Correct sizing of solar
water heating systems is both a science and an art, developed over the last
40 years by scientists and engineers.

There are three main steps involved in performing such an
analysis:

1)   
Determine the monthly energy requirement for the application.
This energy requirement is often referred to Kitchen Table Equipment Leg as the "load".

2)   
Determine the contribution of a solar system to satisfy a
portion of the load. The contribution is also known as the "solar
fraction".

3)   
 Determine the economic
value, such as rate of return or payback time.

Solar hot water calculations are performed on a per month basis.
The inputs are monthly loads and weather data including solar radiation, and
solar collector specifications.

The goal of step number one, determining the load, is to
accurately estimate the monthly energy required to heat water. It is calculated
from the average gallons of hot water required per month, and the rise in
temperature from the cold water mains to the output temperature of the system.
The number of gallons per day can be arrived at using ASHRAE hot water
consumption data for various types of facilities. Often times, more complex
calculations known as "forensic physics" are employed. The best
method is to place a flow meter in the hot water line for a few weeks.
Non-invasive ultrasonic meters are quick to install and remove but not as
accurate as meters placed directly in the line.

The next step of determining the solar contribution involves
calculating the amount of solar energy supplied to the load. First, the monthly
solar radiation data and the solar collector performance numbers are obtained.
Then the monthly load, the radiation, collector parameters, and system size
numbers are combined to produce the final result.

Monthly horizontal surface radiation tables come from satellite
data provided by NASA and posted on NREL, DOE, and NOAA websites. This data
includes monthly radiation on a flat surface, averaged over a 30 year period.

The horizontal surface radiation is translated into the
radiation on a tilted collector using the industry standard F-Chart solar
equations developed in the 1970s by Duffie and Beckman at the University of
Wisconsin. The Canadian government supported the development of a free version
called RETScreen, which is used all over the world. All F-Chart programs use
the equations from Duffie and Beckman.

The collector parameters that are inputs to the F-Chart program
come from tests done at independent laboratories certified by the Solar Rating
and Certification Corporation (SRCC). The Florida Solar Energy Center is the foremost
of these. Collectors are tested to two standards: ASHREA 93 for performance,
and ISO 9806 for durability, thermal shock, etc. Collector testing yields two
numbers that define a straight line efficiency curve. The Y-intercept is the
absolute maximum efficiency of the collector at ambient temperature, and the
slope of the curve represents the drop in efficiency as the temperature
increases.

Inserting the load, collector performance numbers, collector
area, and storage gallons into the F-Chart program produces a table of energy
values. The columns show the monthly values for weather, input loads, solar
contribution, solar fraction of total load and energy output per collector.

No assessment of solar hot water would be complete without
addressing the financial considerations. The results from the solar
calculations are used to determine the economic justification of a solar water
heating system. As the size of a solar system increases, the total solar energy
goes up, but the energy output per collector goes down. For example, the output
of a 32 ft2 collector for different solar fractions is shown here:



Solar Fraction       Output
per Collector
30%                         8.0 million
Btu/yr
80%                        6.5 million
Btu/yr
99%                        4.0 million
Bty/yr

The optimum economic value is the acceptable rate of return, or
payback time, on the system. The value is a moving target influenced by current
and future conventional energy prices, available financial incentives, and the
owner's tax status and internal investment rules.

In general, sizing solar water heating
systems to supply 30-60% of
the total annual load results in the best economic value.