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What is the most efficient way to deorbit+land?


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     When i’m landing on bodies without an atmosphere, I noticed when I de-orbit and turn the engine off, I start regaining velocity I just scrubbed off. So I started doing the de-orbit and landing in one burn. But is that the most efficient way? If it isn’t, what is?

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De-orbit and landing in one burn (a.k.a. the 'suicide burn') is the most efficient, for the reason that you describe.

Well, the small initial burn, that turns your orbit into a trajectory that contacts the surface about where you want to land, might be called the 'de-orbit' burn, but then the large burn to bring you to a stop just before reaching the ground is called a suicide burn.

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On 4/18/2021 at 10:12 PM, OHara said:

De-orbit and landing in one burn (a.k.a. the 'suicide burn') is the most efficient, for the reason that you describe.

Well, the small initial burn, that turns your orbit into a trajectory that contacts the surface about where you want to land, might be called the 'de-orbit' burn, but then the large burn to bring you to a stop just before reaching the ground is called a suicide burn.

it has to be stated that it is also the most dangerous, though, because starting the burn too late will result in a patch of debris on the planet. the later you start the burn, the more efficient it will be, until the point where you crash

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I've asked myself this question a few times. My gut has always said that in order to avoid the issue of "regaining velocity", I want to get periapsis as close to the ground as possible, then do a suicide burn near periapsis. A two burn method. By staying in orbit, I'm not "gaining velocity" until I begin the suicide burn.

In practice this has been very hard to pull off. Usually my rocket has puny engines and I am already starting from a low orbit. In some missions it takes upwards of three minutes full burn to get from low orbit to 0 m/s. In those cases, touching down without wasting too much fuel and without crashing into a mountain can take me several attempts, like in the video.

Still, two burns has been the most efficient method for me in cases where I reverted to check the numbers. It's just much harder to succeed at compared to approaching the surface from perpendicular to it.

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The most efficient way to land on an airless body is as follows:

-find the highest point on the equator and start from an equatorial orbit - this gives you some free velocity due to the body's rotation
-start in a circular orbit at exactly that height
-your landing burn will be all in one go - time it carefully and look for landmarks
-landing burn will be pointed above the horizon such that your vertical velocity is always zero - you neither gain nor lose height during the entire burn. You lose a bit of efficiency to cosine losses but you would lose more to gravity losses if you didn't do this.
-if you time it right you come to zero velocity exactly as you reach the body's highest point

To take off you do the reverse of this. Point above prograde such that vertical velocity is zero the whole time until you're in orbit.

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On 4/18/2021 at 3:36 PM, Wizard Kerbal said:

     When i’m landing on bodies without an atmosphere, I noticed when I de-orbit and turn the engine off, I start regaining velocity I just scrubbed off. So I started doing the de-orbit and landing in one burn. But is that the most efficient way? If it isn’t, what is?

The theoretically most efficient way is to do this:

  1. While in orbit, do just enough of a :retrograde: burn to get into a suborbital trajectory (i.e. lower your Pe below ground level).  Note that this puts your impact trajectory on a shallow angle with the ground.
  2. Put your navball into surface mode, if it's not already.  Set SAS to hold :retrograde:.
  3. Free-fall until you're close to the surface.
  4. At the last possible instant*, slam your throttle to maximum while still holding :retrograde:.
  5. Decelerate to a halt right when you arrive at ground level.  Cut throttle, you're done.

The catch, here-- as you've probably spotted ;) -- is to know just when is the "last possible instant" in step 4.  It's tricky and very finicky.  If you start the burn too soon, you end up braking to a halt while still high over the surface, which is fuel-inefficient.  If you start the burn even a little too late, like a second or two, then you get a practical demonstration of why this technique is called a "suicide burn".

So, the tricky bit is judging that moment for hitting the gas.

If you're amenable to mods, then my mod BetterBurnTime has some help for that, as @FruitGoose is kind enough to point out, above.  :)

If you'd prefer not to use mods, however, there's a slightly clunky way that you can use maneuver nodes to do most of the math for you.  Here's a step-by-step description of the technique:

 

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I’ve been contemplating this further (a dangerous thing). Is the suicide burn thing actually a myth?

If I start my descent at 0m/s (fall straight down) and by the time i impact I’ve reached 500 m/s, I would need a suicide burn of 500 dV timed perfectly so I hit as close to 0 when at the surface.

However, if I wait until my velocity is 250m/s (ie half way between descent start and surface) then cancel that by doing a 250 dV burn, the new velocity at impact would be 250m/s - also half  (airless body = fairly linear velocity change I think? )

Likewise, if I break it down into however many segments I need, the dV requirement is still 500dV when combined.

The issue arises when you have horizontal velocity to scrub off as well, hence to me it’s better to cancel all velocity before descending. Unless the body you’re landing on has an atmosphere then you’re just transferring the energy from one burn to another but it’s still the same amount overall.

In practical terms, as long as you don’t overburn and go into negative velocity (or positive I suppose- I mean start taking off again!) then I’m proposing the dV is the same if you slowly stop in stages vs suicide burn.

This falls down if velocity change is not linear, or if you reach terminal velocity before you hit the surface (my first thought) but I can’t recall noticeably doing that on the mun for example (I usually start from a very low orbit though that may be why). Of course if you DO hit terminal velocity, then that figure can actually be used to calculate your suicide burn time thinking about it (very dangerous).

I will run a series of tests later to test my theory, unless anyone knows or can see an obvious flaw in my reasoning :confused:

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31 minutes ago, FruitGoose said:

unless anyone knows or can see an obvious flaw in my reasoning

The variable you're forgetting is time. Acceleration (gravity!) is, in very simplified terms, velocity added per second. The longer your braking maneuver takes, the longer your craft is subjected to acceleration due to gravity, hence the more total velocity you need to 'neutralize' to avoid a crash by the time you reach the surface.

In other words, the most energy-efficient way to come to a safe full stop at the point of touching the surface is whatever maneuver takes the least time to perform = burning full thrust at the very last instance ... the suicide burn.

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3 hours ago, FruitGoose said:

 unless anyone knows or can see an obvious flaw in my reasoning :confused:

 

3 hours ago, swjr-swis said:

The variable you're forgetting is time. Acceleration (gravity!) is, in very simplified terms, velocity added per second. The longer your braking maneuver takes, the longer your craft is subjected to acceleration due to gravity, hence the more total velocity you need to 'neutralize' to avoid a crash by the time you reach the surface.

In other words, the most energy-efficient way to come to a safe full stop at the point of touching the surface is whatever maneuver takes the least time to perform = burning full thrust at the very last instance ... the suicide burn.

besides that already accurate answer, you can easily see the problem in a test. Start on mun in low orbit, your speed should be around 550 m/s. Now make a small deorbit burn to lower your periapsis at ground level. you will crash on the ground, of course. Look at the speed at which you crash on the ground, it will be around 600 m/s, you only gained a few tens of m/s.

Now try to make a big burn in low orbit to stop your orbit completely. you will fall on the ground; again, let yourself crash on the ground and register your speed. it will be much, much higher than 50 m/s. if you stop on the ground there, you still spent more fuel. you had more time to accelerate towards the ground.

 

those 600 or so m/s are the orbital energy, a sum of kinetic energy and gravitational energy. that's the miminum cost you have to pay to orbit/deorbit, you can't cheat there. if you could make a suicide burn at precisely ground level with an engine with infinite thrust, you'd spend exactly that deltaV. everything more you spend are gravity losses and cosine losses.

Edited by king of nowhere
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3 hours ago, FruitGoose said:

Well that's saved an hour of pointless crashing and landing on the Mun anyway.

:)

One handy way to think of it is this:

Let's say you're landing on the Mun, where surface gravity is 1.63 m/s2.  To keep things simple for purpose of this example, assume you're heading straight down (which normally you wouldn't be, because braking to a halt in orbit and then falling down would be really inefficient).

That would mean that every second until you touch down, you're accelerating downwards an additional 1.63 m/s.  That's 1.63 m/s of additional dV that you'll need, to kill the accumulated pull of gravity.  Basically, you're leaking dV, and the speed at which you're leaking it equals local gravity.

So, the most efficient way to land is the suicide burn-- i.e. fall fast and wait until the last second to brake hard to a halt-- because that's minimizing the time you're leaking dV.  That also helps give you an idea of how much of a penalty you pay if you're not quite hitting an ideal suicide burn.  For example, if you start your burn too soon and as a result it takes 20 extra seconds until you touch down, then that means you would have leaked 20 * 1.63 = 32.6 m/s wasted, compared with an ideal suicide burn.

Note that in the above example, I had you falling straight down, in order to simplify the math.  In reality, that would be a pretty inefficient trajectory-- normally what you'd do is to do just enough of a :retrograde: burn in orbit to lower your Pe to ground level, so that when you're approaching the impact point, actually you're descending at a very shallow angle and mostly moving sideways.  In that case, the timing of your suicide burn is a bit less critical in terms of efficiency, because most of your burn is devoted to just killing that very large sideways velocity, and a relatively small amount of it is fighting gravity.  It's only the last little bit at the end that you approach the vertical, as you continuously thrust :retrograde: and your velocity drops.

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That's why you want to come in completely horizontal, so you're always doing the exact minimum amount of fighting gravity. Pointing retrograde is fine if your TWR is really high, but for a low TWR landing (such as, trying to land on Tylo with nuclear engines), you won't be able to land at all, much less land efficiently. That's why you should burn a bit above retrograde, so you have more time before you crash. And even so, a constant altitude landing and a constant retrograde landing asymptotically approach one another as TWR increases, but the constant altitude landing is always more efficient, and the advantage increases as TWR decreases.

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14 hours ago, camacju said:

Pointing retrograde is fine if your TWR is really high, but for a low TWR landing (such as, trying to land on Tylo with nuclear engines), you won't be able to land at all, much less land efficiently.

Should it not be less efficient than a :retrograde: burn, because of cosine losses?

Yes, there is gravity loss, but you have that regardless, no?  So you can do a :retrograde: burn and have gravity losses, or you can do a constant-altitude burn and have both gravity losses and cosine losses.  What's the rationale for the latter?

It's true that sometimes you can't do a :retrograde: burn because you've got such a low TWR-- i.e. just barely higher than 1-- that you need to burn with your nose pointed higher than :retrograde: just so you don't fall down and crash while you're still trying to kill your horizontal speed.  (The "landing on Tylo with nuke engines" scenario.)  So, yes, sometimes that's necessary.  But that's nnot the same thing as being more efficient, it's just a necessary inefficiency to deal with an extremely low TWR.

And in my experience, Tylo tends to be the only place where that tends to be an issue.  Other vacuum worlds tend to have fairly low gravity and therefore landers are likely to have a local TWR significantly higher than 1, so that's not an issue.

  

14 hours ago, camacju said:

the constant altitude landing is always more efficient

If you're burning anything other than perfectly :retrograde:, you're incurring extra cosine losses and you're not saving gravity losses.

Note that I'm not saying that a constant-altitude landing is a bad idea.  There are reasons it can be appealing to people-- for example, it takes the knuckle-biting out of the landing, you don't have to worry about going splat if you misjudge timing by a fraction.  You have more time to adjust, to bump your nose up a bit if you're getting uncomfortably close to terrain while accelerating, for example.  There's absolutely nothing wrong with landing like that, if it works well for someone.  And in very low-TWR cases, it may actually be necessary, as you point out.

But it's not the most efficient.

The pure :retrograde: suicide burn that I'm describing is riskier, that's why it's called a suicide burn.  And not everyone wants that risk, and that's perfectly understandable-- it's not for everybody.  But it is more efficient; that's why people do it.

(Also, note that when I say "more efficient" or "less efficient", that's a relative term-- depending on the situation, the dV savings from one to the other may not be big enough for the player to care about much, in which case clearly the player should go with whatever landing technique they're comfortable with.)

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The math is a bit tricky, so the best way to test this is empirically. I've done both constant altitude landings and constant retrograde landings, and constant altitude landings are more efficient. In a similar fashion, constant altitude ascents are more efficient. And for some reason, ascents are a lot more intuitive for me, so maybe the following explanation will be sufficient:

For an ascent on an airless planet, the only thing that matters is horizontal velocity, since you don't need to  climb above anything. (Assume that you start from a mountaintop or something, for the sake of argument. Obviously this will be different if you're in a canyon and you need to climb out of it). However, for the sake of argument, we also assume that altitude cannot be lost at all - it must be at least the height of the launch.

Then the key will be to gain horizontal velocity as quickly as possible. The earlier you gain horizontal velocity, the more effective the later segments of the ascent will be, because of the Oberth effect. This means that you want to be burning as horizontally as you can for the entire ascent. And that means burning at an angle to prograde, just enough to counteract gravity, while the remainder of your thrust pushes you horizontally.

If that's not enough to convince you, here are some screenshots of a constant altitude vs. gravity turn ascent from Mun. (Gravity turn is the inverse of a constant retrograde suicide burn)

Starting point:

QccxZjZ.png

1843 m/s of delta-v remaining.

vsPfI8f.png

Constant altitude ascent

Hq36RS0.png

In 9km - 4.3km orbit, 1274 m/s left, 569 m/s of delta-v expended

YIsI6v7.png

I use MechJeb's gravity turn utility for the gravity turn ascent.

j9iAH6g.png

In 6.3km - 5.7km orbit, 1264 m/s remaining, 579 m/s spent

 

In conclusion, the constant altitude ascent let me reach a higher orbit using less fuel, so it seems more efficient.

Edited by camacju
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10 hours ago, camacju said:

In 9km - 4.3km orbit, 1274 m/s left, 569 m/s of delta-v expended

In 6.3km - 5.7km orbit, 1264 m/s remaining, 579 m/s spent

 

In conclusion, the constant altitude ascent let me reach a higher orbit using less fuel, so it seems more efficient.

yes, but the difference is so small as to be negligible in most cases. and a constant altitude ascent is much trickier to pull off. I try to do it, but i must continuously make corrections, and that may easily lose me that little gain

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My point is that that's basically the exact opposite of what @Snark was claiming, which is that constant altitude landing/ascent is easier but less efficient.

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On 4/20/2021 at 9:07 PM, camacju said:

so the best way to test this is empirically. I've done both constant altitude landings and constant retrograde landings

Very nice walk-through with pictures, thank you!  :)

I tried a manual gravity ascent myself, with a craft pretty similar to yours.  Managed a slightly-over-5km circular orbit with 578 m/s of dV spent, so that's a fairly consistent result.

My main impression, from reading your two cases that you tried, was essentially the same as @king of nowhere's.  If you try it twice, and the difference is only 10 m/s of dV, that's so close as to be a negligible difference in these two cases, given the randomness of piloting.

 

On 4/21/2021 at 12:01 PM, camacju said:

My point is that that's basically the exact opposite of what @Snark was claiming, which is that constant altitude landing/ascent is easier but less efficient.

Well, not quite.  Note that @king of nowhere said he had trouble with constant-altitude ascent, not descent.  And I never said that the ascent was easier at constant altitude.  Quite the reverse-- a continuous :prograde: burn is fairly simple, just crank it over to start the turn, set it to hold :prograde: and floor it.  :)

My comment about suicide-burn landing being tricky is purely a matter of judging when to start the burn.  The actual piloting is trivial, just let SAS hold :retrograde: and be prepared to cut thrust when needed, that's it.  I'd say that a constant-altitude landing would require considerably more tweaking of steering and so forth.  Less risk than a suicide-burn descent, but more interaction and, I'd say, more piloting skill needed.

I think that this comment is pretty relevant:

On 4/21/2021 at 7:24 AM, king of nowhere said:

the difference is so small as to be negligible in most cases

Because your approach (@camacju) and mine are, in practice, usually very similar in terms of the actual piloting.  Regardless of whether one is doing a suicide burn or a constant-altitude landing, it's still the case that it's a bad idea to descend steeply to the surface.  My suicide burn advice is that you only lower your Pe just barely underground, so that you're approaching the ground at a very shallow (i.e. nearly horizontal) angle before you start your burn.

So, let's consider a landing, in your proposed case versus mine.  In your proposed use case,

  1. you're going very fast sideways initially...
  2. ...with zero descent rate
  3. you thrust nearly horizontally, with your nose pointed up just slightly so that you can maintain altitude
  4. therefore you have a tiny cosine loss while you're burning
  5. as you slow down more, you'll have to point your nose higher and higher above horizontal, resulting in more and more cosine loss
  6. cosine loss is worst just before touchdown

Whereas in my proposed use case,

  1. you're going very fast sideways initially...
  2. ...with a very low descent rate
  3. you thrust nearly horizontally, with your nose pointed perfectly :prograde:
  4. therefore you have zero cosine loss, but you do have a tiny gravity loss while thrusting because you're not perfectly horizontal
  5. as you slow down more, your path will become more steeply inclined, resulting in more gravity loss.  Still no cosine loss, though
  6. gravity loss is worst just before touchdown

Note how very, very similar these two cases are.  #1 is identical for both cases.  #3 is basically identical in both cases.  #4 is pretty close to identical-- a small loss in both, just of a different nature.  #5 and #6 are likewise extremely similar.

Now consider the fact that none of the Kerbin system's bodies are perfectly flat (except for Minmus' flats, but even those are surrounded by steep slopes that you have to clear).  Which means that you're going to have to be concerned with terrain avoidance.  A constant-altitude landing is generally not going to be able to slide sideways to a perfect stop on the top of a hill-- in practice, the player who wants to use this approach will pretty much always have to make that a constant-altitude that's higher than the target landing point, meaning that they're going to have to transition to a steep or vertical descent at some point in order to come in for a landing.

And if they're doing that... then the shape of the curve that the ship follows is starting to look an awful lot like what a suicide-burn ship is doing, anyway.

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On 4/21/2021 at 2:07 AM, camacju said:

The math is a bit tricky, so the best way to test this is empirically.

Another way to test the comparison is to simulate a descent similar to how KSP models it.
TL;DR A constant altitude descent consistently uses less delta-v than a suicide burn. The difference is bigger the lower the TWR of the craft, closing very rapidly to negligible values as TWR increases.

Here's a chart showing values simulated for Tylo:

BOi6Fy0.png

I modeled the descent trajectory using the differential equations from the paper:
Optimal Trajectory Planning for the Apollo MoonLanding: Descent, Ascent, and Aborts by Duncan Miller

A kOS script integrated the differential equations numerically using Euler's method. During testing this agreed very closely with reported values from KSP,  so seems to be similar to how the game code models things.

The script simulated a "perfect" descent from a 30km circular oribt of Tylo to sea level. For the constant altitude burn a single pass for each TWR was enough. For the suicide burn, an iterative approach was used to determine the right altitude to set the periapsis when starting the burn.
 

Edited by ManEatingApe
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