Ballistic Projectile Flight Time Calculator

Time of flight (TOF): t = 2·v₀·sin θ / g

When a ballistic projectile leaves and lands at the same elevation, its time of flight in vacuum is t = 2·v₀·sin θ / g, with g ≈ 9.81 m/s². Take a heavy round at v₀ = 800 m/s and θ = 30°: that works out to t ≈ 81.6 s in vacuum. Live fire is a different story. With naval guns, howitzers and long-range rifles, air drag can cut the TOF roughly in half for fast rounds shot at distance. That's why operational ballistic computers don't lean on the closed form. The ones built into WWII battleship fire-control, and the ones running today inside simulators like "Lethal Force", solve the problem numerically using a G7/G1 drag coefficient.

Applications

It comes up in heavy ballistics and naval gunnery, field artillery fire-direction (FDC), sniper engagement timing, missile launch windows, and training simulators like Lethal Force, ArmA and Steel Beasts.

FAQ

Why is the real TOF shorter than the vacuum value? Aerodynamic drag bleeds off velocity the whole way, so both the climb and the fall take less time than the ideal parabola predicts.

What angle maximizes TOF? Straight up, θ = 90°, which gives t = 2·v₀/g. Note that 45° gets you maximum range, not the most time aloft.

Does TOF depend on the projectile mass? In vacuum, no. Once drag enters the picture, heavier projectiles hold their velocity better and stay aloft a little longer.