
This is not valid. You immediately assume that a = 0.
a is the very thing you are attempting to solve for!!!! You can't assume it to be zero.
Let's say F of the engines = 200lbs and the mass of the airplane = 500 slugs. And let's assume the wheels to be 1ft in diameter. Yeah, really simplified, I know.
a = F/m
a = 200/500
a = 0.4ft/sec^2
After 2 seconds, v = at = 0.4 * 2
v = 0.8ft/sec
The airplane would try to move forward at that acceleration.
The treadmill accelerates at -0.4ft/sec^2, and also reaches -0.8ft/sec after two seconds.
However, this acts on the wheels. The wheels do not produce a force themselves; they are simply carried forward by a function of being attached to the plane.
If the ground were stationary, the wheels would have an angular velocity dictated by:
v = r?
v = 0.8ft/sec, positive, which is the speed of the wheel relative to the stationary ground.
? = v/r = 0.8/0.5 = 1.6 rad/sec, or about 15.28rpm
But the moving treadmill acts on them too.
Again, ? = v/r
v = 1.6ft/sec now, because the wheel on the stationary ground would see a forward movement of 0.8ft/sec due to the engines, and then because the treadmill below would match that, at -0.8ft/sec. From the wheels' point of view, the ground below is now speeding by at -1.6ft/sec; or, the wheels' speed relative to the ground is 1.6ft/sec.
(For the engines, you can also imagine that the plane is tied to a winch that is pulling it forward with 200lbs of force.)
? = v/r = 1.6/0.5 = 3.2 rad/sec, or about 30.56rpm, while the plane continues to move forward at 0.8ft/sec, and it will also accelerate at 0.4ft/sec^2. The treadmill will do the same thing, in the other direction. However, the opposing force of the treadmill on the plane is directed into the wheels. That energy is dissipated by accelerating the spinning of the wheels. This is just as true as when the plane is taking off from a stationary runway. The ground imparts a resisting force (friction) upon the wheels that would try to hold the plane stationary. But instead of holding the plane stationary, the wheels absorb this resisting force by spinning.
The same applies with a treadmill - the opposing force of the treadmill acts on the wheels. This force has nothing to do with the engines, or if you want, the winch system. They will continue to apply their force to the plane, moving it forward, while the wheels just continue to spin faster and faster so as to mitigate the opposing force of the treadmill.
amish
Diamond Member
- Aug 20, 2004
- 4,295
- 6
- 81
i stand corrected. i thought that there was a special between two teams hoping to break the sound barrier in a car. one was the thrust SSC, but i cannot remember the other car. i remembered that the thrust had rear wheel steering but i thought that it had solid rubber tires. that must have been the other car. i wish i could remember it now.
YOu are talking about a different problem.
The debate is if the plane takes off when the treadmill matches the wheel speed of the plane not ground speed.
One had solid aluminum wheels, and the other one had aluminum wheels with carbon fiber filament spun around them.
I think the other was the Spirit of America.
And I've decided to make the treadmill out of unobtainium. What effect that has on the outcome, I do not know.
amish
Diamond Member
- Aug 20, 2004
- 4,295
- 6
- 81
that's right! though the one that competed in 1997 was the spirit of america 2. thanks for the flashback.
Originally posted by: Jeff7
Um, no?
I said that the plane speed (and thus wheel speed too, since the two are attached) = 0.8ft/sec.
I said that the treadmill speed = 0.8ft/sec.
0.8 = 0.8
By wheel speed I mean the speed of the wheel on a treadmill.
Originally posted by: smack Down
Originally posted by: Jeff7
Um, no?
I said that the plane speed (and thus wheel speed too, since the two are attached) = 0.8ft/sec.
I said that the treadmill speed = 0.8ft/sec.
0.8 = 0.8
By wheel speed I mean the speed of the wheel on a treadmill.
That's would mean both increase in speed infinately, because as the thread mill increased in speed to "match" the speed of the wheel spinning, then wheel speed would increase because the threadmill is going faster, which means the treadmill has to increase it's speed again to match, etc.
Originally posted by: unfalliblekrutch
Originally posted by: smack Down
Originally posted by: Jeff7
Um, no?
I said that the plane speed (and thus wheel speed too, since the two are attached) = 0.8ft/sec.
I said that the treadmill speed = 0.8ft/sec.
0.8 = 0.8
By wheel speed I mean the speed of the wheel on a treadmill.
That's would mean both increase in speed infinately, because as the thread mill increased in speed to "match" the speed of the wheel spinning, then wheel speed would increase because the threadmill is going faster, which means the treadmill has to increase it's speed again to match, etc.
So?
Jeff7
Lifer
- Jan 4, 2001
- 41,596
- 20
- 81
So.....which speed do you mean? Its rotation speed? Its linear speed relative to the treadmill? Its speeds relative to the stationary ground?
This is along the lines of the Hot Wheels car on the treadmill, which I don't see what's so hard to understand.
Disregard friction in the wheel bearings to simplify the simulation.
Set the car on the treadmill. Turn on the treadmill. You know what'll happen?
Absolutely nothing. There will be friction against the wheels, which will make them spin. But that's ALL. The wheels will spin, but they will not move forward or backwards, nor will the car.
The motion of the ground beneath has no effect on the car's motion, because the bearings are frictionless. Since the wheels can spin freely, that's all that they will do.
Now push the car forward with your hand. In this simulation, it wouldn't matter if the wheels are spinning at 1rpm or 30,000rpms. You will still push the car with the same force to acheive the same linear speed regardless of how fast the wheels are going.
The force your hand exerts on the car is the same as the force the jet engines exert on the plane while its wheels are spinning at any irrelevant speed.
I think that and the indestructible wheels are what makes this problem work.
Otherwise, even if you had a tiny bit of friction in the bearings, once you multiply that by the infinite speed of the treadmill it would easily overpower the jet engines.
Originally posted by: smack Down
Originally posted by: unfalliblekrutch
Originally posted by: smack Down
Originally posted by: Jeff7
Um, no?
I said that the plane speed (and thus wheel speed too, since the two are attached) = 0.8ft/sec.
I said that the treadmill speed = 0.8ft/sec.
0.8 = 0.8
By wheel speed I mean the speed of the wheel on a treadmill.
That's would mean both increase in speed infinately, because as the thread mill increased in speed to "match" the speed of the wheel spinning, then wheel speed would increase because the threadmill is going faster, which means the treadmill has to increase it's speed again to match, etc.
So?
So, it makes sense that the original problem would be talking about matching the speed of the airplane itself, and not the wheels, or else it becomes a physical impossibility. However, assuming the treadmill does try to match wheel speed, then one the following would happen:
1. The treadmill would hit a physical limitation in its speed, allowing the plane to continue to take off.
2. The treadmill goes fast enough, and causes enough friction in the wheel, that the plane is unable to attain enough speed for takeoff.
3. The treadmill goes so fast that the plane's wheels are damaged, causing it to be unable to take off
However, it will always be a problem of x = x+1, an endless loop where the treadmill is never going as fast as the plane's wheels. If we ignore the wheel friction as negligable, yes the plane would take off. However, as the limit of the treadmill/wheel speed approaches infinity, it would be greater than whatever thrust the plane's engines can output. In real life, I don't believe any treadmill/wheel could do that to a plane, especially without breaking the plane's wheel assembly somewhere.
Jeff7
Lifer
- Jan 4, 2001
- 41,596
- 20
- 81
I think that infinite speed of a treadmill would create other problems, since at that speed, its atoms might turn into energy, and then you'd have a massive blast of gamma radiation, with a large crater. I guess all of the airplane would become airborne, since it would be completely vaporized by the superluminal treadmill.
Maybe the original problem was just worded poorly.
Maybe it meant to say, "The speed of the treadmill is equivalent to the negative of what the speed of the aircraft would have been relative to ground, were it on a stationary surface."
Originally posted by: unfalliblekrutch
Originally posted by: smack Down
Originally posted by: unfalliblekrutch
Originally posted by: smack Down
Originally posted by: Jeff7
Um, no?
I said that the plane speed (and thus wheel speed too, since the two are attached) = 0.8ft/sec.
I said that the treadmill speed = 0.8ft/sec.
0.8 = 0.8
By wheel speed I mean the speed of the wheel on a treadmill.
That's would mean both increase in speed infinately, because as the thread mill increased in speed to "match" the speed of the wheel spinning, then wheel speed would increase because the threadmill is going faster, which means the treadmill has to increase it's speed again to match, etc.
So?
So, it makes sense that the original problem would be talking about matching the speed of the airplane itself, and not the wheels, or else it becomes a physical impossibility. However, assuming the treadmill does try to match wheel speed, then one the following would happen:
1. The treadmill would hit a physical limitation in its speed, allowing the plane to continue to take off.
2. The treadmill goes fast enough, and causes enough friction in the wheel, that the plane is unable to attain enough speed for takeoff.
3. The treadmill goes so fast that the plane's wheels are damaged, causing it to be unable to take off
However, it will always be a problem of x = x+1, an endless loop where the treadmill is never going as fast as the plane's wheels. If we ignore the wheel friction as negligable, yes the plane would take off. However, as the limit of the treadmill/wheel speed approaches infinity, it would be greater than whatever thrust the plane's engines can output. In real life, I don't believe any treadmill/wheel could do that to a plane, especially without breaking the plane's wheel assembly somewhere.
D O R K :laugh:
Quasmo
Diamond Member
- Jul 7, 2004
- 9,630
- 1
- 76
You realize that the plane has weight, and that until the wings have enough lift under them to make the plane fly, that any motion on the treadmill will cancel out the forward motion created by the propellers, and because there will be no forward motion, you will not get the lift you need, and thus the plane will continue to put it's weight on it's tires. Thus, not take off.
Cerpin Taxt
Lifer
- Feb 23, 2005
- 11,940
- 542
- 126
Originally posted by: smack Down
Originally posted by: unfalliblekrutch
Originally posted by: smack Down
Originally posted by: Jeff7
Um, no?
I said that the plane speed (and thus wheel speed too, since the two are attached) = 0.8ft/sec.
I said that the treadmill speed = 0.8ft/sec.
0.8 = 0.8
By wheel speed I mean the speed of the wheel on a treadmill.
That's would mean both increase in speed infinately, because as the thread mill increased in speed to "match" the speed of the wheel spinning, then wheel speed would increase because the threadmill is going faster, which means the treadmill has to increase it's speed again to match, etc.
So?
So that is why your "interpretation" of the problem is incoherent.
Suppose everything is at rest: the plane, the wheels, the treadmill.
Then, the plane begins to propel itself forward, moving the wheels, say, 1 inch in 1 second.
If we assume that the conveyor must match this speed, then it will move also 1 inch in 1 second, in the reverse direction.
Because of the contact of the wheel with the conveyor, however, the motion of the conveyor will necessarily move the wheel an additional 1 foot in 1 second, meaning in that 1 second interval the wheel will have traveled a net 2 feet with respect to the conveyor.
But if the wheels moved 2 feet in 1 second, then the conveyor is NOT tuned to match the speed of the wheels, because it only moved 1 foot in 1 second when obviously it should've moved 2 feet. It is therefore impossible for conveyor to match the rotational speed of the wheels as they move forward.
Congratulations on being the forum's biggest moron.
Originally posted by: Garth
Originally posted by: smack Down
Originally posted by: unfalliblekrutch
Originally posted by: smack Down
Originally posted by: Jeff7
Um, no?
I said that the plane speed (and thus wheel speed too, since the two are attached) = 0.8ft/sec.
I said that the treadmill speed = 0.8ft/sec.
0.8 = 0.8
By wheel speed I mean the speed of the wheel on a treadmill.
That's would mean both increase in speed infinately, because as the thread mill increased in speed to "match" the speed of the wheel spinning, then wheel speed would increase because the threadmill is going faster, which means the treadmill has to increase it's speed again to match, etc.
So?
So that is why your "interpretation" of the problem is incoherent.
Suppose everything is at rest: the plane, the wheels, the treadmill.
Then, the plane begins to propel itself forward, moving the wheels, say, 1 inch in 1 second.
If we assume that the conveyor must match this speed, then it will move also 1 inch in 1 second, in the reverse direction.
Because of the contact of the wheel with the conveyor, however, the motion of the conveyor will necessarily move the wheel an additional 1 foot in 1 second, meaning in that 1 second interval the wheel will have traveled a net 2 feet with respect to the conveyor.
But if the wheels moved 2 feet in 1 second, then the conveyor is NOT tuned to match the speed of the wheels, because it only moved 1 foot in 1 second when obviously it should've moved 2 feet. It is therefore impossible for conveyor to match the rotational speed of the wheels as they move forward.
Congratulations on being the forum's biggest moron.
In plain english, i will explain.
How does the plane move 1 inch in 1 sec? HOW? only way is by the wheels rotating. YES OR NO?. Is there any other way the plane can move 1 inch? NO. Planes moves forward 1 inch because the wheels have rotated. FACT.
Now, turn on the treadmill. Treadmill counters the rotation of the planes wheels, thus keeping the plane still. no forward movement, no lift, the plane does not take off.
:beer:
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