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There are three steps in the design of a solar system: determination of solar
energy available per unit area of collector, determination of heating load,
and sizing the collector for cost effectiveness.  A series of worksheets
(Section 3.13) has been prepared to facilitate the design process for liquid
systems; see Section 3.22 for air systems.  The worksheets should be
duplicated as needed.  The design method presented here is based
substantially on the systems analysis done at the University of Wisconsin,
Madison (Beckman, Klein, and Duffie, 1977; Klein, Beckman, and Duffie, 1976).
The complex interaction between the components of a solar heating system has
been reduced by means of computer simulation to a single parametric chart of
FIAC versus FLAC with f as parameter (Figure 3-1), where FI is a
function of energy absorbed by the solar collector divided by building
heating load, AC is collector area, FL is a function of solar collector
heat losses divided by building heating load, and f is the fraction of
building heating load supplied by solar heating.  The requirement for advance
knowledge of system temperatures has been eliminated by use of these heat
balance ratios.
The method has been checked with computer simulations for the climates of
Madison, Wisconsin; Blue Hill, Massachusetts; Charleston, South Carolina;
Albuquerque, New Mexico; and Boulder, Colorado.  The standard errors of the
differences _ between the computer simulated and the values estimated by this
_ method of f for the five locations were no greater than 0.014 (1.4% error);
f is the yearly average of the monthly f.  Eight years of data were used for
the Madison, Wisconsin, case.  This method then appears to be sufficiently
accurate for most applications and is a method widely used in the industry.
It is the basis for an interactive computer program FCHART (Durlak, 1979b),
hand calculator programs (Durlak, 1979b), and HUD reports (U.S. Dept HUD,
3.1 Job summary - Worksheet A.  Worksheet A is a summary sheet that shows
the effect of collector size on savings-investment ratio (SIR).  This is the
final desired answer to the question of the design process:  What size
collector (and total system) gives greatest payback?  If all SIRs are less
than 1.0, then a solar system is not economical for the application at the
conditions used in the design.  The number of collector areas (or SIR's) that
need be evaluated will vary with each job.  Maximum accuracy will be obtained
by calculating enough points to plot an optimization curve of collector area
versus SIR.  The most cost effective choice will then be apparent.  A period
of 25 years' fuel saving is used in calculations per NAVFAC P-442 as lifetime
for utilities.  Solar systems can be designed to last this long.  Three
methods are shown in Section 3.7.  Computations completed on subsequent
worksheets will be transferred to Worksheet A.  Note that only the portion of
conventional heating systems cost in excess of that normally required should
be included in solar systems cost analysis.  However, for budgetary purposes
in new construction, then, the total solar system cost is the sum of the
excess cost plus the previously excluded conventional system cost.
3.2 Solar collector Parameters - Worksheet B.  The purpose of Worksheet B
is to gather the variables needed to calculate FI and FL (see paragraph
3.0).  The first two parameters, FR([tau][alpha])n and FRUL represent
the y intercept and slope, respectively, of the [eta] versus [delta]T/I
curve, Figure 2-7, applicable to the chosen collector.  FR is collector
heat removal factor,


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