Polar Curves of C.P. Distribution
All our calculations so far were based on the tacit assumption that the light source was of
equal luminous intensity or candle-power in all directions. However, lamps and other
sources of light, as a rule, do not give uniform distribution in the space surrounding them.
If the actual luminous intensity of a source in various directions be plotted to scale along
lines radiating from the centre of the source at corresponding angles, we obtain the polar
curve of the candle power.
Suppose we construct a figure consisting of large number of spokes radiating out from a
point —the length of each spoke representing to some scale the candle power or luminous
intensity of the source in that particular direction.
If now we join the ends of these spokes by some suitable material, say, by linen cloth, then
we get a surface whose shape will represent to scale the three dimensional candle power
distribution of the source placed at the centre. In the ideal case of a point source having
equal distribution in all directions, the surface would be spherical.
It would be realized that it is difficult to give a graphic representation of such a 3dimensional model in a plane surface. Therefore, as with engineering drawings, it is usual to
draw only one or more elevations and a plan of sections through the centre of the source.
Elevations represent c.p. distribution in the vertical plane and the plans represent c.p.
distribution in horizontal plane. The number of elevations required to give a complete idea
of the c.p. distribution of the source in all directions depends upon the shape of the plan i.e.
on the horizontal distribution. If the distribution is uniform in every horizontal plane i.e. if
the polar curve of horizontal distribution is a circle, then only one vertical curve is sufficient
to give full idea of the space distribution. In Fig.3.20 are shown two polar curves of c.p.
distribution in a vertical plane. Curve 1 is for Vacuum type tungsten lamp with zig-zag
filament whereas curve 2 is for gas filled tungsten lamp with filament arranged as a
horizontal ring.
Fig 3.21
If the polar curve is symmetrical about the vertical axis as in the figures given below, then it
is sufficient to give only the polar curve within one semicircle in order to completely define
the distribution of c.p. as shown in Fig. 3.21.
The curves 1 and 2 are as in Fig. 3.20, curves 3 are for d.c. open arc with plain carbons and
curve 4 is for a.c. arc with plain carbons. However, if the source and/or reflector are not
symmetrical about vertical axis, it is impossible to represent the space distribution of c.p. by a
single polar diagram and even polar diagrams for two planes at right angles to each other give
no definite idea as to the distribution in the intermediate planes.
Consider a filament lamp with a helmet-type reflector whose axis is inclined and crosssection elliptical—such reflectors are widely used for lighting shop windows. Fig. 3.22
represents
distribution of luminous intensity of such source and its reflector in two planes at right
angles to each other. The importance of considering the polar curves in different planes
when the c.p. distribution in asymmetrical is even more strikingly depicted by the polar
curves in YY plane and XX plane of a lamp with a special type of reflector designed for
street lighting purposes (Fig. 3.23).
Fig 3.22
Fig 3.33
It would be realized from above that the polar distribution of light from any source can be
given any desired form by using reflectors and/or refractors of appropriate shape.In Fig.
3.24 is shown the polar curve of c.p. distribution of a straight type of lamp in a horizontal
plane.