Efficient landing procedure?

[numerobis]

They measure gravity in meters per second per second (m/s/s)

To a first order, your intuition is good. Take it one more level though: you're in a rotating frame of reference. Hovering is free if you're in orbit!

[Hotel26]

I may have a slightly different take on this.  If you want to land on a pinpoint and use the minimum possible fuel, you'd do what NASA does and let a computer do it.  Sure, the math/physics is interesting and you'd need that to program the computer, but that is already done: MechJeb.

I am exploring mining operations and efficiency for me is measured in terms of repeatable close grouping of landings of the ore transport lander, to the cluster of drill rigs, the cost being my time to drive the ore transport rover from the drill rigs to the lander...

So do you want to do it "by hand"?  Well, yeah, baby!!

I've been developing a procedure to repeatedly get me within 150 meters of target.  I have a standard, multifunction (6) lander that that can carry 15 tons of fuel into low, lo-grav orbit, so fuel on the way down to the surface "empty" is not my problem.  On my last try, I crashed into the target , just grazed it, on landing.  Don't know yet if it was a fluke, but I've modified the procedure to "detune" the final step in landing.

Here's the procedure as it is so far...

1. I start with a 20-30Km orbit around the Mun, about 545 m/s
2. 90 degrees before the target, I perform a rough inclination change to center trajectory over the target.  (Yes, maybe this requires an informational target display from Mechjeb; certainly the Surface info panel in Mechjeb is indispensable.)
3. 10-15 degrees before the target, I deorbit by reducing the surface horizontal velocity to 400 m/s, then switch to SFC mode on the navball.  I hold attitude stable then and reduce to 300 m/s before 3 degrees before the target; 200 m/s 2 degrees before the target; 100 m/s 1 degree before the target and down to 20 m;/s and less as I approach the target longitude.  This I call the asymptotic method.  It's not the most efficient but it's compatible with the "suicide burn" and it's manageable for a human pilot
4. Next is "ride the ball" and it is hard to describe and it's what makes this procedure deadly (fireball) accurate.  There are 4 symbols on your navball [my notation]: your attitude (+), your retrograde (O), the target (T) and the SFC normal (X) (the middle of the navball)).  + (under thrust) drives your retrograde, O, away.  Your orbit scrolls from O toward X.  O also tends toward X due to gravity!  If your target, T, is not inline with O and X, it will scroll past you.  So you need to use your attitude to drive your retrograde, O, to be in a line, OTX.  Your only control is + which positions O (by driving it away).  When O is inline, OTX: O drives T toward X.  When you get all 4 coincident (with gravity also somewhat in control), you are descending vertically right over your target (and will hit it and die in a fireball).
5. When you get +OTX close enough (coincident) in a line, use the asymptotic rule again to manage vertical progress to land rather than crash.  This is all-attention-consuming so all of these activities get assigned their own phase.  Once you start managing the vertical, you have to let go of the target: you are as close as you are going to safely get on this flight.
6. If you did 4 right (too well), you are going to hit the target and die, or at least, lose the tax payers' equipment...  So this last step is actually part of 5, the vertical management phase, and it is "detuning the result",  As you transition from riding the ball" to "land on terra firma", verify the navball is showing just a little misalignment.    If not, work on getting some before it's too late. 

This explanation is maybe a little cryptic and/or erroneous, so let me know which parts are foggy and I'll do my best.  This procedure is still evolving, too, so I'd love to hear better suggestions!

Here's a mining site with 7 vehicles, http://imgur.com/nzlPK3v , with a 220m spread N-S and quite a lot closer grouping E-W.

Edited February 9, 2016 by Hotel26
final clarification