Design of an Acoustically Treated Amphitheater

8/3/2019 Design of an Acoustically Treated Amphitheater

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CHAPTER IV

DESIGN PROCEDURE AND CALCULATIONS

For every design, there corresponds the appropriate calculation needed to

arrive at the desired output. For the design of an Acoustically Treated

Amphitheater, it is important to calculate for the area of every part of the room

and the volume. The area and the volume, together with the absorption

coefficient of everything that makes up the room will later be used to find the

reverberation time of the sound.

DESIGN PROCEDURES AND STANDARDS:

Amphitheater:

The Amphitheater functions for video and audio reports and speeches. To

provide a favorable acoustical environment, one must address both the need to

hear and understand speech, and the desire to have a pleasant space for music.

A good acoustical design always requires the consideration of the following

areas:

y Related Codes and Standards

y Noise Criteria

y Sound Transmission Class

y Reverberation Time

In designing amphitheater, there are tips, standards and considerations to

be followed. Some of them are:

1. Recommend reverberation time is 1.5-2.5 seconds.

2. Although the seating area will provide absorption, thereby reducing thereverberation time, you will most likely need to add absorption materials to the

other surfaces within the space.

3. It is vital to control the reflections from the back wall. If you dont control them,

the presentation could reflect off the back wall and slap back to the

presenters. This wont necessarily impact the audience, but could be


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disastrous and distracting for the people on stage. Because of this, its usually

necessary to treat the back wall with an absorptive material. A concave back

wall could compound this problem. If you cant avoid a concave back wall, its

imperative that it be treated with absorptive material.

4. Remember the space will be less absorptive when only half full, since the

audience itself is absorptive. By using absorptive seating areas, the

reverberation time will remain more consistent regardless of the audience

size.

5. Noise from lobby area can be disruptive. Be sure openings such as doorways

are properly sealed. Consider a vestibule door system.

DESIGN CALCULATION:

REVERBERATION TIME

RT60 measures the reverberance within a room. RT60 is soon to be

adopted under ADA for classroom acoustic criteria. Reverberation time is the

time required, in seconds, for the average sound pressure level in a room to

decrease 60 decibels after a source stops generating sound. This test is

standard on certain projects, such as THX movie theaters and various

government buildings. Normally, in the design phase, you must demonstrate

(through calculations) that a space will achieve the stipulated reverberation time.

Oftentimes, measurements are required to verify results. Because RT60 is void

of variables, unlike many other tests, it is straightforward and clear-cut. But RT60

does not account for problematic and potentially annoying reflections.

Oftentimes, there is still a need for expert analysis.

Reverberation time is the function of volume, area and absorption

coefficient of the surface areas. To obtain this, the total area, total volume and

total absorption coefficient of the rooms were computed.

The reverberation time and absorptions of the audio visual room are

shown below:


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Amphitheater:

Ray Diagram:

A. (9.493m + 8.844m) 17.097m = 1.24m

B. (4.887m + 3.753m) 3.663m = 4.977m

Computations:

Solving for the areas (refer to the layout)

Area of the top:

Areastage(top) = (h/2)(b1 + b2) + (l x w)

= (7.0m/2)(8.563m + 12.938m) + (8.0m x 1.0m)

Areastage(top) = 83.2535m2

A

B


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Area of the face:

Areastage(face) = (Arectangular face) + 2(Aface of the stairs + Aface front side)

= (8.0m x 1.0m) + 2{[(0.31m x 0.8m) + (0.31m x 0.6m) + (0.31m x

0.4m) + (0.31m x 0.2m)] +

[(2.469m x 1.0m) (0.31m x 0.8m) - (0.31m x 0.6m) - (0.31m x

0.4m) - (0.31m x 0.2m)]}

Areastage(face) = 12.938m2

Area of the stairs:

Areastage(stairs) = 8(Atop step) + 10(Aelevation step)

= 8(1.0m x 0.31m) + 10(0.2m x 1.0m)

Areastage(stairs) = 4.48m2

Total Area of the Stage:

AT (stage) = Areastage(top) + Areastage(face) + Areastage(stairs)

= 83.2535m2 + 12.938m2 + 4.48m2

AT (stage) = 100.6715m2

Afloor(elevation) = (thickness x length) +[ (h/2)(b1 + b2)]steps 1-20

= (0.15m x 14.5m) + [(0.8m/2)(14.5m + 15.0m)] +

(0.15m x 15.0m) + [(0.8m/2)(15.0m + 15.5m)] +

(0.15m x 15.5m) + [(0.8m/2)(15.5m + 16.0m)] +

(0.15m x 16.0m) + [(0.8m/2)(16.0m + 16.5m)] +

(0.15m x 16.5m) + [(0.8m/2)(16.5m + 17.0m)] +

(0.15m x 17.0m) + (0.8m/2)(17.0m + 17.5m)] +

(0.15m x 17.5m) + [(0.8m/2)(17.5m + 18.0m)] +

(0.15m x 18.0m) + [(0.8m/2)(18.0m + 18.5m)] +

(0.15m x 18.5m) + [(0.8m/2)(18.5m + 19.0m)] +

(0.15m x 19.0m) + [(0.8m/2)(19.0m + 19.5m)] +


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(0.15m x 19.5m) + [(0.8m/2)(19.5m + 20.0m)] +

(0.15m x 20.0m) + [(0.8m/2)(20.0m + 20.5m)] +

(0.15m x 20.5m) + [(0.8m/2)(20.5m + 21.0m)] +

(0.15m x 21.0m) + [(0.8m/2)(21.0m + 21.5m)] +

(0.15m x 21.5m) + [(0.8m/2)(21.5m + 22.0m)] +

(0.15m x 22.0m) + [(0.8m/2)(22.0m + 22.5m)] +

(0.15m x 22.5m) + [(0.8m/2)(22.5m + 23.0m)] +

(0.15m x 23.0m) + [(0.8m/2)(23.0m + 23.5m)] +

(0.15m x 23.5m) + [(0.8m/2)(23.5m + 24.0m)] +

(0.15m x 24.0m) + [(0.8m/2)(24.0m + 24.5m)]

Afloor(elevation) = 369.75m2

Area of the front:

Afloor (front) =(2.5m/2)(12.938m + 14.5m) (10.48m x 1.0m)

= 23.8175m2

Area of the rear:

Afloor (rear) =(1.5m/2)(19.25m + 24.5m)

= 32.813m2

Total Area of the Floor

AT (floor) = Afloor (rear) + Afloor (elevation) + Afloor (front)

= 32.813m2 + 369.75 + 23.8175m2

AT (floor) = 426.3805m2


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Adoor= l x w

= 2(1.0m x 2.0m)

= 4m2

A1 = [2(1.676m) x 5.2m] (0.838m x 0.45m)

(0.838m x 0.3m) (0.838m x 0.15m)

A1 = 16.6762m2


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A2-8 = 7[(1.676m x 5.2m) (0.15m

x 0.838m)]

A2-8 = 60.1265m2

A9 = (0.314m x 0.3m) + (5.06m x 1.676m) + (0.838m x 0.15m)

A9 = 8.65336 m2

A10 = (9.953m x 5.65m) (8m x 1m) 2(2m x 1m)

A10 = 44.2345m2


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Area of the rear:

AWall (rear) = Arear wall + Atwo slanted side Atwo doors Acontrol room window= (19.25m x 4.6m) + 2(3.023m x 4.6m) 2(2.5m x 2.0m) (0.5m x 2.0m)

= 105.3616 m2


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Afront wall = 8.563m x 4.650m

Afront wall = 39.81795m2

Total Area of the Wall:

AT (wall) = A1 + A2-8 + A9 + A10 + Awall rear+ Afront wall

= {(16.6762m2 + 60.1265 m2 + 8.65336 m2 + 44.2345 m2 ) X 2} + 105.3616

m2 + 39.81795 m2

AT (wall) = 404.5607m2

Aceiling (rear) = (3.21m/2)(22.5m + 24.5m) + (1.4993m/2)(19.25m + 24.5m)

= 108.2322m2

Aceiling (elevation) =(1.3m/2)(15.5m + 14.688m) +

(0.425m/2)(14.5m + 14.688m) +

[(0.3m x 15.5m) + (1.5997m/2)(15.5m + 16.5m)] +

[(0.3m x 16.5m) + (1.5997m/2)(16.5m + 17.5m)] +

[(0.3m x 17.5m) + (1.5997m/2)(17.5m + 18.5m)] +

[(0.3m x 18.5m) + (1.5997m/2)(18.5m + 19.5m)] +

[(0.3m x 19.5m) + (1.5997m/2)(19.5m + 20.5m)] +

[(0.3m x 20.5m) + (1.5997m/2)(20.5m + 21.5m)] +

[(0.3m x 21.5m) + (1.5997m/2)(21.5m + 22.5m)] +

(0.3m x 22.5m)

= 284.18475m2

Aceiling (front) = (9.5m/2)(14.5m + 8.563m)

Aceiling (front) = 109.5493m2

Total area of the ceiling

AT (ceiling) = Aceiling (rear) + Aceiling (elevation) + Aceiling (front)


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=108.2322m2 + 284.18475 m2 + 109.5493m2

AT (ceiling) = 501.9663m2

Vwhole = [(25.5m/2)(24.5m + 8.563m) + (1.4993m/2)(24.5m + 19.25m)](8.35m)

= 3793.8262m3

Vstage1 = (83.2535m2 x 1.0m) = 83.2535m3

V stairs= 2[(Astairs x 0.8m) + (Astairs x 0.6m) + (Astairs x 0.4m) + (Astairs x 0.2m)] +

= 2[(0.31m2 x 0.8m) + (0.31 m2 x 0.6m) + (0.31 m2 x 0.4m) + (0.31 m2 x

0.2m)]

V stairs = 1.24m3

VT(stage) = Vstage1 + VstairsVT(stage) = 84.4935m

3

Velevation(floor) = (0.15m x 11.8m2) + (0.3m x 12.2m2) + (0.45m x 12.6m2) + (0.6m

x 13.0m2) + (0.75m x 13.4m2) + (0.9m x 13.8m2) + (1.05m x 14.2m2) +

(1.2m x 14.6m2) + (1.35m x 15.0m2) + (1.5m x 15.4m2) + (1.65m x 15.8m2) +


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(1.8m x 16.2m2) + (1.95m x 16.6m2) + (2.1m x 17.0m2) + (2.25m x 17.4m2) +

(2.4m x 17.8m2) + (2.55m x 18.2m2) + (2.7m x 18.6m2) + (2.85m x 19m2) +

(3.0m x 19.4m2)

Velevation(floor) = 531.3m3

Vrear(floor) = 3.15m x 32.813m2

=103.361m3

VT(floor) = Velevation(floor) + Vrear(floor)

= 634.661m3

VT(ceiling) = (2.7m x 109.5493m2) + (3.0m x 19.622m2) + (2.7m x 25.59m2) + (2.4m

x 27.19m2) + (2.1m x 28.79m2) + (1.8m x 30.4m2) + (1.5m x 32.0m2) + (1.2m x

33.59m2) + (0.9m x 35.192m2) + (0.6m x 75.2m2) + (0.6m x 32.7972m2)

VT(ceiling) = 788.95623m3

VT = Vwhole - VT(stage) - VT(floor) - VT(ceiling)

= 3793.8262m3 84.4935m3 - 634.661m3 - 788.95623m3

VT = 2285.71547m3

REVERBERATION TIME

A. Untreated

ABSORPTION BY THE MATERIALS USED

Item Materials Area, s (m2)

Absorption

coefficient, at

1 kHz

Absorption

(sabins)

Stage

floor

Concrete

(unpainted)

100.6715 0.06 6.0403


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Floor Concrete

(unpainted)

426.3805 0.06 25.5823

Ceiling Plasterboard (1/2

) in suspended

ceiling grid

501.9663 0.04 20.0787

Walls Concrete

(poured, rough

finish, un painted)

404.5607 0.06 24.2736

Door Solid wood 18 0.04 0.72

Glass Glass ( plate,

large pane)

1 0.03 0.03

Total absorption from above materials 76.7249

ABSORPTION BY THE CHAIRS AND AUDIENCE

Area, s (m2)Absorptioncoefficient,

at 1 kHz

Absorption(sabins)

252 chairs, unoccupied 75.6 0.07 5.292


252 chairs, occupied 75.6 0.76 57.456

504 chairs, occupied 151.2 0.76 114.912

Material: Theater seats, wood

TOTAL ABSORPTION BY THE CHAIRS AND AUDIENCE


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when the room has no audience: 10.584 sabins

when the room has half the audience: 5.292 + 57.456 = 62.748

sabins

when the room has full audience: 114.912 sabins

TOTAL ABSORPTION = total absorption from the materials used + total

absorption by the chairs and audience

Total Absorption by

the materials used

Total Absorption by

the chairs and

audience

Total Absorption

When the room has

no audience:

76.7249 10.584 87.3089

When the room has

half audience:

76.7249 62.748 139.4729

When the room has

full audience:

76.7249 114.912 191.6369

S

V0.161

60RT !


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B. Treated

ABSORPTION BY THE MATERIALS USED

Item Materials Area, s (m2

)

Absorption

coefficient, at 1kHz

Absorption

(sabins)

Stage floor Parquet on

concrete

100.6715 0.06 6.0403

Floor Carpet 426.3805 0.15 63.9571

Ceiling Plaster: smooth

on brick

501.9663 0.03 15.059

Walls Plaster: smooth

on brick

404.5607 0.03 12.1368

Door Solid wood 18 0.04 0.72

Glass Glass ( plate,

large pane)

1 0.03 0.03

Total absorption from above materials 97.9432

ABSORPTION BY THE CHAIRS AND AUDIENCE


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Area, s (m2)

Absorption

coefficient, at 1 kHz

Absorption

(sabins)



252 chairs, occupied 75.6 0.96 72.576

504 chairs, occupied 151.2 0.96 145.152

Material: Fabric-upholstered seats

TOTAL ABSORPTION BY CHAIRS AND AUDIENCE

When the room has no audience: 133.056 sabins

When the room has half the audience: 66.528 + 72.576 =

139.104 sabins

When the room has full audience: 145.152 sabins

TOTAL ABSORPTION = total absorption from the materials used + total

absorption by chairs and audience


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Total Absorption by the

materials used

Total Absorption by

the chairs and

audience

Total Absorption

When the room has no

audience:

97.9432 133.056 230.9992

When the room has half

audience:

97.9432 139.104 237.0472

When the room has full

audience:

97.9432 145.152 243.0952

S

V0.161

60RT!


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SUMMARY OF REVERBERATION TIME

Reverberation Time (seconds)

UNTREATED:

No audience 4.2149

Half audience 2.6385

Full audience 1.9203

TREATED:

No audience 1.5931

Half audience 1.5524

Full audience 1.5138

Conclusion

For an acceptable design of an amphitheater to be achieved, different

parameters and standards are needed to be met and pursued. These are the

reverberation time, the type of materials to be used, the invulnerability to noise,

the adequate loudness and others. The design complies with the standard or

accepted reverberation of a specific amphitheater. It promotes good quality of

sound and music. The sound absorption of all the materials that were used in the

design was properly identified. It can be well stated that good projection of sound

and music necessary for the design was undoubtedly accomplished and

achieved.

Documents

Design of an Acoustically Treated Amphitheater