Proportional navigation (PN) is the guidance law almost every homing interceptor and many orbital-rendezvous autopilots use: steer so the line of sight (LOS) to the target stops rotating. If the LOS never rotates, chaser and target are on a pure collision course.
r = target_pos − chaser_pos
v_rel = target_vel − chaser_vel
Vc = −(r · v_rel) / |r| (closing velocity)
ωz = (rx·vrel_y − ry·vrel_x) / (r · r) (LOS rotation rate, scalar in-plane)
a_cmd = N′ · Vc · ωz · perp(v̂_chaser) (commanded lateral accel, perp(x,y)=(−y,x))
This engagement is planar, so the full 3D law's cross products (ω = r×v_rel, a_cmd = N′·Vc·(ω×v̂)) collapse exactly to the scalar/perp form above — same physics, same numbers, just worked in the plane the intercept actually happens in.
N′ is the navigation constant (typically 3–5): it multiplies how aggressively the autopilot reacts to LOS rotation. Too low and the chaser cannot keep up with a maneuvering target; too high amplifies sensor noise and can saturate the thrusters against the g-limit below.
- N′ slider — navigation constant in the law above.
- g-limit — maximum lateral acceleration the autopilot can command; when the ideal a_cmd exceeds it, the vector is clamped to this magnitude (readout turns amber and the LOS rate stops being nulled).
- Initial aim error — the chaser's starting heading offset from a perfect collision course, so you can see PN converge from a bad start.
- Straight / Weave / Break-turn — target flight profile. A weaving or break-turning target keeps producing new LOS rotation that N′ must fight; watch the LOS-rate readout spike on a break-turn.
- Drag / scroll the plot — pan and zoom the top-down engagement view manually; it no longer auto-frames once you touch it, use Re-center View to snap back.
Real-world relevance: this exact law (or its "augmented" variant that also feeds forward target acceleration) guides missile terminal homing, and a slowed-down, delta-v-limited version of it is used for autonomous orbital rendezvous and active-debris-removal final approach.