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Datasheet errors: when Qts, Vas and Sd disagree

Thiele-Small parameters are tied to each other by a few exact formulas. When a datasheet breaks one, a box designed from it will be off. Type what the sheet prints and see which numbers hold.

Type what the datasheet prints, leave the rest empty. Units as shown.

Hz
Ω
T·m
L
mm/N
g
cm²
cm
Cone plus about half the surround.

Filled in: the Scan-Speak 18W/8531G00 datasheet. Two checks fail, and the table shows why.

Result

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The formulas that tie the numbers together

Five identities come straight from the definitions (Small, 1972). A good datasheet meets each within rounding:

  • Qts = Qes·Qms/(Qes + Qms), within 2 %.
  • Fs = 1/(2π√(Mms·Cms)), within 3 %.
  • Vas = ρc²·Sd²·Cms, within 5 %.
  • Qes = 2π·Fs·Mms·Re/Bl², within 5 %.
  • Sd = π(D/2)² for the printed effective diameter, within 3 %.

The tolerances are wide on purpose. Sheets round to two or three digits, and makers measure with slightly different air constants: Small’s 1.18 kg/m³ and 345 m/s give a ρc² 0.85 % lower than 1.204 and 343.

Real sheets that fail

Scan-Speak 18W/8531G00. The sheet prints Sd 157 cm² and D 13.8 cm. A 13.8 cm circle is 149.6 cm²: the printed Sd is 4.9 % larger. With the printed Sd, Vas from Cms comes out at 64.6 L against the printed 58.2 L (+11 %). With Sd from D it is 58.6 L, which matches. So the Vas on the sheet was worked out from D, and the printed Sd is the odd one out.

Dayton Audio RSS265HF-4. Cms 0.32 mm/N and Sd 356.3 cm² give a Vas of 57.5 L, 6.5 % more than the 54 L on the sheet. Small, but it moves a sealed box by a few litres.

Peerless SLS-P830669. Fs from Mms and Cms is 31.48 Hz, the same as the sheet. Vas is within 0.9 %. A sheet can be right.

Unit traps

  • Vas in cubic feet typed as litres (or the other way): off by 28.3 times. A 12-inch sub with a Vas of 2.8 L is really 2.8 ft³.
  • Sd in cm² typed as m²: off by 10,000.
  • Xmax peak-to-peak: some sheets print the total travel. Box maths wants one way, half of it.
  • Re against the nominal impedance: a 4 Ω coil measures about 3.2 to 3.6 Ω with a meter. That is Re, and it is normal.

Which number to trust

Fs, Re, Qes and Qms come from an impedance sweep, the most direct measurement. Vas and Cms come from an added-mass or added-box test and scatter more between samples. When the check fails, keep the measured numbers, ask the maker, or measure your own driver. The app marks every value it derived and lets you correct a driver row; your correction stays on your phone.

Sources

  1. Small, R. H., “Closed-Box Loudspeaker Systems”, JAES 20 (1972)
  2. Scan-Speak 18W/8531G00 datasheet
  3. Dayton Audio RSS265HF-4 specifications
  4. Peerless SLS-P830669 datasheet
  5. NIST SP 811, Appendix B.9: cubic foot and inch

Results are design estimates. Check the driver’s datasheet and your amplifier’s minimum load before you build.

Checked against the sources: October 27, 2026

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