Crystal Mine



A Crystal Mine is a building that mines raw crystals. Crystals are one of the three basic resources that are required to progress in the game.

In-Game Description
 "Crystal mines supply the main resource used to produce electronic circuits and form certain alloy compounds. Mining crystal consumes some one and half times more energy than a mining metal, making crystal more valuable. Almost all ships and all buildings require crystal. Most crystals required to build spaceships, however, are very rare, and like metal can only be found at a certain depth. Therefore, building mines in deeper strata will increase the amount of crystal produced."

Requirements

 * Available from the start

Is Required for

 * N/A

Costs by Level
$$ \text{Cost} = {\text{Base Cost}} \times 1.6 ^ {\text{Crystal Mine Level}- 1} $$

(Base Cost is 48 metal and 24 crystal)

Production
$$ \frac{\text{Crystal}}{\text{hour}} = \text{Acceleration} \times 20\times{\text{Crystal Mine Level}} \times 1.1^{\text{Crystal Mine Level}} $$

Where Acceleration is the economic speed of the universe.

Factoring in Plasma Technology levels and the base Crystal production rate of a planet gives the following formula:

$$ \frac{\text{Crystal}}{\text{hour}} = 15A + 20A(1 + PT \cdot 0.0066) \cdot C \cdot 1.1^{C} $$

$$ A \equiv \text{Acceleration} $$

$$ C \equiv \text{Crystal Mine Level} $$

$$ PT \equiv \text{Plasma Technology Level} $$

Energy Consumption
$$ \text{Energy} = 10 \times{\text{Crystal Mine Level}} \times 1.1^{\text{Crystal Mine Level}}$$

Resource Stat Table: Crystal Mine
NOTE: Information in this table is based solely on the formulas found on this page.

*All Numbers are rounded down except for "Energy Use"'', which is rounded up in order to maintain accuracy with the tested in-game values.  Not all in-game values were tested.''

Production and Profit vs Cost
$$ {\text{Time (hours)}} = {\frac{3}{4 \times \text{Crystal Mine Level}}} \times {\left (\frac{16}{11}\right)} ^ {\text{Crystal Mine Level}}$$

The formula above gives the amount of time in which the total crystal production reaches the cost of that level of the crystal mine. Of course, in universes with economic speeds greater than one, the result must also take the universe speed into consideration. In faster economic universes the production is increased but the cost of mines is stable.



The graph above says that, for example, if you built crystal mine of level 14, it will take 10 hours to take your crystal back which you used to built that level. Crystal mine level 14 costs 10808 crystal, and produces 1063 crystals per hour. Indeed, it takes about 10 hours to take your crystal back, in a 1x speed universe. In a 5x speed, it will take 2 hours to take your crystal back.



Example:

From the graph we observe that if you built crystal mine level 30, it will take it 80 days to produce as much as crystal you used to built that level.

Crystal mine 30 costs 19938419 crystals, and it produces 10469 crystals per hour. That makes 19938419 / 10469 = 1909.52 hours = 79.35 days to produce as much as crystal you used to built crystal mine level 30.

$$ {\text{Time (hours)}} = {{\frac{12}{\text{Crystal Mine Level} + 10}} \times {\left(\frac{16}{11}\right)} ^ {\text{Crystal Mine Level} - 1}}$$

The formula above gives after what hours the profit of upgrading crystal mine adds up to catch the cost of upgrading. In other words, upgrading your crystal mine will cause an increment in your crystal production, if you integrate this increment over time, after some time this integration will be equal to the cost of the upgrading. This formula gives this time period.



The graph above says that, if you upgrade your crystal mine from level 12 to level 13, it will take approximately two days to start harvesting your investment.



From the graph above, we observe that if one upgrades his crystal mine from level 28 to level 29, he will start to make profit out of it after approximately 450 days, for level 35 to level 36 it becomes more than 5000 days!

Note that, all these production and profit calculations are considered only on crystal production. We assume that metal and energy is free. If we were to consider metal and energy issues, the formula would have been multi-variable, and the graphs would have been 4th dimensional. So in order to keep things as simple as possible, it is only explained on crystal production.