The Museum of HP Calculators The Museum of HP Calculators
This program was adapted by Dave Hicks 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. | f | 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 00 05 5 Initialize 01 00 0 02 32 CHG SIGN 03 23 x→() 04 12 e initial velocity 05 05 5 06 00 0 07 00 0 08 23 x→() 09 17 d initial distance 0a 01 1 0b 02 2 0c 00 0 0d 23 x→() 10 15 f initial fuel 11 12 e Set up the display 12 27 ↑ 13 17 d 14 27 ↑ 15 15 f 16 57 PAUSE Display the Vel/Altitude/Fuel for 1 sec 17 57 PAUSE 18 57 PAUSE 19 57 PAUSE 1a 57 PAUSE 1b 57 PAUSE 1c 57 PAUSE 1d 57 PAUSE 20 00 0 Replace fuel with zero 21 41 STOP Allow input (default is a zero burn.) 22 27 ↑ Move requested burn into y 23 15 f Fuel in x 24 52 IF x<y Trying to burn more fuel than available? 25 04 4 Prepair to crash! 26 11 9 27 30 x⇄y fuel in y, burn in x 28 34 - fuel left after burn 29 40 y→() 2a 15 f save fuel left 2b 27 ↑ burn → y 2c 05 5 y = burn - 5 (subtract 2d 34 - gravity effect from burn) 30 40 y→() 31 13 a acceleration = burn - 5 32 02 2 compute new altitude 33 35 ÷ y = a/2 34 17 d x = d, y = a/2 35 33 + y = d + a/2 36 12 e x = vel, y = d+a/2 37 33 + y = d + v + a/2 38 40 y→() 39 17 d save new altitude 3a 00 0 3b 53 IF x>y Are we now below ground? 3c 05 5 3d 13 a If yes, go to crash display! 40 13 a x=a, y=d 41 27 ↑ x=a, y=a, z=d 42 12 e x=vel, y=a, z=d 43 33 + x=vel, y=a+vel, z=d 44 40 y→() 45 12 e New velocity = vel + a 46 44 GO TO 47 01 1 48 01 1 Loop Around for another display 49 12 e x=vel; Fuel gone show crash velocity as 4a 27 ↑ x=vel,y=vel; sqrt(v2+2gd) 4b 36 × y=vel2 4c 17 d 4d 27 ↑ x=d, y=d, z=vel2 50 01 1 51 00 0 x=2g (g=5) 52 36 × y=2gd, z=vel2 53 25 ↓ 54 33 + y=vel2+2gd 55 25 ↓ y→x 56 76 √x y=sqrt(vel2+2gd) 57 32 CHS 58 23 x→() 59 12 e Store crash velocity 5a 12 e Generate a hard land/crash display 5b 27 ↑ vel/0/-999999 5c 00 0 Show 0 for crash altitude because 5d 27 ↑ it's too much work to compute 60 11 9 the crator depth 61 11 9 62 11 9 63 11 9 64 11 9 65 11 9 66 32 CHS Fuel at -999999 indicates a crash 67 46 END
d Altitude (d for distance) e vElocity f Fuel a Acceleration
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