High Trajectory Projectile Height Calculator

Apex of high-angle fire: h_max = (v₀·sin θ)² / (2g)

With high-angle (indirect) fire you pick a launch angle somewhere between 45° and 85°, and the round arcs over whatever is in the way: a ridge, a wall, a row of buildings. In vacuum the top of that arc sits at h_max = (v₀·sin θ)² / (2g). Take a standard 81 mm mortar bomb. It leaves the tube at around 250 m/s, and if you fire it near 80° the apex lands somewhere around 4–5 km up before the bomb drops almost straight down onto the target. The 105 mm M119 howitzer and the 105 mm OTO Melara throw lighter rounds at a higher muzzle velocity, so their apex altitudes often clear 6 km once the gun is set for high-angle work.

Applications

Field artillery fire-direction (M119 105 mm, OTO Melara 105 mm Pack), mortar gunnery in the 60/81/120 mm range, Brazilian Army artillery training, and defilade fire that has to clear hills, buildings or trenches.

FAQ

Why use high-angle instead of flat trajectory? Two reasons. It gets the round over terrain masks like reverse-slope positions and urban canyons, and it lets you reach targets that are dug in against direct fire.

Does the apex depend on mass? In vacuum, no. Once you add drag the picture shifts a bit, since denser projectiles bleed off less energy and climb slightly higher.

What angle gives the highest apex? θ = 90°, straight up, though that throws away all your range. In practice mortar crews trade apex against how far the target is, which usually lands them at 70°–80°.