Well, not quite: it's only quadratic, being simply proportional to the area of a circle of the same radius

This is one of the weirder ways in which GC*'s abstractions leak.  GC* components give linear increases in effect, with no per-ship component limits.  Obviously, we all do this with weapons.  You can also do the same with engines (and speed-boosting starbase effects) to create slingshot zones in your backfield, where your rally-pointed doom stacks therein can get a (one-time) speed of 50+ ... which behaves as a stargate or Teleport spell in other games.  (Ergo, there is no separate "stargate" tech, even though a B5-like jump gate is shown in the pre-game cut scene.)

Some other games (e.g. SE*) add more tiers of sensor/anti-sensor duels, e.g. cloaking beats normal sensors, tachyon sensors (shorter range) reveal cloaking, ...

Extreme sensor capability is -- cute, but how do you actually use that to (help) win?  Does it mostly help you to not-lose, cf. Battle of Britain?  (That requires an enemy who's actively attacking you.)  Have you been building new sensor wagons throughout the game, e.g. whenever you get a larger hull or new sensor tech?  I assume you didn't just go from sensor range 6 to 77 in one jump.

This would be a hoot to do in a 100-AI game, just to watch them war upon each other while you stand on the sidelines and cheer both sides.  I wonder: would your game turns bog down in wall clock time, as the poor GC3 graphics engine is forced to render more stuff?

A good AI will, of course, do this to you.  Then your Eyes see each other at range 75 ... and you can read each others' Details

I just dredged up an exemplar where "sensor range" (ahem) did help me "win".  It was ... utterly vile in dastardly ways.  istillbragaboutit

• Unix Empire: multiplayer, brutally realtime (1 update every 6 hours x 2-4 months), no graphics, all alphanumeric.  Played on terminals.
• Map of squares.  You designate sector types (one per square).  Civ and mil are numeric attributes within a square (no units).  Sectors grow from 0% to 100% based on civ and wall clock time: roughly 2 real days to reach 100%.
• Your capital generates Bureaucratic Time Units (BTUs) in wall clock time.  Query commands are free, state-changing actions consume BTUs.  Ground combat losses cost BTUs proportional to your casualties: one nasty 4-on-1 fight vs. a 100% fortress (which gives +300% defender bonus) can drive you to negative BTUs, which wipes you out for 36 real hours.  (Better have your delivery routes humming on autopilot.)
• Guns, planes, and shells (bombs) are also numeric attributes.  During an interactive "fly" command, your planes are a quasi-unit (subject to database racing, ahem).  Landing on a 100% runway or highway is safe.  Landing anywhere else is highly likely to fail, causing any undropped bombs to blow up.  (Ahem!)
• Every nation has local coordinates, with (0, 0) being your own capital.  Every attack is implemented as a separate Unix process, which shows the attack parameters in the attacker's coordinates.  Unix is Unix, ps -al shows the process list.  (ahem!)

So ... in the first evening of reading the rules, I saw this in a flash.  It finally (clock)worked, like this ...

• A bigger nation attacks me.  He's a novice (several games), this is my 1st game ever.
• I know he's to my "north".  I have this peninsula disjoint from the border (roughly Maine, and he's Canada).  I surreptitiously build an airfield at my northernmost extreme, and move some planes and shells in.  (I am totally gambling that the default plane range will suffice.)
• I set a strong flank and weak center (cf. the Greeks at Marathon, although I didn't know that then).  I know he usually logs on in the afternoons.  I lurk online and wait for the telegram ...
• ... that says: You are being attacked at (your x, y).
• Ctrl-Z (suspend), at Unix prompt: type ps -al, command-line repeat it for 5 seconds ... until Unix reveals, in clear print, thatguy | empire att(ack) his-i, his-j
• Ergo, (x+i, y+j) is ... the location of his capital.  I have never seen that far (and never do, until I stroll adjacent to it later).
• I sacrifice some defenders, just to maximize his BTUs lost in combat.  He obliges, and whoops my buttocks in the north.  His final attack must have driven him to negative BTUs.  He's done for at least a few hours.
• fly, from my airfield, all of my planes, with 1 bomb (shell) each.  They do not have the range for a round-trip, so ... I guess they will be landing somewhere in between.  Ahem!
• At (x+i, y+j), observe.  The sector below my cockpit is ... capital.
• Land.  Two planes actually succeed (goshdurnit).  Nine planes fail, and blow up.  Nine bombs blow up with them.

Now my opponent (wiser, larger, stronger) ... is at negative BTUs from combat, and his capital is at 2%, with most of his civs dead.  With 2 planes and 2 shells (formerly mine) sitting intact amidst the rubble.  They belong to him now.  (Later I recapture them!)

At real-time rebuild and regeneration rate ... he will issue no commands for about three weeks.  Win.  (I told him, no it's in the man pages, here here and here ... he quit)

Man, that game was ba-roken in such fun ways.  I loved the emergent tactics that lurked like gems within the rules, requiring only some spelunking gnome to burrow that deep and construct the perfect cascade of harmless elements.

I never considered not using sensors on other ships. Late game I always do this but on large+ hull, survey ship would make more sense, especially since I buy other races' ships for 200 bc the instant I make contact ensuring I get all anomalies