Appendix A: Formulas

Updated: v2026.01.30

This appendix collects the key mathematical formulas that govern Aurora C# mechanics. Understanding these calculations helps with ship design optimization, fleet planning, and economic development.

Organization: Formulas are grouped by game phase – ship design, detection, combat, economy, and population – with related formulas kept together for easy reference.

A.1 Ship Design Formulas

Updated: v2026.01.30

Formulas used during ship design to calculate performance characteristics. For detailed ship design context, see Section 8.3 Engines.

A.1.1 Ship Speed

The fundamental speed formula for any vessel \hyperlink{ref-A-1}{[A-1]}:

Speed (km/s) = Total_Engine_Power * 1000 / Ship_Size_HS

Or equivalently (since 1 HS = 50 tons) \hyperlink{ref-A-2}{[A-2]}:

Speed (km/s) = Total_Engine_Power * 50000 / Ship_Mass_tons

Where:

Total_Engine_Power = Number_of_Engines x Engine_Power_per_Unit (in EP)
Ship_Size_HS = Total ship size in Hull Spaces
Ship_Mass_tons = Ship_Size_HS x 50

Example: A 200 HS ship (10,000 tons) with two engines producing 2,500 EP each:

Speed = (2 x 2500) * 1000 / 200 = 25,000 km/s
Speed = 5000 * 50000 / 10000 = 25,000 km/s (equivalent)

A.1.2 Engine Power

The actual speed depends on your engine technology. Engine power is calculated as:

Engine_Power = Engine_Size (HS) x Power_per_HS x Boost_Modifier

Where \hyperlink{ref-A-3}{[A-3]}:

Power_per_HS is determined by engine technology research (starts at 5 with Nuclear Radioisotope Engine, increases with tech up to 100)
Boost_Modifier ranges from 0.5x to 3.0x (higher boost = more power but reduced fuel efficiency)

A.1.3 Engine Size-Based Fuel Consumption

In C# Aurora, engine fuel efficiency improves linearly with engine size. Fuel consumption is reduced by 1% for every HS of engine size \hyperlink{ref-A-10}{[A-10]}:

Fuel_Consumption_Modifier = 1 - (Engine_Size_HS * 0.01)

Where:

Engine_Size_HS = Engine size in Hull Spaces

This creates efficiency advantages for larger engines:

Engine Size (HS)	Fuel Consumption Modifier	Effect
1	0.99	Minimal efficiency gain
10	0.90	10% more fuel-efficient
25	0.75	25% more fuel-efficient
50	0.50	50% more fuel-efficient

Example: A 25 HS engine has fuel consumption modifier of 0.75, meaning it uses only 75% of the fuel per unit of power compared to a 1 HS engine.

A.1.4 Fuel Consumption Rate

Fuel_per_Hour = Total_Engine_Power x Fuel_Consumption_Rate x Boost_Penalty

Where:

Fuel_Consumption_Rate is determined by fuel consumption technology (base 1.0, reduced by research)
Boost_Penalty = (4 ^ Boost_Modifier) / 4, where Boost_Modifier is the decimal value (e.g., 0.5 for 50% boost, 1.0 for 100% boost) \hyperlink{ref-A-11}{[A-11]}

A.1.5 Range Calculation

Range (km) = Fuel_Capacity / Fuel_per_Hour x 3600 x Speed

Or equivalently:

Range (billion km) = Fuel_Capacity / (Fuel_per_Hour x 1000000)

A.1.6 Shield Strength and Regeneration

Shield_Strength = Strength_Tech x Size_HS x sqrt(Size_HS / 10)  (for generators > 1 HS)
Recharge_per_5sec = Regeneration_Tech_Level x Generator_Size_HS
Shield_EM_Signature = Shield_Strength x 3

\hyperlink{ref-A-5}{[A-5]}

Shields begin at zero when first activated and must recharge to full strength. Regeneration is continuous during combat. The strength formula’s square root scaling means larger generators provide disproportionately more shielding per HS, but recharge at the same rate per HS regardless of size.

A.1.7 Power Plant Output

Power_Output = Power_Tech x Size_HS x sqrt(Size_HS / 10)  (for generators > 1 HS)
Boosted_Output = Power_Output x Boost_Multiplier

Explosion chance when hit is set per boost technology level (not a simple formula) \hyperlink{ref-A-4}{[A-4]}:

Boost	Multiplier	Explosion Chance
None	x1.0	5%
+10%	x1.1	7%
+20%	x1.2	10%
+30%	x1.3	15%
+40%	x1.4	20%
+60%	x1.6	30%
+80%	x1.8	40%
+100%	x2.0	50%

Larger power plants are more space-efficient due to the same square root scaling used by shields and engines.

A.1.8 Engineering Spaces

MSP_Stored = floor(12.5 x Ship_Build_Cost_BP x Engineering_Tons / Total_Ship_Tons)

AFR_Without_Engineering = 0.2 x Ship_Tonnage  (percent)
AFR_With_Engineering = (0.04 / Engineering_Tonnage_Percent) x Ship_Tonnage  (percent)

A.1.9 Tractor Beam Towing Speed

When a tug tows another vessel, its speed is reduced proportionally to the mass ratio:

Towing_Speed = Normal_Tug_Speed * (Tug_Mass / (Tug_Mass + Towed_Mass))

Where:

Normal_Tug_Speed = The tug’s speed when not towing (km/s)
Tug_Mass = The tug’s tonnage
Towed_Mass = The towed vessel’s tonnage

Example: A 10,000-ton tug with normal speed 2,000 km/s towing a 90,000-ton ship:

Tug proportion = 10,000 / (10,000 + 90,000) = 0.10
Towing speed = 2,000 * 0.10 = 200 km/s

Heavier tugs maintain better towing speeds. The return trip (without towed vessel) is at full tug speed.

A.2 Missile Design Formulas

Updated: v2026.01.30

Formulas for missile performance calculations. See Section 12.3 Missiles for tactical context.

A.2.1 Missile Speed

Missile_Speed (km/s) = Missile_Engine_Power / Missile_Mass

Missile engines are typically much more powerful per unit mass than ship engines but have limited fuel duration:

Missile_Endurance (seconds) = Missile_Fuel / Missile_Fuel_Consumption
Missile_Range (km) = Missile_Speed x Missile_Endurance

A.2.2 High-Boost Missile Penalty

For missiles using boost exceeding racial maximum boost technology, an additional multiplier applies:

High_Boost_Modifier = (((Boost_Used - Max_Boost_Tech) / Max_Boost_Tech) * 4) + 1

This creates a linear multiplier from 1x to 5x for high-boost missiles.

A.3 Detection Formulas

Updated: v2026.01.30

Formulas governing sensor detection and electronic warfare. For detailed sensor design and usage, see Section 11.1 Thermal and EM Signatures.

A.3.1 Thermal Signature

A ship’s thermal signature is primarily determined by its engines:

Thermal_Signature = Total_Engine_Power / Thermal_Reduction_Modifier

A.3.2 Passive Sensor Detection (Thermal)

Detection_Range (km) = sqrt(Sensor_Sensitivity x Target_Thermal_Signature) x 250000

\hyperlink{ref-A-12}{[A-12]}

Where:

Sensor_Sensitivity = Sensor_Size (HS) x Sensitivity_Tech_Level
Target_Thermal_Signature = Total_Engine_Power / Thermal_Reduction_Tech

A.3.3 Passive Sensor Detection (EM)

Detection_Range (km) = sqrt(Sensor_Sensitivity x Target_EM_Signature) x 250000

\hyperlink{ref-A-12}{[A-12]}

Where:

Target_EM_Signature is generated by active sensors, shields, and certain other components when active

Ships with no active emissions (shields off, active sensors off) have EM signature of 0 and are invisible to EM sensors.

A.3.4 Active Sensor Detection

The game uses the following formula to calculate active sensor detection range \hyperlink{ref-A-16}{[A-16]}:

Detection_Range (km) = sqrt((Active_Strength x HS x EM_Sensitivity x Resolution^(2/3)) / PI) x 1000000

Where:

Active_Strength = Active Grav Sensor Strength technology level (starts at 10)
HS = Sensor size in hull spaces
EM_Sensitivity = EM Sensor Sensitivity technology level (starts at 5)
Resolution = Sensor resolution setting (in HS)
PI = 3.14159…

Note: Some community resources use a simplified approximation: sqrt(Sensor_Strength x Target_Cross_Section) x 250,000 km, where Sensor_Strength = Size x Resolution x Active_Tech. This approximation omits the EM Sensitivity factor and uses a different constant (250,000 vs 1,000,000), so it does not produce the same results as the full formula. The full formula above is verified against the game database and should be used for accurate calculations.

A sensor designed for resolution-100 detects 5000-ton ships at full range. Smaller ships are detected at reduced range:

Effective_Range = Base_Range x sqrt(Actual_Ship_HS / Sensor_Resolution)

\hyperlink{ref-A-12}{[A-12]}

Example: A sensor with 100M km range at resolution-100 detecting a resolution-20 ship:

Effective_Range = 100M x sqrt(20/100) = 100M x 0.447 = 44.7M km

A.3.5 Missile Fire Control Range

FC_Range (km) = FC_Size x Resolution x FC_Tech_Level x 250000

\hyperlink{ref-A-12}{[A-12]}

The fire control range limits the maximum engagement distance for missiles. Missiles beyond their fire control’s range lose guidance.

A.3.6 Cloaking Effect on Detection

Effective_Signature = Actual_Signature x (1 - Cloak_Percentage/100)

A 60% cloak reduces all signatures to 40% of their actual value, reducing detection range proportionally.

A.3.7 Electronic Warfare Systems

Aurora features three distinct electronic warfare systems, each affecting different combat phases:

System	Target	Effect	Design Placement
Sensor Jammer (SJ)	Enemy active sensors	Reduces active sensor range	Ship component
Fire Control Jammer (FCJ)	Enemy beam weapon accuracy	Reduces beam hit chance	Ship component
Missile FC Jammer (MFJ)	Missile guidance systems	Reduces missile PD accuracy	Missile component

Note: Each jammer type is countered by a corresponding ECCM system. Net effectiveness depends on the difference between jammer level and opposing ECCM level.

Sensor Jammer Effect:

Effective_Sensor_Range = Base_Range x (1 - (Target_SJ_Level - Sensor_ECCM_Level) x 0.1)

Where:

Minimum effective range is 0 (complete sensor denial at 10+ net advantage) \hyperlink{ref-A-17}{[A-17]}
If ECCM >= SJ, no reduction applies

Fire Control Jammer Effect (ECM):

ECM_Mod = max(0, 1 - (Target_ECM - FC_ECCM) x 0.1)

Applied as a multiplier to beam weapon hit chance. See Beam Weapon To-Hit for the complete formula.

Missile FC Jammer Effect:

ECM_ECCM_Mod = 1 - ((Missile_FC_Jammer_Level - CIWS_ECCM_Level) * 0.2)

Minimum 0 (complete jamming). Applied to point defense accuracy against missiles. See Point Defense Accuracy for the complete formula.

A.4 Combat Formulas

Updated: v2026.01.30

Formulas governing weapons, damage, and defensive systems. For tactical combat details, see Section 12.1 Fire Controls.

A.4.1 Time to Destination

Time (seconds) = Distance (km) / Speed (km/s)

For jump point transits, add the transit time (typically instantaneous for military jump drives, or 5 minutes for commercial jump drives including squadron transit).

A.4.2 Beam Weapon To-Hit

Base_Chance = (1 - Range/Max_Range) x 100%
Tracking_Mod = min(1.0, Tracking_Speed / Target_Speed)
ECM_Mod = max(0, 1 - (Target_ECM - FC_ECCM) x 0.1)
Final_Chance = Base_Chance x Tracking_Mod x ECM_Mod

Note: The 0.1 coefficient (10% reduction per net ECM level) is consistent with the database’s integer ECM levels (0-10) and ECCM levels (0-10), but the exact coefficient is embedded in game combat logic. The formula structure is confirmed by community testing.

Example: Laser at 50% of max range, tracking 5000 km/s vs target at 4000 km/s, target ECM-2 vs FC ECCM-1:

Base = (1 - 0.5) x 100 = 50%
Tracking = min(1.0, 5000/4000) = 1.0
ECM = max(0, 1 - (2-1) x 0.1) = 0.9
Final = 50% x 1.0 x 0.9 = 45%

A.4.3 Beam Weapon Damage

Beam weapon damage is governed by two mechanics: damage falloff with range and damage gradient (armor column spread). See Section 12.2.2 for full tactical discussion.

Damage Falloff (Range-Dependent)

Only lasers suffer damage falloff. The formula is a linear reduction:

Damage_at_Range = Base_Damage * (1 - Range / Max_Range)

At point-blank (Range = 0), full damage is dealt. At max range, damage approaches the minimum (1 point). Damage steps down in discrete range increments (typically 10,000 km brackets).

Weapons with damage gradient of 1 deal full base damage at any range within their maximum envelope—no falloff applies.

Damage Falloff by Weapon Type:

Weapon Type	Damage Gradient	Range Falloff	Notes
Lasers	3-4	Linear (formula above)	Primary weapon affected by falloff
Particle Beams	1	None (full damage at all ranges)	Focused single-column penetration
Plasma Carronades	1	None (full damage at all ranges)	Short max range, half-size
Railguns	1	None (full damage at all ranges)	Multiple shots per salvo
Meson Cannons	1	None	Always 1 damage; bypasses armor/shields
Microwaves (HPM)	1	None (full damage at all ranges)	Targets electronics after shields down
Gauss Cannons	1	None	1 damage per shot, high rate of fire

Damage Gradient (Armor Column Spread)

The gradient value determines how many adjacent armor columns receive damage per hit:

Damage_per_Column ≈ Total_Damage / Gradient_Value

Gradient 1: All damage in 1 column (focused penetration)
Gradient 3: Damage spread across 3 columns (standard lasers)
Gradient 4: Damage spread across 4 columns (large-caliber lasers)

Combined Effect (Laser at Range):

For a laser with damage falloff AND gradient spread, both apply:

Per_Column_Damage = (Base_Damage * (1 - Range / Max_Range)) / Gradient_Value
Armor_Penetration = Per_Column_Damage (must exceed armor depth to reach internals)

Example: A 20-damage laser (gradient 3) firing at 50% of max range:

Total_Damage = 20 * (1 - 0.5) = 10
Per_Column = 10 / 3 ≈ 3.3 → each of 3 columns takes ~3 damage
Armor_Penetration = ~3 layers per column

Compare with a particle beam (gradient 1) with 10 base damage at the same range:

Total_Damage = 10 (no falloff)
Per_Column = 10 / 1 = 10
Armor_Penetration = 10 layers in single column

A.4.4 Armor Damage

Armor_Columns = Ship_Width (proportional to tonnage)
Damage_per_Column = Weapon_Damage (applied to random column)
Penetration = Damage_Applied > Remaining_Armor_at_Column

Armor column count scales with ship size:

Num_Columns = Ship_Tonnage / Column_Factor

A.4.5 Internal Damage

When armor at a column is breached:

Component_Hit_Chance = Component_HTK / Total_Internal_HTK
Damage_to_Component = 1 HTK per hit
Component_Destroyed when Current_HTK = 0

A.4.6 Shock Damage

Shock_Chance = Armor_Damage / Ship_Size_HS  (minimum 5% threshold; below = ignored)
Shock_Amount = Random(0 to floor(Armor_Damage x 0.20))

Shields completely negate shock damage. Only damage applied to armor triggers the shock check.

A.4.7 Magazine Explosion

Explosion_Damage = Sum(All_Missile_Warhead_Strengths_in_Magazine)

Applied to the host ship first, excess may damage nearby vessels within blast radius.

A.4.8 Missile Hit Chance (Speed Ratio System)

Base_Hit_Chance = 0.1 * (Missile_Speed / Target_Speed)

Where:

Missile_Speed = The missile’s designed speed (km/s)
Target_Speed = The target’s current speed (km/s)

Example: A 30,000 km/s missile against a 5,000 km/s target:

Base Hit Chance = 0.1 * (30,000 / 5,000) = 0.6 = 60%

Active Terminal Guidance (0.25 MSP component) provides an accuracy bonus from +15% to +60% based on technology level, applied as an additive bonus to the base hit chance \hyperlink{ref-A-13}{[A-13]}.

Key implications:

Against stationary targets, hit chance is effectively 100% (infinite speed ratio)
Faster missiles are more accurate; very fast targets require proportionally faster missiles
Multiple warheads provide additional independent hit rolls

A.4.9 Missile Point Defense

For each PD weapon firing at incoming missiles:

Intercept_Chance = (1 - Range/Max_Range) x Tracking_Mod x 100%

Where Tracking_Mod for PD against missiles:

Tracking_Mod = min(1.0, PD_Tracking / Missile_Speed)

CIWS (Close-In Weapon Systems) fire at range 0 (final defense), making their base chance very high, but they must track the missile’s speed.

A.4.10 Point Defense Accuracy (CIWS Effectiveness)

The complete PD accuracy formula for CIWS and beam weapons in point defense mode:

Hit_Probability = Base_Tracking_Mod * Crew_Training * ECM_ECCM_Mod * CIC_Bonus * Tactical_Bonus * Gauss_Size_Mod * Range_Mod

Where:

Base_Tracking_Mod = min(1.0, FC_Tracking_Speed / Missile_Speed)
Crew_Training = Fractional modifier based on crew training level (1.0 at 100% training)
ECM_ECCM_Mod = 1 - ((Missile_FC_Jammer_Level - CIWS_ECCM_Level) * 0.2), minimum 0
CIC_Bonus = Commander’s Combat Information Center skill bonus
Tactical_Bonus = Commander’s Tactical skill bonus
Gauss_Size_Mod = Per-shot accuracy modifier for gauss cannons below racial standard size
Range_Mod = 1.0 within 10,000 km (Point Blank modes); decreases with distance beyond 10,000 km

Expected Kills per Tick:

Expected_Kills = Shots_per_Tick * Hit_Probability

Example: A triple-turret gauss cannon with rate-of-fire 4 technology fires 12 shots per burst. Against missiles at 80% tracking (FC tracks faster than missile) with no ECM:

Expected kills = 12 * 0.8 = 9.6 missiles per 5-second cycle

A.5 Production Formulas

Updated: v2026.01.30

Formulas for economic output and industrial production. For colony production management, see Section 6.3 Construction.

A.5.1 Construction Factory Output

Annual_BP = Num_Factories x BP_per_Factory x (1 + Governor_Manufacturing x 0.05)

Standard BP per factory = 10/year (increased by Construction Rate technology) \hyperlink{ref-A-6}{[A-6]}:

Technology Level	BP per Factory	Research Cost (RP)
Base	10	–
1	12	3,000
2	14	5,000
3	16	10,000
4	20	20,000
5	25	40,000
6	30	80,000
7	36	150,000
8	42	300,000
9	50	600,000
10	60	1,250,000
11	70	2,500,000

A.5.2 Mineral Mining Output

Annual_Tons_per_Mine = Base_Production x Accessibility x Tech_Modifier

Where Base_Production = 10 tons/year per mine \hyperlink{ref-A-7}{[A-7]}. Mining technology progression:

Technology Level	Tons/Mine/Year	Research Cost (RP)
Base	10	–
1	12	3,000
2	14	5,000
3	16	10,000
4	20	20,000
5	25	40,000
6	30	80,000
7	36	150,000
8	42	300,000
9	50	600,000
10	60	1,250,000
11	70	2,500,000

A.5.3 Fuel Refinery Output

Fuel_per_Year = Num_Refineries x Base_Output_per_Refinery (litres)

Base refinery output is 40,000 litres/year \hyperlink{ref-A-8}{[A-8]}. Refinery technology progression:

Technology Level	Output (litres/year)	Research Cost (RP)
Base	40,000	–
1	48,000	3,000
2	56,000	5,000
3	64,000	10,000
4	80,000	20,000
5	100,000	40,000
6	120,000	80,000
7	144,000	150,000
8	168,000	300,000
9	200,000	600,000
10	240,000	1,250,000
11	280,000	2,500,000

A.5.4 Research Speed

Days_to_Complete = Research_Cost / (Daily_RP_Output)
Daily_RP_Output = Sum_of_All_Labs_on_Project / 365

With diminishing returns for multiple labs \hyperlink{ref-A-15}{[A-15]}:

Effective_Labs = Lab_1 + Lab_2 x 0.5 + Lab_3 x 0.25 + Lab_4 x 0.125 + ...
RP_per_Year = Effective_Labs x RP_per_Lab x (1 + Scientist_Bonus / 100)

Where Scientist_Bonus is the percentage shown in the commander’s profile. This bonus is quadrupled when the scientist works in their specialization field.

A.5.5 Terraforming Rate

Atm_Change_per_Year = Num_Installations x Terraform_Rate x Gas_Modifier

Where:

Terraform_Rate depends on the technology level of terraforming installations
Gas_Modifier varies by the gas being added or removed (some gases terraform faster than others)

Terraforming rate technology progression \hyperlink{ref-A-9}{[A-9]}:

Technology Level	Rate (atm/year)	Research Cost (RP)
Racial Starting Rate	0.00025	—
Terraforming Rate 1	0.00032	3,000
Terraforming Rate 2	0.0004	5,000
Terraforming Rate 3	0.00048	10,000
Terraforming Rate 4	0.0006	20,000
Terraforming Rate 5	0.00075	40,000
Terraforming Rate 6	0.00096	80,000
Terraforming Rate 7	0.0012	150,000
Terraforming Rate 8	0.0015	300,000
Terraforming Rate 9	0.0019	600,000
Terraforming Rate 10	0.0024	1,200,000
Terraforming Rate 11	0.003	2,500,000
Terraforming Rate 12	0.00375	5,000,000

A.5.6 Shipyard Build Time

Build_Time (days) = Ship_BP_Cost / (Shipyard_Capacity / 365) / Num_Slipways

But note: a single ship can only be built in one slipway. Multiple slipways allow parallel construction of multiple ships, not faster construction of a single ship.

Retooling time when changing ship class:

Retool_Time (days) = abs(New_Ship_Tonnage - Old_Ship_Tonnage) x Retool_Factor

A.5.7 Secondary Build (20% Refit Cost Rule)

A shipyard can build any secondary class without retooling if the refit cost is below 20% of the primary class’s total build cost:

Eligible_for_Secondary_Build = (Refit_Cost < 0.20 * Primary_Class_BP_Cost)

Where:

Refit_Cost = Build point cost to refit the primary class into the secondary class
Primary_Class_BP_Cost = Total build point cost of the class the shipyard is currently tooled for

Example: A destroyer with 2,000 BP build cost can build secondary classes whose refit cost is under 400 BP (20% of 2,000). An escort variant swapping missile launchers for gauss cannons at 300 BP refit cost is eligible; a variant replacing engines and adding a jump drive at 800 BP is not.

This allows shipyard flexibility when designing ship families that share expensive components (engines, reactors) while varying cheaper components (cargo holds, troop bays).

A.6 Population and Colony Formulas

Updated: v2026.01.30

Formulas for population growth, habitability, and colony management. For colony management and habitability, see Section 5.1 Establishing Colonies.

A.6.1 Base Growth Rate

Annual_Growth = Population x Growth_Rate x Habitability_Modifier x Infrastructure_Modifier

Where:

Growth_Rate = Base racial growth rate (typically 0.02 to 0.05 or 2-5% per year)
Habitability_Modifier = Planet’s colony cost modifier (1.0 for ideal, reduced for hostile environments)
Infrastructure_Modifier = min(1.0, Infrastructure_Units / Required_Infrastructure)

A.6.2 Growth Rate Modifiers

Condition	Modifier
Ideal planet (CC = 0)	1.0x
Low infrastructure	Proportional reduction
Overcrowding	Growth reduced progressively
Governor bonus	1 + (Admin_Skill x 0.05)
Genetic modification tech	Increases base racial growth rate

A.6.3 Colony Cost and Habitability

Colony_Cost = Sum(Environmental_Penalties)

Environmental penalties include:

Temperature deviation from ideal (per degree of difference)
Atmospheric pressure deviation
Hostile gas presence
Gravity deviation (minor effect)

Required_Infrastructure = Population x Colony_Cost

Without sufficient infrastructure on a hostile world, excess population suffers attrition.

A.6.4 Population Capacity

Max_Supported_Population = Infrastructure / Colony_Cost

For Earth-like worlds (colony cost = 0), no infrastructure is needed and population can grow without limit.

A.6.5 Civilian Infrastructure Production

Civilian shipping lines produce infrastructure for colonies with colony cost > 0, at no cost to the government:

Annual_Infrastructure = 2 * Population (in millions)

Where:

Population = The colony’s population in millions
Only colonies with Colony Cost > 0 demand and receive this production
On low-gravity worlds, civilian production generates LG-Infrastructure at one-third the normal rate

Example: A colony of 10 million on a CC 2.0 world receives approximately 20 infrastructure units per year from civilian production alone.

This supplements but does not replace government construction, especially in early colonization stages when infrastructure needs are urgent.

A.6.6 Agriculture & Environment Workforce

A portion of the manufacturing workforce is diverted to agriculture and environmental support based on colony cost:

Agriculture_Workers_Percent = 5 + (5 x Colony_Cost)
Effective_Industrial_Workers = Total_Population x 0.60 x (1 - Agriculture_Workers_Percent / 100)

Where:

0.60 = Approximately 60% of total population is available as workers (remainder are children, elderly, service sector)
Colony_Cost = The colony’s environmental cost factor (0.0 for Earth-like worlds)

Examples:

CC 0.0: Industrial Workers = Pop x 0.60 x 0.95 = Pop x 0.57
CC 2.0: Industrial Workers = Pop x 0.60 x 0.85 = Pop x 0.51
CC 4.0: Industrial Workers = Pop x 0.60 x 0.75 = Pop x 0.45

A.6.7 Migration

When multiple colonies exist, population can migrate between them based on:

Relative habitability
Available jobs (installations require workers)
Overcrowding at source colony
Automated migration policies set by the player

Migration_Rate = Base_Rate x Push_Factor x Pull_Factor

A.7 Garrison and Unrest Formulas

Updated: v2026.01.30

Formulas for occupation, garrison requirements, and population unrest. See Section 13.1 Unit Types for ground force details.

A.7.1 Required Garrison Strength

The garrison strength required to maintain order on a colony is determined by:

Required_Garrison = Population (millions) * (Racial_Determination / 100) * (Racial_Militancy / 100)

Where:

Population = The colony’s population in millions
Racial_Determination = The race’s determination rating (higher = more resistant to occupation)
Racial_Militancy = The race’s militancy rating (higher = more prone to armed resistance)

For occupied populations, a Political Status Modifier applies:

Political Status	Modifier
Slave Colony	1.5
Conquered	1.0
Occupied	0.75
Subjugated	0.25
All Others	0

A.7.2 Element Occupation Strength

Per ground unit element:

Occupation_Strength = (SQRT(Size) * Units * Morale) / 10,000

When occupation strength exceeds the requirement, the surplus functions as police strength that actively reduces unrest over time.

A.7.3 Unrest and Stability

Population unrest affects productivity. Production output (factories, research, shipbuilding) is reduced by a percentage equal to the current unrest points. At 25 unrest points, all output drops by 25%.

Effective_Production = Base_Production x (1 - Unrest_Points / 100)

Unrest Sources and Annual Point Generation:

Source	Annual Unrest Points	Formula
Radiation	Radiation Level / 10	e.g., radiation 1000 = 100 points/year
Overcrowding	25 x (Missing Infrastructure / Available Infrastructure)	Baseline of 25 if no infrastructure at all
Insufficient Occupation Forces	100 x (1 - Actual Strength / Required Strength)	100 points if no forces present
Insufficient Local Defence	25 x (1 - Total PPV / Required Protection)	Based on Population Protection Value
Forced Labour Construction	+5 per camp when built	Immediate, one-time addition

Required Occupation Strength:

Required = Population x ((Determination + Militancy + Xenophobia) / 300) x Political Status Modifier

Required Protection (PPV):

Required = Population (millions) x (Militancy / 100) x Political Status Protection Modifier

Population Threshold: PPV requirements only apply to colonies with 10 million or more population. Smaller colonies do not generate unrest from insufficient local defence. (unverified — #874 – threshold from community sources, needs authoritative confirmation)

Ships are evaluated by Population Protection Value (hull space allocated to weapons and hangar bays). PPV is calculated system-wide — a single armed ship or PDC provides protection for all colonies in the system.

A.7.4 Unrest Reduction

Natural decline (when the cause is removed):

Fall in Unrest Points = 20 x (1 - (Determination / 100))

Military suppression (when occupation strength exceeds requirement):

Police Strength = Actual Occupation Strength - Required Occupation Strength
Reduction in Unrest = 100 x (Police Strength / Effective Population Size)

Where Effective Population Size = ((Determination + Militancy + Xenophobia) / 300) x Population Amount

Section 5.1 Establishing Colonies — Population growth, colony cost, and habitability mechanics
Section 5.2 Population — Workforce allocation and population capacity
Section 5.4 Infrastructure — Infrastructure production and installation types
Section 6.2 Mining — Production, mining, and refining installations
Section 8.3 Engines — Engine, speed, and fuel consumption design parameters
Section 8.6 Other Components — Tractor beams, power plants, and engineering spaces
Section 9.1 Shipyards — Shipyard capacity, retooling, and secondary build rules
Section 11.1 Thermal and EM Signatures — Sensor range and detection calculations
Section 12.1 Fire Controls — Beam weapons, missiles, armor, and shield combat mechanics
Section 12.3 Missiles — Missile hit chance and speed ratio system
Section 12.4 Point Defense — CIWS effectiveness and PD accuracy formulas
Section 13.1 Unit Types — Garrison strength and occupation mechanics
Section 14.1 Fuel — Fuel consumption and logistics
Appendix D: Reference Tables — Quick-reference tables for minerals, installations, and technology

References

\hypertarget{ref-A-1}{[A-1]} AuroraWiki Engine page – Speed formula: “One unit of engine power is the amount of power required to propel 50 tons (1 HS) at 1000 km/s.” Speed = Total_EP x 1000 / Ship_Size_HS.

\hypertarget{ref-A-2}{[A-2]} Aurora C# game database (AuroraDB.db v2.7.1) – 1 HS = 50 tons is a core game constant used throughout ship design.

\hypertarget{ref-A-3}{[A-3]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem TechTypeID=40 (Engine Technology): 15 engine types from Conventional (1.0 power/HS, 500 RP) through Quantum Singularity Drive (100.0 power/HS, 5,000,000 RP). TechTypeID=130 (Max Engine Power Modifier): x1 through x3 (15,000 RP). TechTypeID=198 (Min Engine Power Modifier): x0.5 through x0.1 (30,000 RP).

\hypertarget{ref-A-4}{[A-4]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem TechTypeID=42 (Power vs Efficiency): 8 boost levels from None (x1.0, 5% explosion, 250 RP) through +100% (x2.0, 50% explosion, 30,000 RP). Explosion percentages are discrete per-level values, not derived from a simple formula.

\hypertarget{ref-A-5}{[A-5]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem TechTypeID=16 (Shield Type): 12 shield types from Alpha (1.0/HS, 1,000 RP) through Omega (15.0/HS, 2,000,000 RP). TechTypeID=14 (Shield Regeneration Rate): 12 levels from 1.0 (1,000 RP) through 15.0 (2,000,000 RP).

\hypertarget{ref-A-6}{[A-6]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem TechTypeID=25 (Improved Construction Rate): 11 levels from 12 BP (3,000 RP) through 70 BP (2,500,000 RP). DIM_PlanetaryInstallation confirms base Construction Factory output of 1.0 (ConstructionValue column), representing 10 BP/year at base tech.

\hypertarget{ref-A-7}{[A-7]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem TechTypeID=26 (Improved Mining Production): 11 levels from 12 tons (3,000 RP) through 70 tons (2,500,000 RP). DIM_PlanetaryInstallation confirms Mine base MiningProductionValue of 1.0 (10 tons/year).

\hypertarget{ref-A-8}{[A-8]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem TechTypeID=32 (Improved Fuel Production): 11 levels from 48,000 litres (3,000 RP) through 280,000 litres (2,500,000 RP). Base refinery output is 40,000 litres/year.

\hypertarget{ref-A-9}{[A-9]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem TechTypeID=57 (Terraforming Rate): 12 levels from 0.00032 atm (3,000 RP) through 0.00375 atm (5,000,000 RP). Base racial starting rate is 0.00025 atm/year per installation.

\hypertarget{ref-A-10}{[A-10]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem TechTypeID=65 (Fuel Consumption): 13 levels from 1.0 L/EPH (base) through 0.1 L/EPH (2,000,000 RP). Engine size fuel efficiency modifier confirmed by community testing.

\hypertarget{ref-A-11}{[A-11]} Aurora Forums, “Sensor Model for C# Aurora” – Boost penalty formula (4\^Boost_Modifier)/4 confirmed by Steve Walmsley. aurora2.pentarch.org

\hypertarget{ref-A-12}{[A-12]} Aurora Wiki, “Thermal Sensor” – C# passive sensor formula: range = sqrt(Sensitivity x Signature) x 250,000 km. Active sensor formula uses sqrt-based calculation with 250,000 km multiplier for simplified form. aurorawiki2.pentarch.org

\hypertarget{ref-A-13}{[A-13]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem TechTypeID=275 (Active Terminal Guidance): 8 levels from 0% (base) through +60% (64,000 RP). Stored as multipliers 1.0 through 1.6.

\hypertarget{ref-A-14}{[A-14]} Aurora C# game database (AuroraDB.db v2.7.1) – DIM_PlanetaryInstallation table confirms base Construction Factory ConstructionValue=1.0. Combined with FCT_TechSystem construction rate techs, base output = 10 BP/year.

\hypertarget{ref-A-15}{[A-15]} AuroraWiki, “Research” – Each lab assigned to a project contributes diminishing RP: first lab at 100%, second at 50%, third at 25%, etc. Scientist bonus percentage is applied as a multiplier and quadrupled in specialization field. aurorawiki2.pentarch.org

\hypertarget{ref-A-16}{[A-16]} Aurora C# game database (AuroraDB.db v2.7.1) – Full active sensor range formula verified against multiple FCT_ShipDesignComponents entries: Range = sqrt((Active_Strength x HS x EM_Sensitivity x Resolution^(2/3)) / PI) x 1,000,000 km. Tested against 10 sensor components with varied sizes (0.1-17 HS) and resolutions (1-121 HS), all matching MaxSensorRange within rounding error. FCT_TechSystem TechTypeID=20 (Active Grav Sensor Strength): 10-180; TechTypeID=125 (EM Sensor Sensitivity): 5-75.

\hypertarget{ref-A-17}{[A-17]} Aurora C# game database (AuroraDB.db v2.7.1) – FCT_TechSystem: Sensor Jammer levels 1-10 (AdditionalInfo=1.0 through 10.0, AdditionalInfo2=1.1 through 2.0). ECCM levels 0-10 (matching structure). At maximum net advantage (SJ-10 vs ECCM-0), the subtractive formula yields 1 - 10 x 0.1 = 0, confirming complete sensor denial is possible with no floor.

Appendix A: Formulas

A.1 Ship Design Formulas

A.1.1 Ship Speed

A.1.2 Engine Power

A.1.3 Engine Size-Based Fuel Consumption

A.1.4 Fuel Consumption Rate

A.1.5 Range Calculation

A.1.6 Shield Strength and Regeneration

A.1.7 Power Plant Output

A.1.8 Engineering Spaces

A.1.9 Tractor Beam Towing Speed

A.2 Missile Design Formulas

A.2.1 Missile Speed

A.2.2 High-Boost Missile Penalty

A.3 Detection Formulas

A.3.1 Thermal Signature

A.3.2 Passive Sensor Detection (Thermal)

A.3.3 Passive Sensor Detection (EM)

A.3.4 Active Sensor Detection

A.3.5 Missile Fire Control Range

A.3.6 Cloaking Effect on Detection

A.3.7 Electronic Warfare Systems

A.4 Combat Formulas

A.4.1 Time to Destination

A.4.2 Beam Weapon To-Hit

A.4.3 Beam Weapon Damage

A.4.4 Armor Damage

A.4.5 Internal Damage

A.4.6 Shock Damage

A.4.7 Magazine Explosion

A.4.8 Missile Hit Chance (Speed Ratio System)

A.4.9 Missile Point Defense

A.4.10 Point Defense Accuracy (CIWS Effectiveness)

A.5 Production Formulas

A.5.1 Construction Factory Output

A.5.2 Mineral Mining Output

A.5.3 Fuel Refinery Output

A.5.4 Research Speed

A.5.5 Terraforming Rate

A.5.6 Shipyard Build Time

A.5.7 Secondary Build (20% Refit Cost Rule)

A.6 Population and Colony Formulas

A.6.1 Base Growth Rate

A.6.2 Growth Rate Modifiers

A.6.3 Colony Cost and Habitability

A.6.4 Population Capacity

A.6.5 Civilian Infrastructure Production

A.6.6 Agriculture & Environment Workforce

A.6.7 Migration

A.7 Garrison and Unrest Formulas

A.7.1 Required Garrison Strength

A.7.2 Element Occupation Strength

A.7.3 Unrest and Stability

A.7.4 Unrest Reduction

Related Sections

References