Difference between revisions of "Formulae"

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This is an explanation page for the various formulae involved in calculating stats in game.
 
This is an explanation page for the various formulae involved in calculating stats in game.
  
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===Augmenter Addition===
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===Augmenter Calculations===
 +
 
 +
====Augmenter Addition====
 
Augmenter addition is a multi-step process. First all augmenters are tweaked using the augmenter tweaking formula below.
 
Augmenter addition is a multi-step process. First all augmenters are tweaked using the augmenter tweaking formula below.
  
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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.
 
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.
  
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===Augmenter Tweaking===
+
====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''.   
 
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''.   
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''Note: All suitability calculations are '''rounded down'''''
 
''Note: All suitability calculations are '''rounded down'''''
  
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===Speed===
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===Construction===
 +
 
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Build time is:
 +
 
 +
<math>Time = \dfrac{M_h\times\mbox{10}}{W_f}</math>
 +
 
 +
====Bulk Construction====
 +
Bulk material discount calculation is:
 +
 
 +
<math>Discount = {0.9\times\mbox{Log}^{B}}</math>
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Where B is the amount building
 +
 
 +
Bulk build time discount calculation is:
 +
 
 +
<math>Time Discount = {0.9\times\mbox{Log}^{B}}</math>
 +
Where B is the amount building
 +
 
 +
===Movement and Agility===
 +
 
 +
====Speed====
 
Speed is defined as distance traveled per second.
 
Speed is defined as distance traveled per second.
  
 
<math>Speed = \dfrac{Distance}{Time}</math>
 
<math>Speed = \dfrac{Distance}{Time}</math>
  
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===Thrust===
+
====Thrust====
 
Acceleration (a) is Thust (T) divided by Weight (W). Acceleration is defined as Speed per second.
 
Acceleration (a) is Thust (T) divided by Weight (W). Acceleration is defined as Speed per second.
  
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</math>
 
</math>
  
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===Turning===
+
====Turning====
 
Turning (T) in revolutions per second is equal to the turning stat (t) times 152 divided by Weight (W).
 
Turning (T) in revolutions per second is equal to the turning stat (t) times 152 divided by Weight (W).
  

Revision as of 04:43, 18 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 is:

Time = \dfrac{M_h\times\mbox{10}}{W_f}

Bulk Construction

Bulk material discount calculation is:

Discount = {0.9\times\mbox{Log}^{B}} Where B is the amount building

Bulk build time discount calculation is:

Time Discount = {0.9\times\mbox{Log}^{B}} Where B is the amount building

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}

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