Theatre Design & Technology - Spring 1975 - 21

ASURVEY OF THEATRE ENGINEERING
APPLICATIONS OF QUANTITATIVE ANALYSIS TO PROBLEMS OF
THEATRE ENGINEERING
MICHAEl KUPFERSCHMID

IZENOUR ASSOCIATES
© 1975 by Michael Kupferschmid.

Introduction. Mathematics and physics can assist
in the solution of many problems which occur in the
design and use of theatres and their equipment.
Many such problems also require for their solution
some knowledge of theatrical production, and may
therefore be of interest to various practitioners in
tech nical theatre.
The study of these special problems and the
discovery of quantitative approaches to their solution
constitute the discipline of theatre engineering. This
survey begins with the consideration of five main

divisions of the subject in order to illustrate its
connections with theatre architecture, equipment
design, the technical design of settings, the administration of scenery construction, and the performance
processes of technical production.
The Design of Theatre Buildings. All sorts of
engineering problems must be solved in the course of
designing any building, but those which are particular to theatre design, and consequently of interest to
theatre engineers, are those concerning acoustics,
sightlines, and the mechanics of kinetic architecture.
It is easy to find illustrative examples from each of
these subdivisions, but, so as not to trouble the
patience of the casual reader, we will consider only
the most familiar problem: seeing the stage from an
auditorium.
Illustrative Example. A simplified analysis of the theatre
seating problem assumes that seats are behind one another in
plan view, so that a section through the auditorium looks like
the picture at the left. S, the point to be seen by everyone, is
level with the eye of the first spectator, who is a distance
0= 10 feet away in the first row of seats. The rows of seats are
uniformly spaced a distance of d = 42 inches apart, and the
distance from each observer's eye to the top of his head is
H 3.6 inches. In order to see over the first spectator's head,
the second row observer's eye must be height h2 above that of
the first-row observer. Similarly, the eye height of the observer
in the nth row must be h n greater than that of the first-row
observer. Find hn as a function of h n -1 and demonstrate an
iterative procedure for finding the successive h's, starting with

s

=

~D

h1'
Solution. With reference to the figure below, it is clear from
similar triangles that

0 + d

0
H

-

h2
Likewise,

o + d
h 2+ H

0 + 2d

s_=

---l

o

.....L-

d

h3

L.

d

In general,

o + nd

o + (n-l)d
hn + H

hn+l

for n = I, 2, ...
Therefore, we conclude that the function sought is given by

+ H) [0 + (n-l) d]

o + (n-2)d

for n
for n

~

THEATRE DESIGN AND TECHNOLOGY

SPRING.1975

2,3, ...

<

1.

21



Table of Contents for the Digital Edition of Theatre Design & Technology - Spring 1975

Contents
Theatre Design & Technology - Spring 1975 - 1
Theatre Design & Technology - Spring 1975 - 2
Theatre Design & Technology - Spring 1975 - 3
Theatre Design & Technology - Spring 1975 - Contents
Theatre Design & Technology - Spring 1975 - 5
Theatre Design & Technology - Spring 1975 - 6
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https://www.nxtbook.com/nxtbooks/hickmanbrady/tdt_1965May
https://www.nxtbookmedia.com