By the way, if anyone wants to help with the code, there's an easy way. Install Unreal Engine from the Epic Games Store, make an empty project, create a new Blueprint, and select a function library. You can then make all kinds of functions with input and output pins. It's all visual, using graphs. You don't need to write a single line of code.
What functions do I need? Here's a list I'll add to.
1. Calculate the divergence of a laser beam according to distance and wavelength. The output should be either an angle in degrees or the diameter of the spot on a hypothetical plane.
2. The spread of hits from firearms. There's a parameter called spread: the area in which more than 50% of shots land. Or 70%; I can't remember right now. The point is that hits aren't distributed uniformly. Noticeably fewer land near the edge of the spread than near the center. We need to study and model this.
3. The thermal balance of a ship's hull: incoming radiation from the star and radiation emitted by the hull itself. Ignore cooling radiators and other systems. The output should be the hull's calculated temperature. The input should also include a negative heat flow from cooling systems. Include several hull coatings, from perfectly black to mirror-like. Materials: aluminum (duralumin), steel, fiberglass, titanium, and tungsten.
That's all for now. These equations and functions aren't as difficult as they might seem. They're all available online, and ChatGPT can help too!