Testing an S1L1 Cycler in Stock KSP

[PLAD]

A cycler is a craft that repeatedly passes between two or more planets. The concept is that a large spacecraft with lots of amenities could be used as a residence for long interplanetary trips, smaller shuttlecraft would do the high-delta-V transporting of the crew between the destination planets and the cycler as it flys by. I've seen it discussed a lot in KSP, but here are some articles on the concept.  
Quick introduction:
Mind-numbingly complicated but thorough:
I'm not sure of the practicality of cyclers over fast high-energy missions, but the search for cycler paths fascinates me a great deal.
Earth-Mars cyclers are the most studied. Almost all papers I've seen make 3 simplifying assumptions about the motions of the planets to ease the search, as follows:
1) The orbits of Earth and Mars are circular and coplanar.
2) Mars' orbital period is 1.875 times Earth's.
3) Mars makes no change to the cycler's path, only Earth does.
As we shall see, these assumptions cause problems when it comes to actually flying these paths.
Some of the cyclers are described are ballistic, that is, after the cycler is placed in its path no further dV needs to be expended other than small course corrections. Others require substantial manuevers to keep them on track, for instance the Aldrin cycler requires a 230m/s or so correction every synodic period. Kerbalnot posted his execution of the Aldrin cycler in KSP here, check it out.

A key element to cycler trajectories is that the positions of the planets and the ship repeat after a set time, this time has to be a multiple of the Synodic period of the two planets. In the case of the ideal Earth-Mars this is 2.143 years, for the real planets it is 779.95 days or 2.135 years, for Kerbin and Duna it is 227.38 Earth days or 909.5 Kerbin days. This means that if your ship leaves Kerbin on a given day, and then comes back to it 454.76 Earth days later with the same energy and moving in the right direction it can repeat the Kerbin-Duna-Kerbin path indefinitely. Note the requirement about the energy! It is easy to find a path that goes K-D-K, and even one that does it in 455 days, but it will come back with much more energy that it left with because of that flyby of Duna! If you don't use a Duna flyby or a deep-space maneuver then it is tricky to get back to Kerbin when it is that extra .135 orbits further in its path, so the big challenge in cycler searches is moving the apsis of your Solar orbit forward.  
In the last few years a very good cycler orbit has been discovered for the Earth-Mars run, it is called an "S1L1-Ballistic cycler". Here's the paper by the original discoverers.
Here's a video of the path:
 Check out the low Earth and Mars intercept speeds, most other cyclers fly by much faster, especially ones that repeat after only two synodic periods. This cycler works even better with Kerbin-Duna because Kerbin's orbit really is circular, so running it in stock KSP is a great way to study it. Also Duna's SOI has a limit, so you can fly fairly close to Duna without it affecting your path unlike in the real world.
So I first figured out the S1L1 path without the flyby of Duna, I wanted to see if Kerbin system could emulate the flyby angles and rotation of the apsis necessary without the complication of flying by Duna. Here it is. Note I'm using Earth time, I'll translate to Kerbin time below. I'm using a great little mod called Slingshotter, it is helpful for planning this sort of thing.

 

Success! My ship returned to Kerbin 456.4 days after leaving it with only 9m/s less V-infinity. It only used 11m/s for course corrections after the initial 1255m/s to get started. Note that one cycler would only do the Kerbin-Duna run once every 2 synodic periods, and only in one direction. You would need another one timed to encounter Duna on the way in for the return trip, and another in-out pair to cover the other synodic periods. These limitations are common to all cyclers, I've seen paths that would require 14 cycler ships in order to be able to get a ride inwards and outwards every synodic period!
So in Earth days if you initially leave Kerbin at 0 you must fly by it again on day 301.24 and day 454.76. In Kerbin time this is day 1205 (2Y 353D) and day 1819 (4Y 115D).
Now I ran the path again, but this time with a flyby of Duna.

 

Ouch! The flyby of Duna added a lot of energy. I think this can be compensated for by flying by alternating sides of Duna, or one could stay outside it's SOI at all times. That leads to spending several days in the shuttle vehicle and a couple hundred m/s of dV to get from the far-away cycler to the planet and back though. The bigger problem is that Duna's orbit is not circular and so it will not be in the same place relative to Kerbin every 454.8 days!  This means you must change the cycler orbit constantly back and forth to pass close to Duna each time. This could be done using flybys of Duna, but I don't have a tool to calculate how to set this up yet. I need something that handles multi-orbit, symmetric double flybys.
In Kerbin time this cycler started Y1 d67.68, flew by Duna Y1 d104.3, 1st Kerbin flyby Y2 d2.8, 2nd Kerbin flyby Y2 d158.4. In Kerbin time this is start Y1 d267.72, Duna Y1 d414.2, 1st K Y4 d190.2, 2nd K Y5 d386.6.

Has anyone else tried this?

[Wallygator]

Wow. Well done!!

i have not the patience remaining from my wasted life to attempt what you have done above. Very interesting and well presented!

I find these types of explorations and testing are quite entertaining and informative even if I choose not to try them out. 

Fab!

[HebaruSan]

20 hours ago, PLAD said:

Has anyone else tried this?

I'll need a few more years of study to get to that point, I'm afraid, but reading posts like yours helps a lot along the way.

This is as much a question asked to learn as it is a suggestion, but rather than directing the Duna energy solar-prograde or -retrograde, what about using it for plane changes, i.e., passing over the north and south poles? Would that help V_inf to stay in the right range?

[dr.phees]

Could be a nice new mod: The cycler calculator!

[PLAD]

23 hours ago, HebaruSan said:

This is as much a question asked to learn as it is a suggestion, but rather than directing the Duna energy solar-prograde or -retrograde, what about using it for plane changes, i.e., passing over the north and south poles? Would that help V_inf to stay in the right range?

That is an interesting question. My guess is that a z-axis only perturbation from Duna will not change the period of the Solar orbit, which is the desired result. I'm going to try it. The trick is that the ship has to stay in the plane of Kerbin's orbit between those two Kerbin flybys so a small thrust might have to be done later to get back in that plane... although it might not if the Duna flyby is just right...

This stuff is tricky. Yesterday I tried to run the S1L1 path when starting with 50m/s more (so 1305 instead of 1255) just to see what happens. It turned out I could still find a path that repeats every 454.8 days, the biggest change was the timing of the 1st Kerbin flyby- instead of 301.25 days it was 299.25 days, but the second leg could be made 2 days longer (so 155.5 days instead of 153.5) by flying by Kerbin a little closer. In other words if one of the two 'legs' of the trip is made longer by adding energy, the other one can be made shorter to compensate just by adjusting the Kerbin flybys. It makes me wonder why the discoverers chose the timing for the 1st flyby that they did- my guess is that they chose it so that the two Earth flybys happen at exactly the same altitude, or maybe it's the minimum energy that works. More experiments!

I could figure it out much faster with the right tools. This is the sort of thing that drove me to write Flyby Finder, but this would be much more complicated and might be beyond me. Here is a paper giving a robust Lambert multi-orbit algorithm, look at equation (5) on page 5, that's the formula that has to be iterated using the values for F'(Xi) and F''(Xi) from the appendix. Holy crap! The even bigger problem is that there can be more than 1 solution for getting from here to there in a set time when multiple orbits are allowed, so how does a program pick the best one, or how do you display all the possibilities in the output? This is what stumped me in trying to add 360-degree double flybys to Flyby Finder.

On the bright side, I will never, ever tire of playing KSP. There are too many interesting things to be tried.

[septemberWaves]

Isn't the general idea of a cycler orbit that you stay far enough away from the SOI of your targets (or in the game, completely out of the SOI of your targets) so that your cycler orbit doesn't get altered by the flyby and you only have to make minimal correction burns? I've been looking into cycler orbits a little for my Jool 500 challenge and from what I can tell you're ideally not supposed to enter the SOI of either Kerbin or your destination planet. Rather, only your surface-to-space and space-to-surface crew transports should be anywhere other than the solar SOI once your cycler is properly set up.

[Jetski]

This is partially true.  My attempt involved missing Duna SOI, but using a gravity slingshot off Kerbin to make the next intercept. I was in a hurry though, trying for an Aldrin cycler with 1 synodic period.

[PLAD]

19 hours ago, eloquentJane said:

Isn't the general idea of a cycler orbit that you stay far enough away from the SOI of your targets ....

You are partly right, one of the simplifying assumptions all the cycler searchers make is that only Earth will affect the path of the ship, Mars will do nothing. There are two problems I see with that though, the smaller one is that in the real world Mars will always have some influence, and even in KSP you have to stay pretty far away from Duna to keep out of it's SOI, and by keeping far away from the destination planet you require a very long ride in your shuttle (depending on how much dV you're willing to have the shuttle use to get from the cycler to Duna). The bigger problem is that Duna's orbit isn't circular so the actual synodic period between it and Kerbin varies from cycle to cycle- in my 2nd test run above the cycler's closest possible pass to Duna to keep it on the right schedule was nearly 2 million km, because Duna was near its perihelion and moving faster than average. (And it's even worse in the RSS.) To me that leads to shuttle rides so long you might as well skip the cycler altogether. In practice the cycler will have to vary from the ideal path and the cheapest way to do that is use Mars to move it. In this paper the people who discovered the S1L1 cycler give an actual mission plan for an S1L1 that takes into account the real motion of Earth and Mars, take a look at table 6, one of the Mars passes is at less than 8000km altitude. Unfortunately this means that actually flying one of these things will require detailed advance planning.

A Kerbin-Jool cycler is an interesting idea, as that is a long trip requiring a large start boost and a big cycler could save a lot of fuel. I took a look for paths using Flyby FInder and couldn't find any acceptable ones. My first suggestion would be to capture the cycler at Jool for free using Tylo, then kick it back to Kerbin for free when your mission is done. If you could do a flyby of Kerbin that goes back to Jool in 1212 days (so 2 solar orbits later, a reasonable near-Hohmann orbit between Kerbin and Jool can have a period of 606 days) without slowing at Kerbin you would have a cycler that goes K-J-K-J-etc. for almost nothing. 606 days is 5.7 Kerbin orbits though so you would only encounter Kerbin once in those 1212 days. Argh...that's no good. I dunno. I'll watch that thread to see if you find something.

-edit-note all times are in given in Earth days.

Edited April 28, 2016 by PLAD

[septemberWaves]

Honestly I might not bother with the cycler since DeepFreeze is now up to date, but if I do decide to do it for the fun of the challenge, I'll probably have a main cycler vessel with space to freeze 50 to 100 kerbals, and a couple of smaller (compared to the main vessel anyway) transports to break off from the main ship probably around a hundred days before nearing the target SOI and stay there until the return window arrives, whilst crew are transferred with in-system vessels. This would probably not be a worthwhile method for Duna, since the crew would spend so long out of the main cycler vehicle that it would defeat much of its purpose. But since the Jool transfer is so much longer it's most likely far more efficient on resources. Additionally, the nature of the Jool 500 challenge means that, if I do decide to use this method, I'll already have the infrastructure to transfer crew around in the Jool system, as well as to refuel the cycler from the Jool system for whenever it does need to make course corrections.

Of course, to do this I'll need a cycler which goes above Jool's orbit and below Kerbin's orbit, so that I can get the desired bidirectional transfer, but that should be possible. I just have to hope that other planets don't get in the way.

[PLAD]

I made another try at an S1L1 cycler, this time using a big carrier and launching crew from Kerbin and landing them at Duna to see how those procedures would go.  I also flew above Duna instead of beside it.

 

Conclusions:
-It takes about 2400m/s to get from LKO to a rendezvous with the cycler as it flies by Kerbin.
-It takes about 200m/s to get from the cycler to Duna's atmosphere if a 20-hour transfer time is allowed.
-With my skill at its current level the cycler uses a couple hundred m/s per one complete cycle.
-Flying more above Duna than to its side allows a reduced flyby effect on the cycler path, and only needs a few m/s of z-axis corrections later.
It is rather difficult (for me anyway) to plan the next cycle because I would need to see the 2nd-from-now Duna flyby before the next Duna flyby occurs, and the game can't reasonably be used to plot that many flybys ahead. As a result I need a lot of course corrections. Therefore I need a tool that plans this like Flyby Finder does.  I shall be messing around with that for a while.
The other option for people trying this would be to accept some very distant Duna flybys, where you never get closer than a million km or two to Duna. It is easy to keep coming back to Kerbin every cycle, the hard part is the Duna encounter.
You'll note that the ships that get from Kerbin or Duna's surface to the cycler have to have more than enough dV to get straight to Duna (or back to Kerbin) on their own, so the only reason to do all this is to have the gravity and habitable volume of the cycler during the interplanetary transfers. And the cycler is only in use for about 10% of the time. It seems a lot of trouble for what you get.

[Geschosskopf]

On 4/25/2016 at 3:10 PM, PLAD said:

A cycler is a craft that repeatedly passes between two or more planets.

.....

Ouch! The flyby of Duna added a lot of energy.......

Has anyone else tried this?

First off, well done!  This is not a trivial exercise.  It requires very careful flying.  Bravo!

That said, cyclers, like most other real world ideas for getting to other planets on the cheap, don't translate well into KSP because the KSP universe is so small compared to the real one.  It hardly costs more to go from Kerbin to Duna than it does to go from Kerbin to Minmus.  Given that Minmus is within range of fairly low tech in career games, there's not much incentive to go to all the trouble of setting up a cycler to get to Duna.  Or even Jool (and beyond, if you have OPM or some such).

But yes, Kerbin-Duna cyclers have been done before.  There have even been challenges about them, but not for a couple years.