Difference between revisions of "Formulae"

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= Construction  =
 
= Construction  =
  
Build time is:
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Build Time (T) in seconds is 10 times Manhours (M) divided by Workforce (W). Workforce is the lesser between Max Workforce and available workers on a base.
 +
 
 +
<math>Time = \dfrac{M\times\mbox{10}}{W}</math>
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<math>Time = \dfrac{M_h\times\mbox{10}}{W_f}</math>
 
  
 
== Bulk Construction  ==
 
== Bulk Construction  ==

Revision as of 20:55, 19 September 2010

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

Augmenter Calculations

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

Initial Suitability (S_i) is calculated by 100 multiplied by the Attributes.

Attribute / Multiplier 0.5 0.75 1.00
Gravity Heavy Low Normal
Temperature Blistering Cold Temperate
Atmosphere Gaseous Noxious Terran

So:


S_i = {100\times\mbox{Gravity}\times\mbox{Temperature}\times\mbox{Atmosphere}}


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}

Note: All suitability calculations are rounded down

Construction

Build Time (T) in seconds is 10 times Manhours (M) divided by Workforce (W). Workforce is the lesser between Max Workforce and available workers on a base.

Time = \dfrac{M\times\mbox{10}}{W}


Bulk Construction

Where B is the amount building, M is the amount of material/time needed for 1 build, and N is the total amount needed for the multibuild.

N = M \times B \times 0.9^{log\left(B\right)}

Movement and Agility

Speed

Speed is defined as distance traveled per second.

Speed = \dfrac{Distance}{Time}

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 stat (t) times 152 divided by Weight (W).


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

Slots

Calculations for slots systems

Slaves

Trade Slaves

Trade Slave Slots (TS_s) is determined by the tech of the slave (S_t), and your skill in Remote Control (RC) and Slave Research (SR). S_s is the Slots per ship. TS_s = RC + S_R This calculation is always rounded up.
S_s = \dfrac {S_t}{2}

Combat Slaves

Are the same as Trade Slaves, however, you are limited to a maximum of 9 slaves, which effectively means any ship that is Tech 4 or under takes 2 slots each.

Drones

Temporary Drones

Temporary Drones don't have slots as such, as a non-Engineer, you get 3 Temporary Drone slots, to lay any Tech of drone. This can be increased to 6 via Drone Mastery, which adds an extra slot every 10 levels.

Permanent Drones

Permanent Drone slot system is much like the slave one. S_t represents total slots, D_t represents Drone tech, S_d represents slots per drone, DD is your Drone Deployment level, and DR is your Drone Research level.

Your total Drone Slots is 4 times that of your Drone Deployment, with DR added on afterwards. Each drone takes the same number of slots as its tech, so: S_t = DD\times\mbox{4}+DR
S_d = D_t