Originally Posted by
D120A
Winemaker has it exactly right. If you don't believe him/her, or me, ask a friendly mathematician to construct a position vector from a fixed point on the earth to an aircraft performing a constant rate turn in a steadily moving airmass, and differentiate it twice to determine the acceleration of the aircraft. It is always towards the centre of the circle of the constant turn, a point which itself is moving with uniform speed over the ground. To demonstrate it in flight, choose a windy day and ask an instructor (better still, a test pilot) to fly an accurate rate one 360 degree turn under the hood while you look out of the window. The acceleration will feel fine, bank angle constant and ball in the middle, but at low level your track over the ground will scare you stiff and illustrate why trying to turn near the ground in such conditions using visual references is so dangerous.