Useful Formulae

Warp-in Points

A warp-in point is where your ship will land in space when warping to an object.

Many external factors may disrupt a warp, e.g. warp disruption fields, insufficient electrical capacity, warp jitter, etc.; these formulas do not account for these phenomenas, they assume perfect conditions.

Ordinary Objects

An ordinary object is any object that does not fall withing any of the other categories described below.

Let the 3D vectors $p_d$ and $p_s$ represent the object’s position and the warp’s origin, respectively; and $\vec{v}$ the directional vector from $p_s$ to $p_d$. Let $r$ be the object’s radius.

The object’s warp-in point is the vector $p_s + \vec{v} - r\hat{v}$.

Large Objects

A large object is any celestial body whose radius exceeds 90 kilometres (180 kilometres in diameter), except planets.

Let $x$, $y$, and $z$ represent the object’s coordinates. Let $r$ be the object’s radius.

The object’s warp-in point is the vector $\left(x + (r + 5000000)\cos{r} \\, y + 1.3r - 7500 \\, z - (r + 5000000)\sin{r} \\ \right).$

Planets

The warp-in point of a planet is determined by the planet’s ID, its location, and radius.

Let $x$, $y$, and $z$ represent the planet’s coordinates. Let $r$ be the planet’s radius.

The planet’s warp-in point is the vector $\left(x + d \sin{\theta}, y + \frac{1}{2} r \sin{j}, z - d \cos{\theta}\right)$ where:

d = r(s + 1) + 1000000

 \theta = \sin^{-1}\left(\frac{x}{|x|} \cdot \frac{z}{\sqrt{x^2 + z^2}}\right) + j

 s|_{0.5 \leq s \leq 10.5} = 20\left(\frac{1}{40}\left(10\log_{10}\left(\frac{r}{10^6}\right) - 39\right)\right)^{20} + \frac{1}{2}


Now, $j$ is a special snowflake. Its value is the Python equivalent of
(random.Random(planetID).random() - 1.0) / 3.0.

Example Implementation

import math
import random

def warpin(id, x, y, z, r):
j = (random.Random(id).random() - 1.0) / 3.0
t = math.asin(x/abs(x) * (z/math.sqrt(x**2 + z**2))) + j
s = 20.0 * (1.0/40.0 * (10 * math.log10(r/10**6) - 39))**20.0 + 1.0/2.0
s = max(0.5, min(s, 10.5))
d = r*(s + 1) + 1000000

return (x + d * math.sin(t), y + 1.0/2.0 * r * math.sin(j), z - d * math.cos(t))


Skillpoints

Skillpoints needed per level

The skillpoints needed for a level depend on the skill rank.

 y_{skillpoints} = 2^{2.5(x_{skilllevel}-1)} \cdot 250 \cdot r_{skillrank}


Skillpoints for common ranks

RankLevel 1Level 2Level 3Level 4Level 5
1 250 1.414 8.000 45.254 256.000
2 500 2.828 16.000 90.509 512.000
3 750 4.242 24.000 135.764768.000
4 1.0005.656 32.000 181.0191.024.000
5 1.2507.071 40.000 226.2741.280.000
6 1.5008.485 48.000 271.5291.536.000
7 1.7509.899 56.000 316.7831.792.000
8 2.00011.31364.000 362.0382.048.000
9 2.25012.72772.000 407.2932.304.000
102.50014.14280.000 452.5482.560.000
112.75015.55688.000 497.8032.816.000
123.00016.97096.000 543.0583.072.000
133.25018.384104.000588.3123.328.000
143.50019.798112.000633.5673.584.000
153.75021.213120.000678.8223.840.000
164.00022.627128.000724.0774.096.000

Skillpoints per minute

The skillpoints generated each minute depend on the primary $(a_{primary})$ and secondary attribute $(a_{secondary})$ of the skill.

y_{skillpointsPerMinute} = a_{primary} + {a_{secondary} \over 2}


Combat

Target lock time

The target lock time ($t_{targetlock}$) in seconds depends on the ship’s scan resolution ($s$) and the target’s signature radius ($r$)

t_{targetlock} = {40000 \over s \cdot asinh(r)^2}


Alignment time

The ship alignment time (t_{align}) depends on the ship’s inertia modifier ($i$) and the ships mass ($m$)

t_{align} = { ln(2) \cdot i \cdot m \over 500000 }