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STAGE MATH

The Following is a collection of math formuals that can prove useful to ligting designers and electricians.

POWER:
  • Watts = Volts * Amps
  • Amps = Watts / Volts
SINE WAVE (VAC):
  • RMS Volts = 0.707 x Peak Volts
  • RMS Volts = 1.11 x Peak Volts
  • Peak Volts = 1.57 x Average Volts
  • Peak Volts = 1.414 x RMS Volts
  • Average Volts = 0.637 x Peak Volts
  • Average Volts = 0.9 x RMS Volts
DC VOLTAGE DROP OF CONDUCTOR (CABLE) OF L LENGTH
  • V = Voltage Drop
  • I = Current
  • R = Resistance of Conductor per 1000 feet
  • L = Length of Conductor in feet
  • R for 18awg = 6.51
  • 16awg = 4.09
  • 14awg = 2.58
  • 12awg = 1.62
  • 10awg = 1.02
  • 8awg = 0.64
  • V = I * L * (R / 1000) * 1.004
UNIT CONVERSIONS:
  • Inches = millimeters / 25.4
  • millimeters = inches * 25.4
  • feet = meters / 0.3048
  • footcandles = lux / 10.8
  • lux = footcandles * 10.8
  • Centigrade = 0.556 * (Fahrenheit - 32)
  • Fahrenheit = 1.8 * (Centigrade + 32)
  • pounds = kilograms * 2.205
  • kilograms = pounds * 0.454
  • degrees = 180 * radians / PI
  • radians = PI * degrees /180

Pattern projection magnification and required pattern size:

  • A = new pattern size
  • B = old pattern size
  • C = new projection size
  • D = old projection size
  • P = projection magnification
  • A = B * (C / D)
  • P = D / B

For standard AQ61 (or Altman 360Q) ellipsoidals, consider old pattern size to be 3" (size of gate), and old projection size to be the beam spread using the field angle information. Check diameter of gate (shutter plane opening) for other fixtures.

DISTANCES, INTENSITIES, SPREADS, AND ANGLES:

As seen in the drawing:

  • D = throw distance
  • V= vertical height
  • H = horizontal distance
  • C = focus angle off horizontal
  • K = focus angle off vertical
  • F = beam or field angle of fixture
  • X = beam spread (beam oval width)
  • Y = beam oval length
  • mf=beam spread
lightPic
CANDLEPOWER:
  • Candlepower = Footcandle * (D * D)
BEAM ANGLE MULTIPLYING FACTOR (mf):
  • mf = 2 * TAN (F / 2)
  • mf = X / D
BEAM ANGLE (F):
  • F = 2 * ATAN (MF / 2)
  • F = 2 * ATAN(X / (2 * D)
BEAM SPREAD (OVAL WIDTH X IF NOT STRAIGHT ON)
  • X = D * (2 * TAN(F / 2))
  • X = D * mf
VERTICAL HEIGHT (V):
  • V = SQUARE ROOT( (D * D) - (H * H) )
  • V = H * TAN( C )
  • V = D * SIN( C )
  • V = D * COS(K)
  • V = H / TAN(K)
FOCUS ANGLE OFF HORIZONTAL ( C ):
  • C = ATAN(V / H)
  • C = ASIN(V / D)
  • C = 90 - ASIN(H / D)
  • C = 90 - K
FOOTCANDLES:
  • Footcandles = Candlepower / (D * D)
THROW DISTANCE (D):
  • D = X / mf
  • D = SQUARE ROOT( (V * V) + (H * H)
  • D = H / COS( C )
  • D = V / SIN( C )
  • D = H / SIN(K)
  • D = V / COS(K)
  • D = SQUARE ROOT(Candlepower / Footcandles)
BEAM OVAL LENGTH (Y) (WHEN BEAM HITS SURFACE AT ANGLE)
  • Y = V * ( TAN(K + F/2) - TAN(K - F/2) )
HORIZONTAL DISTANCE (H):
  • H = SQUARE ROOT( (D * D) - (V * V) )
  • H = V / TAN( C )
  • H = D * COS( C )
  • H = D * SIN(K)
  • H = V * TAN(K)
FOCUS ANGLE OFF VERTICAL (K):
  • K = ATAN(H / V)
  • K = ASIN(H / D)
  • K = 90 - ASIN(V / D)
  • K = 90 - C

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