CTSFD

Ballistics and Trajectory

Work in progress

This wiki is still being written. Pages are incomplete, numbers may change, and some mechanics are not covered yet.

Rounds fall while they fly and kinetic shells lose penetration with distance travelled. Drop, lead and decay all follow from time of flight and calibre.

Distance in studs

Everything about flight is measured in studs, and every armour value is in millimetres. The two conversions below turn up in almost every formula on this wiki.

ConversionValue
1 metre3.57 studs
1 stud280.112 mm of armour

Shell drop

A shell falls the whole time it is in the air, so the correction you need grows with how long the flight takes. Time of flight is distance over speed, which means drop grows with the square of range and shrinks quickly with muzzle velocity.

t=dvdrop≈12 g t2=12 g(dv)2t = \dfrac{d}{v} \qquad\qquad \text{drop} \approx \tfrac{1}{2}\,g\,t^{2} = \tfrac{1}{2}\,g\left(\dfrac{d}{v}\right)^{2}
Doubling the range roughly quadruples the drop at the same shell speed.

Interactive

Time of flight

0.63 s

Drop

1.9 m

Halving the velocity roughly quadruples the drop at the same distance.

Leading a moving target

A round with any travel time lands behind a moving target unless it is aimed ahead of it. The lead needed is simply the target's speed multiplied by the time of flight.

lead=vtarget×t\text{lead} = v_{\text{target}} \times t
Both drop and lead scale with time of flight, so they grow together as range increases.

Penetration lost over distance

Kinetic shells also lose penetration as they fly. The loss is proportional to how far the round has already travelled and inversely proportional to calibre, so large guns keep their punch at range far better than small ones.

P←max⁡ ⁣(P(1−d Δt200 C), Pmin⁡)P \leftarrow \max\!\left(P\left(1 - \dfrac{d\,\Delta t}{200\,C}\right),\ P_{\min}\right)
d is distance flown in studs and C is calibre in mm. The frame time cancels, leaving a real rate of d over 200C per second.
Pmin⁡={C/3AP, APHE0APDS, APFSDSP_{\min} = \begin{cases} C/3 & \text{AP, APHE} \\ 0 & \text{APDS, APFSDS} \end{cases}
AP and APHE bottom out at a third of their calibre. Sabot rounds keep decaying with no floor.

Note

HE, HESH, HEAT and ATGM do not decay with distance. Their effect is created on contact, so they hit as hard at long range as they do up close. Full details on the penetration page.

Missiles accelerate

Kinetic missiles do not launch at full speed. They start at a fifth of their top speed and build up, and because their penetration is scored on kinetic energy it climbs with the square of their speed fraction as they accelerate.

Pkin(v)=min⁡ ⁣(vvmax⁡, 1)2⋅PP_{\text{kin}}(v) = \min\!\left(\dfrac{v}{v_{\max}},\, 1\right)^{2} \cdot P
A missile that hits before it has spooled up carries a fraction of its rated penetration.

See also

  • Penetration : Whether your round punches through, and how angle and range change it.
  • Shell Types : AP, APHE, APDS, APFSDS, HEAT and HE, and what each one is for.
  • Ricochet and Normalization : Why shots bounce, and how the round bends before they do.
  • Reload : How the base reload turns into the time you actually get in game.
  • Spall and Post-Penetration : Getting through is step one. The fragment cone is what does the damage.