1) Are you ever going to publish the starship creation rules you used to make these ships? It looks like the Toughness and armor are based off the Sci-Fi Toolkit but the weapons are different and likely have different space cost.
2) The spinal mount gun on the Battleship pales in comparison to the Quad Heavy Laser Batteries when firing against other capital ships. Is the damage value correct? It seems to me that I would dump it in favor of more heavy laser batteries. They do more damage and don’t require the ship to be pointed at the enemy.
1) No system was used, beyond imagination and ships-have-what-they-need.
2) It all boils down to range, average damage, and AP.
A spinal mount has double the range of heavy laser batteries. You use that while you’re approaching your target.
The average damage of a quad laser battery is 27.5 and the spinal mount is 26. Not much difference. The quad lasers do an average of 45.5, which is enough to Shake a battleship (40 Armor). A spinal mount has enough AP to totally ignore a battleship’s 40 points of armor, which means it inflicts an average of 7 wounds.
Even against a heavy cruiser (30 Armor), the difference in damage is an average of 4 wounds versus 7 wounds. Pop enough shields and you should survive the quad laser battery attack, albeit with damage to your ship. Against a spinal mount you’d need to roll 2 raises just to avoid being disabled.
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