Trajectory Calculation

Launch angle 45°

Muzzle velocity 220 m/s

Drag coefficient 0.30

Crosswind 0 m/s

Range

0 m

Apex height

0 m

Time of flight

0.0 s

Impact speed

0 m/s

How it works

The projectile is integrated frame-by-frame under gravity, quadratic air drag opposing its velocity, and a steady crosswind. The dashed grey curve is the ideal drag-free parabola for comparison — the gap between the two shows exactly how much energy drag removes from the flight.

a = g + wind_accel − (Cd·ρ·A / 2m) · |v| · v
x(t+dt) = x(t) + v(t)·dt
range = x at the moment y returns to 0

Launch angle — elevation of the barrel above the horizontal; range peaks near 45° only in vacuum, lower with drag.
Muzzle velocity — initial speed leaving the barrel.
Drag coefficient — how strongly air resistance decelerates the shell; 0 reproduces the vacuum parabola exactly.
Crosswind — lateral wind that deflects the shell sideways over the flight, visible as curvature away from the vertical firing plane.

This is the same numerical approach real fire-control computers use: since drag makes the equations of motion have no closed-form solution, they step the trajectory forward in small time increments rather than using the textbook range formula.

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