Principles of flight?

[matt dunn]

And that is how the plane took off, because the wheels on the plane relied on the surface below to not counteract their movement.

There is not enough friction without the brakes on for the conveyor to counteract the speed.

But sticking to the exactly matching part, ( which is impossible in reality)

Plane ground speed = Wheel speed - conveyer speed.

Since wheel speed and conveyer speed are exactly opposite,
ground speed is 0 and the plane does not fly.

[pidge]

A wheel has two speeds that can be measured. Its linear speed, and its rotational speed.

There's two sides here. In one, the meaning of the phrase "speed of the wheel" is taken to mean the wheel's linear speed, and "wheelspeed" (rotation speed of the wheel) = "relative speed of the wheel (linear) and the contact surface".

In the other, "the speed of the wheel" = wheelspeed (rotational speed of the wheel), causing peoples brains to trickle out of their ears.

Guess which is simpler?

There's this thing called Occam's Razor, and a related term "parsimony".

from Wikipedia

In science, parsimony is to prefer least complicated explanation for an observation. This is generally regarded as good when judging hypotheses. Ockham's Razor also states this idea.

[AirNZ]

Pidge, that was beautiful. May you live a long and prosperous life.

[V8MOFO]

And that is how the plane took off, because the wheels on the plane relied on the surface below to not counteract their movement.

There is not enough friction without the brakes on for the conveyor to counteract the speed.

But sticking to the exactly matching part, ( which is impossible in reality)

Plane ground speed = Wheel speed - conveyer speed.

Since wheel speed and conveyer speed are exactly opposite,
ground speed is 0 and the plane does not fly.

I think we can all agree with this set up now that a plane can sit at a velocity and not move. Wheather it is 0kmph or 100kmph. But acceleration is a different story. It shows a change in velocity over a period of time. In this situation, ( I will repeat myself here ). The wheels are turned by the travelator and the travelator is turned by the wheels.
In this situation the thrust does not give the wheels or the belt a stopping point for acceleration. As they are not accelerated by the plane's thrust, they are dependent on each other. So it goes the other way around, If they were to accelerate at a constant rate, one of them would have to apply deceleration for the otherone to follow. And what would effect to things acceleration that are completly dependent on each other?
NOTHING! Unless it were either the wheels or the travelator, but they have to mirror the status of one another.

This isn't a question of speed, It is a question of acceleration.

[V8MOFO]

Oh and I must say good thread , Who could have known we could debated 13 pages + on something that is impossible to answer.

Another example

Get two people to punch each other. Say to them, ''you are only aloud to start punching when the other guys has hit you first''
''but you are not allowed to throw the first punch''

[matt dunn]

Oh and I must say good thread , Who could have known we could debated 13 pages + on something that is impossible to answer.

You want a good laugh.

Go back to the start and start reading the posts all over again

[V8MOFO]

Oh and I must say good thread , Who could have known we could debated 13 pages + on something that is impossible to answer.

You want a good laugh.

Go back to the start and start reading the posts all over again

Well I can say it got me thinking alot, I was looking at the smaller picture to begin with I think the funniest thing were the people who called the opposing side ''stupid''.

[pidge]

For the situation described to be solvable, any of the contraints made in the question and assumptions made must result in a solution that does not break the laws of motion, otherwise the question is non-sense. (i.e. the answer is not "no", it's "this question does not make sense, or "fish" )

The point which is causing the problem is the assumption that "speed of the wheels" = "wheelspeed" = "speed of rotation of the wheels" resulting in the plane speed being zero. Let's look the algebra behind that...

The frame of reference for speed measurements is a fixed point on the ground, except for the "wheelspeed" or "speed of rotation of the wheels" is the rate of rotation of the wheel times the circumference of the wheel.

Vp = velocity of the plane
Vc = velocity of the conveyor belt
ws = wheel speed

Positive velocites are for motions from left to right. Postive wheel speeds are for clockwise rotations (i.e. the speed of the wheel at its circumference measured at the top of the wheel and relative to the axle of the wheel).

For a wheel in contact with a surface, without slippage, the wheelspeed is:
ws = Vp - Vc (1)

Here's where we need to decide what the velocity of the conveyor belt is.

The direction of motion of the conveyor belt is such that its rotation is opposite that of the wheel. If speed of the wheel is the wheelspeed, then the conveyor belt speed is:

Vc = -ws (2)

Substiture into (1)

ws = Vp - (-ws) = Vp + ws

Which is solved when Vp=0. (3)

How this interpreted is where you can be caught out.

All the solution (3) says is that for the contraints (1) and (2), the velocity of the plane must be zero. Also note that the wheel speed and the converyor belt speed have not been found - they can be any speed. This is not a useful solution!

(1) is the result of no wheel slippage. Since the landing gear wheels are free to rotate, the wheels will not slip. So this constraint is correct.

(2) is the result of assuming conveyor belt speed = the speed of rotation of the wheel.


Now, if you assume that the "speed of the wheel" = "speed of the wheel's axle" = the speed of the plane (Vp), the conveyor belt now runs in the opposite direction to the planes direction of travel (to keep with the constraint of the "rotation" of the conveyor belt being opposite to that of the wheel)

Vc = - Vp (4)

Substitute this into (1)

ws = Vp - ( -Vp) = Vp + Vp = 2Vp (5)

Which is a useful solution, as it provides the wheelspeed and the speed of the conveyor belt (relative tot he ground), in terms of the speed of the plane (relative tot he ground). Oh and since there is no wind (Va = 0), the planes ground speed is also it's air speed. This is the complicated way of solving the problem!

The other problem with assuming (2) is that by examing the forces applied to the plane (basically, just the engine thrust), and given that the wheels are free to rotate, according to the laws of motion, the plane MUST accelerate. (a net external force applied to an object causes that object to accelerate). The only way (2) can be true is if the wheels are not free to rotate (i.e. the brakes are one) in which case (1) no longer applies. But since the plane "is ready to take off", it is reasonable to assume the pilot has released the brakes to (attempt to?) accelerate down the runway.

If you assume (2), and as a result insist the plane cannot move, your assumption in effect breaks the laws of motion (failing the Occam's razor test), or other assumptions made are incorrect.


I've got a B.Sc. in Physics* - I've probably spent a bit more time doing physics than most people (as in the general population, not just toyspeed). I'm quite confident I know what I'm talking about with regard to this problem.

The question would be perhaps suitable as a Year 12-level Physics question - which is the year that the Laws of Motion are covered - well, they were 17 years ago

* Athough I admit being a bit rusty the Quantum Mechanics, Classical Mechanics, Thermodynamics and General Relativity (still pretty hot on Electronics though)

[V8MOFO]

Pidge you are right. You explained the situation perfectly using speed or velocity. You only mention acceleration once though? and that was of the plane. What happens to the belt or the wheels?

[RedMist]

All the solution (3) says is that for the contraints (1) and (2), the velocity of the plane must be zero. Also note that the wheel speed and the converyor belt speed have not been found - they can be any speed. This is not a useful solution!

You really are stretching Pidge.

Firstly, you are incorrect in your assumption that wheelspeed and conveyor speed can be anything. They can only acclerate until frictional forces over come thrust.
"This cannot be a useful solution" is an emotive comment based on the fact that you cannot generate a logical solution to the answer, however unplausable.

Now, if you assume that the "speed of the wheel" = "speed of the wheel's axle" = the speed of the plane (Vp), the conveyor belt now runs in the opposite direction to the planes direction of travel (to keep with the constraint of the "rotation" of the conveyor belt being opposite to that of the wheel)

Your wrong. If you want to introduce implausable rules, such as rotational speed is not wheelspeed then the conveyor which is a rotational device, never moves as it has no linea translation.

The other problem with assuming (2) is that by examing the forces applied to the plane (basically, just the engine thrust), and given that the wheels are free to rotate, according to the laws of motion, the plane MUST accelerate.

Utter Bollocks. I gather you are talking about Neutons second law of motion? If so I suggest you go back to year 12, study it, and while you are at it have a quick glance at Newtons first law of motion, then revise your statement above.

I've got a B.Sc. in Physics* - I've probably spent a bit more time doing physics than most people (as in the general population, not just toyspeed). I'm quite confident I know what I'm talking about with regard to this problem.

Stating your qualifications does two things.
1. Belittles the B.Sc qualification, which I know is not an easy qualification to obtain.

2. Makes you out to be a complete horn blowing cretin in your attempt to belittle those who do not have your qualifications.

* Athough I admit being a bit rusty the Quantum Mechanics, Classical Mechanics, Thermodynamics and General Relativity (still pretty hot on Electronics though)

[/quote]
Quantum Mechanics, General Relativity... now there we could have a debate.

You also may wish to do a search on the web for wheelspeed. I attempted to find any reference to wheelspeed in a linea fashon, and failed. All references were in regards to rotational speed. There are also some good references to wheelspeed in aircraft. All references rotational. Some aircraft are also fitted with "wheelspeed sensors" for skid detection. I'll let you guess if they are rotational or linea sensors.

And if you want point linea speed. Whats the speed of the wheel at it's circumferance 180 degrees from the contact patch?

[blitza]

And if you want point linea speed. Whats the speed of the wheel at it's circumferance 180 degrees from the contact patch?

as you were being word picky, wheels dont have a 'contact patch' tyres do. and you would be referring to the surface speed of the tyre.

[Chickenman]

linear?



Jesus.



Plane doesn't fly


Get over it.

[AirNZ]

Nah dude, it's chickens that don't fly.

[AirNZ]

silly double posting me

[mr pad]

Nah dude, it's chickens that don't fly.

[V8MOFO]

Nah dude, it's chickens that don't fly.

haha looks like AirNZ got to it first.

[pidge]

Whats the speed of the wheel at it's circumferance 180 degrees from the contact patch?

Assuming the wheel is rolling over a stationary surface without slipping, the point on the wheel at its circumference diametrically opposite the point of contact of the wheels circumference with the surface, is moving in the same direction as the direction of travel of the wheel, at twice the speed that the wheel is moving with respect to the surface.

Also the point of contact is stationary with respect to the ground, since the wheel isn't slipping.

Go unroll a roll of toilet paper on the floor to see this in action.

[pidge]

oh, and those are all instantaneous linear speeds.

[Chickenman]

Nah dude, it's chickens that don't fly.

Alycia once told me that the longest recorded flight of a chicken is 13 seconds...

[V8MOFO]

Nah dude, it's chickens that don't fly.

Alycia once told me that the longest recorded flight of a chicken is 13 seconds...

Chickens used to be able to fly ( well their ancestors did )...
What did they throw the chicken off?