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Planning bi-elliptic interplanetary transfers


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Before I put much time into finding a solution, I thought I'd just ask nicely: Has anyone already figured out how to plan unusual-but-affordable non-hohmann transfers?

I'm looking specifically at Kerbin-Duna shuttles right now. With hohmann-ly transfers, I'm looking at a round-trip time of almost five years. I wonder how expensive it would be to return a shuttle from Duna to Kerbin between transfer windows, so that the same vessel can move from Kerbin to Duna on every standard transfer opportunity.

I've got nearly two years to do so and don't care how much of that time is spent in transit: that's no worse than sitting idle, waiting for the next transfer window.

I wonder if something bi-elliptic might be usable, with a solar PE way down below Eve?

(edit) Example:
bi-elliptic-interplanetary.jpg

Note that this doesn't involve a gravity assist -- after all, I want something I can plan, for, and cannot rely on Eve always being in the right place. dV requirements are, of course, considerably higher than for a hohmann transfer, but not totally ludicrous. In this example, it costs me ~1800m/s to get from Duna to Kerbin-altitude within a year.

Edited by Laie
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If you look at a porkchop plot of near-hohmmannly tranfers to anywhere, you see that the dV cost increases really fast when it's slightly non-optimal. I promise that it continues to increase really fast even off the edges of the porkchop plot. Just for fun one time, I turned on infinite fuel and flew to Jool on a fairly direct and fast intercept ... I calculated the final dV cost of the experiment at somewhere around 26km/s, IIRC.

To leave Kerbin at a non-optimal time, you have to redirect your vector using a gravity slingshot from a flyby of Eve or Duna. There is no other practical way without expending hellish amounts of dV.

 

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1 hour ago, bewing said:

There is no other practical way without expending hellish amounts of dV.

I've updated the OP to show an example of what I'm looking for. Reducing the transfer time to much less than one year quickly becomes expensive again, but it doesn't become quite as hellish quite as quickly as with hohmann transfers.

If it allows me to perform the return trip during the off-years, it might be worthwhile.

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I don't know offhand whether the Kerbol system supports this, but you might explore a Kerbal version of an Aldrin Mars Cycler.

Invented by Buzz Aldrin (yes, the second man to step on the Moon), an Aldrin Cycler rides an orbit that passes Earth and Mars once each cycle (either outbound or inbound -- you need two of them to travel both ways faster than a Hohmann orbit), and uses gravity assist from both Earth and Mars to keep the orbit synchronized with very small dV expenditures for corrections.  This depends on the near-resonance of the orbits of Earth and Mars, with a conjunction every 26 months -- the outbound cycler will pass Earth, and then pass Mars, then spend some time out in the main Asteroid Belt, at every conjunction (the inbound cycler will do the same, but pass Mars, then Earth, while inbound).  As I recall, transit one way is about 3 months, and almost two years for the "idle" portion of the orbit.

The encounter at each end is at a fairly high velocity (a  good bit above Hohmann transfer value), best matched at the Earth end by launching passengers and cargo from the Moon, to slingshot around Earth.  Going to Mars and returning to Earth would obviously benefit from aerobraking, but I'm not sure how the Mars colony is expected to match velocity (though starting from a much shallower gravity well doubtless helps).

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OK, I went at it with a kind of Phase Angle mindset: in the picture above, I'm leaving Duna while it's at the 3 o'clock position. I go around the sun once, lower my AP on the far side, and come back approaching Kerbin's orbit, again in the 3 o'clock position.

Now. For any given day, how much time will I have until Kerbin is at the same angle where Duna was? That determines how long the whole transfer may last, and how low my PE around the Sun has to be.

Turns out that things are not in my favor: Right when I arrive at Duna from a cheap-as-possible hohmann transfer, I have 360days left to go back by the bi-elliptic route. That already requires a PE well inside of Eve's orbit, and things only get worse the longer I wait.

@Zeiss Ikon cyclers are not suitable for what I have in mind. Catching up with a cycler requires more dV in any event, the savings lie in having only a lightweight cargo to accelerate (as in, only crew and supplies in a tiny spacecraft) while all the heavy stuff (radiation shielding and comfort for 3 months) are on the cycler and remain there.

Whereas I have to move heavy cargo to Duna, and not very much back.

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I'm a bit unsure what you actually want to do. Do you want to do a bi-elliptical transfer to save dV? Or do you want to do a transfer outside a transfer window to not to have to wait for a window? If so, then why are you talking about bi-elliptical transfers? Saving dV with a bi-elliptical transfer - compared to a Hohmann transfer - is only possible if you change your orbit (around the sun in this case) by a large fraction anyhow, so it isn't applicable to a transfer to Duna.

In my games I often do interplanetary transfers outside of a transfer window. AFAIK doing a standard transfer from Kerbin to Duna or the other way at a transfer window is the fastest and cheapest transfer. But when I don't want to wait for a window I can spend somewhat more dV and somewhat more time underway, to arrive at the destination earlier than waiting for the window would have meant. Depending on the actual situation sometimes the cost in dV becomes prohibitive, or the trajectory for "leaving right now" becomes so long that it is better to wait for a window (actually: be closer to a window), but often it works well enough. I set up these transfers by: first setting up a maneuver node as for a Hohmann transfer. Then checking where my target is when I reach it's orbit: if it is in front of me, then I need to reach the intercept point earlier - compared to the target - to get an intercept, so I need to get closer to the sun to be "faster" than my target. So I change my ejection angle (i.e. time when I do the burn) to get closer to the sun, which means I need more dV on the burn to get to the target's orbit. If the target is behind me, then I need to be "slower", so I need to get farther away from the sun. (I.e. spend some time hanging around in solar orbit outside the orbits of my start and destination.) Then I fiddle around with the ejection angle and the dV until I get an intercept. If a plane change is needed I include a midway plane-change burn into the fiddling process. Finally I think about whether this transfer is worth the effort, i.e. compare the arrival time at the destination - compared to waiting for a transfer window - to the cost in dV, keeping in mind the increased cost of the capture burn.

Here a quick example for a transfer of my gateway station in 500km Kerbin orbit to Duna. As you can see from the KAC window the next transfer window is in 175 days, together with the 300 days for the transfer itself this means I'd be at Duna in about 475 days.

KAiLN4c.png

Some quick and dirty fiddling later I have an encounter in 345 days, at a large-ish cost in dV (2400 m/s vs. 870 m/s).  I could probably fine-tune this somewhat to shave off some more time and dV, but it's not going to be a fundamental change. In my current situation, with my interplanetary shuttle with 5 km/s dV and refueling stations both at Kerbin and Duna I might go for it, but at the start of my career - when every m/s cost me money and effort - this might be different.

cUbF3QU.png

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5 hours ago, AHHans said:

Or do you want to do a transfer outside a transfer window to not to have to wait for a window?

That's the idea: in order to better utilize my craft, I want to get back to Kerbin in time for the next cheap, standard transfer.

5 hours ago, AHHans said:

If so, then why are you talking about bi-elliptical transfers?

Mostly because I couldn't think of anything else. Some experimenting suggests that bi-elliptic is the lesser evil, btw, if you account for capture at Kerbin. Still 5km/s when leaving Duna at day 500, though.

That's a lot and probably more than I'm willing to afford, yet (gnashing teeth) it's not so much that I'd discard the option outright.

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It's easiest to just "start" with a hohman transfer, then if you wish to shorten the time you'll increase you velocity. As you increase your velocity you notice the orbit & target "shifting", you have to counter this shift by starting the burn earlier (or later). If you take baby steps everything stays manageable and you'll get an encounter at your desired duration.

 

Bi elliptic transfers btw correspond to a different maneuver, they typically take a long, long time. (So much that it's considered impractical). The idea is that you travel as far out as you're willing to wait and at apo apsis do a very minimal burn to reach your target. Ideally at the edge of the sphere of influence (which in reality is way beyond voyager's location - and in ksp since there are no other stars it's at infinity). There's a very definitive point where this maneuver becomes "better", it's when a normal hohman transfer takes about 0.4 * escape velocity, roughly 95k delta-v for kerbol. Below that hohman is cheaper as well as faster. To plan this, since it doesn't *really* matter how far out you go, just go out a fair bit, then at apoapsis do a capture burn. If you don't quite reach your target just increase the apoapsis (making sure to keep doing the return burn at apoapsis), at some point you'll have an encounter.

 

The third transfer, a heloid transfer is the hardest to plan. You'll have to calculate this manually using a numerical solution. "luckily" this is almost certainly irrelevant: you can't keep burning while in timewarp so year long burns aren't really possible. I'd wager that if a mod allows this it also add its own planner.

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22 minutes ago, Laie said:

Mostly because I couldn't think of anything else. Some experimenting suggests that bi-elliptic is the lesser evil, btw, if you account for capture at Kerbin. Still 5km/s when leaving Duna at day 500, though.

Ah, O.K. Usually when people call something a bi-elliptic something they mean a certain form of: Bi-elliptic transfer maneuver.

I usually aerobrake at Kerbin, because I'm returning with only a capsule anyhow. But even when I return with a craft that I want to keep I don't bother with two transfer burns. An now that I think about it, it seems unlikely to me that you can save significant dV by doing a second transfer burn: you don't get any benefit from the Oberth effect around Kerbin or Duna (or wherever you go) for that second burn. Do you have an example where you save dV by doing a second transfer burn? Also 5 km/s for going from Duna orbit to LKO seems a bit excessive.

[.... *boot up KSP*, *open sandbox*, *time-warp 500 days*, *cheat to orbit* ...]

Hmmm... O.K. You need a 3 km/s burn to capture into LKO if you don't do any aerobraking. But the initial 2 km/s burn to get to Kerbin (and a small plane change & correction burn halfway in) is essentially what I regularly do, with the difference that I then slam the capsule into Kerbins atmosphere and make fun of Bill and Bob for passing out. (Valentina is a steely-eyed rocket lady and doesn't mind a dozen g or so. :cool:)

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18 hours ago, AHHans said:

Usually when people call something a bi-elliptic something

I'm aware of that, it's just that I don't think the ratio has to exceed X before one may call it bi-elliptic.

19 hours ago, AHHans said:

[.... *boot up KSP*, *open sandbox*, *time-warp 500 days*, *cheat to orbit* ...]

Too bad that I can like this only once.

And I've been wrong about my numbers: on day 500, it's 1760m/s Duna ejection, 880m/s at solar PE, and finally 1300 to capture & circularize at LKO. A little under 4km/s all told. Considering that even the cheapest hohman transfer costs ~1700m/s to LKO, that's no longer as bad as I first thought.

However, it quickly gets worse with delay. Making a slightly faster transfer on the way to Duna may well pay off.

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1 hour ago, Laie said:

I'm aware of that, it's just that I don't think the ratio has to exceed X before one may call it bi-elliptic.

 

It's not what you can or not can do. It's the idea behind the maneuver. The idea of a bi-elliptic is to increase the apoapsis as far as possible. That is the fundamental part of a bi-elliptic maneuver.

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16 minutes ago, paul23 said:

The idea of a bi-elliptic is to increase the apoapsis as far as possible.

Silly me. I thought the defining element, and reason why it has bi- in it's name, would be going through two intermediary orbits, rather than only a single transfer orbit.

(while we're playing word games, isn't a hohman transfer orbit the particular transfer orbit that happens to be tangential to both the starting and the final orbit?)

 

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