THE TRADE-OFF BETWEEN COLLECTOR 

AREA, STORAGE VOLUME, AND BUILDING 

CONSERVATION IN ANNUAL STORAGE 

SOLAR HEATING SYSTEMS 

SANFORD SILLMAN 

r-lARCH 1981 

PREPARED UNDER TASK No. 1013.00 

Solar Energy Research Institute 

A Division of Midwest Research Institute 

1617 Cole Boulevard 

Golden, Colorado 80401 

Prepared for the 

U.S. Department of Energy 

Contract No. EG-77-C-01-4042 
Printed in the United States of America 

Available from: 

National Technical Information Service 

U.S. Department of Commerce 

5285 Port Royal Road 

Springfield, VA 22161 

Price: 

Microfiche $3.00 Printed Copy $7. 25 

NOTICE 

This report was prepared as an account of work sponsored by the United States Government. Neither the United States nor the United States Department of Energy, nor any of 

their employees, nor any of their contractors, subcontractors, or their employees, makes 

any warranty, express or implied, or 9,SSumes any legal liability or responsibility for the 

accuracy, completeness or usefulness of any information, apparatus, product or process 

disclosed, or represents that its use would not infringe privately owned rights. 
y

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report is the investigation of systems used to supply backup heat to passive 

solar and energy-conserving buildings, as well as to meet standard building 

loads. 

The author extends his appreciation to Frank Baylin, who supervised the 

research leading to this report and provided valuable advice in its preparation, and to Michael Holtz, David Claridge, and Charles Wyman who critically reviewed this work. 

Sanf ord Sillman 

Approved for 

SOLAR ENERGY RESEARCH INSTITUTE 

Michael J. H tz, Chiff 

Building Syst ms Deyelopment Branch / 

J. ichael Davis, P.E., Manager 

Buildings Division 

iii 
DISCUSSION 

A daily-step computer simulation is used to determine the performance of solar heating 

systems as collector and storage size is varied. Simulations are performed for systems in 

four cities in the United States: Boston, Mass., Medford, Oreg., Bismarck, N. Dak., and 

Albuquerque, N. Mex. The study assumes various building load types and includes both 

flat-plate and evacuated-tube collectors at different tilt angles, and single-tank and twotank systems. A unique feature of this study is the investigation of systems used to provide backup heat for passive solar and energy-conserving buildings and to meet standard 

building loads. 

CONCLUSIONS AND RECOMMENDATIONS 

System performance is found to increase linearly as storage size increases up to the point 

where the storage tank is large enough to store all surplus heat collected in summer. 

This point of unconstrained operation represents the optimum design for annual storage 

systems. Only a moderately-sized storage tank is needed for these systems if building 

loads have been reduced by conservation. In contrast to diurnal storage systems, annual 

storage systems show only slightly diminishing returns as overall system size is 

increased. Annual storage systems providing nearly 100% solar space heat may be economically preferable to the more common 50% solar heating systems with diurnal storage. Also, in contrast to diurnal systems, annual storage systems perform well in meeting the load of a passive solar or energy-efficient building. Economic analysis is based on 

the net energy added by the inclusion of storage in the solar heating system. This 

net added energy is found to be MJ/m -yr, depending on location and load type. An assumed storage cost of $30/m is equivalent to a fuel price of The entire 

system is found to be equivalent to a current fuel price of 

v 
2.0 

3.0 

4.0 

5.0 

6.0 

1.2 

Functioning of Seasonal Storage Systems 

Method of Study ...................................................... 

2.1 

2.2 2.3 2.4 

2.5 

2.6 

Location .............................. . 

Flat-Plate Versus Evacuated-Tube Collector 

Collector Tilt ........................................... . 

Bull ding Typ e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 

Nature of Building Load ........................................... . 

Building Design and Extent of Conservation ••••••.••••••••••••••.••••• 

Restll ts .•...••••••••••••. 

3.1 

3.2 3.3 3.4 

3.5 

3.6 

3.7 

3.8 

System Performance ••...•.••.......••••.••......•........... 

N ear-l 00% Solar Systems ......................................... . 

Space Heating Systems ............................................ . 

3.3.1 Net Added Energy and Collector Type •••••.•••••••••••••••.•••• 

3.3.2 Standard, Passive, and Superinsulated Construction ••••••..•••••• 

3.3.3 Performance Variation by Location ••••••••••.••••••••••••••••• 

Hot Water Systems ............................................... . 

Combined Heating and Hot Water Systems ••.••••.•••••••••••••••••••• 

Single-Unit Systems .............................................. . 

Eff ect of Collector Tilt ........................................... . 

Two-Tank Systems ............................................... . 

System Economics. 

Design Methods 

Conclusions .......................................................... 

7.0 References .............. . . ..................................... . 

Appendix A Basic Assumptions on the Solar Heating System 

Appendix B Calculation of Passive and Conserving Building Loads 

Appendix C Simulation Results 

vii 

1 

7 

7 7 7 7 

8 

8 

9 9 

15 

17 

22 

22 

25 26 

27 

31 

31 

33 

37 

41 

43 

45 

47 

49 

57 

-""'---1 
1-2 Monthly Collector Efficiency and End-of-Month Storage 

Temperature for Diurnal and Annual Storage Systems.. . . . . . • • • • . • • • • • • . • 3 

1-3 Schematic of Two-Tank Annual Storage System .•....•••••••......•...•.• 5 

1-4 Monthly Efficiency and End-of-Month Temperature for a Two-Tank 

Annual Storage System .............................................. 6 

3-1 System Performance and Collector Storage Trade-Off Curves for 

a Typical Annual Storage System. . •• . . •• •. •• . • .. . . . . • . . . • • . • .. . .• .•. .• 10 

3-2 Slope of Performance and Trade-Off Curves in Figure 3-1 ••••••••••••••.•• 12 

3-3 Economic Optima in a Region with Linear Design Trade-Off 13 

3-4 Performance of an Annual Storage System with a Large Hot 

Water Load .••....•.•..••••.•..........•.•••••....•.....••••......•. 14 

3-5 Efficiency of Diurnal Solar Systems Versus Solar Fraction.. . . •. .•. . . . . . . • • 16 3-6 Efficiency of Annual Storage Systems Versus Solar Fraction................ 18 

3-7 System Cost per Unit Heat Delivered Versus Solar 

Fraction for Space Heating Systems .•••....•.....••.•....•......•.•..• 19 

3-8 Efficiency Versus Solar Fraction for Combined Space Heat and Hot 

Water Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 

3-9 System Cost Versus Solar Fraction for Combined 

Space Heat and Hot Water Systems. • • • . . . . . • . . . . . • . . . . . . . . . . . . . . • . • • . • 21 

3-10 Monthly Load for Different Building Designs... . . . .••. .• • • •. • • • . • . . • .•. . . 23 

3-11 Performance of Annual Storage Systems with Standard, Passive, and 

Superinsulated Load Types ••••••••••••••••••••••••••••••••••••••••••• 24 

3-12 System Performance with Varying Collector Tilt......................... 32 

3-13 Monthly Efficiency and End-of-Month Storage Temperature for a 

Dual-Use, Two-Tank System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 

viii 
4-1 Life Cycle/Break-even Energy Cost of Annual Storage Systems. . . . . • . . . • • . . • 39 

ix 
- IlIglll -

x 
• 

Active solar energy is the major alternative heat source for building applications for 

which passive solar energy is unsuited or limited in its application. Active solar energy 

uses include hot water, space heat for residential, commercial and industrial buildings, 

backup heat for houses using passive solar heat in northern locations, and retrofit applications. The technical performance of active solar systems is limited by seasonal 

weather patterns. Because summer, the season of maximum sunlight, is also the time of 

minimum heat demand, active solar systems must either be undersized in meeting the 

load or sit idle during a large part of the year. In addition, backup energy is required 

during cloudy periods. 

The use of annual storage both improves the technical efficiency of active solar systems 

by allowing collection of solar heat in summer and extends the capability of active solar 

systems to meet nearly 100% of the load. Annual storage systems rely on a large storage 

tank, usually with water as the storage medium. The storage tank is charged fully during 

summer, and the stored heat then is used to help meet the winter load. In addition, collection of solar heat continues during the winter, and the annual storage tank is used for 

day-to-day storage. The winter load, thus, is met partly by day-to-day collection of solar 

heat, as in a conventional active solar heating system, and partly by stored heat from the 

summer. 

This work presents a comprehensive study of the design trade-offs in annual storage systems-particularly the trade-off between collector and storage size. A unique feature of 

this study is the investigation of systems with several types of building loads, including 

both space heat and hot water loads, and various conservation measures. Also included is 

a study of "hybridll buildings that include both passive solar design and active solar heating with seasonal storage. Previous work in the field has been limited by the locations 

examined, collector type used, or extent of the design trade-offs considered (McGarity 

1979; Baylin and Sillman 1980; Braun and Duffie 1979). 

1.2 FUNCTIONING OF SEASONAL STORAGE SYSTEMS 

The operation of seasonal storage systems can be understood by examining the annual 

building load and solar collection pattern (Fig. 1-1). Without seasonal storage, the system referred to would dump excess heat throughout the summer months and require 

backup heat to meet the difference between solar collection and building load in the winter months. Adding an annual storage tank would enable summer excess to be stored and 

used to provide winter backup. The necessary amount of annually stored heat is determined by the seasonal variation in load and solar heat supply. 

While adding an annual storage tank to a system has the primary effect of matching the 

seasonal pattern of the heat supply with the load, it also has a secondary effect of reducing collector operating efficiency for large parts of the year. Figure 1-2 illustrates the 

difference in operating efficiency between an annual storage system and the equivalent 

active solar heating system with daily storage. Throughout the fall and winter, annual 

storage systems operate at higher temperatures and lower collector efficiency than 

1 
.,. 

500 

-, 

-

400 Load 

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A M J . J A S a N D J F M 

Month 

Figure 1-1. Profile of Monthly Load and Solar Collection for an 

Annual Storage System 

System is designed to provide space and water heat for a 50-unit district 

of apartments in Boston, Mass. System uses flat-plate collectors. Data 

are all based on computer simulations. 

2 

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(a) System Efficiency 

SONDJFM 

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Diurnal Storage 

Diurnal Storage 

Annual Storage 

(b) End-of-Month Storage Temperature 

Figure 1-2. Monthly Collection Efficiency and End-of-Month Storage 

Temperature for Diurnal and Annual Storage Systems 

Systems are designed for Boston, Mass., using flat-plate collectors. 

3 
, 

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to store extra heat in the annual storage tank and simultaneously collect and use 

low-temperature heat during the fall and early winter. Figures 1-3 and 1-4 illustrate system operation and efficiency of the two-tank system, which combines advantages of both 

daily and annual storage systems. 

4 
Annual 

Storage 

Diurnal 

Storage 

Figure 1-3. Schematic of Two-Tank Annual Storage System 

Hot 

Water 

Load 
>. 

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Figure 1-4. Monthly Efficiency and End-of-Month Storage Temperature 

for Two-Tank Annual Storage System 

System is for flat-plate collector system, Boston, Mass., with standard load. 

6 
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enables systems with small- and intermediate-sized storage tanks to be included in the 

study. 

System designs are compared for a number of different locations, collector type and tilt, 

building types, and building design. The following subsections describe the major design 

variables included in the study along with notes concerning the significance of each. 

2.1 LOCATION 

Four locations were selected: Boston, Mass.; Albuquerque, N. Mex.; Bismarck, N. Dak.; 

and Medford, Oreg. Boston was selected to typify the moderate, humid climate of the 

northeastern and midwestern United States. Albuquerque is representative of the sunbelt, the region of the United States that is most favorable to solar applications. Bismarck and Medford were selected to represent climates suitable for annual storageBismarck because of its severe winters and Medford because of its winter rainy season. 

2.2 FLAT-PLATE VERSUS EVACUATED-TUBE COLLECTOR 

The choice of collector type affects the performance of annual storage systems through 

its effect on collector efficiency. Evacuated-tube collector efficiency changes little as 

collector operating temperature changes, while flat-plate collectors show much greater 

swings in efficiency. This difference affects the choice between diurnal (daily) and 

annual storage in two ways. Evacuated-tube collectors permit greater collection of solar 

heat during winter when climatic conditions are worse, thus improving the performance 

of diurnal storage systems and lessening the need for annual storage. On the other hand, 

use of evacuated-tube collectors eases a major problem of annual storage systems: 

reduced collector efficiency due to higher operating temperatures. 

2.3 COLLECTOR TILT 

Two collector tilts are used, one equal to latitude and one equal to latitude plus 

10 degrees. The sharper tilt favors solar collection in winter, while the less sharp tilt 

favors spring, summer, and fall collection. Collectors with the sharper tilt perform better for nearly all systems, while collectors with the less sharp tilt are most advantageous 

for systems with very large storage. Unless otherwise specified, system sizing and performance described in this study all have a collector tilt of latitude plus 10 degrees. 

2.4 BUILDING TYPE 

Four building configurations are modeled: single-family houses with a 50-unit district 

heating system, individual single-family houses, 10-unit apartment buildings with a 

7 
2.5 NATURE OF BUILDING LOAD 

Included are systems for space heating only, systems for hot water only, and combined 

space heat and hot water systems. For combined space heat and hot water systems, the 

ratio of space heat to hot water load is varied among the four building types. 

2.6 BUILDING DESIGN AND EXTENT OF CONSERVATION 

Three basic building types are included: standard construction, passive design, and superinsulated design. The space heat loads are calculated by using an algorithm for calculating day-to-day building loads (see Appendix B). Key param eters in describing the building 

load are (1) gross shell loss, (2) miscellaneous heat gain, and (3) passive heat gain. Tables 

B-1 and B-2 in Appendix B present these values along with final yearly loads for all building types. 

The standard building loads are found by using the degree-day method, with a miscellaneous heat-gain equivalent of 1.5°C temperature difference. Miscellaneous heat typically 

provides 10% of the total yearly heat load in this instance. The passive designs include 

reduced gross shell load and passive gain designs in which heat provides 

15%-20% of the gross shell load and passive solar heat provides 40%-50% of the gross 

shell load. The remainder is provided by the active system.* Superinsulated houses represent a relatively new building concept (Shurcliffe 1980). These are houses built for 

northern climates with very well-insulated walls [20-30 cm (8-12 in.)] and nearly airtight 

construction. Typically, miscellaneous heat provides a significant fraction of the gross 

shell load, which is already reduced far below that of a standard house by insulation. 

Designs used here had 35% of the gross shell load provided by miscellaneous heat and 

35% by passive gain. Both passive and superinsulated designs are assumed for houses and 

small apartment buildings. High-performance passive systems for large buildings may be 

more limited than for small buildings, because of heat distribution problems. Consequently, only two designs are used for large apartments: a standard design and a conserving design in which miscellaneous heat and passive gain supply 30% and 25% of the 

gross shell load, respectively. 

The variation in building design affects annual storage system performance in many 

ways: 'the shape of the annual load is changed; the pattern of day-to-day variations is 

changed, often to the detriment of the performance of active solar systems; and the relative sizes of the space heat and hot water loads are changed. The load sizes are of particular importance. In buildings of standard design, loads are equal; with superinsulated 

design, the hot water load is frequently greater. 

*In Albuquerque, N. Mex., passive design was found by simulation to meet over 80% of the 

building load. Superinsulated houses were not investigated for Albuquerque. 

8 
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two ways. The first method is to examine system performance with varying storage size 

while collector area is held constant. A plot of performance versus storage size shows 

the performance gain attributable to long-term or annual storage. The second method is 

to plot the trade-off between collector and storage size while assuming system performance will remain constant. The trade-off plot is akin to the standard economic technique of plotting performance isoquants in a resource space. Taken together, the system 

performance and collector/storage trade-off plots provide a complete picture of sizing 

options for solar heating systems with long-term storage. 

Figure 3-1 shows the performance and trade-off plots for a typical annual storage system. The patterns shown in Fig. 3-1 permit the identification of three regions with different performance characteristics: a diurnal and weekly storage region (Region A in the 

graphs), an intermediate region (Region B), and an annual storage region (Region C). In 

the diurnal storage region, the storage tank provides day-to-day or week-to-week storage, and the system performance curve slopes sharply upward. In the intermediate storage region, system performance improves steadily with storage size because the amount 

of heat stored from summer to winter increases. The upper bound of Region B represents 

annual storage at the point of "unconstrained operation" (Hooper and Cook 1980). At this 

point, storage is just large enough to store all heat collected during the summer months 

without exceeding its allowed maximum temperature. Larger storage tank sizes 

(Region C) would provide no extra storage capacity, although they do improve collector 

efficiency by lowering system operation temperatures. The pattern of the three regions 

is shown more clearly in Fig. 3-2, which plots the slopes of the performance and tradeoff curves in Fig. 3-1. Figure 3-2 shows that the performance and trade-off curves vary 

linearly throughout the intermediate region, up to the point of unconstrained operation. 

Because of the linear pattern of the performance and trade-off plots, the point of unconstrained operation is the only likely economic optimum. As illustrated in Fig. 3-3, the 

optimum will occur at either the lower or the upper bound of a region of linear system 

performance, but not at an intermediate point. In practice, intermediate optima can 

occur because the performance curves are not perfectly linear. These intermediate 

optima are rare, however, and represent at best a slight savings over diurnal or annual 

storage systems. It may be assumed that optimal systems will be either annual storage 

systems near the point of unconstrained operation or diurnal storage systems. 

The same pattern is repeated for each system investigated in the study. The system performance and collector/storage trade-off plots, shown in Appendix C, all follow a linear 

pattern bounded by the points of unconstrained operation. Consequently, unconstrained 

systems represent the only possible long-term storage optima. Note, however, that 

unconstrained systems do not always have the large storage tank sizes that are commonly 

associated with the term "annual storage." A provides only space heat may 

have a storage-to-collector ratio as high as 5 m to 1 m . A system also P20vides a 

large hot water load may have a storage-to-collector ratio of 1 m to 1 m or less 

(buffer storage) and still be at the point of unconstrained operation. Such a pattern is 

illustrated in Fig. 3-4. These buffer storage systems are used when the need for 

9 
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0.4 

0.3L---------~----------~----------~----------~--------------------~ 0.0 1.0 2.0 3.0 4.0 5.0 

Storage to Collector Ratio (m3/m2) 

(a) System Performance 

Figure 3-1. System Performance and Collector Storage Trade-Off Curves 

for a Typical Annual Storage System 

System is for a Boston, Mass., SUB-50, standard space heat load, using flatplate collectors. The dotted lines separate regions A, B, and C defined 

in the text. 

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Storage Size (m3) 

(b) Collector-Storage Trade-Off 

Figure 3-1. System Performance and Collector Storage TradeOff Curves for a Typical Annual Storage System' (Continued) 

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Figure 3-2. Slope of Performance and Trade-Off Plots in Figure 3-1 

(Slope of Figure 3-1 (a) has been converted to energy units.) 

12 
Resource B 

------- Cost Isoquants 

® Economic Optimum 

Performance 

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Plots (a) and (b) assume different unit costs for resources. 

13 
1600 

1200 

800 

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Region A. / 

400 800 

Region B. 

1200 1600 

Storage Volume (m3) 

Region C. 

0.90 

0.85 

0.80 

0.75 

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Solar Fraction 

0.95 

Figure 3-4. Performance of Annual Storage System with a Large Hot Water 

Load 

System is a two-tank system with flat-plate collectors for Boston, Mass., 

with a SUB-50 superinsulated load. Hot water accounts for 60% of the 

annual load. 

14 
the system performance curve represents the increase in supplied energy resulting from 

an increase in storage size. This parameter will be referred to as the "net energy added 

by storage" and will be expressed in energy lIDits per cubic meter. Theoretically, the net 

energy added by annual storage is at most equal to the amount of heat stored over the 

annual cycle. Based on a 4SoC storage3temperature swing over the annual cycle, the maximum net energy added is 200 MJ/m . per year. The net energy added by storage is 

used to determine whether annual storage is preferable to a system with smaller storage 

and greater reliance on backup power. 

The slope of the collector/storage trade-off curve gives the rate at which collector size 

(in square meters) may SUbstitute for storage (in cubic meters) if2sysjem performance is· to remain the same. This trade-off parameter, expressed in m /m , is used to choose 

between annual storage and diurnal or weekly storage systems once a given level of system performance is specified. A large trade-off parameter means that a large collector 

size may be replaced by a given increase in storage. Consequently, a larger trade-off 

parameter favors annual storage systems over a diurnal or weekly storage system that 

provides the same solar fraction. 

Appendix C presents complete results of the systems study. The tables in Appendix C 

give the following information for each system design: 

• Collector and storage size for the point of unconstrained operation; 

• Net energy added by storage and collector/storage trade-off, explained above; 

• Solar fraction (i.e., the percentage of the total building load met by solar heat); 

and 

• Diurnal solar fraction. This is the solar fraction of an identical system without 

annual storage, assuming the annual storage tank is replaced by a diurnal tank. 

The diurnal solar fraction indicates how significant the annual storage component 

is to the system. 

3.2 NEAR-IOO% SOLAR SYSTEMS 

In the preceding section, the concept of unconstrained operation was developed as a criterion for the optimal sizing of annual storage systems. This criterion may be used to 

size annual storage systems once the solar heat fraction is chosen. In this section, the 

choice of solar heating fraction will be examined in detail. 

Active solar systems with diurnal storage typically show diminishing returns as the system size is increased to meet a large percentage of the load. Figure 3-5 shows how 

system efficiency* decreases for larger diurnal systems, for both space heat and hot 

*System efficiency is defined as the annual amount of heat delivered to the load divided 

by the total yearly insolation incident on the collector surface. 

15 
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0.10 

0.2 0.4 0.6 0.8 

Solar Fraction 

Figure 3- 5. Efficiency of Diurnal Solar Systems vs. Solar 

Fraction 

System for Boston, Mass., a SUB-50, flat-plate collector 

system. 

16 

1.0 
age systems versus solar fraction for systems supplying space heat only. Returns are 

slightly diminishing when the solar fraction approaches 100%. 

Figure 3-7 presents the same data in terms of cost. Cost figures are calculated as the 

sum of collector, storage, and fixed costs (Baylin et al. 1980b) for optimally sized diurnal 

and annual storage systems. The curves for diurnal storage systems show the standard 

pattern of a cost minimum at a solar fraction of 50%. When annual storage is considered, however, cost either decreases or remains constant as the solar fraction 

increases to 100%. The most cost-effective solar option would therefore be a system 

designed to meet 90%-100% of the load, not 40%-60% as is commonly assumed. 

When an annual storage system provides hot water as well as space heat, there may be 

more of a tendency toward diminishing returns. Such systems typically must be large 

enough to provide 80% of the hot water load before any seasonal storage effect occurs. 

As shown in Fig. 3-8, small diurnal storage systems that provide predominantly hot water have a much higher efficiency than annual storage systems. As system size is increased, 

collector efficiency drops steadily until the collector field becomes large enough to permit annual storage. Efficiency then remains constant for all annual storage systems 

sized at the point of unconstrained operation. 

Combined system cost is plotted against solar fraction in Fig. 3-9. The pattern shown is 

one of two economic optima, a diurnal storage optimum and a near-lOO% annual storage 

optimum. The component costs will determine which of these optima will be less expensive. For the prices assumed here, the annual storage-system energy cost is virtually 

equal to the optimal diurnal system cost. Consequently, a near-100% system will be the 

most cost-effective option whenever fuel costs are high enough to favor active solar 

heating. 

The near-lOO% optima for annual storage systems shown in Figs. 3-7 and 3-9 are not 

accidental. Because annual storage systems show near-constant returns as solar fraction 

increases, near-lOO% systems are the likely optim um if annual storage is used at all. The 

design criteria for annual storage systems is now complete. Optimal systems will be 

those designed at the point of unconstrained operation and supplying a large percentage 

(90% or higher) of the given load. The remainder of this study will examine the performance and economics of annual storage systems in specific applications. Annual storage 

system sizes will all reflect these design criteria. 

3.3 SPACE HEATING SYSTEMS 

Systems designed for only space heating are much simpler than combined space and 

water heating systems. Although combined space and water systems are generally 

preferable, space heating systems have applications in commercial buildings that have 

zero or negligible hot water load. 

17 
>. 

u 

c 

Q) ·0 

:;:: 

W 

E 

Q) 

U; 

>. 

CI) 

0.30 0.25 

0.20 

0.15 

0.10 0.05 

-----------

0.2 0.4 

Superinsulated 

Load 

0.6 

Solar Fraction 

0.8 1.0 

Figure 3-6. Efficiency vs. Solar Fraction for Annual Storage Systems 

(Space Heat Only) 

Systems for Boston, Mass., SUB-50 with flat-plate collectors. All systems 

are sized near the point of unconstrained operation. Storage size is roughly 

proportional to collector size for these systems at a ratio of 3 mJ : 1 m2 • 

18 
-

'-

>. 

...... '" 0 

.... 

...... 

-

en 

0 

0 

400 

300 

'-

................... 

-

- -_ .... " .... 

-

Passive 

Load 

, Standard 

"," " 

" Load ...... '" 

, .... '" '- _ .... --.......:::....---

/

 

- - - Optimal diurnal storage systems 

--Optimal annual storage systems 

0.2 0.4 1.0 

Solar Fraction 

Figure 3-7. System Cost per Unit Heat Delivered vs. Solar Fraction for 

Space Heating Systems. 

Systems are for Boston, Mass., with flat-plate collectors, for a 50-unit 

district of single-family houses. Cost is the sum of the collector cost at 

$140Im2; storage cost according to the equation Cs = 385 x [Vol (m3)]072; 

and the fixed cost. Fixed cost is set equal to $200,000 per standard, 

$120,000 for passive construction. All costs are in 1979 dollars. 

19 
>. 

() 

c: 

Q) 

() 

;;::: 

-

UJ 

E 

Q) 

Ui 

>. 

Cf) 

0.5 

0.4 

0.3 

0.25 

0.20 

0.15 

0.10 

0.05 

Superinsulated 

Load '. Annual Systems 

Passive '" 

Load ". 

Standard 

Load 

" '. " "'-. , " , . " ". 

, '. " '. 

, '. 

, .... .... " " .... 

...... 

0.2 0.4 

Standard Load 

Passive Load 

Superinsulated Load 

0.6 

Solar Fraction 

0.8 1.0 

Figure 3- 8. Efficiency vs. Solar Fraction for Combined Space Heat and Hot 

Water Loads 

Annual storage systems are sized for the point of unconstrained operation. 

Annual storage size varies greatly, increasing at larger solar fractions. 

Diurnal storage systems are used when annual storage is not feasible. 

Systems are for standard, passive, and superinsulated SUB-50 loads, 

with flat-plate collectors, Boston, Mass. 

20 
'C" 

<' -, 

a> 

0 

.... 

...... 

-

(/) 

0 

() 

500 f400 "-

300 -

200 -

100 -

\ 

\ 

\ 

\ 

\ 

\ 

\ 

'\ 

'. '. 

, 

, 

...... 

'" 

Standard Load 

_._. Passive Load 

- - - Superinsulated Load 

, .. " .f)------

......... .. 

---

.....·0_._ ... -_.,.,' ---.-.-_ ..... -

0.2 0.4 0.6 0.8 1.0 

Solar Fraction· 

Figure 3-9. System Cost per Unit Heat Delivered vs. Solar Fraction for 

Combined Space Heat and Hot Water Systems 

Systems are for Boston, Mass., SUB 50, with flat-plate collectors as in Figure 3-14. 

Cost is the sum of collector cost at $140/m2, storage cost according to the equation 

C s = 385 x (Vol. (m3»O.72, and the fixed cost. Fixed cost is set at $200,000 for 

standard, $150,000 for passive, and $120,000 for superinsulated construction. All 

costs are in 1979 dollars. 

21 
3.3.1 Net Added Energy and Conector Type 

When evacuated-tube collectors arg used, the net energy added by storage is close to the theoretical maximum of 200 MJ/m • With flat-plate collectors, the net energy added by 

storage is significantly less. When a is used with flat-plate collectors, 

the net energy may be 150-180 MJ/m ; with a single tank, the net energy is 

130-160 MJ/m. The net added energy also shows greater variation among different 

locations and building types when flat-plate collectors are used. 

The net added energy is affected most by the collector operating efficiency. As 

described in Sec. 1.0, collector efficiency tends to be lower in annual storage systems, as 

opposed to diurnal systems, during the fall and early winter months. When evacuatedtube collectors are used, this drop in efficiency is slight and net added energy remains 

high. With flat-plate collectors, particularly in single-tank systems, collector efficiency 

is more sensitive to the collector operating temperature and the efficiency drops sharply 

in fall and early winter. This loss in efficiency is enough to lower the net energy added 

by storage. 

3.3.2 Standard, Passive, and Superimulated Constructioo. 

Passive and conserving building designs have two major characteristics that affect the 

design of an active solar system for backup heat. First, the annual shape of the passive 

and superinsulated building load is different from the load of a standard building. Passive 

buildings rarely need additional heat during spring and fall and, consequently, their yearly 

load occurs within three or four months. A standard building design requires heat in all 

but the summer months (see Fig. 3-10). A second difference is that day-to-day variations 

in load are relatively small for a standard building, reflecting only day-to-day changes in 

temperature. For a passive or superinsulated building, however, the day-to-day load is 

much more sporadic with no heat required on sunny days even in the middle of winter. 

The effect of building design is greatest for diurnal systems. As shown in Sec. 3-2, diurnal system efficiency drops when used with a passive or conserving building load. The. 

poor performance of diurnal systems may be due either to the yearly load shape or to the 

greater day-to-day and week-to-week variations in load. The yearly load shape causes 

the solar collectors to be idle for a large part of the year. The daily load variation hampers system operation because maximum solar collection occurs precisely on those days 

when there is no load for a passive house. Further investigation shows that the monthly 

performance as well as the yearly performance of diurnal systems is poor. This indicates 

that the daily and weekly load variation is a primary cause of poor diurnal performance 

with passive loads, although the uneven yearly load pattern is also a major influence. 

Figure 3-11 compares system performance with storage size for the three different 

building designs. The figure shows that performance drops much more sharply at small 

storage sizes for a conserving load. This indicates that even a diurnal system requires 

larger storage when used with a passive or conserving load. Furthermore, the 

22 
300 

...., 

-

'" o 

,.... 

-

"0 

200 

...J 

100 

-

...., 

'" 0 

"0 

CI:I 

0 

...J 

SUB-50 

Passive Load 

500 

400 

300 

200 

100 

AMJJASONOJFM 

Month 

(109 J) 

150 100 

50 

SUB-50 

Load 

A MJJ A SONOJ FM 

Month 

AMJJASON OJ F M 

Month 

Figure 3-10. Monthly Load for Different Building Designs 

(Boston. Mass.) 

23 
c: 

.2 

t) 

co 

... 

u.. 

... 

co 

"0 

C/) 

1.0 

0.95 

0.80 

0.65 

0.50 

0.35 

Standard 

Load 

..... ' 

,...,. Passive Load 

,.. 

.J/ 

/".r 

..r.r" / .... Superinsulated Load 

..... 

-

..... /' _. 

/" jlr- /" / . // 

/ // 

/ /" 

/// 

// 

/ // 

/ / 

/11 

1/ 

1/ / 

f 

____ Standard Load 

_ _ _ _ _ Passive Load 

Superinsulated Load 

<!) Point of 

U nconstrai ned 

Operation 

0.20 '--____ ..L.-____ L....-___ ____ _..I. ____ __ 

2 3 4 5 

Ratio of Storage-to-Collector Size; m3/m2 

Figure 3-11. Performance of Annual Storage with Standard, Passive, and 

Superinsulated Loads 

Systems are SUB-50, space heat only; with flat-plate collectors, in Boston, 

Mass. Collector size is the same relative to annual load for the three systems. 

24 
than with a standard load, and 20%

30% lower for a superinsulated load. This drop in 

efficiency is due to the annual load shape. Since the passive load is concentrated in the 

winter, yearly storage temperatures must be higher to achieve the same solar fraction as 

a system with a standard load. The drop in efficiency is significantly smaller when 

evacuated-tube collectors are used. Because of the more concentrated annual load pattern, systems also require a larger storage tank in proportion to collector area when used 

with a passive or superinsulated load. 

Use of passive or superinsulated construction can cause the net energy added by storage 

to either increase or decrease. The net added energy may increase with passive buildings 

because storage serves more of a dual purpose, combining daily and weekly with annual 

storage. On the other hand, the average operating temperature tends to be higher for systems with passive building loads, which causes poorer system performance. 

The trade-off parameter is nearly always larger for passive or superinsulated buildings 

than for standard buildings. This is the result of increasingly poor performance of diurnal 

and intermediate storage systems at high solar fractions. It often happens that the net 

added energy is lower for passive buildings (favoring diurnal systems), but the trade-off 

parameter is also larger (favoring annual systems). This type of pattern occurs because 

active systems, with or without annual storage, perform more poorly with passive construction. 

Results of the analysis for systems in are typical. Seasonal storage systems have 

a ratio of storage-to-collector size (m :m ) of 3: 1 with standard construction and 4: 1 

with passive or superinsulated constructioo. The same collector array without seasonal 

storage would provide 60%-66% of the space heat load with standard construction and 

42%-50% with 30r superinsulated constructioo. The trade-off par3ameter ranges from 0.7 to 1.0 m /m for passive loads and from 0.45 to 0.70 m2/m for standard 

loads. The net energy added storage remains uniform for standard, passive, and superinsulated houses at a fairly high level: 160-210 MJ/m3 (near the theoretical 

for evacuated-tube systems and two-tank, flat-plate systems and 140-160 MJ/m for single-tank, flat-plate collector systems. 3.3.3 Performance Variatim by Locatim 

The performance characteristics of space heating systems show some variation among 

the four locations. lhe net energy added by storage is significantly higher in Medford, 

reaching 200 MJ/m even for flat-plate collector systems, and is slightly less in 

Bismarck. The cause of this variation is the climatic pattern in the fall and early winter. 

As previously noted, the use of annual storage results in a reduction in the winter collection efficiency, and the reduced solar collection counts against the net energy added by 

storage. In Medford, winter insolatioo is so small that the poor collector efficiency is 

insignificant. In Bismarck, by contrast, winter insolation is high and reduced efficiency 

more important. 

25 
was found to be very similar between Boston and Bismarck; storage to collector ratios 

were the same, and system performance without seasonal storage was equivalent. This 

apparently reflects the similar climatic pattern of Boston and Bismarck (eastern humid 

continental climate), despite the fact that Bismarck's winter is much more severe. By contrast, the storage component was much larger in Medford. The equivalent system 

without annual storage in Medford would yield a solar fraction of only 52%-58% for 

standard construction and only 25%-30% for superinsulated construction. This is much 

smaller than the corresponding value fer Boston given in Sec. 3.3.2. The storage-tocollector ratio is correspondingly larger in Medford. In Albuquerque, seasona.l storage 

was a smaller component than in the other cities, with daily yielding 65%-72%. 

The storage to collector ratio in Albuquerque was large (4-6 m 1m ), again a reflection 

of increased insolation in Albuquerque. Annual storage appears to be most useful in locations with sunny summers and unusually cloudy winters (Medford), rather than in places 

with unusually cold winters (Bismarck). 

3.4 HOT WATER SYSTEMS 

Seasonal storage tends to have very little usefulness in systems designed to provide hot 

water only, primarily because of the nonseasonal nature of the hot water load. Although 

insolation does vary throughout the year, the gain achieved by storing summer heat fer 

use in winter is more than offset by the loss in efficiency with seasonal storage systems. 

A further important factor concerns the nature of hot water systems. The space heat 

load can be met with heat collected at any temperature above 300 C, but meeting the 

entire hot water load requires collecting heat at 550 C or more. Low-temperature solar 

heat can be used as a hot water preheat. This type of system yields sharply diminishing 

returns as the system size is increased to meet a large percentage of the hot water 

load. It also provides a natural mechanism for matching load with available energy; a hot 

water system may provide substantially preheated water in winter and fully heated hot 

water in summer with the collection of extra heat for seasonal storage. 

The slow reaction time of a seasonal storage tank further encumbers a hot water system. 

When a seasonal storage tank is fully discharged in winter, it may be at a temperature to 

provide only 50% of the hot water load. With a daily storage system, the tank would heat 

to 500 or 600 C on sunny days and provide nearly 100% of the hot water load. The seasonal storage tank would remain at 300 C and continue to provide only 50% of the load. 

This behavior becomes a serious drawback in seasonal storage systems designed to meet a 

large fraction of the load. It also causes the efficiency of hot water systems with annual 

storage to be much lower than those with diurnal storage. 

For these reasons, seasonal storage typically provides zero yield fer hot water systems 

with a single tank. Use of two diurnal storage tanks alone is found to increase 

performance by 10%. A two-tank system with seasonal storage does yield some further 

benefit because the small tank permits both collection and use of low-temperature solar 

heat in fall and the collection of high-temperature solar heat fer hot water in the 

26 
y

p

p

y

The performance of a combined system is influenced both by properties of space heat 

systems, in which seasonal storage has an almost constant value, and hot water systems, 

in which seasonal storage has low value and decreases system efficiency. The most 

important factors in the performance of a combined system are the sizes of the space 

heat and hot water loads relative to each other. 

Combined systems may be analyzed as though they are two separate systems, one for 

space heat and one for hot water. Table 3-1 compares combined systems with systems 

for space heat only. Assuming both systems are annual storage systems designed at the 

point of unconstrained operation and both systems provide the same percentage of solar 

space heat, they will have the same storage size. In addition, the difference in collector 

size between the two systems compares consistently to the collector size of a solar hot 

water system that would meet the same fraction of the hot water load as does the combined system. Typically, the added collector area in the combined system is greater than 

the size of the equivalent hot water system by about 10%. This difference reflects the 

loss in efficiency that occurs when an annual storage system is used to provide hot 

water. With a two-tank system, the extra collector area in the combined system may be 

either greater or smaller than the size of the equivalent two-tank hot water system. 

System performance is significantly worse for combined systems in which the hot water 

load exceeds the space heat load. 

Two-tank systems, initially investigated for space heating (Cha et ale 1979), appear to be 

most useful for combined systems with a large hot water load. For reasons discussed in 

the previous section, single-tank annual storage systems tend to perform poorly in meeting a hot water load. A two-tank system serves a dual purpose here. First, it permits 

the collection of low-temperature heat during November and December. Second, it may 

be used to collect high-temperature heat for hot water in March and April when the 

annual storage tank temperature is too low to provide hot water. This dual-purpose, twotank system enables an annual storage system to provide both hot water and space heat 

efficiently. 

The net added energy and the trade-off parameter for combined systems may also be 

compared to that of space heat systems. The net added energy and the trade-off parameter are the same for two-tank systems as for the equivalent space heat system. For 

single-tank systems, the net added energy is lower by 10%-2596 when compared to space 

heating systems. The drop in the net added energy is greater when space heat loads are 

*These conclusions are based on the assumption that the daily hot water load remains constant throughout the year. There is evidence (Mixon 1976) that daily hot water loads are 

actually twice as great in winter as in summer. In that case, conclusions would be more 

favorable to annual storage systems. Th§l net energy added by storage would rise to 90-

100 MJ/m in Boston and 120-140 MJ/m in Medford. The net added energy in a combined system (see Section 3.5) would be similarly enhanced. 

27 
(

) 

(

) 

* * - Z Z C"I 0 0 E ..... E-< E=: .....-

M 

- C) C) 

N .....- E < < 

..... 

00 

N E-< >t ..... p:: 0 00 < C) E-< E-< Z 

:;E C) c.? ::t: < < :: ..... 

E-< ....:l p:: C) C) ....:l E-< ...... 00 0 < >t 0 E-< 0.. 0 00 C) 00 00 ::t: 

Standard construction, single-tank system 

Combined system 2800 5600 0.77 0.75 0.259 

Space heat system 2270 5900 0.77 0 0.266 

Hot water system 480 36 0 0.75 0.274 

Combined system 3200 7040 0.85 0.77 0.249 

Space heat system 2600 7050 0.85 0 0.254 

Hot water system 520 39 0 0.77 0.260 

Combined system 3600 7920 0.91 0.80 0.235 

Space heat system 2900 8100 0.91 0 0.244 

Hot water system 580 44 0 0.80 0.242 

Combined system 4000 9600 0.98 0.83 0.226 

Space heat system 3350 9400 0.98 0 0.226 

Hot water system 650 49 0 0.83 0.224 

Passive construction, single-tank system 

Combined system 1400 2000 0.70 0.78 0.215 

Space heat system 760 2200 0.70 0 0.226 

Hot water system 520 39 0 0.78 0.254 

Combined system 1600 2900 0.83 0.81 0.211 

Space heat system 910 3000 0.83 0 0.222 

Hot water system 575 43 0 0.81 0.236 

28 
0 

N E < <: 

00 

..... 

-

N 

..... &-< 

0 00 < 0 &-< &-< Z 0 0 ::c: < < ..... 

&-< ...:l 0 0 

Cf.l 0 ...:l 0 < &-< - &-< p." 0 Cf.l C,) Cf.l 00 ::c: 

Passive construction, single-tank system 

Combined system 1800 3600 0.93 0.83 0.203 

Space heat system 1040 3600 0.93 0 0.218 

Hot water system 625 47 0 0.83 0.224 

Combined system 2000 4000 0.98 0.85 0.191 

Space heat system 1150 4000 0.98 0 0.210 

Hot water system 670 50 0 0.85 0.212 

Superinsulated construction, single-tank system 

Combined system 700 600 0.75 0.82 0.198 

Space heat system 250 700 0.75 0 0.193 

Hot water system 390 30 0 0.82 0.230 

Combined system 800 800 0.85 0.84 0.184 

Space heat system 300 840 0.85 0 0.183 

Hot water system 420 31 0 0.84 0.218 

Standard construction, two-tank system 

Combined system 2800 5600 0.79 0.86 0.274 

Space heat system 2200 5500 0.79 0 0.279 

Hot water (single-tank) 735 55 0 0.86 0.205 

Hot water (two-tank) 600 45 0 0.86 0.250 

Combined system 3200 7050 0.89 0.89 0.265 

Space heat system 2600 7000 0.89 0 0.268 

Hot water (single-tank) 830 62 0 0.89 0.188 

Hot water (two-tank) 700 53 0 0.89 0.22 

Combined system 3600 7920 0.96 0.92 0.252 

Space heat system 2900 8400 0.96 0 0.256 

Hot water (two-tank) 800 60 0 0.92 0.20 

29 
U E <: N <: - p:: - p:: ff:J. 

N p:: - Eo-< p:: 0 ff:J. <: u 

Eo-< Eo-< Z ::;E U :c: <: 

Eo-< 

<: 

p:: u 

-

u 

ff:J. 0 0 Eo-< Q., <: 0 Eo-< - ff:J. U ff:J. 00. :c: 

Passive construction, two-tank system 

Combined system 1600 2880 0.84 0.91 0.224 

Space heat system 960 3000 0.84 0 0.228 

Hot water (two-tank) 750 56 0 0.91 0.204 

Combined system 1800 3600 0.94 0.94 0.217 

Space heat system 1020 3600 0.94 0 0.224 

Hot water (two-tank) 860 64 0 0.94 0.190 

Superinsulated construction, two-tank system 

Combined system 600 600 0.63 0.85 0.226 

Space heat system 200 520 0.63 0 0.202 

Hot water (two-tank) 360 24 0 0.85 0.257 

Combined system 700 700 0.75 0.90 0.209 

Space heat system 240 680 0.75 0 0.201 

Hot water system 410 30 0 0.90 0.204 

Combined system 800 960 0.90 0.926 0.199 

Space heat system 320 900 0.90 0.182 

Hot water (two-tank) 550 41 0 0.926 0.182 

*Space heat fraction and hot water fraction refer to the percentage of the space 

heat and hot water loads, respectively, that are met by the solar heating system. 

30 
are particularly useful for buildings with a larger load for hot water than for space heat. 

Although a combined system offers no engineering advantage, it may offer a substantial 

economic advantage through the use of auxiliary equipment (piping, controls, etc.) that 

services both the space heat and hot water loads. Lovins (U.S. Congress 1978) has argued 

that the hot water component of a combined system may be used to justify the cost of 

auxiliary equipment that otherwise would make a space heat system prohibitively expensive for smail building loads. 

3.6 SINGLE-UNIT SYSTEMS 

Annual storage systems for an individual single-family residence (SUB 1) are of interest 

because a number of innovative systems of this type have been built in recent years. 

(Esbensen and Korsgaard 1977; Besant et ale 1978). The major problem with single-unit 

systems is storage loss: while a 50-unit annual storage system may have a storage efficiency of over 90%, a single-unit system such as the Lyngby house (Esbensen et ale 1977) 

may have a year-round storage efficiency of 60% or less. 

Single-unit system were performed, assuming the same level of storage-tank 

insulation (0.11 W/m °C) as assumed for 50-unit systems. Results show that the overall 

system efficiency for a single-unit system is 20%-30% lower than for the equivalent 

50-unit system. The net added energy drops by 30%-50%. These results suggest that 

annual storage works much better for 50-unit districts than for individual houses. This is 

particularly true in light of economies of scale available in obtaining large storage tanks 

(Baylin et ale 1980b). 

3.7 EFFECT OF COLLECTOR TILT 

The two collector tilts used-tilt equal to latitude and tilt equal to latitude plus 

10 degrees-result in slightly different performances. In general, the sharper tilt permits 

greater collection in winter at the expense of collection in the spring, summer, and fall. 

The sharp tilt is advantageous when storage is small. The shallower tilt increases 

summertime collection and thus makes use of larger annual storage tanks advantageous. 

When collector tilt is Shallower, the point of unconstrained operation will occur at a 

larger storage size. 

Figure 3-12 illustrates the difference in performance brought about by the different collector tilts. The sharper tilt is definitely favored when storage is small, and the shallower tilt is favored when storage is very large. The crossover point is typically near the 

point of unconstrained operation. Because the crossover point occurs most often in 

Region C, the sharper tilt is more likely to be economically optimal. However, the shallower tilt permits greater performance for a collector of given size. 

31 
c: 

.2 

() 

ctl 

... 

u. 

... 

ctl 

(5 

en 

1.0 

0.95 

0.80 

0.65 

0.50 

0.35 

Point of unconstrained operation, 

Tilt = Latitude + 10° 

Point of unconstrained operation, 

Tilt = Latitude 

0.20 '------..I.---__ ______ ____ ....1_ ____ ....J... __ _ 

2 3 4 5 

Ratio of Storage to Collector Size (m3/m2) 

Figure 3-12. System Performance with Varying Collector Tilt 

System for Boston, Mass., SUB-50 standard load, space heat system 

with flat-plate collectors. Collector size is 2800 m2 • 

32 
In the original concept as presented by Cha, Conner, and Mueller (1979), the daily storage 

tank in the two-tank system was used only to collect low-temperature solar heat during the late fall and early winter. When used in a combined space heat and hot water system, the daily storage tank may perform the additional function of collecting hightemperature heat for hot water when the annual storage tank is fully discharged. 

Figure 3-13 illustrates this type of operation. During the late winter months, the temperature of the annual storage tank drops to 300 -350 C. Because of its size, the annual 

storage tank does not heat up more than a few degrees on sunny days. As a result, only 

hot water preheat can be supplied during the late winter. During this period, the diurnal 

tank could be heated to 600 C on sunny days and used to provide hot water while the 

annual storage tank continued to provide space heat. 

The algorithm used for this type of operation is as follows. As long as the annual tank 

temperature remains above 550 C, the diurnal tank is used to collect low-temperature 

heat. Heat for the load is taken first from the diurnal tank if available, driving down the 

temperature. Solar heat is collected for whichever storage tank is at the lowest temperature, thus providing the most efficient collection of solar heat. When the annual storage-tank temperature drops below 550 C, the mode of operation changes. Solar collection 

is used to heat the diurnal tank until its temperature reaches 600 C. When the diurnal 

tank temperature exceeds 600 C, solar collection is used to heat the annual storage 

tank. The diurnal tank is used preferentially to provide hot water. In this way, the 

two-tank system improves collectioo efficiency during November and December and also 

provides solar hot water in March and April. 

Simulation results show that using the two-tank system in this way can result in a 3%-5% 

improvement in performance in comparison with a t,wo-tank system using the daily storage tank only to collect low-temperature heat. This improvement occurs only in systems 

with a large solar fraction (85% or over). The major effect of this "dual usell of the 

two-tank system is to increase the amount of solar hot water provided. A single-tank 

system typically provides 80% of the hot water load, even when the system is sized to 

provide 100% of the space heat load. A two-tank system used only to collect low temperature heat (single use) would provide 85% of the hot water load along with 100% space 

heating, while with dual use the percentage of the hot water load supplied jumps to 90% 

or more. Interestingly, dual use also results in slight improvements in the percentage of 

the space heat load provided by the system. These improvements occur on the coldest 

days, when the heat exchange capacity within the building is too small to meet the building load with low-temperature heat from the annual storage tank. On these days, the 

diurnal storage tank provides heat at a temperature high enough to meet the building 

load. When the solar fraction is less, dual use of the two-tank system neither provides a 

significant improvement in performance nor lowers system performance when compared 

to single use of the two-tank system. 

33 
>-

() 

c: 

Q) 

() 

;;::: 

-

UJ 

-

() 

!!-

Q) 

... 

:::l 

-

co 

... 

Q) 

E 

Q) 

r

0.3 0.2 0.1 80 70 60 50 40 

30 

20 

A MJJASONDJF 

Month 

Annual 

Tank 

, " \ 

I \ 

I , I , 

Diurnal \ 

\ Tank \ 

\ 

\ 

\ 

\ 

\ , \ 

A M J J A S 0 N o J 

Month 

____ Efficiency for "single use" 

two-tank system 

Efficiency for dual use system 

/ 

I 

/ 

F M 

Figure 3-13. Efficiency and End-ot-Month Storage Temperature tor a 

"Dual Use" Two-Tank System 

System is for flat-plate collector system; Boston, Mass., TUB-50, standard 

load. 

34 
35 
- III III -

36 
storage. In this section, system economics will be examined in greater detail. The anal

ysis will be based on three tests for cost-effectiveness: the collector/storage trade-off, 

the value added by storage, and the overall system evaluation. The trade-off and valueadded tests are used to compare annual storage systems with solar heating systems lacking annual storage, while the overall evaluation compares solar and conventional heating 

systems. Only when all three indicators favor annual storage is such a system costeffective. 

System economics are difficult to assess because system costs vary greatly. This analysis will assume that system cost in 1979 dollars is the sum of the following three components (Baylin et ale 1980b, Drew and Selvage 1980, King and Carlock 1979): 

• Collector cost at $140/m2 for flat-plate collectors or $200/m2 for evacuatedtube collectors, 

• Auxiliary costs (piping, ductwork, etc) at $100/m2 collector area, and 

• Storage cost as found from the equation (Drew and Selvage 1980) 

Cost = 7.2 Vs + 530 Vs2/ 3 for volume Vs in m3. 

This equation yields a cost of $30-$50/m3 for the system sizes included here. 

Each of these costs is subject to great variation. Estimates for collector and storage 

costs may range from one-half to twice the given values. Collector and auxiliary costs 

assumed here represent a minimum cost estimate based on a survey of solar heating 

installations (King and Carlock 1979). Storage costs may be much higher if poor soil conditions exist or much lower with innovative technologies (e.g., aquifers, solar storage 

ponds, ferrocement tanks). The assumed storage costs are based on surveys of the costs 

of concrete and steel storage tanks (Baylin et ale 1980b, Drew and Selvage, 1980). 

The collector/storage trade-off, as explained in Sec. 3.1, determines whether annual 

storage is preferable to a system with increased collector size substituted for storage. 

Based on ihe3above costs, the break even point for annual storage will be a trade-off of 

0.1-0.3 m /m. Annual storage systems are strongly favored in the three 

northern cities, where the trjdeaoffs are 0.4 m /m or larger. In Albuquerque, the 

trade-off rate is 0.15-0.25 m /m , indicating that a diurnal or weekly storage system 

with a larger collector area may sometimes be favored over an annual storage system. 

The value added by storage is simply the dollar value of the additional energy supplied 

each year (for a fixed collector area) by adding annual storage to a solar heating system. If the value of the added energy is less than the incremental cost of the larger 

storage system, then annual storage is not economically justified. A diurnal solar heating 

system with a backup heating source substituted for annual storage would be preferred. 

For the annual storage systews considered, the yearly energy vglue added by storage 

ranges from 130 to 210 MJ/m . The net added cost is $20-$30/m for large apartments 

and $35-$60/m3 for districts of single family houses, and includes the cost of the district 

heating system (Baylin et al., 1980b). 

37 
useful life of 30 years, the cost of the energy supplied is 

• 6.4tVkWh for a 1096 discount rate, 

• 5.3A'kWh for an 8% discount rate, and 

• 3.5A'kWh for a 496 discount rate. 

These costs may alternatively be viewed as break-even costs for the storage system with 

a 1096 discount rate and 096, 2%, and 696 real escalation in the annual cost of conventional fuels; i.e., if a life-cycle cost analysis is performed for a 1096 discount rate and 

the real cost of electricity is assumed to increase by 296 annually, the annual storage system considered would be preferable wherever the cost of backup heat now exceeds 

5.3A'kWh. 

Overall system economics are evaluated similarly by calculating life-cycle/break-even 

energy costs. Table 4-1 presents costs for combined space heating and hot water systems 

based on the above solar system cost estimates and performance results for the systems 

and locations considered in this study. Results indicate that annual storage systems may 

be cost-effective in large parts of the United States if high fuel escalation rates are 

assumed. Incorporating the solar tax credits would lead to similar conclusions for lower 

fuel escalation rates. 

Due to economies of scale in storage, annual storage systems are most advantageous for 

large apartment complexes or districts. Note that the cost of energy from the storage 

component is often equal to or slightly less than the cost of energy from the entire system. Consequently, the cost of energy from the system will remain essentially constant 

as the solar fraction is increased to 100%, as shown in Fig. 3-9. Whenever the storage 

energy cost is less than or equal to the system energy cost, near-lOO% annual storage 

systems will be preferable to smaller diurnal systems. 

38 
energy system costs are found from the equation: 

Cost = 240 Ac + (7.2 V s + 530 V s 2/3), 

f or a collector size Ac in m 2 and storage size V s in m 3.) 

Fuel Break-even Cost in 1979 tVkWh 

Escalation 

Construction Rate Boston Medford Bismarck Albuquerque 

Standard 2% 7.5 5.7 6.8 4.1 

6% 4.8 3.7 4.4 2.7 

Passive 2% 9.1 7.6 9.1 4.9 

6% 5.8 4.9 5.8 3.1 

Superinsulated 2% 9.8 8.1 10.2 4.9 

6% 6.3 5.2 6.6 3.1 

39 
- III_"I -

40 
for collector efficiency and bimonthly steps was found to yield accurate results for 

standard building loads and was recommended for system design. The question is whether 

a bimonthly simulation remains accurate when used with passive, superinsulated, or other 

conserving building loads. An examination of this question is presented below. 

For single-tank annual storage systems, the nature of the building load has no effect on 

design tool accuracy. The bimonthly utilization model is found to perform accurately 

with all bulding load types, so long as the accurate monthly building load data are provided. A possible problem arises only when the storage tank size is small, so that monthto-month variation in storage tank temperature may exceed 20° C. This will not happen 

for annual storage systems at the point of unconstrained operation, even if the hot water 

load is large. For two-tank systems, however, some inaccuracy may result from using a 

bimonthly model for system design with an energy-conserving building. 

A simple method for sizing systems near the point of unconstrained operation has been 

developed by Drew and Selvage (1980). A summary of their method is presented below: 

(1) The desired maximum and minimum storage temperature is selected for the 

yearly cycle. 

(2) Storage temperature for each month is calculated assuming that storage temperature follows a sinusoidal pattern over the year with maximum occurring on 

1 October and minimum on 1 April (the exact time of yearly minimum and maximum can be adjusted). 

(3) Collector efficiency for each month is calculated by the utilization method 

(Klein 1978), based on the above monthly storage temperatures. Solar heat collection for each month is also calculated. 

(4) The amount of heat supplied to the load from storage is calculated for each 

month based also on the assumed monthly storage temperature. 

(5) Collector and storage sizes for the above system are found by solving two 

simultaneous equations, one for system performance from 1 April to 30 September and one for performance from 1 October to 31 March. During the summer 

half, collected solar energy must equal the sum of (1) load for the period, 

(2) storage losses, and (3) the amount of energy needed to raise storage from its 

minimum yearly temperature to its maximum. During the winter, the heat supply is equal to collected solar energy plus the amount of heat liberated when 

storage temperature drops from its maximum to its minimum value. This heat 

supply must be equal to solar load plus storage losses. This analysis results in 

two equations with only collector and storage sizes unknown. Collector and 

storage size for the system may thus be found. 

41 
42 
• The performance curves for active solar heating systems with storage show three 

distinct regions: a region of diurnal storage, an intermediate region, and a region 

of annual storage. System performance is found to increase linearly as storage 

size increases throughout the intermediate region. The likely economic optimum 

occurs at the point of "unconstrained operation," at which the storage tank is 

large enough to store all heat collected in summer. 

• In contrast to diurnal storage systems, annual storage systems show only slightly 

diminishing returns as the solar heat fraction increases. Optimal annual storage 

systems are sized to meet nearly 100% of the building space heat loads. These 

near-lOO% systems may be preferable to the more common 50%-solar systems in 

many cases. 

• Also in contrast to diurnal systems, annual storage systems perform efficiently 

when combined with passive solar or other energy-efficient building designs. 

• The size of storage necessary for an annual storage system at the point of unconstrained operation varies systems typically have a storage-to-collector ratio of 3-5 m :1 m . Combined space- and water-heating systems have proportionately less storage, especially when the space-heating load is 

sma¥. :w some cases, a system may have a storage-to-collector ratio of 

1 m :1 m or less and still function as an unconstrained annual storage system. 

• Inclusion of annual storage in active solar heating system results in a net 

added2energy of 130-210 MJ/m per Y3ear. Based on a net added energy of 180 MJ/m each year and a cost of $30/m , the break-even cost of energy added by annual storage is The total system breaks even against an energy 

source that costs 

43 
44 
Baylin, F.; Monte, R.; Sillman, S. 1980a. 1980 (June). Annual-Cycle Thermal Energy 

Storage for a Community Solar System-Details of a Sensitivity Analysis. SERI/TR 355-

575. Golden, CO: Solar Energy Research Institute. 

Baylin, F.; Monte, R.; Sillman, S.; Hooper, F. C.; McClenahan, J.D. 1980b. Economic 

Analysis of Community Solar Heating Systems That Use Annual Cycle Thermal Energy 

Storage. Golden, CO: Solar Energy Research Institute. 

Besant, R. W.; Dumont, R. S.; Schoenau, G. 1978. The SaSkatchewan Conservation 

House: Some Preliminary Performance Results. Saskatoon, Canada: University of 

Saskatchewan. 

Braun, J. E.; Duffie, J. A. 1979. Design of Space Heating Systems Employing Seasonal 

Sensible Storage. Madison, WI: Solar Energy Laboratory, University of Wisconsin. 

Cha, B. K.; Conner, D. W.; Mueller, R. O. 1979. "A "Two-Tank" Seasonal Storage Conceptfor Solar Space Heating of Buildings." Proceedings of Second Miami International Conference on Alternative Energy Sources. Miami, FL; 10-13 Dec. 1979. 

Drew, M. S.; Selvage, R. B. G. 1980. "Sizing Procedure and Economic Optimization Methodology for Seasonal Storage Solar Systems." Solar Energy. Vol. 25 (No.1): 

pp. 79-83. 

Esbensen, Torben, V.; Korsgaard, Vagn. 1977. "Dimensioning of the Solar Heating System in the Aero Energy House in Denmark." Solar Energy. Vol. 19 (No.2): pp. 195-199. 

Hooper, F. C.; Cook, J. D. 1980. "Design of Annual Storage Space Heating Systems." 

Fundamentals and Applications of Solar Energy. AIChE Symposium Series 198. Vol. 76: 

pp. 80-91. 

King, T. A.; Carlock, J. B. 1979. Construction Cost Factors Identified in Commercial 

Solar Energy Systems. SOLAR/0822-79/60. Baltimore, MD: Mueller Associates. 

Klein, S.A. 1978. "Calculation of Flat-Plate Collector Utilizability." Solar Energy. 

Vol. 21 (No.5): pp. 393-402. 

Klein, S.; Duffie, W.; Beckman, R. 1977. Solar Heating Design. Wiley and Sons. 

McGarity, A. E. 1979. "Optimum Collector-Storage Combinations Involving Annual 

Cycle Storage." Proceedings of Solar Energy Storage Options. San Antonio, TX: 

19-20 Mar. 1979; pp. 165-173. 

Mixon, W. R. 1976. 1976 (Dec.). "Technology Assessment of Modular Integrated Utility 

Systems." ORNL/HUD/MIUS-25. Oak Ridge, TN: Oak Ridge National Laboratory; 

pp. 3-134. 

45 
U.S. Congress. House. 1980. Hearings before a Subcommittee on Government Operations. Washington, DC: United States House of Representatives; Sept. 1978. 

46 
Flat-plate collector 

Evacuated-tube collector 

Fr (ad 

0.661 

0.397 

FrUl [W/m2] 

6.104 

1.170 

*The terms Fr (a·r) and FrUl are terms from the instantaneous solar collection equation: 

Qc = Fr (aT) I -

where Qc is collected solar heat, I is incident solar radiation, and is the difference between the collector, and ambient temperatures. Collector temperature is assumed 

equal to the average storage temperature. 

B. STORAGE 

Storage losses are calculated based on a constant storage U-value of 0.11 W/m20·C. 

Storage losses are calculated relative to ground temperature, which is assumed equal to 

average year-round ambient temperature. 

Maximum Storage Temperature: 79.5° C. 

C. TRANSMISSION LOSSES 

Transmission losses from collector to storage and from storage to load are ignored. They 

are assumed to be accounted for by storage losses. 

D. HEAT EXCHANGE CAPACITY 

Ability of the heating system to meet the load depends on (a) size of the load, (b) size of 

heat exchange between heat source and load, and (c) temperature difference between 

heat source and room temperature. Assuming that building load is proportional to the 

difference between ambient and room temperature, the fraction of the building load that 

may be supplied by a solar heating system is: 

Ts- Tr 

Solar fraction = Xh T _ T 

r a 

where Tr is room temperature (assumed to be 20°C in this study), Ts is the temperature 

of the lieat source, T a is ambient temperature, and Xh is a coefficient 

(Klein et ale 1977). In this study the coefficient Xh has the followmg values: 

47 
E. HOT WATER PREHEAT 

The fraction of the hot water load that may be met by the solar heating system is similarly dependent on a heat-exchange effectiveness formula. In this simulation the formula 

is 

Ts - 10 

Hot water fraction = 52 _ 10 

where T s is heat-source temperature. This assumes a cold-water temperature of 10° C, a 

hot-water temperature of 49°C, and a heat-exchange effectiveness of 92%. 

48 
q

y, 

p

g

p

p

ing. The purpose of the load algorithm is to generate a load pattern that reflects. the 

daily and monthly load variation of a passive or superinsulated building design, rather 

than an exact load. 

The load algorithm requires four input parameters: 

• Building gross shell loss coefficient, in watts per degree Centigrade; 

• Effective passive collection area, in square meters (the effective area is assumed 

modified to reflect window angles, transmission losses, and other losses); 

• Miscellaneous heat gain, in watts, due to inhabitants and electric appliances; and 

• Effective thermal-mass capacity in watt-hours. This term gives the quantity of 

heat which may be stored without bringing discomfort to the residents. 

The algorithm calculates the heat load for each day in two periods, one for daytime and 

one for nighttime. For each period the following five steps are performed. 

(1) Building gross shell loss for the period is calculated based on the difference 

between room temperature (assumed to be a constant 200 C) and ambient temperature and the shell-loss coefficient. This step parallels the degree-day 

method of calculating building loads. 

(2) Miscellaneous heat gain for the period is calculated and the gain is subtracted 

from the gross shell load. If the miscellaneous heat gain exceeds the load, 

excess heat is stored in thermal mass. 

(3) Passive gain in daytime is calculated from the total daily radiation and the 

effective passive collection area. The passive gain is subtracted from the building load remaining at the end of Step 2. Again, if excess heat remains, it is 

added to passive storage. 

(4) If necessary, heat is removed from thermal mass to meet whatever positive net 

building load remains at the end of Step 3. If stored heat is insufficient to meet 

the building load at this step, the remainder becomes the net building load for 

the period and will be met by either active solar or auxiliary heat. 

(5) The amount of heat stored in thermal mass is carried over to the next period. 

The amount of passively stored heat is not allowed to exceed the effective 

thermal mass capacity. 

When the parameters are set properly, this algorithm generates a load pattern that meets 

the criteria for use in this study. The load size may be set appropriately; and the load 

changes from day to day, reflecting the amount of insolation. For passive construction, 

the effective passive collection area is sized to meet nearly all the load on a sunny winter day. Thermal-mass capacity is set to accommodate nearly all the load of a mild winter night. Thus, on a sunny, mild winter day there would be virtually no load, while on a 

49 
Table B-1 shows a comparison between results of the passive load algorithm and data 

generated by the SUNCAT 2.4 hourly passive simulation (Palmiter). As shown in 

Table B-1, the passive algorithm cannot be used accurately to predict actual building 

loads. The monthly and daily loads, however, are all reasonably close to the SUNCAT 

data. Simulation results with the passive load algorithm should therefore reflect accurately the performance of active solar heating when coupled with a passive building load 

pattern. The monthly and daily load patterns for superinsulated buildings are designed to 

approximate the load pattern of the Saskatchewan Conservation House (Besant 1978) and 

the Lyngby House (Esbensen and Korsgaard 1977). 

Tables B-2 and B-3 give the values of the parameters and building performance for each 

of the types of buildings and each location used in this study. SUB 50, TUB 50, and HUB 

200 refer to the building types, explained in Sec. 2.0. 

50 
Month 

Apr. 

May 

June 

July 

Aug. 

Sept. 

Oct. 

Nov. 

Dec. 

Jan. 

Feb. 

Mar. 

data. The passive load algorithm used the following 

param eters: 

Gross shell loss coeff. 48 MJ/hoC 

Miscellaneous heat gain 80 MJ /h 

Passive gain effective area 700 m2 

Effective thermal mass capacity 10 GJ. 

Monthly Loads Daily Loads 

Passive SUNCAT Day Passive Algorithm Algorithm 

104 1.8 Jan. 1 0.38 

0.6 0.7 Jan. 2 0.22 

0 0 Jan. 3 0.24 

0 0 Jan. 4 0.37 

0 0 Jan. 5 0.28 

0 0 Jan. 6 0.34 

1.0 1.5 Jan. 7 0.26 

6.6 6.0 Jan. 8 0.42 

11.4 10.8 Jan. 9 0.54 

13.6 12.2 Jan. 10 0048 

9.4 9.4 6.5 6.0 

51 

SUNCAT 

0.40 0.21 0.15 0.30 

0.23 

0.30 

0.25 

0.48 

0.42 

0.36 
0 

t-:l- -< t-:l 0 :I:- t-:lZ -< E-<U E-< 

0... < :I:- 0:> :>0... rnU r;::< E-< - :I:J: 

0 rnr;.; .- UU rnr;.; UI-;) < rnr;.; r;.;< 0 <r;.; t-:l OU 

BOSTON, MASS. 

SUB 50 

Standard 53 80 0 0 

Passive 40 80 700 10 

Superinsulated 15 70 250 4 

TUB 50 

Standard 22 40 0 0 

Passive 16 40 220 4 

Super insulated 7 32 100 2 

HUB 200 

Standard 56 120 0 0 

Conserving 25 100 250 5 

BISMARCK, N. DAK. 

SUB 50 

Standard 52 80 0 0 

Passive 40 80 800 12 

Super insulated 13 70 250 4 

TUB 50 

Standard 22 40 0 0 

Passive 16 40 300 5 

Super insulated 6 32 120 2 

HUB 200 

Standard 54 120 0 0 

Conserving 22 100 300 5 

52 
0 

...... ...:l-

...:lE-< 0 ::q ...... ...:lZ ...... E-<U E-< 

p.. ::q ...... 0> >p.. l>-t mU ...... E-< ...... t:t::,.c >E-< UU 

0 .- ...... U UI-;) 0 ...:l OU 

MEDFORD, OREG. 

SUB 50* 

Standard 53 80 0 0 

Passive 40 80 700 10 

Superinsulated 15 70 250 4 

TUB 50* 

Standard 22 40 0 0 

Passive 16 40 220 4 

Super insulated 7 32 100 1 

HUB 200* 

Standard 56 120 0 0 

Conserving 25 100 250 5 

ALBUQUERQUE,N.MEX. 

SUB 50 

Standard 53 80 0 0 

Semipassive 35 70 300 5 

Passive 40 80 600 10 

TUB 50 

Standard 22 40 0 0 

Passive 16 40 200 4 

HUB 200 

Standard 56 120 0 0 

Conserving 30 100 200 4 

53 
0 ...... Eo< < ............ < :s: 

Eo< ::t: 

fi5::t: 

::t: CI.l> U >-t 

Eo< CI.l:;... CI.l U CI.lCl.l < 

-

CI.l- <- CI 

< Q:--l ..... ..... Eo<C"I Z< 

0 0>-t 0>-t ...... Zo 

0-

BOSTON, MASS. 

SUB 50 

Standard 4.441 0.125 0.000 3.890 0.876 

Passive 3.352 0.166 0.472 1.216 0.840 

Superinsulated 1.257 0.356 0.388 0.322 0.548 

TUB 50 

Standard 1.844 0.149 0.000 1.570 0.876 

Passive 1.307 0.209 0.397 0.516 0.840 

Superinsulated 0.587 0.350 0.354 0.175 0.511 

HUB 200 

Standard 4.693 0.173 0.000 3.880 1.752 

Conserving 2.095 0.312 0.280 0.855 1.460 

BISMARCK, N. DAK. 

SUB 50 

Standard 6.602 0.091 0.000 6.000 0.975 

Passive 5.079 0.119 0.478 2.047 0.975 

Superinsulated 1.651 0.297 0.396 0.506 0.657 

TUB 50 

Standard 2.793 0.107 0.000 2.495 0.975 

Passive 1.981 0.151 0.457 0.776 0.975 

Super insulated 0.762 0.295 0.410 0.225 0.657 

HUB 200 

Standard 6.856 0.129 0.000 5.975 1.945 

Conserving 2.793 0.256 0.320 1.186 1.643 

54 
0 

..... :::1 ..... < ...:l ...:lE-< 

...:l ::r:: E-< ...:l 

::r:: s:.. ct:l:> Us:.. ...:l • ...:l ..... ...... ct:l:>, ct:l U ct:lgs <» ...:lo E-< < ...... 

0 gs;:;- of!3 0< PO 

< 0c"I ..... :?1 ..... Z< 

0 Zo ...:l 0 ...... <...:l 

MEDFORD, OREG. 

SUB 50 

Standard 4.101 0.154 0.000 3.471 0.803 

Passive 3.095 0.207 0.497 0.918 0.803 

Superinsulated 1.161 0.433 0.369 0.231 0.511 

TUB 50 

Standard 1.702 0.183 0.000 1.391 0.803 

Passive 1.207 0.261 0.423 0.384 0.803 

Superins ulated 0.542 0.426 0.347 0.124 0.511 

HUB 200 

Standard 4.333 0.212 0.000 3.415 1.606 

Conserving 1.934 0.382 0.299 0.620 1.460 

ALBUQUERQUE, N. MEX. 

SUB 50 

Standard 3.559 1.145 0.000 3.044 0.840 

Semipassive 2.351 0.191 0.502 0.724 0.730 

Passive 2.686 0.191 0.703 0.291 0.840 

TUB 50 

Standard 1.477 0.171 0.000 1.224 0.840 

Passive 0.237 0.636 0.136 0.840 0.840 

HUB 200 

Standard 3.761 0.198 0.000 3.016 1.679 

Conserving 2.015 0.299 0.386 0.636 1.314 

55 
56 
p

The tables present collector and storage sizes foc annual storage systems designed to 

meet 95% of the system space heat load. Both the fraction of hot water provided and 

the total solar fraction vary among the systems presented. This criterion was selected 

for system sizing in order to avoid misleading results that can occur when a predominantly hot water system is compared with a predominantly space heating system with the 

same solar fraction. As discussed in Secs. 3.2 and 3.5, optimal annual storage systems 

typically provide 95%-100% of the building space heat load but only 80%-90% of the hot 

water load. Proper system sizing is therefore based on the system's projected ability to 

meet the space-heating load rather than the total load. All system sizes presented are 

for points of unconstrained annual storage operation, as defined in Sec. 3.0. 

In the two-tank systems, the second storage tank is always sized according to the collector area (Ac)' using the formula 

vs <m 3) = 0.075 Ac<m 2) • 

In addition to collector size, storage size, and total solar fraction, the tables give the 

following parameters: 

• Overall system efficiency for the. annual storage system. This is defined as the 

total heat delivered to the load, divided by the total energy incident on the collector for the year. 

• Diurnal solar fraction. This is the solar fraction foc a diurnal system with the 

same collector area as the given annual system. Storage size in cubic meters is 

one-fifth the collector size in square meters foc the diurnal system. If the 

annual storage system is a two-tank system, the diurnal solar fraction is also 

based on a two-tank system, with the second tank as in the annual 

system. 

• Net added energy. This is based on a comparison 'of the performance of the 

annual storage system and the diurnal system described above. Net energy is 

calculated by the following formula: 

heat delivered by annual system - heat delivered by diurnal system 

Net energy = ---------------------------

annual storage volume - diurnal storage volume 

The annual and diurnal systems, as sized here, represent the boundaries of the 

intermediate storage region in the system-performance graphs (Region B) as 

described in Sec. 3.0. As explained in the text, the net energy added by storage 

gives the slope of the system-performance curve, which is usually a linear curve 

in this regi on. 

57 
the locations, collector types, and building designs included in this study. System plots 

are all for SUB-50 systems. Both space heat and combined systems are presented. 

The system performance curves represent a number of different collector sizes. Collector sizes for each plot are listed below the graph. The y-axis gives solar fraction ranging 

from 0.2 The x-axis gives the ratio of storage size to collector size, ranging from 

zero to 5 m /m collector area. 

The trade-off graphs present isoquant curves for solar fractions of 0.75, 0.80, 0.85,0.90, 

0.95, and 0.99. For combined systems, the last isoquants (with s()lar fractions of 0.95 and 

0.99) may be omitted. This omission occurs because a combined system may need to supply not just 100% solar space heat but also an inordinately large percentage of the hot 

water load in order to meet a high combined solar fraction. Such systems would have to 

be oversized. A typical combined load system may meet 100% of the space heat load and 

85% of the hot water load, for a combined solar fraction of 92%. In such a case, isoquants for higher solar fractions would be omitted. 

In the trade-off graphs, storage volume is plotted on the y-axis and collector area on the 

x-axis. The scale of the x- and y-axes are in the same proportion to each other for all 

trade-off graphs, with one square meter collector area corresponding in scale to one 

cubic meter storage. Also plotted on the trade-off graphs are discrete points representing the region of unconstrained operation. 

58 
0 0 p;

j 

0 - - Z M <: ...:l Eo-< Eo-< S 0 0 0 >; p;::j 0- >- 0 <: <: 0 

>; Eo-<C"I Z 0 

Eo-< o S 0 I OJ 

0 ...:l 

-

0 <: <:M 00 <: ...:l - <:t> 0 ...:l O...:l 0 0 Eo-< 0 -0 ...:l 0 r:n r:n Or:n 

SUB 50 

Standard 3830 8880 0.230 0.925 0.717 124 0.47 

Passive 1800 3960 0.207 0.905 0.677 129 0.63 

Super insulated 850 ll80 0.183 0.889 0.788 87 0.47 

SUB 50 - space heat 

only 

Standard 3120 8740 0.237 0.950 0.660 140 0.55 

Passive llOO 3800 0.210 0.950 0.482 160 0.83 

Superinsulated 350 1000 0.174 0.950 0.486 160 1.10 

SUB 1 

Standard 97 172 0.182 0.929 0.792 90 0.47 

Passive 54 68 0.138 0.905 0.795 80 0.50 

Superinsulated 24 20 0.131 0.901 0.857 51 0.40 

TUB 50 

Standard 2000 3600 0.220 0.903 0.768 llO 0.43 

Passive 1250 1700 0.192 0.885 0.794 85 0.40 

Super insulated 700 560 0.174 0.890 0.852 64 0.35 

HUB 200 

Standard 4500 9100 0.227 0.909 0.744 ll5 0.45 

Conserving 2100 2550 0.200 0.885 0.800 100 0.42 

*System with collector tilt equal to latitude. 

59 
0 0 rIl 

< 0 E:: - Z M ...:l E-o S 0 0 0 

0- >- 0 < < 0 0 

Z 0 ot 

E-o 0 r:.G Q) 

0 ...:l 

-

0 <M < < ...:l 0 Ei:: ...:l O...:l < eJ 0 0 E-o 0 -0 ...:l 0 en en Oen Z::E 

SUB 50 

Standard 3000* 9200 0.284 0.921 0.610 172 0.47 

Passive 1350 3750 0.271 0.897 0.608 172 0.55 

Superins ulated 590 1180 0.258 0.877 0.713 135 0.42 

SUB 50 - space heat 

only 

Standard 2600* 8400 0.278 0.950 0.578 180 0.45 

Passive 850 3200 0.272 0.950 0.406 210 0.77 

Superinsulated 260 1000 0.236 0.950 0.404 170 0.77 

SUB 1 

Standard 73* 200 0.226 0.932 0.675 125 0.38 

Passive 36 80 0.204 0.892 0.694 115 0.33 

Superinsulated 16 25 0.191 0.878 0.791 90 0.25 

TUB 50 

Standard 1500* 4000 0.282 0.895 0.665 160 0.60 

Passive 900 2050 0.256 0.875 0.717 120 0.33 

Superinsulated 460 750 0.259 0.858 0.771 90 0.25 

HUB 200 

Standard 3500* 9300 0.284 0.904 0.650 165 0.40 

Conserving 1460 3000 0.269 0.872 0.708 140 0.40 

*System with collector tilt equal to latitude. 

60 
0 0 

0 - e:: z M <: E-o E 0 >- 0 0 >- <: <: 0 0- 0 

>- E-oC'l Z 0 OC) E-o OE 0_ 0 I Q) <: - <:M 0 0 <: 00 <: - <:C) 0 0 0 0 0 rI.l sSl 

SUB 50 

Standard 3550 7840 0.254 0.944 0.691 170 0.55 

Passive 1800 3700 0.215 0.944 0.691 155 0.67 

Superinsulated 850 1180 0.195 0.946 0.802 145 0.83 

SUB 50 - space heat 

only 

Standard 2800 8000 0.263 0.950 0.620 175 0.53 

Passive 1100 3600 0.212 0.950 0.500 170 0.63 

Superinsulated 350 1000 0.179 0.950 0.520 155 0.77 

SUB 1 

Standard 90 155 0.202 0.944 0.764 130 0.55 

Passive 50 65 0.156 0.946 0.791 100 0.60 

Superinsulated 23 25 0.141 0.944 0.877 52 0.35 

TUB 50 

Standard 1900 3300 0.238 0.938 0.751 155 0.53 

Passive 1200 1700 0.215 0.941 0.791 145 0.60 

Superinsulated 680 600 0.191 0.944 0.863 120 0.60 

HUB 200 

Standard 4250 8600 0.248 0.939 0.725 165 0.50 

Conserving 2000 2700 0.216 0.935 0.790 145 0.55 

*System with collector tnt equal to latitude. 

61 
::E 

0 0 til ::> e:: .... z < ...:I E-< E 

0 >t C,) C,) Q 0- >- C,) < < 0 

>t Z Q 

Eo-< Q CI) 

.... <M Q ...:I C,) < < ...:I Eo-<.e. .... < () 0 ...:I ::>...:1 0 0 0 .... 0 

...:I C,) CI.l QCI.l Z2: 

SUB 50 

Standard 2800* 8100 0.310 0.941 0.612 210 0.47 

Passive 1360 3800 0.283 0.942 0.631 185 0.45 

Superinsulated 590 1180 0.271 0.936 0.734 165 0.47 

SUB 50 - space heat 

only 

Standard 2250* 8200 0.325 0.950 0.542 200 0.45 

Passive 820 3700 0.282 0.950 0.420 185 0.40 

Superinsulated 250 1000 0.246 0.950 0.426 180 0.63 

SUB 1 

Standard 70 160 0.256 0.944 0.685 170 0.45 

Passive 35 77 0.222 0.945 0.708 140 0.45 

Superinsulated 16 23 0.204 0.941 0.818 110 0.50 

TUB 50 

Standard 1460 3400 0.307 0.935 0.670 210 0.45 

Passive 900 1700 0.282 0.938 0.735 180 0.45 

Superinsulated 460 720 0.280 0.930 0.788 160 0.39 

HUB 200 

Standard 3350 8200 0.316 0.938 0.651 220 0.50 

Conserving 1450 2900 0.292 0.931 0.723 195 0.47 

*System with collector tilt equal to latitude. 

62 
:E 

0 0 00 ::;, E= .... Z M < ...:I E- E 

0 0 0 

>-

:>! < < 0 p.. 0- 0 Z :>! oS 0 E- .... 0 

0 ...:I 0 < <M < ...:I .... 0 ...:I ::;,...:1 E-.e. 0 0 t; 0 -0 ...:I 0 00 000 z:;s 

SUB 50 

Standard 2300 8400 0.283 0.920 0.618 160 0.67 

Passive 1000* 4100 0.251 0.885 0.524 155 0.70 

Superinsulated 500 1230 0.220 0.864 0.669 135 0.83 

SUB 50 - space heat 

only 

Standard 1800 8300 0.301 0.950 0.563 180 0.70 

Passive 600 3400 0.242 0.950 0.261 190 1.40 

Superinsulated 170* 920 0.223 0.950 0.238 185 2.00 

SUB 1 

Standard 60* 190 0.215 0.923 0.677 120 0.60 

Passive 31 90 0.178 0.894 0.609 115 0.77 

Superinsulated 14* 33 0.150 0.865 0.715 75 0.60 

TUB 50 

Standard 1200* 3800 0.268 0.897 0.661 140 0.55 

Passive 750 1600 0.232 0.861 0.671 155 1.10 

Superinsulated 420 800 0.224 0.869 0.738 115 0.70 

HUB 200 

Standard 2500* 9700 0.295 0.898 0.623 150 0.63 

Conserving 1250 3200 0.244 0.857 0.684 120 0.55 

*System with collector tilt equal to latitude. 

63 
0 E= - Z M <: ...:I E-o E 0 >t 0 0 0 >- 0- <: <: 0 p:. ... 

>t Z p:. <:p:. 0 E-o 0 - <:M 0 ...:I 0 o;Z <: <: ...:I E-o-e. 0 S ...:I 0...:1 <: c:,) 0 0 E-o p:. 0 -0 ...:I 0 00 00 000 

SUB 50 

Standard 2200 8300 0.303 0.921 0.587 180 0.53 

Passive 900* 3800 0.276 0.880 0.510 175 0.83 

Superins ulated 400* 1180 0.259 0.852 0.640 145 0.67 

SUB 50 - space heat 

only 

Standard 1800* 7700 0.305 0.950 0.540 195 0.63 

Passive 580 3400 0.258 0.950 0.253 190 0.90 

Super ins ulated 160 900 0.235 0.950 0.237 190 1.00 

SUB 1 

Standard 55 180 0.244 0.920 0.642 140 0.47 

Passive 27 82 0.195 0.890 0.685 95 0.77 

Superins ulated 12 27 0.188 0.858 0.696 100 0.55 

TUB 50 

Standard noo 3600 0.291 0.889 0.623 170 0.47 

Passive 600* 1950 0.274 0.850 0.632 150 0.55 

Superins ulated 340 800 0.261 0.855 0.708 130 0.55 

HUB 200 

Standard 2400* 9000 0.305 0.896 0.594 180 0.50 

Conserving 1100 3100 0.277 0.862 0.662 145 0.60 

*System with collector tilt equal to latitude. 

64 
0 

::> - e:: z < ...::! '" E-< S 0 >; C,.) C,.) 0 >- < < ll.. 0- C,.) 

>; E-<C"I Z 0 oS E-< 0_ 0 Q) 

0 < - <'" ...::! C,.) < < ...::! - E-<.e. <C) 0 ...::! ::>...::! 0 0 0 ...::! C,.) a:l 15£ 

SUB 50 

Standard 2100* 7800 . 0.323 0.941 0.595 200 0.70 

Passive 1050 3900 0.260 0.935 0.552 180 0.83 

Superinsulated 500 1220 0.235 0.929 0.685 165 0.83 

SUB 50- space heat 

only 

Standard 1700 7200 0.333 0.950 0.544 210 0.67 

Passive 550* 3500 0.246 0.950 0.280 180 0.83 

Superinsulated 180 900 0.217 0.950 0.288 180 1.00 

SUB 1 

Standard 55 165 0.250 0.939 0.653 160 0.55 

Passive 32 86 0.176 0.932 0.630 130 0.55 

Superinsulated 15 30 0.158 0.929 0.741 105 0.70 

TUB 50 

Standard 1150 3350 0.300 0.929 0.654 195 0.60 

Passive 770 1800 0.244 0.923 0.686 170 0.90 

Superinsulated 420 820 0.244 0.925 0.750 150 0.90 

HUB 200 

Standard 2600 7800 0.311 0.932 0.633 205 0.67 

Conserving 1250 3000 0.261 0.919 0.694 170 0.83 

*System with collector tilt equal to latitude. 

65 
0 

<: D - Z C"') t-':! E-o S 0 C,) C,) 0 0- >- <: <: C,) ..... 

Z 0 

E-o 0 - <:M 0 t-':! 0 <: <: t-':! 0 - t-':! Dt-':! 0 0 0 -0 t-':! C,) 00 000 Z::E 

SUB 50 

Standard 2000* 7600 0.331 0.934 0.601 200 0.77 

Passive 900* 3850 0.294 0.930 0.528 190 0.77 

Superinsulated 400* 1200 0.280 0.920 0.657 175 0.70 

SUB 50 - space heat 

only 

Standard 1600* 7200 0.338 0.950 0.519 215 0.63 

Passive 500* 3300 0.302 0.950 0.256 200 0.83 

Superins ulated 160 880 0.235 0.950 0.267 190 1.10 

SUB 1 

Standard 50 160 0.272 0.940 0.631 170 0.47 

Passive 25 80 0.225 0.934 0.590 160 0.77 

Super ins ulated 12 27 0.200 0.924 0.720 125 0.60 

TUB 50 

Standard 1020* 3500 0.330 0.921 0.618 190 0.53 

Passive 600* 1950 0.297 0.914 0.649 120 0.45 

Superinsulated 350 800 0.282 0.916 0.730 150 0.70 

HUB 200 

Standard 2400* 8300 0.328 0.930 0.608 205 0.50 

Conserving 1020* 3000 0.307 0.910 0.661 185 0.63 

*System with collector tilt equal to latitude. 

66 
t:t: 9 

:;J E= z CI? < ...:l E-o E 0 0 U 

>- >- -< < Q 0- U 

>- E-oC'l z Q 9+" U E E-o 0_ Q 

Q < -0 <M ...:l -< -< ...:l - < 0 ...:l :;J...:l 0 0 0 -0 ...:l u 00 Qoo z::E 

SUB 50 

Standard 5000 16500 0.218 0.935 0.684 113 0.70 

Passive 2400 8200 0.193 0.922 0.623 118 0.83 

Super ins ulated 1000 2600 0.175 0.914 0.726 91 0.70 

SUB 50 - space heat 

only 

Standard * 4000 17000 0.235 0.950 0.618 125 0.77 

Passive 1000 7600 0.200 0.950 0.463 135 1.25 

Sup er ins ulated 470 2000 0.170 0.950 0.445 135 1.40 

SUB 1 

Standard 130 360 0.168 0.935 0.749 80 0.63 

Passive 70 210 0.136 0.923 0.705 66 0.50 

Superinsulated 32 58 0.111 0.922 0.819 50 0.47 

TUB 50 

Standard 2400 7800 0.217 0.922 0.710 100 0.67 

Passive 1450 4000 0.184 0.913 0.734 85 0.53 

Superins ulated 800 1440 0.167 0.913 0.822 65 0.45 

HUB 200 

Standard 5500 17800 0.222 0.927 0.698 110 0.67 

Conserving 2300 5700 0.186 0.914 0.750 90 0.60 

*System with collector tilt equal to latitude. 

67 
Z Z 0::: 

oJ 

0::: 0 0 C/l 

< - - Z M E-o E-o E 0::: 0 U U 

0- >- <: < 0 U 0 

Z 0::: 0 ot E-o 0_ 0 I (J) 

0 < - 0::: ZO::: <M 0::: U < 0:::< E-o.§. o 0 < - < 0 0 0 E-o 0 -0 0:::C'l U 00. 00. 000. Z:;E E-o E 

SUB 50 

Standard 4500 14500 0.242 0.950 0.653 153 0.63 

Passive 2400 8700 0.198 0.953 0.623 123 0.60 

Super insulated 1000 2800 0.183 0.957 0.726 103 0.50 

SUB 50 - space heat 

only 

Standard* 3500 15750 0.266 0.950 0.574 150 0.55 

Passive 1650 8000 0.198 0.950 0.470 130 0.60 

Super insulated 500 2100 0.156 0.950 0.453 125 0.63 

SUB 1 

Standard 120 300 0.182 0.95 0.730 112 0.55 

Passive 65 185 0.160 0.952 0.676 100 0.55 

Superinsulated 30 55 0.122 0.955 0.804 70 0.50 

TUB 50 

Standard 2300 6500 0.235 0.948 0.685 150 0.67 

Passive 1500 3600 0.186 0.956 0.743 113 0.70 

Superinsulated 770 1520 0.176 0.961 0.810 100 0.70 

HUB 200 

Standard 5000 16000 0.248 0.948 0.671 146 0.60 

Conserving 2200 5700 0.201 0.955 0.741 115 0.63 

*System with collector tilt equal to latitude. 

68 
:;E 

z p

0 0 til p:: :;:J ..... ..... Z M <: ...::l E-< E-< E 

p:: 0 C) C) 

>- <: <: 0 0- C) p:: ...::lP:: ot U E Z 0 E-< Cl_ 0 I Q) <: ..... P:: Zp::: 0 C) <t:"" ...:J P:: <: p::<: E-<-e. 00 <: ...::l ..... <1:1 0 ...::l :;:J...::l 0 0 0 ..... 0 ...::l U 00 Om z:;s 

SUB 50 

Standard 4000 13500 0.272 0.933 0.648 160 0.36 

Passive 1800 7200 0.251 0.922 0.597 145 0.45 

Superinsulated 700 2150 0.241 0.910 0.694 122 0.43 

SUB 50 - space heat 

only 

Standard* 3500 13000 0.274 0.950 0.606 168 0.42 

Passive 1300 6500 0.246 0.950 0.449 165 0.63 

Superinsulated 360 1800 0.224 0.950 0.434 150 0.63 

SUB 1 

Standard 95 280 0.230 0.935 0.706 123 0.39 

Passive 40 165 0.210 0.923 0.632 110 0.42 

Superins ulated 20 48 0.174 0.906 0.783 65 0.25 

TUB 50 

Standard 2000 5900 0.268 0.920 0.693 143 0.39 

Passive 1050 3100 0.254 0.912 0.711 115 0.42 

Super insulated 550 1200 0.238 0.910 0.801 85 0.25 

HUB 200 

Standard 4400 14000 0.276 0.923 0.664 155 0.35 

Conserving 1600 4500 0.260 0.893 0.714 120 0.60 

*System with collector tilt equal to latitude. 

69 
:?J Z Z 0:: ..... 0:: 0 0 tI.l 

< 0 ...... ...... Z M Eo-< Eo-< E 0:: 0 ;>i C) C) 0- >- < < Q C) 0:: ..... ;>i Z Q 

Eo-< Q Q) 

...... 0:: ZO:: Cl C) <M 0:: < 0::< < ...... < 0 0 0 Eo-< 0 ...... 0 C) ct:J ct:J Clct:J Z22 

SUB 50 

Standard 3500 12250 0.310 0.945 0.610 200 0.42 

Passive 1800 6400 0.282 0.948 0.615 170 0.43 

Superinsulated 700 2100 0.260 0.948 0.710 140 0.39 

SUB 50 - space heat 

only 

Standard* 3000 12800 0.308 0.950 0.561 190 0.37 

Passive 1300 6200 0.252 0.950 0.474 160 0.50 

Superinsulated 320 1900 0.232 0.950 0.442 140 0.43 

SUB 1 

Standard 90 260 0.248 0.947 0.694 145 0.36 

Passive 40 160 0.222 0.948 0.664 115 0.39 

Super insulated 19 40 0.200 0.950 0.788 105 0.35 

TUB 50 

Standard 1800 5400 0.301 0.944 0.664 195 0.40 

Passive 1000 3000 0.272 0.944 0.714 145 0.36 

Superinsulated 530 1060 0.258 0.950 0.817 125 0.36 

HUB 200 

Standard 4000 13000 0.308 0.942 0.641 195 0.63 

Conserving 1600 4200 0.260 0.944 0.730 155 0.40 

*System with collector tilt equal to latitude. 

70 
?J 

Q 0 til 0 Z M <: Eo- S 0 :>; U U 0 0- >- <: <: u 

:>; Eo-C"l Z 0 ot 

Eo- uS 0_ 0 I Q) <: - p:: 0 p:: u <t:'" <: p::<: S o 0 <: - <: 0 .......... 0 0 0 -0 U 00 000 Z::::E 

SUB 50 

Standard 1300 6200 0.323 0.920 0.729 123 0.17 

Passive 450 680 0.263 0.908 0.836 42 0.25 

Superinsulated 550 1900 0.285 0.908 0.760 95 0.14 

SUB 50 - space heat 

only 

Standard* 1000 7000 0.333 0.949 0.636 140 0.17 

SUB 1 

Standard 32 116 0.259 0.923 0.806 82 0.13 

Semipassive 14 31 0.218 0.908 0.823 65 0.25 

TUB 50 

Standard 700 2300 0.306 0.901 0.798 100 0.14 

Passive 450 180 0.238 0.950 0.936 150 

HUB 200 

Standard 1550 6400 0.318 0.908 0.769 105 0.13 

Conserving 750 1300 0.272 0.902 0.849 85 0.13 

*System with collector tilt equal to latitude. 

71 
:;E Z Z +-

 0 9 til 0 ..... Z M -< Eo-< Eo-< 8 

0 CJ CJ 

0- >- CJ -< -< 0 0 

z 0 ot 

Eo-< 0 I Q) 

..... 

0 CJ -<M o 0 -< ..... -< • 8 -< 0 t'"'- 0 0 Eo-< 0 ...... 0 CJ 00. 00. 000. Z2S 

SUB 50 

Standard 1200 5850 0.354 0.942 0.704 165 0.14 

Passive 475 960 0.265 0.958 0.888 120 0.22 

Sernipassive 530 1900 0.298 0.947 0.791 100 0.22 

SUB 50 - space heat 

only 

Standard* 900 6300 0.375 0.950 0.647 150 0.19 

SUB 1 

Standard 30 108 0.297 0.945 0.790 120 0.15 

Sernipassive 14 32 0.227 0.947 0.857 70 0.17 

TUB 50 

Standard 680 2150 0.334 0.940 0.797 150 0.18 

Passive 400 320 0.270 0.961 0.944 70 0.25 

HUB 200 

Standard 1500 6000 0.344 0.944 0.762 150 0.17 

Conserving 720 1500 0.300 0.946 0.864 110 0.21 

*Systern with collector tilt equal to latitude. 

72 
Z Z 

::8 +

 9 0 CIJ :;:J Z M <: E-< E 

0 U U >- <: <e: 0 r.'l. 0- U 0 

z 0 at E-< u E 0_ 0 I Q) 

0 <: U - <M <: E-<-e. o 0 <: - <: <:.> 0 0 0 0 -0 U 00. 000. Z::E 

SUB 50 

Standard 1300 6400 0.316 0.924 0.653 170 0.14 

Passive 400 880 0.292 0.896 0.808 160 0.18 

Semipassive 500 2100 0.299 0.894 0.697 115 0.20 

SUB 50 - space heat 

only 

Standard* 1050 6400 0.316 0.950 0.567 190 0.21 

SUB 1 

Standard 32 120 0.260 0.923 0.731 130 0.15 

Semipassive 13 35 0.234 0.900 0.775 90 0.18 

TUB 50 

Standard 700 2500 0.300 0.900 0.729 150 0.18 

Passive 350 300 0.291 0.908 0.890 80 0.18 

HUB 200 

Standard 1600 6400 0.310 0.914 0.706 160 0.18 

Conserving 675 1700 0.301 0.890 0.792 115 0.17 

*System with collector tilt equal to latitude. 

73 
Z Z p:: 

p:: 0 0 U) 

< 0 ...... ...... Z M Eo< Eo< 8 

0 U U 

Pol 0- >- U < < Q 0 

Z Q ot Eo< u_ Q Cl.> ...... 

Q U <M 

< s:: < E-<.e. < 0 0 0 0 ...... 0 U rJ:J QCI.l z:;s 

SUB 50 

Standard* 1200 5800 0.340 0.943 0.631 215 0.22 

Passive 420 980 0.304 0.959 0.841 190 0.23 

Semipassive 500 1900 0.316 0.942 0.719 145 0:25 

SUB 50 - space heat 

only 

Standard 950 6400 0.347 0.950 0.553 195 0.19 

SUB 1 

Standard 29 120 0.293 0.941 0.703 160 0.18 

Semipassive 13 36 0.259 0.945 0.786 125 0.20 

TUB 50 

Standard 660 2300 0.338 0.936 0.716 205 0.20 

Passive 350 420 0.307 0.955 0.904 140 0.25 

HUB 200 

Standard 1500 6000 0.340 0.938 0.691 205 0.20 

Conserving 650 1700 0.322 0.941 0.801 165 0.25 

*System with collector tilt equal to latitude. 

74 
< 0 

:;:E Z Z 0 0 

<C t:;:) ..... Z ....:l E-< 

0 u u 0 0- >- u < < p... E-<C"l z 0 

E-< U E 0_ OM < ..... 0 ....:l U <E 

< ....:l ..... < 0 ....:l t:;:)....:l E-<-.... 0 0 0 ...... 0 ....:l U 00 000 Z:;:E 

Boston, Mass. Flat-plate collector 

Single-tank system 1000 400 0.164 0.938 0.935 13 

Two-tank system 1000 600 0.170 0.974 0.956 40 

Boston, Mass. Evacuated-tube collector 

Single-tank system 600 480 0.260 0.892 0.887 12 

Two-tank system 600 480 0.273 0.937 0.906 70 

Medford, Oreg. Flat-plate collector 

Single-tank system 600 960 0.204 0.894 0.854 39 

Two-tank system 600 960 0.220 0.961 0.877 80 

Medford, Oreg. Evacuated-tube collector 

Single-tank system 500 1000 0.249 0.907 0.847 54 

Two-tank system 500 1000 0.265 0.964 0.868 86 

Bismarck, N. Dak. Flat-plate collector 

Single-tank system 800 800 0.183 0.912 0.903 14 

Two-tank system 800 800 0.193 0.960 0.914 70 

Bismarck, N. Dak. Evacuated-tube collector 

Single-tank system 600 720 0.251 0.938 0.921 28 

Two-tank system 600 720 0.262 0.978 0.935 70 

75 
. 

0.0 1.0 2.0 3.G 4.0 S.O 

Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 2800, 3200: 3600, 4000, 4800, 5200, 5600, 

6000,6400.6800,7200,7600,8000 

0 

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Storage Size 

LOCATION: Boston, Mass. 

I 

13.0 

3 

LOAD TYPE: SUB-50, standard load, heat and hot water. 

SYSTEM TYPE: Flat plate collector, single tank system. 

76 
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Storage to Collector Ratio (m3/m2) 

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Collector sizes (m2): 1200, 1400, 1600, 1800, 2000, 2200, 2400, 2600, 2800, 

3000, 3200. 3400, 3600, 4000, 4500, 5000. 

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Storage Size 

LOCATION: Boston, Mass. 

I 

5250.0 

LOAD TYPE: SUB-50, passive load, heat and hot water 

SYSTEM TYPE: Flat plate collector, single tank system 

77 
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Collector sizes (m2): 400,500,600,700,800,900, 1000, 1100,1200, 1300. 

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LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, superinsulated load, heat and hot water. 

SYSTEM TYPE: Flat plate collector, single tank system. 

78 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 2000, 2400, 2800, 3200, 3600, 4000, 4400, 4800, 

5200, 5600, 6000, 7000. 

4) 

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5.5 11.0 

Storage Size 

I 

1'3.5 

3 

LOCATION: Boston, Mass. 

LOAD TYPE: SUT-50, standard load, space heat only 

SYSTEM TYPE: Flat-plate collector, single tank system 

79 
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Storage to Collector Ratio (m3/m2) 

LOCATION: Boston, Mass. LOAD TYPE: SUB-50, passive load, space heat only 

SYSTEM TYPE: Flat-plate collector, single tank system. 

Collector Storage Trade-Off 

If) -

['-. 

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0 0 

0.0 1750.0 3500.0 5250.0 

Storage Size 

SYSTEM TYPE: 800, 1000,1200, 1400, 1600, 2000, 2200, 

2400,2500,3000,3500,4000. 

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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 200,250, 300, 400, sao, 600, 700, 800, 900, 1000. 

Collector Storage Trade-Off 

500.0 1000.0 

storage Size 

LOCATION: Boston, Mass. 

1500.0 

LOAD TYPE: SUB-50, superinsulated load, space heat only 

SYSTEM TYPE: Flat-plate collector, single tank system 

81 
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Storage to Collector Ratio (m3/m2) 

5.0 

Collector sizes (m2): 2800, 3200, 3600, 4000, 4400, 4800, 5200, 5600, 

6000, 6400. 6800, 7200. 

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4.0 8.0 12.0 

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Storage Size 1 0 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, standard load, heat and hot water 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

82 
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Storage to 'Collector Ratio (m3/m2) 

Collector sizes (m2): 1200, 1400, 1600, 1800,2000,2200,2400,2600, 

2800, 3000, 3200, 3400, 3600. 

CD 

N 

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0 0 0 U, 

0 0 

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0.0 2250.0 4500.S f:i750.0 

Storage Size 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, passive load, heat and hot water. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

83 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300. 

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Storage Size 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, superinsulated load, heat and hot water. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

84 
Storage to Collector Ratio (m3/m2) 

. . 

Collector sizes (m2): 2000, 2400, 2800, 3200, 3600, 4000, 4400, 4800, 

5200, 5600, 6000. 

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Storage Size 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, standard load, space heat only. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

85 
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1.0 2.0 3.G 4.0 5.0 

Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 800, 1000, 1200, 1400, 1600, 1800, 2000, 2200, 2400, 

2500,3000. 

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Storage Size 

LOCATION: Boston, Mass. LOAD TYPE: SUB-50, passive load, space heat only 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

86 
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Collector sizes (m2): 200, 250, 300, 400, 500, 600, 700, 800, 900, 1000. 

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500.':1 10GO.S lSOG.O 

Storage Size 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, superinsulated load, space heat only, 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

87 
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SYSTEM TYPE: 2800, 3200, 3600, 4000, 4400, 4800, 5200, 5600, 

6000,6400,6800. 

Collector Storage Trade-Off 

,-

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0-+------.------'------,1 

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Storage Size 1 U 

LOCATION: Boston, Mass. LOAD TYPE: SUB-50, standard load, heat and hot water 

SYSTEM TYPE: Evacuated tube collector, single tank system. 

88 
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Collector sizes (m2): 1200, 1400, 1600, 1800,2000,2200,2400,2600,2800, 

3000, 3200, 3400, 3600, 3800. 

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Storage Size 1 03 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, passive load, heat and hot water. 

SYSTEM TYPE: Evacuated tube collector, single tank system. 

89 
ci 

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Storage to Collector Ratio 

Collector sizes (m2): 400,500,600, 700, 800, 900, 1000, 1100, 1200, 1300. 

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Storage Size 

LOCATION: Boston, Mass. LOAD TYPE: SUS-50, supennsulated load, heat and hot water 

SYSTEM TYPE: Evacuated tube cOllector, two-tank system. 

90 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 2000, 2400, 2800, 3200, 3600, 4000, 4400, 4800, 

5200, 5600, 6000. 

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Storage Size 1 03 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, standard load, space heat only 

SYSTEM TYPE: Evacuated tube collector, single tank system. 

91 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 800, 1000, 1200, 1400, 1600, 1800, 2000, 2200, 2400, 

2500, 3000, 3500, 

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Storage Size 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, passive load, space heat only. 

SYSTEM TYPE: Evacuated tube collector, single tank sysTem 

92 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 200, 250, 300, 400, 500, 600, 700, 800, 900, 1000. 

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Storage Size 

LOCATION: Boston, Mass. 

--, 

1050.0 

LOAD TYPE: SUB-50, superinsulated load, space heat only. 

SYSTEM TYPE: Evacuated tube collection, single-tank system. 

93 
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Collector sizes (m2): 2800, 3200, 3600, 400, 4400, 4800, 5200, 5600, 

6000, 6400 

Collector Storage Trade-Off 

Cl 

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LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, standard load, heat and hot water 

SYSTEM TYPE: Evacuated tube collection, two-tank system. 

94 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 1200,1400,1600,1800,2000,2200,2400,2600,2800,3000, 

3200 

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1750.0 

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3500.0 

Storage Size 

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5250.0 

LOCATION: Boston, Mass. LOAD TYPE: SUB-50 passive load, heat and hot water 

SYSTEM TYPE: Evacuated tube collector, two-tank system. 

95 
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Collector sizes (m2): 400,500, 600, 200, 800, 900, 1000, 1100, 

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500.0 

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Storage Size 

I 

1:;00.0 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, superinsulated load, heat and hot water. 

SYSTEM TYPE: Evacuated tube collector, two-tank system. 

96 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 2000, 2400, 2800, 3200, 3600, 4000, 4400, 4800, 

5200, 5600, 6000. 

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Storage Size 1 0 3 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, standard load, heC!t 9.nly. 

SYSTEM TYPE: Evacuated tube collector, two-tank system. 

97 
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Storage to Ratio (m3/m2) 

Collector sizes (m2): 800,1000,1200,1400,1600,1800,2000,2200,2400, 

2500. 

CD 

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Storage Size 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50 passsive load, space heat only. 

SYSTEM TYPE: Evacuated tube collector, two-tank system. 

98 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 200, 250, 300, 400, 500, 600, 700, 800. 

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450.D 

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Storage Size 

I 

lYiO.G 

LOCATION: Boston, Mass. 

LOAD TYPE: SUB-50, superinsulated load, space heat only. 

SYSTEM TYPE: Evacuated tube collector, two-tank 

99 
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Storage to Collector Ratio (m3/m2) 

Collector Sizes (m2): 1600,1800,2000,2400,2800,3200,3600.4000, 

4400, 6800, 5200, 560q, 6000. 

CD 

N 

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CJ 0 25"1 

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Storage Size 

LOCATION: Medford, Ore. LOAD TYPE: SUS-50, standard load, heat and hot water. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

100 
J.G 1.0 2.0 3.0 4.0 S.Q 7.0 

Storage to Collector Ratio (m3/m2) 

Collector Sizes (m2): 800,900,1000,1250,1500,1750,2000,2250,2500,2750,3000, 

3250,3500,3750,4000,4800,5600,6400,7200. -

Q,) 

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Storage Size 3 

LOCATION: Medford, Ore. 

LOAD TYPE: SUS-50, passive load, heat and hot water. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

101 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 250,300,350,400,500,600,700,800,900, 1000, 

1250, 1500, 1750, 2000, 2250. 

Cl 

0 

0 

n 

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Collector Storage Trade-Off 

1 

fi50.0 

1 

1300.0 

Storage Size 

I 

195C.0 

LOCATION: Medford, Ore. LOAD TYPE: SUS-50, superinsulated load, heat and hot water. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

102 
0-'-__ --". ___ -,, ___ --,-,. ___ ,' ____ ---,1_ ---'1------,1 

1.0 2.0 3.J 4.0 5.J 5.0 7.0 ,.., .. J • .J 

Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 1400, 1600, 1800, 2000, 2400, 2800, 3200, 3600, 4000, 

4400, 4800, 5200, 5600, 6000. 

Q) 

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Collector Storage Trade-Off 

o -' gl· '0 

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1.0 13.0 12 'J 

Storage Size "'" 1 03 

LOCATION: Medford. Ore. 

LOAD TYPE: SUB-50, standard load, space heat only. 

SYSTEM TYPE: Flafpiate collector, single tank system. 

103 
4.0 5.0 S.C 7.0 

Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 400, 600, 800, 1000, 1200, 1400, 1600, 1800, 2000, 

3000, 4000, 5000, 6000. 

CD 

N 

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Collector Storage Trade-Off 

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Storage Size 

LOCATION: Medford, Ore. 

LOAD TYPE: SUB-50, passive load, space heat only 

SYSTEM TYPE: Flat-plate collector, single tank system. 

104 
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Storage to Collector Ratio (m3/m2) 

I 

S.O 

Collector sizes (m2): 120, 160,200,240,280,320,360,400,600,800, 

1000,1200,1400,1600,1800,2000. 

Collector Storage Trade-Off 

0 

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Storage Size 

LOCATION: Medford, Ore. LOAD TYPE: SUB-50, superinsulated load, space heat only 

SYSTEM TYPE: Flat-plate collector, single tank system. 

105 

I 

7.0 
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ca CJ 

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0 

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0.0 1.0 2.0 3.0 4.0 S.O 

Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 3500,4000,4500,5000,5500,6000,8000,10,000,12,000. 

Q) 

N 

(j) 

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Collector Storage Trade-Off 

0 

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Storage Size 

LOCATION: Bismarck, N.D. 

21.0 

>.L 11:3 " U 

LOAD TYPE: SUB-50, standard load, heat and hot water. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

106 
ca 

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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 1600, 2000, 2400, 2800, 3200, 3600, 4000, 5000, 6000, 

7000. 

Collector 

0 

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n n 'J. ,J 3.'j 7.0 

Storage Size 

LOCATION: Bismarck, N.D. 

LOAD TYPE: SUB-50, passive load, heat and hot water. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

107 
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Storage to Collector Ratio (m3/m2) 

I 

5.0 

Collector sizes (m2): 600,800, 1000, 1200, 1400, 1600, 1800, 2000. 

Go) 

N 

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Collector Storage Trade-Off 

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0.0 1250.0 2500.0 

Storage Size 

I 

3750.0 

LOCATION: Bismarck, N.D. LOAD TYPE: SUB-50, superinsulated load, heat and hot water. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

108 
Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 3000, 3500, 4000, 4500, 5000, 5500, 6000, 

8000, 10,000, 12,000, 14,000. 

Collector Storage Trade-Off 

Co) 

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7.r:; is.S 2;2.5 

Storage Size ""lU' 

LOCATION: Bismarck, N.D. LOAD TYPE: SUB-50, standard load, space heat only. 

SYSTEM TYPE: Flat-plate collector, single-tank system. 

109 
ca 

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Storage to .Collector Ratio (m3/m2) 

Collector sizes (m2): 1200, 1600,2000,2400,2800,3200,3600,4000,5000, 

6000, 7000, 8000. 

Collector Storage Trade-Off 

O-+!----------rl---------.I----------. 

J.::; 4.0 S.O 12.fJ 

Storage Size 

LOCATION: Bismarck, N.D. 

1 (-.3 ;w:: tj 

LOAD TYPE: SUB-50 passive load, space heat only. 

SYSTEM TYPE: Flat plate collector, single tank system. 

110 

I 

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1.G 2.0 .- 4. ("I 5. (' ·oJ. "J '-.' ,), 0 7. 

Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 400,600,800, 1000, 1200, 1400, 1600, 2000, 2400. 

Go) 

N 

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cO 

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Storage Size 

LOCATION: Bismarck, N.D. LOAD TYPE: SUB-50, superinsulated load, space heat only. 

SYSTEM TYPE: Flat-plate collector, single-tank system. 

III 

C 
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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 1000, 1200, 1400, 1600, 1800,2000,2200. 

o 

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Collector Storage Trade-Off 

___ -, ____ 

1 C.G 2250.0 4500.0 67:50.0 

Storage Size " 

LOCATION: Albuquerque, N.M. LOAD TYPE: SUB-50, standard load, space heat only. 

SYSTEM TYPE: Flat-plate collector, two-tank system. 

112 
LL 

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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 300, 350, 400, 450, 500, 600. 

0.0 

Collector Storage Trade-Off. 

400.0 600.0 

Storage Size 

I 

1200.0 

LOCATION: Albuquerque, N.M. LOAD TYPE: SUB-50, passive load, heat and hot water. 

SYSTEM TYPE: Flat-plate collector, two tank system. 

113 

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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 500, 600, 700, 800. 

Collector Storage Trade-Off 

o 

0.0 650.0 1300.0 1950.0 

Storage Size 

LOCATION: Albuquerque, N.M. 

LOAD TYPE: SUS-50, semi-passive load, heat and hot water. 

SYSTEM TYPE: Flatplate collector, two tank system. 

114 
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ftS 

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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 1200, 1400, 1600, 1800,2000,2200. 

Collector Storage Trade-Off 

o 

o~I----------'I--------~I·--------~1 0.0 17:-jO.O 3S00.0 5250.0 

Storage Size 

LOCATION: Albuquerque, N.M. LOAD TYPE: SUB-50, standard SYSTEM load, heat and hot water. TYPE: Flat-plate collector, two-tank system. 

115 

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Storage to Collector Ratio (m3/m2) 

Collector sizes (m2): 1200, 1400, 1600, 1800,2000,2200. 

Collector Storage Trade-Off 

o 

o~I----------'I--------~I·--------~1 0.0 17:-jO.O 3S00.0 5250.0 

Storage Size 

LOCATION: Albuquerque, N.M. LOAD TYPE: SUB-50, standard SYSTEM load, heat and hot water. TYPE: Flat-plate collector, two-tank system. 

115