Allocate an incident octave sound-power spectrum across outgoing duct areas and check energy recombination.
Concepts behind this calculation
Allocate a complete incident octave sound-power spectrum among all outgoing duct sections using their clear area fractions. Keep branch division separate from other junction and path effects.
The area-division model allocates incident sound power among all outgoing clear duct sections in proportion to their areas. Each branch’s fraction is its area divided by the sum of every exit area, including the continuing main. The logarithm of that fraction gives a signed level change; reversing its sign gives positive division attenuation. The same geometric allocation applies across the entered octave bands.
Division redistributes the incident power rather than absorbing it, so recombining allocated powers recovers the incident spectrum within arithmetic precision. Actual junction behavior can also include area-mismatch reflection, scattering and regenerated noise, which are separate effects. Airflow fractions are not automatically acoustic area fractions, and allocated branches reaching a common receiver cannot simply be treated as independent sources without considering their paths and coherence.
How to use this calculator
Complete Source spectrum, junction and model reference and establish Area-division basis.
Enter All outgoing duct sections with positive clear areas, including the continuing main and excluding liner from the airway.
Enter all eight Incident sound power bands at the junction. Review area shares, signed changes, positive attenuation and allocated spectra before carrying each branch into its separate acoustic path.
Calculation method and applicability
fi = Ai / ΣAout; signed ΔLwi = 10 log10(fi); positive division attenuation = −10 log10(fi); Lwi(f) = Lwincident(f) + ΔLwi. Recombine powers logarithmically for an energy audit.
Ai = clear outgoing branch area (in²); fi = dimensionless area fraction; ΔLwi = signed sound-power change (dB); Lwi = outgoing sound power level (dB re 1 pW) in each octave band.
Input definitions and units
Source spectrum, junction and model reference
Identify incident source/operating point, all exit areas and why this area-division path factor applies. Record separate reflection/scattering/noise treatment; this is not a complete junction model.
Area-division basis
Confirm complete clear exit areas and compatible unweighted sound-power octave bands, re 1 pW. Overall dBA, NC and receiver Lp are different quantities. Airflow percentages do not automatically equal area percentages. Choices: Not established; Complete exit geometry, sound-power basis and model applicability established.
All outgoing duct sections (ID, clear cross-sectional area in²)
One outgoing section per row; include every branch AND the continuing main. Unique integer ID 1–10000 and positive clear area in square inches, excluding liner thickness from the airway. 1–100 rows; a single exit is the zero-division boundary case. This is area, not airflow or feeder area.
Incident sound power at 63 Hz (dB re 1 pW)
Unweighted octave-band sound power at this same junction and operating condition. Every band is required. Zero and negative levels are valid finite energies; a missing band is not zero. Numerical support −100 to 200 dB does not state instrument accuracy.
Incident sound power at 125 Hz (dB re 1 pW)
Unweighted octave-band sound power at this same junction and operating condition. Every band is required. Zero and negative levels are valid finite energies; a missing band is not zero. Numerical support −100 to 200 dB does not state instrument accuracy.
Incident sound power at 250 Hz (dB re 1 pW)
Unweighted octave-band sound power at this same junction and operating condition. Every band is required. Zero and negative levels are valid finite energies; a missing band is not zero. Numerical support −100 to 200 dB does not state instrument accuracy.
Incident sound power at 500 Hz (dB re 1 pW)
Unweighted octave-band sound power at this same junction and operating condition. Every band is required. Zero and negative levels are valid finite energies; a missing band is not zero. Numerical support −100 to 200 dB does not state instrument accuracy.
Incident sound power at 1,000 Hz (dB re 1 pW)
Unweighted octave-band sound power at this same junction and operating condition. Every band is required. Zero and negative levels are valid finite energies; a missing band is not zero. Numerical support −100 to 200 dB does not state instrument accuracy.
Incident sound power at 2,000 Hz (dB re 1 pW)
Unweighted octave-band sound power at this same junction and operating condition. Every band is required. Zero and negative levels are valid finite energies; a missing band is not zero. Numerical support −100 to 200 dB does not state instrument accuracy.
Incident sound power at 4,000 Hz (dB re 1 pW)
Unweighted octave-band sound power at this same junction and operating condition. Every band is required. Zero and negative levels are valid finite energies; a missing band is not zero. Numerical support −100 to 200 dB does not state instrument accuracy.
Incident sound power at 8,000 Hz (dB re 1 pW)
Unweighted octave-band sound power at this same junction and operating condition. Every band is required. Zero and negative levels are valid finite energies; a missing band is not zero. Numerical support −100 to 200 dB does not state instrument accuracy.
How to interpret the result
Use each branch’s allocated octave sound power as one path-factor input and retain the energy audit. The audit verifies the allocation arithmetic, not the completeness of a junction acoustic prediction or final receiver level.
Worked examples
Worked example
Inputs: Constructed incident Lw of 80, 75, 70, 65, 60, 55, 50, 45 dB re 1 pW at 63–8000 Hz. Outgoing clear areas: 144, 72, 72 in², including the continuing main.
Calculation: Exit area totals 288 in². Fractions are 0.5, 0.25, 0.25. Division attenuations are 3.0102999566, 6.0205999133, 6.0205999133 dB. At 500 Hz, subtract them from incident 65 dB.
Result: At 500 Hz the three allocations are 61.9897, 58.9794, 58.9794 dB re 1 pW. Recombining their energies gives the original 65 dB. The published table rounds the two attenuation values to 3 and 6 dB.
Assumptions and limits
Named historical AHRI 885-2008 Appendix D1.1 area-division factor; not the complete standard, current-standard conformity or code certification. Model applicability and source/geometry evidence must be supplied.
The denominator is the sum of ALL outgoing clear areas, including the continuing main, not automatically the upstream feeder area. Airflow fractions equal area fractions only under corresponding equal-velocity conditions.
The factor redistributes incident acoustic energy; the combined branch energy is conserved. This does not mean allocated branches can be added as independent sources at a common receiver. Coherence, geometry and separate path transfer matter.
This calculation omits feeder/exit area-mismatch reflection, frequency-dependent junction scattering, regenerated noise, other sources, liner/duct attenuation, breakout, end reflection and room transfer. It does not predict complete junction insertion loss or final occupied-space noise.
Inputs are unweighted sound-power bands re 1 pW for one incident source at one operating state. Receiver pressure re 20 µPa, overall dBA, NC and independently specified sources are not interchangeable. Missing bands cannot be assigned 0 dB.
A single outgoing section is an identity boundary case. The 1–100 row and −100 to 200 dB input bounds are implementation support limits, not measurement accuracy or standard acceptance criteria. No zero-dB floor is applied to allocated levels.
FAQs
Should the denominator be the upstream feeder area?
Use the sum of all outgoing clear areas. The feeder area may differ from that sum; its mismatch can create additional reflection, which this allocation factor does not calculate.
Why do branch levels fall if the recombined power is unchanged?
Each branch receives only a share of the original power. Its lower level describes that share, and the energy sum of all shares restores the original total. Division attenuation is therefore not dissipative loss for the complete junction.
Sources
AHRI 885-2008, Appendix D1.1 and Table D2 (manufacturer-hosted original)Original standard Appendix D1.1, printed p.39 (PDF p.47), defines signed 10log(B/T); Figure D1 and Table D2 follow on printed p.40. B/T uses the sum of all exits, including continuing main. This single historical factor is not full-standard conformity.
ASHRAE 2023 HVAC Applications, Chapter 49Duct Branch Sound Power Division and Table 26 corroborate the area-ratio component and separately identify reflection from feeder/exit area mismatch. The listed rounded table values are not exact logarithmic results.
Krueger AHRI 885 calculatorManufacturer tool page inspected as workflow context; it links a downloadable historical Excel acoustic workbook. No live workbook execution or per-branch numeric parity is claimed.
