What's more fuel efficient, orbit or slingshot?

Solution 1:

Parking your ship in low orbit allow for corrections as small differences in ascent produces huge deviations in orbital path

Firing your ship directly from ground forces you to find correct timing and hope variations in ascent profile won't produce too much deviations. Any error early on will only get bigger with time (which requires fuel for correction).

Direct ascent to planet escape velocity by simply going up requires huge Thrust-to-Weight-Ratio to fight gravity, which in turns wastes fuel. If you want to maximize delta-v, you want to save fuel. Saving fuel requires ascent profile with gravity turn. And good gravity turn will leave you almost in orbit, so you can as well go for stable orbit.

For good fuel efficiency once in space you will usually go with low Thrust-to-Weight-Ratio, therefore burn will be long. Long burns and achieving escape velocity without stable orbit do not go in pair. Lack of stable orbit usually implies impeding lithobraking and loses of fuel for fighting gravity.

Parking in low orbit not only gives you plenty of time to correct inclination and select ideal transfer, it also allows you to prepare mission without any haste (haste makes waste, waste not). Launching to low orbit is also routine task, which can be perfected on its own, so it is easier to save fuel on ascent than on skipping orbit step.

Mun and Minmus gravity-assists on escape are, in practice, waste of fuel.

Kerbin escape velocity is ~3500m/s, Mun intercept (from LKO) is ~3000m/s. You can, in theory, save up to 500 on escape and gain few more hundreds m/s of velocity on Solar orbit. But such maneuver is ineffective

There is a lot of problems bound with gravity assists:

• Inaccuracy of burns is rapidly growing in effect with distance you wish to travel. 1m/s mistake in early maneuver can make you miss Jool.
• Slight differences in orbital planes will throw you up or down, a lot.
• Direction with maximum speed gain from gravity-assists will usually differ a lot from your desired path (eg. prograde vs retrograde).
• Requires timing, which is problematic because moons are traveling around planet quite fast.
• Minmus is heavily inclined, which will obliterate your desired inclination.
• Minmus is even further, and a lot smaller, than Mun. Fuel saving will drop, probably below expense on fighting its inclination.
• Binding your timing to moon position breaks your transfer window, which can costs in hundreds of m/s.
• Inaccuracy of gravity-assists require further corrections, read as "more fuel".
• Being ejected into weird orbit costs a lot of fuel to correct.

Note: Mods like MechJeb can perform maneuver with accuracy up to 0.01m/s for good rocket. BetterBurnTime is also very useful. And without some form of precise maneuver node editor (MechJeb got one) don't bother with precise encounters.

Same goes for most of planets and their moons. Moons are generally too far and too small. Except Jool. Jool is gravity-assist heaven.

However there are good use cases (but mostly when you arrive to planet, not leave it)

Moon gravity-assists can give you huge inclination change for virtually no cost

Moons, especially inclined like Minmus, can be abused to launch into inclined orbit. Changing inclination in planet sphere of influence costs a lot less than on solar orbit, and small change can be increased (or decreased!) by gravity-assist.

Moon gravity-assists are very useful in planetary capture.

Even with small rocks like Ike you can:

• Drop your speed by thousand or two. Because with interplanetary speed even small percent becomes a lot.
• Change your orbital path. At small expense of d/v (think in dozens, not hundreds m/s) you can abuse moon to fling around (often reducing speed) and into planet atmosphere for aerobraking.
• And of course greatly change your orbital plane.

Jool is gravity-assist heaven

You wan't some gravity-assist? Go play around Jool.

Having five moons Jool offers insane gravity-assist possibilities (aside of Jool itself being great for it). (Example with three-moon gravity assist)

• Tylo, with 80% of Kerbin gravity but no atmosphere allows for great fuel efficiency as you can get Periapsis very, very low. Gravity-assist alone will be very potent.
• Laythe, also 80% of Kerbin in size, but this time with atmosphere. You can do gravity-assist or aero-braking, or both.
• Other three rocks allows for fine tuning of orbit when Tylo and Laythe are overkill (or inaccessible at the moment)

I will add some screenshots when I'll find time to sling some rocket at some space rocks.

Solution 2:

Scott Manley has a couple of videos where he explains this. Taking advantage of the Oberth Effect for a gravity assist can help you in some cases. But for others it may not worth the trouble.

The most fuel efficient way to attain a desired orbit is to only burn at periapsis (lowest point in your orbit), because at periapsis the gravity of the body you are orbiting helps to max out your speed. If time is not a factor, you can wait while your craft orbits to an optimal position just prior to periapsis, and then burn until you are a little ways past it.

When getting into orbit on a launch from Kerbin, you don't have that luxury. In fact, you're pretty much being forced to burn at apoapsis (highest point in your orbit) when gravity is actually working its hardest against you.

As for slingshotting around the Mun, Scott Manley demonstrates that in this video (Mun slingshot starts at about 4:08):

Here he tries to establish a transfer orbit to Jool, and actually spends more fuel while slingshotting around the Mun vs. a direct burn. Now you might have better luck if you wait for the Mun to line up just right, so you could try experimenting with that.

On the other hand, in this video he demonstrates slingshotting around Jool to get a return trajectory to Kerbin (10:30):

The big difference here is the gravity of Jool is much greater than that of the Mun's, so it has an easier time influencing and helping your transfer orbit.

Now, just because Scott Manley tried it and couldn't make the Mun slingshot yield high rewards doesn't mean it can't be done. Give it a try and see. But even if you can make it work, you probably won't save enough fuel to make it worth the effort.

Solution 3:

Using a gravity-assist around Mun can give you quite a lot of additional delta-v for free. Minmus not so much, because its gravity is so low and it is so hard to hit.

However, gravity assists are much less precise than just doing a single burn. Especially when you want to perform more than one. Also keep in mind that they take time to set up, so when you are going for an interplanetary transfer, you might have trouble meeting your launch window. That means a mission with gravity assists takes a lot more time to plan, and a lot of fiddling with maneuver nodes and minuscule in-flight course corrections. Figuring out a way to get more fuel into orbit can sometimes be a much less time-consuming task.