Radar

Mechanics

The units are omitted here; use the values as you see them in-game, except divide the radar cross-section by [math]\displaystyle{ 10 }[/math]. All units listed in dB should be taken at face value as linear units, as the code makes the necessary conversions; e.g. a sensitivity of -40 dBm should be plugged into the equations as just -40.

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

- radiated power, [math]\displaystyle{ P_t }[/math]
- gain, [math]\displaystyle{ G_t }[/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 (RCS) 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{P_t\,G_t^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 must be sufficiently high for the target to be detected, with the threshold depending on radar type (search radar or fire control radar), radar sensitivity, and presence of jamming. Sensors will check every frame for new targets, but will only update and recalculate existing targets every 0.25s (round down to nearest frame)

Noise

Effective radar range is most often limited by the Signal to Noise Ratio (SNR) rather than the hard maximum range listed in the radar stats. Noise is modeled in-game as the sum of ambient noise and jamming noise.

Ambient noise is fixed at [math]\displaystyle{ N_a = 1 \times 10^{-7} }[/math] for all radars. If jamming is present, the jamming noise will add to the ambient noise. See the EWAR page for the calculation of jamming noise power [math]\displaystyle{ N_j }[/math]. The jamming noise power is the sum of the power from each individual jammer, weighted by diminishing returns. Then the total noise power is:

[math]\displaystyle{ N = (N_a + N_j)*10^{\nu / 10} = (10^{-7} + N_j)*10^{\nu / 10} }[/math]

Search Radars

Search radars have three checks:

First, return power [math]\displaystyle{ P_r }[/math] is compared against ambient background noise [math]\displaystyle{ N_a }[/math]. If the Return Power is less than the background noise [math]\displaystyle{ P_r < N_a }[/math], the target is not seen. Note that this check is unaffected by noise filtering, which means noise filtering cannot bring the overall noise below ambient background noise.

Second, return power is compared against the total noise power. If the SNR is below 1, that is, [math]\displaystyle{ P_r < N }[/math], the target is not seen. Note that, unlike the first check, this check is affected by noise filtering.

Third, the return power is used to compute the Signal Loss [math]\displaystyle{ S_L }[/math], then compared against the radar Sensitivity [math]\displaystyle{ S }[/math]:

[math]\displaystyle{ S_L = 10\log_{10}\left(\frac{P_r}{0.001}\right) = 10\log_{10}({P_r}) + 30 }[/math]

If [math]\displaystyle{ S_L > S }[/math], then the target is not seen. This check is not affected by noise filtering, but is affected by sensitivity buffs.

If any of the three checks fail, the target is not seen. If all three checks succeed, then the target is seen.

The first and third checks are nearly redundant. If the radar sensitivity is greater than -40 dBm, then the third check will be more restrictive than the first check. If the radar sensitivity is less than -40 dBm, then the first check will be more restrictive. This means that search radars have no benefit to sensitivity less than -40 dBm. In summary:

• When there is no jamming and radar sensitivity is greater than -40 dBm, the third check is the only one used: The target is spotted if [math]\displaystyle{ 10\log_{10}({P_r}) + 30 > S }[/math]

• When there is no jamming and radar sensitivity is less than -40 dBm, the first check is the only one used: The target is spotted if [math]\displaystyle{ P_r > 10^{-7} }[/math]

• When there is jamming, the second check is almost always used: The target is spotted if [math]\displaystyle{ P_r > N }[/math]. In the rare case that jamming power is very weak, this can theoretically fall back on the first or second check.

Fire Control Radars

Fire control radars have only one check. If the SNR is greater than the minimum SNR required to lock, the target can be locked:

[math]\displaystyle{ 10\log_{10}\left(\frac{P_r}{N}\right) > \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.

Detection Range

Search Radars

We can solve for [math]\displaystyle{ d }[/math] in the above equations to give a formula for detection range for search radars.

If there is no jamming and the radar sensitivity is greater than -40 dB, we have:

[math]\displaystyle{ d < \left(\frac{P_t \, G_t^2 \, \sigma A}{16 \pi^2 \cdot 10^{-3 + S/10} }\right)^{1/4} \approx 1.586 \cdot (P_t \,G_t^2 \,\sigma A \cdot 10^{S/10})^{1/4} }[/math]

If there is no jamming and the radar sensitivity is less than -40 dB, we have:

[math]\displaystyle{ d < \left(\frac{P_t \, G_t^2 \, \sigma A}{16 \pi^2 \cdot 10^{-7} }\right)^{1/4} \approx 15.863 \cdot (P_t \,G_t^2 \,\sigma A)^{1/4} }[/math]

The formula for jamming is complicated and cannot be easily solved for detection range in every case. See the Electronic Warfare page for a more detailed breakdown. The most common scenario is for a set of jammers at the same range as the target that are significantly stronger than the ambient noise, which can be solved for range as follows:

Assume that we have [math]\displaystyle{ N }[/math] identical jammers all at range [math]\displaystyle{ d }[/math] each with radiated power [math]\displaystyle{ P_j }[/math] and gain [math]\displaystyle{ G_j }[/math]. The diminishing returns of multiple jammers give an effective multiplier of [math]\displaystyle{ M = \sum_{n=1}^{N} e^{-((n-1)/2.75)^2} }[/math]. The detection range is then:

[math]\displaystyle{ d < \left(\frac{P_t\,G_t \,\sigma A}{4\pi \,P_j \, G_j \,M} \right)^{1/2} \cdot 10^{-\nu/20} }[/math]

If desired, we can make a catch-all equation by computing all 3 detection ranges and taking the minimum. This exercise is left to the reader.

Fire Control Radars

For fire control radars with weak or no jamming, lock range is given by:

[math]\displaystyle{ d < \left(\frac{P_t \, G_t^2 \, \sigma A}{16 \pi^2 \cdot 10^{\textrm{SNR}_\textrm{min}/10} } \cdot 10^{\nu/10}\right)^{1/4} \approx 0.282 \cdot (P_t \,G_t^2 \,\sigma A)^{1/4} \cdot 10^{(- \textrm{SNR}_\textrm{min} -\nu )/40} }[/math]

Except for the Parallax, unjammed fire control radars have this distance above the hard maximum range of the radar, so they are generally not limited by this calculation. For a fire control radar being jammed by it's target (with the same setup as the search radar case above), we get the lock range:

[math]\displaystyle{ d < \left(\frac{P_t\,G_t \,\sigma A}{4\pi \,P_j \, G_j \,M} \right)^{1/2} \cdot 10^{(- \textrm{SNR}_\textrm{min} -\nu )/20} }[/math]

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 radiated power (the normal radiated power multiplied by the Burn-Through Power Mult.), 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. These burn tracks are similar to regular radar tracks, and carry both position and velocity data (velocity data is not displayed in game but attacks fired on the track will account for it). 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.

These tracks serve to update the range memory of jamming LOBs.

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. Both search radars and fire control radars can take advantage of this (but radar guided missiles will not)

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 potentially detect it ~2km farther than their max range.

Components that modify the ship's signature will also 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 reductions (eg, prowler, radars off), which can be used to counteract sig bloom from other sources.

Note that sig radius only increases maximum range; radars still have to pass the noise and signal loss checks against the target's return power to detect a target, so radars may not always be able to make full use of the signature bloom if it can't detect the signature at max range.

Radar Illumination

See EWAR page

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.

Velocity inaccuracy is not a constant value despite what the game uses for the unit. The true error in velocity is [math]\displaystyle{ \frac{\text{v}\delta_v}{2} }[/math], where [math]\displaystyle{ \text{v} }[/math] is the target's true velocity, and [math]\displaystyle{ \delta_v }[/math] is 1/10th of the listed value. This error is then pointed in a random direction and the full value is added to the actual velocity. For example, velocity error listed as 5m/s can be translated to 0.5x or 50%, so a track moving at 15m/s will have 7.5m/s of velocity inaccuracy.

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 the natural logarithm of the SNR; 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 to 30.0 dB, where error hits a floor at various amounts between roughly [math]\displaystyle{ 0.1\delta_r }[/math] and [math]\displaystyle{ 0.3\delta_r }[/math] depending on the exact radar. 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 4.0 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 30.0 dB (not practically achievable except for situations such as a battleship within 3km and no jamming).

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 on the same ship will only use one radar to pass 'guesses' to the network (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.

The most common counter to radar jamming is illuminators. See the EWAR page for details on how return power is calculated. We use the same jamming setup as seen above in this page with [math]\displaystyle{ N }[/math] jammers all at the same range as the target. We then also assume that there are [math]\displaystyle{ N' }[/math] illuminators near the ship trying to get a track, with stats as follows:

• Illuminator radiated power [math]\displaystyle{ P_{i,n} }[/math]
• Illuminator gain [math]\displaystyle{ G_{i,n} }[/math]

We also assume that there is no edge falloff (which is automatically the case if you're track firing the illuminators). Recall that illuminators simply add return power without any diminishing returns. So the maximum detection range for a jamming target being illuminated paired with a search radar is:

[math]\displaystyle{ d < \left(\frac{\left(P_t\,G_t + \sum_{n=1}^{N'} P_{i,n}\,G_{i,n}\right)\sigma A}{4\pi\, P_j \,G_j \,M}\right)^{1/2}\cdot 10^{-\nu/20} }[/math]

And with a fire control radar:

[math]\displaystyle{ d < \left(\frac{\left(P_t\,G_t + \sum_{n=1}^{N'} P_{i,n}\,G_{i,n}\right)\sigma A}{4\pi\, P_j \,G_j \,M}\right)^{1/2}\cdot 10^{(-\textrm{SNR}_\textrm{max}-\nu)/20} }[/math]

The most common use-case is attempting to illuminate into jamming to maintain a lock with a fire control radar. We can simplify this by comparing [math]\displaystyle{ P_t\,G_t }[/math] to [math]\displaystyle{ P_i\,G_i }[/math]. Let's look at the relationships for the 3 common pairings:

• The Floodlight and Bullseye are have approximately similar stats, so [math]\displaystyle{ N' }[/math] Floodlights improves lock range by a factor of [math]\displaystyle{ \sqrt{N'+1} }[/math]
• The Spotlight has roughly half the stats of the Bullseye, so they improve lock range by a factor of [math]\displaystyle{ \sqrt{N'/2 + 1} }[/math]
• The Lighthouse has exactly half the stats of the Pinpoint, so they improve lock range by a factor of [math]\displaystyle{ \sqrt{N'/2 + 1} }[/math].

ELINT

ELINT detectors (such as the Pinard) allows a ship to passively detect enemy radar emissions, such as those from search radars or fire control radars, at up to 1.25x of that radar's max range. One ELINT module will show a rough line of bearing toward the emitter, while two will produce a crossfix. ELINT will also be able to identify what type of radar it is (or more specifically, it can reveal the ELINT category of the radar) and will display it on the ELINT LOB or crossfix. If the ship is equipped with multiple types of radars, the track will display all detected types.

The categories are generally self explanatory, most internal search radars (spyglass, huntress, etc) are Search/Track. All turreted fire control radars (Bullseye, Pinpoint) are Fire Control. The Early Warning Radar is the only radar that will be specified as Early Warning. Parallax using the locking function will still classify as Search/Track. Bloodhound is classified as Search/Track

Most directional radars like FCRs also have sidelobe patterns, allowing ELINT to detect these radars at reduced range even if they're not pointed at the ELINT set. These sidelobe patterns can be viewed on their component page here: http://nebfltcom.wikidot.com/component:list.

ELINT is not able to detect integrated FCRs on PD turrets

ELINT is not able to detect illuminators.

ELINT is not masked by hull, and a ship with two ELINT detectors will not have a blindspot between the ELINT sets (as ELINT is measured from the center of the ship rather than from the set itself).

External Links

• NotSoLoneWolf's Radar Calculator V8.3 - can simulate radar and comms jamming across a wide variety of parameters
• Marion's Illuminator vs Jammer Calculator - Shows maximum lock range for varying numbers of illuminators and jammers compared against ship RCS