How to measure it--beats me?
Here's a stab at it:
In a level turn the flight path angle is 90 degrees in the horizontal plane and 0 degrees in the vertical plane. The sine of 90 is 1 so the actual turn radius is 1 x the radius for the given bank angle and TAS derived from the turning nomogram.
If the flight path is 10 degrees below or above the horizontal then the turn radius will be the horizontal turn radius described above x sine 80 (90-10) = 0.98481.
If the flight path is 45 degrees below or above the horizontal, multiply the horizontal radius x sine 45 = 0.7071.
At 90 degrees below or above (vertical) the horizontal turn radius would be 0 (sine 0 = 0)
Every fighter pilot knows this instinctively but doesn't actually bother to work it out in the heat of combat.
All theoretical and of little practical use to any but fighter pilots since at extreme angles the challenge would be to keep the TAS constant while converting potential energy to kinetic energy and vice versa and thus eliminate dynamic changes to the horizontal turn radius.
Will that do?
WS (ex-fighter pilot)