EE 365-ELECTRICAL SERVICES
DESIGN
D. Kwegyir
Department of Electrical & Electronic Engineering
College of Engineering
January 2023
1
Unit 3: Polar Curves
2
Unit 3: Polar Curves
Overview
Horizontal polar curve
Vertical polar curve
Determining MHCP and MSCP using polar curves.
www.knust.edu.gh
1 Unit 3.1: Overview
In practice and in almost every lamp or any other
source of light, the luminous intensity in all the
direction is not uniform.
This is because of the shapes of the lamps. The
luminous intensity in all directions can be represented
by polar curves.
www.knust.edu.gh
2 Unit 3.1: Overview
If the actual luminous intensity of a source in
various directions are plotted to scale along lines
radiating from the center of the source at
corresponding angles, we obtain the polar curve of
the candle power.
www.knust.edu.gh
3 Unit 3.1: Overview
A polar curve is a curve on the polar coordinates
showing how the luminous intensity of a source varies
with direction along the surface of a cone which has its
apex at the source.
Polar curves are used to determine the M.S.C.P. etc. of a
source and actual illumination of a surface.
www.knust.edu.gh
1 Unit 3.2: Polar Curves for Horizontal Plane
It is the curve which represents the candle
power of a source in horizontal plane.
The candle power of the source is measured in
the horizontal plane about a vertical axis
for equal angular displacement and the
curve obtained from the results is called polar
curve for the horizontal plane.
www.knust.edu.gh
1 Unit 3.3: Polar Curves for Vertical Plane
These curves are drawn by measuring
the candle powers of a source at an
equal angular displacement in a
vertical plane and about a vertical
axis. The type of such curves have
been shown on the right.
www.knust.edu.gh
1 Unit 3.4: Uses of Polar Curves
If the light source or attached reflector is of
symmetrical type, then two halves of the polar
curve will be similar and in such case, the polar
curve can be represented by indicating only a half
portion.
For luminous intensity from a light source of
unsymmetrical shape, curves in a number of planes
are drawn to represent the adequate distribution
of luminous intensity.
www.knust.edu.gh
2 Unit 3.4: Uses of Polar Curves
By using polar curves, mean horizontal candle power
(MHCP) and mean spherical candle power (MSCP) can
be determined. It is also used to determine actual
illumination on a surface from vertical polar curves by
calculating luminous intensity in that particular direction.
www.knust.edu.gh
3 Unit 3.4: Uses of Polar Curves
The Mean Horizontal Candle Power (MHCP) of a lamp
can be determined from the horizontal polar curve by
taking the mean value of the candle power in a horizontal
direction.
The Mean Spherical Candle Power (MSCP) of a lamp can
be found from the vertical polar curve by applying
Rousseau’s construction.
www.knust.edu.gh
1 Unit 3.4: Determining MSCP Using Polar Curves
Consider a vertical polar curve consisting
of two symmetrical lobes along YOY'
axis. Then the Rousseau's curve can be
constructed as follows;
Firstly, a circle of any radius is drawn by
taking the center (o) as the pole of the
polar curve.
www.knust.edu.gh
2 Unit 3.4: Determining MSCP Using Polar Curves
Draw a line AB equal and parallel to the
vertical diameter (YOY’) of the circle.
Draw a line OCD such that C lies on the
polar curve and D lies on the circle.
Let E be the projection of line OCD onto
the parallel line AB.
www.knust.edu.gh
3 Unit 3.4: Determining MSCP Using Polar Curves
From point E, erect an ordinate in such a
way that EF=OC (radius of the polar
curve)
Similarly, from line AB, ordinates equal
to the corresponding radius on the polar
curve are erected such as IJ=OG,
MN=OK, BR=OP and so on.
www.knust.edu.gh
4 Unit 3.4: Determining MSCP Using Polar Curves
The curve obtained by joining the ends of
these ordinates is know as Rousseau’s curve.
From the curve the mean spherical candle
power of the lamp is determined by the
equation
www.knust.edu.gh
5 Unit 3.4: Determining MSCP Using Polar Curves
This is further determined as
The area under the Rousseau’s curve can
either be determined on a graph paper or
found by Simpson’s rule.
www.knust.edu.gh
Example 1
A streetlight is suspended at a height of 10m along the centre
line at regular intervals of 24m. The polar curve of a lamp with its
reflector can be obtained by the data in the table below:
C.P 240 270 290 260 190 130 50 15
Angle to the vertical 0o 10o 20o 30o 40o 50o 60o 70o
Plot a polar curve for the data above and determine the mean
spherical candle power (MSCP)
www.knust.edu.gh
The End
www.knust.edu.gh
