# How to calculate the area of solar collector?

(1) Design daily average water consumption: “Code for Design of Water Supply and Drainage in Buildings” (GB50015-2003) stipulates that the hot water load should be calculated based on the highest daily domestic water quota, and heating equipment should be selected to meet the water supply under the most unfavorable conditions. However, the frequency of the maximum daily water consumption in a year is relatively low, and a solar water heating system designed according to this requirement may reach the design load on very few days in a year. In most cases, the water temperature may be too high or some collectors may be disabled, resulting in a waste of resources. In addition, solar energy is a low-density and uncontrollable energy source, and it is impossible to require it to provide hot water supply on any day of the year to meet the requirements. Usually solar water heating systems are equipped with auxiliary heating equipment, which can provide heat when the solar radiation is insufficient and the water temperature does not reach the preset temperature. Therefore, the design water consumption should be more reasonable according to the average daily water consumption, so that both the collector and the solar energy can be used to the maximum extent.

The “Code for Design of Water Supply and Drainage in Buildings” (GB50015-2003) only stipulates the maximum daily water consumption standard for residential buildings, but there is no data on the average daily water consumption. Generally, the lower limit of the maximum daily water consumption is used. The “Water-Saving Design Standards for Civil Buildings” (GB50555-2010), which has been implemented since December 1, 2010, stipulates the average daily water consumption of residential hot water, which is specially used for the selection of water quotas for solar and heat pump hot water systems.

(2) System solar energy guarantee rate: The solar energy guarantee rate F refers to the percentage of the total load of the solar water heating system borne by the solar energy, which is a key factor in determining the area of the solar collector and an important parameter affecting the economic performance of the system. Its calculation formula is as follows:

F=Q/L (1.1)

In the formula, Q is the effective heat gain of the system from the sun; L is the total load of the system.

Before the system design, it is necessary to determine the appropriate solar energy guarantee rate. The higher the F value, the higher the proportion of the heat provided by solar energy to the total heat demand of the system, the larger the required area of solar collectors, the larger the initial investment of the system, and the longer the payback period of the system investment. Conversely, the lower the proportion of the heat provided by the solar energy of the system to the total heat demand, the lower the area of the collector and the initial investment of the system. But at the same time, the proportion of heat that the auxiliary heat source needs to provide increases. Since the auxiliary heat source is generally non-renewable energy such as electricity and gas, this will increase the energy cost during use.

Determine the F value according to factors such as solar energy resources, calculate the total area of the solar collector, design the corresponding system components, and estimate the annual energy saving cost and investment recovery period of the system. This F value is selected if the collector area meets the conditions for building installation and meets the expectations of developers and users for the system recovery period. If it can not meet the requirements, further adjustment is required, the F value is re-determined and the system design is carried out.

Many mandatory installation policies in some countries have put forward specific requirements for the solar energy guarantee rate. For example, the Spanish national decree requires that the minimum guarantee rate of solar household hot water systems must reach 30%~70%. For embedded solar water heaters installed on roofs and walls, the minimum solar guarantee rate requirements can be slightly reduced, with a reduction of 10% to 15%. The Spanish code specifies different situations according to the indoor hot water load in the building, local climatic conditions and the type of auxiliary energy.

China’s current mandatory installation policy does not impose a mandatory solar guarantee rate. The main reason is that there are great differences in solar energy resources, climatic conditions, and energy consumption habits in different regions of China. The F value is recommended to be within the range of 30% to 80% in the “Technical Specifications for the Application of Solar Water Heater Systems in Civil Buildings”. The “Civil Building Solar Water Heater System Engineering Technical Manual” provides the selection range of solar energy guarantee rate in each district according to China’s solar radiation resource division (annual total solar radiation on the horizontal plane). The solar water heating system used throughout the year can take the middle value, and the small value can be taken for the system with a small investment scale, which is mainly used in spring, summer and autumn, and does not want to produce excess solar water heating in summer; for a system with a large expected investment, focusing on use in winter, hoping to obtain sufficient solar hot water in winter, and comprehensive utilization in summer by other means, it is preferable to take a larger value.

(3) Estimation of collector area value: At the beginning of the architectural design, if there is no detailed relevant information, the total area of the collector can be estimated according to the solar energy conditions in the area where the building is located. The “Technical Specifications for the Application of Solar Water Heater Systems in Civil Buildings” (GB50365-2005) provides the recommended value of the total area of the system collectors required to generate 100L of hot water.

(4) Calculation of collector area: According to the different heat transfer types of solar water heating systems in the Technical Specifications for the Application of Solar Water Heater Systems in Civil Buildings, the area calculation of solar collectors is divided into two cases:

①Calculation of the area of the direct system collector: The total area of the direct system collector can be determined according to the user’s daily water consumption and water temperature, and is calculated as follows:

In the formula, A_{C} is the total area of the direct system collector, m²; Q_{W} is the average daily water consumption, L; C_{W} is the constant pressure specific heat capacity of water, 4.187kJ/(kg·C); t_{end} is the design temperature of the water in the water storage tank, ℃, generally 60 ℃; t_{i} is the initial temperature of the water, C, the temperature of cold water in different regions can be calculated according to the “Code for Design of Water Supply and Drainage in Buildings GB50015” ; ρ is the density of water, 1.0kg/L; J_{T} is the annual average daily solar radiation on the lighting surface of the local collector, kJ/m², which can generally be calculated according to the monthly average daily radiation on the lighting surface of the collector in the month of the spring and autumn equinox; f is the solar energy guarantee rate, %, which is determined after comprehensive consideration of factors such as solar radiation, system economy and user requirements during the service period of the system, and should be 30%~80%; η_{cd} is the annual average heat collection efficiency of the heat collector, which should be 0.25~0.50 according to experience, and the specific value should be determined according to the actual test results of heat collection products; η_{L} is the heat loss rate of the water storage tank and the pipeline, and the value should be 0.20~0.30 according to experience.

②Calculation of indirect system collector area: the indirect system needs to consider the heat exchange factor of the heat exchanger. Therefore, compared with the direct system, to obtain the same amount of hot water, the required area is relatively large. The calculation formula of the collector area is as follows:

In the formula, A_{IN} is the total area of the indirect system collector, m²; A_{c} is the total area of the direct system collector, m²;F_{R}U_{L} is the total loss coefficient of the collector, W/m²·C, for flat plate collectors, it should be 4~6W/m²·℃, and for vacuum tube collectors, it should be 1~2W/m²·C, and the specific value should be determined according to the actual test data of the collector products; U_{hx} is the heat transfer coefficient of the heat exchanger, w/m²·C; A_{hx} is the heat exchange area of the heat exchanger, m².

③ Contour lighting area and floor space of the collector: The area of the collector calculated above is the contour lighting area of the collector, which refers to the maximum effective area of sunlight projected to the collector. When estimating the collector area and arranging the installation space, the focus is on the footprint of the collector. If the collector is installed at a certain inclination angle, it needs to be converted into the projected area on the horizontal plane according to the angle, which is the footprint of the collector. The calculation methods of the contour lighting area of different forms of collectors are different, as shown in Figure 1. It can be seen from the figure that the contour lighting area of the flat-plate collector is the same as that of the collector, but the calculation method of the contour lighting area of the tubular collector is different when different surface reflections are used. This means that even if their contour lighting areas are the same, the number of tubes and spacing of different collectors are different, resulting in different floor areas. Therefore, when designing, the architect needs to calculate the actual floor area and arrange the installation space according to the type of the selected collector and the inclination and azimuth of the solar collector installation.