Sunday, July 29, 2012

There's always one more thing...

...This time it is deploying various jettisonable objects. I could just Do It, but there is always a philosophy problem.

Jettisoning things is easy. We know the exact time and place ahead of time where each object will be jettisoned. It's easy to get an exact analytical solution ahead of time so that all we need is the time an object is jettisoned, and its position, velocity, and orientation at that time. There is an analytical solution to its future trajectory, and just apply some random spin to its orientation.

Except, I don't know that there really is an analytical solution when drag is significant. We can fake it with the entry balance masses, since drag is not a big part of their lives. But what about the heat shield? What about the backshell and parachute? What about the descent stage in its flyaway phase? We'll save that for last.

Apparently there is such an analytical solution, but only for drag proportional to the velocity, not the square of the velocity, which is the regime in which conventional drag coefficients work. There is another solution, but the horizontal and vertical velocities are implicit functions of each other. So, it's on to everyone's favorite brute force application! No, not a hammer, a numerical integrator. Almost the same thing though, I can see why there would be confusion.

Now the problem with numerical integration is that it requires a state. It requires memory. And due to the nature of the animation loop (I haven't restored persistent variables to Megapov yet, and it wouldn't do well in the Atomic Banana Peeler anyway) there is no convenient way to maintain this state. So, on each frame, we get to integrate all the way from the time of jettison to now. We can stop when we know the object in question is off-screen, so it will be for a few seconds at most.

Here's the current version of the animation, with the art for the descent stage and rover in place. Almost all the art is done now. I need some decorations on the backshell, to match reality and to show the capsule rolling (or not). Then I still want to char the backshell, and perhaps the heatshield too, as a function of integrated heat.

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