Physics Question for you.....

[Anna]

19 pages........ Do I hear 20??

Hey, this is educational.

I learned quite a bit. Took a while, but I'm convinced. Besides, I didn't know that the wheels on a Hot Wheel are free spinning, too.

Alex, I think the "trick" to the question is that the plane's wheels are practically frictionless. I mentioned in one of my posts that if the system is frictionless, the plane will takeoff. I didn't realize that in the real world case, the system does approximate a frictionless system.

The conveyor belt will not be able to "pull" on the plane to keep it from taking off. We can have the conveyor going 10x the speed of the plane, and the plane will still take off because it takes very little thrust to overcome the small amount of friction between the wheels and the conveyor belt.

The ballpark numbers:

Friction force ~ 0.04 x weight of plane
Plane thrust ~ 0.3 x weight of plane

For a 10,000 lb small jet, you'll need about 400 lbs of force to keep the plane from moving with a conveyor belt, no matter how fast the belt goes. I don't think the wheels will slip because of the plane's wheel design. If you apply 401 lbs, the plane should start to move forward. You'll need a little more to counteract the drag force eventually, but the idea remains the same.


P.S. I have to add: All the arguments about the plane's thrust acting on the air were also misleading. It doesn't matter where the plane is getting the force from. You can tie a rope on the plane's nose with the plane's engine off, apply enough force, whether by several guys pulling or with a truck or whatever, and the plane will still move. Move fast enough, and the plane will take off. Of course, with the engines off, bets are off on how long it stays afloat. But it will take off.

[JeffG78]

So long as the engines provide enough thrust to overcome the friction in the wheels, then "a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction)" is essentially impossible to achieve. (Because if the plane appears to be moving forward, then the control system is not working.)

Is this right?

Sort of. The conveyor cannot ever achieve the speed of the plane's TIRES since they will always be going faster than the conveyor while the plane is moving relative to the control tower. The original question simply states that the conveyor matches the PLANE'S speed. Airplane's speed is measured as air speed, not wheel speed like in a car. Since the wheels of a plane only come into play during take-off and landing, it would be rather useless to track their speed. The speed of the plane can indeed be matched by the conveyor if that speed is the air speed.

[Alex Franke]

So long as the engines provide enough thrust to overcome the friction in the wheels, then "a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction)" is essentially impossible to achieve. (Because if the plane appears to be moving forward, then the control system is not working.)

Is this right?

[Russianwolf]

19 pages........ Do I hear 20??


Yep Anna, You got it. In fact if you watch a video of a plane landing, before ground contact is made the wheels aren't spinning at all. That's why you get that screach on the landing, the rubber skids instantaneously until the wheel speed can catch up to air speed. It only takes a split second , but it's noisey.

I think the Youtube Video shows it pretty good. He had the conveyor running faster than the plane is capable of accelerating, yet the plane can still move forward almost as if the conveyor was off. I bet the wheel on the hot wheels car were spinning pretty good though.

[williamr]

Your are right on this illustration (I think). After thinking it over, I used a "not so good" analogy.

What we need here are not theorists or physicists, but lawyers and judges with a grammarian thrown in. They would figure out the wording.

As it is stated, if the

The heart of a good riddle is a dash of misdirection.

---
will

[williamr]

I don't really know much about planes, so the suggestion that the plane's wheels are freely spinning threw me off a bit. Having thought about this some more, doing the requisite free body diagrams, and learning a little more about planes and their vital statistics in the process... I have to concede.

The plane will take off.

Women are always right -- so you are right again. QED

---
will

[leehljp]

Actually, yes. It pretty much doesn't matter what the speed of the runway is. If the plane's thrust exceeds something like 0.04 x weight of the plane, the plane will move forward. The "0.04" is the ballpark friction coefficient on the wheel (bearings and rolling).

The statement of the problem is very misleading. It says that the conveyor belt will match the speed of the plane. That statement is misleading because even if it matches the ground speed of the plane, it will not be able to keep the plane from moving forward.

Everyone who said that the wheels will only spin twice as fast was right.

One other way to look at it is the case when the plane is landing. Say the runway is moving in the opposite direction with the same air speed as the plane. When the wheels touch the runway, is the plane going to stop moving with respect to the ground? I think the wheels will just spin more rapidly, but the forward motion of the plane is still the same.

It's actually pretty amazing. I was really sure about my initial answer. Oh, well. At least this "problem" makes sense now.

Your are right on this illustration (I think). After thinking it over, I used a "not so good" analogy.

What we need here are not theorists or physicists, but lawyers and judges with a grammarian thrown in. They would figure out the wording.

As it is stated, if the

[niki]

[Anna]

If a runway was 1000 miles long and was going 150 mph in one direction, could a 120 mph Cessna setting on it facing the other direction get up enough speed to ever take off?

Actually, yes. It pretty much doesn't matter what the speed of the runway is. If the plane's thrust exceeds something like 0.04 x weight of the plane, the plane will move forward. The "0.04" is the ballpark friction coefficient on the wheel (bearings and rolling).

The statement of the problem is very misleading. It says that the conveyor belt will match the speed of the plane. That statement is misleading because even if it matches the ground speed of the plane, it will not be able to keep the plane from moving forward.

Everyone who said that the wheels will only spin twice as fast was right.

One other way to look at it is the case when the plane is landing. Say the runway is moving in the opposite direction with the same air speed as the plane. When the wheels touch the runway, is the plane going to stop moving with respect to the ground? I think the wheels will just spin more rapidly, but the forward motion of the plane is still the same.

It's actually pretty amazing. I was really sure about my initial answer. Oh, well. At least this "problem" makes sense now.

[leehljp]

I do realize the tires generally have little to do with it beyond initial movement and that it will take off. Restating: if there is EVER any differential in inertia/speed between the two then it will take off. BUT, and that is a big but, if speeds are matched to the billionth power, exactly, totally, nothing different to the point that NO differences, then no.

If the plane does start moving forward (or backwards due to wheel friction) in relation to the ground or tower, then it IS moving faster/different) than the rolling runway, it broke the inertia/kenetic energy (lost my long ago physics terminology) barrier of a standstill.

Look at it this way, suppose the runway starts backwards first at 10 mph, after the plane has moved backwards 100 yards, the engine accelerates to bring it up to 10 mph making it effective ground speed as "0"; Keep doing this - accelerating the runway first until the plane is catching up with the runway speed on a 100 mile long runway. Eventually the runway will be doing 100mph, the plane is slowly catching up and finally reaches 100mph on the runway, the weight and minor wheel friction will still keep it on the runway because no wind is flowing over the wings yet.

IF the plane were to speed up 1/10 of 1 mph faster than the runway, then it would begin forward movement and take off.

HOWEVER, with the specific question that was asked, until a canceling inertial difference is overcome, it won't take off. But once an inertial difference is overcome, it will take off, - but then they are not equal.

If a runway was 1000 miles long and was going 150 mph in one direction, could a 120 mph Cessna setting on it facing the other direction get up enough speed to ever take off?

This is the OTHER side to the main question. Everything being exactly equal, no, but that kind of precision measurement doesn't exist, so for the question - no, for reality - yes - unless the runway does go backwards faster than the plane can accellerate.

Lastly, if the plane is allowed to move forward as much as one inch, you should allow the possibility for the runway to move in the reverse at the beginning - faster than the plane can accelerate forward, taking it backwards. If this statement is considered not to be fair, then neither is a plane that accelerates forward beyond the speed of the runway. It boils down to timing - which comes first. If equal, no. If unequal, it is possible.

[Anna]

I don't really know much about planes, so the suggestion that the plane's wheels are freely spinning threw me off a bit. Having thought about this some more, doing the requisite free body diagrams, and learning a little more about planes and their vital statistics in the process... I have to concede.

The plane will take off.

[Alex Franke]

Alex, what does holding the brakes on have to do with anything? The brakes would have to be held on the same amount on a stationary runway to have the same effect. The question isn't whether of not a plane can be kept from flying while holding the brakes on.

That's not my point anyway. My point is this: If there's enough friction in the system (wheels, water, ice, magnet, whatever) dragging the plane backward at a rate that effectively cancels out its forward movement (so that the plane appears stationary from the tower) then I can't see the plane flying. If the plane appears stationary from the tower, then it will not lift off the ground. The original question -- to me -- suggests that the plane will appear stationary from the tower throughout the experiment.

If, however, the plane can muster enough thrust to overcome the friction and propel the plane forward (relative to the tower) along the runway (or magnet, or river, or whatever) then it can lift off. Now I'm sure any real plane can surely overcome the friction in a wheel, but a hypothetical plane on a hypothetical conveyor with hypothetically far-from-ideal wheels would be dragged backward by the conveyor, and if it were accelerated backward by the conveyor at the rate it's accelerated forward by the engines, then it will appear stationary to the tower and won't lift off.

So, if this magical conveyor could somehow keep the plane stationary to the tower, then would the plane still take off? "Tuning the speed to be exactly the same but in the opposite direction", to me, means that the plane somehow, some way, appears stationary to the tower.

[JeffG78]

This is where the difference is in questions.

The question was: IF the speed of the rolling runway matches the speed of the plane, will it take off?

IF they matches each others speed, the air speed relative to ground is "0".
ZERO speed of air equals no flight!

But the original question states that the conveyor matches the plane's speed, it does not say it matches the speed of the plane's tires. The plane accelerates down the runway with relation to the control tower and the conveyor accelerates at the same rate. When the plane reaches X speed to take off, the conveyor's speed would be exactly the same. Now, if the original question said that the conveyor EXACTLY matches the plane's tire's speed, then both the tires and the conveyor would need to be stopped because as soon as the engine was revved up, the plane would begin to move down the runway meaning that the tires are going faster than the conveyor. Since the tires are assumed to not skid, the only time that the speeds could match would be when the tires and conveyor are both going zero. The only rational way to measure a plane's speed is either via the plane's airspeed indicator or a radar gun. Neither of which uses wheel speed. Knowing what a plane's wheel speed is, is rather useless.

[leehljp]

But Hank, there IS air over the wing since the plane is moving down the runway (as seen from the control tower) just like when there is no conveyor. Nobody is saying that the plane will fly if it is standing still. The whole point of the question is not whether or not the plane will fly, but rather if the plane will move down the runway when viewed from a fixed position like the control tower. The video clearly shows that the plane does move down the runway rather than sitting in one place.

This is where the difference is in questions.

Original question on this forum 2 years ago: A plane is standing on runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in opposite direction).

Rephrasing the question was: IF the speed of the rolling runway matches the speed of the plane, will it take off?

IF they matches each others speed, the air speed relative to ground (control tower) is "0".
ZERO speed of air equals no flight!

IN the Myth Busters, the plane was going forward faster than the rolling runway was going backwards. If the plane moves FORWARD of its starting position as much as 1 foot, then it is going forward faster than the runway is going backwards. In this case, if the speeds are not matched, then that fact nullifies the point of the question above.

Again, the question was - If both are going the same speed in opposite directions . . .

It seems to me that some people want to visualize the plane moving forward at some point in which it could take off, but at that point the two objects would not be going equal speeds in opposite directions.

For the life of me, I can't see what people are talking about saying it can take off under these conditions. Myth Busters did not meet these conditions.

I do get the point that once inertia takes over and it does start moving forward as much as one inch, then it doesn't matter if the rolling runway is going 1000 mph, the plane will not be dependent on the speed of the runway/wheel, but rather its own inertia and power - and it will take off!

[JeffG78]

Alex, what does holding the brakes on have to do with anything? The brakes would have to be held on the same amount on a stationary runway to have the same effect. The question isn't whether of not a plane can be kept from flying while holding the brakes on.

Like you said, wheels have very low friction relative to the power of an engine. The only difference the moving conveyor makes is the speed of the tires. More speed equals slightly more friction, but the difference isn't enough to matter.