Mission to Mun

“It ain't all buttons and charts, little albatross. Know what the first rule of flying is? ... Love. You can know all the math in the 'verse, but take a boat in the air that you don't love, and she'll shake you off just as sure as the turnin' of the worlds. Love keeps her in the air when she oughta fall down, tells you she's hurtin' 'fore she keens ... makes her a home.”
~ Capt. Malcolm Reynolds, Firefly

This is a recollection and log of the events that led to the first big milestone of my space program: a manned mission to the Mun which landed kerbonauts and safely returned them to Kerbin.

The mission

I spent a considerable amount of time designing the mission, which included running the calculations of just what's required to achieve this feat, testing out various rocket launch stages for the mission components, as well as practicing orbital rendezvous operations.

The final design was that of the Apollo missions "Lunar Orbit Rendezvous" mission mode: a two-module ship leaves the planet and travels to the natural satellite and gets into orbit. Then one module decouples, lands on the moon, gets back into orbit and makes a rendezvous and docks with the module left in orbit (hence the name of the mission concept), The combination then returns to planet. The main difference between my mission design and the Apollo misions is that in my design the two modules were launched separately and docked together in low Kerbin orbit.

The first component of the mission vehicle is the Command Module (CM), shown below:

The core is the command capsule with capacity for three kerbonauts; this is the part that is meant to return them safely to Kerbin, having a heat shield (in theory), and three parachutes. The command capsule sits on top of three decent-sized fuel tanks and a big engine. Together, they constitute the ship with the capacity to take the lander to the Mun and back.

Here's the calculations that were involved in designing this. In order to reach Mun orbit from a low Kerbin orbit, you need a Δv of 860 m/s for the Mun intercept, plus 210 m/s for getting into orbit. That's 1070 m/s total. Since it's got to make the return trip too, the actual requirement is double that figure: 2140 m/s.

Since it's quite heavy (it weighs 34.8 tonnes fully loaded) it needed a fairly powerful launch rocket:

The final stage (stage 2 in the screenshot) is the Command Module itself. In this screenshot, a Δv budget of 4226 m/s is shown. But don't forget that the Command Module will push the lander all the way and back, so you have to consider its mass too (including fuel).

In order to simulate the effect of the docked lander (which weighs 8.74 tonnes full load), I stuck an extra fuel tank with a comparable mass (there's a tank with a mass of 9 tonnes) on top of the CM, just so that MechJeb factors in the extra weight. With this, it said that the last stage had now a Δv budget of about 3000 m/s. This is considerably more than the required 2140. But I'd rather have 50% extra since it's my first attempt at such an enterprise and cost is not an issue in the game yet.

As for the launch rocket shown in the image above, remember that around 4550 m/s (eek!) of vaccum Δv are needed to get into low Kerbin orbit. Since this stage launches only the CM (the lander goes up separately), the Δv figures shown there are appropriate. The rocket has three stages with a total combined Δv of around 4800 m/s, so it should be enough to take the CM into orbit and still have enough fuel to do the orbital maneuvering required for rendezvous with the lander module (with some room left for error).

The second component of the Mun mission is the lunar (munar?) lander, or Lunar Module (LM):

The design is simple: a capsule for two, landing legs, a small fuel tank and an engine (and other assorted parafernalia: small solar panels to maintain electrical power, a retractable ladder for the kerbonauts, some flood lights). In order to get from a low (14 km) Mun orbit to the surface, you need a Δv of 640 m/s (quite a lot!); again double that to factor getting back, so around 1300 m/s total. As you can see from the screenshot, MechJeb says the actual lander (stage 0) has a Δv budget of 2249 m/s, so again I have a considerable room for error.

Another important consideration for the lander design is the thrust-to-weight-ratio (TWR): the thing has to be able to slow itself down to zero for touchdown, and then lift itself up back into orbit. As you can see, MechJeb calculates the TWR for each stage. For the lander, it says it's 0.57. Not good, right? But this figure is for Kerbin gravity. Kerbin has the same surface gravity as the Earth: 9.8 m/s² (and since it's about 10 times smaller, they had to make it 10 times denser to keep the same gravity¹: Kerbin has a mean density of 58 g/cm³; Earth has about 5.5). Mun also has the same surface gravity as our Moon: about one sixth of Earth gravity, or 1.6 m/s². Hence the lander's TWR on the Mun would be:

TWR = thrust / mg = 50 kN / (8.74 tonnes * g_Mun) = 3.51

So it seems we're good. I'm not sure what an optimal TWR is (we don't want the engine to be too powerful either, as it will not only be heavier and use fuel faster, but it'll also make the craft harder to control because of excess thrust), but at least it's well above 1.0.

The ascent rocket for the Lunar Module is smaller, of course:

Again, I used the required Δv to orbit to guide my design. The combined Δv of the final designed turned out about 4900 m/s (needed: 4600), so again it should be enough to take the payload into orbit and then have some left for maneuvering (and maybe even deorbiting spent stages, since you only need to get them into the upper atmosphere).

Continue to Launch ...

^{^} Since g ∝ M/R² and ρ ∝ M/R³, we have g ∝ ρR. So if Kerbin's radius is 10 times smaller than the Earth's, its density must be 10 times larger for them to have the same surface gravity.

Launch >