Ships Detection Mechanics

I recently replied to a thread regarding sensor mechanics over on the main forum with some of my own research. So I thought I would re-post here where its more appropriate and where it won't get bumped off by all the fleet carrier/vr/Odyssey threads.

Here you go:

So what I've come up with is that every ship has an intrinsic property related to how "stealthy" it is. This is the "Average Emissions" referred to in the Sensor module's description blurb. As far as I can tell this value cannot be changed in any way; I've tried with different ratings and sizes of power plants, different bulkheads, different power distributors, different thrusters, etc and nothing appears to modify this value.

The range at which another ship will detect you (as a resolved contact) is

Code:
 (Heat Dissipation/Average Emissions)^2 * Typical Emissions Range

That's all there is to it.

Some of the Average Emissions that I know of are:

ShipAverage Emissions
Federal Corvette9.1
Imperial Cutter8.1
Krait Mk28
Krait Phantom8.3
Alliance Crusader7.5
Type 97.8
Keelback6.3
Any Human SLF3.4
Vulture6.7
Eagle Mk. 25.3
Sidewinder4.5
Mamba6
Viper Mk. 36.1
Federal Assault Ship7.9
Keep in mind that these are approximations, due to there being a kind of fuzzy zone at the very edge of your detection range where ships slip in and out of contact.



In order to use that formula you also need to know a ship's heat capacity, which you can find in this post by Frenotx:
[Research] Detailed Heat Mechanics


You can also obtain these values on your own by doing the following:

1.) Calculate the Thermal Load of the ship you are in by adding up its power usage and multiplying by the powerplant efficiency
2.) Go into silent running and pop a heat sink.
3.) Once the thermal drain from the heat sink expires, start a stopwatch and stay in silent running
4.) Time how long it takes it get various temperatures.
5.) Calculate the ship's thermal content based on the Thermal Load and the elapsed time
6.) Calculate the ship's heat capacity based on the thermal content from Step 5 and the corresponding Thermal Gauge.

Since silent running traps all heat inside the ship, and you know how much heat the ship is generating, you know how much heat is in the ship at any given time.

For example, let's say I'm in a Keelback and its Thermal Load is 5.67. After doing the heat sink test I get the following results (this is just a sample of the results):

Elapsed Time (seconds)Thermal Content (elapsed time x thermal load)Thermal Gauge (%)
6.637.42212%
12.470.30822%
17.9101.49332%
From this I concluded that 37.422 is 12% of the ship's heat capacity, 70.308 is 22% of the ship's heat capacity, and 101.493 is 32% of the ship's heat capacity. That corresponds to Heat Capacities of 311.85, 319.582, and 317.17; taking the average of those to smooth out rounding and UI errors, and I get a value of 316.2.







You also need to know the cooling rate formula for the ship you are interested in. The cooling rate is something that Frenotx clued us all in to a few years ago in this thread. As noted in the first post, the cooling rate is proportional to the heat content of your ships, which you can estimate by looking at the heat gauge in your cockpit. Frenotx's post says the constant of proportionality is 0.2; however, during testing, I've found that this constant is an intrinsic property that varies from ship to ship. So far I've found that this value is 0.2, 0.25 or 0.3, and nothing seems to modify it in any way

As for what this coefficient refers to, its the "A" in the following formula:

Code:
A * (Thermal Gauge)^2 * Heat Capacity

This formula refers to the rate at which your ship dissipates heat, and is how you figure out what to put in for the "Heat Dissipation" term in the ship detection formula from above. As an aside, you can use this formula to figure out what your resting thermal gauge would be; your resting thermal gauge is where the thermal load from your ship balances out against the cooling rate of your ship

Code:
PWR * Eff - A * (Thermal Gauge)^2 * Heat Capacity = 0

Where:
PWR = Ship Power Consumption
Eff = Power Plant Efficiency

Solving for the above, you get:
Code:
Thermal Gauge = Sqrt(PWR * Eff/Heat Capacity/A)

So let's look at a few examples to see how all of this fits together. First we need some information:

ShipHeat CapacityCooling CoefficientAverage Emissions
Federal Corvette4980.39.1
Krait Phantom4500.258
Keelback3160.26.3
Let's say that all 3 ships are sitting at 20% thermal gauge, and a ship with a (unengineered) 4C Sensor with a TER of 5,600 m is trying to target them. Each ship's heat dissipation would be:







Code:
Cooling Coefficient * 20%^2 * Heat Capacity

and the sensor lock range would be:

ShipHeat DissipationSensor Lock Range (TER of 5600 m)
Federal Corvette5.9762415.05
Krait Phantom4.51771.875
Keelback2.528901.70
So those are the major points for how I think it all works. Other things I think you should be aware of are the different sources of heat in the game (beyond just powering modules). These include:





1.) Recharging/Regenerating shields through SYS capacitor. Thermal Load for that is simply the rate at which you recharge your shield

2.) Thruster thermal load, which depends on Acceleration, NOT Speed. If your speed is constant, or more accurately your velocity vector is not changing in any way, thermal load from thrusters is zero. Thermal Load for when you are accelerating is the ship's thrust percentage (which you can control in FA Off) multiplied by the listed thermal load on your ship's thruster module information page. If you are changing speed with FA On, your thrust percent is 100%. If you are using more than one directional thruster (forward and lateral, for example) Thermal Load is proportional to whichever thrust percent is greatest.

There is also some evidence to suggest that angular acceleration generates thruster thermal load. But this is hard to test, so I just assume it works the same way as the thermal load from linear acceleration.

Boosting generates heat, as everyone knows. The amount of heat generated is 3x PD Draw. This is in addition to the Thruster thermal load due to acceleration noted above. As an example, the Krait Phantom uses 13.33 MJ of ENG Capacitor for its boost; so it generates 40 units of heat every time you boost.

3.) Being near hot objects, like stars, increases thermal load. I worked out a pair of formulas to describe this thermal load but I don't have it handy at the moment. (see below for formulas). One thing to note about them, is that the thermal load from star heat doesn't actually depend on the temperature of the star; only its radius and your distance from it. The formulas are also only valid for main sequence stars and only when you are in supercruise; you get much lower values once you drop down into normal space, I've noticed.

Code:
Star Heat = M x D + 100

Where:
D= Distance (ls)

M=18.7/(R^0.9)

R=Star Radius

For the data I used to generate this equation, see below:
For this test I used a Krait Phantom with a Thermal Load (due to power consumption) of 6.108. I was using an unengineered A-rated power plant at the time

StarRadiusGauge PeakDistance (ls)Heat Added
Ninsun
0.828​
0.52​
3.34​
24.312​
Ninsun
0.828​
0.59​
3​
33.05325​
Ninsun
0.828​
0.64​
2.76​
39.972​
LP 448-41 A
0.5263​
0.5​
2.3​
22.017​
LP 448-41 A
0.5263​
0.33​
2.75​
6.14325​
LP 448-41 A
0.5263​
0.57​
2.03​
30.44325​
LP 448-41 A
0.5263​
0.62​
1.78​
37.137​
Alrai Sector GR-V b2-3 A
Alrai Sector GR-V b2-3 A
0.3562​
0.54​
1.5​
26.697​
Alrai Sector GR-V b2-3 A
0.3562​
0.57​
1.4​
30.44325​
Alrai Sector GR-V b2-3 A
0.3562​
0.61​
1.3​
35.75325​
LTT 14478
0.4282​
0.57​
1.69​
30.44325​
LTT 14478
0.4282​
0.6​
1.59​
34.392​
LTT 14478
0.4282​
0.62​
1.45​
37.137​
LHS 3602
0.555​
0.51​
2.37​
23.15325​
LHS 3602
0.555​
0.56​
2.15​
29.172​
LHS 3602
0.555​
0.58​
2​
31.737​
LHS 3602
0.555​
0.63​
1.87​
38.54325​
Gyvatiges
0.7289​
0.48​
3.24​
19.812​
Gyvatiges
0.7289​
0.53​
2.93​
25.49325​
Gyvatiges
0.7289​
0.57​
2.75​
30.44325​
Gyvatiges
0.7289​
0.64​
2.36​
39.972​





Note, thermal gauge and heat has no effect on your detectability in supercruise. While in supercruise you can see and target any ship that is 40x your speed (in c) away from you, and vice versa. So if you are traveling at 10c, for example, you can see any ship that is 40 x 10 c= 400 ls away from you. They, in turn, can see you even if they are traveling at minimum speed.

4.) Firing weapons generates heat as well. I'm not sure where I first read the information for this, but I saw a post that said the thermal load from weapons is: Found the source, it is from baqar79 in this post.

Code:
Heat Added = Thermal Load (1 * (4*(Wep Cap - Wep Current + PD Draw)/Wep Cap))

Where:
Thermal Load = Listed on the weapon's information page
Wep Cap = Power Distributor maximum WEP Capacitor
Wep Current = Power Distributor current WEP Capacitor
PD Draw = Power Distributor Draw of the weapon being fired

This heat is added on a per-shot basis. If you fire two (or more) weapons at the same time: the game will calculate the heat for one weapon with whatever state your WEP capacitor is in; then deduct the first weapon's PD draw before calculating the next weapon's heat addition; and so on.

As an example, let's look at a Medium Railgun (unengineered). This weapon has a Thermal Load of 20 and a PD Draw of 5.11 MJ. If your ship has a weapon capacitor of 100 MJ, and it is currently full, firing that railgun will add this much heat to your ship:

Code:
Heat Added = 20*(1+4*(100-100+5.11)/100)
Heat Added = 24.088

If your WEP capacitor were only half full, heat added would be:

Code:
Heat Added = 20*(1+4*(100-50+5.11)/100)
Heat Added = 64.088

Or 2.66 times as much in this example.

For the Thermal Vent experimental effect, cooling is 3x the listed value in the weapon's information page. Note that this effect is combined with the heat addition as calculated from the formula above. So if the heat added is greater than the heat removed by the cooling effect, you will end up gaining heat instead of losing it.


That's all I've got for now...

Maybe to-do in the future:

1.) Gimbal weapons tracking angle: I know the maximum possible angle is 15 degrees, and that the actual angle your ship achieves depends on your target's thermal signature and your distance from them. But what is the exact relationship? [Started some testing, and posted results here]

2.) Related to the above, several years ago Frontier tried to push through changes that would affect gimbal weapon's relationship to ship sensors. The changes never made it to live, for the reasons stated by Mark Allen in this post. But the post also says dropping the proposed changes would " mean that sensors once again aren't linked to much, but there are other options to address that."

So what are those "other options"?

3.) Also related to the above, turret tracking as described by Mark Allen in this post. More specifically I'm interested in this statement:

"It's all based on the acceleration of the target in the plane perpendicular to the vector from the weapon to that target - each weapon has thresholds that it can cope with (smaller weapons work better against faster targets where large weapons have problems), above one threshold confusion increases, below a different one confusion decreases"

The explanation of how it all works sounds like it would be hard to reverse-engineer, involving a bit of randomness. The post is also from 2015, and clearly states they were still figuring out how to alter things.

So what is a reasonable approximation of how it works now?

4.) The game manual states, on page 151:
"During planetary flight your sensors work as normal, though their ability to detect signatures is greatly reduced as they are designed for space flight."

Is this fluff made of 100% hand-wavium, to justify why ships can't pinpoint Points of Interest on the ground? Or are there actual in-game mechanics behind that statement?
 
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Thanks for the work, and the reply in the old thread.

Was thinking if having better grade or longer range sensors might be better for bounty hunting... but since the BIG ships are the better ones, maybe the usual D grade is ok.
 
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No problem!

It would be better in the sense that you’d be able to pick out potential targets farther away.

Btw, very few combat-oriented ships have sensors larger than Size 4. In fact, only 10 ships total have sensor sizes 5 and up.

Like most modules, sensor performance/cost revolved around the C-rated version. In that, a C-rated sensor of any size has just 200 m more range than the size below it; and the B- and A-rated version have 10% and 20% more range than the C-rated version, while consuming 20% and 40% more power. And it’s the opposite on the other side, for D- and E-rated sensors: 10% and 20% less range, in exchange for 20% and 40% less power. This implies that E-rated sensors are the most efficient, but least powerful, while A-rated sensors are the most powerful but least efficient. This is usually the case with all modules in game; the main exception being power plants.

All that to say that your choice of Engineering will probably have a bigger impact on your bounty hunting experience than the size/rating of your sensor. Unless you’re going for a very specific, finely-tuned build.
 
No problem!

It would be better in the sense that you’d be able to pick out potential targets farther away.

Btw, very few combat-oriented ships have sensors larger than Size 4. In fact, only 10 ships total have sensor sizes 5 and up.

Like most modules, sensor performance/cost revolved around the C-rated version. In that, a C-rated sensor of any size has just 200 m more range than the size below it; and the B- and A-rated version have 10% and 20% more range than the C-rated version, while consuming 20% and 40% more power. And it’s the opposite on the other side, for D- and E-rated sensors: 10% and 20% less range, in exchange for 20% and 40% less power. This implies that E-rated sensors are the most efficient, but least powerful, while A-rated sensors are the most powerful but least efficient. This is usually the case with all modules in game; the main exception being power plants.

All that to say that your choice of Engineering will probably have a bigger impact on your bounty hunting experience than the size/rating of your sensor. Unless you’re going for a very specific, finely-tuned build.
I'm sorry to interrupt, but it's not from consumption, it's from weight, which essentially affects the ship's maneuverability.
 
I'm sorry to interrupt, but it's not from consumption, it's from weight, which essentially affects the ship's maneuverability.
You mean sensor weight? I suppose you could see it that way. But how big of a difference does it actually make? I’m assuming you have in mind the Corvette and Anaconda, which carry around those size 8, 160 ton, sensors; so let’s have a look at one of those.

Let’s say you go for Dirty Drive 5 + Drag Drives on some 7A thrusters, and that your ship’s total mass is 1900 tons. This configuration would give you a thruster performance multiplier of roughly 145.5%. For a Corvette that translates to a speed of 291, boost speed of 378, and pitch speed of 40.7.

If your sensors weighed 120 tons less (same as size 6 sensors), your performance multiplier would rise to 147.3%, meaning a speed of 294.6, boost of 383, and pitch speed of 41.2.

So a roughly 4 m/s increase in speed for shedding 3/4 of your sensor’s mass. Not much of a performance increase, at least in my eyes.

Of course other ships and configurations may be more sensitive to mass changes; especially those that use enhanced performance thrusters. But in most cases I would argue that a sensor’s base mass doesn’t really have that big of an impact on the ship’s performance

Now, on the stealth/power consumption side, still looking at the Corvette
Let’s say you’re using a Low Emissions A-Rated power plant, and that you max it out at 27.93 MW, before accounting for the sensor’s power consumption. An 8A sensor’s 2.07 MW consumption accounts for 6.9% of your power plant’s 30 MW output (and heat) while an 8C sensor’s 0.69 MW accounts for just 2.4% of your power plant’s 28.62 MW.

With the 8A sensor, your resting thermal gauge would be 15.9%, and at that heat level you would be detectable out to 17.22% of your opponent’s sensor range.

With the 8C sensor, your resting thermal gauge would be 15.5%, and you’d be detectable out to 15.67% of your opponent’s sensor range.

Not a huge difference either. But, due to the way detection and heat dissipation works in game, with the 8C sensor it would take about 11.8 seconds to go from 17% heat (detectable at 22.4% of range) to 16% heat; whereas with the 8A sensor it would take about 25.3 seconds..

But, you know, different strokes for different folks. So you should prioritize whatever is important to you 😊
 
Sorry my engl.
8A sensors - 160t - range 7.68 km
...
8E sensors - 160t - range 5.12 km
Laser Long Range - range 6 km
 
I'm sorry I didn't write that clearly.
But there are still boundaries. What do I do with Sensor E if the target is at a distance of 5.5 and can be hit by laser turrets.
It depends on your target. Just because your sensor range is only 5.5 km doesn’t mean you can only see out to 5.5 km; my initial post was about exactly that, in a sense.

The short version is that as a ship heats up, it can be seen/targeted from farther and farther away. As a general rule of thumb, a ship that is emitting twice as much heat as it’s average emissions rating can be targeted out to 4 times whatever your sensor range happens to be; a ship that is emitting half of its average emissions can be targeted out to just 25% of your sensor range.

Average emissions is a property of a ship that isn’t listed anywhere, as far as I know; and has to be determined empirically.

In your case, if you’re trying to hit a, let’s say Krait Mk2, that is 6 km away but your sensor range is only 5.5 km; you’d still be able to target them if they were emitting 8.36 thermal units (or more) per second. This corresponds to a thermal gauge of 27.25%. Note: you wouldn’t be able to see in game what your target’s thermal emissions are; just whether or not you can target them or not.

If you can’t target them because they are too cold, or you’re too far away.. move closer 😜
 
that is 6 km away but your sensor range is only 5.5 km; you’d still be able to target them if they were emitting 8.36 thermal units (or more) per second.
I'm sorry, but I guess I don't understand you.
What is the wrong sensor distance limit number in the game ?
 
As a (hopefully) helpful tool, I also made this spreadsheet to calculate how your "detectability" changes as your ship heats up and cools down. It also includes a sheet to add in thermal loads from firing weapons.

Heat Curve

It's not the most user-friendly thing; but it should hopefully give you an idea of what the benefits and trade-offs are for different outfitting options.
 
It depends on your target. Just because your sensor range is only 5.5 km doesn’t mean you can only see out to 5.5 km; my initial post was about exactly that, in a sense.

The short version is that as a ship heats up, it can be seen/targeted from farther and farther away. As a general rule of thumb, a ship that is emitting twice as much heat as it’s average emissions rating can be targeted out to 4 times whatever your sensor range happens to be; a ship that is emitting half of its average emissions can be targeted out to just 25% of your sensor range.

This is the thing that confuses players. When they say "Sensor Range", why does that not mean "the range at which the sensor stops working"? <- Rhetorical.

Eg Enemy Sensor Range = 5k, is what it sounds like, but we get Oh, it will detect between 3.4 to 6.3 depending on your vessel size and heat, and you DON'T know what grade sensor your enemy even has anyway, or if it's modded for longer or shorter ranges. So maybe it's not 5 k to start with.

This is compounded by the differences between NPC behaviour and players. Things lack consistency.

What I'm trying to say is that they made it complex, but we get no usable gameplay from it, we get Physics Experiments instead.

In practice, once you shoot an NPC, it pretty much knows where you are. Persuing stealth mechanics in combat is pointless, since the DBS railgun meta, but it could be helpful in escaping maybe?

Does Silent Running/ ejection of Heatsinks matter to an enemy 's ability to target and hit your running ship? Maybe, depending on how you open the range?
So we need to be small, cold and fast?
 
This is the thing that confuses players. When they say "Sensor Range", why does that not mean "the range at which the sensor stops working"? <- Rhetorical.

Eg Enemy Sensor Range = 5k, is what it sounds like, but we get Oh, it will detect between 3.4 to 6.3 depending on your vessel size and heat, and you DON'T know what grade sensor your enemy even has anyway, or if it's modded for longer or shorter ranges. So maybe it's not 5 k to start with.

I don’t have an official response for you, but I’m guessing it’s to allow variation in stealth capabilities for different ship’s/outfitting. If it worked the way you proposed, with the sensor “not working” beyond a specified range no matter the circumstance, there would never be a reason to get Clean Drives over Dirty Drives for Thrusters; or Low Emissions over Armored/Overcharged for Power Plants; or Efficient over Overcharged/Short Range Blaster for Weapons.

This is compounded by the differences between NPC behaviour and players. Things lack consistency.

What I'm trying to say is that they made it complex, but we get no usable gameplay from it, we get Physics Experiments instead.

In practice, once you shoot an NPC, it pretty much knows where you are. Persuing stealth mechanics in combat is pointless, since the DBS railgun meta, but it could be helpful in escaping maybe?

Does Silent Running/ ejection of Heatsinks matter to an enemy 's ability to target and hit your running ship? Maybe, depending on how you open the range?
So we need to be small, cold and fast?

Hmm, the answer to this is vague; I believe intentionally so. There was a dev livestream about a year ago where they discussed stealth effects on NPCs. If I recall correctly, after an NPC loses lock on you they still retain knowledge of where you were for a short while. They can also see you, as long as you are within a set distance (I think 3 km?) and within a 70 degree cone that serves as their field of view.

Aside from that, NPCs that don’t have a sensor lock on you fire less accurately at you, and don’t use gimbals/turrets against you.

As for the “Physics Experiments”, I think that’s the general gist of how Frontier expects people to play the game. Enough of the game is kept vague and only briefly hinted at that it seems it’s a deliberate design decision to give players many things to figure out on their own.

The stuff I posted here is less a guide on how to outfit your ships, and more of a look at a collection of in-game mechanics that work together; so you’ll have an idea of the trade offs for designing your ships in different ways.
 
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I don’t have an official response for you, but I’m guessing it’s to allow variation in stealth capabilities for different ship’s/outfitting. If it worked the way you proposed, with the sensor “not working” beyond a specified range no matter the circumstance, there would never be a reason to get Clean Drives over Dirty Drives for Thrusters; or Low Emissions over Armored/Overcharged for Power Plants; or Efficient over Overcharged/Short Range Blaster for Weapons.



Hmm, the answer to this is vague; I believe intentionally so. There was a dev livestream about a year ago where they discussed stealth effects on NPCs. If I recall correctly, after an NPC loses lock on you they still retain knowledge of where you were for a short while. They can also see you, as long as you are within a set distance (I think 3 km?) and within a 70 degree cone that serves as their field of view.

Aside from that, NPCs that don’t have a sensor lock on you fire less accurately at you, and don’t use gimbals/turrets against you.

As for the “Physics Experiments”, I think that’s the general gist of how Frontier expects people to play the game. Enough of the game is kept vague and only briefly hinted at that it seems it’s a deliberate design decision to give players many things to figure out on their own. Like that spreadsheet I made. Or all of the accumulated knowledge that went into making EDSY. Or Ian Doncaster’s BGS research. Or Jane Turner’s.

Gamers are notorious for picking apart every last detail of the games they play, and Elite Dangerous is no different.

This idea extends to the moment-to-moment gameplay (at least in combat) where you are given SOME information, and the rest you have to infer based on observing what your opponent is doing. Best example of that is the little squiggly line over your fuel gauge that indicates your thermal emissions. It’s not a number, or a bar graph, or anything that could be quantified at a glance. It’s just a squiggly line...
And that’s the only concrete information you get to work with as a readout for how “stealthy” you are.

The stuff I posted here is less a guide on how to outfit your ships, and more of a look at a collection of in-game mechanics that work together; so you’ll have an idea of the trade offs for designing your ships in different ways.
I remember when I played Elite 1 and saw bouncing dots on the radar (the ship is near but not in the sensor area) I thought it was a bug in the program ;).
 
Since posting this I've done a bit more experimenting to figure out how sensors tie in to gimbal weapon tracking. I haven't done extensive testing, but enough to draw some conclusions. Here it is:

1.) Sensors do not affect gimbal tracking angle in any way whatsoever. Surprise!
2.) Maximum possible tracking angle is 15 degrees (as measured from the center of your screen)
3.) Actual tracking angle is dependent on the target's distance and thermal signature. Lower thermal signature/larger distance = lower tracking angle

The testing I did was on an Eagle using 2D sensor (Long Range 3), an Eagle using a 2A sensor (unengineered), and a Corvette using an 8D sensor (Long Range 3). All tests were targeting a stationary Sidewinder

For the Size 2 sensor tests, the Sidewinder had a thermal signature of 1.244. The test results were as follows:

Distance (m)2D LR3 Angle (deg)2A Angle (deg)
7506.636.48
10005.545.34
15003.853.88
21502.882.86

The 2D and 2A sensors had roughly the same Typical Emissions Range, of roughly 6300 m. The 2A sensor had a higher value for what I assume "sensor acuity" is (Typical Emissions Range/Maximum Range); 0.78 for the 2A and 0.585 for the 2D.

From these results I can conclude that neither sensor rating nor "sensor acuity" affect tracking angle.
-----------------------

For the 8D sensor on the Corvette, I varied both the thermal signature AND distance to target. The results were:

DistanceSignature = 0.504Signature = 1.335Signature = 8.632
5004.798.3215.0
10003.035.1314.95
15002.223.8111.07
20001.883.118.45
All angles are in degrees

The 8D sensor had a Typical Emissions Range of 8210 m, and a "sensor acuity" of 0.72
Looking at the middle column, the thermal signature is roughly the same as it was for the testing with Size 2 sensors...and the results are likewise pretty similar.

From this I can conclude that Typical Emissions Range doesn't affect gimbal tracking angle.

Looking at the last column, at a distance of 1000 m you get roughly the same angle as at 500m: 15 degrees. This result suggests the maximum tracking angle for gimbal weapons is 15 degrees.

I didn't notice any changes in tracking speed, or targeting "sway" during testing; but an old post I stumbled across from a Frontier Dev suggested this sway is tied to ship acceleration so it would not have shown up during the tests I did (all ships used were stationary)

---------------
I've been trying to come up with an equation that can model the relationship among thermal signature, distance and angle. But I think I need to do some more tests, and maybe on different ships.
 
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