I was wondering if you could explain the formula on how to figure tracking speed?Well I sure can!
Tracking speed is measured in Radians / second instead of meters per second because the number of meters depends on the size of radius. ... I'm going to need a picture, aren't I? Ok, give me a sec.
The angle of that triangle can be measured in degrees, but the math to figure out tracking speed in meters per second is more involved than if you measure it using the length of the arc it describes as portion of the radius. Why? Because, and this is the important part, the actual length of the arc is a fixed ratio to the size of the radius. In other words, regardless of the size of the circle the ratio of radius to arc length will always be the same for the same angle.
Fine, but what does it all mean?
If your tracking speed is X radians / second and your target is Y meters / radian away, then multiplying the two factors gives you the speed your gun can move on the arc of the circle , which is XY meters/second.
In layman terms, multiplying the tracking speed times the distance to the target will give you the speed your gun can keep up with. For example, a tracking speed of 0.05 shooting at something 5000 meters away can hit it as long as the transversal is 250 meters/second or less.
The upshot of this is that as the target gets closer the size of the maximum transversal you can hit decreases proportionately, and vice versa. This is why optimal range is named thus: its considered optimal because the farther something is away from your ship, the easier guns can track it, but any farther and the accuracy of guns starts to come into play.