Pinpoint Landings (again)

[Hotel26]

(Apologies in advance for opening a topic again on something that's been discussed a lot but don't want to reopen old discussions either...)

Apologies also if someone has already pointed out what follows...   S = 1/2 a.t^2

The concensus in the forum seems to be that the best way (no atmosphere) to take off and the most efficient way to land is expend the greatest percentage of work on the horizontal velocity component to either establish or eliminate orbital speed.  This is in line with Newton's idea that if he could climb a high enough mountain and shoot a baseball toward the horizon at a high enough (instantaneous) speed, it would come back to hit him in the head 90 minutes later. 

The problems with screaming in low and fast for a landing are terrain clearance; pilot reaction time (as this will effectively be a suicide burn which is what makes it efficient); and therefore inaccuracy.

I just tried this at my mining camp on Moho and touched down softly 24m from the target.

(For those who religiously don't use MechJeb, leave the autopilots alone but MechJeb provides essential displays; in this case: Orbit Info; Surface Info; Vessel Info and Rendezvous Info.)

I suggest the procedure is as follows:

• perform any desired inclination change 270 degrees before the target;
• lower the periapsis to a few km above the target, 180 degrees before the target;
• on the first attempt, use the altitude of the highest mountain as your target periapsis to avoid premature contact;
• watch true altitude for a minimum which will tell you how much you can lower the target periapsis on future landings;
• your speed will increase as you get lower which means that your orbital speed will serve only as an initial (low) approximation;
• Vessel Info displays your max deceleration rate.  Reducing speed from 828 m/sec with a deceleration of 16.18 m/sec/sec will take 51.2 secs;
• S  = 1/2 a.t^2 suggests that in that 51.2 secs you will travel 21.2 kilometers;
• when the Rendezvous Info display says you are 21.2 km from the target (or a little before if you are nervous), fire Full Astern;

Using a periapsis of 6km above the target, I arrived 2km over the target and a little after the target (because I got distracted and fired late).  And vertical and horizontal speed zeroed out approximately together, which is what you'd expect from retrograde.  (The MSA for this approach is actually around 5.1km, so I possibly can tune this down near 1.1 km above target.)

You exit suicide burn at this time or a little earlier, when your confidence is ready.  Then fly the navball in what is pretty close to a short vertical descent.

The reputation is that this low, screaming approach is inaccurate, but if you are avoiding terrain anyway, it adds up to "landing" (arrival) a kilometer above the target and then a short walk in the park to get down and dusted off.

The hard part is knowing when to fire and this is where the equation above is your friend.  A quick manipulation of that equation gives you the following:

S = 1/2 v^2/a

S = 1/2 828*828/16.18 = 21.186 km

(If there's enough interest, I'll make a video.)

Edited July 16, 2016 by Hotel26
typo

[jlcarneiro]

Nice explanation, thanks!

Just didn't get what quick manipulation you did on the equation to go from S = 1/2 a.t^2 to S = 1/2 v^2/a...

[GoSlash27]

jlcarneiro,

 It's a substitution.

t=v/a, so at²= a(v/a)² = av²/a² = v²/a

Neat insight!

-Slashy

[jlcarneiro]

Oops! Let's say I missed it because it's early in the morning here...

Thanks, @GoSlash27!

[purpleivan]

My missions use formula more like this.

Entertainment = ((KSP + TV - cooking_dinner)/work) / Time * (luck + rule_of_thumb) + send_more_fuel_later

Improvements on this much appreciated.

[klesh]

Thankfully, I am able to land in a pinpoint fashion next to things with my trusty Mk1 eyeball.  I'm not so good at maths.  

 

http://steamcommunity.com/sharedfiles/filedetails/?id=536432659

[Rocket In My Pocket]

5 minutes ago, klesh said:

Thankfully, I am able to land in a pinpoint fashion next to things with my trusty Mk1 eyeball.  I'm not so good at maths.  

 

http://steamcommunity.com/sharedfiles/filedetails/?id=536432659

Yeah, real pilots fly by the seat of their pants!

[LordFerret]

3 minutes ago, klesh said:

Thankfully, I am able to land in a pinpoint fashion next to things with my trusty Mk1 eyeball.  I'm not so good at maths.  

 

http://steamcommunity.com/sharedfiles/filedetails/?id=536432659

Pretty much likewise. From what I'm reading of Hotel26's post, that's pretty much my approach for Mun and Minmus landings now. But I'll be giving his procedure a try later on this afternoon.

[Hotel26]

Thanks for the humor! 

I have found that waiting 180 degrees to land from a low orbit means you can't warp and who can wait?

So I am working on refining this for steeper approaches.  Distance from target as a trigger for braking can still be used.

And by the same token, if one is in an all-fired hurry to get down, coming down like a fireball is pretty exciting!

Pinpoint landings are always going to come from either the Mk 1 eyeball or Mk 1 navball at the final stage, yeah?

Edited July 17, 2016 by Hotel26
typo

[Sirine]

Pilot pinpoint landing. Better to understand the reel than the math.

 

[Blaarkies]

On 7/16/2016 at 11:39 AM, Hotel26 said:

• perform any desired inclination change 270 degrees before the target;
• lower the periapsis to a few km above the target, 180 degrees before the target;

You should do those in reverse. I mean, do the Pe drop first, so that you are moving slower when doing the Inc. change(makes for a cheaper Inc. burn). Doing Inc. change at 270' vs 90' before landing is essentially the same(just burn opposite direction to move the landing marker).

If you could combine those two burns into one Maneuver, it could become even cheaper(but that affects the landing angle and many other factors that are of a higher priority here) 

[Hotel26]

@Blaarkies, thanks for the comment!

I don't know about that because the deorbit burn (Pe 30km down to 6km) performed 180 degrees before the target only lowers speed by a very few m/s.  And then the speed steadily picks up especially by the point 90 degrees before the target, which (with 270) is the best place to perform an inclination change, at which time you are also starting to get very busy.  And then that inclination change will affect your Pe which may then need to be readjusted.

And finally, I only put the inclination change in the list for completeness; the usual situation is that the craft and its target originated from the same station in an equatorial orbit and everything is all aligned.
 

@all, my mistake for entitling this post "Pinpoint Landings" because what is on my mind, as you can tell from the introduction, is "most efficient landings", revisited.  And the purpose of my "horizontal hockey stick suicide burn" is not to place you at a pinpoint location on the surface but to set you up in a manageable location very close to the target to allow you then to enter the pinpoint landing phase, performed however you normally do that.

Let me put that another way: my usual algorithm had been to use an asymptotic rule at my orbit altitude of 20km to halt my orbital speed directly over the target.  Then be in the bird's eye position to spot my landing, right up nice and close as you please.  But is it *efficient* to land from miles above, reading the comix while you wait for the lunar gravity to get you down?  One more comment: if you spot your landings by flying your lander as if it's a helicopter, your boss is not going to like your fuel bill.

Please stay tuned for an announcement... 

Edited July 18, 2016 by Hotel26
correct errors

[Tyko]

This is a great guide! My challenge is that I'm often landing in craters and if I do my de-orbit burn 180 degrees away I'm coming in too flat and too high because I have to avoid smacking into the leading crater edge with are usually higher then the preceding terrain.

[Hotel26]

@tjt, thank you.  You can play with the periapsis you set; typically this approach dumps you out just a kilometer or two above the target.  It's not meant to put you directly on the ground.

If you overshoot a vertical suicide burn, you have committed suicide.
If you overshoot a horizontal suicide burn, you have only overshot your target.

The first one I did was over Moho at the strong end of the log-grav spectrum and it was a 51 second burn and I was amazed when it finally pulled up so close to the target.  The experience is worth trying once.
You do have to watch as your speed picks up as you near the periapsis and you do have to recalculate the trigger distance, but once you've calibrated from the the first approach, you're good.

I'm working on using the technique from however a late and steep approach you want.  Just draw a maneuver node and end it in the dirt somewhere a kilometer or two past your target.  I'm still tuning the details, though...

(I've also watched Sirine's video a few more times, as well.  )

[Tyko]

6 hours ago, Hotel26 said:

If you overshoot a vertical suicide burn, you have committed suicide.
If you overshoot a horizontal suicide burn, you have only overshot your target.

 

WORD...   

[Hotel26]

Earlier in this thread, I proposed that you could start a de-orbit burn for a target on the surface of an airless body when:

S = v^2/(2 * a)

[substitute t = v/a into s = 1/2.a.t^2]

where S is the distance indicated to the target when the burn should commence, v is your orbital speed and a is the (KER-reported) max acceleration rate of your craft.

---

I investigated the effect of reduction of vessel mass during the burn due to consumption of fuel and concluded that, even for relatively light vessels, it was not significant.

What is a good refinement however is to make the following compensation.  Your distance to the target is reported line-of-sight, which means that it contains a vertical as well as horizontal component.  We can use Pythag as follows.

If my orbital altitude is 10km and the target on the surface is known to be at 4km altitude, then the vertical component is 6km.  If the equation above indicates that the deceleration should start at 10km horizontal distance, then using Pythag:

sqrt(10 * 10 + 6 * 6) = 11.66km.  So you should commence your de-orbit burn when the target is at 11.7km.  This may seem like a small difference in distance but it works out to being whether you land 1.7km from the target or a mere 20 meters from it.

It really is quite an exhilarating feeling to pull to a dead stop on that ole fire pole and then just slide down to the target and land next to it.

---

That having been said, the most efficient burn is a full-throttle Surface retrograde burn.  Not a complete stop in the horizontal direction and then a long fall to the target.

Therefore, use the above to perform a full-throttle Surface retrograde burn.  The result is a hockey stick trajectory that is mostly horizontal until the final moments.    But as some of the thrust will naturally then be directed against the vertical motion (induced by Old Man Gravity), be aware that the maneuver is going to have a slight overshoot built into it.  Rather than a bad thing, this will probably just prevent you from colliding with your target on the ground and ending your day in a fiery conflagration.

Good luck.

Edited March 25, 2018 by Hotel26