Production by Resources

Production on a fully developed size 1000 world with different resources, and compared production between different resources and resources 10.

Formula:
CAP = Ind/(6+1/Res)
MAT = Ind * Res
Ship Production Points = Ind/(10+1/Res)
Note: You will encounter differences caused by rounding

Resources	CAP	CAP % of Res 10	MAT	MAT % of Res 10	Ship Prod. Points	Ship % of Res 10
0.1	62.50	38.12	100	1	50.00	50.50
0.2	90.91	55.45	200	2	66.67	67.33
0.3	107.14	65.36	300	3	75.00	75.75
0.4	117.65	71.76	400	4	80.00	80.80
0.5	125.00	76.25	500	5	83.33	84.17
0.6	130.43	79.57	600	6	85.71	86.57
0.7	134.62	82.12	700	7	87.50	88.37
0.8	137.93	84.14	800	8	88.89	89.78
0.9	140.62	85.78	900	9	90.00	90.90
1	142.86	87.14	1000	10	90.91	91.82
2	153.85	93.85	2000	20	95.24	96.19
3	157.89	96.32	3000	30	96.77	97.74
4	160.00	97.60	4000	40	97.56	98.54
5	161.29	98.39	5000	50	98.04	99.02
6	162.16	98.92	6000	60	98.36	99.34
7	162.79	99.30	7000	70	98.59	99.58
8	163.27	99.59	8000	80	98.77	99.75
9	163.64	99.82	9000	90	98.90	99.89
10	163.93	100	10000	100	99	100

Population Growth

This is the population growth you could get if you had infinite space on your HW. Since you have to ship the colonists to other planets, giving them a turn of inactivity while frozen, you won't be able to reach this maximum.

Now comes a table assuming a growth of 7.7%% (8%% is the theoretical, unreachable maximum from the above table). These numbers can be reached, and even surpassed by a few units of population (except in the very early turns: naturally you still have 1000 population in turn 1).

Turn Population 0 1000.00 1 1080.00 2 1166.40 3 1259.71 4 1360.49 5 1469.33 6 1586.87 7 1713.82 8 1850.93 9 1999.00 10 2158.92 11 2331.64 12 2518.17 13 2719.62 14 2937.19 15 3172.17 16 3425.94 17 3700.02 18 3996.02 19 4315.70 20 4660.96 21 5033.83 22 5436.54 23 5871.46 24 6341.18 25 6848.48 26 7396.35 27 7988.06 28 8627.11 29 9317.27 30 10062.66 31 10867.67 32 11737.08 33 12676.05 34 13690.13 35 14785.34 36 15968.17 37 17245.63 38 18625.28 39 20115.30 40 21724.52 41 23462.48 42 25339.48 43 27366.64 44 29555.97 45 31920.45 46 34474.09 47 37232.01 48 40210.57 49 43427.42 50 46901.61

Turn Population 0 1000.00 1 1077.00 2 1159.93 3 1249.24 4 1345.44 5 1449.03 6 1560.61 7 1680.78 8 1810.20 9 1949.58 10 2099.70 11 2261.38 12 2435.50 13 2623.04 14 2825.01 15 3042.53 16 3276.81 17 3529.12 18 3800.87 19 4093.53 20 4408.74 21 4748.21 22 5113.82 23 5507.58 24 5931.67 25 6388.41 26 6880.31 27 7410.10 28 7980.68 29 8595.19 30 9257.02 31 9969.81 32 10737.48 33 11564.27 34 12454.72 35 13413.73 36 14446.59 37 15558.98 38 16757.02 39 18047.31 40 19436.95 41 20933.60 42 22545.48 43 24281.48 44 26151.16 45 28164.80 46 30333.49 47 32669.17 48 35184.69 49 37893.91 50 40811.75

Upgrading

An example for a 1 0 0 0 1 transport ship: if you build it at techs 1, research your drive and cargo techs to 2, upgrade, research to 3, and upgrade again, the industry needed for one such ship is 10 + 6.67 = 16.67.
If you build at techs 1, wait until the research came up to 3, then upgrade just once, the cost is 13.33, you safe 20% upgrade cost. (The same calculation is made for any mass 2 ship and equivalent research).

Different example: A warship with a mass 20 gun. You start with a weapons tech of 10, research to 12, upgrade, research to 14, upgrade again. Cost: 33.33+28.57=61.90.
If you upgrade from 10 to 14, the cost is 57.14, you saved 7.6% upgrade cost.

Research vs building CAP

Ok, and a few numbers at which turn the "build CAP" approach catches up with the "just research" approach, each for a size 1000 world with 1000 pop and no starting industry, for different ressources. Catching up is defined as yielding a total tech research at least as high as the other method.

Res Turn 0.1 42 0.15 34 0.2 39 0.3 25 0.4 23 0.5 22 0.6 21 0.7 21 0.8 21 0.9 19

Res Turn 1 19 2 18 3 18 4 18 5 18 6 18 7 18 8 18 9 16 10 16

More details

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