Nanite Factory



Nanite Factory produces nano-sized robots, which are considered the ultimate achievement in Robotic technology. These are capable of greatly increasing construction speed of buildings, defenses and ships.

In game terms, the Nanite Factory halves the construction time for all buildings, ships, and defense cumulatively for every level that is upgraded. Thus it is the only building which, assuming you don't change your Robotics level past the level 10 requirement, always takes the same time to upgrade (~55h).

Leveling up the factory is useful at the lower levels for drastically cutting down production times. However, keep in mind that defenses and ships never take any longer to build and so the production time decrease is less each subsequent level. For example: A ship that would take 1 hour to build would be decreased 30 minutes after one level, 15 the next, and only 7 and a half after that. Meanwhile, the cost of the factory itself is doubling every level. However, as the building time of a mine doubles every level, it may be a good idea to level up the factory every so often if you want to build high level mines.

While upgrading the Nanite Factory, you cannot build ships or defenses.

Requirements:
 * Robotic Factory Level 10
 * Computer Technology Level 10

Is Required For:
 * Terraformer (Level 1)

Resulting construction time
$$t = \frac{\text{Metal}+\text{Crystal}}{2500\cdot(1 + \text{Robotics Factory Level})\cdot 2^{\text{Nanite Factory Level}}\cdot \text{Universe Speed}}$$.

or shorter

$$t = \frac{1}{2500\cdot(1 + \text{Robotics Factory Level})\cdot \text{Universe Speed}}$$

NOTE : It seems that at least in some universes this value needs to be multiplied by 2/(7 - Current level of the building constructed), until the said building is level 5 (Nanites factories excepted). Can someone confirm this for all universes ?

This formula also works for calculating building times of ships and defences, except that the shipyard level should be filled in for Robotic Factory Level

So the Equation for ship and defense build times would be:

$$t = \frac{Metal + Crystal}{2500*(1 + Shipyard Level)*2^{Nanite Factory Level}* Universe Speed}$$

Since most players once having reached the Nanite Factory stop building Robotic Factory at level 10, to calculate your building time you can use this simplified formula.

Simplified Construction Time
This will only work if the level of your Robotic Factory remains unchanged:

$$ T = \mbox{Displayed Time}\times 0.5^{\mbox{Increase In Nanite Factory}}$$

T is the final time in hours

Displayed Time is the actual time you see in your buildings or shipyard's page

Increase In Nanite Factory is the difference between the Nanite Factory level you have now and the number you'll have as this construction time is attained. For instance, If you have level 5 Nanite Factory and you calculate with 3 as Increase, the time given will be attained with level 8 Nanite Factory.

Examples - 2h(displayed time) x 0.5(fixed rate) ^ 1(lvl1 Nanite Factory) = 1h Construction time,

2h(displayed time) x 0.5(fixed rate) ^ 2(lvl2 Nanite Factory) = 30m Construction time,

2h(displayed time) x 0.5(fixed rate) ^ 3(lvl3 Nanite Factory) = 15m Construction time.

Number of Nanite Factories for a desired resulting time
This formula calculates the Nanite Factory level you'll need to construct something in a certain time. As with the preceding formula, your number of Robotic Factory must remain unchanged.

$$ \mbox{Increase In Nanite Factory}=\log_2 \left (\frac {\text{Displayed Time}} {\text{Desired Time}}\right ) $$

Increase In Nanite Factory is the number of Nanite Factories you'll need to attain the time you want. This number will most likely be a decimal; you will have to round up to achieve at least your desired time. For instance, if the increase is 2.1, building 2 Nanite Factories will get you almost but not quite to your desired time, while building 3 will do even better than your desired time.

Displayed Time is the time you see in the buildings or shipyard page.

Desired Time is the time you want to attain.

Times can be in any unit you like (including seconds, minutes, hours, or days), as long as you use the same unit for both desired and displayed time. To calculate a log in base 2, you can use this online scientific calculator or use the relation:

$$ \log_{2}x=\frac{\ln x}{\ln 2} $$

where $$\ln$$ is the natural logarithm, $$ \log_{e} $$

Time conversion - H:M:S to S
To calculate time in H:M:S display, use this formula:

$$ T = (\text{Days}\times 86400) + (\text{Hours}\times 3600) + (\text{Minutes} \times 60) + \text{Seconds}$$