Any Physisists/Mathmemeticians?

I don't want everyone to go posting their answers to this problem again - I already know the answer. What I need is a mathematical proof or some other definitive answer to prove to some people in another totally unrealated forum the correct answer to the "airplane on a treadmill" problem. We've already done this here, and to me it was adequately covered at the time - however, no matter how I attempt to simplify and explain that the plane does in fact take off in this other forum there are one or two knuckleheads who don't seem to understand that an airplane's wheels don't actually drive it down the runway. Can anyone help?

Originally posted by st00p1dfac3
I don't want everyone to go posting their answers to this problem again - I already know the answer. What I need is a mathematical proof or some other definitive answer to prove to some people in another totally unrealated forum the correct answer to the "airplane on a treadmill" problem. We've already done this here, and to me it was adequately covere ...[text shortened]... tand that an airplane's wheels don't actually drive it down the runway. Can anyone help?

I can help. All you have to do is provide sufficient detail in the question (unless you want to trick people at the end). The thing people get hung up on is what's providing the airflow.

If you tell people that the propellers are on while the plane is on the treadmill, most of them will have no problem understanding the answer. If you leave it vague, pretending that the treadmill turns the wheels and somehow provides airflow around the wings, they will rightly balk at the answer.

When you want to get your point across, often times a spoonful of sugar helps the medicine go down. 🙂

Originally posted by PBE6
I can help. All you have to do is provide sufficient detail in the question (unless you want to trick people at the end). The thing people get hung up on is what's providing the airflow.

If you tell people that the propellers are on while the plane is on the treadmill, most of them will have no problem understanding the answer. If you leave it vague, pret ...[text shortened]... u want to get your point across, often times a spoonful of sugar helps the medicine go down. 🙂

I've done that, the question is sufficiently clear that any chimpanzee can understand it, but they don't (btw, it was someone else who posted the infernal thing, I just (stupidly) replied with the answer.) Now I need idiot-proof proof - irrefutable by even those whose brains seem to have gotten lost a few rungs back on the evolutionary ladder.

I have searched the web, and found no answer better than my own. I have even resorted to creating an account on the Discovery channel website in the hope that those Mythbuster fools will take my advice and do a damn show to prove these sub-normals wrong. I don't even have the Discovery channel!! I am so irritated by their inability to grasp the concept of freely rolling wheels not providing thrust that I have sunk to embarrassing new lows in my quest for righteous intellectual vindication.

Jesus Chrysler!! Won't someone help me...?!?

I'm not going near that one again. The problem was the people disagreed over what the question meant. If you can't get over that you've got no chance of agreeing on an answer.

Originally posted by mtthw
I'm not going near that one again. The problem was the people disagreed over what the question meant. If you can't get over that you've got no chance of agreeing on an answer.

This is why I didn't actually post the question again, however, if it helps I'll post a very specific version of the question which leaves no argument about what it means. If I do that, it also answers the question for anyone brighter than a burnt-out light bulb. That, of course, didn't help on the other site.

Originally posted by st00p1dfac3
This is why I didn't actually post the question again, however, if it helps I'll post a very specific version of the question which leaves no argument about what it means. If I do that, it also answers the question for anyone brighter than a burnt-out light bulb. That, of course, didn't help on the other site.

This is posted assuming some of the "knuckleheads" have done highschool level physics.

Ask them to draw you a force vector diagram of the forces acting on the plane.

They should draw a forward force of the propellers thrust, a downward force of gravity on the plane and the reciprocal upward force of the treadmill on the plane (which stops the plane getting pulled through the treadmill to the centre of the earth).

Then you can say to them "See there is a net force acting on the plane, the plane must start moving"

They'll say something like "no the treadmill slows the plane down"

You say "No, the wheels de-couple the plane from the treadmill, no horizontal force can be applied to the plane via unpowered, freewheeling wheels with frictionless bearings".

Hopefully then they'll say "Oh OK, you're right". (But realistically i doubt it, some people just won't listen - they may be capable of understanding what you're saying but they won't try)

Good luck with your sisyphean task

Originally posted by st00p1dfac3
This is why I didn't actually post the question again, however, if it helps I'll post a very specific version of the question which leaves no argument about what it means. If I do that, it also answers the question for anyone brighter than a burnt-out light bulb. That, of course, didn't help on the other site.

It would help to state the problem as you stated it to the people in this other forum, there may be something in that that's confused the issue. As far as I can tell from the discussion here (I can't be bothered to search through the threads to find the original) you have an aeroplane on a runway which is designed like a treadmill. The plane's wheels are free to spin. Initially the plane is moving backwards relative to the air traffic control tower (which I've chosen as a fixed reference point) and is stationary relative to the runway. The engines are started, and the plane starts to move forward relative to the runway, but is still going backwards relative to the tower. At some point it will be stationary relative to the tower. In order to actually take off the wing has to be moving relative to the air at whatever the plane's takeoff speed is. The air is stationary with respect to the tower (let's assume it's a nice day) so it takes longer than normal to take off. Turn the plane round and it takes less time as the treadmill will to some extent act like a catapult.

Now make the runway stationary relative to the tower and move the air - any pilot will tell you that it is always better to take off into the wind - and the problem is essentially the same as taking off with a tail-wind.

Basically I think the magic words are groundspeed and airspeed. Although that should help sort it out the odds are they won't listen. Especially if they think that the wheels are generating thrust. My uncle is a glider pilot and was having a similar argument with some people on Wikipedia about how gliders stay airborne - they were convinced that the wing was somehow generating thrust, which of course it doesn't unless there are engines on it and then it ain't a glider. They refused to believe the correct explanation that the glider is continuously losing altitude to keep the airspeed up.

Nevermind (thanks for the help all) but I've finally managed to turn most of them toward the light of correct-thinking... (well, me and the others who were right from the beginning.)