Advanced Cannon

Advanced Cannons, or Advanced Projectile Systems (APS), are even more customizable than CRAM Cannons, at the cost of maximum shell size.

Currently being reorganised and expanded.

= Cannon components = An advanced cannon system consists of two main parts, the cannon itself, and ammunition production.

Firing Piece
The Adv. Firing Piece is the Core Block of the cannon itself. The number of barrels can be selected from one to six.


 * Overclocking: A cannon can "borrow" up four seconds of cooldown. Once this time is used up, the cannon returns to its normal sustained rate of fire. Recoil and inaccuracy are multiplied by a factor (1 + overlock seconds used), i.e. up to 5x.

Mantlet
A mantlet goes directly on the front of the Advanced Firing Piece. It determines the traverse range of the barrel. The first, lower number corresponds to what a 500mm gauge, while the second, higher number corresponds to a 50mm gauge.

Mantlets count as 1m in barrel-length – If you'd need a 5m barrel for propellant burn, it's sufficient to use a mantlet and a 4m barrel.

Multiple barrels results in an additional effective gauge for the purposes of traverse range:

Traverse range is always at least 5 degrees in each direction. Cannons can be built without a mantlet, in which case this is their traverse range.

Barrel
Barrels go on the front of the mantlet. More barrels increase accuracy, and may be required to achieve maximum muzzle velocity for a given amount of propellant.

The cannon's Q-menu allows to split these to allow for multi-barrel setups. This decreases the gauge. Each barrel cools down independently, allowing a higher maximum rate of fire.

For a barrel length $$\ell_b$$ and $$n_b$$ barrels the traverse per second is

$$\frac{1}{\left(0.1 + 0.25 \pi d^2 \ell_b n_b\right)^{0.7}} \approx \frac{287^\circ}{\left(1 + 2.5 \pi d^2 \ell_b n_b\right)^{0.7}}$$

Note that this does not apply to heavy barrels. These have lower traverse speed, but unknown how much lower exactly.


 * Barrel
 * Heavy Barrel
 * Bore Evacuator
 * Muzzle Brake

Gauge Snake

 * Gauge Increase (APS)
 * Gauge Increase Right Left Splitter: The forward end must go towards the Firing Piece.
 * Gauge Cooling Unit: Cooldown time is multiplied by 0.92 for each Cooling Unit.

Gauge Increases go behind the Advanced Firing Piece. Gauge refers to the diameter of shells that are fired from the cannon. For a single-barrelled cannon, the diameter starts at 60 mm. The first Gauge Increase adds another 60 mm; additional Gauge Increases are each 0.98 times as effective as the last. The cap is 500 mm at 8 Gauge Increases.

Having multiple barrels will divide the gauge by 20/10 for 2 barrels, 20/9 for 3, 20/8 for 4, and so on.

Ammo

 * Autoloader: These go on the sides of the Advanced Firing Piece or Gauge Increases or next to each other. Each Autoloader can hold one cartridge ready for firing.
 * Belt Feed Autoloader: Fires 5 times as fast as a conventional 1m autoloader, but cannot fire and reload at the same time, and cannot start firing until 6 seconds after its clip is full.
 * Ammo Clip: These go on the sides, top, or bottom of Autoloaders, or the top only of Belt-Fed Autoloaders. They hold cartridges ready for loading.
 * For cartridges of up to 250 mm gauge, one ammo clip holds $$\min \left( \left\lceil \frac{2}{d} \right\rceil, 64 \right)$$ cartridges in two stacks.
 * For cartridges of greater than 250 mm gauge, one ammo clip holds $$\left\lceil \frac{1}{d} \right\rceil$$ cartridges in a single stack.
 * Ammo Input Feeder: These go on the front or back of Autoloaders or Ammo Clips. These transfer cartridges from the supply to the clip.
 * Ammo Ejector: These go on Autoloaders. When an associated ejector, autoloader, or clip is destroyed, instead of detonating, all associated shells will be ejected at a speed of 50 m/s, plus a random value of up to 15 m/s along each axis. This prevents the propellant from detonating. An Emergency Ejection Fuse makes this completely safe, otherwise the shells can still trigger inside your craft.

Stored ammunition explodes when an autoloader or clip is destroyed. Powder modules do 20% as much damage as flak modules for this purpose, but are computed separately from true flak modules.

Railguns
Railguns use electricity to increase the velocity of the fired shells. The increased velocity also increases the kinetic damage and AP.


 * Railgun Magnet Attaching Feature: Attaches to the side of the Firing Piece.
 * Railgun Barrel Magnet: Attaches in a line to the Attaching Feature. Analogous to Laser Destabilizers. The first magnet discharges a base of 2% of stored energy per shot, with subsequent magnets discharging 0.9 times as much as the last. For $$n_m$$ magnets, the proportion discharged per shot is
 * $$20 \% \cdot \left(1 - 0.9^{n_m} \right)$$


 * Railgun Charger: Attaches to Gauge Increases, Gauge Coolers, or Connectors. Each charger provides 100 charge per second times the railgun overclock, and each unit of charge costs energy equal to the railgun overclock.

Ammo Controller
The Ammo Controller is the core component of ammunition production.

Ammo Customisers
Ammo Customisers go in a line in front of the ammo controller. Each customiser adds two shell-modules – A single module customiser allows to make shells with an uneven number of modules, often allowing for another module without exceeding the Autoloader's length. The maximum amount of shell modules you can have is 20, regardless of shell diameter.

= Strategy and Examples =

Choosing a Shell-Type
If you don't know what to pick: Fragmentation will work in almost any situation. HESH is another good choice – better vs thick armour, but unusable for airburst.

Other shell-types are more special-purpose.

= Maths =

Scary numbers to optimise shells and cannons further, or design things without opening the game. None of the following is necessary to design effective cannons.

Shell Design
To avoid confusion with the consumable resource "ammo parts", we will refer to the items in a cartridge as "modules".

We will refer to the entire collection of modules as the "cartridge" and the modules minus the casing as the "shell". Let $$n$$ be the number of modules in the cartridge, and $$n_s$$ be the number of modules in the shell.

Modules
Each module is a cylinder with diameter specified by the shell diameter $$d$$ in metres, and length equal to the diameter. The volume of a cartridge is then

$$V = \frac{1}{4} \pi n d^3$$

Likewise, let $$V_s$$ be the volume of the shell (projectile) only.

Muzzle Velocity
Let $$n_p$$ be the number of propellant modules.

Let $$l_p$$ be the length of the gunpowder casings, $$l_s$$ be the length of the shell without the casings and $$l$$ be the length of the whole shell (all in metres). The muzzle velocity from propellant is:

$$v = 700 \frac{l_p}{l} s V_s^{0.03} \approx 695 \frac{l_p}{l} s l_s^{0.03} d^{0.06}$$

$$s$$ is the speed coefficient, defined below.

Projectiles inherit the velocity of the cannon they are fired from, and this affects all velocity-dependent characteristics, namely AP and kinetic damage.

Once in flight, projectiles are affected by gravity and drag in water (but not air). However, this does not change AP or kinetic damage.

Railguns
For a charge expenditure of $$q$$ and $$n_r$$ railgun casings, the muzzle velocity is increased by

$$v_r = \frac{8^{0.5} q^{0.5}}{n_s^{0.25} \left(5d\right)^{0.75}} s \approx 0.8459 \frac{q^{0.5}}{n_s^{0.25} d^{0.75}} s $$

Railgun casings increase this by a factor

$$\left(1 + 5 \left(1 - 0.9^{n_r} \right)\right)$$

Speed Coefficient
A factor in muzzle velocity is the speed coefficient, which is a weighted average of the speed modifiers $$s_i$$ of the (non-casing) parts, where each component $$i$$ starting at the head has half the weight of the previous:

$$s = \frac{\sum 0.75^i s_i}{\sum 0.75^i}$$

The head will thus always determine at least 25% of the speed coefficient.

For example, suppose the shell has a Composite Head (speed modifier 1.6), a Solid Warhead Body (speed modifier 1.3), and a Supercavitation Base (speed modifier 0.9). Then we have

$$s_0 = 1.6$$

$$s_1 = 1.3$$

$$s_2 = 0.9$$

$$s = \frac{0.75^0 \cdot 1.6 + 0.75^1 \cdot 1.3 + 0.75^2 \cdot 0.9}{0.75^0 + 0.75^1 + 0.75^2} \approx 1.33$$

(Since 2.3.3.1 s=s1+(0.10248*(summ(s)-s1))/(ns-1)

Propellant Burn
The length of barrel needed for optimal propellant burn is

$$\ell_{bp} = 16 n_p d$$

If the barrel is too short, muzzle velocity will be reduced proportionally.

Effective Time
The time a shell will travel before suffering drag is

$$10 s n_s$$

Effective Number of Modules
Generally the effective number of modules is used rather than the actual number of modules in the maths since some modules count as less than one module. Casings only count as one quarter of a module and modules that have a maximum size (i.e. fuses) can count as less than one module.

If $$n_p$$ is the number of gunpowder casings, the effective number of modules is:

$$ n_e = \frac{n_p}{4} + \frac{l_s}{d}$$

Ammo Cost
$$c = 50 n_e d^{1.8}$$

Filling Ammo Clips
This is the reload time of a particular shell. Specifically, after this many seconds pass, each Input Feeder checks whether it can reload its associated autoloader. If there is space, the Input Feeder moves one cartridge from the supply to the autoloader's clips. Otherwise, it retries every second.

$$t = 17.5 \left( \frac{d}{0.5} \right)^{1.35} \left( 2 + n_e \right)$$


 * Input Feeders may be attached directly to the Advanced Firing Piece. Feeders attached like this will reload an available clip or autoloader but only if that autoloader is attached directly to the firing piece; it will otherwise act like a normal direct input feeder if this is not the case. If the Firing Piece has no autoloaders, it can hold one cartridge ready for firing.

Loading
This is the equation to find the RpM of an advanced cannon, this value should be set in the main firing piece to prevent the gun from burst firing. Let $$n_a$$ be the number of autoloaders attached to the firing piece and $$n_{cf}$$ be the number of faces of the autoloader with a clip attached.

$$RpM = \frac{60 n_a \left( n_{cf} + 1 \right)}{t}$$

This is the equation for the "seconds per shell" (the time that passes in between each shell being fired):

$$t_s = \frac{t}{n_a \left( n_{cf} + 1 \right)}$$


 * If beltfed autoloaders are used set the number of clips $$n_{cf}$$ in the RpM equation to $$\frac{10}{3}$$ as this will account for the $$30%$$ beltfed bonus; the RpM given will be for the "firing phase" of the autoloaders.


 * If an autoloader has no clips, $$n_{cf}$$ is 0

Barrel Cooldown
The base barrel cooldown of a particular shell is:

$$t_{bc} = 32.8125 \left( \frac{d}{0.5} \right)^{1.35} n_p^{0.35}$$

Let $$n_c$$ be the number of coolers. For a single barreled gun the overall cooldown time is roughly:

$$t_c \approx \frac{t_{bc} 2.549^{1.8} d^{0.5}}{n_c + 2.549^{1.8} d^{0.5}}$$

The exact equation for the above isn't yet known, nor is the equation for multiple barrels or bore evacuator.

Recoil
Let $$\ell_h$$ be the total length of Hydraulic Recoil Absorbers. The displayed recoil is

$$J_D = \left( \frac{2 \times 10^4}{0.2^{1.95}} \cdot n_p^{0.65} d^{1.95} + 10 q \right) 0.95^{\ell_h} \approx \left( 4.613 \times 10^5 \cdot n_p^{0.65} d^{1.95} + 10 q \right) 0.95^{\ell_h} $$

The units are kN frames, and currently depend on game speed.

Inaccuracy
Let $$l_b$$ be the length of the barrel, including all variants as well as the Mantlet. Let $$l_s$$ be the length of the shell (ignoring casings) and $$l_c$$ be the length of the casings (all in metres). Then inaccuracy for a single barrel is:

$$\theta = 0.3 \left( \frac{4 d^{0.75}}{l_b} \right)^{0.4}$$

Now let $$n_p$$ be the number of barrels on the gun. For more than one barrel the inaccuracy equation is:

$$\theta = 0.3 \left( \frac{4 d^{0.75}}{l_b} \right)^{0.4} \left( 1.2 + 0.05 \left( n_b - 1 \right) \right)$$

If a base bleeder is used then the final inaccuracy is multiplied by $$1.35$$

If railgun charge is used to boost accuracy, the accuracy is improved by a factor of

$$1 + \frac{0.001 q}{n_s d}$$

Health and Detection
Shells have a health of $$1000 V_s$$ times any modifiers from modules.

Detectable range is $$500 V_s^{2/3}$$ times any modifiers from modules, times a factor from firing altitude. This increases linearly from 1 at 10 m to 4 at 400 m.

AP
Let $$a$$ be the AP coefficient of the shell.

$$a = \frac{\sum 0.75^i a_i}{\sum 0.75^i}$$

If the shell has fewer than 3 modules, the missing modules are treated as having an AP modifier of 0.5.

$$\text{AP} = 0.01 a v$$

Kinetic Damage
Let $$k$$ be the kinetic damage coefficient. Unlike the speed and AP coefficients, this is an unweighted average.

$$k = \frac{\sum k_i}{n_s}$$

If the shell has fewer than 3 modules, the missing modules are treated as having a kinetic modifier of 0.5.

The kinetic damage is then

$$D = 1.25 k v \left( \frac{d^3 n_s}{0.2^3} \right)^{0.65} $$

HE Warheads
For $$n_w$$ HE modules (count Shaped Charge and Squash Heads without HE modules as half a HE module), the explosive damage is approximately

$$D = 500 \left( \frac{d}{0.2} \right)^{1.95} n_w^{0.8}$$

and the radius is

$$r = \left( \frac{D}{10} \right)^{0.5}$$

Note that all explosives have a hard cap on radius of 30m.

EMP Warheads
For $$n_w$$ EMP modules, the EMP damage is approximately

$$200 \left( \frac{d}{0.2} \right)^{1.95} n_w$$

Flak warheads
For $$n_w$$ flak modules, the explosive damage is approximately

$$D_f = 250 \left( \frac{d}{0.2} \right)^{1.95} n_w^{0.8}$$

and the radius is

$$r_f = D_f^{0.5}$$

The flak effect is completely separate from any HE effect. All explosives have a hard cap on radius of 30m. Note that flak can "snap" onto a target-vehicle that is within its radius, and will then deal damage within 30m from the closest point. Also, the cap only applies to blocks - missiles and the avatar can be damaged at any range.

Fragmentation warheads
The number of fragments is

$$\left(.015\left({d}\right)+7\right)\cdot\left({m}\right)^{.3}$$

and the total damage of all fragments is

$$.052\left({d}\right)^{1.8}\cdot\sqrt{\theta}+2.5\left(.052\left({d}\right)^{1.8}\right)$$

Where $${m}$$ is amount of modules, and $$\theta$$ is the frag cone angle in degrees. Fragments have AP 6.

Squash heads
Spalling metric is

$$15 \left( \frac{d}{0.2} \right)^{1.95} n_w^{0.65}$$

where $$n_w$$ is the total special factor of all HE warheads, counting the squash head itself as 0.5.

Upon hitting a surface the squash head ejects damaging particles on the opposite side. The number of particles is equal to the spalling metric divided by the number of AC-metres passed through.

Each particle does 200 damage and has AP equal to twice the armour of the last material passed through.

Thump damage is

$$400 \left( \frac{d}{0.2} \right)^{1.95} n_w^{0.65}$$

and is applied at AP 10.

Shaped charge head
For penetration factor $$\alpha$$, penetration metric is

$$30 \left( \frac{d}{0.2} \right)^{1.95} \left(\alpha n_w \right)^{0.65}$$

and particulate count is approximately

$$10 \left( \frac{d}{0.2} \right)^{1.95} \left(\left(1 - \alpha \right) n_w\right)^{0.65}$$

where $$n_w$$ is the total special factor of all HE warheads, counting the shaped charge head itself as 0.5.

Regardless of the values shown in the customizer, the actual penetration factor $$\alpha$$ is always between 0.05 and 0.95, and the actual special factor for HE warheads cannot be less than 0.01.

Each particulate deals 200 damage at AP 10.

Graviton ram base
Each point of kinetic damage converted produces 100 kN s of impulse. The translational component of the force may be converted to torque using the slider.

Skimming
On reaching within 0.25 m of the surface of water, a shell has a 50% chance to skim (reflect) off once provided the shell is travelling no more than $$\arcsin 0.15 \approx 8.63^\circ$$ from horizontal. This instantly reduces the velocity of the shell by 10%. Some shell modules induce different behaviour:


 * A shell with a Supercavitation Base will never skim unless it also has a Skimmer Tip.
 * A shell with a Skimmer Tip will skim up to 1000 times with 100% probability, and the maximum skim angle is increased to $$\arcsin 0.30 \approx 17.46^\circ$$.

Drag
Shells are unaffected by drag when in air, until reaching their effective time (as listed in the Ammo Customiser screen). In water, they slow down exponentially with an (instantaneous) deceleration rate of 70% of their velocity per second. Shells with a Supercavitation Base ignore underwater drag.