Lunar Excursion Module

This program is a Lunar Excursion Module (LEM) landing simulation, originally by David Ahl and adapted for the ZX81/TS1000. The player manually controls retro-rocket burn rate (0–16,500 lb/sec) each 10-second interval, trying to achieve a soft touchdown on the Moon. Physics are handled by a Taylor-series approximation subroutine at line 1000, which computes updated velocity and altitude using five terms of a power-series expansion to avoid division-by-zero issues during the burn. Landing outcomes range from a perfect soft landing through craft damage, stranding, and crater-formation based on the final impact velocity in MPH. The program uses SLOW/FAST toggling loops for blinking effects at lines 310–314 and 5000–5003, and inverse-video characters for highlighted on-screen text output.

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Program Analysis

Program Structure

The program is organised into clearly separated phases:

1. Title and introduction (lines 0–75): scrolling title, narrative text, and delay loops.
2. Initialisation (lines 80–117): sets up simulation constants and variables.
3. Main simulation loop (lines 118–180): displays state, accepts burn rate input, steps physics.
4. Fuel exhaustion handler (lines 185–205): computes free-fall trajectory after fuel runs out.
5. Landing outcome display (lines 265–325): five outcome branches based on impact velocity.
6. Physics subroutine (lines 1000–1015): Taylor-series burn computation.
7. Replay prompt (lines 2000–2030): asks player to try again.
8. Blink effect subroutine (lines 5000–5005): FAST/SLOW toggling for screen flash.
9. Utility tail (lines 5020–5050): STOP, CLEAR, SAVE, RUN stubs.

Simulation Variables

Variable	Meaning	Initial value
L	Elapsed time (seconds)	0
A	Altitude (miles)	140
V	Velocity (miles/sec, downward positive)	1
M	Total mass (lbs, including fuel)	33000
N	Empty (dry) mass (lbs)	16500
G	Lunar gravity (miles/sec²)	1×10⁻³
Z	Exhaust velocity factor	1.8
K	Burn rate (lbs/sec, player-supplied ÷10)	0
T	Time remaining in current 10-sec interval	10
S	Sub-interval time step	varies

Physics Subroutine (lines 1000–1015)

The subroutine at line 1000 avoids direct integration of the rocket equation by using a Taylor-series expansion around the mass-ratio term Q = S*K/M. This is the classic Ahl LEM approach: rather than computing LN(1-Q) directly (which would require a LOG function and risks domain errors near zero), the natural logarithm is approximated as:

-Q - Q²/2 - Q³/3 - Q⁴/4 - Q⁵/5

This gives updated velocity J and altitude I without needing LOG, making it suitable for systems where accuracy of the transcendental function may vary or to keep the computation self-contained.

Burn Rate Input Handling

The player enters a burn rate at line 123 (INPUT K). The value is then divided by 10 at line 124 (LET K=K/10). This scales the user-friendly 0–16500 range down to internal units. Notably, line 117 initialises K=0 and line 118 immediately performs LET K=K/10 (a no-op on zero), which appears to be a remnant of the input loop structure rather than intentional logic — the division at line 118 is redundant on first entry but harmless.

Sub-interval Clamping

At line 145–150, the time sub-step S is clamped so that the fuel consumed (S*K) does not exceed the remaining fuel (M-N). If there is insufficient fuel for a full step, S is shortened to exactly exhaust the remaining fuel, ensuring M never undershoots N.

Altitude-Below-Zero Handling

Lines 370–395 handle the case where computed altitude I goes negative within a sub-step (i.e., the craft has crossed the surface). The code bisects the time step using a velocity/distance estimate (D = V + SQR(V²+2*A*(G-Z*K/M)), giving S = 2*A/D) and iterates until S < 5E-3 seconds, at which point it falls through to the landing display at line 205.

Landing Outcome Branches

Condition (W = impact MPH)	Outcome
W <= 1.2	Perfect landing — congratulations
1.2 <= W <= 10	Good landing with screen blink (subroutine 5000)
10 < W <= 60	Craft damage, stranded
W > 60	No survivors; crater depth printed as W*0.277 feet

SLOW/FAST Blinking Effects

Two places in the program toggle between SLOW and FAST display modes inside a FOR–NEXT loop to create a visible flicker effect. The crash sequence at lines 310–313 runs 370 iterations; the good-landing blink at lines 5000–5003 runs only 10. This is a well-known ZX81/TS1000 technique for producing attention-grabbing screen animation without any graphics primitives.

Notable Idioms and Quirks

• The display header at line 85 uses inverse-video characters (rendered via % escapes) to produce a highlighted column label row for the simulation table.
• TAB is used in line 120 to align columns: time, altitude (integer miles), fractional feet, MPH, and remaining fuel.
• Line 122 checks L>190 to trigger a SCROLL, preventing the table from overflowing the 24-line display — a simple but effective guard.
• The INPUT H$ at line 2022 reads a string and tests H$(1) for “Y” or “N”, a standard ZX81 idiom for single-character menu choices.
• Lines 5020–5050 (STOP, CLEAR, SAVE, RUN) are unreachable utility stubs, likely used for development convenience rather than normal execution.
• The power operator ** is used at line 1005 (Q**3), which on the ZX81/TS1000 is equivalent to ^ — an unusual notation sometimes seen in early BASIC ports.