An AFP head lays parallel courses of composite tow (fixed physical width w) that follow a steered, curved reference path across a doubly-curved tool surface — here a fuselage panel. Each course is offset from the reference course by a normal distance c·w (course index c).
Offsetting a curved path along its normal does not preserve arc-length spacing: a course on the outside of a bend must cover more surface than the tow material provides, while the inside is compressed. To first order, the local gap or overlap between adjacent courses is
κ(t) = (x'y'' − y'x'') / (x'² + y'²)^1.5 (signed path curvature)
defect(t, c) ≈ w² · κ(t) · c (mm, +gap / −overlap)
where x(t), y(t) is the steered reference path (a sinusoidal steering law here, controlled by amplitude and frequency) and w is the tow width. This is the same first-order geometric argument used to size steered courses in real AFP process planning: the further a course sits from the reference (larger c) and the sharper the local turn (larger |κ|), the bigger the defect.
- Steering amplitude / frequency — how sharply the reference course bends, i.e. how much curvature κ(t) the head must follow.
- Tow width — the physical tape width w; wider tow amplifies defects for the same curvature.
- Tolerance — the maximum gap/overlap (mm) the process spec allows before a segment is flagged (yellow = gap, red = overlap).
- Feed rate — how fast the head advances along each course (visual playback speed).
Real AFP machines fight this with course splitting, tow drop/add (cutting individual tows mid-course) or fibre steering algorithms — all trade-offs this simplified model exposes directly: flatten the steering and defects vanish; steer hard with wide tow and they spread.