I kinda wish bouv had done that two months ago when he first posted a little thread about planes and treadmills.
He meant to ask the same question that Cecil asked. Instead, he wrote that “The conveyer belt is designed to exactly match the speed of the wheels at any given time.” That spawned 9 more ugly pages of discussion, Cecil’s column on the topic, and now this thread. (Up to what, 6 pages now? 7?)
BTW, welcome to the boards. Keep listening, and keep arguing. Seems like you’ll fit right in.
Because, as interpreted by those saying it doesn’t take off, the belt is matching the rotational speed of the wheels. As soon as the aircraft moves, the wheels rotate, and the belt accelerates to match that rotational speed. Obviously the faster the belt goes, the faster the wheels turn, so it gets into some wild feedback loop. Treis and Zut are saying that there is a value for acceleration of the belt that will counter the thrust from the engines. The belt and wheels will then sit there accelerating until the world explodes. Meanwhile the aircraft stays motionless, and flightless.
The puzzle was not handed down in a Single Correct Version by the hand of God. There are numerous versions of it around. Cecil mentions two versions himself. treis is talking about the second version. He has always made it completely clear that he is talking about the second version.
Why the heck you are so determined to hold his answer up against a question he isn’t answering, stuffed if I know.
Cecil is right, and the answer is right there in the question (or the statement of the problem). I quote: “The plane moves in one direction, while the conveyor moves in the opposite direction.” Now, with emphasis: “The plane moves in one direction…” It MOVES ! It does not stand still! By definition!
So, if the plane moves, the only question is how fast can the wheels spin before they fly apart. I can imagine the conveyor rolling backwards at a thousand MPH with great futility trying to keep the plane from moving. It will not be able to hold back the plane all by itself no matter how fast it “conveys” backwards.
OK - let me pile on just a little more. Picture a radio-controlled model sitting on a treadmill, which in turn is sitting on the floor. Turn on the treadmill. How much thrust must the model’s engine create to overcome the negligible friction of the wheel bearings in order to keep the plane sitting still relative to the floor. Maybe 0.01 oz? Now, run up the engine to full thrust. All that power, minus 0.01 oz, goes to moving the plane forward through the air, no matter how fast the treadmill is going.
All of you anti-Cecilites are assuming the plane sits still. It does not. The question states that.
Bye,
-CCoD-
CantConfirmOrDeny, the mindset of this thread is split between Cecil’s column, and a two-month old thread in the General Questions forum where a slightly different question was asked:
That other question pretty much implied that the plane wasn’t allowed to move. So there you go. Two entirely different explanations of what should have been the same problem. Both were (eventually) correct – just depends which conditions you look at.
Sigh. For the third time, in capital letters:
BECAUSE THIS IS NOT A CONTEST, IT’S A THOUGHT EXPERIMENT. THERE’S NOTHING TO WIN. Do you have any idea what a thought experiment is? I’ll be happy to explain.
If it makes you feel better, then consider this, also posted three times, also in capital letters: WHAT IF THE PLANE IS A RADIO-CONTROLLED SCALE MODEL? IS THIS A RIDICULOUS QUESTION?
You are absolutely correct, but pretty much everyone in the thread agrees with you. The disagreement is more centered around the question at the end of Cecil’s column:
This version of the question is more interesting, and Cecil’s answer is at best misleading and incomplete.
This, IMHO, is where this thread should end. Le’s never fight again.
I only came here to defend Cecil’s explanation which I believe is the only reasonable explanation that there is to this puzzle.
But now, to muddy the water a bit more, let’s talk about if the belt were designed to match the wheel speed.
OK, first you have to define what wheel speed is. If we define the ground as the stationary reference, then what does wheel speed mean? The belt can’t match RPM in a reverse direction. And RPM will vary with wheel size including the tire. The belt is designed to only move straight backward to match the wheel speed.
But let us say that the belt is designed to match the speed in reverse as measured at the bottom of the tire that is in contact with the belt. Remember the ground is the stationary reference. Will the airplane move forward?
And I must now confess that I actually believe that it is possible to make a belt that can do this.
How do you measure that?
The same way that you measure any speed talked about here. Just assume that it is possible to measure this speed relative to the ground.
Generally one meaures speed by by determining the time to go form point A to point B on a line. On a moving wheel, what is point A and point B, and where and how long is the line?
That is exactly right for something that is actually moving.
But take point A as being the point where the bottom of the tire first contacts the belt and point B as being the point at the bottom of the tire where it last touches before it leaves the belt.
That will be the speed at the bottom of the tire relative to the ground for a belt that is matching its speed in reverse relative to the ground.
On a moving wheel, what is point A and point B, and where and how long is the line?
Does that not in essence refer to the rotational speed of the wheel, rather than a straight line measurement?
Point A and point B are on the same plane. And the speed is straight line speed relative to the ground.
This is the part that people are ignoring, and I can’t figure out why. If you built something that created enough friction to offset the force of a jet engine, the heat produced would melt the plane and pilot, in which case it would not take off, because molten human flesh doesn’t fly. Other people seem to be proposing magical treadmills that somehow keep the plane in place, via magical friction that does not destroy the plane and treadmill, or some unstated means that equally defies physics.
If we are proposing a treadmill that holds back the plane, then the question becomes “how sticky is the treadmill?” With wheels on the plane, it is near zero. If we take the wheels off, and lay the plane on the treadmill, then the answer is “really sticky”, and you probably wouldn’t even need to have the treadmill moving to prevent the plane from taking off (unless it had HUGE engines). The way the question is proposed is with a regular treadmill and regular plane, in which case the plane would quickly move off the treadmill. Alternatively, you can assume the treadmill can accelerate to infinite speed, and you also have to assume infinitely good bearings on the plane and treadmill, in which case the plane still moves forward until the plane’s bearings break down and we get the “fuselage on treadmill” problem.
Are there still people who believe that a treadmill can hold back a plane with functioning wheels? If you are proposing a magical treadmill that can do so (via friction or other means), then no, the plane would not take off. If you are assuming a treadmill-plane setup similar to the way the real world works, then it would take off because the treadmill would do virtually nothing to slow the plane’s forward motion.
Why is that difficult to see?
Mmmm… but the speed at the bottom of the tire matches the speed of the treadmill (assuming no slip) by definition. So the treadmill will force itself to zero speed. Interesting, perhaps, as a control-of-the-treadmill problem, but not so interesting as a treadmill-plane interaction problem.
Admittedly, the exact wording of the question (“The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.”) is open to interpretation, but I think the spirit is clear: the treadmill tries to keep the fuselage of the plane from moving in either direction.
Love the Google ads for this thread
Is it just me or are there an inordinate number of guests on this topic?