When to launch for orbital rendezvous?

[Pie Guy 13]

I'm building up my first space station (named LKO-1 for Low Kerbin Orbit One), and I've had a recurring problem of having to orbit a few times before I can get a good intercept. So, I'm coming here for help: what position should LKO-1 be in when I launch to intercept? It orbits at ~115 km.

[bewing 3,070]

You need to know how long it takes for your rocket to get to orbit. Then you need to know how far downrange from KSC it is once it gets there. Then you need to know how fast your station is moving. Then you multiply and subtract.

Or, you can do it the easy way, and just pick out a landmark, and practice a few times. When the station crosses over the landmark, you launch.

Once you get a huge amount of expertise at all this, there is something called a "high-speed rendezvous". By adjusting your thrust during launch, and paying close attention to your resulting orbit, you can achieve a fairly close rendezvous even with a minute of variability in your launch timing. Your rocket changes its velocity by a huge amount, so varying timing of that velocity change can modify the amount of time it takes to get to orbit by a lot.

[Reactordrone 601]

It will depend a little on your thrust to weight ratio and flight profile but in general you want to launch before the station gets to your position, roughly when it reaches the western shore of the continent where the space centre is.  If you launch a bit early you just increase your apoapsis to rendezvous. If you launch late keep your apoapsis low to catch up.

[Hotel26 2,202]

tldr: many adhere to the rule of thumb of when your target is over the nearest southern tip of the desert to the West of KSC and over one body of water.  That's 110W or 36 degrees uprange [KER Rendezvous display Phase Angle 324 deg.].

                                                                                     

I find KAC, Better Burn Time and KER indispensable for a "direct launch to rendez-vous".

If the initial phase of the launch goes well, it's easily possible to tune the apoapsis directly from the KAC "Closest Approach" display for "within 1 orbit".  With practice you can get a rendez-vous at or near launch apoapsis within a few kilometers.  You really need Better Burn Time due to the massive closure rate for this rendez-vous to know when to fire.  This maneuver will be performed Target Retrograde.  And it's performed in place of circularization, so it's an alteration to the typical launch pattern.

To be clear: your lift-off burn continues until you get the closest approach indicated (rather than a particular apoapsis).  Then instead of circularization (if everything works out), your target retrograde burn completes the rendez-vous (zero relative velocity) and you are hopefully much closer to your target than 10 km!

I know of no maneuver or operation in KSP more exhilarating than this one: stopping within several kilometers directly at the end of launch (precisely because, until the very last couple of seconds, you remain in complete disbelief that you will be stopping in time!).

[You beat me to the punch, @bewing!]

Edited March 7 by Hotel26

[Empiro 108]

You can launch just as it flies overhead. You'll be behind your target and you should go into an orbit just over 70km. You'll be catching up and shoud be able to get an encounter fairly quickly. 

[paul_c 424]

Personally in KSP I don't worry too much about when to launch, to rendezvous with something, if its on the equatorial plane.

If its not equatorial, then obviously there is a defined (well, two) instantaneous "launch windows" per day which will intercept with no extra plane change.

It is much more important to 1) get the launch right (for other stuff, eg staging, get the Ap high enough, don't lose comms, etc) and 2) get as good as possible onto the same inclination. Yes, even if the station is on the eq plane you could still waver off it with a manually flown launch, so its worth looking at it when ascending. It is far cheaper on fuel to match the inc on the way up, than get into a low orbit then change it. And there's an amount of skill in flying it to a precise inc - you need to think about the left/right as well as the gravity turn, also bearing in mind for some of it you'll be coasting up so you can't turn/change then.

Personally if the station is at 115x115km I'd launch deliberately 'late' (a bit) to a 70x70 or thereabouts orbit, then change it to 70x115, then do a few orbits to catch up (but not overtake) the station, then gradually match the orbit eg 110x115, 114x115 to get a nice close intercept, then with about 2km to go (or less if you're using tools to help you fly) start pointing and flying at the station.

Edited March 7 by paul_c

[Hotel26 2,202]

 

A night-time launch; couldn't be helped.  (Tremendous screw-up @ 5:55, but survived.)

Critique:

1. I should have selected Retrograde immediately after selecting Target Mode.
2. and waited for attitude stabilization before S2 separation
3. out of habit, I used a long, flat trajectory which delays the rendez-vous, resulting in a bulging apoapsis (121km) for a target at 90km altitude.

It does demonstrate, however, that this approach is quite resilient to noise in the inputs.  All that matters is a) how close you get, b) how prompt you are on triggering that target-retrograde burn and c) your inclination is not too far off (as that will be the final arbiter on accuracy).

Edited March 7 by Hotel26

[18Watt 103]

@Pie Guy, if you are getting rendezvous within a few orbits, you are doing fantastic, I consider getting a rendezvous within 4 or 5 orbits a success.

I usually play stock KSP (no mods).  It is possible to launch directly to rendezvous without mods, but I find it extremely difficult.  In particular, I have trouble timing the final circularization burn.  The mods @Hotel26 suggested, KAC and Better Burn Time, will make it much easier to achieve a launch to rendezvous.

My suggestion is that while practicing this, plan on using more fuel than you normally would.  Eventually, you will be able to launch direct to rendezvous without using much additional fuel, but my first attempts required an extra 600 DV or so.  I’m not saying launching direct to rendezvous is inefficient, but rather that on my first attempts I made a lot of mistakes that cost me fuel.

[paul_c 424]

The danger (well its not really a danger....an inefficiency) with shooting for a "direct to rendezvous" is overshooting then needing a correction (and possibly another correction, etc). Each correction 'costs' fuel, because in orbital mechanics, changes cost fuel not time; and the bigger the change needed, the more the cost.

Compare it with a "conventional" rendezvous, lets assume to a 100x100 station:

1. Launch to (say) 75x75 initial orbit, which might take 10-15 orbits to intercept or thereabouts I don't know the maths but that might be 90deg phase behind
2. Observe the distance apart and at (say) 1-2 orbits to go, burn for a 75x100 orbit.
3. Then take another few orbits, then go to (say) 99x100, and take another few, then make a tweak to intercept close, by orbiting (say) 99.7 x 100
4. Once close, dock

Steps 1-3 all "go in the same direction" and of course, note that for a controlled docking at slow speed, the orbits must be similar so the final orbit will always be ~99x100.

By setting a time pressure on the docking, you lose the ability to remain doing the closing approach from "one side" over a number of orbits, instead you must do a big "get the intercept" then another big "slow down to control approach speed" burn.

Sure its possible with the same fuel use, but it would need an amount of precision in the ascent to know quite precisely, where you'd be to do that big, (less than) one orbit "get there" encounter. Think about it.....in the worst case scenario, as you sit on the launch pad, the station is whizzing around at >2000m/s. So as each second passes, its 2000m further away than the previous second. So your precision to get within 2000m is a single second of "launch window", assuming you know exactly how the ascent will go. Fair enough its true to say that the actual way to fly it would lie somewhere between the "conventional" and the "hit it in one" style, ie you'd do sensible corrections during the ascent, but with the margin (of not worrying about when you'll encounter/dock) taken away, efficiency can no longer be maximised.

I appreciate its a lot of fun and dynamic if you can pull it off though!

[Hotel26 2,202]

17 hours ago, paul_c said:

I appreciate its a lot of fun and dynamic if you can pull it off though!

Every interesting challenge KSP presents is fun to study and master.  That's why I don't think this is either-or.

It's good to start with exactly the question the OP is asking and the result is important when you have a minimal dV launch that fails if it is not efficient.[*]

Then (as you say) it's fun and instructive to master the direct launch to rendez-vous.  So master both.

                                                                                       

Then think of SpaceX and its "burn back" self-landing boosters.  These CANNOT be optimally efficient in terms of orbital mechanics because the overall dV delivered to the payload (and upper stages) has to be less, as some thrust is reserved for the burn-back.  Why does SpaceX do it?  Due to the commercial/economic equation of fast recovery/recycling.

                                                                                       

Which sets us up then to think about how we play KSP.  Once you've demonstrated the ability to do the super-efficient, tight-budget launch, do you want to repeat this for every launch for the rest of your KSP career?  I'm referring to all the time for all of those finicky rendez-vous maneuvers.  I finally decided I didn't.  (Although I still have occasion to use both kind of launch.[*])

So: choose both.  Double your fun.  Maximize your own, personal playing efficiency.  Life is short.

[*] above.  Titan 3 is exactly the kind of launch that I would normally do "super-efficiently" to a 72-75 km circular orbit -- with NO rendez-vous -- and just leave wherever it arrives.  The client space stations simply then send nuclear tugs with a relatively large fuel capacity to come rendez-vous with the Titan; and then cart the fuel back to the space station.  Or in some cases, directly to a client ship waiting in orbit for a refuel prior to interplanetary departure.  A whale with pilot fish...

Edited March 8 by Hotel26

[18Watt 103]

3 hours ago, Hotel26 said:

Then think of SpaceX and its "burn back" self-landing boosters.  These CANNOT be optimally efficient in terms of orbital mechanics because the overall dV delivered to the payload (and upper stages) has to be less, as some thrust is reserved for the burn-back.  Why does SpaceX do it?  Due to the commercial/economic equation of fast recovery/recycling.

Well said.  I suspect very few real-world orbital launches use a profile optimized only for fuel efficiency.  With humans on board, you have to consider acceleration forces and abort scenarios.  Aside from that, you may need to reduce aerodynamic stress, avoid overflying populated areas, or have launch window restrictions.   Even if the engine(s) are throttleable and/or re-lightable, you might want to limit the number of re-lights you need to do to increase reliability.

[Hotel26 2,202]

So, just for fun, I've started testing this with regard to the OP's question.  I'll describe the methodology and then publish some results when I get finished.

Two things become clear at the start:

1. Differences:
   • different vehicles perform differently
   • different pilots fly differently
   • different days: different results (but hopefully this will average out)
2. It should be possible on any standard launch to rendez-vous in one orbit.

The conclusion of point 1 above is that everyone interested would have to test this for themselves.

I used to fly a fairly high trajectory but find these days that I use a flatter, faster trajectory that gets me a lot further downrange before apoapsis.  I've already found I need to wait later before launch.

                                                                                                      

I put a small craft into a perfect 100x100km equatorial orbit as my reference target.

When it hits the "mark" (nominally starting for me at this 36 degree uprange point) I launch and then fly the launch vehicle in a standard way: e.g. 60 m/s pitch-down 5 degrees and then fly SAS Sfc Prograde until AP becomes 100km .  Circularize at 100km altitude and then note the distance to the target: before or ahead.

Then tune the AP upward if ahead or PE downward (but no lower than 70 km) if behind.  I do this looking also at the intersection markers in the Map View, tuning the nearest distance to a minimum.  That should get me rendez-vous in one lap unless the launch window or flight trajectory was really wrong.

Your closing dV as you initiate the target retrograde burn (times 2) is a measure of the inaccuracy penalty of your operation.

Returning to the target distance at circularization, this is the amount to tune the target launch mark by.  Note that 1 degree longitude is equivalent to 10.47km circumference (not quite the same as line-of-sight, but near enough for government work).

It seems like this exercise is worth doing for each vehicle that one flies frequently.  Knowing this launch point should similarly optimize the DL2RV (direct launch to rendez-vous).

 

Edited March 9 by Hotel26

[Spricigo 1,146]

7 hours ago, Hotel26 said:

Once you've demonstrated the ability to do the super-efficient, tight-budget launch, do you want to repeat this for every launch for the rest of your KSP career? 

Personally..Yes.

As you said, it boils down to how we play KSP. Is not the extra fuel required  for an "inefficient" launch that bother me, but rather the extra effort/attention. So, I take my time to design LVs capable of automatically following the same flight profile each time. Then is a matter of selecting the LV, wait/warp to the launch window, fire and forget. 

However, I'm in full agreement with what seem to be your main point :  Is often a good idea to compromise some "efficiency" to be "effective".

More often than not,  are the missed opportunities that make you inefficient.

[Hotel26 2,202]

OK, so I finished my testing with the following variables being noted:

1. target station at 100km altitude
2. my launch vehicle was a Genesis
3. Hotel26 at the controls (YMMV)

And I found that a target phase angle of 335 gave me a 14.1 km intercept (which I ignored), an actual closest distance of 10km (while still performing the circularization burn) and a final lagging distance of 19km.  (That's less than 5 secs of travel at orbital speed).

If I were to do another test iteration i would try phase 333, which translates to a target longitude of 102W.

Hopefully, it the above doesn't actually answer the OP's question, it details the methodology to self-determine it.  (And I learned something myself in the process.)

Edited March 9 by Hotel26