Lander is a 2D extension of the "classic" lander app for the HP-15C.

The code might/might not fit in a 15C (26 regs + 39x7=273 bytes?, to confirm, keep an eye on the MEM report and optimisations).

Phases

The simulation has two phases: descent, and ascent.

Descent

The task is to deorbit (from near-circular orbit), and steer the lander so that it touches down smoothly (negative altitude and both velocity vectors < 25km/h).

Zero altitude displayed means success, flashing negative altitude reports the depth of the crater that will be named after you. Velocities, thrust, and time are zeroed (last horizontal/vertical V are still in the stack). Pitch is set to 0 (so this should allow a "jump" to another location...).

Output:

T: hor V (km/h)
Z: vertical V (km/h)
Y: range since release (km)
X: altitude (m)

Abort

Should it be necessary, the descent stage can be jettisoned by initiating the ascent phase.

Ascent

This phase can occur after touchdown, or after abort.

The ascent stage separates from the descent stage, and the task is to reach the CSM that has remained in orbit.

There is no check for success (yet). Try to close in within 1km, vh<10, vv<10.

Prior to initiating the ascent, and unless an abort is performed during descent, the CSM should move forward (or back) in its orbit to be repositioned correctly. This is achieved by specifying a (maybe negative) time increment as input to routine 'C'.

Output:

T: closing *ground* speed (km/h) (+= overtaking CSM)
Z: vertical V (km/h)
Y: *ground* range to CSM (km) (+=before)
X: altitude difference to CSM (m) (+=above)

Note: to skip descent phase and start from surface, execute following steps:

1. (GSB E)
2. 0 GSB C (initialise ascent mode without time offset)
3. 0 STO 6 STO 7 (zero current velocity)
4. GSB .4 (initialise to surface, takeoff values)

Using the app

1. Select scenario (B or C, see 'Labels' below) to initialise data.
2. Throttle inputs:
   • STO 1: throttle value (0.0 ... 1.0)
   • STO 2: total burn time (s) (suggested: 10s!)
   • STO 3: pitch (angle from vertical, +=prograde, deg)
3. Press 'A' to run the burn time. Calculator will run in predefined time segments (r14) until burn time or remaining fuel has been consumed.
4. Intermediate (PSE) output:
   • altitude
   • remaining time

Apollo profile

Note: these data are informative.

Descent

• From: 50kft (15.24km), 6014.64 km/h
• Target: 260NM (480km) (~12')
• 6': 100%
• 2': 50%
• 4': 50%-25%

Ascent

• Target: alt: 60kft (18.24km), 6009.4 km/h (~level) @range: 167NM (309km) (~7')
• roughly circular, the real orbit was slightly elliptic (~ 16 x 90 km)
• 10": 0
• 5': 50-70
• 2': 70-90
• current implementation does not change initial CSM altitude (15.24km / 6586s)

See also LM-1.

Tips

• remember that weight changes over time, which means that acceleration due to thrust will increase
• if not enough fuel left, burn time is reduced to match remaining fuel
• CSM continues orbiting, this has an impact on when to initiate lift-off.

Notes

Simple formulas used ("Euler symplectic"), don't expect stable orbits: as as simple example, just run idle in the initial orbit and observe the decay. You might also notice a lag between acceleration and velocity response, and - rather unacceptable - vv that increases while engine off and ascending... This is more a game than a realistic simulation; deviations get also worse with larger time steps (r2). It might be interesting to have an idea of the lower bound for the time step before other effects start to appear.

Programming

MEM report

This app was implemented on a Swiss Micros DM15C firmware DM15_M1B_V16 (max memory variant=230 reg).

DM15_M1B :  26 133 71-0

Note: these values might not have been updated with every commit or release. A "pure" HP15C variant is in the TODO list.

Labels

 A main burn routine
 B init descent phase
 C init ascent phase. repositions CSM first by fast forwarding time (X: advance CSM time in orbit, seconds)
 D -
 E -
 
 0 -
 1 -
 2 -
 3 -
 4 -
 5 -
 6 sub: compute distance to CSM
 7 sub: STO (x) (consumes X)
 8 sub: RCL (x) (consumes X)
 9 sub: init moon params
.0 section: output
.1 section: compute fuel used
.2 sub: general init
.3 sub: return circular orbit vc for given h (above sfce)
.4 sub: crash analysis, followed by landing configuration (zero speed, height, thrust)
.5 section: main calc loop
.6 section: stop, generate output
.7 section: calc new pos, v
.8 section: reduce fuel left
.9 sub: calc eng + grav acc

Registers

Notes:

• '>' Lander registers user can manipulate
• '' statistics registers

List:

0   mf - fuel left (kg)
1 > th - throttle (.%)
2\> t - burn time (s)
3\> b - pitch (0=vertical, +=prograde) (deg)
4\  h - height (m) /ascent: altitude above CSM (int: R)
5\  d - ground range covered since descent initiation /ascent: ground range before CSM (intermediate: delta) (km)
6\  vv - velocity/vertical (km/h)
7\  vh - velocity/horiz /ascent: hor. closing *ground* speed (km/h)
8   px (m)
9   py (m)
.0  vx (m/s)
.1  vy (m/s)
.2  ax (m/s2)
.3  ay (m/s2)
.4  dt0 - delta t internal step (s)
.5  g0 - gravity, surface (m/s2)
.6  r0 - central body radius (m)
.7  dt - user delta t (fuel clipped if necessary) (s)
.8  fu - fuel used for current burn segment (kg)
.9  T - remaining time in calculation loop (s)
  
(indirect:)
20 f - max fuel flow (kg/s)
21 F - max thrust (N)
22 m0 - vehicle mass, dry (kg)
23 mf0 - initial fuel (kg)
24 CSM alt (circular orbit)
25 CSM vel (vc)
26 total time

Flags

0 -
1 fuel empty
2 ascent mode: if set, output (range, alt and vh) refer to orbiting CSM
3 -
4 -
5 -
6 -
7 -
8
9 crashed

About the files

The dumps have been generated with Swiss Micros (modified, see /vendor/swissmicros/master) [encoding/decoding scripts](/extern/swissmicros/decode RAM dump.htm).

• code_dump.txt: decoded program, line per line; sometimes contains comments
• mnemonic.txt: equivalent program in mnemonic form. note that this file /might/ be more recent than the DM file.
• HP.xml: simple Notepad++ syntax highlighter
• DM15_M1B.txt: can be uploaded via the serial link (see also firmware and instructions)

RELEASE HISTORY

V1.2 (2014-10-30)

• changed: ascent init requires time advance (repositions CSM)
• bug: CSM distance
• bug: time was reset in 'C', now only in 'B'

V1.1 (2014-10-21)

• bug: CSM distance wrong in output (Y)
• bug: crash test did not take r7 (vh) into account

V1.0 (2014-10-18)

• new add orbiting CSM (constant circular orbit, r24)
  • ascent phase
  • abort option
• new total time counter (r26)
• changed pitch coordinates (0=up)
• changed use Velocity Verlet to improve accuracy (a bit...)
• bug: descent stage did not take ascent stage weight into account
• update data
• refactor indirect register accesses
  • cost: -2x7 = -14 bytes (subroutines)
  • benefit:
    • +5 (get rid of STO/RCL I; R_down; STO/RCL(i))
    • -2 (ENTER) per STO subroutine call
    • -1 per RCL subroutine call

v0.4.1 (2014-10-11)

• new: add some docs
• change: crash criteria
• solve: bug in crash analysis

v0.4 (2014-10-09)

• add crash detection
• show intermediate altitude
• markdown (doc)

v0.3 (2014-10-08)

• check routines in Earth orbit
• range bug/velocity convert
• remove Earth stuff
• add Apollo profile
• lander routines
• change V output system (from v/elev to vert/hor)

v0.2 (2014-09-27)

• "bug in firmware" appears to be a bug in my head (ENTER/RCL issue, see UM P36)

v0.1 (2014-09-21)

• test version for SwissMicro HTML decoder issue

Upcoming

DONE

• CSM phase issue

BUSY

TODO

• use same variables in all versions
• review units? (use US system?)
• raise CSM orbit for ascent
• add input checks
• compute output after init
• add some screenshots of the logic
• add CSM rejoin check
• add scoring
  • within X km of planned touchdown
  • within X params of CSM
  • with minimum fuel used
• optimizations
  • speed (variant?)
    • skip burn calcs on zero throttle
    • precomputed factors? (needs regs)
      • LBL 6: CSM period is constant
    • r10-r19 need 6 steps for adressing: can they be swapped for normal (r0-r9) regs?
    • verlet: refactor thrust (is constant across step)
    • reorganise subroutine calls to avoid too much searching for the label
  • accuracy
    • Verlet: moment of fuel update (STO-0)
    • take RCS mass change (~60kg) into account?
    • RK4?
  • handling
    • renumber variables according to keyboard layout
    • interrupt flag

RPN notes

1. BST in run mode should backstep repeatedly when held
2. RCL (i) should have a variant RCL (x); IMO latter should consume X.
3. some sequences that bit me as an RPL user (and I wonder how novices dealt with it):
   • assuming the stack looks like this: T:1 Z:2 Y:3 X:4, then keying
   • 888 [X<>Y] 999
     • expect: T:2 Z:3 Y:888 X:999
     • get: T:3 Z:888 Y:4 X:999
   • [x^2] [ENT] [RCL]
     • expect: T:3 Z:16 Y:16 X:[r]
     • get: T:2 Z:3 Y:16 X:[r] (Owner's Hb, Ed 2.4, p.36)
4. Number of steps is not very helpful, because some steps actually use two bytes. (LBL ./GTO/(GSB?) ./flags/x></DSE/ISG/STO/RCL /(i) - see UM p. 218)
5. USER mode has subtle differences when programming: u STO x (see p. 176)

Links

1. https://delicious.com/axd/moonlanding,HP15C
2. https://www.physicsforums.com/threads/improving-the-accuracy-of-a-java-simulation-of-n-orbital-bodies.380098/
3. http://stackoverflow.com/questions/4038554/2d-orbital-physics
4. http://space.stackexchange.com/questions/8911/determining-future-orbital-position
5. https://en.wikipedia.org/wiki/Apollo_Lunar_Module
6. http://www.klabs.org/history/apollo_11_alarms/eyles_2004/eyles_2004.htm
7. http://spaceref.com/missions-and-programs/nasa/apollo/apollo-lunar-landing-mission-symposium/apollo-lunar-module-landing-strategy.html

Another simulation (data only)

Very interesting pages, might prove my implementation is a joke, anyway, here you are... I didn't compare the results (yet).

1. http://www.braeunig.us/apollo/LM-descent.htm
2. http://www.braeunig.us/apollo/LM-ascent.htm