Radar

Mechanics
The units are omitted here; use the values as you see them in-game, except divide the radar signature (cross-section) by $$10$$.

Radars have a few stats that affect their ability to see objects: - radiated power, $$P_t$$ - gain, $$G$$; - aperture size, $$A$$; - sensitivity, $$S$$; - noise filtering, $$\nu$$; - and for fire control radars, minimum signal-to-noise, $$\text{SNR}_\text{min}$$.

Return Power Density
Given the radar cross section] of an enemy ship $$\sigma$$ at a distance $$d$$, The returned power density, $$P_r$$ is calculated by:

$$P_r = \frac{\left(\frac{P_t G\sigma A}{4\pi d^2}\right)G}{4\pi d^2} = \frac{P_tG^2 \sigma A}{16\pi^2 d^4}$$

On a burn-through sweep, $$P_t$$ is multiplied by the Burn-Through Power Mult. stat.

Return Power is factored into both Noise and Signal Loss calculations to determine effective radar range

Noise
Effective radar range is most often limited by Noise

In normal conditions, return power is compared against ambient background noise. if the Return Power is less than the background noise $$P_r < 1\times 10^{-7}$$, the target is not seen. Note that this is unaffected by noise filtering, which means noise filtering cannot bring the overall noise below ambient background noise for search radars.

If jamming is present, a radar has to be able to distinguish a real signal from the jamming noise.

For total jamming power], $$J = \sum_i j_i$$, noise felt by the radar is given by,

$$N = (1\times 10^{-7} + JG)*10^{\nu / 10}$$

Search radars require higher return power than the felt noise $$P_r > N $$ to see targets. If the return signal from the target also beats signal loss (see below), the target //is// seen, and a track appears.

Fire control radars require a higher *return power to noise ratio* (SNR) than the minimum SNR required to lock:

$$10\log_{10}\left(\frac{P_r}{N}\right) > \text{SNR}_\text{min} $$

Fire control radars are not restricted by the background noise floor, so noise filtering will reduce background noise for locking and will increase their effective range.

Signal Loss
Signal Loss is another factor that limits effective radar range. Search radars will also need enough Sensitivity ($$S$$) to distinguish targets and beat Signal Loss in order to see them.

Signal loss ($$ S_L$$) is simply calculated from Return Power:

$$S_L = 10\log_{10}\left(\frac{P_r}{0.001}\right)$$

If sensitivity is less than signal loss $$S < S_L$$ then the target is seen.

This means that sensitivity reaches its maximum benefits at -40dB, as that point where search radars are limited by noise from ambient noise instead.

Fire control radars do not have a sensitivity stat, and therefore are not affected by signal loss.

Fire Control Radars/Radar Locking
Certain types of radars like Fire control radars and multifunction radars can lock targets. This usually gives a very precise track and changes the track to a special icon. Ships will also know when they have been successfully locked and will display it on their status panel.

Each ship can only lock one enemy ship at a time, even if equipped with multiple fire control radars. However, fire control radars can split their locks when automatically locking incoming missiles.

Locks otherwise function mostly like regular radar tracks, as listed above

Track Quality
In game, track quality is graded on a scale from TQ15 to TQ1, where TQ15 is a near perfect track, and TQ1 is nearly unusable. This is calculated by the formula:

$$\text{TQ}=\lfloor 15^{1.02-0.005\delta_R}\rfloor$$, clamped between 1 and 15,

where $$\delta_R$$ is the position error of the track in meters.

This can be used to convert TQ into an approximate meters of inaccuracy

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