If the sum total of the dopers can’t seem to agree on it, this has mythbusters written all over it.
That’s a little misleading.
I went back and read your post 74 (although I didn’t download the pdf) and you start by saying “the plane will take off”, which assumes “speed of wheel” means the forward velocity (as you point out).
The problem, is that I bet most people would interpret (correctly or incorrectly) “speed of wheel” to mean the speed it is rotating (you know what I mean, circumference, etc. etc.), which means by definition no forward progress can be made relative to an observer on the ground.
You should really point to either your post on page 3 where you do make it clear the 2 assumptions create different results, or to KeithT’s post where the same is clearly spelled out.
Thats post 89, just trains and rocketmen instead of conveyor belts and airplanes.
You guys wondering why the pilots of the SDMB are not flocking in to this thread?
I have no life, I read the whole thread.
I did not know we had this many cluless folks here on the SDMB
Bawahahahaha …
*::: shakes head and wanders away :::: *
Why are we assuming the wheels turn? If we do assume frictionless bearings in the plane’s wheels, and in the belt’s wheels, there is friction in the contact point between the wheel surface and the belt surface. No friction at the contact point would cancel out the rotation of the belt and wheels, and the plane would slide down the belt, wheels and belt spinning furiously.
With a magic frictionless conveyor belt, my personal bet would be that there would be no force placed on the wheels of the plane. As such, the plane would move forward with it’s wheels NOT spinning, and the conveyor belt would rotate forward, “pushed” by the wheels.
If the coneyor belt was long enough then yes, the plane would take off.
I think the “speed of the wheels” stipulation of the OP stems from the persistent problem of comparison with the parallel situation of a car on a treadmill.
I am therefore going to assume that we do not adjust the treadmill’s speed according to the angular momentum of the wheels, but according to the amount of thrust provided by the plane’s engines. We measure the thrust with some sensor or other, calculate what acceleration on solid ground that would translate to, and cause the treadmill to to provide the directionally opposite acceleration.
Forgive me if what follows has been done to death. I’m mostly just trying to work it out in my own head here in the hope that it may help the unconvinced.
We must remember that the plane’s wheels are not there to provide propulsion, at least not during take-off (taxiing is a different story), but to provide less friction against the ground than the body of the plane would provide while waiting for the airspeed across the wings to increase to a point that lift occurs.
The engines begin applying thrust. The treadmill begins accelerating backward. The engines push air backward, moving the plane forward, the wheels spinning (the thrust of the engine moving their axles forward, the friction with the surface of the treadmill pushing the contact point with the wheel backward) faster than they would on solid ground because of the acceleration of the treadmill. but since the reaction of the plane is with the air and not the ground, the plane moves forward and eventually takes off.
Unless of course, for some reason, the friction in the wheel bearings can not allow them to maintain the higher angular velocity. Consult your handy dandy local mechanical engineer for info on whether this would ever be an issue for real. Actually, don’t. As soon as you describe the situation he’ll just bog the conversation down by asking derisive, jargon-laden questions about the specifics of how you plan to build a working, extra-high-velocity treadmill of airport runway dimensions. (Why, yes, I DO work with a former mechanical engineer, however could you tell?)
If the friction within the bearings provides additional drag, the wheels will spin more slowly (if the friction with the treadmill is greater) or stop spinning altogether and begin skidding if possible (if the friction with the treadmill is less). If the thrust from the plane’s plane’s engines is not adjusted to overcome this extra backward acceleration, this would be the only situation where the plane may not achieve sufficient airspeed for liftoff (either not moving forward fast enough, or even being moved backward by the treadmill).
Did I miss anything?
Taxiing is not a different story - the plane is still moving by reaction to air being pushed backwards, not by drive to the wheels.
You’re misunderstanding what Raft is saying. Here’s the relevant portion of your post 89:
You’re assuming that the “wheel speed” is equal to the hub speed. Nothing wrong with that of course, but another perfectly legitimate interpretation of “wheel speed” is “circumferential speed”–cirumferential speed with respect to the hub, if you prefer–or [symbol]w[/symbol]r.
Lots of correct answers in this thread, just a lack of explicitly-stated assumptions.
Think of it this way.
- A plane is attempting to take off from a self driven belt.
- A belt is trying to match the speed of the planes wheels.
Both of these things cannot happen. Any forward movement of the plane will by definition mean that the belt is not matching it’s wheel’s speed.
It’s not that the plane can’t take off, it’s that the belt can’t keep up.
As soon as thrust is applied the wheel turn in relation to the ground. I understood the OP to mean that that turning would be counteracted by an equal movement (in the opposite direction) of the belt. As the plane increased its speed, the belt would increase in speed as well.
What would happen in this thought experiment is that the plane would take off and the belt would be unable to keep up.
This is the simplest, best, most accurate answer in this whole God-forsaken thread. I tip my (propeller beanie cap) hat to you, zut
Exactly. The only reason we can’t agree on an answer is we all have different interpretations of what exactly that means. There’s also some discrepancy on which forces you ignore. (Incidentally, “thought experiment” does not necessarily mean “dumbed down to high school level”. It’s perfectly reasonable to include friction, air resistance, tire failure, etc. in a thought experiment, as long as we’re clear on what we’re including and what we are ignoring.)
Do you mean “sensor reads 1000 lb thrust, and the plane would normally accelerate at 0.1 G at that thrust, so I’m going to accelerate the treadmill at 0.1 G”? In that case I agree with your analysis.
Another possible interpretation is that the treadmill is designed for automobiles, and therefore has a sensor that measures the wheel rotation speed and matches that speed. (That is, match the linear speed of the tire tread corresponding to that RPM). In that case, as the plane’s engine is throttled up, the plane starts to move forward, and the wheel starts to roll forward. Treadmill moves backwards to match that speed. But unlike an automobile, the plane is moving by pushing on air, not the treadmill. So the plane continues to move forward, and the treadmill cannot catch up with the rotational speed of the wheel - unless the treadmill can exert enough backward force on the airplane through acceleration of the wheel and friction of the wheel bearings.
Another possibility is that the treadmill has a sensor that detects position of the vehicle, and moves to try to keep it stationary. In that case the same thing happens - the treadmill will move backwards very fast to try to stop it, and may or may not succeed.
The ground, or the belt?
As did I, but if the wheels are on a slippery surface, a heavily greased runway, or a smooth flat sheet of ice, the plane could move without the wheels turning at all.
There is contact and friction between the wheels and the belt, right?
I think this is the trick part of the question, the wheels don’t have to turn, the plane just has to move forward.
Why can’t the belt keep up?
If it’s a real world experiment I can see that there can be limitations on the efficiency of the parts.
In a purely hypothetical, a magic frictionless conveyor belt etc, then DanBlather’s and Sage Rat’s answers seem to make more sense (at least to me!)
This is all making my head hurt 
!
It’s not that the belt can’t keep up; it’s that it doesn’t exert enough force to keep the plane from moving.
Again, just turn it around and look at it like this: Start the conveyor belt first, assuming frictionless bearings and infinitely tough tires. The belt moves. The plane doesn’t. Speed up the belt. It goes faster. The plane doesn’t move. Crank the belt up to the plane’s takeoff velocity. The plane doesn’t move.
Then start the jet engines and have them apply thrust to the plane, not the belt. The plane moves, accelerates, and takes off, because the belt has absolutely nothing to do with any part of the jet but the wheels, and it can’t exert enough force through the wheels to counteract the force of the engines, which is what is needed to keep the jet from moving.
OK, my question.
How in God’s name did this thread make it to 6 pages?
I did not know that.
As the old saying goes, “It’s taking longer than we thought.”
I meant to an onlooker on the ground (off of the belt) the wheel would be spinning.
Well, of course. I understand that given enough friction (and speed) the belt could keep the jet from taking off.
It could moving infinitely fast. But as this is not a real world solution, I (admittedly arbitrarily) ignored it.
This does make one’s head hurt. There have been several ‘correct’ answers given based on the posters interpretation of the OP.
My guess is that the original framer of this question did not understand the real world physics involved in this situation. For if they had, it would either be better spelled out or not asked at all.
In a real(ish) world experiment, as I’ve said friction could overcome the thrust of the jet. Though I really don’t think that was the intent of the hypothetical. The question, to me, assumes two things that can’t happen at the same time. Kind of inadvertently a trick question.
Here’s another:
A lady is walking her tiny dog. She wants to turn left to go home but the dog chases a squirrel to the right. Given that the dog is going to the right how can the woman go home?
You could say, three right turns or bending space time but the real life answer is that she would overcome the dog and pull it to the left.
Just as the real life answer to the OP is, Yes, the jet hits the throttle, accelerates and takes off. All the while the belt is madly trying to compensate (but failing).
Front loading the question is the real problem, IMHO.
Well, the thread was started on a frictionless treadmill as long as a runway. People keep trying to get this thread to take off, but the force of the Bernoulli Principle factored in with the speed of light prevents anyone from understanding why the thread is going to crash and burn while the gravity of the treadmill impacts Issac Newton’s ability to jump off the end of this post into a black hole.
Don’t you get it man?
Now i get it!