Formulae

This is an explanation page for the various formulae involved in calculating stats in game.

Augmenter Addition

Augmenter addition is a multi-step process. First all augmenters are tweaked using the augmenter tweaking formula below.

Then the tweaked bonus is converted to a factor (F) using one of two formula, depending on if it is a positive augmenter or a negative augmenter. If the tweaked augmenter gives +83% then by adding 1 the tweaked bonus (B) is 1.83. In a similar fashion, if the tweaked augmenter gives -83% then B is .17.

$F = \begin{cases} B \ge 1, & B - 1 \\ B < 1, & \dfrac{-1}{B} + 1 \end{cases}$

Now we sum all of the factors for all augmenters together:

$F_{sum} = F_1 + F_2 + F_3 + F_4 + F_5 + F_6 + \cdots$

Next we convert this factor sum back to a bonus:

$B_{sum} = \begin{cases} F_{sum} \ge 1, & F_{sum} + 1 \\ F_{sum} < 1, & \dfrac{-1}{B - 1} \end{cases}$

It is this B that can be used to multiply with some stat to get the augged stat. For a bonus that can be compared to augmenter stats, we just subtract 1. 1.83 corresponds to +83% and .17 corresponds to -83%. Given the above calculation, one should take note that negative augmenters provide a greater effect than positive augmenters of the same magnitude.

Augmenter Tweaking

For example, a ship with one augmenter equipped to grant +56% to some statistic would receive the following bonus, as a function of the player's level of Augmenter Tweaking, labeled AT, Imperial Tweaking, labeled IT, and Engineer Class, labeled EC.

$\left(1+.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\times.56$

Similarly, if the equipped augmenter granted -56% instead, the resulting penalty is calculated as follows.

$\dfrac{1-.56}{1+\left(.56\times\left(.04\times\mbox{AT}+.02\times\mbox{IT}+.005\times\mbox{EC}\right)\right)}$

Colony Suitability

Final Suitability ($S_f$) is Initial Suitability ($S_i$) times the bonus from Colonial Administrator (CA) plus the bonuses from Terraforming $T_{sum}$.

$S_f = \left( S_i \times \left(1 + .05 \times CA \right)\right) + T_{sum}$

Speed

Speed is defined as distance traveled per second.

Thrust

Acceleration (a) is Thust (T) divided by Weight (W). Acceleration is defined as Speed per second.

$a=\dfrac{T}{W}$

Turning

Turning (T) in revolutions per second is equal to the turning listed on an engine (t) times 152 divided by Weight (W).

$T=\dfrac{152\times\mbox{t}}{W}$