Optimal Descent (to the Mun)

[Zephram Kerman]

Gubs! That\'s awesome.

I had the same trouble with the mountaintop trick. Fortunately, my work at KGSS involved some scouting the highlands in the Jeb\'s Landing area. So I knew exactly where to aim... I missed it by a mile, but the whole area is pretty high up anyway.

[closette]

The mass units in KSP are a bit of a mess right now. For now I would modestly propose that the fuel unit displayed as 'kg' be a kerbal-gram, while the mass of parts be measured in 'pods' since a Mk1A command pod has a mass shown in the VAB as 1.0.

By comparing the empty and full weight of a fuel tank, one finds that 1 fuel unit (displayed as 'kg') equals (1.25-0.2 pod units) / 250 fuel units = 0.0042 of these 'pod' units.

Some places, such as the KSP Wiki http://kspwiki.nexisonline.net/wiki/Category:Default_Part, refer to the pod mass as 1 kilogram, but a more reasonable guess is that it has a mass of 1000 kilograms or 1 metric ton.

It\'s been a while since I looked into it, but if I recall correctly, 1000 kilograms per pod means that the Solid Rocket Booster part works out to have a ~realistic density, and will explain why a full one will sink in Kerbin\'s ocean while an empty one will float (try it!).

That would make 1 'kg' kerbal-gram fuel unit equal to 4.2 terrestrial kilograms.

But one 'pod' unit of mass could be 600 Earth kilograms for all we know, or some other number in between, with other units (fuel, thrust) scaling along with it.

It gets worse when dealing with the atmosphere: its density, and drag vs. frontal area of parts etc. but I\'m enjoying the break from thinking about the atmosphere in this thread so I won\'t derail it! (And of course we happily accept that Kerbin, Mun and Minmus are all denser than lead!).

I understand that parts may undergo re-scaling of their dimensions for the upcoming 0.16 version, so that the Kerbals can make reasonable EVAs. So there may be some more unit confusion coming our way, but I hope it can be resolved soon after 0.16 comes out.

[JellyCubes]

@Jellycubes, that landing spot looks perfect! Is there any chance of an image or two showing the location you landed at?

Don\'t have an exact image of the landing spot. I think people have created topographic maps of Mun, though.

If the whole specific impulse based engines goes ahead in 0.16, then the \'kg\' unit will mean something.

[Tarmenius]

...parts may undergo re-scaling of their dimensions for the upcoming 0.16 version...

If the whole specific impulse based engines goes ahead in 0.16, then the \'kg\' unit will mean something.

I imagine there will be a great number of changes when 0.16 comes out. I\'m really looking forward to seeing how it affects this and the Optimal Ascent challenge.

I finally managed a mountain landing, though I had a little too much altitude when I began the final descent maneuver and ended up using too much fuel. Coincidentally, it was near where JellyCubes marked the 2.7km peak.

[mager42]

My try with mechjeb

147,7

Land on Muun.

Safe back at Kerbin. /with exploded engine/

[Tarmenius]

Excellent work, mager42! And even managed to get them back to Kerbin. Very impressive.

[Apotheosist]

@JellyCubes, thanks for the map, just what I needed I think I will try to land there now.

[BlazingAngel665]

Drat Mager42 now I have to reclaim my rediculously worthless title of best use of autopiliot, congrats on getting them home though, it really is ugly when you do your white knucle retro at 3k with only a little gas left in your tank. . .

I had a revolutionary Idea actually, could you raise your apoapsis, then do your retrograte to kill your lateral velocity at a higher altitude where you are moving slower? If you do this on the back side of the Mun (in relation to it\'s orbit) then it is pulling you along instead of barelling toward you leaving you with even less vertical velocity as you start a direct descent hopefully toward some mountain top, I tried it and got 144.4 Gubs in my tank, but I suck at piloting and I was using mechjeb (not the most efficient) so maybe someone can be more effective.

[Zephram Kerman]

Intriguing! Is that a bi-elliptic transfer orbit? My initial reaction is it 'probably' would not work because I did a few direct descents and found them very inefficient compared to the low periapsis style.

But... 144.4 Gubs is impressive. Most of the delta-V goes into the de-orbit burn. So I\'m not sure which is better. Sounds like it\'s time for more experimentation!

Here\'s a wacky idea: put your periapsis between the canyon walls, so that your orbit starts climbing back up before screeching to a stop on the highlands east of the canyon. If anyone can get that to work, I\'ll invent a new medal for them!

[Tarmenius]

BlazingAngel665, that is definitely an interesting idea. I\'ll be trying it out shortly. And Zephram, if I remember correctly it is indeed a bi-elliptic transfer. Also, I tried your 'wacky idea' a couple days ago, but I was so busy enjoying the scenery that I didn\'t brake in time. Poor Kerbals... Sounds like I\'ll have to give it another go.

[closette]

As with other challenges this one has inspired me to do a lot of reading and learning about orbital mechanics, even though I\'m not so great at the challenge itself.

Regarding a bi-elliptic transfer, which I think means adding velocity to the 100km circular orbit, coasting to the resulting higher apoapsis, then subtracting velocity to lower your periapsis (or even to land directly), I don\'t think that can beat the 2-impulse + gravity turn method that most people are using. There would also be the question of what apoapsis to use for the intermediate ellipse?

First I played with the KSP Orbit Mechanic Java tool available here http://kerbalspaceprogram.com/forum/index.php?topic=4707.0 selecting 'Mun', 'High to Low' and 'Bielliptic transfer' and trying out some intermediate orbits, but the total delta-v including killing the final tangential velocity before touchdown is always bigger than the ~ 670 m/s of the 2-impulse method. Also, compared to the method we\'ve been using, the bi-elliptic transfer:

- increases your speed over the ground at periapsis, compared to the smaller intermediate orbit.

- burns less fuel on the first impulse, which unfortunately means that you end up with a more massive spacecraft close to the ground. So the higher mass and higher velocity will take more fuel to slow down for a vertical landing.

Still, I had to give it a try, boosting up to ~ 300 km first and then retro-firing to get a 1km periapsis. I was surprised that the fuel budget wasn\'t as bad as I thought. I was also surprised by the landing! It was on the night time side of the Mun so I could not see what was below, and as soon as I had killed my horizontal speed and pitched up vertical, I was on the ground!

Screenshots attached. I have also attached paper on orbit transfers that deals with transfers between coplanar elliptical orbits. What has that got to do with landing on the Mun? Well we start out in an elliptical orbit (circular is a special case), and are trying to transfer to an elliptical 'orbit' with an apoapsis just above the ground and an eccentricity close to 1.00. The paper pretty much confirms that the 2-impulse method we have been using is close to optimal.

[Tarmenius]

I\'m not so great at the challenge itself.

We\'ve all done pretty damn well in my book. The difference between 1st and 10th is only 12.7 kg/Gubs which really isn\'t very much. Plus, you managed a night-time Munar landing without using MechJeb. No small feat from where I sit.

And I looked through the paper you attached. If I could understand a tenth of what they were saying, I\'m sure I\'d find it very helpful indeed. It will take a mind way more mathmatically competent than mine to make full use of it It did give me some ideas about how to better incoporate plane changes into the typical Hohmann transfer, though.

After a couple tries with the bi-elliptic method, I managed to use less fuel than the 'direct descent' method, but still 20-30 kg/Gubs more than the one we\'re already using. So I think it\'s safe to say that the most efficient method is to drop your Pe as low as you dare then kill horizontal velocity, turning the craft to vertical slowly while throttling back a bit to perform a 'reverse gravity turn' just before touchdown. If that sounds right to everyone, I\'ll add it to the bottom of the original post so that passersby can benefit from what we\'ve learned here. Of course, anyone who wants to can still try for a top spot on the Leaderboards and I\'m certainly not giving up on the mountaintop landing goal.

[Majiir]

Bi-elliptic transfers become more efficient as the elliptical becomes more pronounced (higher eccentricity transfer orbit). Mathematically speaking, it\'s more efficient—but in practice, you need to follow the mathematics. It\'s possible that the SOI limits of the Mun make a proper bi-elliptic descent impractical.

However, if you planned your Mun insertion trajectory with a bi-elliptic transfer in mind, I think you could achieve non-trivial fuel savings. However, a proper descent computer (which, by the way, I don\'t think plugins have yet achieved) will save you more in the end.

[Zephram Kerman]

...So I think it\'s safe to say that the most efficient method is to drop your Pe as low as you dare then kill horizontal velocity, turning the craft to vertical slowly while throttling back a bit to perform a 'reverse gravity turn' just before touchdown. If that sounds right to everyone, I\'ll add it to the bottom of the original post so that passersby can benefit from what we\'ve learned here...

That\'s a good idea! The results of experiments we\'ve done here are useful to every KSP pilot. Putting the findings in the first post makes it much easier to find the good stuff.

[Tarmenius]

However, if you planned your Mun insertion trajectory with a bi-elliptic transfer in mind, I think you could achieve non-trivial fuel savings.

Excellent point. I\'ll be sure to make it clear that this method is only the most efficeint from an already-established Munar orbit and that through proper insertion planning, better results can certainly be achieved.

You\'ve also given me an idea to expand this challenge to begin just before entering the Mun\'s SOI so we can factor in the insertion as well. Although perhaps that would be better served in a new-but-related challenge...

[EDIT] The original post has been updated. Please let me know if there are inaccuracies or if it\'s difficult to follow.

[PakledHostage]

However, if you planned your Mun insertion trajectory with a bi-elliptic transfer in mind, I think you could achieve non-trivial fuel savings.

You could also achieve non-trivial fuel savings by bypassing the orbital insertion and making your landing directly from a hyperbolic fly-by trajectory. I did some 'back of the envelope calculations' using patched conics. It is an idealised calculation which assumes that the Mun\'s surface is perfectly spherical with an altitude of 0 m. Also, all burns are assumed to be impulsive except the TMI burn:

Starting with the challenge stack in a 100 km altitude circular orbit about Kerbin

Option 1:

- burn to 3084.1 m/s at 100% throttle. Yields a 100 km munar periapsis at 720.5 m/s (relative to Mun\'s centre of mass).

- retro burn to 466.0 m/s for insertion into 100 km munar orbit (-254.5 m/s).

- retro burn to 417.4 m/s for DOI (-48.6 m/s). Yields a 1 km x 100 km descent orbit.

- retro burn to 0 m/s relative to munar surface at 1 km Pe (-614.0 m/s).

- freefall from 1 km altitude to 0 km altitude, followed by impulsive burn to arrest the descent (-57.0 m/s)

Net delta-V (post TMI burn) = 974.1 m/s

Option 2:

- burn to 3082.8 m/s at 100% throttle. Yields a 1 km munar periapsis at 853.0 m/s (relative to munar surface).

- retro burn to 0 m/s relative to munar surface at 1 km Pe (-853.0 m/s).

- freefall from 1 km altitude to 0 km altitude, followed by impulsive burn to arrest the descent (-57.0 m/s)

Net delta-V (post TMI burn) = 910.0 m/s

That\'s an improvement of 64.1 m/s for the case where landing is initiated directly from hyperbolic flyby trajectory (65.4 m/s if you include the difference in delta-v between the two TMI burns).

[Majiir]

You could also achieve non-trivial fuel savings by bypassing the orbital insertion and making your landing directly from a hyperbolic fly-by trajectory. I did some 'back of the envelope calculations' using patched conics. It is an idealised calculation which assumes that the Mun\'s surface is perfectly spherical with an altitude of 0 m. Also, all burns are assumed to be impulsive except the TMI burn:

Starting with the challenge stack in a 100 km altitude circular orbit about Kerbin

Option 1:

- burn to 3084.1 m/s at 100% throttle. Yields a 100 km munar periapsis at 720.5 m/s (relative to Mun\'s centre of mass).

- retro burn to 466.0 m/s for insertion into 100 km munar orbit (-254.5 m/s).

- retro burn to 417.4 m/s for DOI (-48.6 m/s). Yields a 1 km x 100 km descent orbit.

- retro burn to 0 m/s relative to munar surface at 1 km Pe (-614.0 m/s).

- freefall from 1 km altitude to 0 km altitude, followed by impulsive burn to arrest the descent (-57.0 m/s)

Net delta-V (post TMI burn) = 974.1 m/s

Option 2:

- burn to 3082.8 m/s at 100% throttle. Yields a 1 km munar periapsis at 853.0 m/s (relative to munar surface).

- retro burn to 0 m/s relative to munar surface at 1 km Pe (-853.0 m/s).

- freefall from 1 km altitude to 0 km altitude, followed by impulsive burn to arrest the descent (-57.0 m/s)

Net delta-V (post TMI burn) = 910.0 m/s

That\'s an improvement of 64.1 m/s for the case where landing is initiated directly from hyperbolic flyby trajectory (65.4 m/s if you include the difference in delta-v between the two TMI burns).

Neat analysis. You should note, though, that assuming deorbit burns are impulsive is a pretty big assumption! Most Mun landings are far from perfectly impulsive. I wonder if that would change the conclusion, though.

[PakledHostage]

Neat analysis. You should note, though, that assuming deorbit burns are impulsive is a pretty big assumption! Most Mun landings are far from perfectly impulsive. I wonder if that would change the conclusion, though.

You\'re right, but much of the analysis in this thread makes the same assumption. The assumption allows calculation of a rough estimate of the minimum fuel burn required for a given landing trajectory.

Interestingly, the top placed entries on the leader board are achieving fuel burns close to those predicted by calculations that use this assumption.

[closette]

Agreed, even when full of fuel this spacecraft has a starting thrust/weight ratio in Munar gravity of about 7.5, which is not 'infinity' but is greater than 1, i.e. during the burn the thrust force overwhelms the gravitational force.

Also, perhaps more relevant, the burn times at apomun and perimun are short compared to the transfer time between them, so they appear _almost_ impulsive. Not using time warp would make this very apparent!

It was completely reasonable to question the assumption, all the same. It is not quite so true for the gravity turn final descent, which may be one reason why some of the challenge leaders are beating the theoretical ideal maximum fuel remaining.

PakledHostage your numbers for landing from a realistic SOI entry and fly-by look about right. Personally on Mun missions I try to set up a ~10 km periapsis for the fly-by, then time-warp to it, take a look at the Mun\'s surface and if I like what I see, either start a landing gravity turn, OR establish a 10km circular orbit which is a good altitude to look ahead for interesting landing spots. This is all in the same equatorial plane - doing a plane change would be 'cheaper' if done further out when the craft is falling at a much lower speed.

[PakledHostage]

Obviously there are compromises to be made when choosing an orbital altitude for Munar capture, approach and landing. I certainly haven\'t considered all the factors, but I imagine that objectives like minimising communications blackouts (requiring a higher orbit) and minimising fuel burn during the descent to and ascent from the surface (requiring a lower initial orbit) would be key. The ability to choose a suitable landing site and the relative safety of the approach and landing would also be extremely important. Initiating the descent to landing directly from a low Pe flyby trajectory isn\'t very practical, but the analysis of this option seems to illustrate that inserting into a lower initial orbit about the Mun is significantly more fuel efficient than inserting into a higher orbit.

Looking at Figure 1 in the article that Tarmenius linked to, a ~60 NM high lunar orbit was used in the Apollo program. When scaled down into the Kerbalverse, that\'s equivalent to a 12-13 km orbital altitude about the Mun. That\'s right in line with your method, Closette. And since setting up for insertion into a non-equatorial orbital plane can be done very economically during the TMI burn, I don\'t think plane change manoeuvres are a critical consideration unless the mission requires them for some reason.

It will be interesting to revisit this challenge when docking is finally added to the game. Hopefully it will be possible to build some low delta-V lander and ascent stages, such that efficient trajectory design is actually critical to successful completion of the mission.

[closette]

Well on the subject of entering the Mun\'s SOI, here\'s a question I\'ve pondered and can\'t seem to answer without going through the math, but I feel I should be able to figure out conceptually, so please help...

Let\'s say I arrive in the Mun\'s SOI on a hyperbola which has a periapsis of 200 km altitude (so 400 km from Mun\'s center) , and I want to end up in a 10km circular orbit (radius 210 km) for surveying a landing spot. No plane changes needed and time is no object.

Should I either:

- retro burn while far out to reduce the hyperbola\'s periapsis to 10km altitude, coast to this periapsis, then circularize,

OR

- coast to the 200 km periapsis of the hyperbola, retroburn into a transfer ellipse with a 10km periapsis, coast around the orbit to that ellipse\'s periapsis, then circularize (like a Hohmann transfer).

Which is more fuel efficient (and why?). Or is there an even more efficient method (e.g. with 3 burns)?

[Tarmenius]

Well I managed to fly through that gorge, but I overshot the peaks a little bit. Even so, with the slight plane change maneuvers and correcting my Pe (I dropped it too low at first), I still managed to retain 134.9 Gubs. Not good enough to advance my position on the Leaderboards, but still a decent result all things considered.

PakledHostage, we may not need to wait for docking to have a lander with such a tight fuel budget. I\'ve got a couple design ideas I\'ll mess around with and if I come up with something workable, I\'ll let you guys know.

closette, my gut reaction is that your first option may be more efficient since you\'d be moving slower during the initial burn, maximizing the effects of your thrust. Of course, I don\'t know for sure because in that case, you\'d have a slightly higher velocity once you reached the 10km Pe. I guess it depends on the net difference between the two.

And now I really want to expand this scenario to include the insertion. Would you guys use it if I made a new persistent.sfs with the same lander, but just outside the Mun\'s SOI? Or should it be more toward halfway between Kerbin and the Mun?

[closette]

Tarmenius that\'s an excellent idea - perhaps it should be in a separate Challenge thread though (with a link back to this one).

Just outside the Mun\'s SOI or just inside - I\'m not sure which is better. If just outside you do give us the additional option of changing the insertion point, true, but at least let\'s make sure that the velocity will still take a coasting spacecraft well inside the SOI (with some large periapsis on the hyperbola all the same), not just grazing the outer edge.

In fact if you can manage it, an initial velocity vector typical of a 'free return' trajectory from Kerbin would be a good candidate for a Mun-mission-like challenge. (So if one does nothing, one leaves the Mun\'s SOI on a path towards Kerbin\'s SOI). Breaking out of free return and into a landing profile with high efficiency could provide some useful results for everyone.

It would be nice if the challenge were still do-able by those with the 0.13.3 version of the game (it will encourage them to pay up and upgrade at a later date!). They don\'t have patched conics visible, but many of us did just fine without them.

These challenges are hard to set up well, but you did an amazing job with this one.

P.S. Thanks for your input into my question - still not sure what the best strategy is though. And some great flying through the gorge - the Force is strong with you.

[Tarmenius]

I was thinking it would be best as a separate-but-related challenge, too. And if I were to set it up with the craft outside the Mun\'s SOI, it would definitely be on a path to take it inside. I was contemplating on just how far inside the Mun\'s SOI to make it, until you mentioned a free-return. That would definitely be both a realistic scenario and a good middle-gound between the possible TMI options.

Although my ideas for a new, low-delta-v lander (inspired by PakledHostage\'s post) would require parts not found in the demo, I\'d like it to be accessible to as many players as possible. So maybe I\'ll have two versions... This\'ll be fun to set up.

[EDIT]: I just checked the Demo and this challenge wasn\'t compatible with it, so the next one won\'t be either. Of course, this just means that anyone who wants to participate will have to upgrade, as if they needed a reason beyond KSP\'s full greatness.

By the way, thanks for the suggestions and the compliment. I was a little unsure of myself when I set the whole thing up, so it\'s nice to hear I did alright.

[PakledHostage]

Should I either:

- retro burn while far out to reduce the hyperbola\'s periapsis to 10km altitude, coast to this periapsis, then circularize,

OR

- coast to the 200 km periapsis of the hyperbola, retroburn into a transfer ellipse with a 10km periapsis, coast around the orbit to that ellipse\'s periapsis, then circularize (like a Hohmann transfer).

Which is more fuel efficient (and why?). Or is there an even more efficient method (e.g. with 3 burns)?

I can\'t speak to the relative efficiency of my method because I haven\'t compared it analytically with other methods but I would bump my periapsis down to 10 km as soon as I cross the Mun\'s SOI by burning normal to the spacecraft\'s motion but within the plane of the hyperbolic orbit. I would then wait until reaching periapsis to close down my orbit because that would take maximum advantage of the Oberth effect.

Intuitively, it makes sense that this is an efficient method. Imagine approaching the Mun from within the Mun\'s orbital plane. Now imagine a 'gate' located on the circumference of the Mun\'s orbital radius at some distance from the Mun\'s centre of mass. Any hyperbolic trajectory originating at the spacecraft\'s current position with a given orbital energy is uniquely defined by the position of such a 'gate'. The hyperbolic Pe distance can therefore be adjusted by 'turning' to pass through one of these uniquely defined 'gates'. Gates that are farther from the Mun\'s centre of mass result in higher Pe, while gates nearer to the Mun\'s centre of mass result in a lower Pe. As we all know, 'turning' is done most efficiently by burning perpendicular to the spacecraft\'s velocity. At large distances, burning in the direction of the Mun\'s orbital motion is roughly perpendicular to the spacecraft\'s trajectory while still in the hyperbolic orbital plane. Also, at large distances, the amount of 'turning' required (and consequently the delta-V required) to change the gate position is very small. Therefore, burning E or W as required to raise or lower the Pe imediately after crossing the Mun\'s SOI, when approaching the Mun from within the Mun\'s orbital plane, would seem to be an efficient method of adjusting the approach trajectory. The orbit could then be closed down to a circular orbit at the hyperbolic Pe to take maximum advantage of the Oberth effect.

This is also the method that I would use for trimming my orbital plane during inital approach. For example, if I entered the Mun\'s SOI in the equatorial plane with some random hyperbolic Pe but I wanted a polar orbit, I\'d bump the Pe down to -200 km (i.e. in line with the Mun\'s centre of mass) then orient N or S (as required for the intended orbital direction) and bump the Pe back up to something above the Mun\'s north or south pole. I\'d then close down my orbit upon reaching the hyperbolic Pe.

And Tarmenius, I think it would be most objective to start from low Kerbin orbit and fly the whole transfer. As I showed in my comparison between Option 1 and Option 2 in my post above, it is possible to yeild very different munar periapses with very small differences in TMI burn lengths. Expending fuel to adjust one trajectory into another would bias the results in favour of the initial trajectory. That may not be practical though, so feel free to set it up however you feel like. As Closette said, you did an excellent job setting this challeng up.

If you want to set up a free-return trajectory for your next challenge, you might want to reference my entry to the free-return trajectory challenge back in January. You can find the details here: http://kerbalspaceprogram.com/forum/index.php?topic=4449.msg70498#msg70498 and here: http://kerbalspaceprogram.com/forum/index.php?topic=4449.msg57476#msg57476