On a 4-axis cutter the hot wire is a straight line between two tower planes — and your foam block sits somewhere between them, never touching either (belts, bearings and rails live there). That one fact has a consequence every wing cutter discovers eventually: the shapes the towers drive are not the shapes that appear on the foam.
The problem
Say you cut a tapered wing: big root profile, small tip profile. If the towers simply drove the root and tip outlines, the wire would form those shapes at the tower planes — and your foam faces, sitting somewhere in the middle, would each receive a blended, shrunken in-between profile. The bigger the gap between tower and face, the worse the error. (On a straight constant-profile cut both tower paths are identical, the wire sweeps a prism, and there is no error at all — which is why nobody notices until their first tapered wing.)
The fix: project the faces out to the towers
The designed profiles belong on the foam faces. For every synchronised point pair, extend the straight wire line through both face points outward and solve where each tower must be:
T1 = P1 + (P1 − P2) × d1 / w T2 = P2 + (P2 − P1) × d2 / w
- P1, P2 — designed points on the near / far foam face
- w — block width along the wire (your Z size in the Material block panel)
- d1 — gap from the left tower to the near face (your Z offset)
- d2 — gap from the far face to the right tower (tower span − d1 − w)
- T1, T2 — where the towers actually move
The towers trace larger, distorted versions of the profiles — overshooting on purpose — and the straight wire passing through the block delivers exactly the right shapes at the faces.
The pinch in the preview: the crossover point
Watch a tapered wing cut in the 3D preview and the wire's swept ribbon does something startling on the small-profile side: it narrows to a point and re-opens inverted before reaching the tower. That pinch is not a bug — it is the projection's signature, and it is exactly what the machine must do:
Extend a tapered wing past its tip and the chord keeps shrinking — at w·c_root/(c_root−c_tip) beyond the root face it reaches zero (the apex of the cone the wing belongs to). Every straight wire line passes through that neighbourhood. If the apex falls in the gap between the far foam face and the tower — which happens whenever the taper is strong and the gap is generous — the tower path passes through zero size and comes out the other side mirrored: the U/V tower traces a tiny, upside-down copy of the profile. The wire still sweeps exactly the right surface through the foam; only the empty-air part of the sweep crosses itself.
- It is correct. The part only exists between the faces — everything outside is the wire travelling through air.
- It explains the "wrong-looking" tower numbers. On a strongly tapered panel the small-side tower can legitimately travel less than the tip profile, or move opposite to it.
- Straight wings have no pinch — equal profiles make the wire lines parallel, the apex sits at infinity, and both towers trace the profile 1:1.
- The pinch never sits inside the foam. It lives beyond the small face, in the extension of the part — by the time the taper reaches zero you are outside the block by definition.
What cncfoam.com does automatically
Every generated shape — wings, gears, wall panels, hypars, characters, AI shapes, and two-profile morphs from the Load-parts dialog — is designed on the foam faces and projected to tower paths automatically, using your machine's tower span (⚙ Settings → the L→R distance) and the material block's Z size + Z offset. Move or resize the block and the toolpath re-projects live — the faces always receive the designed profiles, wherever the block sits. Straight cuts and rotation cuts drive both towers identically, so projection passes them through unchanged. The block-side preview windows show the proof: the profile on each foam face matches the design, while the 3D wire visibly swings wider at the towers.
Two things follow from the maths, and the tool warns about each:
- Towers out of bounds — projection amplifies every root↔tip difference by the gap-to-width ratio. A strongly tapered part in a narrow block far from the towers can demand more tower travel than your machine has. The fit-warning tells you by how much.
- Large amplification — when the gaps are much bigger than the block width (over ~1.5×), an advisory appears: the cut is still correct, but tower travel and any mechanical slop are multiplied with it.
Block placement rules of thumb
- Centre the block between the towers (the "Center material on machine" button does it in one click) — it splits the amplification evenly.
- Keep the gaps small relative to the block width. A 300 mm block centred in an 850 mm span (gaps ≈ 275 mm each) roughly doubles the root↔tip differences at the towers — normal and fine. The same block pushed against one tower puts ×3 on the far side.
- For strongly tapered panels, a wider block (cut two panels from one block) reduces the ratio more effectively than anything else.
Feed rate is face-referenced too
Your feedrate setting is the speed of the wire through the foam, not the tower speed. Since the projected tower paths are longer than the face paths, the exported G-code raises each cutting line's F by that move's tower:face travel ratio — so the foam always sees the set feedrate and the kerf stays constant root→tip on tapered panels. (Without this, the tip side of a tapered wing cuts slower and melts a wider kerf exactly where the part is thinnest.) Travel moves outside the foam stay at the plain feedrate. The cut-time and contour numbers in the status panel are face-referenced for the same reason.
Imported G-code
Imported G-code is never re-projected — files from other CAM are assumed to already contain tower coordinates, exactly as saved. The simulator's block-face previews, cut time and melt checks still evaluate them at the foam faces, so you can verify what a foreign file really cuts before running it.
Related
See the material block & envelope for the block controls, Morphing two profiles for the 4-wire mechanism, and the wing generator where projection matters most. For the shareable story version of this page, see Why your foam cutter's towers cut an upside-down wing.