(1)Computer Simulation of the Acoustics of Mosques and Byzantine Churches
The EU project CAHRISMA (Conservation of the Acoustical Heritage by the Revival and Identification of the Sinans Mosques Acoustics) investigates, among other things, the acoustics in some of the old churches and mosques in Istanbul, Turkey. The present paper deals with acoustic computer simulations of churches and mosques within this project. Three Byzantine churches and three mosques were modeled in the Odeon room acoustic program. These geometries are dominated by spherical and cylindrical (concave/convex) shapes; especially large domes dominating the ceiling. Another feature in the rooms is numerous columns and galleries obstructing the direct sound. In the models, calculation parameters such as transition order (TO), number of rays and the number of subdivision into plane surfaces of concave/convex surfaces are changed. This is done in order to investigate the effect on the results for the different room acoustic parameters (according to ISO 3382). The simulations are compared with room acoustic measurements made in the real rooms.
Introduction
From the six models made in Odeon of the buildings investigated in the CAHRISMA project, two of the models have been chosen for further investigation. These are; the Byzantine church Saint Irene and the Selimiye Mosque. Various calculation parameters have been changed and the simulated results have been compared with the measured results, to optimize the models. This is mainly done to examine the effect of concave/convex surfaces (domes, arches etc.), and to examine which of the two calculation methods; ray-tracing or image-source, are best suited for this purpose (Odeon uses a hybrid method). The following is a listing of the altered calculation parameters.
Comparing rooms and models
In order to compare the simulated with the measured results, an error value is calculated. This is done in the following manner:
(1)
Where,
APmeasured is the measured value of the current acoustic parameter.
APsimulated is the simulated value of the current acoustic parameter
SL is a subjective limen for the current acoustic parameter (see ref. 1 ex. one SL for EDT is 5 %)
This error is calculated for each position, frequency band (1/1 octave) and acoustic parameter. For each of the three models with different geometrical resolution, a reference model is made. This is done by adjusting the absorption of the surface material having the largest absorption area, so a global estimate of the reverberation time matched the measured values within one SL. From this reference model, calculations were done using three different TO, the three different geometrical resolutions and using 10 different number of rays for Selimiye and 11 for Hagia Irene.
Results - The Selimiye mosque
The following diagrams (fig. 1) show the error values as a function of the number of rays used. The error is calculated from an average over the six acoustic parameters: EDT, T30, Ts, C80, D50 and LF80 (according to ISO 3382). Furthermore it is spatial and frequency averaged (125 4000 Hz). The diagrams show the error for the two TO 0 and 2, and the effect of the three resolutions are compared in each diagram.
FIGURE 1: Average error for the six room acoustic parameters as a function of number of rays for TO 0 and 2, and the three orders of resolution. For high-resolution TO 2, ray-numbers 800.000 and 999.999 are not calculated due to long calculation times.
From figure 1 it is mainly seen that the higher the TO, the higher the error. For TO 0 the three resolutions almost give the same magnitude error, and the lowest error is found at low geometrical resolution using 50.000 rays (error = 1,51).
Furthermore it is seen that using a ray number higher than 1000 does not improve the error. For TO 2 it is seen that high resolution gives a much higher error for all ray numbers compared to the two other resolutions The smallest error for high resolution is found at the lowest ray number, and increases with increasing ray number. Low and medium resolution almost show the same error values but also increases with increasing ray number.
From these results it is generally seen that using TO 0 and any of the three resolutions, and using 1000 rays or above gives the smallest error. To get the fastest calculation time and still get optimum results, it seems sufficient to use the lowest resolution and 1000 rays.
The fact that TO 0 generally gives the lowest error can be explained by the domination of the domes. The domes (mainly the center dome) are placed at a height, which gives the sound a large amount of diffusion, which can also be seen from the measured T30, which has a spatial standard deviation of 0,16 sec. (freq. Average from 125 4000 Hz). The spatial average value is 6,21 sec., so it is within one SL.
Results - Saint Irene Byzantine church
Below are shown the TO 2 results for Saint Irene, in the same type of diagram as for Selimiye. The TO 0 results looks like the one from Selimiye.
FIGURE 2. Average error for the six acoustic parameters as a function of number of rays for TO 0 and 2, and showing the three different geometrical resolutions.
For Saint Irene the error does not depend nearly as much on the resolution as for Selimiye. For Saint Irene it is TO that determines the error. The higher TO, the higher the error. For TO 2 the error decreases from 100 to 23.000 rays, where it reaches a minimum, and then it has a steady increase to 999.999 rays.
The numerous domes in Selimiye compared to Saint Irene can explain the fact that the error does not depend on the resolution as much as for Selimiye. The domed surfaces in Selimiye take up a greater portion of the total surface area, than the ones in Saint Irene.
Conclusion
This study generally shows that, for complex rooms with many curved surfaces, modeled with relatively small plane surfaces, the ray-tracing method yields the best results (TO = 0).
References
1. Ingolf Bork., A comparison of Room Simulation Software The 2nd Round Robin on Room Acoustical Computer Simulation, ACUSTICA acta acustica, Vol. 86 (2000) 943-956