Build Math

How to Calculate Tonewood Yield, CNC Time, and Cure Time for Instrument Builds

A step-by-step walkthrough of the five formulas that govern instrument production math, with units, worked examples, and where each input comes from.

Every instrument build reduces to five recurring calculations, and each one starts from a source document you already keep. Tonewood Blank Yield reads off the grading log. CNC Body Machining Time reads off the work order and a machine cycle log. Lacquer Finish Cure Time reads off the finishing traveler. String Setup Labor reads off a bench time study. Final Tuning Capacity reads off the tuning room schedule. Learn to run these by hand and the calculators become a check on your arithmetic rather than a black box. Keep units consistent: blanks, parts per minute, coats per minute, instruments per minute, and hours. Mixing minutes and hours is the single most common arithmetic error in this workflow.

Start with material, because it decides more of your cost than any downstream step. Tonewood blank yield is usable blanks divided by total blanks graded, times 100. Grade one Sitka spruce billet and you record 40 usable tops out of 60 graded: 40 divided by 60 is 0.667, so 66.7 percent yield. The second formula line, yield gap to target, subtracts your target from actual, so against a 70 percent target you sit 3.3 points short. Always tie the denominator to one billet or one kiln load. Aggregate three billets into one count and a single runout-ridden log disappears into the average, hiding exactly the diagnosis you need.

CNC body machining time converts a batch into spindle hours in two steps. Base time is batch size divided by machined parts per minute, and required time multiplies that by an allowance factor of one plus your setup and tool-change percentage. Take 120 body blanks at an effective rate that works out to 12 blanks per machine hour: 120 divided by 12 is 10 base hours. Apply a 10 percent allowance for fixturing, work-offset probing, and swapping between roughing and finishing bits, and 10 times 1.10 gives 11 hours of spindle occupancy. Pull parts per minute from a timed run, never the spec sheet, and keep one stock thickness per batch so the single rate holds.

Lacquer finish cure time uses the identical two-line structure but answers a different question: how long the booth and racks are tied up. Base finish time is finishing batch size divided by coats cleared per minute, then multiply by one plus a booth and cure-window allowance. For 120 parts at a rate clearing 12 coats per booth hour, base time is 10 hours, and a 10 percent allowance for flash-off, racking, and booth turnaround gives 11 hours. Treat this strictly as scheduling occupancy. It does not replace the lacquer maker's chemical cure window. A nitrocellulose job may spray in an hour but need three to four weeks of cure before buffing, and that dwell is a separate calendar constraint you honor on top.

String setup labor is again batch divided by rate times an allowance, but here the hours map almost one to one onto skilled bench-tech staffing rather than a shareable machine. Base labor is instruments in the setup queue divided by instruments set up per minute, then times one plus a bench allowance. Run 120 instruments at a rate of 12 per bench hour and base labor is 10 hours; a 10 percent allowance for restrings, retests, and second passes lifts it to 11 bench hours. Keep one instrument type per queue. A bolt-on bass and a floating-bridge archtop set up at very different rates, so blending them corrupts the single per-minute figure the formula depends on.

Final tuning capacity works the opposite direction from the time formulas: it starts from available time and yields good units. Gross capacity is instruments per tuning cycle times tuning cycles available. Good capacity multiplies that by tuning room uptime and first-pass tuning yield, both as decimals. Suppose 4 instruments per cycle across 90 cycles in a shift gives 360 gross; at 90 percent uptime and 97 percent first-pass yield, good capacity is 360 times 0.90 times 0.97, which is roughly 314 ship-ready instruments. That is the honest number to promise against, not the 360 gross figure. The two yield-style multipliers are where optimistic planners quietly overstate what a shift can actually clear.

Chain these correctly and the units cancel cleanly. Tonewood Blank Yield gives a percentage and a raw usable count that seeds your raw billet purchase. Feed the usable body count into CNC Body Machining Time as batch size to get spindle hours. Feed the same parts into Lacquer Finish Cure Time for booth hours, then into String Setup Labor for bench hours, and finally test the whole flow against Final Tuning Capacity to confirm the tuning room can absorb the throughput. Each handoff is a count of parts or a rate in the same time base, so the arithmetic stays consistent from rough billet to ship-ready instrument.

Two habits keep these calculations honest. First, always re-time your rates on a real batch every quarter, because an optimistic parts-per-minute or coats-per-minute figure compounds through every downstream estimate and quietly understates hours. If a scheduled run consistently overruns the computed time, the rate is wrong or the allowance is too small, so re-time and adjust both. Second, never let a single blended rate cover mixed work. Segment by species, stock thickness, finish system, and instrument type. The formulas are trivial arithmetic; the discipline that makes them accurate is refusing to average across decisions that behave differently, which is what turns a clean number into a defensible schedule.

Published 2026-07-01.