How to calculate optimal descent profiles?

[AceMgy]

I ask this because I seem to be unable to land on a target on the Mun while saving fuel. I just put down a lander with 2000 delta-v and 3.1 TWR on the Mun's surface (yes I know it's over-engineered, but it had to carry two rovers and five kerbals). I landed on target but ended up with 449 dv, not enough to get back to orbit. Now I know my flying isn't perfect and this will probably get better with practice, but I think the descent profile I'm using is bad. Here it is:

@ 20km: -200 m/s vertical

@ 15km: -100 m/s vertical

@ 5km: -50 m/s vertical

@ 1km: -20 m/s vertical

@ 500m: -10 m/s vertical

@ 50m: -1 m/s vertical

Thing is, that was just a guess which has a ton of safety room built in. I'd be very interested to know how to calculate the most fuel-efficient descent profile based on the body and the craft's TWR. I'm trying to think how to calculate that, must be something simple, but it's not coming to me...

Till then I'll try to get an emergency refueling mission together.

[Hannu]

It seems that you are very careful. It takes 50 s from 50 m to surface and uses over 150 m/s delta v. Before I got Mechjeb, I descended at least 100 m/s to about 2 km and lowered then speed to about 20 m/s. When I saw a shadow I lowered speed to 3-5 m/s. Typically I needed 1 attempt to find out what is surface level at landing area.

Optimal descent is so called suicide burn, which means that you brake at full throttle so that speed is 2-3 m/s at surface. It is very risky because any problem in any time means that you can not decelerate enough before hitting the ground. It can be calculated by writing motion equations and solving them by using calculus. It is not very hard task if you have all information about mass, ISP, thrust, gravity, possible drag etc. and basic knowledge about numerical calculus and some programming skills, but unfortunately there is not any simple formula to calculate velocity profiles because ship's mass and planet's gravity changes during descent.

[Eric S]

There's a video floating around here somewhere that shows a highly efficient and mostly safe landing method for celestial bodies that have no atmosphere. It basically involves setting up a periapsis that is barely above the ground and an apoapsis that isn't much higher, then you go full throttle not exactly retrograde. You want to thrust just far enough below the horizon to keep your altitude steady. This means that you'll be gradually transitioning to vertical as you kill your orbital velocity, and at some point, you'll probably need to throttle down.

This is a lot easier to do than a traditional suicide burn because if you start burning a little late, you're going sideways instead of down, so you've still got plenty of time to react.

[Hiddos]

I usually descent to 600km/s at 10KM height, then from 6KM slowly to 300m/s, then at around 2KM to 150km/s and at around 800m to 50m/s.

Don't start burning too early as it's really a waste of fuel

[Nao]

The most fuel efficient way to land would be to make a low circular orbit first (at around 5km altitude) and then slow down before target while slowly descending, so you could stop the ship just above ground. The advantage of such method is also that if you start your burn too late you just overshoot your target instead of lithobraking on the Mun.

But if you want to make a "suicide burn" or maybe just stop orbit at higher altitude and slowly descent vertically, you can use simple maths to judge how late you can start to slow down and not waste fuel hovering at high altitudes.

For example: You have a ship capable of Mun TWR of 3.1 Firstly determine what is its actual acceleration capability.

To switch TWR for accelaration: mun gravity 1,63 * TWR 3.1 = 5 [m/s^2].

Let's assume the ship is on Munar landing approach with 200m/s vertical velocity.

To get minimum height required for safe landing we subtract mun gravity from ships acceleration (5 - 1,63 =~ 3,4 available "maneuver acceleration" [m/s^2]) (a constant that can be counted before flight)

Then assuming 100% thrust: 200m/s divided by 3,4m/s^2 =~ 60s burn time to stop from 200m/s

To get desired minimum altitude simply divide time by 2 and multiply by vertical speed 60/2*200 = 6000m

[Kosmo-not]

There's a video floating around here somewhere that shows a highly efficient and mostly safe landing method for celestial bodies that have no atmosphere. It basically involves setting up a periapsis that is barely above the ground and an apoapsis that isn't much higher, then you go full throttle not exactly retrograde. You want to thrust just far enough below the horizon to keep your altitude steady. This means that you'll be gradually transitioning to vertical as you kill your orbital velocity, and at some point, you'll probably need to throttle down.

This is a lot easier to do than a traditional suicide burn because if you start burning a little late, you're going sideways instead of down, so you've still got plenty of time to react.

This video?

[tavert]

As far as calculating the optimal profile, it's not very simple. I've been meaning to code something up, but have had too much real work to do.

I don't have any proof yet that the constant-altitude profile shown by Kosmo-not is optimal, but I do know that it is definitely more efficient than doing a retrograde suicide burn. The difference is more noticeable at low TWR. The constant-altitude trajectory is also a bit simpler to do the calculations for, I posted the results recently here: http://forum.kerbalspaceprogram.com/showthread.php/39812-Landing-Delta-V-vs-TWR-and-specific-impulse. I can go through the math I used in that thread if you're interested.

[Eric S]

This video?

That's the one, thank you :-) I'm going to start practicing that one. It won't help much for suborbital hops and will be more difficult to pull off in hilly areas, but still involves a lot less guesswork than a traditional retrograde burn landing.

I don't have any proof yet that the constant-altitude profile shown by Kosmo-not is optimal

I wouldn't be surprised if it is at least very close to optimal, as it's basically a reverse of the optimal launch for an airless body, which is to say that you're putting as much delta-v into your orbital velocity as possible without impacting the ground. Optimal would involve touching down while still at full throttle to minimize gravity losses, but I'm pretty sure that timing it out that well is beyond my reflexes.

[AceMgy]

The most fuel efficient way to land would be to make a low circular orbit first (at around 5km altitude) and then slow down before target while slowly descending, so you could stop the ship just above ground. The advantage of such method is also that if you start your burn too late you just overshoot your target instead of lithobraking on the Mun.

But if you want to make a "suicide burn" or maybe just stop orbit at higher altitude and slowly descent vertically, you can use simple maths to judge how late you can start to slow down and not waste fuel hovering at high altitudes.

For example: You have a ship capable of Mun TWR of 3.1 Firstly determine what is its actual acceleration capability.

To switch TWR for accelaration: mun gravity 1,63 * TWR 3.1 = 5 [m/s^2].

Let's assume the ship is on Munar landing approach with 200m/s vertical velocity.

To get minimum height required for safe landing we subtract mun gravity from ships acceleration (5 - 1,63 =~ 3,4 available "maneuver acceleration" [m/s^2]) (a constant that can be counted before flight)

Then assuming 100% thrust: 200m/s divided by 3,4m/s^2 =~ 60s burn time to stop from 200m/s

To get desired minimum altitude simply divide time by 2 and multiply by vertical speed 60/2*200 = 6000m

That is what I was looking for. I knew there was a good way to approximate it but I had a total brainfart and couldn't get past it. The good thing about that method is that it's always an overestimate as the TWR would increase as fuel is burned and Mun's gravity is lower as you go higher. I'd still add 10% for safety at least.

There's a video floating around here somewhere that shows a highly efficient and mostly safe landing method for celestial bodies that have no atmosphere. It basically involves setting up a periapsis that is barely above the ground and an apoapsis that isn't much higher, then you go full throttle not exactly retrograde. You want to thrust just far enough below the horizon to keep your altitude steady. This means that you'll be gradually transitioning to vertical as you kill your orbital velocity, and at some point, you'll probably need to throttle down.

This is a lot easier to do than a traditional suicide burn because if you start burning a little late, you're going sideways instead of down, so you've still got plenty of time to react.

That does sound very interesting as it's the limit towards total fuel efficiency and potentially safer if done right, however I can't imagine getting my timing down good enough to land perfectly on target like I have been practicing. Plus on Minmus where most of my operations take place the mountains would make that a little too perilous. It's a vertical approach for me, thank you.

[arq]

Yup, the more time you spend on a suborbital trajectory the more dV it will cost. As stated above, the most efficient approach is to start from as low an orbit as possible, burn full retrograde to drop most of your horizontal speed, and then land from there. The lower and faster your vertical ascent (after ditching horiz), the more efficient.

[brusura]

The most fuel efficient way to land would be to make a low circular orbit first (at around 5km altitude) and then slow down before target while slowly descending, so you could stop the ship just above ground. The advantage of such method is also that if you start your burn too late you just overshoot your target instead of lithobraking on the Mun.

But if you want to make a "suicide burn" or maybe just stop orbit at higher altitude and slowly descent vertically, you can use simple maths to judge how late you can start to slow down and not waste fuel hovering at high altitudes.

For example: You have a ship capable of Mun TWR of 3.1 Firstly determine what is its actual acceleration capability.

To switch TWR for accelaration: mun gravity 1,63 * TWR 3.1 = 5 [m/s^2].

Let's assume the ship is on Munar landing approach with 200m/s vertical velocity.

To get minimum height required for safe landing we subtract mun gravity from ships acceleration (5 - 1,63 =~ 3,4 available "maneuver acceleration" [m/s^2]) (a constant that can be counted before flight)

Then assuming 100% thrust: 200m/s divided by 3,4m/s^2 =~ 60s burn time to stop from 200m/s

To get desired minimum altitude simply divide time by 2 and multiply by vertical speed 60/2*200 = 6000m

This was enough simple for me to understand and so made and excel sheet to calculate this thing , but while testing my result I found some problem with TWR calculated by me and the TWR displayed by kerbal engineering.

This is my sheet ( https://www.dropbox.com/s/l1uyr4hjestggp5/suicide%20burns.xlsx ) and surface gravity is taken from the wiki, but for Moho and Minmus look like is wrong, is wiki or kerbal engineering wrong?

PS: now if someone would be so kind to make a nice little mod that show just altitude and burn time without switching to my excel sheet my alt+tab would be very happy ( and me of course )

Edited August 6, 2013 by brusura
update

[rodentgun]

Sorry for the thread necromancy, but this advice is still sound in KSP 1.05. I tested it on my Mun lander. Shaved around 150 dV off in the budget, or around 10%. So putting it simple:

The most efficient descent profile is to burn retrograde while keeping descent to 0 m/s so you effectively are flying horizontal until you are at "full stop" on the Surface speedometer. Do it from as low an altitude as you dare to.

Then descent.

 

Thanks

[Plusck]

Well, that's still debatable and was the subject of another thread recently. It depends a lot on how low "as low an altitude as you dare" is, and therefore how close the nearest mountain or crater is, and how close to a given target location you need to be. And what your TWR is.

What is certain is that you want your incoming angle to be as shallow as possible. And you want to mimic the most efficient re-orbit in reverse. Since I haven't seen anyone claim or show that a constant-altitude return to orbit is the most efficient, it is a bit of a stretch to claim that the reverse is true for landing. On taking off, you want to minimise the vertical component while gathering horizontal speed, but you also need to clear the terrain so you will always add a vertical component while accelerating. To lift off, you try to get your acceleration as close to prograde as your TWR allows, and you stay at full acceleration throughout. There is no reason to think that landing should adopt a different profile.

[rodentgun]

That is a lot of if's. I tried it on my last landing on the Mun and compared left over dV after landing. I did shave off around 100 m/s or so by doing as described above instead of a continous retrograde burn. My terrain altitude was around 1000 m from the surface of the East Crater after I cleared the mountain range encircling it (That was a paint scraping moment btw).

I did find it easier to land with the full stop method however. Perhaps this is a reason for efficiency being a human player. I had only to navigate 1000 m down and that made my final approach with vertical retrograde trusts much more precies and short. hence the efficiency gain.

Edited January 11, 2016 by pistolhamster

[Plusck]

I don't doubt that it was both easier and more efficient in practice - and I agree that the human factor probably does count for a lot in that.

I was merely responding to the statement that "The most efficient descent profile is...". I know you were simplifying but still

[tutike2000]

Landing is just taking off in reverse. On an airless body, that is.

So just think of the most efficient way to take off: Full thrust, pitch over as soon as possible to just barely avoid the terrain. Circularize at Ap.
Do that in reverse:
- Pick any point in your orbit, ideally your Pe

- Burn retrograde so that your new Pe brushes against the terrain

- Suicide burn to land

 

This all assumes near-infinite TWR, realistically you'll be pointing a bit 'upwards' from your retrograde during your suicide burn.

[Warzouz]

Having a high dV lander is NOT over engineered. It's very efficient when you start hopping from biome to biome. If your lander can only land and return, you'll burn more fuel than land-hop-hop-hop-return. It's much more science/fuel efficient.

But, if your objective is only to land and plant flag, then, it's too much.

PS : my "generic" lander has 3000m/s of dV, that gives it very large capacity to land, hop, recover kerbals even on retrograde orbit, rescue other landers without fuel.

On 13/7/2013 at 11:46 PM, Eric S said:

There's a video floating around here somewhere that shows a highly efficient and mostly safe landing method for celestial bodies that have no atmosphere. It basically involves setting up a periapsis that is barely above the ground and an apoapsis that isn't much higher, then you go full throttle not exactly retrograde. You want to thrust just far enough below the horizon to keep your altitude steady. This means that you'll be gradually transitioning to vertical as you kill your orbital velocity, and at some point, you'll probably need to throttle down.

This is a lot easier to do than a traditional suicide burn because if you start burning a little late, you're going sideways instead of down, so you've still got plenty of time to react.

I remember it, very instructive. This video doesn't describe a fuel-efficient landing procedure, it describes a safe landing procedure. When you have a low TWR, the suicide burn may not be possible (you gain too much speed you don't have time to cancel later), so the "hover" landing is the only way you can land safely.

Tested myself on Tylo with a 14T SSTO Lander with 0.98TWR at 30km orbit. I landed and back to orbit for 6000m/s. The low TWR and hover procedure cost quite a lot... I tried suicide burn and crashed every time, even with MJ.

[Snark]

1 hour ago, tutike2000 said:

Landing is just taking off in reverse. On an airless body, that is.

So just think of the most efficient way to take off: Full thrust, pitch over as soon as possible to just barely avoid the terrain. Circularize at Ap.
Do that in reverse:
- Pick any point in your orbit, ideally your Pe

- Burn retrograde so that your new Pe brushes against the terrain

- Suicide burn to land

This all assumes near-infinite TWR, realistically you'll be pointing a bit 'upwards' from your retrograde during your suicide burn.

Agreed with all of the above, except for the last sentence.  Unless you have quite a low TWR, want to be pointing surface-retrograde for your whole suicide burn.  (Though admittedly, if you do choose to point slightly above retrograde, it won't hurt much-- cosine losses are pretty small for low angles..)

[Warzouz]

1 hour ago, tutike2000 said:

Landing is just taking off in reverse. On an airless body, that is.

So just think of the most efficient way to take off: Full thrust, pitch over as soon as possible to just barely avoid the terrain. Circularize at Ap.

...

True, but landing with a very flat angle and a suicid burn will moslty result in hitting terrain. You can't really control what terrain you'll get while landing, but you cans anticipate the terrain you'll encounter when you take-off (it's near and easy to locate from your location)

[Snark]

11 minutes ago, Warzouz said:

True, but landing with a very flat angle and a suicid burn will moslty result in hitting terrain. You can't really control what terrain you'll get while landing, but you cans anticipate the terrain you'll encounter when you take-off (it's near and easy to locate from your location)

Depends what you mean by "very flat".  For example, do you consider 15 degrees from horizontal to be "very flat"?  I come in at angles like that all the time and have no problem at all.  And mathematically, that is "very flat."  The purpose of the shallow angle is to minimize gravity losses.  Gravity loss is basically local gravity times (1 - cosθ), where θ is your angle from horizontal.  At a 15 degree angle, that's just 3.4% of local gravity, which is pretty darn small.  Moral of the story:  shallow angles are good, but too shallow doesn't buy you a whole lot.  By the time you're down to 15 degrees, you've already gotten most of the benefit.

And I would contend that you can control the terrain while landing, at least to a reasonable extent.  That's what map view is for.  It's pretty easy to see from zoomed-in map view whether you're landing in a fairly flat area, and whether there are any inconvenient mountain ranges in the way.

Edited January 12, 2016 by Snark

[rodentgun]

Sooooooooooooooooo. What is the conclusion then, if any? Did I do wrong with the approach I used on Mun to land in Eastern Crater? I find the optimal suicide burn thingy impossible to achieve when playing as a gamer, not a physicist. Should I do the horizontal burn but at a small -15 degree tit from horizontal?

[Plusck]

34 minutes ago, pistolhamster said:

Sooooooooooooooooo. What is the conclusion then, if any? Did I do wrong with the approach I used on Mun to land in Eastern Crater? I find the optimal suicide burn thingy impossible to achieve when playing as a gamer, not a physicist. Should I do the horizontal burn but at a small -15 degree tit from horizontal?

I don't think an absolute conclusion is possible without either a very good test method (which I'm thinking about, but it won't be tomorrow) or, preferably, some serious maths (which I cannot provide).

What I am certain of is that there are a number of variables to be taken into account, especially the ruggedness of the terrain and the TWR and manouverability of the craft. Also the changing fuel mass, which means that the perfect descent and the perfect ascent profile cannot be quite identical (but they will be very close).

So no, I don't think you did anything wrong at all. I think that a perfectly-informed computer would do something similar to a suicide burn at the end of a very shallow and almost horizontal trajectory, but we cannot because we would probably crash.

At the end of the day, the best manouvre for you is the one that saves you the most fuel and is the most satisfying, which was the case here. My only objection was when you categorically stated : "The most efficient descent profile is...", because I don't think any of us are yet in a position to know that. Yet. : D

Edited January 12, 2016 by Plusck

[Snark]

38 minutes ago, pistolhamster said:

Sooooooooooooooooo. What is the conclusion then, if any? Did I do wrong with the approach I used on Mun to land in Eastern Crater? I find the optimal suicide burn thingy impossible to achieve when playing as a gamer, not a physicist. Should I do the horizontal burn but at a small -15 degree tit from horizontal?

Actually, optimal (or, at least, near-optimal) suicide burns are pretty easy to do as a gamer... and no calculations required!  There's a simple trick you can do with a maneuver node to let the game do the calculations for you:

1. Put yourself on a path that intersects the surface.  You want to be coming in at a shallow angle above the horizontal.  Doesn't have to be super horizontal; say, 15 degrees is fine.  Even 20 or 25 isn't bad.  Just don't be coming in vertical.
2. In map view, place a maneuver node right at the spot where your trajectory intersects the surface.
3. Drag the node's retrograde handle and hold it until your projected post-maneuver trajectory collapses to a point and the node's prograde/retrograde handles start flipping back and forth.
4. The maneuver node now has all the info you need.  Time to node = time to impact.  Estimated burn time = how long you need to stop.
5. Put your navball into surface-relative mode, and set your craft to hold retrograde.
6. Wait until the time until maneuver is about 70% of the estimated burn time.
7. Hit 100% throttle, brake to a halt at ground level.
8. Change shorts.

In reality, step #7 will slow you down to near stationary when you still have some ground clearance.  The "70%" figure that I use above is a handy rule of thumb that works practically always, as long as your local TWR is reasonably high.  There's some built-in safety margin there.

One drawback to the above approach is that it relies on the game's built-in estimated burn time indicator, which is notoriously flaky.  If you'd like a more reliable readout (and also not have to muck around with maneuver nodes every time you do a suicide burn), there's a little mod I wrote that you may find useful.