When glass producers observe the glass from different angles, they will feel that the reflection and transmission states of the glass after being irradiated by light (especially natural light) are different. So what are the changes in the SHGC and Tv values of architectural glass at different angles? This article will focus on this topic, and propose the use of movable external shading, built-in movable shading, color-changing glass and other measures to carry out the shading work of architectural glass.

#### 1. The statement of problem

Solar heat gain coefficient SHGC and visible light transmittance Tv are important photothermal parameters related to solar irradiation in doors, windows, and curtain walls.

The solar heat gain coefficient (SHGC), also known as the total solar transmittance, refers to the indoor heat gain from the solar radiation through the light-transmitting envelope (doors and windows or light-transmitting curtain wall) and the projection to the light-transmitting envelope (doors, windows or light-transmitting curtain wall) The ratio of the amount of solar radiation on the outer surface. The solar heat gain coefficient SHGC value reflects the transmission characteristics of architectural glass in the 300-2500 nm solar spectrum band (including direct transmittance and secondary heat transfer).

The heat gain represented by the total solar transmittance includes two parts, one part is the solar radiant heat entering the room directly through the glass, and the other part is the heat radiated into the room after the glass and components absorb the solar radiant heat. Here, the wavelength of solar radiant heat includes the entire wavelength range from 300 nm to 2500 nm.

The alculation formula of total solar transmittance:

g=τe+qi

In this formula,

g——represents the total solar transmittance of the sample, %;

τe——represents the direct sunlight transmittance of the sample, %;

qi——represents the secondary heat transfer coefficient of the sample to the indoor side, %.

The formula for calculating the solar heat gain coefficient (SHGC) specified in the international standard "Code for Thermal Engineering Design of Civil Buildings" is as follows:

In this formula,

g——the total transmittance of sunlight in the light-transmitting part;

Ag - the area of the light-transmitting part (m2);

ρ——the sunlight absorption ratio of the non-transparent part;

K——the heat transfer coefficient of the non-transparent part [W/(m2*K)];

αe——Convection heat transfer coefficient of the outer surface of the non-transparent part [W/(m*K)];

Af——the area of the non-transparent part (m2);

Aw - the sum of the light-transmitting and non-light-transmitting areas (m2);

The right side of the equal sign of the formula is divided into two parts, where Σg*Ag/Aw is the heat gain of the transparent part, which is the heat gain of the glass;

Σρ*K/αe*Af/Aw is the heat gain of the non-transmissive part, generally, It is the heat gain of profiles, glue, and hardware of doors, windows or curtain walls.

SHGC is used to determine solar heat gain through glazing. SHGC for some specific spectra and angles of incidence should be included along with heat transfer coefficients and other energy properties. Since the optical properties transmittance ratio and absorption ratio vary with the angle of incidence, according to the definition of SHGC, the solar heat gain coefficient is a function of the angle of incidence. Once the solar radiation intensity and SHGC for a particular angle of incidence are known, the solar heat gain can be calculated as:

qb=SHGC*ED

Where: qb is the solar heat gain per unit area (W/㎡ ), and ED is the solar radiation intensity (W/㎡ ).

The optical properties of glass also vary with wavelength, the transmittance and absorbance ratios are spectral averages. The solar heat gain coefficient value is based on a standard spectral distribution with an air mass ratio (the ratio of the actual observed solar path to the solar path at standard atmospheric pressure when the observer is at sea level and the sun is at the zenith) of 1.5. This spectrum is recommended by the National Window and Door Evaluation Board for evaluating the energy performance of windows and doors using specified environmental and incident radiation conditions. For the actual solar heat gain calculation conditions or the glass exhibits spectral selectivity, the used projected solar spectrum should be corrected according to the standard spectrum, which is more in line with the local atmospheric conditions and calculation time.

The standard spectrum is not the same as the distribution of the solar spectrum projected on doors and windows under different atmospheric conditions and angles of incidence of the sun. This difference has little effect on glasses that do not have strong spectral selectivity. But glasses with strong spectral selectivity will have different solar heat gain coefficient values than the standard spectrum. Visible light transmittance is not sensitive to changes in the solar spectrum. However, for glasses with very strong spectral selectivity in the visible part, the visible light transmittance ratio is also sensitive to the incident spectral shape.

Visible transmittance (Tv) refers to the ratio of the visible light flux passing through a transparent material to the visible light flux projected on its surface. The Tv value reflects the transmission characteristics of architectural glass in the visible spectrum band of 380-780nm.

When testing the SHGC and Tv values of glass in the laboratory, a spectrophotometer is generally used. The emitted light is usually at normal incidence during the test, so the measured results are the SHGC and Tv values at normal incidence.

In practical engineering, the angle of the sun changes all the time, and it often irradiates the glass surface of doors, windows, and curtain walls at different angles.

So here comes the question:

(1) Are SHGC and Tv values consistent with a normal incidence at different angles of incidence, and how does the angle affect them?

(2) For the glass of doors, windows, and curtain walls, the sun is only irradiated for a short period of a day. What are the more reasonable measures for shading and heat insulation?

#### 2. Discussion on SHGC and Tv Values at Different Incident Angles

The WINDOW software developed by LBNL can calculate all optical and thermal properties of monolithic glass, insulating glass, glass doors, and windows, such as visible light transmittance, shading coefficient, heat transfer coefficient, etc. Its WINDOWS5 software contains an International Glass Database (IGDB), which provides optical data of more than 1,800 kinds of glass and related products from major international glass manufacturers, including all optical performance indicators of glass and related products, and timely updates with new data. The software also contains the performance database of commonly used door and window frame materials, and the performance database of insulating glass inert gas. WINDOW software calculates the SHGC and Tv values of architectural glass at different angles. Taking a 5mm ordinary glass as an example, the results of SHGC and Tv values at different angles are shown in the figure below.

Figure 1 The results of SHGC and Tv values under different sunlight irradiation angles

The graphs of SHGC and Tv values changing with the angle are as follows.

Figure 2 The graph of SHGC, Tv value changing with incident angle of light

It can be seen that when the incident angle (the direction of the incident light and the normal line of the glass surface) exceeds 60°, the SHGC and Tv values of the glass itself decrease significantly.

Jinan LIJIANG Glass has researched various other glass configurations, and because the laws are similar, they will not be listed here.

#### 3. Some thoughts on the influence of angle on SHGC and Tv values

The above study shows that when the solar incident angle exceeds a certain value (about 60°), the SHGC and Tv values of the glass are greatly reduced. What value does this have for our engineering design?

The first is the problem of setting sunshade measures for external windows with different orientations in summer. Take the changes in the sun height and the length of day and night at the vernal equinox, autumn equinox, summer solstice, and winter solstice in the area of 40° north latitude as an example, see the figure below.

Figure 3 The influence of sunlight Incident angle on SHGC and Tv values

It can be seen that the height angle of the sun at noon in summer is relatively high (over 60°), and the azimuth angle during the solar irradiation period is relatively large, resulting in a large angle between the south-facing window glass and the sun. Play a certain role in self-shading.

In summer, due to the lower sun altitude angle in the morning and evening, the glass SHGC value is higher, and the indoor heat gain is more, especially in the west direction, which is also the main reason for "west sun", and shading measures should be taken.

The second is the setting of shading measures at different periods.

Due to the short-term characteristics of solar radiation in a certain direction, shading is not required for most of the day, so it is recommended that the SHGC value be a short-term dynamic value, which can ensure short-term shading of solar radiation.

Short-term dynamic shading means that measures such as movable external shading, built-in movable shading, and color-changing glass should be used as much as possible.

#### In conclusion

Solar heat gain coefficient SHGC and visible light transmittance Tv are important photothermal parameters related to solar irradiation in doors, windows, and curtain walls. What are the changes in glass SHGC and Tv values at different angles?

The glass SHGC and Tv values are not static values but change with the incident angle of sunlight. When the incident angle (the incident light and the normal direction of the glass surface) exceeds 60°, the glass SHGC and Tv values drop significantly.

Summer is the key period when we need shading. In most parts of our country, the sun altitude angle is high at noon (more than 60°), and the glass SHGC will be reduced at this time, which has a certain self-shading effect.

In summer, due to the lower sun altitude angle in the morning and evening, the glass SHGC value is higher, and the indoor heat gain is more, especially in the west direction, which is also the main reason for "west sun", and shading measures should be taken.

Direct solar radiation has short-term characteristics, and shading facilities are not required for most of the day. Therefore, it is recommended that the SHGC value be a short-term dynamic value, which can ensure short-term shading of solar radiation.

Some developed countries have carried out some research work on the determination of solar heat gain of windows and solar heat gain coefficient, and have formed a preliminary theoretical system in terms of measurement conditions, instruments, and equipment, measurement process, calculation steps, etc., and have formulated provisional standards. In the standard issued by the American Society for Testing and Materials (ASTM), it is proposed to measure the heat flow through the test piece and the thermophysical properties of the material by the protected hot plate method or the heat flow meter method and measure the heat transfer of the window by the hot box method. A range of methods to measure the physical properties of materials, such as coefficients or thermal properties of building components.

Standard methods for temperature measurement and test methods for determining the performance of solar collectors are presented in the ASHRAE standard. The National Window and Door Evaluation Committee of the United States draw on some methods in the American Society for Testing and Materials and ASHRAE standards, and based on these methods, it proposes the steps of measuring the solar heat gain coefficient of windows when the sunlight is vertically projected, and the method of measuring the solar optical properties of glass materials. . However, the method of measuring the solar heat gain coefficient of windows adopted by the National Window and Door Evaluation Committee of the United States is still tentative, and it still needs to be further improved and perfected, and the relevant information about the actual equipment for measuring the solar heat gain coefficient of windows has not been disclosed. Methods for measuring solar radiation are given in the standard ISO 9060 Specifications and Categories of Instruments for Measuring Hemispherical and Direct Solar Radiation, ISO 15099 Detailed Calculation of Thermal Performance of Windows, Doors and Shading Facilities "The specific method of thermal calculation suitable for computer programming is given. The publication of these standards has laid a good foundation for the use of experimental methods to measure the solar heat gain coefficient of windows. At present, the United States and Canada have established the Window Annual Energy Rating System. The so-called window energy consumption grade evaluation system is to integrate the solar heat gain coefficient and heat transfer coefficient of the window into a unified parameter for the heating season and the cooling season and uses it to evaluate the thermal performance of the window. Two systems in the United States and Canada each give a number to rate the energy consumption levels of various windows during the heating and cooling seasons and limit their use in low-rise dwellings.

Of course, this article is only a preliminary discussion on the changes in glass SHGC and Tv values from different angles. The study of building thermal environments is a specialized discipline, which requires us to study and understand more deeply.