Maybe this is about the difference between „aerodynamic climb angle“ and flight path angle, the former being ARCSIN(VS/TAS) and the other one ARCTAN(VS/GS); with VS vertical speed, TAS true air speed, GS ground speed. The former would depend only on aircraft climb performance, the latter additionally on wind.
– Cpt ReynoldsFeb 20 '18 at 10:18
If you climb a flight of stairs on a cruise ship traveling at 50 kts, does the speed of the cruise ship affect how steep the stairs are?
– Charles BretanaFeb 20 '18 at 13:23
@CharlesBretana: When something is moving, you therefore have two frames of reference, the "fixed" one, and the moving one. When you talk about ship speed and stair dimensions, you use different frames, the "steepness" of the stairs in the user frame of reference is unchanged, regardless of the ship speed, as long as the acceleration is null. You could also introduce the orbital speed of Earth (100,000 km/h), and the Milky Way drift, that wouldn't change anything for the user.
– minsFeb 20 '18 at 18:40
@mins, actually, the "steepness" of the stairs, like everything else, is totally dependent on what frame of reference you measure it in. That's the entire point of my comment. Too often, we lose sight of the simple "change of frame of reference" and the Transformation necessary for any and all measurements made in one frame of an event or property in another frame. If it takes you a minute to climb the stairs, and the cruise ship travels 100 feet/minute, then you have climbed vertically the height of the stairs, and horizontally the length of the stairs plus 100 feet.
– Charles BretanaFeb 21 '18 at 02:52
The point is that the issue ALWAYS depends on which frame of reference you measure in. And all frames are equally valid. Everything is relative. The op's question is about nothing more than understanding this. The "Flight Path angle" (measured in the frame of the moving block of air), is different than the "climb angle" measured in the frame of reference of the ground. Which one of these the phrase "climb gradient" refers to is only definitional, (semantics). It is not substantive.
– Charles BretanaFeb 21 '18 at 02:52
@mins, No worries. I understand. (although, respectfully, I might point out that even using the language as you did, referring to the two frames of reference as "fixed", and "moving" implies that one of them, the "fixed" one, is somehow more "real" than the other, and this implication, or understanding that some might get from reading this language, is the crux of the issue. No frame of reference is any more "real" than any other.
– Charles BretanaFeb 21 '18 at 21:38
@CharlesBretana: That's the reason "fixed" is between quotes, contrary to "moving".
– minsFeb 22 '18 at 07:44