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Falling: A Beginner's Guide

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Thanks to not_cub for helping out with the maths.

NOTE:- This article is published under the terms of the Open Gaming Licence. All material derived wholly from the D20 SRD is highlighted in the following manner.

This is open gaming content.

The version of the Open Gaming Licence we are publishing under, together with the appropriate copyright notices can be found here.

The Scene: The International Space Station, some years from now. On board, ace Cosmonaut Sergei Tereshkov. For a day and a night he has fought to save the crippled station as it circles down toward the Earth's atmosphere, but now he must admit defeat. Already the wispy tendrils of the Earth's atmosphere are reaching out to grasp Alpha's steel skeleton. Soon she will plunge Earthward.

And so will Sergei.

Sergei Tereshkov (10th Level Pilot / 6th Level Engineer / 2nd Level Scientist / 3rd Level Cosmonaut*)

*Cosmonaut is a prestige class similar to the standard Astronaut prestige class, but with additional munchkin features added.

He must leave. But there is one problem. His Soyuz lifeboat departed two days ago with his remaining crew mates. He's taking this ride on his own. He gets into his space suit, enters the air lock, and pushes himself away.

At 75 miles of altitude, somewhere above West Africa, Sergei begins to feel the tug of the atmosphere. At a speed of 18,000 miles per hour, he re-enters, and begins his long fall to Earth. A few minutes later he blazes a trail over Greece, still moving at more then 5000 miles per hour.

He sails over the Kazakh desert at a thousand miles per hour, decelerating all the while in long lazy arcing swoops. Within minutes, with his arms and legs spread to generate the maximum drag, he has slowed to around 120 miles per hour and is preparing to make his final landing.

He falls toward the ground, hits, rolls, bounces, and skids to a halt in the desert sands, bruised, battered, but very much alive. He gets up, and begins to walk toward to the sound of the arriving rescue helicopter.

Calculating PCFS

Okay, so Sergei survived, but would you? Well it all depends on your PCFS. Here's how to calculate it, and be warned, there is a certain amount of mathematics here.

Disclaimer:- I don't understand any of the maths, so I can't guarantee any of it. If you hurl your PC off a cliff and he ends up a blob of strawberry jam, don't come blaming me. And given that I don't understand the maths and not_cub doesn't know the gaming system, the potential for a fuck-up is quite high.

Firstly, you will need to know:

H which is your number of hit points.
S which is your fortitude saving throw.

Now there are two formulas, depending on whether you have more than 50 hit points.

If you have more than 50 hit points then the formula is:

PCFS = 100 - (f(H) + (f(50) - f(H)) * (14-S) / 20) * 100

But if your hitpoints are less than or equal to 50 points then the formula is:

PCFS = 100 - f(H) * 100

At this point, you will of course be asking: "What the fuck* is f?"

* Feel free to insert a culturally appropriate expletive here.

Don't panic. "f" is simply a lookup table. So if you need to work out say "f(29)" you find the row which has 29 in the left-hand column, and take the value that is in the right-hand column. For values of less than 25, you the value for 25 (1.0) and for values of greater than 120, use the value for 120 (0).

This is the table:

25 - 1.0 26 - 0.9999999999
27 - 0.9999999998
28 - 0.9999999992
29 - 0.9999999973
30 - 0.9999999919
31 - 0.9999999771
32 - 0.9999999395
33 - 0.9999998481
34 - 0.9999996363
35 - 0.9999991664
36 - 0.999998165
37 - 0.9999961101
38 - 0.9999920392
39 - 0.9999842379
40 - 0.9999697504
41 - 0.9999436373
42 - 0.9998978899
43 - 0.9998198966
44 - 0.9996903533
45 - 0.9994805217
46 - 0.9991487689
47 - 0.9986363825
48 - 0.9978627449
49 - 0.996720071
50 - 0.9950680592
51 - 0.9927289662
52 - 0.9894837678
53 - 0.9850701894
54 - 0.9791834481
55 - 0.9714805164
56 - 0.9615885711
57 - 0.9491180175
58 - 0.9336800829
59 - 0.9149084835
60 - 0.8924841243
61 - 0.8661612639
62 - 0.8357931294
63 - 0.8013546902
64 - 0.7629602377
65 - 0.7208736299
66 - 0.6755095356
67 - 0.6274247313
68 - 0.5772993946
69 - 0.5259092951
70 - 0.4740907049
71 - 0.4227006054
72 - 0.3725752687
73 - 0.3244904644
74 - 0.2791263701
75 - 0.2370397624
76 - 0.1986453098
77 - 0.1642068706
78 - 0.1338387361
79 - 0.1075158757
80 - 0.08509151654
81 - 0.06631991707
82 - 0.05088198247
83 - 0.03841142889
84 - 0.02851948364
85 - 0.02081655189
86 - 0.01492981058
87 - 0.01051623222
88 - 0.007271033829
89 - 0.004931940797
90 - 0.003279928977
91 - 0.002137255072
92 - 0.001363617494
93 - 0.0008512310757
94 - 0.0005194782842
95 - 0.000309646734
96 - 0.0001801034409
97 - 0.0001021100728
98 - 0.00005636268488
99 - 0.00003024958968
100 - 0.00001576207331
101 - 0.00000796078366
102 - 0.000003889879868
103 - 0.000001834983593
104 - 0.0000008336563089
105 - 0.0000003637307988
106 - 0.0000001519107662
107 - 0.00000006049749584
108 - 0.00000002286818703
109 - 0.000000008159519203
110 - 0.000000002729527498
111 - 0.0000000008488376669
112 - 0.0000000002427712077
113 - 0.00000000006296499558
114 - 0.00000000001453164595
115 - 0.000000000002906329191
116 - 0.0000000000004843881985
117 - 0.00000000000006318106936
118 - 0.000000000000005743733578
119 - 0.0000000000000002735111228
120 - 0.0

Example:

Joe has 82 hit points and a Fortitude save of +12.

He has more than 50 hit points, so the formula to use is:

PCFS = 100 - (f(H) + (f(50) - f(H)) * (14-S) / 20) * 100

This becomes:

PCFS = 100 - (f(82) + (f(50) - f(82)) * (14-12) / 20) * 100

Looking up the values for the 82nd and 50th rows from the table (0.05088198247 and 0.9950680592 respectively) gives us:

PCFS = 100 - (0.05088198247 + (0.9950680592 - 0.05088198247) * (14-12) / 20) * 100 = 85.46994099

Bit of bashing on the calculator gives us:

PCFS = 85.46994099

Or in real terms:

PCFS = 85.5%

So if Joe jumps off a very tall cliff, he has a better that 85% chance of walking away, conscious, from the impact. Doncha just love a heroic system?