Physics Question

[ordinaryjoe]

So the other day, I had a heated debate (an argument) with my physics teacher about a question in a paper we were doing, and want to see what you think.

Suppose that there is an aeroplane, which is tilted to the right side slightly. Ignoring air resistance, and all forces other than the lift of the wing and mavity, what path would the aeroplane follow?



Path 1 is half of a parabolic curve (y=|root x|) , whilst path 2 is a circle (evidently )

I shall say what way I argued later as to not make people bias.

Edit:
The plane is not increasing/decreasing in altitude
The lift in the plane obviously goes through the centre of mass
The only forces in play are the lift and mavity
The wings are the same and the lift is constant on both wings
The elevators exert no force on the plane

 

[ordinaryjoe]

How can we ignore air resistance yet keep lift?

Bah I'm sure you are capable of ignoring this slight flaw

 

[ordinaryjoe]

It's not an aeroplane, it's a UFO. Tilt proves it.

I don't get it Explain?

 

[ordinaryjoe]

You say it's tilted - is the rudder turned at all? 'cause otherwise that plane is just going to continue on in a straight line isn't it?

Nope... No tilt on the rudder... Just the plane

A few things to clear things up:

The plane is not increasing/decreasing in altitude
The lift in the plane obviously goes through the centre of mass
The only forces in play are the lift and mavity
The wings are the same and the lift is constant on both wings

 

[ordinaryjoe]

Hmm, id say 2. However number 1 looks like it could either be a slow right hand turn, or a very long circle?

Im guessing you were going for a righ hand turn.

No... 1 is meant to be a half of a parabolic curve (i.e. the same shape as the top half of y=root x)

 

[ordinaryjoe]

Ok my view... Path 1 because:
mavity and the upwards verticle component of the lift cancel (No change in altitude)
The horizontal component of the lift provides an acceleration (to the right in this diagram)
The plane can not twist, as all forces act through the centre of mass (mavity always does, and the lift would have to to counter mavity), so there is nothing to change the direction which the plane faces, and therefore, the horizontal component is always in the same direction.

This would give a parabolic curve (mine isn't an exact diagram, but shows the point) because if we call forward the y axis and sideways the x axis:
y is proportional to t
x is proportional to t squared so t is proportional to root x
Therefore, y is proportional to root x giving the parabolic curve

 

[ordinaryjoe]

Why? There's no air resistance to create drag, a constant force forwards from the engines will continue to accelerate the plane forwards.

I said the only 2 forces are the lift and mavity. The engines' thrust is ignored (i.e. considered zero)

Why cant the plane twist? surly it can rotate about its three axis?

Not is all forces act through the centre of mass... It is not possible

 

[ordinaryjoe]

Didnt realise we were ignoring the tail, my bad.

Seems very complicated rules for this debate, might as well just said it was a frisbee :s

The only 2 rules are:
1: the only forces included are mavity and lift from the wings
2: The aeroplane stays the same altitude

Everything else is a consequence of this

 

[ordinaryjoe]

Not enough information. In reality for the aircraft to maintain level flight it must have a slight nose up attitude. This would mean that the bank would pull the nose around and the aircraft would fly in a circle. If there is no nose up attitude then it would follow path 1 (assuming that there is no thrust).

No it wouldn't... It's perfectly possible to produce a plane which could be straight or even tilting very very slightly down and maintain level flight... The lift from the wing is caused by lower air pressure above than below caused by the shape of the wing... Not by tilting it up to get a reaction force from pushing the air down

 

[ordinaryjoe]

The plane starts of moving forward yeah, bottom to top in your picture? Your parabolic solution reduces this velocity, how? What you describe is a straight 'diagonal' accelerating trajectory.

It doesn't increase in velocity forwards. The acceleration means that the velocity is increasing horizontally, so for example, if the velocity is 1 m/s and the acceleration is 1 m/s squared

at t=0, y=0, x=0
t=1, y=1, x=0.5 (average horizontal velocity is 0.5 m/s)
t=2, y=2, x=2 (average horizontal velocity is 1.5 m/s)
t=3, y=3, x=4.5 (average horizontal velocity is 2.5 m/s)

So you can see that this would produce a curved flight path

edit: The average horizontal velocity is for that second only of course

 

[ordinaryjoe]

Ah yeah, okay. The way your planes are drawn on the picture suggests it's slowing down in the y direction.

Oh yeah I see... They are too close together near the end of the path

 

[ordinaryjoe]

I think what matters is the position of the centre of lift in relation to the centre of mass.

If the lift is forward of the COM then it will drag the nose around and the aircraft will turn in a circle like path 2. If the lift is applied at the COM then there is no turning force and the aircraft will simply drift right as in path 1.

Lift going through the centre of mass is probably not an at all realistic assumption.

Lift going through the centre of mass is completely realistic for a plane which is staying at the same altitude... Otherwise the plane would twist and completely change what way it is facing, and do all kinds of horrible things.

But what force makes it steer out of the turn. The force that started the turn doesn't just vanish. its either there or not so it would Carry on in a direction unless acted on.

The force doesn't make it 'turn'... It is still facing the same way, but it is not going in exactly the direction it is facing.

Jesus guys don't you get it! Whats a curve called that goes on forever?

Strictly speaking, a parabola goes on forever, and is always slightly curved (although it becomes incredibly slight after a while)

Path 2 isn't constant acceleration!

Well for it to go in a circle, it would require a centripetal force, which would exert a centripetal acceleration toward the centre of the circle

Centre of mass hasn't much to do with making a wing work centre of mavity and centre of air pressure is.

What exactly is the difference between centre of mavity and centre of mass?


And for those of you mentioning asymptotes, I don't think that is right, as parabolas don't have asymptotes. Asymptotes are lines which the curve will approach, but never ever reach. e.g. The curve, y=1/x would have an asymptote of y=0, as no real value of x would give y a value of 0. There is however, no asymptote for the curve y=x^(1/2)

 

[ordinaryjoe]

No it doesn't

Well quoting me a bit out of context, I was referring to my question where I explain what the question was asking, and seeing as the altitude stays the same, where do you suggest the lift acts though? If it acted anywhere else, with just the 2 forces included, the plane would effectively be hanging from wherever the lift is.

 

[ordinaryjoe]

Christ almighty people...

THERE IS NO TURN/YAW/ROTATION

Don't expect them to learn too quickly

 

[ordinaryjoe]

Ah, the confusing bit is in the phrasing of the question, the two answers provided make you immediately think the plane is turning. So will it just move in a diagonal then like previously posted?

If you look at the diagram on the bottom left, it shows that the plane is not turning.

And for all you saying that the plane would drop in altitude, it would not necessarily. If it turned 3 degrees, it would still have 99.9% of the upwards force, which could easily have been compensated before the question started by flying slightly faster. However, over 5% of the magnitude of the lift would be accelerating it sideways (so an acceleration of about half a metre per second, which over a few minutes is very significant)

 

[ordinaryjoe]

Come on then OP, what's the answer and justification from your Physics teacher?

I eventually managed to convince my physics teacher that answer 1 was correct. I explained in the 2nd page:

Path 1 because:
mavity and the upwards verticle component of the lift cancel (No change in altitude)
The horizontal component of the lift provides an acceleration (to the right in this diagram)
The plane can not twist, as all forces act through the centre of mass (mavity always does, and the lift would have to to counter mavity), so there is nothing to change the direction which the plane faces, and therefore, the horizontal component is always in the same direction.

This would give a parabolic curve (mine isn't an exact diagram, but shows the point) because if we call forward the y axis and sideways the x axis:
y is proportional to t
x is proportional to t squared so t is proportional to root x
Therefore, y is proportional to root x giving the parabolic curve

I then talked about how silly my physics teacher was and how difficult it was to explain something which seemed obvious to me to a friend who I thought was good at physics, only for him to take my teachers original view, saying the force to the right was a centripetal force, which is wrong, as the force would have to consistently be going towards the centre of the circle. Bah he's wrong and I'm right

 

[ordinaryjoe]

Well the original question had this plane with a forces diagram showing only the lift and mavity, showing the plane travelling at a known speed in a circular path of a known diameter, and we had to work out the angle which the plane was banking. I then told my teacher that it wouldn't go in a circular path and then came this question. That is why it is 'oversimplified' (although who is to say how simplified the question should be if the person who posed it can't?) And even with it being this simple, people seem to disagree plenty.

 

[ordinaryjoe]

Neglecting things is what is getting this thread in a tangle!

"Imagine a plane, that has absolutely nothing in common with an actual plane and ignores 99% of the forces and behaviours that make a plane a plane" does not make for a well structured question.

A boat with two perpendicular propellers makes far more sense

argh I am seriously getting fed up with people moaning that I have said to ignore most forces... The question would be perfectly fine if you read which forces are to be included. Is it really THAT hard to consider 2 forces and nothing else, and say what would happen?? Why does it matter that '99%' of the forces are ignored?? If we included every single force, it would be a completely different style question, but how it is, it is perfectly adequate. This is evident as a whole load of people have somehow managed the almost impossible feat of answering without moaning "You've ignored too many forces!!!!!!!!!!!!!!"... Seriously........

 

[ordinaryjoe]

Yeah sorry I was just getting fed up with the number of people who have complained that the question is too simple to answer :-/

And Joe isn't a woman's name!

 

[ordinaryjoe]

Well to be honest, it is pretty standard in A levels to have a 'story', then to be told which forces to consider, and which to ignore. It really isn't that hard. A question doesn't have to be realistic to have a correct answer.