Each shell obeys Newton's second law under gravity and quadratic aerodynamic drag: m·dv/dt = -m·g − ½·ρ·Cd·A·|v|·v where A = π(d/2)² is the cross-sectional area set by caliber d, and Cd is the drag coefficient. The ballistic coefficient BC = m / (Cd·A) measures how well a shell resists drag deceleration: larger, heavier calibers have a higher BC, so they shed velocity more slowly and can outrange a smaller shell fired at the same muzzle velocity — the core caliber-selection trade-off between payload/mass and range explored in the article. Trajectories are integrated numerically (semi-implicit Euler, small fixed time-step) rather than the flat parabola formula, so drag curvature is visible even at high elevation.