[LT] Rated ST for bows and crossbows

[SuedodeuS]

Originally Posted by Anthony

No, from collision rules damage is linear in velocity.

Kinetic energy is 0.5*m*v^2. GURPS damage is 3.5*C*v*m^(1/3)/100, with C being 2 for living, 4 for unliving, and 8 for homogenous; and m being mass in pounds per G. If we drop the constants (which are unimportant for scaling) and square damage, we have KE as m*v^2 and damage^2 as m^(2/3)v^2. This is rather close to equal, although when v is low the difference in m is more pronounced.

Originally Posted by Anthony

However, bow efficiency varies with the weight of the arrow relative to the weight of the bow, which generally forces a heavier bow to use heavier arrows, and the scaling is only 1/3 in the weight of the projectile (due to how HP progression works).

This is part of why I noted the scaling as being very rough. May we assume that a bow that is 2x heavier gets normal efficiencies out of an arrow that is 2x heavier?

Originally Posted by Ze'Manel Cunha

Gotta rate it somehow...

If we assume arrows to be homogenous objects (for HP calculations), this gives out typical 0.1 lb arrow between 3 and 4 HP (3.71 HP). Average collision damage is typically calculated as 3.5*3.71*v/100. This means each +1 corresponds to around 7.7 yards per second (16 mph) - or it would, were it not for the rule that impaling objects get half normal collision damage. This boosts our speed for each +1 to 15.4 yards per second (31 mph). It may be appropriate to disregard the half-damage rule here, in which case every +1 to ST corresponds to a +3.8 yards per second boost (every +2 is a +1 to damage).

Note this implies an ST 12 longbow flings arrows at around 70 mph, while maintaining the half damage rule (and thus having 7.7 yards/sec per +1 ST) means such arrows fly at a rate of 140 mph. I have no idea how fast an longbow flings arrows, so I can't rule which (if either; keep in mind GURPS arrow damage is probably on the high side) is more realistic.