Negative sir,
At no point in the OP does he state helix or spiral flight path. On the other hand he does state smooth orbit and true circle as descriptors. In fact the title of the thread includes orbit like circle.
Just because you think differently and interpreted the OP in one complex manner of a possible flight path, it does not preclude the initial assumption that approach the target at 10 feet could be interpreted to mean 10 foot AGL then rise to 150 and complete a smooth orbit flight path. He even gives you another clue in English, at some radius distance from the center of the property, again a possible clue to initiate a vertical climb from 10 feet AGL to 150 feet AGL then immediately go into a smooth orbit.
Visualize the side of a cylinder as opposed to an advanced approximation of a golden ratio 3D spiral that you so eloquently argue for. Your approach is timeless as the golden ratio spiral when expressed in a manner that incorporates the Z axis as a function of time is much more artistic. But I somehow tend to doubt he put near as much thought into his question as you did in your numerous attempts to answer.
And I bet he even spent less time thinking about his question than I spent putting together my reply to your response to my initial post. All that aside I am very impressed with your mathematical analysis skills and ability to conceptualze intricate geometric flight missions.
I look forward to learning much more from you in your future posts. BTW thank you for turning me on to Drone Harmony and the ability to fly a preprogrammed vortex flight path with gimbal settings and either inward facing or outward facing camera positions. Sometimes KISS is the better answer.
I do have one additional question, can that vortex path be changed to a cylindrical profile like the stripes on the outside of a barber pole?