Quote:
Originally posted by porsche996:
OK. I'm confused.. (not really)

Once again, since the obvious things didn't work...

If a plane is flying at 80 mph (close to stall speed of a Cessna), directly over a treadmill (as long as a runway, so there's enough space to do the test) that is currently running at 80 mph, the two objects are moving at the same speed, are they not?

Ok. So that's confirmed; the plane is flying over the treadmill at 80mph, as the treadmill is moving at 80mph.

Next step. The plane lowers his altitude *just* enough so that his tires are in now contact with the treadmill. The plane continues at 80mph forward. The treadmill continues at 80mph in reverse direction as the plane. BUT, you'll notice, the tires of the plane are now revolving at 160 mph equivalent.

So, multiple choice question:

The plane at this time is now moving at:

(A) 0 mph
(B) 80 mph
(C) 160 mph

If you guessed (A) or (C) you would be incorrect.

The correct answer is (B). Therefore the plane has forward movement at the same speed as the treadmill, in the opposite direction. The tires have an angular velocity of the plane's speed and the treadmill's speed, equivalent. But the plane only has 1 speed: 80 mph.

Angular velocity and velocity are NOT the same thing. They are a product of each other in the case of a wheel, but they are not a 1:1 relationship. They do not add or subtract directly to cancel each other out. Ever. Angular Velocity is the forward velocity divided by the circumference of the tire.

In this particular example, at 80 MPH, when you do the math, you'll find the tires will be spinning (angular velocity) (18.368) / (radius of tire) in radians per second. So if it's a 2' tall tire, the observed motion of the tire is that it's spinning at 36.7 radians per second. You don't observe the MPH equivalent the tires are spinning; it's a DEPENDENT property. The INDEPENDENT property is the net velocity (the sum of the airplane and the treadmill velocity).

In other words, the tires spin as a result of the horizontal motion of the airplane and the treadmill. It is a DEPENDENT motion. It is not physically measurable in "MPH", but is physically measured in RAD/S or DEGREE/S, and then converted using the radius of the tire to a MPH. You have to sort that out in your head, and be able to realize that angular velocity does not EVER get added or subtracted to motion velocity at any time; you can't act like they're the same thing, and add an independent to a dependent; math doesn't work that way, as it's a physical impossibility.

Whoops. Almost forgot. To finish it off, the very next second after proving the airplane will still continue forward at 80 mph, even if his tires are on a moving surface that's moving at negative 80 mph to him, the pilot pulls back on the stick, and viola: THE PLANE TAKES OFF...

If you REALLY want to think about it another way...Take this same example, only the treadmill is moving FORWARD at 80 mph. As the plane touches down onto the treadmill, the plane is moving forward 80 mph, the treadmill is moving forward at 80 mph, and the tires are rotating at a whopping 0 rev/s... The tires stand still, yet the plane is moving at 80 mph forward... And it still takes off. Example/Proof, yet again, that the angular velocity the tires move does NOT control the forward motion of a plane...

And one more, 'cause I just can't resist...Treadmill moving forward at 40 mph, plane moving forward at 80 mph. Plane touches down, and the wheels are only revolving at 40 mph equivalent, yet the plane is still moving at 80 mph... Oops. Lookie lookie...angular velocity of the tires still doesn't control the plane's movement...

But just in case I haven't annoyed you enough, yet..

Let's look at the case when the treadmill goes forward, and let's assume the argument of the "can't fly" bunch... If the plane moves at the same speed as the conveyor in the "backwards running conveyor", y'all have assumed the plane can't take off, 'cause the tires are moving at the same speed as the conveyor.

So, if the conveyor is moving forward at 80 mph, and the tires are moving forward at the same speed (80 mph equivalent), how fast is the airplane going?? If you said 80 mph, you'd be incorrect... the plane would be moving twice as fast as the conveyor, it'd be 160 mph!!

[insert "can't fly" protest]Argh!!! It CAN'T be moving at 160 mph, 'cause the tires are moving at the same speed as the conveyor!! But..........but I don't understand....[/insert "can't fly" protest]

Yep, that's right... the angular velocity of the tires isn't the same thing as the speed of the airplane... And since that's true for the conveyor moving forward, then it's true for the conveyor moving backward as well.

Guess what? [b]The plane takes off.[/b]
The question isnt about wether the plane can touch and go.

It is asking if it can take off.

Quote:
Originally posted by chumpmann:
Ok, Lets forget all the analogies. Dynos arent a good example, they only move the wheels. A treadmill will move the whole object.

How about the analogy of a plane on a treadmill.

A plane sits on a treadmill, on a calm day, no wind, it is 72 degrees. There is a tree in the ground next to the plane even with the tail.
Now, the treadmill starts to move, the plane starts to move backward on the treadmill. The pilot looks out his window and sees the tree moving from behind him towards him, as the plane is moving backwards on the treadmill. Now the engines start to push the plane to the speed of the treadmill, the tree is now even with the pilot as the engines push the plane, to be even with the tree, on the treadmill. Now as the engines push more the treadmill goes faster, the pilot can look out his window and see the same tree, not moving.
The engines push faster, the treadmill moves faster, the tree is still even with the pilot as he looks out his window. The air around the wings of the plane is as still as the trees next to the plane, the pilot can move his flaps all he wants, he does not have the air resistance to take off.
Quote:
Originally posted by chumpmann:
that isnt the question.
It is that the plane is moving at the same speed as the treadmill and vice versa, not faster than the treadmill.
If the plane moves forward on the treadmill, that means it is going faster than the treadmill.

If you suddenly start the treadmill, the plane will eventually start to move backwards, until the engines push it to the same speed as the treadmill.

It doesnt matter if there are wheels or not, if it is sliding on its belly, and the engines are pushing the plane at the same speed of the treadmill, It stays in the same place, with no air resistance under the wings.

All you guys are saying is that the plane can move faster than the treadmill, yes that can happen. But that is not the question.

I understand the physics of a plane taking off.
You arent understanding the question.

If you arent explaining with the actual question in mind, then there is no reason to try and explain it.