What factors affect the minimum time to go from point A to point B? I've created this trajectory for a small RC aircraft to go from 15m to 61m as quickly as possible (e.g. quickest time to get from point A to point B). I'm trying to perform a sanity check for why the aircraft would go to the lowest allowed altitude to maximize velocity before beginning it's climb. Can anyone provide an explanation for why this would be most time-efficient for this problem?
The reason that the aircraft does not fly lower than 5m is because I set 5m as the lowest possible constraint. If that constraint was not in place, it would try to fly at 0m.
Edit:
The reference listed for this type of problem is given as 'J. Betts. SOCS Release 6.5.0, 2007.'. This is an inappropriate place to ask for this, but I have tried searching for whatever this paper/journal this may be referencing and cannot find it. If anyone has any tips/tricks on how to actually find this source, please let me know
It looks to me like your airplane, starting with a very low velocity, is trying to climb a height of 46m (61m - 15m).

Because it has a low initial velocity, your basic choices are:


Start climbing immediately, demanding engine power both for velocity and climb rate, and climbing very slowly.
Fly level for a period of time to build up velocity, then begin the climb.
Use gravity and engine power together to get more velocity quickly, then begin climbing at a much faster rate.


The velocity you need to achieve is called $V_y$, or best rate of climb.
Based on the Yellow color on the main segment of the climb, it looks like this plane's $V_y$ is about 26 $m\over s$.

It looks like your software package chose #3.  While it makes intuitive sense, without the math behind it, I cannot tell you the details.