User:Naya ryo/Turret tracking visualization

This will be the personal draft space for elaborating the idea.

Widget will be released on github or something...

The heatmap of hit chance, from a stationary 200mm Autocannon I without any ammo or skill, tracking an orbitting object.

Visualization formula derivation

It is recommended to read the Turret_mechanics#Hit_chance section beforehand, as this explanation assumes a basic understanding of turret mechanics.

According to the hit chance formula, we have:

$$\begin{gathered} \text{Chance to hit}=0.5^{({\left(\frac{\text{Angular}\times 40,000\text{ m}}{\text{Tracking}\times \text{Signature}}\right)}^2+{\left(\frac{\max (0, \\ \text{Distance}-\text{Optimal})}{\text{Falloff}}\right)}^2)} \end{gathered}$$

To visualize this complex formula intuitively, we apply the following constraints to simplify the setup:

• The attacker is stationary.
• The target is either stationary or moving in a perfect circular orbit around the attacker.
• The scenario takes place on a 2D plane.

First, consider the distance term.

$$\begin{gathered} {\left(\frac{\max (0, \\ \text{Distance}-\text{Optimal})}{\text{Falloff}}\right)}^2 \end{gathered}$$

This term shows that hit chance decreases the further the target is beyond optimal range. This relationship can be visualized along a 1D axis.

Next, consider the tracking term:

${\left(\frac{\text{Angular}\times 40,000\text{ m}}{\text{Tracking}\times \text{Signature}}\right)}^2$

We can visualize the target's orbiting motion as an arc. The length of this arc over one second represents the target’s orbital velocity. For a given orbital velocity, the angular velocity (how quickly the target moves across the turret’s aim) increases as the orbital radius (distance to the attacker) decreases:

$\text{Angular Velocity}=\frac{\text{Orbitting Velocity}}{\text{Orbitting Distance}}$

This means: the closer the target is while orbiting at the same speed, the harder it is for the turret to track.

From this, we can interpret the turret's tracking stat as a kind of "maximum allowable angular velocity" it can handle. Visually, this forms a 2D cone shape where hit chance remains high within the cone and falls off outside of it.

By combining the 1D distance-based falloff term with the 2D angular velocity-based tracking cone, we can visualize the hit chance on a 2D plane using a heatmap.

Examples for parameters change and practical usage (web, TP, tracking computer etc.)

Title 2

Table for different weapon types

Small autocannon v.s. 100 sig static object	Small pulse laser v.s. 100 sig static object	Small blaster v.s. 100 sig static object

Table for different signatures

Small autocannon v.s. 100 sig static object	Small autocannon v.s. static Amarr shuttle	Small autocannon v.s. static Praxis battleship

Table for same weapon category

Small autocannon v.s. 100 sig static object	Small artillery v.s. 100 sig static object	Medium autocannon v.s. 100 sig static object

Title 3

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