Banked Curve Mechanics in the sky (1 Viewer)

[m1tch37]

Question: (Cambridge Ex7.6 Q4)

"At what angle should an aircraft be banked when flying at the speed of 100m/s in a horizontal circle of radius 4km"

Isn't the whole basis of banked curve mechanics that there is actually a physical curve (rail, track, anything...) to provide a reaction force to the vehicle travelling around it?

Wouldn't the mechanics not at all apply in the sky? Despite aerodynamic reasons (which are obviously beyond the syllabus) I see no reason why a plane has to bank in order to turn.

I got the answer the book was looking for (14°19') but I'm not happy with it.

Opinions?

 

[duckcowhybrid]

Think about it logically. Planes definitely have to bank to turn, they can't turn flat. Haven't you ever been in a plane that's been circling around an airport. The mechanics (whatever it is I'm not that far into 4U) still works, but I don't know what exactly the force is.

 

[untouchablecuz]

i THINK a centrifugal force constitutes the normal force in this case

correct me if i'm wrong

 

[m.jakaran]

Well in this particular example you just have the thrust from the wings in place of the normal force from the "banked track." If you think about it you can say that the thrust from a plane's wings is perpendicular to the wings and the angle at which the wings are banked constitutes the angle at which the "track" is banked.

just use tanx =v^2/Rg

By the way the plane could hypothetically only use rudder but I presume that they meant that it was using ailerons and tilting.

 

[m1tch37]

Okay so the wings are the 'track', and the normal force that would normally be newtons 3rd law from the ground, in this case is the lift from the wings.

There are some assumptions, but given them I suppose that it makes sense. Thanks.

I had no problems with the maths side of things here, I just personally like to understand the physics behind these mechanical problems.

And FYI, a plane can turn without banking simply using its rudder, although only very slightly.