Kerbal Space Program

Posted on Wed 25 August 2021 in games

I am usually late to proverbial parties, but I think I’ve outdone myself by discovering the computer game Kerbal Space Program roughly 10 years after it first became playable. It’s the kind of game that triggers my “I’ll optimize this by writing a script”, so here are a few of the tools I wrote, or interesting tools I found online:

And some random notes:

  • When launching from KSC to rendez-vous with something in a circular orbits at 100km altitude: For vertical launches with "my usual ascend profile", launch when the target is 26º before the KSC position (viewable as Phase Angle). For spaceplane launches (with RAPIERs and 10º pitch up all the way), launch when the target is 16º before the KSC.

  • When starting from a 100km circular orbits around Kerbin, a deorbit burn down to Pe=40km will touch down 152º later. Craft consists of:

  • For interplanetary travel, you need ~930m/s of Δv to leave Kerbin SoI starting from a 100kmAGL orbits, and an additional 100~1000m/s to reach other planets. Design for a high enough TWR to do this in a reasonable time. Multi-impulse departures are possible: as long as the apoapsis is < 8.9MmASL (9.5Mm), the Mun will not alter your orbits. The below table tries to keep burns <2 minutes until we cross the orbits of the Mun.

TWR [GKerbin] Burns for escape Burns for 2100m/s
1.79 53s 120s
1.5 63s 56s + 87s
1.0 95s 84s + 130s
0.75 111s + 15s 111s + 174s
0.696 120s + 16s 120s + 186s
0.5 120s + 47s + 23s 120s + 47s + 261s
0.25 2×120s + 94s + 45s 2×120s + 94s + 522s
0.1 6×120s + 115s + 113s 6×120s + 115s + 1305s

  • Most engines produce a constant thrust while on. Its fuel consumption scales with the time the engine is on. But the energy scales with the distance the force is applied. This means that running an engine at a higher speed, yields more kinetic energy for the same amount of fuel. This is known as the Oberth effect.

    When starting out at Minmus, this means that it could be beneficial to first spend some ∆v to dive into Kerbin, and burn at periapsis for the escape trajectory. Escaping from Kerbin from a Minmus orbits requires at least ~115m/s. The boundary seems to be 274.1m/s: for ∆v's above that, it's optimal to first burn 228.1m/s to put our Kerbin periapsis at 70km (just above the atmosphere), and burn the rest of our ∆v there. For a 500m/s total ∆v, this boosts our hyperbolic excess velocity from 670.1m/s (when expended at Minmus orbits) to 1294.8m/s when diving first and spending the remaining ∆v near Kerbin. This is the case for all trajectories to other planets.

    Hyperbolic Excess Velocity after burn(s) from Minmus Orbit

  • The orbits of Minmus has an inclination of 6°. Ideally, we want to launch in this orbital plane to avoid plane-change maneuvers. Launching into a 6° inclined orbits can be done from launch sites with a latitude of less than 6°, i.e. the Kerbal Space Center. The Longitude of the ascending node of Minmus’s orbits is 78°. So we can either launch slightly northbound when KSC passes 78° right ascension, or slightly southwards when KSC passes 258°. In-game, it’s not easy to read out the current right ascension. We can, however see the Longitude of the Ascending Node (LAN) of our current orbits in the second orbital info pane:

    Orbital pane 2

    Since KSC is in the southern hemisphere, our current position is 90° before our ascending node. In other words: launch slightly south (97°) when LAN reads 348°, or slightly north (83°) when LAN reads 168°. You need to eyeball these directions, especially at the beginning of the launch, when mostly vertical, where the Heading-indicator is very sensitive. I do my gravity turns to the right. In that case, you can align the 90° line on the navball with the longer tick mark of the G-meter for 83° departures. 97° departures should aim for the letter G in the G-meter.

    Navball aimed for 83° departure Navball aimed for 83° departure

  • Launch windows for the first few years:

Departure Date Arrival Date Destination ∆v (m/s)
Y1 D98 Y1 D64 Moho 5165
Y1 D196 Y4 D138 Jool 5043
Y1 D231 Y2 D75 Duna 1678
Y1 D242 Y6 D227 Eeloo 3635
Y1 D269 Y1 D405 Moho 5031
Y1 D390 Y3 D93 Dres 3526
Y2 D86 Y2 D243 Moho 4833
Y2 D160 Y2 D357 Eve 2741
Y2 D242 Y5 D304 Jool 4978
Y2 D245 Y2 D386 Moho 5242
Y2 D257 Y7 D20 Eeloo 3556
Y2 D393 Y3 D86 Moho 5748
Y3 D83 Y3 D225 Moho 4481
Y3 D120 Y4 D283 Dres 3072
Y3 D270 Y7 D63 Eeloo 3644
Y3 D275 Y6 D216 Jool 4902
Y3 D305 Y4 D160 Duna 1645
Y3 D366 Y4 D63 Moho 5695
Y3 D401 Y4 D162 Eve 2560
Y4 D84 Y4 D207 Moho 4179
Y4 D226 Y6 D108 Dres 3348
Y4 D289 Y5 D40 Moho 5383
Y4 D294 Y7 D365 Eeloo 3943
Y4 D306 Y7 D159 Jool 4976