Tài liệu Handbook of Mechanical Engineering Calculations P17 doc

17.1
SECTION 17
SOLAR ENERGY
Analysis of Solar Electric Generating
System Loads and Costs
17.1
Economics of Investment in an
Industrial Solar-Energy System
17.4
Designing a Flat-Plate Solar-Energy
Heating and Cooling System
17.6
Determination of Solar Insolation on
Solar Collectors Under Differing
Conditions
17.13
Sizing Collectors for Solar-Energy
Heating Systems
17.15
F Chart Method for Determining Useful
Energy Delivery in Solar Heating
17.17
Domestic Hot-Water Heater Collector
Selection
17.24
Passive Solar-Heating System
Design
17.29
Determining if a Solar Water Heater Will
Save Energy
17.36

Sizing a Photovoltaic System for
Electrical Service
17.37
Economics and Applications
ANALYSIS OF SOLAR ELECTRIC GENERATING
SYSTEM LOADS AND COSTS
Analyze the feasibility of a solar electric generating system (SEGS) for a power
system located in a sub-tropical climate. Compare generating loads and costs with
conventional fossil-fuel and nuclear generating plants.
Calculation Procedure:
1. Determine when a solar electric generating system can compete with
conventional power
Solar electric generation, by definition, requires abundant sunshine. Without such
sunshine, any proposed solar electric generating plant could not meet load demands.
Hence, such a plant could not compete with conventional fossil-fuel or nuclear
plants. Therefore, solar electric generation, is at this time, restricted to areas having
high concentrations of sunshine. Such areas are in both the subtropical and tropical
regions of the world.
One successful solar electric generating system is located in the Mojave Desert
in southern California. At this writing, it has operated successfully for some 12
years with a turbine cycle efficiency of 37.5 percent for a solar field of more than
2-million ft
2
(1,805,802 m
2
). A natural-gas backup system has a 39.5 percent effi-
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Source: HANDBOOK OF MECHANICAL ENGINEERING CALCULATIONS

17.2
ENVIRONMENTAL CONTROL
Cooling tower
Pre-heater
Steam
generator
Superheater
Reheater
SI Values
FC
559 293 C
735 391 C
FIGURE 1 Solar-generating-method schematic traces
flow of heat-transfer fluid. (Luz International Ltd. and
Power.)
ciency. Both these levels of efficiency are amongst the highest attainable today with
any type of energy source.
2. Sketch a typical cycle arrangement
Technology developed by Luz International Ltd. uses a moderate-pressure state-of-
the-art Rankine-cycle steam-generating system using solar radiation as its primary
energy source, Fig. 1. In the Mojave Desert plant mentioned above, a solar field
comprised of parabolic-trough solar collectors which individually track the sun
using sun sensors and microprocessors provides heat for the steam cycle.
Collection troughs in the Mojave Desert plant are rear surface mirrors bent into
the correct parbolic shape. These specially designed mirrors focus sunlight onto
heat-collection elements (HCE). Each mirror is washed every two weeks with de-
mineralized water to remove normal dust blown off the desert. The mirrors must
be clean to focus the optimal amount of the sun’s heat on the HCE.
3. Detail the sun collector arrangement and orientation
With the parabolic mirrors described above, sun sensors begin tracking the sun

before dawn. Microprocessors prompt the troughs to follow the sun, rotating 180
Њ
each day. A central computer facility at the Mojave Desert plant monitors and
controls each of the hundreds of individual solar collectors in the field and all of
the power plant equipment and systems.
During summer months when solar radiation is strongest, some mirrors must be
turned away from the sun because there is too much heat for the turbine capacity.
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SOLAR ENERGY
SOLAR ENERGY
17.3
Solar mode
FIGURE 2 Firing modes are shown for typical summer day, left, and typical winter day, right.
Correlation of solar generation to peaking power requirements is evident. (Luz International Ltd.
and Power.)
When this occurs, almost every other row of mirrors must be turned away. However,
in the winter, when solar radiation is the weakest, every mirror must be employed
to produce the required power.
In the Mojave Desert plant, the mirrors focus the collected heat on the
HCEs—coated steel pipes mounted inside vacuum-insulated glass tubes. The HCEs
contain a synthetic-oil heat-transfer fluid, which is heated by the focused energy to
approximately 735
Њ
F (390.6
Њ
C) and pumped through a series of conventional heat
exchangers to generate superheated steam for the turbine-generator.
In the Mojave Desert plant, several collectors are assembled into units called

solar collector assemblies (SCA); generally, each 330-ft (100.6-m) row of collectors
comprises one SCA. The SCAs are mounted on pylons and interconnected with
flexible hoses. An 80-MW field consists of 852 SCAs arranged in 142 loops. Each
SCA has its own sun sensor, drive motor, and local controller, and is comprised of
224 collector segments, or almost 5867 ft
2
(545 m
2
) of mirrored surface and 24
HCEs. From this can be inferred that some (5867 /80)
ϭ
73.3 ft
2
(6.8 m
2
) per MW
is required at this installation.
4. Plan for an uninterrupted power supply
To ensure uninterrupted power during peak demand periods, an auxiliary natural-
gas fired boiler is available at the Mojave Desert plant as a supplemental source of
steam. However, use of this boiler is limited to 25 percent of the time by federal
regulations. This boiler serves as a backup in the event of rain, for night production
when called for, or if ‘‘clean sun’’ is unavailable. According to Luz International,
clean sun refers to solar radiation untainted by smog, clouds, or rain. Figure 2
shows the firing modes for typical summer (left) and winter (right) days. Correlation
of solar generation to peaking-power requirements is evident.
As shown in the cycle diagram, the balance-of-plant equipment consists of the
turbine-generator, steam generator, solar superheater, two-cell cooling tower, and
an intertie with the local utility company, Southern California Edison Co. The
Mojave Desert installation represents some 90 percent of the world’s solar power

production. Since installing it first solar electric generating system in 1984, a 13.8-
MW facility, Luz has built six more SEGS of 30 MW each. Units 6 and 7 use
third-generation mirror technology.
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SOLAR ENERGY
17.4
ENVIRONMENTAL CONTROL
5. Determine the costs of solar power
SEGS are suited to utility peaking service because they provide up to 80 percent
of their output during those hours of a utility’s greatest demand, with minimal
production during low-demand hours.
Cost of Luz’s solar-generated power is less than that of many nuclear
plants—$0.08/kWh, down from $0.24 /kWh for the first SEGS, according to com-
pany officials. Should the price of oil go up beyond $20/barrel, solar will become
even more competitive with conventional power.
But the advantages over conventional power sources include more than cost-
competitiveness. Emissions levels are much lower—10 ppm—because the sun is
essentially non-polluting. SEGS are equipped with the best available technology
for emissions cleanup during the hours they burn natural gas, the only time they
produce emission.
Related Calculations. Luz International Ltd. has installed more capacity at the
Mojave Desert plant mentioned here, proving the acceptance and success of its
approach to this important technical challenge. That data in this procedure can be
useful to engineers studying the feasibility of solar electric generation for other
sites around the world. Luz received an Energy Conservation Award from Power
magazine, from which the data and illustrations in this procedure were obtained.
There are estimates showing that the sunshine impinging the southwestern United
States is more than enough to generate the entire electrical needs of the

country—when efficient conversion apparatus is developed. It may be that the
equipment described here will provide the efficiency needed for large-scale pollu-
tion-free power generation. Results to date have been outstanding and promise
greater efficiency in the future.
ECONOMICS OF INVESTMENT IN AN
INDUSTRIAL SOLAR-ENERGY SYSTEM
Determine the rate of return and after tax present value of a new industrial solar
energy system. The solar installation replaces all fuel utilized by an existing fossil-
fueled boiler when optimum weather conditions exist. The existing boiler will
be retained as an auxiliary unit. Assume a system energy output (E
s
)of3
ϫ
10
9
Btu
/yr (3.17 kJ
ϫ
10
9
/yr) an initial cost for the total system of $503,000 based on a
collector area (A
c
) of 10,060 ft
2
(934.6 m
2
), a depreciation life (DP) of 12 yr, a tax
rate (
␶

) of 0.4840, a tax credit factor (TC) of 0.25, a system life of 20 yr, an
operating cost fraction (OMPI) of 0.0250, an initial fuel cost (P
f 0
) of $3.11/MBtu
($3.11/ 947.9 MJ) and a fuel price escalation rate (e) of 0.1450.
Calculation Procedure:
1. Compute unit capacity cost (K
s
) in $/million Btu per year
initial cost of system $503,000
K
ϭϭ
s
9
E 3
ϫ
10 Btu /yr
s
$167.67
ϭ
($167.67/ 947.9 MJ /yr).
1 million Btu/ yr
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SOLAR ENERGY
SOLAR ENERGY
17.5
2. Compute levelized coefficient of initial costs (M ) over the life of the system
CRF TC

R,N
M
ϭ
OMPI
ϩ
1
ϪϪ
(
␶
ϫ
DEP)
ͫͩ ͪ ͬ
1
Ϫ
␶
1
ϩ
R
CRF
R,N
is the capital recovery factor which is a function of the market discount
rate (R)* over the expected lifetime of the system (20 yr) and is determined as
follows:
R
CRF
ϭ
R,20
Ϫ
20
1

Ϫ
(1
ϩ
R)
DEP is the depreciation which will be calculated by an accelerated method, the
sum of the years digits (SOYD), in accordance with the following formula:
21
DEP
ϭ
DP
Ϫ
ͩͪ
DP(DP
ϩ
1)R CRF
R,DP
where DP is an allowed depreciation period, or tax life, of 12 yr.
Prepare a tabulation (see below) of M values for various market discount rates
(R).
3. Compute the levelized cost of solar energy (S), for the life cycle of the
system in $/million Btu ($/MJ)
Use the relation, S
ϭ
(K
s
)(M). Since M varies with R, refer to the tabulation of S
for various market discount rates.
4. Compute the levelized cost of fuel (F) in $/ million Btu ($/MJ) and
compare to S
N

P 1
ϩ
e 1
ϩ
e
ƒ0
F
ϭ
CRF 1
Ϫ
ͫ ͩ ͪͩ ͫ ͬ ͪͬ
R,N
␩
R
Ϫ
e 1
ϩ
R
where
␩
is the boiler efficiency for a fossil fuel system which supplies equivalent
heat. Referring to the tabulation, the value of F is tabulated at various market
discount rates for
␩
values of 70, 80, and 100 percent. The rate of return for the
solar installation is that value of R at which F
ϭ
S.For
␩
ϭ

70 percent, R is
between 7.5 and 8.0 percent. For
␩
ϭ
80 percent, R is between 6.5 and 7.0 percent.
These rates of return should exceed current interest (discount) rates to attain eco-
nomic feasibility.
5. Compute the after tax present value (PV) of the solar investment if the
existing boiler installation has an efficiency of 70 percent
1
Ϫ
␶
PV
ϭ
E (F
Ϫ
S)
ͩͪ
s
CRF
R,N
In order to have a positive value of PV, F must exceed S. Therefore, select a market
discount rate (R) from the tabulation which satisfies this criteria. For example, at a
5 percent discount rate,
*See tabulation on page 17.6.
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SOLAR ENERGY
17.6

ENVIRONMENTAL CONTROL
9
3
ϫ
10 1
Ϫ
0.484
PV
ϭ
(20.00
Ϫ
13.91)
ϭ
$117,489.02
ͩͪ
6
10 0.08024
Note that at 8 percent or higher PV will be negative and the investment proves
uneconomical against other investment options.
F
R* CRF
R,N
CRF
R,DP
DEP
(SOYD)
MS
␩
ϭ
100%

␩
ϭ
80%
␩
ϭ
70%
4.5 0.07688 0.10967 0.8210 0.07915 13.27 14.29 17.86 20.41
5.0 0.08024 0.11283 0.8044 0.08295 13.91 14.00 17.50 20.00
5.5 0.08368 0.11603 0.7882 0.08686 14.56 13.71 17.14 19.59
6.0 0.08718 0.11928 0.7727 0.09093 15.25 13.43 16.79 19.19
6.5 0.09076 0.12257 0.7577 0.09511 15.95 13.16 16.45 18.80
7.0 0.09439 0.12590 0.7431 0.09940 16.67 12.89 16.11 18.41
7.5 0.09809 0.12928 0.7290 0.10382 17.41 12.63 15.79 18.04
8.0 0.10185 0.13270 0.7154 0.10833 18.16 12.38 15.47 17.69
*As used in engineering economics, R, discount rate and interest rate refer to the same percentage. The
only difference is that interest refers to a progression in time, and discount to a regression in time. See
‘‘Engineering Economics for P.E. Examinations,’’ Max Kurtz, McGraw-Hill.
REFERENCE
Brown, Kenneth C., ‘‘How to Determine the Cost-Effectiveness of Solar Energy Projects,’’
Power magazine, March, 1981.
DESIGNING A FLAT-PLATE SOLAR-ENERGY
HEATING AND COOLING SYSTEM
Give general design guidelines for the planning of a solar-energy heating and cool-
ing system for an industrial building in the Jacksonville, Florida, area to use solar
energy for space heating and cooling and water heating. Outline the key factors
considered in the design so they may be applied to solar-energy heating and cooling
systems in other situations. Give sources of pertinent design data, where applicable.
Calculation Procedure:
1. Determine the average annual amount of solar energy available at the site
Figure 3 shows the average amount of solar energy available, in Btu /(day

⅐
ft
2
)
(W/m
2
) of panel area, in various parts of the United States. How much energy is
collected depends on the solar panel efficiency and the characteristics of the storage
and end-use systems.
Tables available from the National Weather Service and the American Society
of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE) chart the
monthly solar-radiation impact for different locations and solar insolation [total
radiation form the sun received by a surface, measured in Btu/(h
⅐
ft
2
) (W/m
2
);
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SOLAR ENERGY
SOLAR ENERGY
17.7
FIGURE 3 Average amount of solar energy available, in Btu / (day
⅐
ft
2
) (W/m

2
), for different
parts of the United States. (Power.)
insolation is the sum of the direct, diffuse, and reflected radiation] for key hours
of a day each month.
Estimate from these data the amount of solar radiation likely to reach the surface
of a solar collector over 1 yr. Thus, for this industrial building in Jacksonville,
Florida, Fig. 3 shows that the average amount of solar energy available is 1500
Btu/ (day
⅐
ft
2
) (4.732 W/m
2
).
When you make this estimate, keep in mind that on a clear, sunny day direct
radiation accounts for 90 percent of the insolation. On a hazy day only diffuse
radiation may be available for collection, and it may not be enough to power the
solar heating and cooling system. As a guide, the water temperatures required for
solar heating and cooling systems are:
Space heating Up to 170
Њ
F (76.7
Њ
C)
Space cooling with absorption air
conditioning From 200 to 240
Њ
F (93.3 to 114.6
Њ

C)
Domestic hot water 140
Њ
F (60
Њ
C)
2. Choose collector type for the system
There are two basic types of solar collectors: flat-plate and concentrating types. At
present the concentrating type of collector is not generally cost-competitive with
the flat-plate collector for normal space heating and cooling applications. It will
probably find its greatest use for high-temperature heating of process liquids, space
cooling, and generation of electricity. Since process heating applications are not the
subject of this calculation procedure, concentrating collectors are discussed sepa-
rately in another calculation procedure.
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SOLAR ENERGY
17.8
ENVIRONMENTAL CONTROL
FIGURE 4 Construction details of flat-plate solar collectors. (Power.)
Flat-plate collectors find their widest use for building heating, domestic water
heating, and similar applications. Since space heating and cooling are the objective
of the system being considered here, a flat-plate collector system will be a tentative
choice until it is proved suitable or unsuitable for the system. Figure 4 shows the
construction details of typical flat-plate collectors.
3. Determine the collector orientation
Flat-plate collectors should face south for maximum exposure and should be tilted
so the sun’s rays are normal to the plane of the plate cover. Figure 5 shows the
optimum tilt angle for the plate for various insolation requirements at different

latitudes.
Since Jacksonville, Florida, is approximately at latitude 30
Њ
, the tilt of the plate
for maximum year-round insolation should be 25
Њ
from Fig. 5. As a general rule
for heating with maximum winter insolation, the tilt angle should be 15
Њ
plus the
angle of latitude at the site; for cooling, the tilt angle equals the latitude (in the
south, this should be the latitude minus 10
Њ
for cooling); for hot water, the angle
of tilt equals the latitude plus 5
Њ
. For combined systems, such as heating, cooling,
and hot water, the tilt for the dominant service should prevail. Alternatively, the tilt
for maximum year-round insolation can be sued, as was done above.
When collector banks are set in back of one another in a sawtooth arrangement,
low winter sun can cause shading of one collector by another. This can cause a
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SOLAR ENERGY
SOLAR ENERGY
17.9
FIGURE 5 Spacing of solar flat-plate collec-
tors to avoid shadowing. (Power.)
TABLE 1

Spacing to Avoid Shadowing, ft (m)
Њ
loss in capacity unless the units are carefully spaced. Table 1 shows the minimum
spacing to use between collector rows, based on the latitude of the installation and
collector tilt.
4. Sketch the system layout
Figure 6 shows the key components of a solar system using flat-plate collectors to
capture solar radiation. The arrangement provides for heating, cooling, and hot-
water production in this industrial building with sunlight supplying about 60 percent
of the energy needed to meet these loads—a typical percentage for solar systems.
For this layout, water circulating in the rooftop collector modules is heated to
160
Њ
F (71.1
Њ
C) to 215
Њ
F (101.7
Њ
C). The total collector area is 10,000 ft
2
(920 m
2
).
Excess heated hot water not need for space heating or cooling or for domestic water
is directed to four 6000-gal (22,740-L) tanks for short-term energy storage. Con-
ventional heating equipment provides the hot water needed for heating and cooling
during excessive periods of cloudy weather. During a period of 3 h around noon
on a clear day, the heat output of the collectors is about 2 million Btu/ h (586 kW),
with an efficiency of about 50 percent at these conditions.

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SOLAR ENERGY
17.10
ENVIRONMENTAL CONTROL
FIGURE 6 Key components of a solar-energy system using flat-plate collectors. (Power.)
For this industrial building solar-energy system, a lithium-bromide absorption
air-conditioning unit (a frequent choice for solar-heated systems) develops 100 tons
(351.7 kW) of refrigeration for cooling with a coefficient of performance of 0.71
by using heated water from the solar collectors. Maximum heat input required by
this absorption unit is 1.7 million Btu/h (491.8 kW) with a hot-water flow of 240
gal/ min (909.6 L/ min). Variable-speed pumps and servo-actuated valves control
the water flow rates and route the hot-water flow from the solar collectors along
several paths—to the best exchanger for heating or cooling of the building, to the
absorption unit for cooling of the building, to the storage tanks for use as domestic
hot water, or to short-term storage before other usage. The storage tanks hold
enough hot water to power the absorption unit for several hours or to provide
heating for up to 2 days.
Another—and more usual—type of solar-energy system is shown in Fig. 7. In
it a flat-plate collector absorbs heat in a water/antifreeze solution that is pumped
to a pair of heat exchangers.
From unit no. 1 hot water is pumped to a space-heating coil located in the duct
work of the hot-air heating system. Solar-heated antifreeze solution pumped to unit
no. 2 heats the hot water for domestic service. Excess heated water is diverted to
fill an 8000-gal (30,320-L) storage tank. This heated water is used during periods
of heavy cloud cover when the solar heating system cannot operate as effectively.
5. Give details of other techniques for solar heating
Wet collectors having water running down the surface of a tilted absorber plate and
collected in a gutter at the bottom are possible. While these ‘‘trickle-down’’ collec-

tors are cheap, their efficiency is impaired by heat losses from evaporation and
condensation.
Air systems using rocks or gravel to store heat instead of a liquid find use in
residential and commercial applications. The air to be heated is circulated via ducts
to the solar collector consisting of rocks, gravel, or a flat-plate collector. From here
other ducts deliver the heated air to the area to be heated.
In an air system using rocks or gravel, more space is needed for storage of the
solid media, compared to a liquid. Further, the ductwork is more cumbersome and
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SOLAR ENERGY
SOLAR ENERGY
17.11
FIGURE 7 Solar-energy system using flat-plate collectors and an antifreeze solution in a pair of
heat exchangers. (Power.)
occupies more space than the piping for liquid heat-transfer media. And air systems
are generally not suitable for comfort cooling or liquid heating, such as domestic
hot water.
Eutectic salts can be used to increase the storage capacity of air systems while
reducing the volume required for storage space. But these salts are expensive, cor-
rosive, and toxic, and they become less effective with repeated use. Where it is
desired to store thermal energy at temperatures above 200
Њ
F (93.3
Њ
C), pressurized
storage tanks are attractive.
Solar ‘‘heat wheels’’ can be used in the basic solar heating and cooling system
in the intake and return passages of the solar system. The wheels permit the transfer

of thermal energy from the return to the intake side of the system and offer a means
of controlling humidity.
For solar cooling, high-performance flat-plate collectors or concentrators are
needed to generate the 200 to 240
Њ
F (93.3 to 115.6
Њ
C) temperatures necessary for
an absorption-chiller input. These chillers use either lithium bromide or ammonia
with hot water to for an absorbent/refrigerant solution. Chiller operation is con-
ventional.
Solar collectors can be used as a heat source for heat-pump systems in which
the pump transfers heat to a storage tank. The hot water in the tank can then be
used for heating, while the heat pump supplies cooling.
In summary, solar energy is a particularly valuable source of heat to augment
conventional space-heating and cooling systems and for heating liquids. The prac-
tical aspects of system operation can be troublesome—corrosion, deterioration,
freezing, condensation, leaks—but these problems can be surmounted. Solar energy
is not ‘‘free’’ because a relatively high initial investment for equipment must be
paid off over a long period. And the equipment requires some fossil-fuel energy to
fabricate.
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SOLAR ENERGY
17.12
ENVIRONMENTAL CONTROL
But even with these slight disadvantages, the more solar energy that can be put
to work, the longer the supply of fossil fuels will last. And recent studies show that
solar energy will become more cost-competitive as the price of fossil fuels continues

to rise.
6. Give design guides for typical solar systems
To ensure the best performance from any solar system, keep these pointers in mind:
a. For space heating, size the solar collector to have an area of 25 to 50 percent
of the building’s floor area, depending on geographic location, amount of in-
sulation, and ratio of wall to glass area in the building design.
b. For space cooling, allow 250 to 330 ft
2
(23.3 to 30.7 m
2
) of collector surface
for every ton of absorption air conditioning, depending on unit efficiency and
solar intensity in the area. Insulate piping and vessels adequately to provide fluid
temperatures of 200 to 240
Њ
F (93.3 to 115.6
Њ
C).
c. Size water storage tanks to hold between 1 and 2 gal/ ft
2
(3.8 to 7.6 L/m
2
)of
collector surface area.
d. In larger collector installations, gang collectors in series rather than parallel. Use
the lowest fluid temperature suitable for the heating or cooling requirements.
e. Insulate piping and collector surfaces to reduce heat losses. Use an overall heat-
transfer coefficient of less than 0.04 Btu/ (h
⅐
ft

2
⅐ Њ
F) [0.23 W /(m
2
⅐
K)] for piping
and collectors.
f. Avoid water velocities of greater than 4 ft/ s (1.2 m /s) in the collector tubes, or
else efficiency may suffer.
g. Size pumps handling antifreeze solutions to carry the additional load caused by
the higher viscosity of the solution.
Related Calculations. The general guidelines given here are valid for solar
heating and cooling systems for a variety of applications (domestic, commercial,
and industrial), for space heating and cooling, and for process heating and cooling,
as either the primary or supplemental heat source. Further, note that solar energy
is not limited to semitropical areas. There are numerous successful applications of
solar heating in northern areas which are often considered to be ‘‘cold.’’ And with
the growing energy consciousness in all field, there will be greater utilization of
solar energy to conserve fossil-fuel use.
Energy experts in many different fields believe that solar-energy use is here to
stay. Since there seems to be little chance of fossil-fuel price reductions (only
increases), more and more energy users will be looking to solar heat sources to
provide some of or all their energy needs. For example, Wagner College in Staten
Island, New York, installed, at this writing, 11,100 ft
2
(1032.3 m
2
) of evacuated-
tube solar panels on the roof of their single-level parking structure. These panels
provide heating, cooling, and domestic hot water for two of the buildings on the

campus. Energy output of these evacuated-tube collectors is some 3 billion Btu (3.2
ϫ
10
9
kJ), producing a fuel-cost savings of $25,000 during the first year of instal-
lation. The use of evacuated-tube collectors is planned in much the same way as
detailed above. Other applications of such collectors include soft-drink bottling
plants, nursing homes, schools, etc. More applications will be found as fossil-fuel
price increases make solar energy more competitive in the years to come. Table 2
gives a summary of solar-energy collector choices for quick preliminary use.
Data in this procedure are drawn from an article in Power magazine prepared
by members of the magazine’s editorial staff and from Owens-Illinois, Inc.
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SOLAR ENERGY
SOLAR ENERGY
17.13
TABLE 2
Solar-Energy Design Selection Summary
DETERMINATION OF SOLAR INSOLATION ON
SOLAR COLLECTORS UNDER DIFFERING
CONDITIONS
A south-facing solar collector will be installed on a building in Glasgow, Montana,
at latitude 48
Њ
13
Ј
N. What is the clear-day solar insolation on this panel at 10 a.m.
on January 21 if the collector tilt angle is 48

Њ
? What is the daily surface total
insolation for January 21, at this angle of collector tilt? Compute the solar insolation
at 10:30 a.m. on January 21. What is the actual daily solar insolation for this
collector? Calculate the effect on the clear-day daily solar insolation if the collector
tilt angle is changed to 74
Њ
.
Calculation Procedure:
1. Determine the insolation for the collector at the specified location
The latitude of Glasgow, Montana, is 48
Њ
13
Ј
N. Since the minutes are less than 30,
or one-half of a degree, the ASHRAE clear-day insolation table for 48
Њ
north lat-
itude can be used. Entering Table 3 (which is an excerpt of the ASHRAE table)
for 10 a.m. on January 21, we find the clear-day solar insolation on a south-facing
collector with a 48
Њ
tilt is 206 Btu/(h
⅐
ft
2
) (649.7 W/m
2
). The daily clear-day
surface total for January 21 is, from the same table, 1478 Btu/ (day

⅐
ft
2
) (4661.6
W/m
2
) for a 48
Њ
collector tilt angle.
2. Find the insolation for the time between tabulated values
The ASHRAE tables plot the clear-day insolation at hourly intervals between 8
a.m. and 4 p.m. For other times, use a linear interpolation. Thus, for 10:30 a.m.,
interpolate in Table 3 between 10:00 and 11:00 a.m. values. Or, (249
Ϫ
206)/ 2
ϩ
206
ϭ
227.5 Btu/(h
⅐
ft
2
) (717.5 W /m
2
), where the 249 and 206 are the insolation
values at 11 and 10 a.m. respectively. Note that the difference can be either added
to or subtracted from the lower, or higher, clear-day insolation value, respectively.
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SOLAR ENERGY
17.14
TABLE 3
Solar Position and Insolation Values for 48
Њ
N Latitude
Њ
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SOLAR ENERGY
SOLAR ENERGY
17.15
3. Find the actual solar insolation for the collector
ASHRAE tables plot the clear-day solar insolation for particular latitudes. Dust,
clouds, and water vapor will usually reduce the clear-day solar insolation to a value
less than that listed.
To find the actual solar insolation at any location, use the relation i
A
ϭ
pi
T
,
where i
A
ϭ
actual solar insolation, Btu/(h
⅐
ft
2

) (W/m
2
); p
ϭ
percentage of clear-
day insolation at the location, expressed as a decimal; i
T
ϭ
ASHRAE-tabulated
clear-day solar insolation, Btu /(h
⅐
ft
2
) (W/m
2
). The value of p
ϭ
0.3
ϩ
0.65(S/
100), where S
ϭ
average sunshine for the locality, percent, from an ASHRAE or
government map of the sunshine for each month of the year. For January, in Glas-
gow, Montana, the average sunshine is 50 percent. Hence, p
ϭ
0.30
ϩ
0.65(50/
100)

ϭ
0.625. Then i
A
ϭ
0.625(1478)
ϭ
923.75, say 923.5 Btu/(day
⅐
ft
2
) (2913.7
W/m
2
), by using the value found in step 1 of this procedure for the daily clear-
day solar insolation for January 21.
4. Determine the effect of a changed tilt angle for the collector
Most south-facing solar collectors are tilted at an angle approximately that of the
latitude of the location plus 15
Њ
. But if construction or other characteristics of the
site prevent this tilt angle, the effect can be computed by using ASHRAE tables
and a linear interpolation.
Thus, for this 48
Њ
N location, with an actual tilt angle of 48
Њ
, a collector tilt angle
of 74
Њ
will produce a clear-day solar insolation of i

T
ϭ
1578[(74
Ϫ
68)/ (90
Ϫ
68)](1578
Ϫ
1478)
ϭ
1551.0 Btu/ (day
⅐
ft
2
) (4894.4 W/m
2
), by the ASHRAE ta-
bles. In the above relation, the insolation values are for solar collector tilt angles
of 68
Њ
and 90
Њ
, respectively, with the higher insolation value for the smaller angle.
Note that the insolation (heat absorbed) is greater at 74
Њ
than at 48
Њ
tilt angle.
Related Calculations. This procedure demonstrates the flexibility and utility
of the ASHRAE clear-day solar insolation tables. Using straight-line interpolation,

the designer can obtain a number of intermediate clear-day values, including solar
insolation at times other than those listed, insolation at collector tilt angles different
from those listed, insolation on both normal (vertical) and horizontal planes, and
surface daily total insolation. The calculations are simple, provided the designer
carefully observes the direction of change in the tabulated values and uses the
latitude table for the collector location. Where an exact-latitude table is not avail-
able, the designer can interpolate in a linear fashion between latitude values less
than and greater than the location latitude.
Remember that the ASHRAE tables give clear-day insolation values. To deter-
mine the actual solar insolation, the clear-day values must be corrected for dust,
water vapor, and clouds, as shown above. This correction usually reduces the
amount of insolation, requiring a larger collector area to produce the required heat-
ing or cooling. ASHRAE also publishes tables of the average percentage of sun-
shine for use in the relation for determining the actual solar insolation for a given
location.
SIZING COLLECTORS FOR SOLAR-ENERGY
HEATING SYSTEMS
Select the required collector area for a solar-energy heating system which is to
supply 70 percent of the heat for a commercial building situated in Grand Forks,
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SOLAR ENERGY
17.16
ENVIRONMENTAL CONTROL
TABLE 4
Solar Energy Available for Heating
Minnesota, if the computed heat loss 100,000 Btu/h (29.3 kW), the design indoor
temperature is 70
Њ

F (21.1
Њ
C), the collector efficiency is given as 38 percent by the
manufacturer, and collector tilt and orientation are adjustable for maximum solar-
energy receipt.
Calculation Procedure:
1. Determine the heating load for the structure
The first step in sizing a solar collector is to compute the heating load for the
structure. This is done by using the methods given for other procedures in this
handbook in Sec. 16 under Heating, Ventilating and Air Conditioning, and in Sec.
16 under Electric Comfort Heating. Use of these procedures would give the hourly
heating load—in this instance, it is 100,000 Btu/ h (29.3 kW).
2. Compute the energy insolation for the solar collector
To determine the insolation received by the collector, the orientation and tilt angle
of the collector must be known. Since the collector can be oriented and tilted for
maximum results, the collector will be oriented directly south for maximum inso-
lation. Further, the tilt will be that of the latitude of Grand Forks, Minnesota, or
48
Њ
, since this produces the maximum performance for any solar collector.
Next, use tabulations of mean percentage of possible sunshine and solar position
and insolation for the latitude of the installation. Such tabulations are available in
ASHRAE publications and in similar reference works. List, for each month of the
year, the mean percentage of possible sunshine and the insolation in Btu /(day
⅐
ft
2
)
(W/m
2

), as in Table 4.
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SOLAR ENERGY