Very Small Sizes: What Modifier?

[Captain Joy]

Look at B19 and B550 for the smaller sizes. The table loses integrity at the -5 modifier point. Which table should I use? Better yet, if someone in-the-know knows what equation is used to come up with these tables, do tell. (I suspect one of the tables is suffering from rounding error.)

I can see that it's something along the lines of

Bonus or Penalty = 6 • ln (Size in yards / 2) / ln(10)

and

Size in yards = 2 • e^[Bonus or Penalty • ln(10) / 6]

I'm sure about the 10's and 6's; they are what make the size penalty increase by a factor of 10 for every 6 jumps in size modifier. I'm not sure about the 2's. Those values make the equation agree exactly with the table when the size modifier = 0. Choosing that value is what is going to have a significant effect (noticeable at two digits of precision) for sizes smaller than 12 inches.

I eagerly await the collective knowledge of this fine forum.

[Anthony]

Originally Posted by Captain Joy

Look at B19 and B550 for the smaller sizes. The table loses integrity at the -5 modifier point. Which table should I use?

The formula is 6 * log10( size ) - 2, so B19 looks correct, but B550 is not dramatically different.

[gilbertocarlos]

For every extra 0 you add 6 in SM, so, reverse it and you get for each 0 lacking, -6.

So, up to 2y is 0.
20y is +6
0.2y(7") is -6
0.02y(0.7") is -12
0.002(0.07" or 1/16 of an inch) is -18
0.0002(0.007" or 1/128 of an inch) is -24
0.00002(0.0007" or 1/1256 of an inch) is -30

[Captain Joy]

Originally Posted by Anthony

The formula is 6 * log10( size ) - 2, so B19 looks correct, but B550 is not dramatically different.

Thank you! This is exactly what I was looking for. Comparing the equation to GURPS RAW (SM and Size columns):

Size	SM	6•log(Size)-2
----    --      -------------
2	0	-0.19
3	1	0.86
5	2	2.19
7	3	3.07
10	4	4.00
15	5	5.06
20	6	5.81
30	7	6.86
50	8	8.19
70	9	9.07
100	10	10.00

and

SM	Size	10^[(B+2)/6]
--    ----      -------------
0	2	2.15
1	3	3.16
2	5	4.64
3	7	6.81
4	10	10.00
5	15	14.68
6	20	21.54
7	30	31.62
8	50	46.42
9	70	68.13
10	100	100.00

So, you can see the formula is exact for the 10^x sizes. Everything else is rounded to a more playable value.