Handbook for Sound Engineers

174 Chapter 7

According to Fig. 7-34, this is the superelevation of the
visual line (virtual line between eye and reference point)
of a tier n + 1 as against tier n.
With a tier arrangement having a constant step height
(continuous sloping in the longitudinal direction of the
room), it is not possible to achieve a constant superele-
vation c. Mathematically it is the curve of a logarithmic
spiral in which the superelevation increases alongside
the distance from the reference point that realizes a
constant superelevation of the visual line.^34

As this implies, however, steps of different height for
the individual tiers, a compromise must be found by
either adapting the step height or by combining several
tiers in small areas of constant sloping. In concert halls,
the areas arranged in the shape of vineyard terraces (see
Section 7.3.3.2.1) constitute, in this respect, an acousti-
cally and optically satisfactory solution.

The eye level y(x) is calculated with

Figure 7-32. Echo phenomena due to edge reflections.

1

2

S

A. So-called theater echo.

B. Edge reflections under circles and galleries.

Figure 7-33. Geometry of circle arrangement in A. Music

and opera houses, multigenre theaters and B. concert halls.

Figure 7-34. Sloping of tiers (schematic view).

A. Music and opera houses, multigenre theaters.

B. Concert halls.

Room Music and opera

houses, multigenre

theaters, Fig. 6-33A

Concert hall

Fig. 6-33B

Circle depth D

Angle Q ¾25° ¾ 45°

¾ 2 H < H

y

yn

Reference point d

x

c

(a,b)

xn xn + 1

yn + 1

(a,b) = Coordinates of the first row (eye level).

(xn, yn) ) = Coordinates of the nth row.

(xn + 1 , yn + 1) = Coordinates of the (n + 1)th row.

c = Sight line superelevation (requirement: c = constant).

d = Tier spacing.

y = Eye level = tier level + 1.2 m.