Page 162 - Offshore Electrical Engineering Manual

Lighting Calculations 149

The integral known as the parallel plane aspect factor is a function of the shape
of the intensity distribution in the axial plane inclined at θ to the horizontal and the
angle β (the aspect angle) subtended by the luminaire at P, which must be opposite
one end of the luminaire, as in Fig. 2.14.3.
The shape of the intensity distribution is similar in any axial plane for most fluo-
rescent luminaires, and for a given luminaire, the aspect factor is independent of θ,
varying only with β, so that it may be denoted by AF(β).
Most diffuser cross-section shapes can be expressed mathematically, so that
AF(β) can be found by integration. For a uniform diffuser, for which I(α) equals I(0)
cos α:
β
AF (β) =∫ cos 2α dα
0
= (β+ sin β cos β) (2.14.4)
A numerical method of integration may be used, such as dividing the axial curve
into a number of equiangular zones.
To calculate the illuminance produced at a point opposite the end of the luminaire
on a plane parallel to the luminaire (CD in Fig. 2.14.3) the aspect angle β is deter-
mined and the value of AF(β) is entered in Eq. (2.14.3).
I (0 , θ)
E = cos θ cos ϕ AF (β) (2.14.5)
lh
Should the point concerned not be opposite the end of the luminaire, the principle
of superposition can be applied. If it is opposite a point on the luminaire, then the
illuminance due to the left and right hand parts of the luminaire are added. If it is
beyond the luminaire then the illuminance due to a luminaire of extended length is
reduced by the illuminance due to the imaginary extension.
Fig. 2.14.4 shows a typical calculation sheet for linear source lighting.
The same method may be used for calculating the illuminance on a plane per-
pendicular to the axis of the luminaire (AFP in Fig. 2.14.3). The derivation followed
above applies, with sin α replacing cos α cos ϕ in Eq. (2.14.2), resulting in a final
expression for the illuminance at P of:
I (0 , θ) cos θ β I (α , θ)
E = ∫ 0 sin α dα
lh I (0 , θ) (2.14.6)

The integral expression is now the perpendicular plane aspect factor AF(β).
Again this is substantially independent of θ in most practical situations, resulting
in:
I (0 , θ)
E = cos θ AF (β)
lh (2.14.7)
which determines the illuminance on a plane perpendicular to a linear luminaire.