# CRAM Cannon

CRAM Cannons are customizable projectile weapons. The name apparently comes from "cramming" the different kinds of pellets into the shells.

## Internal volume

The diameter of the shell is increased by adding gauge increasers. For a gun with $g$ gauge increasers, the diameter is:

d = 200 + 2000(1 - 0.95^g)

For a diameter $d$ and $f$ fuses, the internal volume of a shell is: $V = \left( \frac{d}{400 \text{mm}} \right)^{1.8} - 0.25 f$

For a 2000 mm shell with no fuses, this is about 18.1.

## Muzzle velocity and base kinetic damage

Base muzzle velocity scales linearly from 60 m/s at 200 mm diameter to 100 m/s at 2000 mm diameter. This can be up to doubled by using a long barrel.

Base kinetic damage is $2Vv$ where $v$ is the muzzle velocity. The highest base kinetic damage possible is about 7247.8.

Base AP is 3, plus the muzzle velocity divided by 150 m/s.

Kinetic damage and AP can be increased using hardener pellets.

## Pellets

The power of a CRAM shell is largely determined by the pellets packed into them by material boxes. There are four types of material boxes:

• Hardener
• High explosive
• EMP
• Fragmentation

### Packing rate

Packing rate is equal to 0.1 per second per effective material box. Each box counts as 0.5, plus 1 for every autoloader it is attached to.

### Packing density

The density is $\rho = \frac{p_\text{total}}{V}$

In other words, one density unit holds $V$ pellets depending on gauge. While it is possible to pack up to 100 density, each density is only 90% as effective as the last. The effective number of pellets is approximately (the real implementation is piecewise linear rather than smooth): $p_\text{eff} = 10 \frac{p_\text{raw}}{\rho} \left(1 - 0.9^{\rho} \right) = 10 V \frac{p_\text{raw}}{p_\text{total}} \left(1 - 0.9^{\rho} \right)$

For shells with multiple pellet types, the density is computed from the total number of pellets, then the effective number of pellets of each type using the number of pellets of that type. Another way of saying it is that the effective pellets are proportioned the same as the raw pellets.

### Effects

Each (effective) pellet has the following effects:

• Hardener: +100 kinetic damage per pellet, +1.5 AP per pellet.
• High explosive: +200 explosive damage per pellet.
• EMP: $+10V$ EMP damage per pellet.
• Fragmentation: $V$ fragments per pellet. Each fragment deals 100 kinetic damage at AP 6 regardless of the main shell's stats. If more than 60 fragments would be created, the same total damage is instead distributed among 60 fragments.

### Example

Suppose we have:

• 5 volume
• 75 high explosive pellets
• 25 hardener pellets
• 10 second pack time

After 10 seconds, the total number of (raw) pellets is 100, for a density of $\rho = \frac{p_\text{total}}{V} = \frac{100}{5} = 20$

The total number of effective pellets is $p_\text{eff} = 10 V \left(1 - 0.9^{\rho}\right) = 10 \cdot 5 \left(1 - 0.9^{20} \right) \approx 43.9$

Since three-quarters of the raw pellets are explosive, three-quarters (32.9) of the effective pellets are explosive; at 200 explosive damage each this is 6588 explosive damage. The rest (11.0) are hardener; at 100 kinetic and 1.5 AP each, this is a bonus of 1098 kinetic damage and 16.5 AP.

## Health

A CRAM shell has a health of $2,000 d^2$

or a maximum of 8,000, reached at 2m calibre.

Minimum reload time is $T_\min = \left( \frac{d}{400 \text{mm}} \right)^{1.5}$

Net reload time is: $T_\text{net} = T_\min \left(1 + \sqrt{\frac{10}{1 + n}} \right)$

where $n$ is the number of connections between autoloaders and ammo boxes.

## Barrels

### Traverse

Traverse speed is proportional to the number of Motor Driven Barrels plus one and inversely proportional to the total barrel volume + 0.1. For a 2000 mm cannon, ignoring non-proportional factors, the traverse speed is about 8 degrees per second.

## Fusing

Main article: Fusing