Could you post the equations for active detection range? I'm confused about how TCS fits in. It looks like your original post went the way of the Dodo.
Active sensors are a lot simpler than passive. Their range is equal to sensor detection strength per HS * Sensor Size * Resolution in HS * 10,000 km.
So a sensor of 1HS with detection strength 10 and a resolution of 1 would have a range of 1 * 10 * 1 * 10,000 = 100,000 km.
A sensor of 5HS with detection strength 16 and a resolution of 40 would have a range of 5 * 16 * 40 * 10,000 = 32,000,000 km
The TCS (Target Cross Section) is the size of the ship for resolution purposes. So a 2000 ton ship (which is 40HS) has a TCS of 40 and can therefore be detected by sensors with a resolution of 40 or less. I will adding both stealth technology and blip enhancers in the future to decrease or increase the TCS so a ship's TCS will not always be equal to its size
Steve