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Polar Curves of CP Distribution

This document discusses polar curves, which graphically represent the candle power (luminous intensity) distribution of a light source in different directions. Polar curves are constructed by plotting the candle power along lines radiating from the center of the source at corresponding angles. They allow visualization of the three-dimensional candle power distribution of a source. Elevations and plans are used to represent the distribution in vertical and horizontal planes. Polar curves are important for determining properties like mean spherical candle power and calculating actual illumination, as the candle power value in the given direction is used. They reveal how the distribution can be modified using different reflector shapes.

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Ivan-Jeff Alcantara
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449 views2 pages

Polar Curves of CP Distribution

This document discusses polar curves, which graphically represent the candle power (luminous intensity) distribution of a light source in different directions. Polar curves are constructed by plotting the candle power along lines radiating from the center of the source at corresponding angles. They allow visualization of the three-dimensional candle power distribution of a source. Elevations and plans are used to represent the distribution in vertical and horizontal planes. Polar curves are important for determining properties like mean spherical candle power and calculating actual illumination, as the candle power value in the given direction is used. They reveal how the distribution can be modified using different reflector shapes.

Uploaded by

Ivan-Jeff Alcantara
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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1908 Electrical Technology

49.7. 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
Fig. 49.20

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 3-dimensional
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. 49.20 are shown two polar curves of
Fig. 49.21 c.p. distribution in a vertical plane. Curve 1 is for
Illumination 1909
vacuum type tungsten lamp with zig-zag filament whereas curve 2 is for gas filled tungsten lamp with
filament arranged as a horizontal ring.
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. 49.21.
The curves 1 and 2 are as in Fig. 49.20, curves 3 is 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 symmterical 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 cross-section
elliptical—such reflectors are
widely used for lighting shop
windows. Fig. 49.22 represents the
distribution of luminous intensity of
such source and its reflector in two
planes at right angles to each other.
The importance of considering Fig. 49.22
the polar curves in different planes when the c.p. distribution in asymmetrical is even more strikingly
depicted by the polar curves in Y Y plane and X X plane of a lamp with a special type of reflector
designed for street lighting purposes (Fig. 49.23).

Fig. 49.23
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. 49.24 is shown the polar curve of c.p. distribution of a straight type of lamp in a horizontal
plane.

49.8. Uses of Polar Curves


Polar curves are made use of in determining the M.S.C.P. etc. of a source. They are also used in
determining the actual illumination of a surface i.e. while calculating the illumination in a particular
direction, the c.p. in that particular direction as read from the vertical polar curve, should be
employed.

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