Chimney Stack Directivity Correction
The calculation below is taken from Annex B — Table B.1 of ISO 9613-2:2024. The calculation provides the directivity correction ($D_c$) for chimney stacks as a function of two values:
- Radiation angle ($\theta$) relative to the vertical stack axis
- The Parameter ($ka$) (dimensionless product of wave number and chimney radius)
$D_c$ (dB) is the angle in degrees between vertical and the receiver.
The parameter $ka$ is calculated from:
$$ ka = \frac{2 \pi a f}{331.4 \sqrt{1 + \frac{T}{273}}} $$
Where:
- $T$: Temperature at the chimney mouth
- $f$: Frequency in Hz
- $a$: Opening radius
- $c$: Speed of sound (343 ms-1 typically)
So, before you use the table below you will have:
- One angle value; and
- Several ka values (one for each frequency considered).
There will be a $ka$ value for each frequency band you are calculating for.
Use the lookup table below to calculate the attenuation in dB for each frequency ($ka$ and $D_c$ pair)
| θ (deg) | $ka$=4.0 | $ka$=5.0 | $ka$=6.3 | $ka$=8.0 | $ka$=10.1 | $ka$=12.7 | $ka$=16.0 | $ka$=20.2 | $ka$=25.4 | $ka$=32.0 |
|---|---|---|---|---|---|---|---|---|---|---|
| 30 | 2.4 | 2.1 | 1.9 | 2.0 | 2.1 | 2.6 | 3.1 | 3.4 | 3.4 | 3.3 |
| 45 | 4.0 | 3.4 | 3.1 | 3.1 | 3.4 | 4.0 | 4.4 | 4.6 | 4.6 | 4.5 |
| 60 | 4.0 | 3.4 | 3.1 | 3.1 | 3.4 | 4.0 | 4.4 | 4.6 | 4.6 | 4.5 |
| 75 | 2.4 | 2.1 | 1.9 | 2.0 | 2.1 | 2.6 | 3.1 | 3.4 | 3.4 | 3.3 |
| 90 | -2.4 | -2.2 | -2.0 | -1.9 | -1.9 | -1.9 | -1.9 | -2.1 | -2.3 | -2.7 |
| 105 | -4.3 | -4.6 | -5.0 | -5.4 | -5.9 | -6.4 | -6.9 | -7.3 | -7.6 | -7.9 |
| 120 | -6.3 | -7.0 | -7.7 | -8.2 | -8.7 | -9.1 | -9.6 | -10.2 | -11.0 | -12.1 |
- For $ka > 32$ just use the ‘32’ column
- For $\theta < 30^\circ$ use the ‘30’ row.
- For $\theta > 120^\circ$ use the ‘120’ row.
Note that:
- The data are based on measurements of large brick industrial chimneys.
- They represent downwind propagation conditions (~3 m/s).
- For chimneys of different design the results should be treated as approximate.
How we use this
Chimney-stack directivity is a routine input to our noise impact assessments for combustion-engine generators, biomass boilers, CHP plant and process exhausts. Getting Dc right at each receptor angle can change the predicted specific level by 5–10 dB(A), which is often the difference between an adverse-impact result and a clean BS 4142 assessment.