User-defined Directivities

User-defined directivities are entered into CadnaA’s local library in order to later get assigned to the relevant source.

Open the table Directivity (local) on the menu Tables|Libraries (local).
Select from the context menu (right mouse button) the command „Insert after“ and double-click into the new row. The dialog to enter directivities is opened.
Enter as a name e.g. „Directivity 1“ and the ID „DIR1“.
Since the calculation makes use of A-weighted levels with the main frequency of 500 Hz enter the directivity just for the 500 Hz octave as below.

Input data for directivity 1

Activate the option „normalized“. This setting normalizes the specified levels to an energetic sum of 0 dB. Thus, not altering the emitted sound power level as specified on the source’s dialog.
The normalization of directivity is carried out for the corresponding nominal frequency and angle.
Close the dialog with OK.
Open the dialog Directivity by a double-click onto the row in the table Directivity (local) again. Consider that the intermediate directivity values have been interpolated by CadnaA.
Enter a point source with an A-weighted sound power level of 100 dB(A) and define a calculation area around that source.
On the source’s dialog click the button „Directivity“ and select the user-defined directivity „directivity 01“ from the list box. For the time being, keep the setting "Automatic Direction".
Calculate the horizontal grid after having the grid spacing to 1x1 m and appearance to „Lines of Equal Sound Level“.

Normalization of directivity

The normalization is based on the following formula:

$L_{i,\ norm} = L_i - L_{mean}$

$L_{mean} = 10 \cdot log \left[ \frac{1}{A_{total}} \cdot \left(\sum_{i=0}^{N} 10^{\frac{L_i}{10}} \cdot A_i \right)\right]$

with

$L_{i,\ norm}$: Normalized sound pressure level for a norminal frequency, e.g. 500 Hz, of a frequency band
$L_{mean}$: Mean sound pressure level of a norminal frequency
$A_i$: Patch area of a sphere
$A_{total}$: Total surface area of a sphere

Point symmetrical propagation by a point source

Obviously, no directivity was considered in the xy-plane since the propagation is point symmetrical. The ground acting as near reflector causes the directivity vector to be orientated automatically into the positive z direction.

Select the object Vertical Grid from the toolbox and draw a line from two polygon points across the point source from left to right.
Double-click on the vertical grid and click on the button "Calculate".

Vertical grid for a point source with automatic directivity in z-direction

To aim the directivity in the xy-plane, the option "Automatic Direction" has to be deactivated and a suitable direction (i.e. 0°-direction) to be entered.

Open the point source dialog and click the button „Directivity“. As can be seen, CadnaA has orientated the directivity vector into the positive direction of the z-axis automatically (x = y = 0, z = 1).
Select the option „Vector" to enable the input of x,y,z-coordinates.
Enter the coordinates x = 1, y = 0, and z = 0, to point the normal direction (0°-direction) into the direction of the positive x-axis (so, pointing to the right).
Close all dialogs with OK and start the grid calculation. This results in the following representation:

Open the dialog Directivity of the point source once more.
Enter for the vector’s coordinates x = 1, y = 1 and z = 0 to aim the directivity vector to 45° (i.e. the angle bisector between positive x and y-axis).
Close all dialogs by OK and start the grid calculation.

The coordinate input on the dialog Directivity refers to the unit circle. The triple (x, y, z) = (1, 1, 0) points into direction of 45°. With respect to the unit circle this results in the values x=y=0.7071. CadnaA displays those values upon reopening the dialog Directivity. The following calculation formulae for the non-normalized directivity vector into direction ϕ (in degrees) apply:

$x=\cos\varphi\sin(90-\vartheta)$

$y=\sin\varphi\sin(90-\vartheta)$

$z=\cos(90-\vartheta)$

Where, ϕ is the angle between the directivity vector - projected on the xy-plane - and the positive x-axis. The angle ϑ is the angle between the directivity vector and the xy plane.

Polar coordinates and orthogonal coordinates

For the orthogonal coordinates, normalized to the unit circle, it holds:

$x'=\frac{x}{|r|}; y'=\frac{y}{|r|}; z'=\frac{z}{|r|}; $

with

$|r| = \sqrt{x^2+y^2+z^2}$