Aurora 4x
C# Aurora => C# Mechanics => Topic started by: SBBurzmali on January 06, 2021, 11:59:44 AM
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An incident where I shipped population to a planet only to watch the available worker population drop to zero inspired me to look a little harder at how colonies divide up population into Agriculture and Environmental, Service industries and Manufacturing sectors.
So, based on a bit of wiki and forum hunting as well as some reverse engineering based on around 20 colonies, here are the basic formulas:
- Agriculture and Environmental (%) = 5 + Colony Cost x 5
- Service industries (%) = 17. 75 x Population0. 2505 with a maximum of the lesser of 70% and 100 - Agriculture and Environmental (%)
- Manufacturing (%) = 100 - Agriculture and Environmental (%) - Service industries (%)
I checked the rest of my colonies, and these formulas seem to hold.
This led me to a few interesting observations:
- Colonies with a Colony Cost >= 5 have a finite capacity for manufacturing workers that is reached long before the colony hits its Population Capacity
- Colonies hit a local maximum worker population at the total population of (4. 28 - 0. 225 x Colony Cost)4
after that, the worker population will drop until either it hits 0 (for Colony Cost >= 5) or it begins to increase again at around 241. 5m total population when Service industries (%) hits its max at 70% (for Colony Costs between ~1. 5 and 5).
In practice, this means that if you have a colony with a Colony Cost of 2, you shouldn't bother pushing the population beyond 189m unless you are willing to wait for it to get beyond 250m when you will see a net worker increase. The worse case is colonies with Colony Cost close to 5, with a colony cost of 4. 9, you hit your initial max worker amount of 14. 25m at a total population of 100. 8m, but exceed that and you won't see 14. 25m workers at that colony again until you hit 2845m total population.
Up to this point, my policy for marginal worlds that weren't particularly strategic, has been to slap down a colony, feed it some infrastructure and let it grow naturally until it could support some mines and maybe a handful of construction factories to bootstrap it into usefulness, but I often ran into problems that the available worker amount would go negative and no amount of shipping over population would do much to help. These formulas explain why, and I'm not really sure how I want to proceed, probably massive orbital stations that either terraform or strip mine these planets.
This also explains why planets that are optimal to colonize, Colony Cost 0 - 1. 5, still hit a slump between around 200m to 240m total population, around that point virtually every million pop you push in just pushes up the Service industries (%) enough to minimize the increase to maximum available workers.
Here's a quick chart of some of the low to mid Colony Costs for Population vs. Maximum Available Workers. It's interesting to see, and usual to keep in mind when planning colonies and prioritizing terraforming.
(https://docs. google. com/spreadsheets/d/e/2PACX-1vS66umXJOTanuqaL-vNGJIuZxWVOo1ITV730YQOXa3fi6uwJfM1cMci6z99ua_hwwueNtgeMGV23vo4/pubchart?oid=108506175&format=interactive)
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That is actually really useful for me to know, I recently ran into the very same issue of the working population on one of my moons shrinking instead of growing, and eventually disappearing completely (CC > 5). Now I know for my 7.2058 CC moon to stop sending people when it hits 50m. Here's a plot of your formula for the local maximum (https://www.desmos.com/calculator/urvnkpgivb), aka. the point after which the manufacturing sector starts shrinking.
So the cut-off at which the service sector reaches 70% (it's maximum) is always at 239.24m pop, which is why the graphs just become linear at that point.
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This is going into my spreadsheets, thanks a lot!
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Now that orbital habitats are being revisited in 2.0 (http://aurora2.pentarch.org/index.php?topic=12523.msg159464#msg159464), I think that it might be useful to review when it is worth building habitats versus infrastructure, specifically in terms of the cost to support a desired workforce size.
Based on SBBurzmali's original post, we have: w = p * (1 - 0.05*(c+1) - min(0.7, 0.1775*p^0.2505), where
- w = industrial workers in millions
- p = population in millions
- c = colony cost (habitats have an de facto colony cost of -1 since they have automated life support)
We also have the following infrastructure costs in Aurora C# 1.13:
- Infrastructure: $=2*100*c*p (in practice much lower due to civilian manufacturing/trade)
- LG infrastructure: €=4*100*c*p (in practice slightly lower due to civilian manufacturing/trade)
Orbital habitats Ark Modules: £=200*5*p (in practice slightly higher due to crew quarters, etc.)
This gives us the following equations for workers per build cost.
- Infrastructure: w = ($/200/c) * (1 - 0.05*(c+1) - min(0.7, 0.1775*($/200/c)^0.2505)
- LG infrastructure: w = (€/400/c) * (1 - 0.05*(c+1) - min(0.7, 0.1775*(€/400/c)^0.2505)
- Orbital habitats: w = (£/1000) * (1 - min(0.7, 0.1775*(£/1000)^0.2505)
If we graph by build cost and colony cost, then we get the attached log-log graphs. CC=0 is omitted since it doesn't make sense to compare orbital habs to nonexistent infrastructure; CC>=5 is omitted since such colonies will eventually deindustrialize into hordes of farmers and service workers.
- At colony cost 1, all forms of fixed infrastructure beat orbital habs.
- At colony cost 2, orbital habs are cost-competitive with LG infrastructure.
- At colony cost 3, orbital habs are cost-competitive with regular infrastructure.
- At colony cost 4, orbital habs beat all forms of fixed infrastructure!
tl;dr If colony cost is at least 2, then consider building orbital habs instead of LG infrastructure. If colony cost is at least 3, then consider building orbital habs instead of regular infrastructure.
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tl;dr If colony cost is at least 2, then consider building orbital habs instead of LG infrastructure. If colony cost is at least 3, then consider building orbital habs instead of regular infrastructure.
You need to also consider cost of habitats compared to the two.
Strictly speaking, yeah, habitats good if only to save the 5% that would instead go to habitability.
They are a pretty massive expense tho, usually not easy to mass unless you get good RNG.
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tl;dr If colony cost is at least 2, then consider building orbital habs instead of LG infrastructure. If colony cost is at least 3, then consider building orbital habs instead of regular infrastructure.
You need to also consider cost of habitats compared to the two.
Strictly speaking, yeah, habitats good if only to save the 5% that would instead go to habitability.
They are a pretty massive expense tho, usually not easy to mass unless you get good RNG.
The above equations and graphs use build cost, not total population, as their input, so habitat cost should have already been taken into account (unless one has a shortage in a specific TN material).
In my opinion, the primary advantage that (LG) infrastructure has is that it can be manufactured for free by civilians - it's hard to compete with free! That does raise the question though: will DSPs (http://aurora2.pentarch.org/index.php?topic=12523.msg159432#msg159432)produce infrastructure as a trade good?
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This is a useful thread. Just the last couple days I've seen two people already who were confused about why their 8+ CC colonies were running out of workers.
It also seems a little weird to me that a low-gravity rock with no atmosphere is for some reason a lot harder to live on than in a deep space ark habitat colony. I mean, arks/ habitats don't have a peak value for possible workers, unlike CC5+ asteroids, right?
- Service industries (%) = 17. 75 x Population0. 2505 with a maximum of the lesser of 70% and 100 - Agriculture and Environmental (%)
SevenOfCarina on the Discord said that the right formula for service industries is:
Service Sector Fraction = (pop in billions)^0.25
No idea which is correct, but these numbers sound a lot more round.
I assume this will affect the formula for the worker peak per CC as well.
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SevenOfCarina on the Discord said that the right formula for service industries is:
Service Sector Fraction = (pop in billions)^0.25
No idea which is correct, but these numbers sound a lot more round.
I assume this will affect the formula for the worker peak per CC as well.
It turns out that both are correct, to within a small margin of error as you'd expect from doing a numerical fit to data.
If you consider P as the population in millions, then the pop in billions is 0.001*P. Then, (0.001*P)^0.25 = 0.1778 * P^0.25, which is basically what the OP obtained within 0.2% margin of error.
Since the pop in billions works out pretty much exactly and is more straightforward I would prefer that one, but either works - and either way you will obtain the maximum of 70% service population at 240m pop.