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.