Artillery Mechanics & Ballistics

Name: WardogTools.gg
Author: WardogTools.gg

This chapter breaks down the mathematical equations used in the WardogTools.gg artillery calculator. Artillery in Wardogs (both infantry Mortars and heavy Self-Propelled Howitzers like the SPH-2) operates on parabolic ballistics governed by angular mil measurements, gravitational acceleration, horizontal drag decay, and topographical terrain differences.

1. Spatial Coordinate System & Geometry

Every position in the game world is expressed in standard Euclidean three-dimensional coordinates:

\text{Point} = (x, y, z)

Where $x$ represents the East-West horizontal axis, $y$ represents the North-South horizontal axis, and $z$ represents vertical elevation Above Sea Level (ASL). In the Unreal Engine client coordinate system, 1 Unreal Unit (UU) = 1 centimeter = 0.01 meter.

The planar horizontal distance $d$ between firing battery $(x_b, y_b)$ and target $(x_t, y_t)$ is:

d = \sqrt{(x_t - x_b)^2 + (y_t - y_b)^2}

When evaluating direct laser rangefinder line-of-sight measurements, the 3D slant range is:

d_{\text{slant}} = \sqrt{d^2 + (z_t - z_b)^2}

2. In-Game Compass (360°) vs. NATO STANAG 4119 Angular Mils

The in-game compass operates in standard $360^\circ$ bearings, while indirect-fire artillery weapon systems and optics evaluate elevation in the NATO STANAG 4119 angular system dividing a circle into 6,400 angular mils (milliradians):

360^\circ = 6,400\text{ mils} \implies 1\text{ mil} = \frac{360^\circ}{6400} = 0.05625^\circ

The Field Artillery Rule of Thumb (1-in-1000)

The 6,400-mil system is designed for direct mental arithmetic in the field:

\text{Lateral Deviation} \approx \text{Distance (km)} \times \text{Deflection (mils)}

At a range of 1,000 meters, an azimuth deflection of 1 mil produces exactly 1 meter of lateral shell displacement on the ground.

To convert world Cartesian coordinates into an azimuth bearing, the two-argument arctangent ( $\operatorname{atan2}$ ) with clockwise grid-north orientation is computed:

\theta_{\text{deg}} = \left(\operatorname{atan2}(x_t - x_b, y_t - y_b) \times \frac{180}{\pi} + 360\right) \pmod{360}

\text{Azimuth}_{\text{mil}} = \operatorname{round}\left(\frac{\theta_{\text{deg}}}{360} \times 6400\right)

3. Ballistic Tables & Piecewise Linear Interpolation (PLI)

The game client defines empirical firing tables mapping flat horizontal distance to required tube elevation in mils:

Artillery Platform	Range Envelope	Elevation Range	Trajectory Arc
Infantry Mortar	132m — 684m	150 — 850 mils	High Parabolic Arc Only
SPH-2 Howitzer	780m — 2,629m	20 — 1,390 mils	Dual: Low Arc & High Arc

Between any two calibrated table entries $(d_1, m_1)$ and $(d_2, m_2)$ , the baseline elevation angle is calculated via piecewise linear interpolation:

\text{Elevation}_{\text{base}}(d) = m_1 + \left(\frac{d - d_1}{d_2 - d_1}\right) \times (m_2 - m_1)

4. The Downhill Trajectory Paradox & Equivalent Flat Range

Why Direct Angle of Site (AOS) Fails

In direct-fire flat-trajectory rifle marksmanship, vertical target displacement is compensated by adding the Angle of Site ( $\text{AOS} = \operatorname{atan2}(\Delta z, d)$ ).

In high-angle mortar artillery, shells lob at steep descent angles ( $60^\circ$ to $80^\circ$ ). When firing downhill ( $\Delta z < 0$ ), the shell does not impact at flat ground elevation; it continues downward along its terminal descent vector, traveling further downrange. Subtracting AOS causes shells to severely overshoot. Furthermore, on mortars, higher elevation mils raise the tube toward vertical, shortening range.

To solve this, the fire-control engine derives the terminal descent angle $\omega$ at impact:

\omega_{\text{mortar}} \approx \frac{1}{2}\left(\pi - \arcsin\left(\frac{d}{d_{\max}}\right)\right)

\omega_{\text{low}} \approx \frac{1}{2}\arcsin\left(\frac{d}{d_{\max}}\right) \quad \text{(SPH-2 Low Arc)}

\omega_{\text{high}} \approx \frac{1}{2}\left(\pi - \arcsin\left(\frac{d}{d_{\max}}\right)\right) \quad \text{(SPH-2 High Arc)}

The horizontal carry adjustment and the equivalent flat-ground range $d_{\text{equiv}}$ are:

\Delta d_{\text{carry}} = \frac{\Delta z}{\tan(\omega)}

\mathbf{d_{\text{equiv}} = d + \frac{\Delta z}{\tan(\omega)}}

Worked Downhill Example:

Target distance: $d = 400\text{m}$
Elevation drop: $\Delta z = -50\text{m}$ (target in a valley)
Terminal descent angle: $\omega \approx 70^\circ \implies \tan(70^\circ) \approx 2.747$
Carry offset: $\Delta d = \frac{-50}{2.747} \approx -18.2\text{m}$
Equivalent flat range: $d_{\text{equiv}} = 400 - 18.2 = 381.8\text{m}$
Result: Because $381.8\text{m} < 400\text{m}$ , looking up this range in the ballistic table yields a higher (+) elevation mil value. Raising the mortar tube causes the round to drop earlier, striking the valley floor dead-on target.

5. Time of Flight (ToF) Mechanics

Time of Flight is evaluated from the average horizontal projectile velocity:

t_{\text{tof}} = \frac{d}{\bar{v}_{\text{horizontal}}}

Mortar Velocity Profile

Average horizontal speed: ~75 m/s

132m → 1.8 seconds flight time

684m → 9.1 seconds flight time

SPH-2 Velocity Profile

Average horizontal speed: ~240 m/s

780m → 3.2 seconds flight time

2,629m → 11.0 seconds flight time

Put the Ballistics into Action

Experience real-time indirect fire calculations on live topographical maps

The interactive artillery solver runs these piecewise tables and downhill carry adjustments instantly with real-time sub-pixel elevation sampling.

Launch Artillery Fire-Control