How It Works

Here is everything EliteRange's ballistic engine accounts for between the moment you press the trigger and the moment the bullet reaches the target. Every parameter below has a real effect on the trajectory, and the engine combines them all to solve the firing solution.

The calculation relies on a step-by-step numerical integration of the trajectory (adaptive Runge-Kutta 4-5 method): the path is rebuilt point by point, applying at each instant the real physical forces acting on the bullet.

Environmental parameters

The conditions of the moment

Parameter	Unit	Why it matters
Air temperature	°C	Warm air is less dense: less friction on the bullet, so it slows down less and flies farther at the same speed.
Atmospheric pressure	hPa	Denser air under high pressure creates more drag. It is one of the three factors that make up air density.
Relative humidity	%	Counter-intuitively, humid air is slightly less dense than dry air, because water vapour is lighter than air. It also affects the speed of sound.
Altitude	m	Sets the reference pressure when no local measurement is provided, using the standard atmospheric model.
Wind speed	m/s	Pushes the bullet sideways throughout its entire time of flight: the longer the flight, the greater the drift.
Wind direction (relative to the line of sight)	°	A crosswind drifts the bullet; a head or tail wind mainly changes its residual velocity. The engine breaks the wind vector down along this angle.
GPS latitude	°	Required to compute the Coriolis effect, the deflection caused by the Earth's rotation: negligible at short range, measurable at very long range.
Firing azimuth (rifle orientation)	°	Combined with latitude, it determines the direction and magnitude of the Coriolis effect.

Ammunition parameters

The cartridge and its bullet

Parameter	Unit	Why it matters
Bullet weight	grains	Determines inertia: at equal ballistic coefficient, a heavier bullet resists air deceleration better, but reacts less to the same powder energy.
Muzzle velocity	m/s	The starting point of the whole trajectory, and the single most decisive variable for range and time of flight.
Ballistic coefficient (BC, G1 or G7 model)	unitless	Sums up the bullet's ability to keep its speed against the air. The G7 model represents modern, long, pointed bullets better than G1.
Drag curve Cd(Mach)	table of points	When available (measured in a wind tunnel or supplied by the manufacturer), it replaces the BC with a real drag curve as a function of speed: more accurate than a single BC, especially in the transonic region.
Bullet diameter	mm	Determines the frontal area exposed to the air (drag) and feeds into the spin-drift calculation.
Bullet length	mm	Feeds into the gyroscopic-stability calculation: a long, thin bullet is harder to stabilise than a short one.
Ammunition temperature	°C	Powder burns faster when hot: with an identical load, a cartridge left in the sun leaves faster than one taken from a cooler.

Weapon parameters

The rifle and its scope

Parameter	Unit	Why it matters
Scope height above the bore	mm	The line of sight and the bullet's actual path do not start from the same point; this offset must be compensated, especially at short range.
Zeroing distance	m	The distance at which the scope and the point of impact coincide: it serves as the reference for computing the barrel's launch angle.
Barrel twist (twist rate)	inches per turn	Sets the spin rate given to the bullet as it leaves the barrel, a necessary condition for its stability in flight.
Twist direction	right / left	Determines the direction of the spin drift (right or left), not just its magnitude.

Shot parameters

The geometry of the shot

Parameter	Unit	Why it matters
Distance to target	m	Defines how far the trajectory integration must be computed.
Look angle (uphill or downhill shot)	°	Gravity acts differently on a bullet fired flat, uphill or downhill. Ignoring this angle systematically makes you aim too high or too low on hilly or mountainous terrain.

The physical phenomena simulated in flight

What the engine applies at every instant of the trajectory

Phenomenon	What it is
Gravity	The bullet drops the moment it leaves the barrel; its fall is resolved along the look angle for angled shots.
Drag (air friction)	The force that slows the bullet, computed from the BC or the real drag curve and the current air density. It is the dominant effect on speed loss.
Variable air density	Continuously recomputed from temperature, pressure and humidity: never a fixed value.
Speed of sound (humid air)	Computed precisely rather than taken as a constant, because it sets the bullet's Mach number, which directly influences its drag, notably through the transonic region where the bullet's behaviour becomes less stable.
Spin drift	The rotation that stabilises the bullet also produces a slow lateral drift, cumulative over distance and all the more pronounced the longer the shot.
Aerodynamic jump	A crosswind at the instant the shot breaks, combined with the bullet's rotation, produces a small initial vertical offset, distinct from ordinary wind drift.
Coriolis effect	Deflection caused by the Earth's rotation: tiny at short range, measurable beyond several hundred metres depending on latitude and firing azimuth.
Spin decay	The bullet's rotation speed decreases slightly during flight under friction, which is accounted for when the ammunition has a complete data curve.
Gyroscopic stability (Sg)	Computed and displayed: it indicates whether the bullet spins fast enough, given its length and weight, to stay stable in flight under current conditions. Cold, dense air demands more stability than warm air.

Automatically computed values

Results, not inputs

Current Mach numberat each distance
Residual velocityof the bullet at each distance
Time of flight
Remaining kinetic energy
Barrel launch anglesolved automatically so the bullet passes through the zero point, recomputed when conditions change
Gyroscopic stability factorat the moment the shot breaks