Landing a Rocket on the Mun

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sardia
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Landing a Rocket on the Mun

Postby sardia » Tue Dec 29, 2015 2:10 am UTC

I was trying to figure out the cheapest delta v to land on the Mun from a parking orbit, and it seems people were arguing for a reverse gravity turn, vs the Constant altitude landing + suicide burn.
https://www.reddit.com/r/KerbalSpacePro ... burn_good/
Suicide burn is defined as a burn where if you waited 1 second longer to fire your engines, you crash.

Suicide burn: Pointing retrograde to kill horizontal velocity makes then firing engines til you land softly makes sense, but is inefficient.
Constant Altitude landing: Using a Hohmann transfer to get low in altitude/orbit in order to do a suicide burn that is more efficient overall makes sense.
How does the reverse gravity turn work, if at all in a more efficient way?

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Re: Landing a Rocket on the Mun

Postby wumpus » Thu Dec 31, 2015 5:24 pm UTC

First: the most efficient means of landing will be a suicide burn. This follows from the Obererth effect: the point you light the engines will be at maximum velocity, thus giving you highest efficiency in your rockets.

The most efficient landing on a world without an atmosphere should be the same trajectory as the most efficient takeoff. I would guess that you should burn at apogee until your trajectory just barely intersects with the Mun and perform your suicide burn at pure retrograde. Following pure retrograde is likely not optimal for orbits that intersect more steeply, but I suspect that for those that "just graze" the surface it will work.

Finally, such a "suicide burn" is almost certainly suicide on the [paid] 1.0.5 edition of KSP. The Mun [as of 1.0.5] is just too rocky and finding a good landing spot is hard. It might work on Minmus (just look for the purple "seas") or on the demo edition (the Mun is pretty flat on what steam gave me over the holidays, but I've heard it was the "wrong" one). Also, my [possibly out of date] edition of Kerbal Engineer doesn't seem to give valid "suicide burn" times for non-vertical travel. Make sure you know what you are looking at before waiting for the last second.

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Re: Landing a Rocket on the Mun

Postby Izawwlgood » Thu Dec 31, 2015 5:32 pm UTC

wumpus wrote:The most efficient landing on a world without an atmosphere should be the same trajectory as the most efficient takeoff.
Right, which in a vacuum is as shallow an angle as possible. I think for landing this is less plausible as killing any horizontal velocity is pretty important to prevent tipping, but the more shallow your approach the better.
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Re: Landing a Rocket on the Mun

Postby SuicideJunkie » Mon Jan 11, 2016 7:25 pm UTC

It should be noted that the 'horizontal suicide burn' isn't much of a 'suicide' burn, since if your timing is slightly off, it only affects how far downrange you land.
In all cases, plan to come to a halt a couple hundred meters up, and then hover around to a flat spot to land. Safety margin! When you have the option, thrusting a few degrees to the side of retrograde early on can get you to the flat spots if you have good eyes.

Optimal launch off mun would be wait for the right angle and then launch straight upwards and out of the SOI on to your desired course. Don't waste any dV on horizontal stuff like going to orbit first.

If you need time to figure out which way to go, or if orbit is your actual destination, then it is orbit time.
With no atmosphere, there is no drag and angle of attack doesn't matter so you don't need to start vertically. If the world was also a perfect sphere, the starting angle should be just enough to get 1/6th g of vertical accel and the rest horizontal, then tipping towards fully horizontal as you approach orbital speed, resulting in a 0km x 0km orbit as quickly as possible.

With terrain, your starting angle will be a hand-wavy "get enough upwards velocity to clear the local terrain features", and tip from there to horizontal and make orbit, which in theory could be a very tight turn, but in practice means going full throttle and then turning to horizontal as fast as your attitude control can get you there because by the time your landing gear leave the surface, you're already lagging behind the curve.
Landing on the east side of a hill will help since you're already tilted the right way. If you're feeling adventurous, you could also retract the eastern landing gear before you gun it.

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Re: Landing a Rocket on the Mun

Postby Copper Bezel » Mon Jan 11, 2016 9:19 pm UTC

SuicideJunkie wrote:It should be noted that the 'horizontal suicide burn' isn't much of a 'suicide' burn

*Blink* You do seem to be the expert. = .
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Re: Landing a Rocket on the Mun

Postby Izawwlgood » Mon Jan 11, 2016 10:59 pm UTC

SuicideJunkie wrote:Optimal launch off mun would be wait for the right angle and then launch straight upwards and out of the SOI on to your desired course. Don't waste any dV on horizontal stuff like going to orbit first.


Yeah, I don't think this is true?
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Re: Landing a Rocket on the Mun

Postby sevenperforce » Tue Jan 12, 2016 1:48 pm UTC

Izawwlgood wrote:
SuicideJunkie wrote:Optimal launch off mun would be wait for the right angle and then launch straight upwards and out of the SOI on to your desired course. Don't waste any dV on horizontal stuff like going to orbit first.


Yeah, I don't think this is true?

I suppose it would depend on your T/W ratio, your highest acceptable gee-rating, the Mun's gravity, and the Mun's rotational speed. If the body has low gravity but reasonably rapid rotation and you have sickeningly powerful engines with a hardened payload, this might be the case.

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Re: Landing a Rocket on the Mun

Postby Izawwlgood » Tue Jan 12, 2016 1:54 pm UTC

I mean, yes, you don't need to orbit a body before leaving it, but I don't think you save fuel by opting to do it this way.
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Re: Landing a Rocket on the Mun

Postby sevenperforce » Tue Jan 12, 2016 3:13 pm UTC

Izawwlgood wrote:I mean, yes, you don't need to orbit a body before leaving it, but I don't think you save fuel by opting to do it this way.

Not in a two-body problem, no. But if you are heading to another body's SOI, you've got a chance if your engines are powerful enough and you don't mind pulling really high gees.

Mostly unrelated: this is such a cute moon rover!

One idea mentioned is to somehow "melt" pathways into the lunar surface to allow rovers to move across predetermined trackways more rapidly. Could a compact lens be used to focus solar radiation enough to accomplish this, albeit slowly?

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Re: Landing a Rocket on the Mun

Postby sardia » Sat Jan 16, 2016 3:44 am UTC

I do apologize for the late reply, I've been very busy at work. Let's do some tests based on what you guys have told me.

Base stats
Orbiting with an 100km x 100km with a velocity of 466m/s.
1911m/s delta v.
4635kg.
Spoiler:
Image

Scenario 1.
Initial Burn of 43m/s will set up an PE of 10km and 100 AP.
2nd burn to kill horizontal velocity at 10km altitude.
1270 m/s delta v left.
3rd burn, suicide burn to land.
1096 m/s delta v left.
Total usage= 1911-1096 = 815 delta v used to land.

Scenario 2.
Activate autoland which immediately burns twice.
1st burn to deorbit.
2nd burn to land.
Delta v left is 1224 m/s.
Total usage = 1911-1224 = 687 delta v to land.

Scenario 3.
1st burn to establish new orbit of 100x10km.
1867 m/s delta v left.
2nd burn by auto pilot to deorbit.
1798 m/s delta v left.
3rd burn to land by autopilot.
1234 m/s delta v left.
Total usage = 1911-1234 = 677 delta v to land.

I don't think the autopilot is the most efficient, so I'll try to beat it via manual piloting.
Bah, 1181 m/s delta v left via hohmann transfer to 7km PE, a burn to kill horizontal velocity,and a final burn to land.
2nd attempt got me to 1206 delta v left, but that's still not better than the autopilot.

Some thoughts,
Say I'm theoretically flying across a smooth sphere, in the lowest possible orbit without crashing. If I were to simply burn horizontal, I would slowly lose altitude at the rate of local gravity. This limits how long I have to burn horizontal that is correlated with my altitude, which should be less than a second. Therefore, I should dedicate just enough thrust to maintain my altitude, and dedicate the rest to reducing my horizontal speed. This gives me infinite time to reduce my horizontal velocity. Once horizontal velocity reduces to 0, then I can tilt the ship to the sky and land. Is this the theory behind a Constant Altitude landing?

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Re: Landing a Rocket on the Mun

Postby Izawwlgood » Sat Jan 16, 2016 12:32 pm UTC

Test in reverse. From landed, get into a circular orbit. The delta-v is a good benchmark for what to aim for on landing.
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Re: Landing a Rocket on the Mun

Postby sardia » Sun Jan 17, 2016 11:30 pm UTC

Izawwlgood wrote:Test in reverse. From landed, get into a circular orbit. The delta-v is a good benchmark for what to aim for on landing.

Scenario 1. Initial burn from the Mun, coordinates 0,0 (on the equator) to a 100x100km orbit. Final delta v is 1096.
1911-1096 delta v = 815 m/s.

Scenario 2. Initial burn lifts rocket to 100m, and then a hard right until AP is at 100km. Circularization burn gets me to 108x91km orbit. Final delta V is 1211m/s.
1911-1211 = 700m/s delta V used.

Scenario 3. Manual burn up to 100m, and tilt hard right. I point radial just enough to clear the mountains, but I burn mostly prograde the whole way. Final delta v is 1204m/s.
1911-1204 = 707m/s delta v used.

Based on launching from the same location on the moon, 700m/s is what you need to get off or land onto the moon. Most of the error is based on how high of a mountain you land on. I wonder if you can use a bi-elliptic transfer to shave off some more delta v. It says
"While they require one more engine burn than a Hohmann transfer and generally requires a greater travel time, some bi-elliptic transfers require a lower amount of total delta-v than a Hohmann transfer when the ratio of final to initial semi-major axis is 11.94 or greater, depending on the intermediate semi-major axis chosen.[1]"
Should be possible?

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Re: Landing a Rocket on the Mun

Postby Izawwlgood » Mon Jan 18, 2016 3:42 am UTC

Yeah, the lower angle on take off the better your total delta-v. Think Pythagoras.
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Re: Landing a Rocket on the Mun

Postby SuicideJunkie » Tue Jan 19, 2016 3:53 pm UTC

Izawwlgood wrote:
SuicideJunkie wrote:Optimal launch off mun would be wait for the right angle and then launch straight upwards and out of the SOI on to your desired course. Don't waste any dV on horizontal stuff like going to orbit first.


Yeah, I don't think this is true?
I had the opportunity to test it while planting a radio relay beacon on the trailing side of the mun.
Burning straight up (and thus retrograde to the mun's orbit) and all in one go near the surface cost me only 800m/s to put the ship into a direct aerobraking course to Kerbin. (I initially overshot into a lithobraking course and had to slow down)

Roughly a 20% discount compared to going to orbit and then making a transfer, but only applies if you're on the correct side of mun because it is tidally locked and you can't just wait until your launch site is facing the desired direction.

PS:
I should note that this was done with a 909 pushing a 4 ton vehicle so the burn was fairly long, and there was no pilot so I also had to steer manually. Burning faster and less drunkenly should reduce the dV required further.

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Re: Landing a Rocket on the Mun

Postby sevenperforce » Tue Jan 19, 2016 4:44 pm UTC

Is a trajectory straight into the trailing side of a tidally locked satellite then the minimum possible delta-v for a landing? Or would it be better to aim for an orbit tangent to the surface and then thrust retrograde?

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Re: Landing a Rocket on the Mun

Postby SuicideJunkie » Tue Jan 19, 2016 6:16 pm UTC

I don't think the tidal locking factors into it noticeably. The difference would be a slight offset and angle to the approach vector.
Consider at the extreme cases; you could have a surface rotating at either orbital or just over escape velocity and I expect the optimum angle for one of those would be to come in tangent to the surface. Or, if the surface wasn't rotating at all, you'd come straight down. The tidally locked case is in between.

Tidal locking is a big disadvantage in that you only have one choice for your straight-up exit vector rather than 360 degrees worth of choice if you are willing to wait for the surface to turn you around. (EG; if you change your mind from wanting to descend to the planet to wanting to escape from the planet.) Very slightly faster or slower rotation wouldn't change the descent profile much, but would change your wait time from infinity to mere years/months/days.

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Re: Landing a Rocket on the Mun

Postby sevenperforce » Tue Jan 19, 2016 8:36 pm UTC

Suppose we have two spacecraft: one in a (reasonably) low circular parking orbit over the surface of a body without an atmosphere, and one at rest on the surface. The one in a parking orbit has high fuel reserves and a high-vacuum-Isp engine with high thrust; the one on the surface has low fuel reserves and a moderate-vacuum-Isp engine with moderate thrust. Our goal is to mate the two spacecraft while burning as little fuel as possible but still reserving a decent margin for error. The goal is to get off the ground with the engine inside the lander, but mate to the parking-orbit craft so its higher Isp and fuel reserves can do an orbital injection burn.

This isn't what the Apollo lunar orbit rendezvous did. With the Apollo missions, the lander's ascent module had sufficient fuel and Isp to make an orbital injection on its own and did an orbital rendezvous with the command module. Here, we're going to need to slow down the craft in the parking orbit to match the ascent trajectory of the lander, allowing enough free-fall time to successfully mate and re-orient the craft before the larger engine can be re-ignited.

Presumably, you'd want to fire the larger craft's engines in an inclined retrograde, reducing its horizontal speed and adding vertical speed. At the same time, the lander would make its ascent so as to intercept.

What sorts of trajectories could we use here?

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Re: Landing a Rocket on the Mun

Postby SuicideJunkie » Tue Jan 19, 2016 9:16 pm UTC

Is this a rescue mission for a landing that went horribly wrong?
I'd recommend having an extra seat on the orbiter, and leaving it in orbit. Use the lander to boost as best you can, and then "stage" to the EVA jetpack to make orbit and rendezvous normally.
Switching control between two vehicles in low suborbital trajectories is difficult at the best of times, and not allowed at worst (can't switch vehicles when surface collision imminent).

My Dad actually lost about half of his mun landers that way; after designing the dV budget down to what the math said, and then finding that he didn't have enough safety margin in practice. Open the airlock, grab the surface sample baggies, and then jump as hard as you can. :mrgreen:

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Re: Landing a Rocket on the Mun

Postby sevenperforce » Tue Jan 19, 2016 10:25 pm UTC

The Martian, of course.

Not really. Though it did bug me a bit, the whole astrodynamics thing. Supposedly the author did all the math appropriately...but if the Chinese probe had enough dV to catch up with the Hermes mothership, wouldn't it have had enough dV to make it to Mars along the same trajectory anyway? Maybe I'm missing something.

No, I was thinking about an actual planned mission profile to our Moon, one using a Falcon Heavy and the Dragon V2. I just posted the question in this thread because y'all were talking about getting onto and off of an atmosphereless body with minimal dV.

The point would be to land on the moon, take off, and land again on Earth all using the same craft. But since the Dragon V2 can't possibly carry enough fuel to make it from lunar orbit to the lunar surface and back again, let alone make the trip back to Earth, it needs assistance from the Falcon upper stage. The idea was to do a suicide burn using the Falcon upper stage to a near-standstill at a marginally safe distance above the lunar surface, then use the Dragon's abort capabilities to separate from the Falcon upper stage and then land under its own power while the now-unencumbered Falcon upper stage boosted back up to into a low parking orbit.

That's simple enough...it's the return that would be godawfully tricky. Hence the idea of having the upper stage execute an inclined retrograde burn which the Falcon V2 could match. There are two possibilities:

vertical takeoff.png
vertical takeoff.png (4.09 KiB) Viewed 7266 times
sideways action.png
sideways action.png (4.05 KiB) Viewed 7266 times


The nearer to vertical the Dragon V2's ascent is, the less speed it has to pick up, but the less time you have and the more energy the orbiter will waste. The nearer to horizontal the Dragon V2's ascent is, the more dV it requires, but it offers more time and saves more of the orbiter's energy. Obviously, the extreme of the first case is that the Falcon upper stage comes to a full stop and the lander's ascent is completely vertical, while the extreme of the second case is that the lander actually goes right on up to orbital velocity to match the Falcon upper stage.

There's got to be some in-between case where the optimal parking orbit and trajectories lie...

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Re: Landing a Rocket on the Mun

Postby SuicideJunkie » Tue Jan 19, 2016 11:04 pm UTC

I'm just handwaving here, but wouldn't the best option be to have the lander go all the way to orbit and then rendezvous, so as not to waste fuel doubly accelerating the heavier ship?
The corresponding worst option would be to have the heavy orbiter come to a complete stop (at zero altitude for a really worst case), dock and then burn back to orbit?

The in-between option would then depend on how much dV the lander has to provide, with modifiers based on how quickly the orbiter can make the maneuvers, and how much safety margin you can afford to build in.
I presume you'd want to make it as much like a truncated burn to orbit as you can for efficiency, with extra vertical speed to allow the orbiter to clear any terrain before it pops up to match, and for looser docking deadlines.

As for the images, I expect you'd want to have the red line be a straight and simple orbit until it crosses the green line, then burn sharply to exactly match course and position in one go.
In the first case you get more altitude, but have to kill and build more horizontal speed to make orbit.
In the second case you get less altitude, but have to kill and build less horizontal speed to make orbit (although the orbital velocity will be a bit higher, the lander's horizontal speed should more than make up for that).

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Re: Landing a Rocket on the Mun

Postby sevenperforce » Wed Jan 20, 2016 12:30 am UTC

Oh, taking the lander all the way to orbit would unquestionably be the ideal case. It's just not possible because of the lander's lower Isp and very limited mass fraction. The truly opposite extreme, where the orbiter burns retrograde all the way to zero velocity at zero altitude, is also impossible because it's not set up for a landing. The idea was to see whether clever rocket dynamics could be engineered to plan a viable moon landing using craft that exist right now and are designed for Earth-based missions, rather than scratch-designing something limited only to this mission.

The best option is probably to give the lander a launch trajectory with as much horizontal speed as possible for its dV. IIRC the Dragon V2 would be able to manage around 65% of lunar orbital velocity if fitted with additional internal fuel tanks, but some of that needs to go toward the landing.

What would the optimal altitude for the parking orbit be? One added factor is that these are craft designed for Earth, not the moon, so they have hella T/W ratios. The Dragon V2 could get extremely high altitudes very fast, which might be able to allow a slower orbital speed and a longer transition/docking window.

EDIT: Another factor - since it's a manned mission, there's really no need to establish a stable orbit following docking. Just aim for Earth and use that big-ass Merlin 1D V to blast away, with gravity drag only the faintest of afterthoughts. That's another reason why a more vertically-oriented ascent trajectory for the lander might prove promising.

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Re: Landing a Rocket on the Mun

Postby SuicideJunkie » Wed Jan 20, 2016 10:24 pm UTC

Doing a vertical burn straight towards earth with docking and finishing burn would be possible, but the moon being tidally locked means you're very limited in the choice of landing spots if you want to do that.

Maybe if there happens to be resources right there, or if you build out a spaceport with roads to drive to where the real moonbase action is?

You can probably determine the optimum choice using a spreadsheet with a few simplifications.
1) Assume infinite thrust, instant docking, and no terrain so only dV matters
2) Plot the lander's horizontal speed vs peak altitude
3) Plot the orbiter's orbital speed at various altitudes
4) Orbiter then needs to burn the difference in horizontal speed twice, first unloaded and secondly with the lander attached.

Though, do you really need the lander to come home or even to orbit?
If you conserve some dV for the pop up which gives the crew extra time to transfer from lander to orbiter, you can let the lander crash and just boost the orbiter up to orbit/earth transfer.

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Re: Landing a Rocket on the Mun

Postby sevenperforce » Thu Jan 21, 2016 1:48 pm UTC

SuicideJunkie wrote:You can probably determine the optimum choice using a spreadsheet with a few simplifications.
1) Assume infinite thrust, instant docking, and no terrain so only dV matters
2) Plot the lander's horizontal speed vs peak altitude
3) Plot the orbiter's orbital speed at various altitudes
4) Orbiter then needs to burn the difference in horizontal speed twice, first unloaded and secondly with the lander attached.

Though, do you really need the lander to come home or even to orbit?
If you conserve some dV for the pop up which gives the crew extra time to transfer from lander to orbiter, you can let the lander crash and just boost the orbiter up to orbit/earth transfer.

Oh, you definitely need the lander; the lander is going to be landing on Earth too. Which is, you know...important. Using the same lander for both worlds is the key point of the mission profile, and it allows for significant endpoint dV savings because the lander's hypersonic lift and mass-distribution maneuverability can easily convert a lithobraking trajectory into an aerobraking one.

The limiting factor is probably going to be the dV of the lander.

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Re: Landing a Rocket on the Mun

Postby KarenRei » Fri Jan 22, 2016 2:24 am UTC

Re: suicide burns: back when I played Kerbal I usually had "emergency rockets" on my craft - at least one inefficient but high thrust/mass ratio rocket, in addition to my primary, efficient but low thrust/mass ratio rockets. So if my suicide burn on turned out to be more suicidal than anticipated I could hit the hotkey to turn on my emergency engine(s) and burn some of my reserve fuel to stop from... well, dying. ;)


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