The formulas by which we can calculate the direct illumination due to light from rectangular source of uniform brightness are apparently rather complicated.The author shows that they are not so in reality and how easily they can be calculated, with simple nomographic charts, especially for the case in which the sides are parallel to the illuminated surface. The daylight factor and sillfactor-ratio for direct illumination, too, can be deduced.
To calculate the incident flux on a rectangular area, which is parallel or perpendicular to the source, when a pair of opposite sides of the former is parallel to that of the latter, Lambert';flux function may be used.The author shows another flux function, which is expressed by
phi; (ω) =1/2(ω-1/2 tan ω log sin ω + 1/2 cot ω log cos ω)
which has the relations
φ (ω) =tan ω·φ (ω)
where φ (ω) is Lambert's,
and φ (ω)+φ(π/2-ω)=π/4·
The value of φ (ω) is always finite while that of φ (ω) becomes infinite if φ approaches π/2. φ (ω) can be easily interpolated.
Making use of two reciprocation theorems, we can express generally the amount of incident flux on a rectangle, emited from another rectangular source which is perpendicular or parallel to the former and whose one side is parallel to that of the former. Those expressions ate algebraic sum of the function F (
x, y) which is
xyφ [tan
-1 (
x/
y)].
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