Very good work. I think it works for most conventional firearms. But if I may suggest some changes, here they are:
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Empty Weight = (D x S / P)² x B x A
D is dice of damage.
S is 2 for most guns, or 1 for “super” versions of non-superscience guns.
P is 5 for conventional firearms.
B is for the barrel-array value: 0.25 for tiny, 0.5 for very small, 0.8 for small, 1 for medium, 1.25 for large, 1.6 for very large, or 2 for extremely large.
A is for automation value: 1 for single-shot, 1.25 for semi-auto or light automatic, 2 for heavy automatic, and 3 for rotary
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Well, this is the problem, the Dices of Damage don't represent the energy of the shot, but the armor piercing power. At the same amount of energy, one small caliber (like the 5.56x45mm NATO) has more penetration power (and consequentially, dices of damage) than one medium caliber (like the 9x19mm Parabellum). So, instead of using Dices of Damage to calculate the weight, use a formula that uses the Energy in Joule of the shot (but this certainly complicates the calculations and refers to Cole formula that uses the energy and the caliber of the bullet).
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Shots
Firearms are loaded with magazines, either classified as compact “Sticks” or bulkier, more efficient “Boxes.” Decide on how many rounds you want a chosen magazine to hold, and record the weight of the ammo. Then, calculate the weight of the empty magazine using the following formulas:
Stick Weight = (square root of Shots) x Wa x 6.7
Box Weight = (cube root of Shots) x Wa x 2.4
Wa is the weight per shot
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I think that this formula does too heavy empty magazines. I suggest to reduce the constant, such as:
Stick Weight = (square root of Shots) x Wa x 3
Box Weight = (cube root of Shots) x Wa x 1.2
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Strength Requirement
Calculate the weapon's ST requirement using the formula below with loaded weight.
Pistol or Holdout ST = (square root of weight) x 6.3
Rifle ST = (fifth root of weight) x 6.3
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Well, for pistol or holdout ST I believe that this formula is more accurate:
Pistol or Holdout ST = (cube root of weight) x 6.3
With the first formula, you must have ST 13-14 to fire w/o penalties with a 2kg pistol.
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Recoil
Recoil depends on the size of ammunition fired from the firearm: 2 for pi- or pi, 3 for pi+, and 4 for pi++.
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Recoil doesn't depends only to caliber. In most cases, your formula is right, but if the firearm is too light for the energy of the shot, Recoil will increase.