Plane banking: Pitch and roll axes

Alrighty-then

1. The problem statement, all variables and given/known data
This is from a book called "Engineering by Design." It sucks. Really. It asks problems and doesn't provide sufficient information to answer them. Now that I have complained, here is the question:

Explain with sketches why a combination of rotations about the pitch and roll axes results in a plane banking through the air (with the rudder then used for slight corrections in the turn).

I am a little lost on this to say the least. I know no one can draw it out for me, but if someone could at least briefly explain the procedure, I might be able to wing it --no pun.

Does the order of the rotations matter? That is, pitch first, then roll....or the other way around? Or does it not matter?

Any clues would help

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Cyrus

If you turn the yoke on the airplane, the airplane will roll in the same direction.

This causes the lift vector to bank at the same angle as the airplane. So if the airplane is flying level, Lift= weight. When you turn, the lift in the z -axis is now only Lcos(theta).
So the plane is going to pitch down unless you correct for that by pulling back on the yoke, giving it up elevator.

If you turn the yoke on the airplane, the airplane will roll in the same direction.

This causes the lift vector to bank at the same angle as the airplane. So if the airplane is flying level, Lift= weight. When you turn, the lift in the z -axis is now only Lcos(theta).
So the plane is going to pitch down unless you correct for that by pulling back on the yoke, giving it up elevator.
Perfect! I was just looking at a website I found that was explaining this! But your way is much more concise.

Thanks

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