Acoustic Competition for the Golden Medal of Crowd Noise Level: Insights on the Stadia and Sport Buildings in Ancient Times

Abstract

Ancient stadia and circuses were considered by Greeks and Romans to be excellent places for live events. Back in ancient times, many people participated in public entertainment from athletic games, as typical of Greek traditions, to combats between gladiators and wild beasts. Among all of them, the most acclaimed were the horse races conducted with chariots, and this was the main sport of ancient Roman stadia. This paper deals with the digital reconstruction of three stadia belonging to the 2nd century B.C. (i.e., Panathenaic Stadium) and to the 1st century A.D. (i.e., Circus Maximum and Stadium of Domitian). The digital models have been rebuilt based on historical resources and archaeological discoveries to conduct the acoustic simulations and understand the acoustic behavior within these places. After the assessment of the main acoustic parameters, the noise levels from crowds have been predicted in different ways: based on information gathered from historic annals, and the comfort used for modern stadia to predict the ancient conditions with reference to the crowd noise levels measured in modern stadiums. The results indicate that the acoustic response of ancient stadia is very similar to the modern ones, in terms of both reverberation and noise level from crowds.

1. Introduction

The passion of practicing sport always existed in ancient times. A brief introduction of the environment from which ancient stadia have been developed is necessary to understand the shape, the geometry, and the political power showed to people. This paper deals with the acoustics of three ancient stadia: the Panathenaic stadium, the Circus Maximum, and the Stadium of Domitian, realised in different contexts and influenced by different culture on sportive competitions.

The word used to indicate the athletic games was agone, which included marathon, as well as combats between gladiators and horse races [1]. While agone for Greeks meant a manifestation to celebrate the religious feasts close to the sanctuaries as part of the cultural education of citizens, in Rome, the physical preparation was directly connected to military conduct [1]. In Greece, the athletic games included light (e.g., running) and hard competitions (e.g., fights and boxing) [1]. In this context, the Panathenaic stadium was realised, to host spectators around the development of running and other athletic games.

Different is the situation in the Republic Rome, where ludi and munera were the main spectacles requested by people. It shall be remembered that Romans were great fans of chariot races and cruel combats against beasts (circenses) [1]. There is a time in history when Greek and Roman culture about sport came to a point of contact. Marcus Fulvius Nobilioris organised in Rome the first athletic games in 186 B.C., repurposed again in 80 B.C. by Sylla and 55 B.C. by Pompey. The first time when the athletic games became periodic in Rome was in 30 B.C., honoured to Octavianus, from which the games were repeated every five years. The Greek agoni (called capitolia in Rome) was officially introduced in the calendar by Emperor Domitian only in 86 A.D. [1].

In Rome, the certamen capitolium corresponded to the Greek athletic competitions, articulated in three different competitions: musicus (musical), equestris (dedicated to the horse races), and gymnicus (athletics). These three competitions were conducted after the poetry competitions, which were performed in both Greek and Latin languages. All the athletic competitions were not categorised into classes based on weight or age as occurring in contemporary times; the young men could fight with older ones [1].

Sportive and artistic spectacles were used by emperors to enlarge the popular consent to their political strategies. For this reason, many buildings dedicated to spectacles were erected for different types of exhibitions, as the stadia in Imperial Rome. The politics by Flavian emperors was characterised by the utilization of Neronian structures made available to people so that the spectacles found rooms in dedicated monumental spaces [1]. With the creation of a stadium, Domitian gave identity to the Campus Martius with the establishment of the Greek games [1]. Cassius Dionis said that Emperor Traian was very generous and magnanimous to embellish the Circus Maximum as it was immortalised on a stone board with a sentence declaring that the circus was sufficiently adequate for Romans [2]. All buildings realised for the spectacles represented the places where the emperor demonstrated to be very close to people by sharing his time and by participating in the shows. All these public places were built in a very organic urban context, to be close to the thermal baths or to theatres and odeia mainly used for musical performances. Stadia were remarkably huge to allocate the order of 250–450,000 spectators in comparison to any other public space, like theatres and odeia whose capacity was limited to up to 3–5000 seats.

Horse races were the games loved by Romans, just as much as the gladiators’ combats usually performed in the amphitheatres. The competitors of the horse races were usually organised into four teams, as shown in one of the original mosaics preserved in the National Roman Museum of Palazzo Massimo alle Terme, reported in Figure 1. The representation is related to four jokers (agitatores) dating back to the 2nd century A.D., during the reign of Emperor Settimius Severus.

It is interesting also to understand all the movements around ancient stadia. The organization of the horse races were managed by private societies (factiones) who provided stipulated contracts with the organisers of the races. Every joker had a different colour of uniform (quadrigaria) which gave the name to the team: blue for veneta, white for albata, green for prasina, and red for russata. The joker used to wear a leather helmet with a feather. The jacket was characterised by a series of wires to which the horses were attached; the risk of this type of clothing consisted of being dragged by the running horses in case of any incident. At that point, the joker could only cut the wires with a dagger (pugio) to avoid death. This costume was not acquired by the Greeks, where the jokers used to control the horses by their hands. It is still unknown if the jokers were slaves or liberti (i.e., slaves after conquering their liberty).

2. Research Aim

This paper deals with the acoustics of three ancient stadia: the Panathenaic Stadium in Athens, the Circus Maximum, and the Stadium of Domitian in Rome, which disappeared and no longer exists. The resources nowadays available on these heritage buildings are only referring to the architectural and archaeological discoveries while the acoustics were never studied. This represents the novelty deeply studied from different perspectives on a building type where knowledge is limited to architectural composition. Various resources report different numbers of spectators’ capacity, which have been calculated in terms of noise levels from the crowd. All these notions have been taken into consideration for the comparison of noise levels produced by a different number of attendees.

In addition, the absorption and scattering coefficients of materials have been assigned to the digital models based on real measurements conducted inside existing Roman theatres. This methodology is usually applied when the historical building is no longer existing, and some archaeological traces support the description of the manufacture that can only partially fulfil the research study.

3. Construction Elements of an Ancient Circus/Stadium

The building types dedicated to the horse races were three: circus, stadium, and hippodrome. They were characterised by a geometry where the longitudinal axis was dominant compared to the transversal one. The long sides were usually parallel to each other, while the short sides terminate with a round shape (exhedra), like the cavea of a Roman theatre, and with an arched porch on the opposite edge of the perimeter (carceres) dedicated to the preparation of horses and chariots before the race.

The first public shows within the city (ludi) were mainly religious events that included different types of exhibitions, comprising triumphal ceremonies (ludi scaenici), horse races, and gladiators’ combats. Based on the function of these public spaces, praise to the divinities were represented by the monuments along the main axis (spina), delimited by two specific points, called metae [2]. Basically, the spina divided the whole width of the circus/stadium such that the runway was circled, corresponding to a lap.

The audience area was called cavea and was divided by a corridor (praecinctio) in two main sectors (maeniana): ima and media cavea [2]. The praecinctiones interrupt the rhythm of the steps, determining in this way different sectors. The upper gallery, whereas in place, was called summa cavea and was usually characterised by a porch (porticus), under which the timber benches were installed [3].

The boxes for the horses’ preparation (carceres) were on the opposite side of the stepped semicircle. After the horses were hooked to the chariot, they waited in a long line before the start (alba linea) [3]. The race consisted of 7 complete laps around the spina [3].

The Greek stadia were not provided with any spina since the athletic games could be spread over the sandy ground, and they were not provided with any porch at the top of the steps.

The Greek and Roman citizens were seated in different zones, based on their social class. The first steps were dedicated to astrologers, magicians, and fortune tellers, as they were close to the sacred monuments placed along the spina (in Rome); only in Rome, the first steps were also reserved for the knights as well. Women and men could seat freely across the steps with no boundaries [2].

4. Materials and Historical Background

4.1. Panathenaic Stadium in Athens

The Panathenaic Stadium was originally built around 330 B.C. with the purpose of hosting the Panathenaic games as part of a religious and athletic festival celebrated every four years to honour the goddess Athena [4]. The stadium was rebuilt during the 2nd century A.D. by Herodes Atticus, a wealthy Greek-born Roman senator who built many other public buildings in Athens. Herodes Atticus increased the length of the stadium, from 204 × 34 m to 261 × 129 m, approximately close to the current dimensions. It was built in Pentelic marble with the minimal use of concrete [5]. The stadium would have been able to accommodate around 50,000 people, as shown in Figure 2, very similar to the capacity of the Stadium of Domitian in Rome [5]. Only the front seating row was provided with a backrest (proedria). This stadium was abandoned in the 4th century as directed by Emperor Theodosius II and was not in operation until the late 19th century when it was excavated and subsequently rebuilt to host the reborn modern Olympics [6]. Nowadays, the stadium is occasionally used for musicals and dance venues but continues to be the centre of the Athens marathon and Olympic Games.

4.2. Circus Maximum in Rome

The Circus Maximum is still the biggest public space dedicated to sportive games, whose dimensions are still not exceeded by any other stadium [2]. Located in the Murcia valley, the first boxes for the chariots (carceres) were built in wood in 329 B.C. These wooden structures were adjacent to the stone steps where the audience was seated (maeniana) [2]. The Circus Maximum was built in stone during the Republic time, with the definition of the starting and ending points of the races (metae) around the central row of monuments (spina) dedicated to divinities, which was 370 m long [3].

The Circus Maximum was characterised by a canal (euripus) running along all the perimeter of the race ground, which was 3 m deep and 3 m large [2]. This canal was covered by Nerone in 59 in order to obtain more seats for the knights. The big fire of Rome in 64 started from the Circus Maximum but this building was rebuilt reasonably quickly to be ready in 68 for the emperor Neron on his way back from Greece. Emperor Domitian contributed to refurbish and embellish the circus by building a great arch in the centre of the semicircle to be dedicated to his brother Titus [3].

Under the dominion of Traian, the Circus Maximum reached a capacity between 385,000 and 485,000 spectators [2]. This capacity increased gradually along the years since Dionigi during the 1st century reported a capacity of 150,000 spectators against the datum reported by Pliny (250,000 spectators) who was referring to the Flavian period [2]. Traian contributed to fix the steps in stone of the ima and media cavea [2].

In terms of dimensions, Pliny the Older says that the Circus Maximum is 533 m long and 177 m wide, which are the dimensions applicable to the race ground (excluding the audience area). Archaeological discoveries estimate that the overall length is equal to 601 m and its width is equal to 140–150 m [3], as shown in Figure 3. The cavea was certainly 32 m wide, while the total height from the roadside was 22–23 m, considering that the level of the race ground was 4–5 m below the road level. The steps were developed on a width of 35–38 cm and a height of 28 cm, as found also in the Circus of Massenzio [3].

Between 800 and 900 A.D., the first excavations were executed, where some parts of the radial walls of the semicircle were discovered. During the fascist time, the Circus Maximum was selected for expos and shows. Nowadays, the race ground is only a green park, and some radial walls are left visible, while the rest is destroyed or buried [3].

4.3. Stadium of Domitian in Rome

Directed by Emperor Domitian, the stadium was built in 86 A.D. to celebrate the officiality of the Agon Capitolinus, the Greek-style games, honoured to Iovis, which included musical competitions, horse races, and athletic games [7]. The stadium has dimensions of 275 × 106 m, with the long sides parallel and jointed with a semicircle, while on the opposite side, the carceres were slightly inclined with respect to the orthogonal directions of the axes [7], as shown in Figure 4. The cavea was 27 m wide in travertine marble, which was employed also for the walkway of the external ambulacrum. The main entrances were decorated with columns in Corinthian style and provided with three naves [7]. The taverns, usually located under the cavea, in this stadium could facilitate communication through openings in the walls [7]. The race ground was composed of a layer of ceramic gravel below the final sand to drain the rainwater. Many statues decorated the external elevation placed below the arches, probably 120 pieces, crafted by famous artists and representing mythological characters [7]. Because the supply of potable water was of primary importance, the stadium was provided with water from aqueducts [8]. The Stadium of Domitian was built close to two thermal buildings: Agrippa’s and Nerone’s thermae, from which the water was also distributed through fountains [8]. After the structure was dismissed, different buildings were erected on the marble of the cavea, decreeing the end of the magnificent public space. The variety of buildings that occupied the field of the Stadium of Domitian include churches and private multi-storey properties [8].

5. Materials and Preparation of Digital Models for Acoustic Simulations

Among all considered case studies, only the Panathenaic Stadium is still existing, while Circus Maximum and Stadium of Domitian are no longer in place. The digital reconstruction of these three archaeological sites as they appeared in their original shapes were realised with the aid of historical drawings, notes, and descriptions coming from the outcomes of archaeologists, as indicated in Section 3.

Table 1. Architectural characteristics of ancient sport buildings.

Description	Panathenaic Stadium	Circus Maximum	Stadium of Domitian
Dimension of longitudinal axis at the external perimeter (m)	262	601	275
Dimension of transversal axis at the external perimeter (m)	128.5	160	106
Width of ground (m)	42.7	84	50
Length of spina (m)	-	369	130
No. of maeniana	2	3	2
Total no. of steps	48	63	28
Total capacity (no. of spectators)	50,000	385–450,000	50,000
External height (m)	20.7	66.5	19.5
Volume (m3)	Approx. 650,808	Approx. 5,852,997	Approx. 248,187

summarises the architectural features of the stadia as they have been digitally rebuilt using their original aspects.

All the surfaces were drawn as flat planes in AutoCAD 2024 software, while the layers were grouped by material, which were mainly:

• stone for the steps,
• timber for the steps under the porch (case of Circus Maximum),
• sand for the ground where the games were played.

Regarding the material properties applied to the digital surfaces, the coefficients related to stone and wood are taken from in situ measurements inside the Roman theatre of Tyndaris by using the Laser Doppler Vibrometer (LDV) as a non-invasive methodology appropriate for archaeological sites [9]. The material properties of sand are taken from previous research on granular silica experimental tests [10]. Absorption coefficient equal to α = 1 across all the frequency bandwidth is applied to the opening surfaces. The acoustic simulations are conducted in unoccupied conditions and with 100% audience occupancy [11]; this latest scenario has been simulated by applying the coefficients of light upholstery to the steps [12], excluding the corridors (praecinctiones) separating the maeniana.

Table 2. Surface, absorption, and scattering coefficients applied to the surfaces of ancient stadia: Panathenaic Stadium (PT), Circus Maximum (CM), and Stadium of Domitian (SD).

Materials	Area (m2)	Octave Band Centre Frequency (Hz)—Absorption						Scattering (@500–1000 Hz)
		125	250	500	1000	2000	4000
Stone	36,299 (PT) 127,958 (CM) 32,644 (SD)	0.01	0.01	0.01	0.01	0.01	0.01	0.01
Solid wood	−(PT) 11,229 (CM) −(SD)	0.08	0.20	0.10	0.05	0.03	0.02	0.08
Sand	9189 (PT) 94,145 (CM) 20,825 (SD)	0.08	0.10	0.20	0.25	0.30	0.35	0.05
Audience	28,220 (PT) 57,089 (CM) 16,896 (SD)	0.51	0.64	0.75	0.80	0.82	0.83	0.40
Openings	40,830 (PT) 118,832 (CM) 34,871 (SD)	1.00	1.00	1.00	1.00	1.00	1.00	0.01

summarises the absorption and scattering coefficients applied to the surfaces of the digital models.

Since there was no possibility to conduct acoustic measurements in these ancient stadia, the calibration process is not included as one of the steps of the full procedure to run the acoustic simulations. This represents a limitation of this study. However, the reliability of the results consists of the site measurements on materials existing in other Roman theatres and amphitheatres, conducted by the authors with innovative techniques, as anticipated in the previous paragraph [9].

6. Theory, Methodology, and Calculation

6.1. Acoustic Parameters through Digital Simulations

The acoustic simulations have been performed with Ramsete 3.13 software [13] by placing the omnidirectional sound sources along the axes of the horse race runway. The virtual microphones have been uniformly distributed across the audience area at 1.6 m height from the steps, for a number equal to 331 inside the Panathenaic Stadium, 385 inside the Circus Maximum, and 259 microphones inside the Stadium of Domitian [14,15]. The simulations have been carried out without and with a full audience capacity, as shown in the results of Figure 5, by considering the main acoustic parameters as defined in ISO 3382 [16]. These results are obtained as an average of 10 times repetitions of the simulations in order to ascertain the degree of variance due to the repeatability of digital computations.

Figure 5a shows that the highest EDT values are found in the Circus Maximum, to be around 5 s in unoccupied conditions, while the results in the Panathenaic Stadium and in the Stadium of Domitian are very similar to each other, fluctuating around 3.5 s for the same scenario. When fully occupied, the EDT values are shifted by 1.2 s downwards for the Circus Maximum, to be equal to 3.5 s, while the EDT values relative to the Stadium of Domitian and Panathenaic Stadium are around 2.3 s and 1.8 s, respectively [17].

In terms of reverberation, Figure 5b shows that the T20 values in the Circus Maximum reach 6.7 s when unoccupied, while a differentiation of 0.8 s is evident between the Panathenaic Stadium and the Stadium of Domitian, indicating that the T20 values are more reverberant in the latter stadium, to be around 3.9 s. When fully occupied, the T20 values in the Circus Maximum are lower and found around 4.3 s. The presence of audience results in more absorbtion in the Panathenaic Stadium than the Stadium of Domitian, with a downward shift of 2.3 s related to the first case study and equal to 1 s related to the latest one [18]. This is due to the quantity of surface area left to stone that is more in the Stadium of Domitian, as it is applied to the parapet (balteum) of the first and second maenianum, and to the area of corridors that includes also the walkway located at the end of the steps. In the Panathenaic Stadium, the surface area left to stone is only the parapet at the level of ground and only one corridor separating the two sectors of steps [19].

As anticipated previously, the acoustics of these three stadia are very good and comparable to a large Roman theatre like Verona [20], considering that their room volumes are consistent.

6.2. Ambient Noise Level from Crowd

Like in a modern stadium, the noise level of the crowd is to be also accounted for ancient stadia, where the attendees acclaimed the jokers playing with their chariots for the horse races. The noise level from the crowd is directly proportional to the number of the spectators, other than to the room volume and reverberation time, as determined by Equation (1) [21].

$$L_{N,A}={\displaystyle \frac{1}{1-c}}·\left(69-c·45-10\log \left(g·\left({\displaystyle \frac{0.16V}{T_0·N}}+A_p\right)\right)\right) \left(\mathrm{dB}\right)$$

(1)

where $A_p$ is the absorption that is given to a person and is expressed in m², $c$ is the Lombard slope coefficient which depends on the background noise level, $g$ is the group size determined as the average number of people per speaking person ($g=N/N_S$). This equation studied for the first time by Rindel in a context of eating establishment rooms [22] indicates that the most accurate results are obtained with $c=0.5 \mathrm{dB}/\mathrm{dB}$ and $A_p=0.2-0.5 {\mathrm{m}}^2$. The calculation of acoustic capacity ($N_{max}$) is simplified by Rindel with the following Equation (2).

$$N_{max}={\displaystyle \frac{V}{20·T}} \left(\mathrm{dB}\right)$$

(2)

where V is the room volume and T is the reverberation time in furnished but unoccupied conditions at medium frequencies. Among all the parameters, the most variable could be the value assigned to the group size g, which goes from 2 when the gathering is very lively to 3–4 for more common settings like a gathering of people in a restaurant or food court. The g value can even have a value equal to 8 but this is for an extreme situation of people-gathering.

Based on archaeological discoveries, the laps of the horse races were about 7 [2], corresponding to a duration of approximately two hours, with an additional hour given to the preparation of the chariots before the race and to the acclamation and celebration of victories, which can be translated to a total duration of 3–4 h. The limitation of this computation is that Equation (1) is referring to enclosed spaces instead of open-air places like ancient stadia. Another factor influencing the results in relation to the standards of modern computation is completely different from the space comfort of ancient times and this is discussed in the following section.

7. Results

Based on archaeological and historical discoveries related to the Circus Maximum [23], the number of 385,000–450,000 loca in relation to the spectators was reported. It is difficult to interpret this datum reported by the catalogues, which refers to a huge number of spectators. It has been proposed that this number corresponds to the calculation of seats reported in Roman feet. Anyway, the descriptions given by Dionigi Halicarnassus in the 1st century A.D. [24] indicate a capacity for the Circus Maximum equal to 150,000 spectators, against the indications given by Pliny of 250,000 spectators [25], which sound more reasonable.

Since the number of spectators is fundamental for the calculation of the noise level of the crowd, it is possible to compare the capacity of ancient stadia based on different computations; this comparison includes the computation of the spectators’ number (N) based on the following resources:

• N1: from historical information;
• N2: from Equation (2);
• N3: outcome obtained by assigning a certain square metre per person over the surface area of only steps (excluding the ground for the horse races).

Table 3. Comparison of different types of computation in relation to the number of spectators in the ancient stadia.

	Steps Surface Area in Plan (m2)	Surface Area per Person (m2)	N1	N2	N3
Panathenaic Stadium	22,308	0.39	50,000	7675	8700
Circus Maximum	46,020	0.39	450,000	45,918	17,948
Stadium of Domitian	14,255	0.39	50,000	3300	5559

summarises three types of calculation as previously described, where it is possible to see the wide difference between the three methodologies. As such, the calculation of noise levels of the crowd takes into account all the numbers of spectators for each stadium.

Based on Table 3, the noise levels from the crowd are computed by following the indications of Equation (1). Since Romans used to wear the tunica as the most popular cloth, the absorption coefficient to a person (Ap) has been assigned to be equal to 0.2. As per previous discussion, the g value can be equal to 1–2 for a very crowded gathering where everyone is speaking in the group, as would be for the participation in horse races (ludi equestris). Considering the full capacity of the selected stadia, the noise level related to the crowd is summarised in

Table 4. Predicted noise levels produced by the crowd at full capacity in ancient stadia.

	Absorption per Person—Ap (m2)	Lombard Slope—c (dB/dB)	$\mathit{g}=\mathit{N}/{\mathit{N}}_{\mathit{S}}$	Noise Level (dB) with N1 Spectators	Noise Level (dB) with N2 Spectators	Noise Level (dB) with N3 Spectators
Panathenaic Stadium	0.2	0.5	2	90	76	77
Circus Maximum	0.2	0.5	2	93	76	69
Stadium of Domitian	0.2	0.5	2	95	76	81

.

8. Discussion

The results of the noise levels from the crowd, as shown in Table 4, vary widely, passing from 76 dB to a maximum of 95 dB. For modern stadia, the noise levels from the crowd during sport matches can vary from 80 to 95 dB (without PA system in operation) recorded even with a smaller number of spectators than the stadia selected for this research study, although the finish material is very similar in terms of absorption coefficients (plastic seats on concrete for modern stadia against stone steps for ancient stadia) [26]. As such, it can be said that the number of spectators reported by the history (N1) is considered the most plausible result since the noise level is found to be very similar to the noise levels measured in modern stadia [26,27].

Another aspect that can be noticed is that the noise levels found in the Circus Maximum is comparable to what was found in the other two smaller stadia, although the number of spectators in the first is 9 times larger; this means that the other factors of Equation (1) are also important for the determination of the result, as it is referring to the reverberation time, room volume, Lombard slope, and so on.

Considering that the stadia in ancient times were placed close to other public building such as thermal baths and squares, a development of this study can be applied to the break-out noise to the surrounding buildings. This would be a problem only for daytime, since the spectacles used to run between 0900 and 1500 approximately [28], without any impact on sleep disturbance for night-time.

In summary, predictions on noise from the crowd can be predicted for any place by using Equation (1); the important thing is understanding the number of people gathering together, as well as the absorption coefficient given to the clothing worn, the reverberation time of the room, and the relative room volume. The other important parameter is the number of people talking in a group and the Lombard slope coefficient. Regarding this latest variable, it has been studied that children are more likely to increase their voices more than adults if the background or masking noise becomes louder [29].

It should be clear that this research study is based on different assumptions, mainly related to material properties that can be one of the major factors in determining the acoustic response of the ancient stadia. The geometry of the models is obtained from the archaeological discoveries, but a little percentage of uncertainty can be represented by the digital reconstruction, although it could negligibly engrave the results since small details would be less effective on a large volume of buildings. A further uncertainty is represented by the repeatability of the acoustic simulations, which is not extensively explored by scholars for the precision of reliable results, and this concept has been identified as “error propagation” [30].

9. Conclusions

The ludi equestris were a type of sport very acclaimed by Romans, along with the agoni as developed in Greece. In ancient times, people spent different hours assisting in horse races and other sportive competitions, as part of the live spectacles running on a daily basis along with the combats between gladiators and beasts (ludi circenses) and many others.

The acoustic investigation carried out on three stadia which disappeared from history allowed the digital reconstruction of the models as they would have appeared in ancient times. Among them, the Circus Maximum was the largest one, containing up to 450,000 spectators, in comparison with the other two that have full capacity of 50,000 attendees. The acoustic simulations have been conducted to study the acoustic behaviour inside these three case studies, in unoccupied conditions and with a full occupancy. The simulated results indicate that the acoustic response of the ancient stadia is very similar to many modern stadia built without roofs, in relation to both reverberation time and speech clarity that shall be designed for the suitability of the PA system.

Starting from the acoustic parameters and the geometric information, the noise level from the crowd has been predicted for the ancient stadia by using a computation valid for enclosed spaces that is regulated by modern standard requirements and comfort (e.g., absorption area per person). The results of the noise level from the crowd have been calculated based on numbers of spectators obtained in different ways: from historical resources, from Equation (2), and by assigning a certain value to the absorption surface area per person. The results, as summarized in Table 4, show that the most plausible noise levels have been found with the number of spectators as indicated by the historical resources since the results are very similar to the noise levels produced by modern stadia [27].

Despite some limitations of this research study regarding the assignment of different values to the factors determining the noise level as computed with Equation (1), and also the comfort requirements that are different between ancient and modern times, the noise level from the crowd has been found to be very similar to modern stadia.

Another datum that can be observed is related to the number of spectators between the three case studies that give comparable noise levels from the crowd, although the capacity of the Circus Maximum is 9 times larger than the Panathenaic Stadium and Stadium of Domitian, meaning that the characteristics of the room, in terms of volume size and reverberation, are also important factors.

This research study can be used by firms working in the field of cinema when reproducing the soundscape of movies filmed in ancient times, as the reproduction of sounds can be based on scientific discoveries never studied up to now. In addition, the data found with this research can also be used for any virtual reality or gaming whose ambient exploration is willingly dated back to the Greek or Roman period (e.g., the Prince of Egypt game). On the other side, the reconstruction of the digital models created by archaeological discoveries can also be reproduced for museums by 3D printing the geometrical features at a specific scale, to be added to the existing exposition of columns and other pieces found in the archaeological sites. Overall, the acoustics of these three ancient stadia can remain a great example for modern designers who would like to adapt new modern stadia for both sportive events and musical concerts provided with extraordinary, amplified audio systems.