Lowest Delta-V to Eeloo

[PLAD]

The goal of this challenge is to get from a low orbit around Kerbin to the surface of Eeloo with the least amount of delta-V expended. It is similar to the Lowest Delta V to Moho challenge that Otis made a while ago, the difference here is that the delta-V recording does not start until you are in a low orbit (apiapsis less than 80000 meters altitude). I feel that getting into orbit cheaply is a very different engineering problem from the vacuum part of the mission so I cut it out. The rules:

1) Accurate delta-V recording is key. So one ship only, no docking, and no air-burning, kraken, or exotic-physics motors that would taint the dV readings. You must use Mechjeb or a similar mod that displays the expended dV in all screenshots, which are taken before all major (>20m/s) manuevers. Please also give the KSP UT time of the major points of the mission-departure, flyby periapsis and landing (in the screenshots is best). Edit:I shall also accept entries that give enough information to accurately compute dV used by telling the Isp of the motor(s) used and the ship mass at the start, finish, and before and after staging events.

2) Start- First shot must show the ship in LKO, with altitude and orbital speed visible, or the map view with the AP flag highlighted showing the apoapsis is <80000m. Note you can get the ship there any way you like, multiple-launches, even Hyperedit. No Hyperedit after that though!

3) Arrival- Your ship must end up on the surface of Eeloo undamaged. Last screenshot must show delta-V expended and UT time. (Edit: and ship mass if not using Mechjeb)

4) Mods- any mod that doesn't affect the dV recording or allow you to survive a landing faster than the stock landing struts would (12m/s) is fine, as long as no motor has a thrust-to-weight ratio higher than the best stock motor, which is 39.2 (the Kerbodyne KR-2L).

5) Scoring-lowest dV expended wins. In the unlikely event of a dV tie the shorter elapsed time wins.

This is going to be all about finding and executing flybys. We have some great tools that didn't exist a few months ago to use for this- I direct you to Arrowstar's TOT and to my Flyby Finder (FF) and LambertE spreadsheet.

Leaderboard:

1. PLAD 1934m/s

2.

3.

4.

5.

Honorable mention:

allmhuran: estimate around 2200m/s

Edited July 15, 2016 by PLAD
July 2016 update to dV computation method

[PLAD]

And here is my entry.

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How I found it- Arrowstar demonstrated in my Flyby Finder forum that TOT can do 7 flybys in one calculation- he used a K-E-K-E-K-J-Ee flight path. Look at it here. I used LambertE to discover that the first K-E could be eliminated and some small changes made to the start and finish encounters that would make for a very low-dV mission. So although I'm calling this my entry I give a lot of credit to Arrowstar for finding this window. I admit that it pains me no small amount that TOT, because it finds flybys that have a periapsis thrust, can find a better path to Eeloo than FF can. Once FF can do double flybys that might change.

I saw Immelman's trip to Eeloo and it is good, but when you add the Eeloo landing in it would be over 2344m/s. Immelman's mission reports are so good with so many details that I used them to test my flyby programs as I was writing them. Maybe we could find a fair way to estimate what it would take to land from a 22x20km orbit?

[immelman]

This is so cool, I'm interested in retrying this, but exploring further using Jool's moons to try and reduce the Jool periapsis burn...

[PLAD]

Yup, my guess is that if someone can figure out how to use a large moon or maybe even Jool's atmosphere to slow down they will win. The thing I can't figure out is how to use them to slow down and still leave Jool moving in the right direction.

[John FX]

you could always use jool to slingshot way outside eeloos orbit without braking then brake next orbit (in a few years), you might have a better angle, maybe less Dv to scrub off. I did that once, I noticed I had a slingshot from Jool that landed me on Eeloo (but years away)

That seemed pretty efficient. Might be worth running the numbers.

[metaphor]

It's definitely possible to eliminate the Jool periapsis burn. The main problem here is that Jool's orbit is closer to a Jool-Eeloo transfer orbit in energy than to a Kerbin-Jool transfer orbit. That means that you have to bleed off some energy in Jool's SOI in order to get a Hohmann transfer to Eeloo. (In other words, the v_inf when arriving at Jool from Kerbin is higher than the v_inf when departing Jool to Eeloo.)

There's a few ways to do that. In one of my missions to Eeloo I used the atmosphere of Jool to aerobrake some speed off, which put me into an Eeloo transfer orbit. It's pretty hard to aim it though. Another way is to use one of Jool's moons to remove some speed, but that's probably even harder to plan. A third way is to just get an Eeloo encounter while on a more energetic transfer orbit, and then use multiple Eeloo flybys coupled with deep-space maneuvers to lower the orbital insertion burn. That will take a while at 100,000x time warp.

[allmhuran]

I don't really want to do it all again, so this won't meet the requirements for a submission to the challenge as such, but in my final 0.23.5 "starting parts only" grand tour I send Jeb to Eeloo via the following course. Even with the unnecessary Moho step, and obviously excluding the Pol and Bop landings, the total dV from LKO to Eeloo insertion is very small. I don't have the exact numbers (although every burn larger than about 1 m/s is shown in the video), but I would estimate something like:

LKO

> Eve slingshot - 1100 m/s

(Moho step)

> Kerbin slingshot - 10 m/s

> Kerbin slingshot - 10 m/s

> Duna slingshot (normal correction for Jool intercept) - 15 m/s?

> Jool aerocapture - free

(Pol and Bop step)

> Wait for Eeloo ascending node

> Multiple small satellite slingshots - 10 m/s

> Tylo ejection slingshot - 30 m/s

> Eeloo landing - ??

The total depends on how much is required for Eeloo insertion and landing, I don't have good numbers for that. You could also reduce the numbers further by taking longer (the reason for this is explained in the video)

The best route I know of would be similar to that but simply excluding Moho, Bop and Pol. I would still go for a Jool aerocapture followed by a Tylo slingshot, since you can get a much better Eeloo encounter than you would by slingshotting directly from Jool.

http://youtu.be/HcWwWAJt4dM

[PLAD]

allmhuran-

That is an impressive trip to Eeloo (and everywhere else). I think I saw you start the deboost burn into Eeloo orbit at around 950m/s? That suggests something around 1000m/s or a bit more depending on gravity losses total for going from Eeloo SOI to landing. With the other known burns that puts your LKO to Eeloo surface at Round 2200m/s but I can't say exactly because the effect of your maneuverings around Jool system are hard to be sure of. I think you beat my score. You figured out how to cut the Jool periapsis burn out- you aerobraked into orbit around Jool and took the time to set up a Tylo slingshot to Eeloo. That may be the best possible way to do it. I can't make this a formal entry though but I'll put an honorable mention in the listings.

Great video- my favorite parts were the takeoff from Bop (the soundtrack made it) and the timing on running out of fuel around Ike. Talk about luck!

[Vector]

I know it's heresy to speak of using gravity assists from the Mun to go interplanetary, but it can save a couple hundred m/s delta-V. The trick is making multiple passes by the Mun. As many people have observed, a gravity assist from the Mun can get you out of Kerbin's SOI but not anywhere interesting, and burns in interplanetary space are horrendously inefficient. But if you intercept Kerbin a year later and make a second pass at the Mun (and a third), you can build up energy and eventually reach Eve. And once you reach Eve, with skill you can gravity-assist yourself anywhere.

I haven't perfected the technique, but it does work. You can get to Eve for not much more than the cost of getting to Mun. I'm finding that it works best to leave Kerbin neither prograde nor retrograde but radially, to keep the same orbital period as Kerbin for the second intercept. Once in interplanetary space it is possible with extremely small adjustments to tweak the phase of the Mun at the second intercept, so it is in the proper position for a boost. It is a bit time consuming, but for those of you adept at gravity-assists, it's very doable.

[cantab]

I might give this a go myself. It's always nice to pull off some good gravity assists. Also, if I use the Kerbal X I can prove that contrary to

, it wasn't the engineers to blame in that mission.

[PLAD]

Vector-That is an interesting idea. I'm a big fan of Munar flybys. I'm particularly proud of this mission where I got from LKO to Jool orbit for 1011m/s. I saved 87m/s by using a Munar flyby, and I thought that was the best that could be done. But your suggestion of using multiple Munar flybys could blow that out of the water. Normally if you leave Kerbin's SOI and just coast around back into Kerbin's SOI without flying by anything else or making any deep space maneuvers then you will enter with the same speed you exited with. All you can change is the direction you leave Kerbin at. But going Kerbin-Mun-Kerbin-Mun could get around this. Do you have record of a mission where you did this? I see why you should try to get in a solar orbit that has a period of exactly 1 Kerbin year if you used a minimum-energy flight to Mun (856m/s from a 75x75km Kerbin orbit) since you won't have the energy to get in an orbit that gets back quickly (for instance a 10:9 resonance orbit would take 9 years to get back and be a major pain).

What could the savings be? I figure the minimum V you have to depart Kerbin with to get a useful Eve flyby works out to a start boost at 75x75 of 1044m/s, 1 Munar flyby can reduce that by about 90m/s, so about 954m/s is the minimum with 1 Munar flyby. The minimum speed to get to Mun is about 856m/s so potential savings are about 98m/s minus maybe a 10m/s correction budget per flyby. Enough to win a challenge if everything else is optimal. Gawd will it be tricky to execute though.

[Vector]

So I tried again to see how efficiently I could get to Eve from LKO, and I encountered a few things.

First, the radial ejection idea is something that should work in principle but I was unable to pull it off because I kept having trouble lining up the ejection as Kerbin kept moving around the Sun. Eventually I gave up and just ejected in whichever direction, but even if I had been able to eject radially, I would have needed to tweak the final Mun flyby to set up a Kerbin encounter 1 year in the future. Unfortunately, when you're in Kerbin's SOI, you can't set it as a target, nor can you get "Closest Approach" indicators one year in the future. You have to compute the orbital period using the periapsis and apoapsis. In the past I hadn't ever tried to actually eject radially and I had gone for a resonance to minimize deep-space correction.

For this test run I did not ejected radially and I also made an error in the calculation for orbital period, and I had to wait 7 years AND burn 42 m/s to get another Kerbin encounter. Awful on both counts.

I was able to get another Mun flyby, and lower my solar periapsis down to Eve's orbit, but as a proof of concept I had not taken care to eject near AN/DN (too focused on trying to leave radially), so I was actually still quite far from Eve. Ideally one would time the ejection properly and this wouldn't be a problem.

All told, I spent 911 m/s from LKO, and 42 of that was due to a blunder, so I think 870 to 880 m/s could be very realistic if all is done well. This is also assuming that you are willing to possibly wait a while to get an encounter with Eve. The final flyby that gets your orbit to intersect with Eve's orbit will allow you some "leverage" to get an Eve enounter, but you won't have much room to move so you might have to aim for an encounter several years out.

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[allmhuran]

The thing about performing multiple slingshots is that there is only a gain to be had doing so until your ejection angle is perfectly prograde (or perfectly retrograde, depending on your objective) with respect to your target solar orbit.

In other words, let's say you burn from LKO into a Munar slingshot that ejects you in a perfectly solar-retrograde direction, lowering your solar periapsis. There is no further gain that can be had from further Munar slingshots, since any further slingshot will actually "suck up" some of that solar retrograde velocity by bending it into some other direction that is away from solar retrograde and, therefore, closer to solar prograde, thus increasing your solar velocity at the solar altitude of Kerbin and therefore raising your solar periapsis.

[Vector]

I agree with that as long as you are only ever interacting with one body. With multiple slingshots you can get assists that would have been available if the body had higher mass (or smaller diameter), but you can't get more than that.

When you interact with multiple bodies it's not true because you can take advantage of the relative motion of the bodies. When you leave Kerbin's SOI and intercept a year later, you are interacting with multiple bodies, so the single-body upper limit doesn't apply. You could theoretically get unlimited velocity off of Kerbin and the Mun, for the same reason you can get unlimited velocity off of Kerbin and Eve.

But you must leave Kerbin's SOI to do so, or else you are subject to the single-body limitation you mentioned.

[allmhuran]

True, I suppose if you managed to find a trajectory whereby you get some nontrivial bending of your trajectory from Kerbin that then gives you an intercept with the Mun that results in an escape trajectory back towards the direction you want, that would indeed work, picking up bonus velocity up to (theoretically) 2x the velocity of the Mun relative to Kerbin.

Edit: Actually I think in this case the ideal scenario results in a gain of 1x the velocity of the Mun relative to Kerbin doesn't it? Your optimum trajectory would, I think (just doing the geometry in my head here), be...

- Enter Kerbin SOI heading (say) directly solar prograde

- Trajectory bent to perfectly solar radial out

- Enter SOI of the Mun

- Trajectory bent by Mun to perfectly solar prograde

- Leave Mun's SOI having gained velocity equal to the velocity of the Mun relative to Kerbin

...Assuming no significant bending of trajectory by Kerbin between leaving the Mun and leaving Kerbin.

Gah, edit again: This assumes that (in a more general case) the relative velocity of the body in place of the Mun to its parent is lower than the relative velocity of that parent to its own parent. If that's not true, then you can go for 2 full 180 degree bends and get a kick equal to 2x the higher relative velocity minus 2x the lower relative velocity, which could be better, depending on the relative relative velocities!

Wait.. no... because if you get a 180 degree bend off the first body (in this case, Kerbin) then you would intercept the Mun at a position when it is heading solar radial out, not solar prograde. So after performing that maneuver youd have to use another encounter to convert that gain back into prograde.

Sheesh, orbital mechanics...

Edited July 16, 2014 by allmhuran

[Vector]

In pictures, to clarify, suppose you leave Kerbin prograde:

And suppose your velocity relative to Kerbin is insufficient to reach Duna or Eve.

To recap the single-body limitation, if you return to Kerbin and sling-shot around Kerbin,

you will have exactly the same velocity relative to Kerbin, and you will be still unable to reach Duna or Eve. The best you can do is to be perfectly prograde or perfectly retrograde and you can't get beyond that. No matter how many Kerbin fly-bys you do, you will have the same relative velocity relative to Kerbin. You can try an Oberth burn but you can't gravity slingshot yourself anywhere.

With an extremely small deep-space maneuver, you can aim for the Mun and for a moment ignoring the relatively low mass of the Mun, you could sling shot around the Mun like this:

Now you have retrograde velocity relative to Kerbin that is greater than the prograde velocity you had before. Specifically it's equal to your previous velocity plus twice the velocity of the Mun relative to Kerbin.

Then on your next Kerbin intercept you can aim for this:

and you can again leave Kerbin with more prograde velocity than you had retrograde velocity before. And you could continue this without limit.

In reality, the mass of the Mun is too low for it to work like this, and prograde/retrograde velocity means lengthy waits for intercepts. What I've been aiming for, but so far unable to pull off is something like this:

where most of the velocity is radial so the orbital period is the same as Kerbin, but you still get a small boost once each year. By fine-tuning the fly-by, it should be possible to precisely control the amount of prograde/retrograde velocity and thereby precisely control the orbital period to line up the intercept the following year. In principle it should be possible to get a small boost every year for several consecutive years with only tiny correction burns.

Then the easy part would be to ultimately swing the accumulated radial velocity into prograde or retrograde and go to Eve or wherever.

[allmhuran]

Yeppers, that's pretty much exactly the picture I had in my head when talking about the "double (theoretical) 180 degree/2 encounter" and "double (theoretical) 90 degree single encounter" scenarios.

In that final image, if we assume Kerbin bends you from solar prograde 90 degrees into solar radial out, thus intercepting the Mun while it is travelling solar pograde relative to Kerbin, and the Mun then bends you from solar radial out 90 degrees into solar prograde, you will escape Kerbin's SOI at a velocity higher than that at which you entered, with the amount of the difference being the orbital velocity of the Mun around Kerbin.

Edited July 17, 2014 by allmhuran

[LethalDose]

I know it's heresy to speak of using gravity assists from the Mun to go interplanetary, but it can save a couple hundred m/s delta-V. The trick is making multiple passes by the Mun. As many people have observed, a gravity assist from the Mun can get you out of Kerbin's SOI but not anywhere interesting, and burns in interplanetary space are horrendously inefficient. But if you intercept Kerbin a year later and make a second pass at the Mun (and a third), you can build up energy and eventually reach Eve. And once you reach Eve, with skill you can gravity-assist yourself anywhere.

I haven't perfected the technique, but it does work. You can get to Eve for not much more than the cost of getting to Mun. I'm finding that it works best to leave Kerbin neither prograde nor retrograde but radially, to keep the same orbital period as Kerbin for the second intercept. Once in interplanetary space it is possible with extremely small adjustments to tweak the phase of the Mun at the second intercept, so it is in the proper position for a boost. It is a bit time consuming, but for those of you adept at gravity-assists, it's very doable.

Didn't the Galileo or Cassini-Huygens mission do something like this? I feel like I remember reading about an outer planets probe that used a Venus fly-by to set up a second Earth gravity assist to fling it out further?

Actually, it looks like they both did. Galileo used 2 Earth fly-bys and one Venus fly-by, and Cassini used 2 venus fly-bys and one Earth Fly-by

Edited July 17, 2014 by LethalDose

[Vector]

In that final image, if we assume Kerbin bends you from solar prograde 90 degrees into solar radial out, thus intercepting the Mun while it is travelling solar pograde relative to Kerbin, and the Mun then bends you from solar radial out 90 degrees into solar prograde, you will escape Kerbin's SOI at a velocity higher than that at which you entered, with the amount of the difference being the orbital velocity of the Mun around Kerbin.

Yes. You clearly have a good grasp of the mechanics, and there are probably additional ways to take advantage of the Mun that I haven't thought of. The simple cases are good for establishing the principles, even if unrealistic, and then from there the actual maneuvers can be understood and executed.

As for Earth/Venus fly-bys, this is true but not really the same thing. It is already well-established in KSP that Kerbin-Eve-Kerbin can give you a big boost, but using multiple Mun fly-bys is not common. Conventional wisdom seems to be that Munar gravity assists are not worthwhile for going interplanetary.

[Idrryl]

Oh my... I thought only NASA does these complex gravity assists, but here we are, discussing it like real physicists. Looks like I have to practice my gravity assists

[PLAD]

That is a very impressive series of Munar flybys Vector did. He didn't even encounter Mun at the same point in its orbit each time. Now some egghead analysis...

I think Vector's Mun flyby mission proved 2 things and gave them some numbers as well. The first 3 flybys showed the benefit of multiple Mun flybys to adjust the Mun departure vector to be tangential to Mun's motion and thereby as efficient as possible. It looks like when he entered Kerbol orbit he was moving at 8709m/s, Kerbins Vcircular is 9284m/s so his V leaving Kerbin's SOI (I'll call it VSOIK) must have been about 575m/s. This equals a V over Vcirc in a 75x75km Kerbin orbit of 985m/s, since he started with 862 the total gain from the 3 Mun flybys was 123m/s. Just 42m/s more (at the 75x75 orbit start) and that would be enough to get to Eve all by itself. Probably only a 30m/s or so gain over just doing one really low Mun flyby on the way to Eve though.

The 4th flyby was much more powerful. He went from a 7:6 resonance-with-Kerbin orbit (SMA about 12.272 million km) to a Kerbin-Eve Hohmann transfer orbit (SMA 11.716 mkm). The V apoapsis of those are 8768 and 8505m/s respectively. This means he entered SOIK at 516m/s and left at 779m/s. The 4th Mun flyby gave him 263m/s VSOIK! To be fair, at a Kerbin distance of 12000km (where Mun is) the speed change (relative to Kerbin) is 878 to 1054m/s or only 176m/s but that's still a lot. And I agree it should be possible to do that again and again, although the faster you flyby the less energy you can steal from Mun so it would be diminishing returns. There's also the pain of many-year coasts between encounters.

It would be nice to see the VSOIK is when entering and leaving around a Munar flyby, if possible, to better quantify the effect. I'm missing something, leaving SOIK at 575m/s and doing a 42m/s burn suggests returning at 533m/s but I calculate 516m/s. I'm missing 17m/s somewhere, probably from bad transfer orbit SMA guesses.

[Vector]

So I kept trying, and I was able to actually reach Eve this time, spending only 873 m/s.

The radial approach turned out to be a bad idea. The problem with radial is that there is no way to control the phase of the Mun at intercept time. Moving radially (same SMA but different eccentricity) predetermines the location of the intersection between the orbits of the ship and Kerbin and if the Mun is not in the right phase, there's not much you can do.

Moving prograde or retrograde (resonant orbit), there are a range of available locations, so minor adjustments to the orbital period will shift the phase of the Mun and can put it wherever is best for a gravity assist.

High level summary of the mission:

1. Mun flyby, try to get Kerbin Ap + Pe = 22,800,000m so orbital period matches Mun's orbital period.

2. One month later, another Mun flyby, this time leaving Kerbin prograde and shooting for nearest resonance, which happens to be 6:7. Use future Ap+Pe to guide fine tuning of second Mun flyby.

3. 7 years (and 6 orbits) later, Mun flyby, boosting speed and apoapsis for 4:3 resonance

4. 4 years (and 3 orbits) later, another Mun flyby, boosting speed but turning a bit radial inward instead of pure prograde, to retain 4:3 resonance with higher eccentricity. (Not enough boost to reach 3:2 resonance)

5. 4 years (and 3 orbits) later, another Mun + Kerbin flyby drastically changing orbit to mostly retrograde velocity, lowering periapsis to Eve.

6. Small burn to get Eve intercept 6 orbits in the future

Also, I have a script which makes it easy to grab snapshots of the quicksaves along the way, so if you're interested in detailed quantification and the maneuvers, you can download them from here. I've included a quicksave for each of the screen shots in the image album.

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[PLAD]

Vector- KLO to Eve surface for 873m/s has got to be an all-time record. That is spectacular. All previous low-dV records can now be reduced by at least 100m/s with this trick. My god, you could probably get to Jool for less than 900m/s with care.

Thank you for putting the saves up there, I ran one and found I could leave Kerbin after 2 Mun passes and get into a 6:5 Kerbolar orbit (with a bonus Minmus flyby no less) but that would not reduce the ultimate dV total to Eve at all.

I am thinking that we need to have a general 'Lowest dV to'... challenge that includes lowest dV to all bodies in the Kerbol system. The lowest dV paths to Moho and Jool will start with a flight to Eve, and the lowest to Eeloo and Dres will then continue from Jool, so making this incredibly low-dV flight to Eve could lead to record flights to 4 other worlds! The concept could take you directly to Duna too, of course. None of them would be easy, but we do these things not because they are easy, but because they are hard...

In the meantime, my Eeloo and Jool record flights still stand.

[PLAD]

LKO to Eeloo surface: 1934m/s.

I figured out a way to avoid the 230m/s burn when flying by Jool on the way to Eeloo. I used the atmosphere. I knew the VSOIJ I would have when coming from Kerbin and the VSOIJ I needed to leave with for an efficient path to Eeloo and calculated the equivalent energy reduction at 135km above Jool (so just in its atmosphere). It worked out to 150m/s, and 3 trial shots were enough to determine the necessary periapsis for the atmosphere to do that- 134150m. Once I set up a Jool flyby with a 134km periapsis I put a node there and a 'fake' 150ms retrograde burn so I could fiddle with what to do after that. I finally found a good place to do a burn to correct for the directional error that using the atmosphere caused. Enough yacking- here it is:

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Of course now we know there's a way to leave Kerbin for about 100m/s less, but for the rest of the flight I think this is pretty close to the minimum possible. Maybe 50m/s could be shaved by flying by Jool at a better point in its orbit, since I used 298m/s to brake into a 10x10 orbit around Eeloo, and about 247m/s looks like the lowest possible when coming from Jool.

Note that if your ship has different drag from mine then it would need a different Jool periapsis.

For those who haven't seen it, this mission uses my 1011m/s to Jool flight up to just after the 2nd Kerbin flyby.

Edited July 19, 2014 by PLAD

[specialopsdave]

Wait a sec... I'm fairly new to this gravity assist thing, but... Would it theoretically be possible to, when using the Mun as an assist, somehow assist on Minmus directly afterwards to reduce the amount of passes you have to make? I'm not sure if it works that way, but I think it might work.