Reverse-engineer a Hockey-Stick Burn and Live To Laugh About The Exploit

[Hotel26]

My buddy, First Lieutenant Dunry Kerman, spent yesterday evening trying out an idea for me.

This is Dunry in the jump seat of a Hawk tug/lander with an empty fuel pod attached.  It's in the landing configuration: Hawk tanks are full and the fuel pod is bone dry.

First task was to have Dunry take the Hawk to a 10 x 10km orbit using his standard departure procedure, which is:

1. lift-off checklist complete; SFC Radial Out; 1/4 throttle to get off the surface 100m;
2. cut engine; rotate nose to a few degrees above the easterly horizon and go full throttle
3. cut engines when 10km apoapsis is established
4. coast to 10km and then circularize.

This is typically a very flat and horizontal trajectory.

In this case, I had Dunry climb 300m before the orbit injection burn.  We later realized that 1km is better.  I also had him set Target on the fuel truck on the ground at the departure point, so as to measure distance from it.

Dunry departed and noted the following 3 numbers for me:

1. D1: distance from the fuel truck, 3.6km, as soon the Reliants shut down after the orbit insertion burn
2. V1: speed at commencement of the circularization burn, 338 m/s.
3. D2: distance from the fuel truck when the circularization burn reached completion, 43.1 km

Second task, which Dunry practiced maybe about a dozen times last night was to reverse-engineer this sequence:

Starting from a 10 x 10km orbit, reaching 40 km [*], D2, from the truck, use Surface-Retrograde to reduce speed to V1:  338 m/s.  Now on a hockey-stick trajectory back to a point 300m [*] directly above the target!

A very exciting trajectory, Dunry told me after the first go, with tears of joy still streaming down his cheeks.

Don't Panic.  (We're having a little placard made up for the tank on the Hawk, just in front of the jump seat.)  Wait for it; wait for it, D1: 3.6km.  Full Surface-retrograde burn upon reaching 3.6km DME to the target truck.  Burn until motionless and find oneself 600-800m above the target.  Land as usual.

Needless to point out, if the departure trajectory at your surface base is clear of obstructions, such as e.g. mountains, but the approach path is not, you need to apply some common sense about all this.

* the departure is flatter than a hockey-stick Surface-retro burn, which is the way we aim to return, so we found that 1km would have been a better safety margin to use in the first task above.  We compensated for this simply by using D2 = 40km, instead of 43.1km, which extends the landing trajectory over the target, which effectively just builds a slight amount of altitude into the curve above the target.

Edited March 30, 2018 by Hotel26

[MechBFP]

I’m so confused right now. What does this have to do with suicide burns?

[Snark]

4 minutes ago, MechBFP said:

I’m so confused right now. What does this have to do with suicide burns?

The hard part of a suicide burn is figuring it out, i.e. when to start the burn, at what altitude and speed, etc.

The insight here, which is nearly true, is "A suicide-burn landing is just an efficient takeoff in reverse."

So he's doing a takeoff, noting down the numbers, and then using those to reverse the sequence to do a suicide-burn landing.

I say "nearly" true, above, because the analogy between takeoff and landing isn't perfect.  They differ slightly because fuel is consumed.  The rocket taking off is heaviest on the surface; the rocket that's landing is heaviest when it's high up in the sky.  Thus, the acceleration profiles will differ somewhat in the two cases.

But as long as the amount of fuel you burn during the takeoff-or-landing sequence is fairly small as a percentage of total ship mass, the difference in ascent/descent profiles may be small enough for the technique to work.

[Hotel26]

14 minutes ago, Snark said:

I say "nearly" true, above, because the analogy between takeoff and landing isn't perfect.

Yup.  Thanks for yours above.  I resurrected an old thread (of mine) here:
https://forum.kerbalspaceprogram.com/index.php?/topic/143921-pinpoint-landings-again/&do=findComment&comment=3334163

to mention a refinement in my previous approach and that I had recently investigated some approach via calculus to account for diminishing fuel.  I determined it wasn't worth thinking about.

But the general problem with my old approach is that you stopped precisely over the target but way too high, which is a waste of fuel. 

This new approach can be potentially tuned as low as you want to risk. 

23 minutes ago, MechBFP said:

I’m so confused right now. What does this have to do with suicide burns?

I understand the confusion.  A suicide burn to the surface is suicidal.  My aim is to come to a dead-stop just a few hundred meters above the target.  Which doesn't seem so suicidal at all.  But a lot more useful.

The most important thing about the term is actually that full-throttle SFC retrograde is the most efficient use of fuel in deceleration.  Snark summed it up very well.

Edited March 27, 2018 by Hotel26

[Snark]

My personal favorite "sneaky" technique for suicide burns is the good ol' maneuver-node trick. 

Spoiler

The maneuver-node trick for a suicide burn, for anyone unfamiliar with it:

1. You start out in a suborbital trajectory, headed for a landing on the surface.
2. Go into map view.
3. Place a maneuver node right exactly at the spot where your trajectory intersects the surface, i.e. at your projected impact point.
4. Drag the handle on the maneuver node until your predicted post-maneuver path collapses to a point right at the node.
5. The node now tells you when you will impact (if you don't burn), and the estimated burn time tells you how long you need to burn to reduce your velocity to zero at the surface.
6. So just wait until the time-until-node is about 60-70% of the estimated burn time, and then burn surface- at 100% throttle.

For example, if the maneuver node tells you that you'll need a 10-second estimated burn time, you'd wait until you're 6 or 7 seconds before impact (i.e. 6 or 7 seconds before maneuver) to hit the gas.

I used to use that all the time, and then it eventually got sufficiently tedious that I wrote BetterBurnTime so that it does what amounts to the same thing, automatically, so now I don't have to mess with it.

[Hotel26]

I think there is also a discrepancy in my approach due to the rotation of the surface body.  On departure, the truck is chasing you.  On arrival, the truck is fleeing.

Dunry did it twelve times and put it on the orbital line with some deviation up and down it, generally about a hundred meters from the truck, except one time he got off focus.  [We had a spat then when I called him "Dunderhead"...]

But I can say that the results were excellent.  It does work as desired.  The numbers depend totally on how you fly the lift-off.  I have another set today: 5.3km, 435 m/s, 64.2km.  This is a much flatter departure/approach and potentially much more efficient.  The margin for error may be smaller.

Lastly, for anyone who doesn't think this is a suicide burn, I recommend you try it.  Done right, I guarantee you'll live but you won't be confused about the relevance anymore, either!  Dunry assured me it was "very exciting".  He was quite agitated. 

Edited March 27, 2018 by Hotel26

[MechBFP]

Ah I see now what you mean. Thanks!

Almost all my landing are like this. 

I usually get within 1 km of the surface and then burn about 99% horizontal until I have nearly cancelled out all of my horizontal speed, then plop onto the surface with only about 100 to 300 vertical meters left to deal with. 

It is indeed quite efficient. 

[Hotel26]

I think my ultimate objective is to perform an efficient de-orbit burn followed by an efficient deceleration burn that places my vessel in a cone above the target at low speed and altitude such that I have just enough time and maneuvering room to tune the approach to touch-down 10m from the target.

This "cone above the target" is a vertical simile  to the ILS localizer/glide slope used in aviation.

Edited March 28, 2018 by Hotel26

[Pthigrivi]

22 hours ago, Snark said:

My personal favorite "sneaky" technique for suicide burns is the good ol' maneuver-node trick. 

  Reveal hidden contents

The maneuver-node trick for a suicide burn, for anyone unfamiliar with it:

1. You start out in a suborbital trajectory, headed for a landing on the surface.
2. Go into map view.
3. Place a maneuver node right exactly at the spot where your trajectory intersects the surface, i.e. at your projected impact point.
4. Drag the handle on the maneuver node until your predicted post-maneuver path collapses to a point right at the node.
5. The node now tells you when you will impact (if you don't burn), and the estimated burn time tells you how long you need to burn to reduce your velocity to zero at the surface.
6. So just wait until the time-until-node is about 60-70% of the estimated burn time, and then burn surface- at 100% throttle.

For example, if the maneuver node tells you that you'll need a 10-second estimated burn time, you'd wait until you're 6 or 7 seconds before impact (i.e. 6 or 7 seconds before maneuver) to hit the gas.

I used to use that all the time, and then it eventually got sufficiently tedious that I wrote BetterBurnTime so that it does what amounts to the same thing, automatically, so now I don't have to mess with it.

Betterburntime really is the shiz, man. 

[Snark]

5 hours ago, Hotel26 said:

touch-down 10m from the target

You set a pretty high bar. 

Personally, I generally aim to get within about 50 meters-- mainly because going for 10-or-less means there's a high chance that I'll end up actually colliding with the target, or demolishing it with my rocket exhaust, and then I would haz a sad.  TL;DR:  "10 meters or less" is very doable, but "under 10 meters, but not less than 5" makes for some pretty tricky concentration during the final landing approach.

5 hours ago, Hotel26 said:

I think my ultimate objective is to perform an efficient de-orbit burn followed by an efficient deceleration burn that places my vessel in a cone above the target at low speed and altitude such that I have just enough time and maneuvering room to tune the approach

It's actually not too bad, with a little bit of practice.  Assuming that you're doing this in stock without the aid of navigational mods, here's an approach that works reasonably well:

1. Set up your deorbit burn so that you are on a suborbital trajectory aimed at the target.  For efficiency's sake you want the approach to be fairly shallow, e.g. your projected trajectory is still mostly horizontal at the point where it intersects terrain-- say, within 10 degrees of horizontal.
2. When you're setting up that trajectory, make it so that you overshoot the target by a few kilometers, i.e. so that you're projected to pass directly overhead the target and then hit dirt a fair ways on the other side.
3. When you're around 1/6 to 1/8 of the planet's circumference away from impact, fine-tune your inclination to make sure you'll be passing directly overhead the target.  This is easy to do:  just go to map view, you should see your AN/DN sitting right on top of the target.  If it's not quite there, just do a small or burn to adjust.
4. Make sure your navball is in surface mode.  Roll the craft so that the horizon's nice and horizontal on the navball.
5. As you approach the target, do a burn until your projected terrain impact location is just a few hundred meters past the target.  (In other words:  still overshooting, but not overshooting quite as far.)  This is so that your angle coming at the target isn't quite so shallow, which makes it a lot easier to navigate on final approach.  Exactly when you do this burn will depend on your craft's TWR, but it's typically on the order of 1x to 2x the original overshoot amount that you set up in step 2 above.
6. Do the maneuver-node trick (from my previous post) so you'll know when to do your main braking burn to land, and get ready for the fun bit. 
7. From here on out, it's all about the navball.  Make sure it's in surface-relative mode, and set your SAS to hold .
8. Watch the navball carefully.  The two markers you care about are and .  Since you're on a path to overshoot slightly on final approach, and also since your path is going to be curving downwards as you decelerate, the marker should be directly above (i.e. towards the zenith, relative to) the marker.
9. Understand how these markers move, what affects them, and what you're trying to accomplish:
   • is going to slide upwards on your navball as you approach the target.  If you did nothing (just let yourself coast to impact), it would slide all the way up to the zenith (which is the point at which you're directly above the target), and then keep going past the zenith (which would mean you've actually overshot the target).
   • is also going to slide upwards on your navball, because gravity is curving your path downwards as you descend.  If you just let yourself coast to impact, though, this marker will never actually reach the zenith, because that happens only when you're going perfectly straight downards, which can't happen without engine thrust.
   • So, here you have these two markers, and , both sliding upwards towards the zenith at different speeds.
   • Your goal is for them both to reach the zenith at the same time, right about at the time when you land.  That's because if they're both at the zenith, you're directly above the target and descending vertically.
10. So, there you are, watching these markers slide upward on the navball.  You can make slide upwards faster by increasing your throttle, or slower by decreasing it.
11. You can also affect it by pointing the nose of your craft above or below the marker.  Tip your craft above , and you "push the marker down" towards the horizon.  Dip your nose down below , and you "push the marker up" towards the zenith.  In general you don't want to do this too much, because any time you're pointing any direction other than , you're incurring cosine losses and therefore are not at optimum efficiency.  But a brief nudge up or down can help to fine-tune the vector without costing too much extra fuel.

So, that last final approach is going to be one where you're watching the navball intently, with your peripheral vision keeping track of how close you are to the surface.  You're working the throttle and your pitch angle to coax the marker into reaching the zenith right at the time that does, and then it's just a regular vacuum landing.   

The first time or two is a bit tricky, but I think you'll find that with a little bit of practice you'll rapidly get the hang of it.

[Hotel26]

Good to have this discussion with an expert.  I opened a topic on this here: How Do You Fly the Navball? and I think this may be a kind of black art.  I'm always hoping someone could bottle the elixir: i.e. explain this clearly.  It's one thing to do it and another to explain it to someone else.

There's an algorithm and if you follow it exactly you have a 50% chance of colliding with the target, so the last step actually is reaching a low enough altitude simply desist tracking the target with the navball and just land!

I think a video would be great.  I landed once on the Mun from inside the cockpit and it was pretty thrilling.  I don't remember how close to the marker I got but I think the supreme challenge would be to lay out 3 flags in a small triangle and land inside them with a non-stop trajectory (no hovering or horizontal translation) from inside the cockpit.  Last time I looked the navball inside the cockpit was somewhat indistinct, but I think it can be done.

I actually set up a world save with this scenario prepared for a challenge: Instrument Landing.  Land within the markers -- from inside the cockpit (once the de-orbit burn is made) -- pilot down with the most fuel still onboard takes the prize.

Kinda breath-taking to consider... 

 

Edited March 28, 2018 by Hotel26

[Hotel26]

9 hours ago, Snark said:

You can make slide upwards faster by increasing your throttle, or slower by decreasing it.

I read through your whole description very carefully and it's quite cogent and comprehensible.

I like this point (quoted above) because it's another technique in the armory to consider.  And I think an experienced pilot will use an amalgam as circumstances indicate.

My approach is not to keep the engine running, but to turn and use small thrusts to shepherd the markers where I want them.  With experience, this can be done without over-controlling and, generally, the off-pitch angle ["cosine loss"] is not great.  It keeps the approach moving faster until the end (which is good).  It also becomes a bit more necessary when you're intercepting a target that is NOT on the equator.

In my thinking, where you point the nose and use the throttle in combination repel the marker that indicates direction of flight.  That one in turn repels the target location.  You are the nose.  Your travel is the sheepdog.  The target is the sheep.  And the "zenith" is the pen.  Good teamwork does not chase the sheep all over hill and dale but gently coaxes its trend.

Really appreciate your input and experience on this [fanatical] subject!

Edited March 29, 2018 by Hotel26

[Kerbart]

On 3/27/2018 at 9:24 AM, Snark said:

I say "nearly" true, above, because the analogy between takeoff and landing isn't perfect.  They differ slightly because fuel is consumed.  The rocket taking off is heaviest on the surface; the rocket that's landing is heaviest when it's high up in the sky.  Thus, the acceleration profiles will differ somewhat in the two cases.

Well that's the one difference. The other difference is that the outcome of "getting it almost right" is rather dramatic.

[Snark]

14 minutes ago, Kerbart said:

The other difference is that the outcome of "getting it almost right" is rather dramatic.

Thus the name of the maneuver. 

[Kerbart]

2 minutes ago, Snark said:

Thus the name of the maneuver. 

I guess "Waaaaaaaaaaaaaah SPLAT!" didn't make it past the naming committee?

[Hotel26]

I resurrected my old "Race" world from my 1.2.1 workspace.  I refitted the archaic lander I was using in it with my current Hawk, "Gang Star", carrying a Mk 1-3 capsule atop.

I just tried 2 landings.  Here's the first (note the fuel levels):

Then I repeated the exercise, but went "under the hood" for a purely instrument landing (i.e. performed from inside the cockpit with no external references[*]) as soon as the de-orbit burn had been completed:

I'm trying to figure out now some way to repeat this, perhaps in a video, in some way to "prove" there's nothing fake here.  I know it's probably possible also to record from a camera positioned on the ground.  (I would really like to have seen what that second landing looked like!  My biggest difficulty was, on the ground, trying to be sure I really was on the ground.)

Incidentally, a huge Attaboy to Leo Kerman who stood in the middle of the triangle and acted as target.  He bet me 1,000 Kroner I couldn't get it in the triangle [he won] and I bet him a 1,000 Kroner he'd run like hell when he saw me coming.  He laughed afterwards that he was so paralyzed by fear that he couldn't run anyway, so he won that bet too.  I'm out 2,000 Kroner to Leo, but it was worth it.

* All manual in the cockpit: no way I know to set modes on SAS as I usually jump back and forth between SFC Radial and SFC Retrograde.  Had to do it all the old-fashioned glove-and-stick way...

One more note: both flights were started from a save file with Gang Star in circular 10x10 km orbit just approaching the FAF [Final Approach Fix, 70km].  An inclination change was made by eyeball and then the de-orbit commenced at the 40km mark, reducing speed to 338 m/sec.  Thence, inside the cockpit...  Note the instrument approach took an extra minute since I had to conservatively judge the deceleration burn purely from the navball, not having a DME reading to the target.

Edited March 30, 2018 by Hotel26

[Hotel26]

One more footnote to the above.  The whole point of a fuel-efficient approach via the ball is to keep the descent going to a precise landing without helicoptering.

Both landings pictured above were continuous descents shepherded to landing with the following proviso:

in every landing, close to the surface, I deliberately reduce speed momentarily to 0 because it's a sure way to kill horizontal motion which could otherwise topple your landing.  Once this is done, you are committing to land straight down, with no further tuning of horizontal distance to target.  So it's done very close to the surface.  It has to be done with alacrity.  So it's usual for me (and happened on both approaches) that the SFC retrograde/prograde direction markers momentarily interchange, then revert, indicating an unintentional, positive "float" [throttle overshoot].  Apart from that, the approaches were continuously downward with direction to the target also being tuned continuously.

Edited March 30, 2018 by Hotel26

[wumpus]

On 3/27/2018 at 9:24 AM, Snark said:

I say "nearly" true, above, because the analogy between takeoff and landing isn't perfect.  They differ slightly because fuel is consumed.  The rocket taking off is heaviest on the surface; the rocket that's landing is heaviest when it's high up in the sky.  Thus, the acceleration profiles will differ somewhat in the two cases.

If you haven't put it together yet, maneuver nodes have this exact error (although typically you don't use maneuver nodes while suffering gravity losses).

[Snark]

11 minutes ago, wumpus said:

If you haven't put it together yet, maneuver nodes have this exact error (although typically you don't use maneuver nodes while suffering gravity losses).

Yep.  In my experience, though, it usually isn't too much of a problem with the maneuver-node-trick-for-vacuum-landings technique, for a couple of reasons:

First, the large majority of vacuum landings tend to be on worlds with much lower gravity than Kerbin (i.e. Mun or smaller).  Which means that the local TWR of the landing craft tends to be really high, like 5 or more, which means that gravity losses are fairly minimal and usually the burn isn't using a large fraction of the ship's mass in fuel.

Second, yes, there is a bit of an error because of the mass loss... but it's in the right direction:  the maneuver node will overestimate the burn time slightly (since it's assuming constant acceleration, when in fact your acceleration will increase), with the result that you're given a slight safety margin on landing.  (It would be really bad if the error were in the other direction, and it underestimated, because then you'd go splat.)  With a slight overestimate, that gives you a bit of wiggle room, and you can compensate for it by slightly reducing throttle as you brake, once you get close enough to the surface to use visual surface speed as a helpful progress indicator.

[Hotel26]

9 hours ago, Snark said:

bit of an error because of the mass loss

I measured the practical effect of this and it is negligible on the practical outcome.  You'd need to integrate an inverse to handle this mathematically, which -- as a fuel truck orbiter guy -- is way above my pay grade [I found a nice paper on this].  I used KER to read the max decel rate at start and end of burns.  I used an average (still not mathematically exact) and it made no practical difference to the objective of getting the vehicle low and slow in the approach cone [think ILS].

Meanwhile, the big picture is how to use the efficiency of a suicide burn -- do all the work close to the surface to minimize time in flight -- to get close enough to the surface to spot land.  Without helicoptering.

I'm taking the mining view company perspective and the shift-worker pilot's perspective  to think that 10m arrival is a world of difference to 150m-distant touch-down.  It might be the difference between a 1-man operation and 2-man.

Assuming it isn't all automated (0-man), in which case they are integrating that inverse and landing at 9.8m from the truck, each time, every time.

The maneuver-node trick is valid and useful in combination with flying the nav-ball at the end for the spot landing.  It's a great technique to know.  But note that I landed 6m from the pin without maneuver nodes using only what is inside the cockpit [interior view].

The nav-ball rocks!

Edited March 31, 2018 by Hotel26

[Snark]

14 minutes ago, Hotel26 said:

The nav-ball rocks!

That it do. 

[Zeiss Ikon]

10 hours ago, Snark said:

That it do. 

I'll second that.  Learning to fly docking on the nav ball saved me having to choose which docking alignment mod was going to bog down my old (thermal limited) computer.  The nav ball helps me launch, both to the usual zero inclination and to polar orbit (which I haven't done yet in my career, because I don't take "put a satellite in orbit X" contracts).  If we didn't have the nav ball, someone would have to make a mod to create it... 

[Bill Phil]

16 hours ago, Hotel26 said:

I measured the practical effect of this and it is negligible on the practical outcome.  You'd need to integrate an inverse to handle this mathematically, which -- as a fuel truck orbiter guy -- is way above my pay grade [I found a nice paper on this].  I used KER to read the max decel rate at start and end of burns.  I used an average (still not mathematically exact) and it made no practical difference to the objective of getting the vehicle low and slow in the approach cone [think ILS].

One (cheaty) way to minimize the error here is to put the lander on the ground using cheats (can you do that?) and record the numbers... Then just revert to VAB or something.

[Hotel26]

6 hours ago, Bill Phil said:

and record the numbers

Kerbal Engineering Redux in its Vessel display gives you the stats you need.  Max acceleration and mass are the key metrics.

[Bill Phil]

1 hour ago, Hotel26 said:

Kerbal Engineering Redux in its Vessel display gives you the stats you need.  Max acceleration and mass are the key metrics.

As far as I recall it makes some assumptions that may not be very helpful. 

Mass and acceleration are always changing during a burn...