How the combination search works
The solver expands each declared quantity into a distinct physical block, splits the inventory, generates bounded combinations on both sides, and matches complementary sums. This meet-in-the-middle search evaluates combinations up to the selected five-block limit without repeatedly using a block that exists only once. If one or more nominal stacks land inside the requested tolerance, fewer blocks rank before a smaller residual error. Otherwise the closest nominal alternatives are shown.
Sine-bar calculation
For center distance L and target angle θ, required height is H = L sin θ. Each candidate is converted back with θ = asin(H/L); its angular error is reported in arcseconds. The displayed worst-case angular limits combine the linear sum of entered block tolerances with the entered center-distance tolerance. They do not include bar geometry, roll cylindricity, surface-plate condition, temperature gradients, setup sag, contact, or reading uncertainty.
Nominal fit versus tolerance containment
“Nominal fit” means the calculated stack center lies inside the requested target band. “Band contained” is stricter: the entire nominal stack plus or minus the sum of supplied block tolerances lies inside that band. Linear tolerance addition is deliberately conservative and is not interchangeable with a GUM uncertainty calculation or the uncertainty stated on a calibration certificate.
Use and safety boundary
This is a setup-planning aid, not calibration or acceptance authority. It does not know actual calibrated deviations unless you enter them as adjusted sizes, and it does not model thermal expansion, wear, burrs, cleanliness, wringing quality, material differences, gravity, cosine/Abbe error, surface-plate flatness, or instrument resolution. Never force, grind, or casually handle precision blocks. Follow the block and sine-bar manufacturers’ procedures and your quality system.
Frequently asked questions
Why does the solver prefer fewer blocks?
When several nominal stacks meet the requested tolerance, fewer blocks mean fewer wrung interfaces and a simpler setup. That preference does not override block condition, calibration evidence, stability, or your procedure.
Should I add a wringing-film correction?
Normally no. NIST’s historical discussion notes that the wringing layer became part of the block-length definition. The adjustment field exists only for a separately documented laboratory correction.
Can I enter calibrated block values?
Yes. Enter corrected or measured lengths as the sizes and corresponding remaining tolerances if that matches your controlled procedure. Keep the source certificate and traceability record outside this tool.
References
NIST’s Gauge Block Handbook covers definitions, physical characteristics, calibration, corrections, handling, and measurement assurance. NIST’s historical overview explains wringing and composite gauge stacks. Mitutoyo lists angle measurement with a sine bar among standard gauge-block applications.