Tracking-Free Spherical Solar Collector - A Design Concept
S. M. Situmbeko and K.L. Kumar
Department of Industrial Design and Technology,
University of Botswana, Gaborone, Botswana
situmbeko@mopipi.ub.bw, kumarkl@mopipi.ub.bw
Abstract
Most of the existing solar collector systems require tracking with respect to the ‘daily path of the sun’ which
is different at all the places on the earth and varies every day between the two extremes in local winter and
summer. For example, at Gaborone in Botswana, the mid-winter sunrise occurs at 58o NE and sunset at 58o
NW whereas the mid-summer sunrise and sunset occur at 112 o SE and 112o SW respectively. The tracking
mechanism required for a conventional flat-plate, parabolic or paraboloid solar collector must be threedimensional and controlled to track synchronously with the path of the sun. Some recent developments
suggest ‘optimum orientation’ of the collectors mounted on ground supports or installed on slanting roofs but
these are very limited success stories. The concept of optimum orientation is useful to the design of buildings,
workshops, laboratories, solar farms, etc. but not for design of efficient solar collectors. The authors have
proposed a design of universal spherical convex solar collectors which have the maximum possible thermoconversion efficiency. This paper presents a conceptual framework of a spherical convex surface studded with
photoelectric solar cells. It may also be manifested as a dome-shaped roof of a building installed with a large
number of solar cells. The idea behind the proposal is that the parallel rays of the sun incident at any angle
and at any place on the earth will be harnessed to operate the photoelectric cells which receive the rays. The
proposed spherical convex solar collector needs no tracking and it is suitable at any place on the earth.
Keywords
solar collector, tracking, spherical convex, thermo-conversion efficiency
1. Introduction
Most of the existing solar collector systems require
continuous tracking with respect to the ‘daily path of
the sun’ which is different at all the places on the
earth and varies every day between the two extremes
in local winter and summer. For example, at
Gaborone in Botswana, the mid-winter sunrise occurs
at 58o NE and sunset at 58o NW whereas the midsummer sunrise and sunset occur at 112o SE and 112o
SW respectively. This is shown in Fig.1. The tracking
mechanism required for a conventional flat-plate,
parabolic or paraboloid solar collector must,
therefore, be three-dimensional and controlled to
track synchronously with the path of the sun.
Some recent developments suggest ‘optimum
orientation’ of the collectors mounted on ground
supports or installed on slanting roofs but these are
very limited success stories. The concept of optimum
orientation may be useful to the design of fixed
structures, e.g., residential and office buildings,
workshops, laboratories, solar farms, etc. but not in
general as it does not represent a design
improvement.
Figure 1 Sun-path in Gaborone in Summer
and Winter
The authors have proposed a novel design of
universal spherical convex solar collectors which
should have the maximum
conversion efficiency.
possible
thermo-
2. Literature Survey
1. Available Wattage per unit Projected Area
The solar intensity I varies from sunrise to sunset at
any given place. At a time t, referred to sunrise, when
the sun subtends an angle θ with the horizon, i.e.
sunrays arrive at an angle θ with the horizontal. The
projected area at which the sunrays fall normal, as
shown in Fig.2 is given by:
The authors undertook a comprehensive literature
survey but did not find anything close to what they
have conceived themselves. This concept is inspired
by the ‘shape of the universe’, i.e., common shape of
galactic bodies including our own planet earth as well
as the sun. Different shapes and types of solar
collectors are currently in use. The shape in most
cases being influenced by the type of application.
Common solar collector shapes are planar and
parabolic. Some of them are reviewed as follows:
A "flat plate collector" contains an absorber plate that
uses solar radiation to heat a "carrier fluid," like oil or
water, or air. Because these collectors can heat carrier
fluids to around 80o C, they are suited for residential
applications.
Figure 2 Projected Area
D 2
4
Figure 3 A Flat Plate Collector
 Cos
(1)
Solar power at that instant is given by
PI
whence,  
P
D 2
D 2
4
 Cos
(2)
 I  Cos
4
The solar energy, E, collected per unit projected area
from sunrise at T1 to sunset at T2 is given by
T2
E   I  Cos
(3)
T1
where I = f(t) must be looked up from the tables.
Average solar power, i.e. wattage per unit projected
area will then be
Pav 
E

T T 
2
1
 T2


I  Cos 


  T1

T  T  (4)
2
1
The integrand consists of I and θ, both of which vary
with time t.
Concentrating collectors are intended for larger-scale
applications such as furnaces and air conditioning,
where larger heating potential is required. The rays of
the sun from a relatively wide area are focused into a
small area by means of reflective mirrors, and thus
the heat energy is concentrated.
This method
has the potential to heat liquids to a much higher
temperature than flat plate collectors can alone. The
heat from the concentrating collectors can be used to
boil water. This is reflected in application of
concentrating collectors for solar cooking. [1]
Figure 4 Solar Cooker based on a
Concentrating Collector (Photo:
courtesy of STC Consultants, Zambia)
The concept of spherical and cylindrical solar
collector is being applied in solar cookers where the
external side of the black coated pot exposed to the
sun acts as a direct collector whilst the other side that
is shielded is supplied by solar energy reflected off
the parabolic collector surface. For solar photovoltaic
applications, the planar solar collector surface has so
far been the commonest. [2]
Figure 6 A 2 MW utility scale photovoltaic
with a total output of 354 MW (photo:
courtesy Kramer Junction Operating
Co.)
3. Tracking Mechanisms
Solar trackers may be active or passive. Some
trackers only have one axis for adjusting while others
are adjustable on two axes. There are two main ways
to make the solar cells more efficient, one is to
develop the solar cell material and make the panels
even more efficient and another way is to optimise
the output by installing the solar panels on a tracking
base that follows the sun.
The end-users generally prefer the tracking solution
rather than a fixed ground system to increase their
earnings because:
 The efficiency increases by 30-40%
 The space requirement for a solar park is
reduced, and they keep the same output
 The return of the investment timeline is reduced
 The tracking system amortises itself within 4
years (on average)
Figure 5 One of nine solar electric energy
generating systems at Kramer Junction,
California, power plant near
Sacremento, California (photo:
courtesy DOE/NREL, Warren Gretz)
Tracking the sun from east in the morning to west in
the evening is believed to increase the efficiency of
the solar panel by 20-62% depending on whom you
ask and where you are in the world. Nearer the
equator, higher the benefit of tracking the sun.
Increased efficiency will give the owner of the solar
panel (producer of energy) more money as the
payment is based on how much energy you can
produce.
4.1 Single axis tracking systems
As the name says, a single axis tracking system is a
system that moves over one axis. Single axis solar
trackers can either have a horizontal or a vertical
axle. The horizontal type is used in tropical regions
where the sun gets very high at noon, but the days are
short. The vertical type is used in high latitudes (such
as in the UK) where the sun does not get very high,
but summer days can be very long.
Figure 7 A Single Axis Tracking System
sun, the efficiency of the solar panels can be
increased by 30-40%. Double axis solar trackers have
both a horizontal and a vertical axle and so can track
the Sun's apparent motion exactly anywhere in the
World. This type of system is used to control
astronomical telescopes, and so there is plenty of
software available to automatically predict and track
the motion of the sun across the sky. However, the
same tends to be expensive particularly when we are
attempting to use ‘free’ solar energy around us.
The dual axis tracking system is also used for
concentrating a solar reflector toward the
concentrator on heliostat systems. [3]
Figure 9 Dual axis tracking used to orient a
mirror.
Figure 8 Solar panels with single axis
Tracking
The panels can for instance be fixed in an angle
towards south. As the sun rises from the east and
goes down in the west, the panels adjust accordingly
to increase the efficiency of the panels. The single
axis tracking system is the simplest solution and the
most common one used.
4.2 Dual axis tracking systems
A dual axis tracking system is a system that follows
the sun in multiple angles ensuring that the sunbeam
angle is 100% correct on the panel. By tracking the
Figure 10 A Vertical Axis Solar Tracker [4]
Authors have seen a comprehensive tracking system
at RIIC Kanye. It was under repair when seen last. In
fact, it was this huge and complicated tracking
system which led us to think to get rid of it!
A simplified schematic diagram of a vertical-axis
solar tracker fitted to a solar panel located in the UK
(high latitude Northern Hemisphere) is shown in
figure 10. A pair of sensors (typically a type of
cadmium sulphide photoresistors are used) point to
the East and West of the location of the Sun. The
light detected by the Eastward-facing sensor is at a
lower intensity to that detected by the Westwardfacing sensor. Therefore, the solar panel must be
turned westwards (by the motor controlled by the
solar tracker circuit) until the levels of light detected
by both the East and the West sensors are equal. At
that point the solar panel will be directly facing the
sun and generated electricity optimally. Obviously,
real world solar trackers (such as the one pictured
above) are neither simple nor cheap. A solar tracker
must be able to reset itself at sunset so it is ready for
sunrise, it must cope with all weather conditions like
dust storms, hailstorms and rain. It must work
reliably 365 days a year. In addition the mount for the
solar panel must be strong enough to cope with the
winds.
in Figure 12. [5] The Sphelar® cell captures light
from all directions, which means it can catch
reflected light and diffused light. In addition, there is
no need for the superfluous operation of tracking the
sun. The spherical light-receiving surfaces achieve
unprecedented high generation efficiency.
4. Concept Design of Spherical Convex
Surface
Figure 12 Existing Solar Cell Collectors
5. Suggested Concept for Design
Figure 11 Designs to Capture Reflected
Light
The reason why a room does not become dark even if
it does not receive direct sunlight is because it
receives a variety of reflected and diffused light.
However, conventional flat solar cells are unable to
effectively harness this indirect light. In addition, the
sun takes on many different positions according to
the season and time of day, so in order to obtain a
continuous operation, there is a need to change the
orientation of the solar cell by constantly following
the sun. Two existing solar cell collectors are shown
Based on the structure of a C60 Carbon molecule
consisting of 12 pentagons and 20 hexagons – an
almost perfect sphere, also commonly known as a
Buckminsterfulerene or Buckyball [6], it would be
possible to use flat pieces of base material on which
conventional flat solar cells would be laminated thus
reducing the cost of developing solar cells fitting a
perfectly spherical form.
The inclusion of a back spherically-shaped reflective
surface is also proposed in order to harness most of
the light which would otherwise escape.
Figure 15 Upper 150 Degrees of the Hemisphere
Figure 13 Buckyball structure
The design is ‘universal’ in the sense that it can be
used at any place on the earth and it can employ any
method of harnessing solar energy regardless of its
location. The collector can be installed on top of a
roof of a building or in an open space, say in a field.
The lower part, including the 15 degrees peripheral
base can be used to reinforce the shell structure and
serve to mount the collector.
In doing so, the collector would capture a large
fraction of the available wattage thoughout the day at
any place on the earth. From the foregoing expression
for average wattage per unit area W,
 T 2 I  Cos 


E

Pav 
  T1
T 2  T 1
T 2  T 1
Figure 14 Soccer ball solar array
Fortunately for us, the sun rises above the horizon
due East and it sets down the horizon due West
regardless of the place on the earth. This fact reduces
the shape of the tracking-free collector to a
hemisphere. Further, sun rays are very weak in the
early hours and they also lose heat before the sunset.
It enables us to cut out the first 15 degrees and the
last 15 degrees above the base of the hemisphere, i.e.,
limited to 150 degrees as shown in Figure 15. The
convex surface of the hollow spherical shell can be
used to instal photoelectric solar cells all over it.
Alternatively, small size solar collector panels can be
installed on it so that the rays are concentrated at a
desired point inside the shell. One is, therefore, free
to use the technology of heat collection or thermo
electric devices on the spherical surface.
(5)
the energy ‘E’ collected by the collector with a
diameter ‘D’ and projected area ‘A’ over a ‘H’ hour
day becomes
E=WxAxH
(6)
in appropriate units.
6. Summary/ Conclusion
The authors have thus proposed a design concept of a
tracking-free hemispherical solar collector, providing
liberty of employing panels of lenses or any type of
solar cells on the upper curved convex surface. The
design allows greater effectiveness at all places on
the earth throughout the year and it can be operated
under all weather conditions.
Literature survey was useful in understanding the
complexity of the tracking systems, which led the
authors to propose a more practical but, perhaps, a
more expensive system which does not need any
tracking mechanism.
References
[1] Situmbeko, S.M., Solar Thermal Applications –
Solar Energy Workshop, University of Botswana, 13
December 2000, Gaborone, Botswana
[2]http://www.powerfromthesun.net/chapter1/Chapte
r1.htm; April 2008
[3] http://www.solar-tracking.com/; 2008
[4] http://www.reuk.co.uk/Solar-Tracker.htm; 2008
[5]http://www.kyosemi.co.jp/product/pro_ene_sun_e
1.html; May 2008
[6] Baxter M, Product Design, Stanely Thornes
(Publishers) Ltd¸Chtenham, UK, 1999 ISBN 0
7487416 p 66