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I also ran the numbers. At full upgrades on everything, a Steam Thumper will supply 4 Gathering Posts and people working the pile directly, but doing all of that produces only slightly more coal per hour than a single Advanced Coal Mine. 163.6 per hour for the Thumper, versus 124.2 per hour from the Mine. And when you get to late game and you kind of need to use Automotons to keep it all running, you're gonna need 6 Automotons for the Thumper setup versus just the 1 for the Advanced Mine. That's also 6 Cores for the Thumper versus only 4 for the Mine.
Personally, it's just not worth it.
I'm not sure if just one advanced coal mine with all upgrades matches that, but the number of cores isn't that imbalanced. Granted, at the end when you have to use automotons for everything, my output falls into the red, but I planned for that by stockpiling over 30k coal.
1 gathering post from the thumper get around 19 coal per hour, while you only get about 20 per mine with automatons
You can raise Automotons to 90% efficiency through the normal techs, and by completing the relevant quest line you can get an extra 5% (might be 10% if you don't immediatley have a Steam Core for the third stage, only did that once). In addition to this, the Medical Automoton Efficiency techs give you more efficiency. I don't rememeber the increase off the top of my head, but Infirmaries staffed by max research Automotons generally reach 158% efficiency (though that includes things like Organ Transplants).
It's a lot more complicated than that based on whether or not you have the relevant efficiency techs or not.
A Coal Thumper @ 10 employees adds 65.9/h to the pile, while a Steam Thumper adds 142.3/h. After the Injectors tech, these values are increased by 15% to 75.8/h and 163.6/h.
With 15 people on the Coal Pile itself, you're getting 20.9/h. This is increased by 15% for each of the Gathering techs, to 24/h first, then 27.1/h.
Each Gathering Post @ 10 employees collects, per Pile in range, 27.5/h. This is also increased by the Gathering techs, to 31.6/h first, then 35.8/h.
At full research, to collect 100% of the Thumper's output requires 4.5 Gathering posts (or 3.8 while working the Pile). That totals to 6 work sites whether you work the Pile or use the extra Gathering Post, so would require 6 Automotons to man, which in turn costs 6 Steam Cores.
Coal Mines have 3 levels -- Basic, Steam, and Advanced. With 10 employees, Basic produces 27.6/h -- Steam produces 69/h -- Advanced produces 103.5/h. There are 2 Coal Mining techs, each one increasing the output by 10%. This increases Basic to 30.4/h first, then 33.12. Steam is increased to 75.9/h first, then 82.8/h. Advanced is increased to 113.9/h first, then 124.2/h.
They will cost 1, 2, and 3 Steam Cores respectively, but each one is only a single work site, and as such requires only a single Automoton (and only a single additional Steam Core) to man.
Full utilization for a Steam Thumper complex only produces 39.4 more Coal per hour than a single Advanced Coal Mine. If you are manning them with people, the Steam Thumper will not cost you a single Steam Core, while the Advanced Coal Mine will cost you 3. Using Automotons instead will cost 6 Steam Cores for the Thumper complex, while the Mine will only require 1 additioan Core.
Interestingly, due to the Gathering Post method from the Thumpers, you don't actually need extra Gathering Posts per Thumper -- since the Gathering Posts rate is per pile, you could arrange your Thumpers and rotate them in such a way that the Piles are placed as close together as possible. This gives them a synergistic property when built en masse that is absent from the Coal Mines. Coal Mines are static in this regard. In A New Home, Coal Mines get hit with that event which you can choose to sacrifice population or lose 80% Coal Mine rate as well, where Thumpers do not get affected by this.
So if you are building several Thumpers, it is more efficient, both in manpower and Steam Cores, than Coal Mines. Using all 3 Mine Sites would cost you 12 Steam Cores -- 3 per Advanced Mine, and 1 for each Automoton crew -- where as building 3 Thumpers would still only be 5 Gathering Posts, so 8 Steam Cores. But this also costs you significantly more space, as Thumpers are quite large buildings.
Trade-offs, trade-offs, trade-offs.....