A note about aeroplanes on treadmills, and other thought experiments
Via xkcd, I see a puzzle that's apparently been floating around the internet for some time. It goes a little like this:
"Imagine a 747 is sitting on a conveyor belt, as wide and long as a runway. The conveyor belt is designed to exactly match the speed of the wheels, moving in the opposite direction. Can the plane take off?"
The answer is that the plane will indeed take off. A constant tiny amount of thrust from the plane will always keep it stationary no matter how fast the treadmill moves, so any larger amount of thrust will cause it to take off.
(If the first half of that leaves you confused: Imagine standing on a skateboard on a normal treadmill. You'll have to lightly hold onto something to keep stationary, but you needn't hold on any more tightly to keep stationary if you speed the treadmill up. The basic point is that it's only friction on the bearings on the wheels which sends you backwards, and this friction is independent of the speed of the treadmill.)
Regardless, the small note I wanted to make was this. It's quite reasonable to interpret the example differently. The question might be thought of as one trying to get listeners to understand that planes need to move forward relative to the air, not the ground, in order to take off. It's just that the questioner picked a poor way of demonstrating that thought, since a treadmill wouldn't prevent a plane from moving forward relative to the air.
So two points to take from that worry are:
a) Descriptions of thought-experiments need to be careful in their wording in order to avoid endless debate about ambiguity in the example.
b) Sometimes the point of a thought experiment is in the principles at work, and not the details of the example. Those new to philosophy are sometimes (often?) disposed to misinterpret examples and worry about the details rather than the overall point being made. Teachers ought to be careful to specify which details are central and which are irrelevant.
"The answer is that the
"The answer is that the plane will indeed take off. A constant tiny amount of thrust from the plane will always keep it stationary no matter how fast the treadmill moves, so any larger amount of thrust will cause it to take off."
I get the feeling you have misunderstood. It is true that a plane needs to move relative to the air, not the ground, to take off. However, assuming there is no wind, then the speed relative to the air and the speed relative to the ground are the same thing. The conundrum mentioned is nothing to do with speed vs air compared to speed vs ground.
Also, the plane will not "remain stationary however fast the treadmill moves", the whole point is that the plane will move. As stated in point (2) on xkcd, the wheels will spin twice as fast as normal, but otherwise it will be a normal take off - the plane will accelerate down the run way, and at the point it reaches maybe 100mph relative to the ground (at which point the treadmill will be going backwards at 100mph and hence the wheels we be spinning at 200 mph) the air rushing over the plane's wings will create lift and the plane will take off.
Mentioning "thrust" is also irrelevant, planes take off once they gain sufficient lift, all thrust does is create forward momentum.
"Imagine standing on a skateboard on a normal treadmill. You'll have to lightly hold onto something to keep stationary, but you needn't hold on any more tightly to keep stationary if you speed the treadmill up. The basic point is that it's only friction on the bearings on the wheels which sends you backwards, and this friction is independent of the speed of the treadmill"
This is false, and also a different issue to the plane conundrum. It is friction on the tires of the wheels that sends you backwards, and the faster the speed of the treadmill the higher the friction, and therefore the harder you will have to hold on.
and actually whilst I'm at it
I disagree with xkcd, too. He says:
"The practical answer is “yes”. A 747’s engines produce a quarter of a million pounds of thrust. That is, each engine is powerful enough to launch a brachiosaurus straight up (see diagram). With that kind of force, no matter what’s happening to the treadmill and wheels, the plane is going to move forward and take off."
But if you interpret the question as in (3) (vC=vW+vB, where the treadmill moves infinitely fast), rather than (2) (the version where the plane takes off with the wheels moving twice normal speed), then I would have thought the practical answer depends on how well constructed the treadmill is. If the treadmill is able to accelerate to a great enough speed to destroy the plane's wheels, then the plane will collapse on to its underbelly. The thrust from the engines will then push the plane along the rubber conveyor belt on its underbelly. I reckon the huge amount of friction created by this would destroy the plane before it picked up enough speed to take off.
Hi James, "assuming there is
Hi James,
"assuming there is no wind, then the speed relative to the air and the speed relative to the ground are the same thing"
It's true that one way for speed relative to ground and air to differ is if the air is moving: if there is wind. But I don't see why it's false to think that the other way for them to differ is if the ground is moving: if the ground is effectively a treadmill.
As for the rest of what you write, I think you've misunderstood what I said. The point is that the only thing pushing the plane backwards on a treadmill is friction on the wheels (hence the skateboard analogy). So:
(a) A small amount of thrust is necessary to outweigh the friction and keep the plane stationary.
(b) Any more speed on the treadmill does nothing to drive the plane backwards, since the friction on the wheels is independent of the speed at which they turn.
(c) Any more thrust from the plane makes the plane move forwards, since there's nothing else to stop it from doing so.
I'm not a physics expert, so I might be wrong, but even if I am, I'm pretty sure you've misunderstood what I meant.
This post is the best explanation of the whole issue that I've found.
Alex
ok
OK, you do generally understand - the plane must move and the wheels are largely irrelevant. But I still think your explanation of the friction on the wheels being "constant" and independent of the speed of the wheels is wrong, because you ignore rolling resistance.
Imagine you have a toy car, and you give it a shove along a wooden floor. It will slow down and come to a halt. Now put bigger tires on the car and try again. It will slow down sooner. Now try giving the car a shove on an ice rink. It will keep going for ages. This is nothing to do with friction in the bearings, it is to do with the friction between the tires and the ground.
Now put hold the toy car on a treadmill. The faster the treadmill goes, the more force you will have to exert on the car to prevent your hand from being pushed backwards.
http://en.wikipedia.org/wiki/Rolling_resistance