Why your foam cutter's towers cut an upside-down wing
Cut a tapered wing on a 4-axis machine and watch the far tower: it traces a tiny aerofoil — inverted. Meanwhile the near tower draws a profile much bigger than your root chord. Neither tower draws the wing you designed. And if they did, your wing would come out wrong.
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The setup everyone forgets
A hot wire is a straight line between two tower planes — and your foam block sits somewhere between them. It physically can't touch either tower: that's where the belts, bearings and rails live. So the shapes you care about exist on the foam faces, while the machine only ever drives the towers. Those are different places — and on any cut where the two profiles differ (taper, sweep, washout, any morph), they demand different shapes.
Drive the towers with your root and tip outlines directly and the wire delivers blended, shrunken in-between profiles at the faces. Constant-chord wings hide the error completely (both tower paths are identical, so there is nothing to blend) — which is exactly why most people never notice until their first strongly tapered panel comes out wrong at the tip.
The fix bends the paths outward — sometimes through zero
Correct CAM extends every straight wire line through both face points outward to the tower planes — tower projection. The towers trace amplified, distorted versions of the profiles, and the wire passing through the block delivers exactly the designed shapes at the faces. Here is where it gets beautiful:
Extend a tapered wing past its tip and its chord keeps shrinking — it hits zero a fixed distance past the root face (the apex of the cone the wing belongs to). Every wire line converges toward that point. When the apex falls in the air gap between the far foam face and the tower — strong taper, generous gap — the projected tower path passes through zero size and comes out the other side mirrored. The far tower really does cut a tiny, upside-down wing. In empty air. While the foam, between the faces, receives exactly the aerofoils you asked for.
What this means for your machine
- If your CAM never asks where the block sits (offset from a tower + block width), it cannot be projecting — every tapered panel it has ever produced is blended toward the mean. Slightly wrong root, slightly wrong tip, washout diluted.
- Feed rate needs the same treatment. The towers travel farther than the faces, so a fixed F means the wire crosses the foam slower than you set — and kerf grows at the tip, exactly where the part is thinnest. The F on each cutting line should rise by that move's tower:face ratio.
- Tower travel is the price. Projection amplifies every root↔tip difference by the gap-to-width ratio. Keep the block roughly centred and the gaps smaller than the block width, or watch your machine run out of axis.
Or let the tool do it
cncfoam.com does all of the above automatically: shapes are designed on the foam faces, projected to tower paths for your block position (moving the block re-projects live), with face-referenced feed compensation per cutting line — and the 3D preview shows the crossover happening, which is honestly half the fun. The deep-dive lives in the wiki: tower projection.