# Analysis Methods for Solar Water Heating Systems – How to Get it Right the First Time!

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 as the “load”. For domestic hot water (DHW) loads, the gallons per day is a starting point. The cold water inlet temperature and conventional hot water outlet temperature are then used to define the enegy needed to heat the water. For space heating, the load can be expressed various ways, all leading to Btu/month.

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.

For installations on new buildings with no energy history, the number of gallons per day can be estimated from ASHRAE and other hot water consumption data tables for various types of facilities. Often times, more complex calculations known as “forensic physics” are employed.

For existing buildings it is possible to place a flow meter in the hot water line for a few weeks. Non-invasive ultrasonic meters are quick to install and remove for temporary reading, but are more expensive than meters placed directly in the line. In both cases finding a straight run of pipe long enough to get a good reading can be a challenge.

One important and frequently overlooked item is the variation in load over a week or month period. This is called the “duty cycle”. For example, if a business is shut down on the weekend then the duty cycle is 5/7 of a week. If there are vacation periods, or holidays, or school breaks, they need to be considered in the load for that period. A hospital or prison may have a 100% duty cycle. A hotel at the beach may have a high duty cycle in the summer, and a low on in the winter. Hotel owners know the average occupancy for each month of the year, for example.

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 (area of collectors, storage gallons) 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. There are other energy modeling programs that are much more elaborate than the F-Chart. They model the entire heating system from the tip of the collectors all the way through the building to the the drip at the tap. Unfortunately, much of the input data is not accurately known, such as the cold water inlet water temperature, and the duty cycle of the system, so calculations that are accurate to 32 digits may not be any better than ones to 3 digits. All solar performance calculations are estimates.

The collector parameters that are inputs to the solar calculation program come from tests done at independent laboratories certified by the Solar Rating and Certification Corporation (SRCC). 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 as illustrated below (MBtu = million Btu).

The columns show the monthly values for weather heating days, input loads (DHW & Space Htg), 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. That is, the efficiency of the system decreases. For example, the output of a 32 ft^{2} 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.

Also, sizing a solar water heating system is specific to the region were the system is located. In the sunny southwest, and solar fraction of 80% may be optimal, but in the cloudy northeast, a 30% solar fraction may give the best economic return. The US government has established an average 30% reduction in energy for all new and retrofit governmetn buldings.

If you’re looking for some assistance with a specific solar hot water project, let me know what I can do to help.

Dr. Ben