Over the years with KSP1 and KSP2, I've come up with a set of mental rules for how to do low-fuel manoeuvres.
Understanding how orbital mechanics works is one thing. But getting a good feel for how to set up manoeuvres that minimize fuel is much harder, because it's harder to know if another trajectory would work better (and it's tedious/impossible to check all the different routes).
Here is my set of rules-of-thumb for the best way to achieve various goals.
Help me out, are any of these wrong? Or am I missing tricks?
LAUNCH
In vacuum, start off at around 45° above the horizon, for a few seconds, then switch to horizontal ASAP (subject to clearing terrain, and TWR). With ∞ TWR, you'd go horizontal (East) immediately, but need to gain a teeny bit of height in practice. In an ideal world, your Ap would appear directly opposite on the far side of the planet (180° from launch site) but there's no real efficiency gain if it's only 90° ahead. TWR has no impact on δv required (as long as it's high enough that ~nearly all time is spent burning prograde = horizontal).
In atmosphere, burn upwards, set up a small angle fairly early on (5-10°) so you can accumulate some horizontal speed. Keep angle of attack fairly shallow and follow the gravity turn around. Eve needs a sharp hairpin with quite steep AoA once out of atmosphere. Duna AoA is lower as you can turn earlier. Kerbin somewhere in between. Aim for Ap just above the atmosphere, coast to Ap, and circularise. Ideally a lot of the time raising the Ap is spent burning close to horizontal (and always with low AoA = close to prograde marker).
LANDING
In vacuum, do a tiny burn to bring Pe down to kiss the surface, then fiddle with the manoeuvre node to work out when to start a suicide burn. Ideally, you'll end up at 1km altitude with 100m/s of mostly-horizontal velocity, and can then coast down to do one final burn of 150-200m/s at ~45° above horizon to touch down.
In atmosphere, just use aerobraking / chutes / wings etc (Duna fuel-assist). Not many ways to waste δv really.
MUN TRANSFER
The "tutorial way" is optimal (to my knowledge). No assists possible.
From a perfectly circular orbit (LKO), add a manoeuvre node, add pure prograde until the orbit kisses the Mün's orbit, then drag in around until you find the moment of transfer. At most one LKO's worth of delay (no need to pack snaks for your crew). It will be around 90° behind the Mün.
If the initial orbit isn't perfectly circular, then you'll have to fiddle with the prograde quantity as you drag the node around.
With minimal cost, you can enter Mün at any inclination (eg get a polar orbit there for free) just by adding a few m/s of normal component.
Use RCS for mid-course correction around halfway through a transfer, if you couldn't get a nice close Pe with the trans-Münar burn. (I like to limit my throttle usage to ≥10% or ≥50% depending on how much realism I want. Makes is harder to execute manoeuvres to the nearest 1m/s or less.)
Capture burn at Mün Pe, Nothing to say there.
MINMUS TRANSFER
You can use a Mün assist. Here's where it gets harder.
I don't know how to get a good transfer window for these assists! Any hints gladly accepted. It's basically very hard to eyeball, and the game's tools are insufficient.
Ideally, you'd do a Mün transfer, pick up your gravity assist, and have Minmus lined up so that on exit from Mün you head out for an encounter immediately. Tough to predict those windows.
What you don't want to do is end up with a rubbish Minmus encounter with high a Minmus-relative velocity. Defeats the point of the Mün assist!
The Mün assist should try and reduce the Minmus-relative inclination as much as possible.
So, I pack snaks for my Kerbals, and do a Mün assist at any old time, to raise my Kerbin Pe out to an orbit close to Minmus. Then I do some fairly small Ap/Pe adjustments to "rendezvous" with Minmus. If you're in a hurry: do bigger Ap/Pe adjusts, so you get the encounter within a few orbits (= months...). If not in a hurry (probe core), then do small adjusts and wait several orbits until you see the intersect is fairly close, so a small adjustment will yield an encounter.
You can't get a second assist off the Mün (unless you were going for Mün assist — Minmus assist – Mün assist — Minmus capture; but I highly doubt you could make significant savings that way, as the first assist already kicks you out to an orbit close to Minmus, so the capture is already cheap, and any extra assists will chew up δv for adjustments).
DUNA/EVE TRIP
The basic way is: burn prograde at a transfer window to get an encounter in one burn from LKO + one mid-course correction.
But how you do actually get those quoted numbers for optimal transfers?
• Burn prograde only (to start with), on the dark side of Kerbin to go to Duna (from prograde=Eastwards LKO orbit), the light side of Kerbin to get to Eve.
• Drag around the start time of the manoeuvre node until you see your departure path from Kerbin going absolutely parallel to Kerbin's orbit. That's your "radial component" (towards Kerbol, not Kerbin) of the transfer, which you get not from burning radially, but from timing when you start the transfer burn.
• When you're bang on the transfer window, the most efficient burn will have you leave Kerbin's SOI going parallel to Kerbin (correct me if I'm wrong).
• If you're even a little off, you'll have to drag the node a bit until you get the encounter, ie add in some Kerbol-radial component to force the encounter.
Finally, there's a choice to be made.
1. You can either have zero normal component in your transfer burn, and do all your inclination adjustment mid-course.
2. You can split your inclination adjustment: include some with the transfer burn, to reduce the relative inclination, and move the AN/DN to be further from Kerbol. Adding in 200-300m/s of normal to your transfer burn is basically "free", and can reduce the mid-course correction a lot.
3. If going to Duna/Eve (or returning to Kerbin!) then you don't need to match inclination. Instead, you just add a big normal component to the departure burn, to shift the AN/DN to the point of intercept. Then you'll get a very very high-cost encounter (with very very high relative velocity) but you can use a heat shield to soak it all up.
And... which of these cheapest? Well it depends. I think that for a Duna/Eve transfer, there's not much in it between 1 & 2, but trying to minimise inclination adjustment as part of the departure is generally (always?) slightly cheaper. It's hard to be sure, because each departure window has slightly different cost, due to the AN/DN falling at a different point during the transfer. If you're happy arriving at high inclination, I've found (3) to be competitive with the mid-course correction but I think not always (depends, for your current transfer window, where the AN/DN falls).
No assists from any planets possible on the way to Duna/Eve. (It would be perverse to get an assist off Jool to get to Eve, or off Eve to get to Duna. I don't think any saving at all is possible. It's possible a Jool assist could save cost on the way to Duna? I've not plotted that route myself though to check.)
You can get an assist from the Mün to aid the departure burn. Pretty fiddly to set up, but I do it sometimes. When you're at the transfer window for Duna/Eve, you warp until Mün is 90° behind your planned departure course (ie Kerbol-Kerbin-Mün are in a line). Then do your transfer as normal, but, by the time you're passing Mün's orbit you'll get an encounter. You have really limited wiggle-room: Mün just is where it is, and you can wait 1/2/3/4 orbits to get a couple of choices for where it is when you encounter it, but you that's it. Luckily, it's OK to end up with a high relative-velocity encounter with Eve/Duna (assuming you're aerobraking), so you can still get a decent low-Pe assist from Mün and still make the encounter.
I think if you're aiming to minimise the capture burn (eg doing propulsive capture at Duna/Eve) then the Mün assist could actually make things worse, if the Mün's position as you pass forces you choose an intercept with Duna/Eve at a higher relative angle. (Rule of thumb: kissing orbits = cheap capture; orbits crossing at a larger angle = expensive capture.)
BI-ELLIPTIC TRANSFER
It's nice in textbooks. But not needed for any missions in KSP2 (so far). The planets are all quite closely spaced, and you start out at Kerbin in the middle. The KSP1 mission "put a probe in retrograde Kerbolar orbit" required it.
RENDEZVOUS
Assume any two coplanar orbits, and you need to rendezvous.
Do a minimal prograde burn to get a kissing orbit on the target. If target orbit is higher than the initial orbit then obviously want to burn near the Pe (rather than the Ap). This might not be a burn at Ap/Pe, because you drag the node around to bring your Arg-of-Pe into alignment. For most (all?) starting configurations, I think this is the optimal strategy, but I wouldn't be surprised if there are situations where it isn't quite.
Then you have a tradeoff between patience and efficiency. Doing a biiiig burn at the touching point will get an encounter in one orbit.
I sometimes use a spreadsheet. Set up columns for "one orbit; two orbits; three orbits" and put in your orbital period, the target period, and the amount of time you need to lose/gain to gain an intercept. Then brute-force it. Eg if target period = Z days, current period = 0.5×Z days, and you need to gain 0.1×Z days, then you can see that once the target has done 3 orbits and we have done 5 orbits, we'll get a very close intercept, so a teeny adjustment will make it happen.
Or, just watch the orbits go around until the intercept is close, and do one adjustment at the kissing point to make it happen on the next round.
Finally, you simply reduce relative velocity to ~zero at the intercept. This should be almost entirely prograde/retrograde.
MOHO TRANSFER
Moho is special. It's the only planet where the cost of the inclination change outweighs the cost of the Hohmann transfer.
So, it's better to do the departure burn at Kerbin-Moho's AN/DN, not worry about getting an encounter at all (just get that rel inclination to zero), and then do a deep-space adjustment (no Oberth effect) when you hit Moho's orbit to bring about an encounter in not-too-many orbits. Pack snaks for Kerbals!
Hopefully you won't need to change the orbit much to get the encounter. Then capture at Moho as normal.
But better still: interplanetary slingshots!
I think this is the optimal strategy for a one-assist journey to Moho. (But if another route via Duna or Eve is better I'd be happy to learn.)
• Do a standard Eve transfer - but work backwards so that when you encounter Eve, it's at the Eve-Moho AN/DN. This can take some looking ahead over the transfer windows - and you won't be picking an "optimal" transfer to Eve.
• Remember - for assists where you want to reduce your eccentricity, you need to encounter the body you're passing at a high angle (orbits not tangent). Encountering at low angle (target orbits) will increase your eccentricity.
• So for the Eve assist to bring your Kerbol Ap down to Moho, you actually need to encounter it at a steep angle, which means you're not aiming for a conventional transfer window at all.
• Obviously you fiddle the normal component of the Eve encounter to get your correct inclination for Moho. You don't need to meet Eve at zero rel inclination to Eve.
• If you work backwards from an Eve encounter at Eve-Moho AN/DN, then you won't get a Moho encounter directly, you'll have to rendezvous with Moho as previously.
I haven't assessed two-assist journeys. (Does anyone know the best routes? Duna then Eve, or Eve then Duna?) Some further savings should be possible, but I have no hard data or intuition on which routes are the best.
DRES/JOOL/EELOO TRANSFER
TBD. I have some transfer tricks I use, but I'm really not confident I know which is the best one-assist or multi-assist route out & back. All I know is that lining up more than one assist without tool-aided planning is hard (for me).
