Growth Rate Equation

!!! While the equation works with ~100% accuracy for Syntis planets with a temperature of 0 degrees, I am not certain yet if it works for all races. It has been tested on a couple of non-Syntis planets, and it is fairly accurate, but the temperatures were not as close to 0 degrees as I would have liked. !!!

City Multiplier * (Race Growth Multiplier * Planet Happiness * 792 – (560 * |(optimal landmass – planet landmass)|)) = Growth/h for any colonised planet with a temperature at optimal temperature.

  • Should be on the dot for planets at optimal temperature. Needs more testing to make sure it is correct, it works for the Syntis race at least though. Also works best for Syntis as happiness is exact, not rounded.

  • Is able to estimate growth rate for planets around optimal temperature, but becomes less accurate the further it is from optimal temperature

More data is needed to confirm it is accurate (If anybody has non-home planets with either exactly optimal temperature/landmass, it would be greatly appreciated if you could message me with the following details: Your race, your race’s optimal temperature, your race’s optimal landmass, your race’s growth multiplier, the planet’s happiness, the planet’s landmass, the planet’s temperature, your race’s growth range for temperature, the number of cities and levels of each of them, how much percentage growth your race’s cities contribute to the planet at each level. Sorry about asking for race details too, many details on the wiki are incorrect and I currently only know the stats for the Syntis).

Other notes:

  • Syntis happiness is (I’m fairly certain) 99% for every planet.
  • Use decimals for landmass. E.g: A planet with landmass 40%, optimal landmass 90% for race (0.90-0.40). Also for happiness (50% happiness = 0.5).

Example of use of equation:
You have a Syntis planet with 2 level 1 depositors, 1 level 2 depositor, a landmass of 35% and a temperature of 0 degrees.
Syntis optimal landmass is 90%.
Syntis level 1 depositors give a 1.03 multiplier, level 2 depositors give 1.06 multiplier.
(1 + 0.03 + 0.03 + 0.06) * ((0.8 * 0.99 * 792) – (560 * (0.90 – 0.35))) = 357.57568/h

Currently working on getting the full equation, for temperature and not just landmass.

Saw you working on this in the chat earlier today, and it insipred me to take this back up again! I gathered growth data during terraforming several planets during A3 with the intent of getting a derivation, but couldn’t quite make it work at the time. Here’s what I’ve found since.

The growth-formula is based on a quadratic equation of the form:

Growth/hr = (a*T^2 + c)HCen ,

where a = -1.425 (to yield negative growth outside of tolerable temp. ranges), T is the distance away from the civ’s optimal temperature in degrees C, c is a positive constant giving the maximum growth at the optimal temp and the planet’s land mass (which is not necessarily optimal!), H is the happiness multiplier (between 0.0 and 1.0), and Cen is the cumulative growth bonus for any City Centre structures built. For A4 home worlds with five Megalopolises (9% buff each), Cen = 1.45.
Using all this for a planet optimal for humans (50% landmass, +22C), at 100% Happiness and with no City Centres (because they were naff in A3), the observed maximum growth rate of 792/hr is recovered. This can be extended outwards to calculate the death rate when colonising hostile worlds.

There are a couple more complexities to go through: the happiness modifier only applies when growth rates are positive. When it is at 0.8, we can see the behaviour below. Red points are the ones I took in real time while terraforming, and extrapolated (as our function is symmetric). Black crosses are what you get once Happiness hits 100%.

The land mass dependency is tied up in the positive constant c, which can be broken down as:

c = 792G - |(7.11LD)|,

where G is the growth multiplier of the chosen civ and LD is the difference between optimal landmass and the planet’s current land fraction (for factions with a Land affinity). This assumes there is at least some space for your chosen civ - 100% water worlds are always dangerous to colonise (at least initially).

That should all hold up! If it does, I’ll get this onto the Populations wiki page when I’m able.

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Temperature effects are definitely not linear, and all observations seem to be that it’s polynomial order 2.
Landmass effects absolutely appear to be linear.

Racial effects and happiness only apply when growth is positive.

If population is over max, growth is fixed at a large negative number, either -792 or -1000 times racial and morale modifiers.

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