Hello, I was juggling with numbers recently to find optimal combinations of sensor suites. I wanted to know when the dropdown of a long-range sensor (or any 'further ranged' than another one type) would get ousted by its sharper resolution brother array, so that I could eventually adjust sensor in a way where this 'weakest point' wouldn't be in a spot where it hurts (..such as where you encounter alot of enemy ship masses in). So here I present the results, absolute in theory, open to discussion in conclusion.
First of all we need the sensor formulas. The formula for maximum range depends only on resolution and goes like this:
M is the sensor resultion measured in tons (thus the conversion factor of "/50" for HS). ..I just like to use official units more than artificial ones. The sg, se and sm stand for grav sensor technology, em sensitivity and sensor size. Since those all and the 10.000 basic kilometers form a constant, they are referred to as B(-asis) from now on.
Next the formula for the reduced sensor range against units smaller than the minimum resolution:
m is the targets' mass if it was smaller than M. Basically, the standard formula from before receives this ("target mass"/"minimum resolution")^2 factor that arranges a exponential loss of range. A target of half resolution would be detected only on 1/4th of the maximum, a target of a tenth of the resolution on only 1/100th and so on.
Now the important step of combining the two. The question is at which target mass the longer ranged low resolution sensor with resolution M1 has lost enough power to have exactly the same detection range as the maximum output of the initially shorter ranged, but higher resolution sensor with M2. Because that is where the second sensor actually starts to become efficient, and as said in the beginning, this point is to be positioned nice for optimal performance.
Keep in mind that it is possible to have such a high tech secondary sensor (B2), that it could theoretically bust the equation by making the meeting mass higher than the so called "long range" sensors maximum range. If that happens, take the hint! Your beloved old sensors are sooo obsolete that now they don't improve your ship detection by even a milimeter anymore!
However, if you are like me and always have maximum sized and identical tech grade sensors installed, then both B's will be identical, simplifying the formula to:
Again, 1<2 in resolution.
So what was that for? Maybe the meaning of calculations like this is not entirely obvious, so I will use the help of graph to illuminate:
Basically, whenever you have a very long ranged low resolution sensor, that automatically means that a shorter ranged high res. one will be better at some point, since higher resolution also means they reach their peak performance faster. The last formula is used to calculate the position of the point where both of the graphs above they meet. Any target lower in mass than that point will now be detected much further than before with only the long range sensors. (for optical pleasures I highlighted the 'total gain' area in red - a new territory of range/mass combinations given visibility through the improved suite)
What you want to do with this now is to position this, uhh, kind of a semi-blind-spot, the spot of least efficient sensor detection if you will -which is exactly the meeting point of the graphs- and lay it into territory where you rarely encounter enemy ship masses in. This way it wouldn't matter to be inefficient when there is nothing to see anyway.
So I made some example against the usual remnant aliens, which are known to appear exactly in the two ship size combinations ~16kt, and ~8kt. Those two spots you would want to be well covered:
Okay, firstly I have to say that putting more than 2 active sensors on a ship(including missile detection already) appears kind of wasteful to me, since I normally completly equip any of my military ships with a full suite.(I like big individual ships with survey shuttles better than entire fleets) It appears however a viable thing to do if you only have one sensor ship in a larger fleet, or even in a squadron of fighters. The advantage is quite obvious as here the the detection range of one of the most common enemy types has increased by nearly factor 3. ...Good for early tech times I think, while later I would rather just drop the 16k one since detection gets so good that you can cover an entire system just with that anyway. However, at that time again, a fast attack craft detector at 1kt (here in red) might be useful (detection range improvement of factor ~4.5 compared to the missile sensor who would otherwise be your guide at that enemy size) ...if you plan to kill them with rockets from afar that is.
..Anyway, back to the point. Here the sensors directly cover the two most important points, which btw. must not always be the case. The result here however puts the weakest spot into the range of around 13.5kts, where I frankly I have never seen anything in, not remnant nor alien civ, so that is a pleasing result. Should you tailor your sensors to match some distinct common sizes of another empire, or even a player, then it might sometimes be necessary to not directly target those two ship sizes to either spread the coverage to other needed areas (who says the enemy always has to have two major war-important size classes?), or avoid getting weak in this third area which might prove vital, because...
...On the counter-intelligence side, this study also reveals which size you should likely make your stealth craft to be if you go against another player.
For enemies with two sensors and up, those spots reveal the maximum size you can make your craft and still be in the enemies nearest detection range. In the graph above that would be the non marked spot where the green and red graph meet.(about 4800 tons -- well, and 472 tons fighters, where missile detection would take over {not shown in the graphic})
I am currently not sure if alien civs have their sensors adjusted to fit the remnant threat (like a 8k res sensor), or if they don't care about efficiency at all and just take some near random equipment with them.(could be researched however) If so, then for example the sweet spot between a 8k sensor and the missile detection grid would be at exactly 2250 tons. Anything with less mass is pretty much wasted opportunity since that doesn't give any advantage(against active sensor that is), as you you will show up on missile detection anyway. Higher is detected more easily by the long range scanner though.
Same data would be interesting to know about remnant ships.(maybe just look it up in builder mode? sounds like cheating, hmm.)
Ok, I am done so far. Contribution analysis for the archive.
