Not now, no. But I do think that zut has a point that if you state an answer to the problem without discounting interpretations of the question you regard as absurd or invalid, it tends to start the whole mess again. Because some doofus will come in and start arguing you’re wrong (because they are working off different assumptions) and then it takes about six pages before you get things straight.
Of course, even if you do state all your assumptions some doofus will come in and start arguing you’re wrong because they haven’t carefully read your statement of assumptions, but hey, at least that might get sorted out in about, say, three pages. Which has to be an improvement.
See, the plane is like a grilled tomato, sliding of the cheese sandwich, and the Branston Pickle retards the tomato, but gravity pulls harder than the friction due to the pickle. Ummm.
Except that most of the doofi are working off of assumptions which are not just different from mine, but unphysical. One could rule out all such assumptions by stating that one is solving the problem according to the physical laws under which the world operates. But should one really need to state that explicitly?
Anyone who’s to the point of using zut’s argument about the rotational inertia of the wheels already adequately understands the problem and the methods used for its solution, so my explanation is not targeted towards such folks. Where most folks stumble is in assuming that it’s possible for the treadmill to spin fast enough to stop the airplane, but it isn’t. That’s the key point I’m trying to get across.
Later, three men chipped in equally to buy the model, but one of the engineers made a mistake with the price and sent his assistant after them with the change, but there was much confusion over a missing dollar. The three men later gave the model to Billie Joe MacAllister, who threw it off the Tallahatchie Bridge.
What Princhester said. There’s a world of difference between “I’m explicitly ignoring effects that will transfer horizontal force to the plane for such-and-such reason” and “I completely forgot about/didn’t know about/will vociferously argue against such effects.” The issue is (at least with this particular problem) that people tend to believe everyone has the same initial assumptions about the problem. If their conclusion is different from your conclusion ("…there’s nothing the treadmill can do to stop it."), then the tendency is to think you’re wrong, without stopping to wonder if their assumptions are different from your assumptions.
Not that everyone has the physics correct, anyway, but since the assumptions define the problem, it helps to be talking about the same problem.
But that’s not an initial assumption; that’s an intermediate step (at least, if I understand “negates all force between ground and plane” correctly). You’re assuming something about the realtive motions of the plane and treadmill, and the construction of same; THEREFORE there’s no horizontal force on the plane; THEREFORE the plane will take off.
There’s nothing wrong with disallowing super-treadmills and super-wheels, of course, but a few points:
First of all, this is a thought experiment, so there’s nothing wrong with allowing super-treadmills and super-wheels, either.
Second of all, if you really can’t stomach super-treadmills and super-wheels, I will point out that nothing in the problem statement talks about the construction of the plane. Most people assume we’re talking about a 747 with a full tank of fuel, but there’s no reason we can’t discuss the problem in the context of a rubber-band-driven model plane with lead wheels and sandpaper axles. That’s nonintuitive, I’ll grant you, but interesting nonetheless.
Third of all, people who subscribe to the “alternate interpretation” you describe might very well say, “the problem explicitly states that the treadmill matches the wheel speed, which forces the plane to remain stationary, which means it won’t take off. Any suggestion that the plane moves with respect to the ground violates the problem statement, so any solution that includes plane motion is absurd.” And then they get frustrated because you’re doing the problem “wrong” and you get frustrated because they’re doing the problem “wrong” and a six-page thread results, which was essentially my point to begin with.
By the way, in reality, you don’t need a treadmill to keep a plane from taking off. Based on my experience from 4 flights in the past month, all you need to do is put the plane on the ground at JFK airport. Once there, it will take at least 3-4 hours for it to get airborne.
Especially if the plane is full of people.
Even moreso if the plane is full of crying babies.
Okay, I understand that the airplane on a treadmill will always take off simply the props are pulling the aircraft forward, and the wheels are simply freewheeling.
What about a seaplane trying to take off against a strong current? I’m sure that it’s a practical consideration with floatplanes; can they take off? If not, is it due to water drag, or because operating in a current is just too dangerous?
The plane does not care about ground speed to get in the air. It cares that the air travels over its wings at a certain speed. If a plane was sitting still and a headwind of 200mph came up, and it had a pilot who flew it forward at 200mph, to those on the ground it would appear to be hovering.
Now if you turn the plane around so it faced forward on the treadmill and the plane wheels did not turn but the treadmill pushed it forward, it would eventually take off with enough speed, like from an aircraft carrier.
But like in the first paragraph, it all has to do with the wind speed over the wings. That’s how wind tunnels work. The plane sits still and the wind moves over the plane. The plane knows no difference.
So in a nutshell:
The treadmill moves in direction A at 200mph. The plane, through the use of its engines, moves in direction -A at 200mph. The airplane will appeare to be stationary to someone standing on the sidelines. As far as the plane is concerned, it is saying, “Hey I have enough thrust to move at 200mph but I am not ascending. I guess the wind is coming from behind me at 200mph.” It wouls then need to accelerate to 400mph to actually take off (assuming 200mph is its liftoff speed). This is a reason why planes never take off or land with a tailwind if they can help it. If they land at 150mph and have a tailwind of 200mph, they will have a ground speed of 350mph, and then when they slow down enough for the wind from behind to be going faster than the airplane, they could flip over or worse.
Remember, planes go by the air ove the wings. Ground speed is irrelevant. That’s why planes go into the 800mph jet steam at 700mph and to the person on the ground the plane appears to be going 1300mph.
A plane on a treadmill accelerating so as to remain still on the treadmill will not take off any more than an airplane sitting parked and motionless on the tarmac.
You’re confusing things. If it’s moving in direction -A at 200mph, and all that matters is the speed of air over its wings, (which is correct) and its takeoff speed is 200mph, it’ll take off. If it has enough thrust to go 200mph, why won’t it go 200mph?
I think people get led astray by the whole magic treadmill matching the speed of the airplane deal when the real situation is much simpler. The plane needs a certain speed of air blowing at it to achieve lift. The normal way to achieve that it to use an engine to propel itself forward along the ground towards stationary air. If you put it on the magic treadmill, then although the plane is moving at the proper speed relative to the treadmill surface, you are preventing it from moving relative to the air, eliminating the windforce.
This is analogous to (ignoring any ability to aim the engine) attempting to fly a jet plane on a normal ground (sans treadmill) in a vacuum. You would go very fast on the ground but would never achieve liftoff.
And a practical experiment is possible. Since we know the real world speed needed for liftoff, we don’t need a magic treadmill that precisely matches the speed of the wheels on the airplane. All we need is a treadmill that matches the liftoff speed. That will be sufficient to keep the plane from ever lifting off.
The opposite situation is helpful to think about. If you chain an airplane to the ground (with a little slack) such that it can’t move forward, but put a huge fan in front of it blowing the same speed as liftoff speed, the airplane will remain in the same spot but will liftoff/levitate.
No. Aircraft wheels are bogies. In order for the treadmill to slow the plane down, it has to go fast enough to overcome the wheel bearings – much, much, much faster than the takeoff speed.
Depending upon the assumptions you are making about what the problem means - see above - I think it is true to say that most interpretations of the problem involve no mechanism by which the treadmill will prevent the plane from moving forward.
Another post proving that the basic thought experiment underlying the question stumps most people. :smack:
Now, listen carefully:
The treadmill imparts no significant force upon the plane. The engines do. Unlike cars, the airplane is not propelled through contact between the wheels and the surface. Therefore, the treamill matters not; the wheels simply spin faster as the plane rolls forward to takeoff.
