Nano-Active Hull

The Nano-Active Hull utilizes Polytechnic Federation Technology to employ trillions of nano-bots that repair segments of the hull during warp travel.

Stats
* Only achievable with the unique Comet Shop processors

** Only achievable with additional PWR-48 from Relic Hunters

Formula for Repair
The amount repaired depends on the maximum hull capacity and the hull integrity before jump. The equation for hull integrity after a jump is given by:

$$Hf = 0.8*Hi + 0.2*Hmax$$

where Hf is the hull after the jump, Hi is the hull before the jump, and Hmax is the total hull capacity. This equation holds for all levels of the nano-active hull. For example, suppose you have 200/3000 hull prior to jump. After 1 jump, the hull will be:

$$Hf = 0.8*(200) + 0.2*(3000) = 760$$ (560 hull repaired)

For the next jump:

$$Hf = 0.8*(760) + 0.2*(3000) = 1208$$ (448 hull repaired)

As you can see, the higher your initial hull, the less it repairs. In the event of a decimal result, the game uses standard rounding (53.4 = 53, but 53.5 = 54).

Another way to think of this is by terms of how much hull is repaired per jump;

If $$Hf=0.8Hi + 0.2Hmax$$

Then $$Hf-Hi = 0.2 * (Hmax - Hi)$$

So, the amount healed per jump is 20% of the amount missing.

Formula:

$$New\,Integrity=Old\,Integrity+(Max\,Integrity-Old\,Integrity)*0.2$$