Basic Lighting Math

Power:

Watts = Volts * Amps

Amps = Watts / Volts

Sine Wave (VAC):

RMS Volts = 0.707 x Peak Volts

RMS Volts = 1.11 x Average 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

Meters = feet * 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

ÊRadians = 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

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.

A = B * (C/D)

P = D / B

Distances, intensities, spreads, and angles:Ê

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 multiplying factor

ÊFootcandles:

ÊFootcandles = Candlepower / (D * D)

Candlepower:

Candlepower = Footcandles * (D * D)

Beam angle multiplying factor (mf):

mf = 2 * TAN(F / 2)

Êmf = X / D

Beam angle (F):

F = 2 * ATAN(mf / 2)

F = 2 * ATAN(X / (2 * D) )

Beam spreadÊ (oval width X if not straight on):

X = D * (2 * TAN(F / 2))Ê

X = D * mf

Beam oval length (Y) (when beam hits surface at angle):

Y = V * (TAN(K + F/2) - TAN(K - F/2))

Ê

Throw distance (D):

ÊD = X / mf

ÊD = SQUARE ROOT( (V * V) + (H * H) )

ÊD = H / COS(C)

ÊD = V / SIN(C)

ÊD = H / SIN(K)

ÊD = V / COS(K)

ÊD = SQUARE ROOT(Candlepower / Footcandles)

Horizontal distance (H):

ÊH = SQUARE ROOT( (D * D) - (V * V) )

ÊH = V / TAN(C)

ÊH = D * COS(C)

ÊH = D * SIN(K)

ÊH = V * TAN(K)

Vertical height (V):

ÊV = SQUARE ROOT( (D * D) - (H * H) )

ÊV = H * TAN(C)

ÊV = D * SIN(C)

ÊV = D * COS(K)

ÊV = H / TAN(K)

Focus angle off horizontal (C):

ÊC = ATAN(V / H)

ÊC = ASIN(V / D)

ÊC = 90 - ASIN(H / D)

ÊC = 90 - K

Focus angle off vertical (K):

ÊK = ATAN(H / V)

ÊK = ASIN(H / D)

ÊK = 90 - ASIN(V / D)

K = 90 - C