Loudspeaker Lab
Loudspeaker Lab
The abrasive alternates shade once per turn so you can count the wraps. Orange marks the two angled cuts — note how each one lies flat along the rim rather than running off the end of the drum.
The drum surface cut open along one line and laid flat. This is the view that shows correctness directly: the stripes must tile the rectangle with no bare slivers and no double-covered bands, and a stripe leaving the top must re-enter at the bottom exactly in line, because those two edges are the same circle on the real drum.
The blank as it lies on the roll. The two ends are drawn at true scale, so the angle on screen is the angle to cut; only the redundant middle is removed. Both cuts are parallel — the blank is a parallelogram, not a trapezoid, which is the single most common mistake.
These checks do not evaluate the formula again — they measure the resulting wrap by unrelated means and compare. Everything re-runs whenever an input changes.
A miscut shows up one of two ways depending on how you lay the strip. If you keep the seams tight, the pitch stays right and the error appears at the ends — a corner of the paper hangs off the drum or falls short of it. If instead you trust the ends and seat both cuts against the rims, the error accumulates in the seams, turn after turn.
And because the cut length is the circumference, an error in measuring the drum feeds through to the cut one-for-one:
Roll width is a purchasing decision, so here is what each common width would mean on this drum.