The Museum of HP Calculators The Museum of HP Calculators
This program was adapted by Johnny Nestor from Dave Hicks' HP 9100 adaptation from the "HP-25 Applications Programs" book Copyright © 1975 by Hewlett-Packard and is used here by permission.
This program is supplied without representation or warranty of any kind. Hewlett-Packard Company and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.
Imagine for a moment the difficulties involved in landing a rocket on the moon with a strictly limited fuel supply. You're coming down tail-first, free-falling toward a hard rock surface. You'll have to ignite your rockets to slow your descent; but if you burn too much too soon, you'll run out of fuel 100 feet up, and then you'll have nothing to look forward to but cold eternal moon dust coming faster every second. The object, clearly, is to space your burns just right so that you will alight on the moon's surface with no downward velocity.
The game starts off with the rocket descending at a velocity of 50 feet/sec from a height of 500 feet. The velocity, height and fuel are shown in the HP-9100's three line display as
-50 (Velocity 50 ft/sec downward)
500 (Altitude 500 feet)
120 (Fuel left: 120 units - this line changes to 0
after 1 second.)
The velocity is shown with a negative sign to indicate downward motion. The Fuel is displayed for just a second and then changes to zero. This lets you perform a 0 fuel burn by simply pressing the CONTINUE button (CONT on the HP-9100B.) (Otherwise the default burn would be all your fuel which is usually not what you want.)
A perfect landing shows as three zeros. A display like:
-velocity 0 -999999
means you have landed (or crashed) with non-zero velocity. In real life, you'd probably survive if the velocity is around -1 but at say -10, you wouldn't be coming back.
You will start the game with 120 units of fuel. You may burn as much or as little of your available fuel as you wish at each step of your descent; burns of zero are quite common. A burn of 5 units will just cancel gravity and hold your speed constant. Any burn over 5 will act to change your speed in an upward direction. You must take care, however, not to burn more fuel than you have; for if you do, no burn at all will take place, and you will free-fall to your doom! The final velocity shown will be your impact velocity (generally rather high). If the fuel flashes by and you forget it, you may recall it by pressing f.
We don't want to get too specific, because that would spoil the fun of the game; but rest assured that the program is solidly based on some old friends from Newtonian physics:
x = x0+v0t + (1/2)at2
v=v0 + at
v2 = v02 + 2ax
where x, v, a, and t are distance, velocity, acceleration, and time.
Notes:
| Step | Instructions | Input Data/Units | Keys | Output Data/Units |
| 1 | Enter program | |||
| 2 | Initialize | END CONTINUE | -50/500/120 | |
| 3 | Key in burn, compute new speed and distance. (For burn of zero, just press CONTINUE.) |
Burn (if non-zero) |
CONTINUE | new Vel/Alt/Fuel |
| 5 | Perform step 3 till you land or crash | |||
| 6 | To see remaining fuel after it has been cleared. | a | Vel/Alt/Fuel | |
| 8 | To Start a new game goto step 2 |
The following outputs are shown with the decimal wheel set to zero but that's not a requirement of the program
END CONTINUE -50/500/120 (the fuel units will change CONTINUE -55/488/120 to zero after a second) 5 CONTINUE -55/393/115 30 CONTINUE -30/350/85 CONTINUE -35/318/85 CONTINUE -40/280/85 CONTINUE -45/238/85 CONTINUE -50/190/85 10 CONTINUE -45/143/75 CONTINUE -50/95/75 10 CONTINUE -45/48/65 25 CONTINUE -25/13/40 Looking dangerous! 20 CONTINUE -25/0/-999999 Crash!!!
LINE CODE KEY COMMENTS 000 05 5 Initialize 001 00 0 002 32 CHG SIGN 003 23 x→() 004 14 b initial velocity 005 05 5 006 00 0 007 00 0 008 23 x→() 009 00 0 010 00 0 011 00 0 initial altitude 012 01 1 013 02 2 014 00 0 015 23 x→() 016 13 a initial fuel 017 51 LABEL 018 00 0 Label 0 019 14 b Set up the display...velocity 020 27 ↑ 021 23 x→() 022 00 0 023 00 0 024 00 0 ...altitude 025 27 ↑ 026 13 a ...fuel 027 57 PAUSE Display the Vel/Altitude/Fuel for 1 sec 028 57 PAUSE 029 57 PAUSE 030 57 PAUSE 031 57 PAUSE 032 57 PAUSE 033 57 PAUSE 034 57 PAUSE 035 00 0 Replace fuel with zero 036 41 STOP Allow input (default is a zero burn) 037 27 ↑ Move requested burn into y 038 13 a Fuel into x 039 52 IF x<y Trying to burn more fuel than available? 040 44 GO TO 041 51 LABEL 042 01 1 Prepare to crash! 043 47 CONTINUE (conditional 4-step placeholder) 044 30 x⇄y fuel in y, burn in x 045 34 - fuel left after burn 046 40 y→() 047 00 0 048 00 0 049 00 0 save fuel left 050 27 ↑ burn → y 051 05 5 y = burn - 5 (subtract 052 34 - gravity effect from burn) 053 40 y→() 054 00 0 055 00 0 056 01 1 acceleration = burn - 5 057 02 2 compute new altitude 058 35 ÷ y = acc/2 059 67 x←() 060 00 0 061 00 0 062 00 0 x = alt, y = acc/2 063 33 + y = alt + acc/2 064 14 b velocity → x, y = alt + acc/2 065 33 + y = alt + vel + acc/2 066 40 y→() 067 00 0 068 00 0 069 00 0 save new altitude 070 00 0 071 53 IF x>y Are we now below ground? 072 44 GO TO 073 51 LABEL 074 02 2 If yes, go to crash display! 075 47 CONTINUE (conditional 4-step placeholder) 076 67 x←() 077 00 0 078 00 0 079 01 1 x=acc, y=alt 080 27 ↑ x=acc, y=acc, z=alt 081 14 b x=vel, y=acc, z=alt 082 33 + x=vel, y=acc+vel, z=alt 083 40 y→() 084 14 b New velocity = acceleration + velocity 085 44 GO TO 086 51 LABEL 087 00 0 Loop Around for another display 088 14 b x=vel; Fuel gone show crash velocity as 089 12 x2 x=vel2; √(v2 + 2 g alt) 090 27 ↑ x=vel2, y=vel2 091 67 x←() 092 00 0 093 00 0 094 00 0 x=alt, y=vel2 095 27 ↑ x=alt, y=alt, z=vel2 096 01 1 097 00 0 x=2g (g=5) 098 36 × y=2g×alt, z=vel2 099 25 ↓ 100 33 + y=vel2 + 2 g alt 101 25 ↓ y→x, z→y 102 76 √x y=sqrt(vel2 + 2 g alt) 103 32 CHS 104 23 x→() 105 14 b Store crash velocity 106 51 LABEL 107 02 2 Hard land/Crash 108 14 b Generate a hard land/crash display 109 27 ↑ vel/0/-999999 110 00 0 Show 0 for crash altitude because 111 27 ↑ it's too much work to compute 112 11 9 the crator depth 113 11 9 114 11 9 115 11 9 116 11 9 117 11 9 118 32 CHS Fuel at -999999 indicates a crash 119 46 END
a Fuel b Velocity 000 Altitude 001 Acceleration
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