Missile Interception & Proportional Navigation

Sailors have known this for centuries: if another ship stays on the same compass bearing while getting closer, you are going to collide. The line of sight between you never rotates — you are both sliding down two sides of a shrinking triangle whose shape stays fixed. Proportional navigation turns that observation into a control law. It measures how fast the line-of-sight angle is rotating (λ̇) and commands a lateral acceleration proportional to it: a_cmd = N · V_c · λ̇. Drive λ̇ to zero and the bearing is frozen — intercept guaranteed, without ever predicting where the target will be. The navigation ratio N (usually 3–5) sets how hard it corrects. Pure pursuit, by contrast, simply points the nose at the target; against anything that crosses your path it forces an ever-tighter turn and loses the race. Every modern air-to-air and surface-to-air missile flies proportional navigation.

A puppy chasing a thrown ball runs straight at wherever the ball is right now, so it always curls in behind and arrives late. A person catching it does the opposite: they move so the ball holds a steady angle in their view and meet it where it will be. Flip this tool between Pure Pursuit and proportional navigation to feel that difference — against a crossing target, aiming at the current position always costs a longer, tighter, losing path.

Long before guidance engineers, dragonflies were flying proportional navigation. High-speed footage shows a hunting dragonfly steers to keep its prey pinned at a fixed angle against the background — exactly the constant-bearing trick behind a_cmd = N · V_c · λ̇ — and it does so with a brain smaller than a grain of rice, capturing prey on well over 90% of attempts. Evolution found this collision geometry roughly 300 million years before the first homing missile.