Airplane physics question

I read my old mechanics book and I fear I'm not right in #2259. Or let's say #2259 is incomplete. The translational speed v_plane = delta_s / delta_t is fully compensated by the rotatory speed of the wheel in the opposite direction of the translational movement at the point of contact of wheel and belt. This point of contact is called "Momentanpol" in German. Don't know what it is in English.

And this has nothing to do with the frame of reference, no matter whether it's static or floating.

So indeed both speeds match, even when the plane moves. No kinematic constraint is violated. Can't blame the author for that as I did before.

(1) When a wheel runs over a non moving runway than its speed at the point of contact is always zero despite of the translational speed of the wheel itself. Reason is, as stated in several posts above, no slip at point of contact.

(2) When the plane is not moving and the belt is already running, then speeds match. Speed at point of contact equals belt speed. I think we all agreed on that.

(3) One can combine (1) and (2). The speed of the wheel at the point of contact still equals the belt speed, no matter at which speed the plane moves! This is the case, because the faster the plane moves forward, the more its wheels spin backward.

John, Zach, others, who claim "Question doesn't allow answer.", have a look at this:

Explanation (unfortunately in German, use Google translator): http://de.wikipedia.org/wiki/Momentanpol

Corresponding drawing: http://upload.wikimedia.org/wikipedia/de/thumb/7/74/MomentanPol.svg/500px-MomentanPol.svg.png

Therefore I have to revise my statements of post #2240 again.

Result: Plane will fly and no constraints violated in any case!

 

Ka Ching!

What I've been trying to tell for years now.

 

Ach so, der question was made up by a mad German szhientist, probally Herr frankemsteins bruder.
Aufveidersehn .

 

Ok its time to break out my daughter's crayons.

Suzy the plane needs let's say wind speed at the wings of 100kmh.

When the conveyor spins so do her wheels but Suzy is still asleep.

When Suzy yells contact and her engine coughs and chugs to life she starts spinning her propeller. Her propeller pulls her faster and faster. Because Suzy's wheels are free spinning they can go as fast as they want, and regardless of how fast the conveyor is spinning her wheels just spin away.

When Suzy gets to 100kmh she takes off.
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That's pretty good except one problem.


"Because Suzy's wheels are free spinning they can go as fast as they want, and regardless of how fast the conveyor is spinning her wheels just spin away. "

You are ignoring the statement in the original question that requires Suzy's wheel speed and the speed of the conveyor belt match exactly at any given point in time.

While I do appreciate your artwork- you have drawn the wheels spinning 100 kph and the belt spinning 200 kph ( violating the question).

If you go back and read original question and redraw the Suzy with the wheel speed AND conveyor belt moving 100kph, Suzy will not be moving forward, no airpseed, and no flight

 

Why do they have to match?

And saying that at any given point in time, suggests that they will match at some point but not at all points in time.

I'm not getting sucked into this.

The plane will fly.

 

In the interest of science, wheel/surface speeds are equal at all times, without one iota of deviation.


via rubber ducky

 

Please please please. Read the original question. Page 1. First in the thread.

"The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation."


Not quite sure how the statement above can get much clearer.... It was copied from the original statement.

 

As long as the wheels are touching the conveyor without slipping their "speeds" match and the condition is met. The whole "moving in the opposite direction of rotation" part is irrelevant and unnecessary.

 

"Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.
There is no wind.
Can the plane take off?"


So you want to ignore 50% of the question because it doesn't give you the conclusion you want?

 

I'm suggesting that those words are meaningless and just cause some to be confused. As long as there is no slippage it doesn't matter what the conveyor does, it can't affect the motion of the plane and is irrelevant.

 

If the wheel rotates clockwise the belt rotates counterclockwise and the other way around. No problem there.

 

I'll check back in 6 months, I'm sure nothing will have changed. The plane will still fly.

Have fun

 

It always will.

 

It will only fly if you ignore the last half of the question. Suzy proves it.

 

C'mon Fave. Please draw another picture where the wheel speed and the conveyor belt speeds are equal and the plane moves forward.
It's impossible

Plane cannot take off unless it is a Harrier

 

.
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Someone who understands the question, and the paradox within. Thank you.

 

We are not considering skid.
You agree with drjohngober and myself, then, that, without skidding, the wheels cannot match the belt speed if the plane is moving forward, right?

 

I've got the translation now: "Momentanpol" is called "instant center of rotation" in English.

http://en.wikipedia.org/wiki/Instant_centre_of_rotation#Instant_centre_of_a_wheel_rolling_without_slipping

"The wheel rotates around its axis M, which translates in a direction parallel to the road. The point of contact P of the wheel with road does not slip, which means the point P has zero velocity with respect to point M. Thus, at the instant the point P on the wheel comes in contact with the road it becomes an instant centre."

That's the key. Therefore wheel speed at the point of contact is always belt speed if there is no slip.

 

Rob is correct.

If skid,skip and friction were mentioned in the question then these conditions should be taken into account. But, the only additional statement in the original question is that there is no wind.

Remember in school when we were asked questions regarding what temp water freezes at, speed of sound, how fast will an object fall if dropped from the Empire State Building?
In these questions, as in the original question, coefficient of drag, friction,skid,slip,altitude,pressure and temp are not mentioned therefore not to be considered in the answer.

If you were asked at what temp does water freeze, we would all agree 0 degrees C.
But, if the next part of the question added that this water was at an altitude of 5,000 meters, you would have to take that additional statement into account and the answer would not be 0 degrees.

Same as this question.
You cannot ignore the condition of wheel speed matching exactly the conveyor belt speed at any point in time. That is the main premise of the question.

Also, you cannot expect to add conditions as slip,skid or friction. If these conditions were to be considered , the original author would have included these just as he did when he stated there is no wind.

In the question as written, the plane cannot possibly fly.

Game,set, match.

 

Okay, let's try it the other way around:

Belt is not moving (= usual runway). Wheel rolls over the belt.

Which one is the axis of rotation: P or M?

http://en.wikipedia.org/wiki/File:Wheelrotation.png

 

Wrong, any time the wheel is in contact with the belt, at the point of contact their speeds match. No skidding required.

Plane flies.