Will it fly?

[md]

bugger,  doesn't work. It makes subscripts for anyone interested.

[Nyrd]

Quote:

You missed the kinetic friction between the bearings and the wheels as well as the kinetic friction between the wheels and the treadmill, and finally the rolling friction of the wheels. (Some of them will replace each other as the speed increases).

Will not the kinetic friction between the wheels and the bearings irrelevant? The friction inside the wheels will have no impact on the forward motion of the plane other than making it take a bit longer for the plane to reach take off speed. Furthermore, since we're assuming that the wheels are turning, will there not be no kinetic friction between them and the treadmill? (don't turning wheels only experience static friction -> That being the reason that you'll stop faster in a car if you pump the breaks not slam them? - knowing of course, that kinetic friction is less than static).

In any case though, all of these forces exist even when taking off of a solid runway. The only thing that could increase with the treadmill is the heat inside the wheels because they are moving faster (And that's not because friction increases with speed, but rather, the same amount of heat released because of the friction is released in a shorter time). since we're assuming that they won't melt, explode etc even this shouldn't be a problem.

- Of course correct me if I'm wrong, I'm just working with high school physics and the idea that Friction does not increase with speed

[md]

Nyrd @ 2008-04-07, 1:55 pm wrote:

Will not the kinetic friction between the wheels and the bearings irrelevant? The friction inside the wheels will have no impact on the forward motion of the plane other than making it take a bit longer for the plane to reach take off speed. Furthermore, since we're assuming that the wheels are turning, will there not be no kinetic friction between them and the treadmill? (don't turning wheels only experience static friction -> That being the reason that you'll stop faster in a car if you pump the breaks not slam them? - knowing of course, that kinetic friction is less than static).

The friction is small, but at large enough wheel speeds it does matter. Mostly because it builds up heat - which causes bearings to seize. Then the wheels stop spinning which causes significantly more friction. There is friction between the wheel and the treadmill, which how cars work Also, the reason pumping your breaks stops you faster is that on cars without ABS slamming the brake pedal to the floor locks the wheels, and sliding rubber has a lower coefficient of friction then static rubber. Pumping your breaks helps prevent the wheels from locking. If you have ABS pumping the brakes actually stops you slower.

Nyrd @ 2008-04-07, 1:55 pm wrote:

In any case though, all of these forces exist even when taking off of a solid runway. The only thing that could increase with the treadmill is the heat inside the wheels because they are moving faster (And that's not because friction increases with speed, but rather, the same amount of heat released because of the friction is released in a shorter time). since we're assuming that they won't melt, explode etc even this shouldn't be a problem.

Um, what? The heat would be greater because the wheels are spinning faster - and the heat from the friction would build up faster then it can be dissipated. Also, we are NOT assuming that they won't melt or explode (they being tires I would assume); these are actually very real possibilities (see my previous post about infinite speeds).

Nyrd @ 2008-04-07, 1:55 pm wrote:

- Of course correct me if I'm wrong, I'm just working with high school physics and the idea that Friction does not increase with speed

But of course we shall correct you! Someone is wrong on the internet!

[r691175002]

Here is perhaps an explanation that will hit home.
Let us consider the epitome of modern technology, the fan car:

Now before you laugh at the idiot who invented this, consider its similarities to a plane. Aside from its lack of wings (Or common sense), it is the perfect invention to show why either physics will break or the plane will not take off.

If I were to ask you, given a treadmill of potential infinite speed, could you stop this car from moving forwards, what would you say? (The correct answer is yes).
This is simply because the wheels are not frictionless. If you pushed this car forward (With giant fan of death turned off), it would eventually come to a stop. The faster the wheels are turning, the more the bearings heat up (And friction happens) and try to stop the wheels from spinning (Which in turn allows the treadmill to pull it back).

Same deal with a toy balloon powered car (Everyone has made one of these at some point). I can guarantee you that if you stuck one of those on a treadmill on maximum speed, it would fly backwards like no tomorrow.

As a matter of fact, the wheels have absolutely no bearing on the problem whatsoever, this is simply a box with a low coefficient of friction with a fan attached. Clearly if I dropped a block of ice + fan onto a treadmill it would not keep moving forwards.

The fact that it is a plane is completely irrelevant. If the treadmill is moving fast enough, it can counteract any amount of force provided to the plane.
The key word is fast enough, which is generally such an implausible speed that the question gets sidetracked.

[Nyrd]

Quote:

Nyrd @ 2008-04-07, 1:55 pm wrote:

In any case though, all of these forces exist even when taking off of a solid runway. The only thing that could increase with the treadmill is the heat inside the wheels because they are moving faster (And that's not because friction increases with speed, but rather, the same amount of heat released because of the friction is released in a shorter time). since we're assuming that they won't melt, explode etc even this shouldn't be a problem.

Um, what? The heat would be greater because the wheels are spinning faster - and the heat from the friction would build up faster then it can be dissipated. Also, we are NOT assuming that they won't melt or explode (they being tires I would assume); these are actually very real possibilities (see my previous post about infinite speeds).

Hmm. That's what I meant . . . perhaps I'm too tired to write :S

Quote:

The friction is small, but at large enough wheel speeds it does matter. Mostly because it builds up heat - which causes bearings to seize. Then the wheels stop spinning which causes significantly more friction.

Though if the wheels seize, and stop moving, the treadmill (which goes the exact speed of the wheels) would also have to stop moving. Leaving the plane to take off with frozen wheels. -> Difficult yes, but technically possible

Quote:

The key word is fast enough, which is generally such an implausible speed that the question gets sidetracked.

Taking into account the fact that wheels seize after a certain speed though, and the treadmill must also consequently stop moving, that speed could never be reached?
And I actually think that the guy who invented the fan car is a genius

[Nyrd]

Though this seems to be where the interpretation of the question comes in. Does the treadmill match the rotational speed of the wheels? :S

[r691175002]

Nyrd @ Mon Apr 07, 2008 7:35 pm wrote:

Though this seems to be where the interpretation of the question comes in.

Indeed. There are too many factors that would come into play that make the question irrelevant and more of a wording problem.