Radar

Mechanics

The units are omitted here; use the values as you see them in-game, except divide the radar signature (cross-section) by [math]\displaystyle{ 10 }[/math].

Radars have a few stats that affect their ability to see objects:

- radiated power, [math]\displaystyle{ P_t }[/math],
- gain, [math]\displaystyle{ G }[/math],
- aperture size, [math]\displaystyle{ A }[/math],
- sensitivity, [math]\displaystyle{ S }[/math],
- noise filtering, [math]\displaystyle{ \nu }[/math],
- and for fire control radars, minimum signal-to-noise, [math]\displaystyle{ \text{SNR}_\text{min} }[/math].

Return Power Density

Given the radar cross section of an enemy ship [math]\displaystyle{ \sigma }[/math] at a distance [math]\displaystyle{ d }[/math], The returned power density, [math]\displaystyle{ P_r }[/math] is calculated by:

[math]\displaystyle{ 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} }[/math]

On a burn-through sweep, [math]\displaystyle{ P_t }[/math] 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 [math]\displaystyle{ P_r \lt 1\times 10^{-7} }[/math], 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 [[[mechanics:electronic-warfare|jamming power]]], [math]\displaystyle{ J = \sum_i j_i }[/math], noise felt by the radar is given by,

[math]\displaystyle{ N = (1\times 10^{-7} + JG)*10^{\nu / 10} }[/math]

Search radars require higher return power than the felt noise [math]\displaystyle{ P_r \gt N }[/math] 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:

[math]\displaystyle{ 10\log_{10}\left(\frac{P_r}{N}\right) \gt \text{SNR}_\text{min} }[/math]

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 ([math]\displaystyle{ S }[/math]) to distinguish targets and beat Signal Loss in order to see them.

Signal loss ([math]\displaystyle{ S_L }[/math]) is simply calculated from Return Power:

[math]\displaystyle{ S_L = 10\log_{10}\left(\frac{P_r}{0.001}\right) }[/math]

If sensitivity is less than signal loss [math]\displaystyle{ S \lt S_L }[/math] 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

Burn-through sweep

Some radars can perform a Burn-Through Sweep, or more simply "Burn sweep". A burn sweep releases a single pulse with greatly increased emitted power, capable of detecting stealthy targets or penetrating through jamming.

Anything the burn sweep detects will me marked as a purple circle, which will be called a burn track. Note that burn tracks are only a single snapshot, and do not update unless another burn sweep is performed. This means that burn tracks will become progressively inaccurate if the target moves away.

Burn tracks last for 30 seconds. They will replace ELINT tracks, but are in turn replaced by regular radar or vis tracks

Ships can detect when they are hit by a burn sweep, and will display an indicator when it happens.

Signature radius & bloom

[wip]

Some signatures (such as ships), have a "sig radius" (calculated from half the max component of the signature's boxcollider) that can allow radars to detect the signature beyond the radar's nominal max range. Under normal conditions, this sig radius is a small value, ranging from 39.5m (sprinter) to 138m (solomon). This means that by default, every radar actually has slightly more range than their listed max range. Note that every radar based sensor can take advantage of this, including the locking mode on multi mode radars (e.g. parallax) and radar seekers on missiles.

Any modifier that increases signature size will "bloom" radar sig, multiplying the sig radius by the same amount. For example, a +1500% sig increase (for a total of 1600% signature) will increase the sig radius from 135m to 2160m, so search radars can detect them ~2km farther than their max range.

Any component that applies a percentage modifier to the ship's signature will factor into this, such as masquerades, EWAR emitters, raider engines, etc, but the radius difference is usually too minor to notice except for very large sig increases from components like railguns or mass drivers.

Sig Radius is also affected by signature decreases (eg, prowler, radars off), but this cannot reduce the sig radius below the default.

Note that this only increases maximum range; radars will still have to pass the noise and signal loss checks to detect a target even with signature bloom.

Track Quality

Track Quality	Inaccuracy (m)
TQ15	0.0 - 4.0
TQ14	4.0 - 9.1
TQ13	9.1 - 14.6
TQ12	14.6 - 20.5
TQ11	20.5 - 26.9
TQ10	26.9 - 34.0
TQ9	34.0 - 41.8
TQ8	41.8 - 50.5
TQ7	50.5 - 60.3
TQ6	60.3 - 71.7
TQ5	71.7 - 85.2
TQ4	85.2 - 101.6
TQ3	101.6 - 122.9
TQ2	122.9 - 152.8
TQ1	152.8+

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:

[math]\displaystyle{ \text{TQ}=\lfloor 15^{1.02-0.005\delta_R}\rfloor }[/math], clamped between 1 and 15,

where [math]\displaystyle{ \delta_R }[/math] is the position error of the track in meters.

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

Radar Accuracy and Error

Each radar lists a position and velocity error stat, [math]\displaystyle{ 10\delta_r }[/math] and [math]\displaystyle{ 10\delta_v }[/math]. That is, divide the values you see in-game by 10 to use the formulas below, then take your final answer and multiply by 10 again to get back to meters.

The true error in velocity is simply [math]\displaystyle{ 2\text{v}\delta_v }[/math], where [math]\displaystyle{ \text{v} }[/math] is the target's true velocity, pointing in any random direction.

Position error is more complicated. First, each radar has its own deviation curve which gives a deviation [math]\displaystyle{ \delta_d }[/math]. For search radars, the deviation scales with received noise; at 0 dB SNR or below, [math]\displaystyle{ \delta_d }[/math] is 100% of the listed error in-game, [math]\displaystyle{ \delta_r }[/math]. The curves extend all the way to 300 dB, where error falls to various amounts between roughly [math]\displaystyle{ 0.1\delta_r }[/math] and [math]\displaystyle{ 0.3\delta_r }[/math]. See the component pages for each radar to see their curves (not implemented yet). For fire control radars, the deviation is based on the ratio of the target distance to the radar's max distance.

Then the true position error is a random point //inside// a sphere, whose radius is the product [math]\displaystyle{ \delta_d \delta_r }[/math]. (If the radar is locking, multiply also by the Lock Multiplier stat.) To consider how the position accuracy affects your shots, the average distance of this position error from the center of the track in the plane facing your guns is approximately [math]\displaystyle{ \frac{3\pi}{16}\approx0.59 }[/math] times that radius.

For example, the Frontline radar shows 30 m inaccuracy for the position error. The maximum true error at 0 dB SNR would be 10(3*3) = 90 m. Until roughly 40 dB SNR, inaccuracy rapidly drops down to 30%, where a Frontline would have 90*0.3 = 27 m max error. This then slowly approaches 10% inaccuracy at 300 dB (not practically achievable).

When multiple radars on the network see the same track, the game chooses the best (lowest) error for the track. This has the effect of improving your track quality, but note that multiple radars of the same type on the same ship do not stack (for balance reasons). For radars of the same type on multiple ships, the following table gives the combined average error in the plane facing your guns as a fraction of the maximum error [math]\displaystyle{ \delta_d\delta_r }[/math]:

# of Radars	Average Error
1	0.59
2	0.46
3	0.39
4	0.34
n	[math]\displaystyle{ \frac{\sqrt{\pi}\,\Gamma\left(\frac{3n+2}{2}\right)}{2\,\Gamma\left(\frac{3n+3}{2}\right)} }[/math]

Radar Panel status

The status of a ship's radar panels can be viewed at a glance by selecting a ship and looking at the dotted lines that point outward, representing the radar panels on the ship. Light blue means the panel is functioning, red means the panel is disabled or destroyed

Radar Jamming and Counter Jamming

For more information on this section, please refer to EWAR.

External Links

• NotSoLoneWolf's Radar Calculator V7 - A tool to simulate radar and comms jamming performance across a wide variety of parameters