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Some links:
Lighting design at the Harvard Theatre and Performance website
There is an entire lighting course online at Stage Lighting 101, I'm not quit sure how good it is, but there is a lot of information.
There is a lighting design glossary which is a bit technical, but you can find out what a beam angle is.
Instrument specs at the manufacturer Altman stage lighting for ellipsoidals and for fresnels, and PARs.
Download hookup sheet as excel doc or as PDF file
download plans of the theaters

Lighting Instruments: The ellipsoidal, the fresnel, the PAR

Ellipsoidal Reflector Spotlight
The most common focusable unit used in the theatre today is the ellipsoidal reflector spotlight (ERS, or in theatrical slang, "leko"). The output of an ERS is a round (conical), well-defined beam of light. Ellipsoidal reflector spotlights come in a variety of beam spreads specified either by their actual beam spread in degrees, or by the lens diameter and the focal length of the lens. Specification by beam spread is relatively new to the industry so older units will most likely be specified by the latter method. A few commonly available ERSs are 5º, 10º, 20º, 30º, 40º, 50º, 4 1/2 x 6”, 6 x 9, 6 x 12, 6 x 16, and 6 x 22. Because of the precise light control possible with the ERS, these units, assuming the appropriate beam spread is chosen, are effective from any position in the theatre.

Beam spread angles and multiplying factor (MF)
for Altman ellipsoidals
instrument
all model # 360Q
beam
spread
multiplying
factor
4.5 x 6.5
55º
1.03
6 x 9
37º
.68
6 x 12
26º
.48
6 x 16
19º
.34
6 x 22
11º
.18

Beam Spreads for Altman Ellipsoidals

The Fresnel
A lightweight, short throw, all purpose lighting device the 6" fresnel produces a soft edged beam which varies in diameter from 4.2 feet to 21 feet at a throw distance of 15 feet for the 65Q. The 65Q is designed for operation with a long life, high intensity tungsten halogen lamp.The Luminaire is used in theatre for acting area lighting where beam shaping is not required or in television studios for key and backlighting.

Beam spread angles and multiplying factor (MF)
for Altman fresnels
instrument
6" model # 65Q
field angle
spread
multiplying
factor
spot focus
16º
.28
flood focus
70º
1.40
instrument
8" model # 75Q
8" fresnel

weight: approx.

18 lbs

spot focus
12º
.32
flood focus
45º
.91

6" Fresnel beam spread

PAR
The PAR64 is a low cost, versatile luminaire designed for diverse applications. Intensities and beam spreads are a function of the lamp selected for use in the fixture. One unit can serve multiple purposes simply by changing the lamp. The PAR has an oval shaped beam and is usually lamped at1000 watts.

PAR64 Lamp Data
Watts ANSI Code Manufacturer Lamp Code Color Temp (°K) Rated Life (Hours) Beam Lumens Beam Shape Candlepower (Candela) Beam Angle (Degrees) Field Angle (Degrees)
1000 - Q1000 PAR 64/NSP
Narrow
3000 4000 8,500 NSP
narrow
180,000 8 x 15 14 x 31
1000 - Q1000 PAR 64/MFL
Medium
3000 4000 10,000 MFL
medium
80,000 12 x 28 22 x 45
1000 - Q1000 PAR 64/WFL
Wide
3000 4000 13,500 WFL
wide
33,000 24 x 48 45 x 72
Par 64 Lamp Performance Chart
Distance
10'
20'
30'
40'
50'
Lamp
Center
Beam
FC
H
W
Center
Beam
FC
H
W
Center
Beam
FC
H W
Center
Beam
FC
H W Center
Beam
FC
H
W
1000 watt
NSP-narrow
1800
2.5
5.5
450
4.9
11.1
200
7.4
16.6
113
9.8
22.8
72
12.3
27.7
1000 watt
MFL-medium
800
3.9
8.3
200
7.8
16.6
89
11.7
24.9
50
15.6
33.1
32
19.4
41.4
1000 watt
WFL- wide
330
8.3
14.5
83
16.6
29.1
37
24.9
43.6
21
33.1
58.1
13
41.4
72.7

Calculation reference for beam spreads

The Beam Angle is the angle between the two directions opposed to each other over the beam axis for which the luminous intensity is half that of the maximum luminous intensity.
The Field Angle is the angle between the two directions opposed to each other over the beam axis for which the luminous intensity is 10% that of the maximum luminous intensity.
The Beam Spread is a general term, describing the angle between the two directions opposed to each other over the beam axis for which the luminous intensity is a certain fraction of that of the maximum luminous intensity. The amount of that fraction needs to be given in each specific case.

1.  Calculate: BEAM WIDTH of any angle (beam, field or cut-off)
BEAM WIDTH = ANGLE x .018 x DISTANCE, or
BEAM WIDTH = MULTIPLYING FACTOR x DISTANCE
                  
     ----------------------------------------------------------------------
     
     2.  Calculate: MULTIPLYING FACTOR of any angle, as follows:
     
             BEAM WIDTH                           
         MF = --------   -or-   MF = ANGLE x .018
              DISTANCE                           
     ----------------------------------------------------------------------
      
     3.  Calculate: ANGLE, as follows:
     
                  MF                    BEAM WIDTH 
         ANGLE = ---     -or-   ANGLE =  --------
                .018                   DIST. x .018 
     
     ----------------------------------------------------------------------
     4.      WIDTH OF LIGHTING BEAM - AT ANY SPREAD ANGLE & DISTANCE
     ---------------------------------------------------------------------- 
     D.in|                         ANGLE (in degrees)
      ft.|   10    15    20    25    30    35    40    45    50    55    60  
         |------------------------------------------------------------------ 
      5  |   .9   1.4   1.8   2.3   2.7   3.2   3.6   4.1   4.5   5.0   5.4  
     10  |  1.8   2.7   3.6   4.5   5.4   6.3   7.2   8.1   9.0   9.9  10.8  
     15  |  2.7   4.0   5.4   6.8   8.1   9.5  10.8  12.2  13.5  14.9  16.2  
     20  |  3.6   5.4   7.2   9.0  10.8  12.6  14.4  16.2  18.0  19.8  21.6  
     25  |  4.5   6.8   9.0  11.3  13.5  15.8  18.0  20.3  22.5  24.6  27.0  
     ---------------------------------------------------------------------- 
     30  |  5.4   8.1  10.8  13.5  16.2  18.9  21.6  24.3  27.0  29.7  32.4  
     35  |  6.3   9.5  12.6  15.8  18.9  22.0  25.2  28.4  31.5  34.7  37.8  
     40  |  7.2  10.8  14.4  18.0  21.6  25.2  28.8  32.4  36.0  39.6  43.2  
     45  |  8.1  12.2  16.2  20.3  24.3  28.4  32.4  36.5  40.5  44.6  48.6  
     50  |  9.0  13.5  18.0  22.5  27.0  31.5  36.0  40.5  45.0  49.5  54.0  
     ---------------------------------------------------------------------- 
     55  |  9.9  14.6  19.8  24.8  29.7  34.7  39.6  44.6  49.5  54.5  59.4  
     60  | 10.8  16.2  21.6  27.0  32.4  37.8  43.2  48.6  54.0  59.4  64.8  
     65  | 11.7  17.6  23.4  29.3  35.1  41.0  46.8  52.7  58.5  64.4  70.2  
     70  | 12.6  18.9  25.2  31.5  37.8  44.1  50.4  56.7  63.0  69.3  75.6  
     75  | 13.5  20.3  27.0  33.8  40.5  47.3  54.0  60.8  67.6  74.3  81.0  
     ---------------------------------------------------------------------- 
     80  | 14.4  21.6  28.8  36.0  43.2  50.4  57.6  64.8  72.0  79.2  86.4  
     85  | 15.3  23.0  30.6  38.3  46.0  53.6  61.2  68.9  76.5  84.2  91.8  
     90  | 16.2  24.3  32.4  40.5  48.6  56.7  64.8  72.9  81.0  89.1  97.2  
     95  | 17.1  25.7  34.2  42.8  51.3  59.9  68.4  77.0  85.5  94.1 102.6  
     100 | 18.0  27.0  36.0  45.0  54.0  63.0  72.0  81.0  90.0  99.0 108.0
     ---------------------------------------------------------------------- 

Lighting Inventories for the Loeb EX or Loeb Mainstage

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