Brake Line

This weekend was busy with hiking on Cougar Mountain, attending the Puyallup State Fair (quite an Internet-savvy fair; see the URL), and having company over. My friend Pedro tried out the lunar-lander-on-a-disc game I've been gradually making. He figured out the trajectory plots quickly, but found the rocket's auto-rotation confusing. I need to get more data points on that. The rest of his complaints were things I know about and plan to fix: landings need to be more emphatic, with less bouncing and floating around. Landing targets need better visibility from orbit.

Up until now I've had three trajectory plots: the ballistic trajectory, which is where you go under gravity's influence alone; the powered trajectory, which shows where you go if you thrust continuously in your current aim direction; and a braking trajectory which shows the quickest way to reach zero velocity. This last one I have been unsatisfied with. It gives a rough idea of the turnaround point for deceleration, but I want something that gives more information. Here's what I've got so far:



The red line is the brake line. It's a closed curve made out of the points of minimum velocity for all thrust directions. In other words, if you thrust continuously in a particular direction, when your velocity reaches a minimum it will be somewhere on that curve. The powered trajectory plot's inflection point sweeps around the curve as you change its heading. (It doesn't quite touch in the picture above; this is because for my initial prototype I'm assuming a constant gravity vector for the brake line plot.) The intensity scales with the difference between the rocket's current velocity and the velocity at each point on the curve.

The goal is to kind of show you what the powered trajectory will do as you sweep it around in a full circle, without you having to do that. It is pretty much as I'd envisioned it, but I'm still learning to fly with it so I'm not sure yet about whether I like it or not. I've posted a version to the game's site if you want to try it out and weigh in with an opinion. Remember that the gravity part doesn't match up, though, so it is not yet good enough for precise maneuvering. (There's also the issue that this represents the rocket's center of mass; the actual rocket occupies space around that so you have to take that into account. I might eventually try a Minkowski sum of the rocket's bounding circle with the curve if I'm feeling ambitious.)