How to calculate Solar energy transmittance

To calculate Solar energy transmittance 


What is Solar [energy] transmittance (@AM 1.5)

Solar energy transmittance is the rate at which solar energy enters to the indoor directly through a glass window.

The percentage of energy flowing into the indoor which the radiant energy of 300 nm to 2 500 nm being emitted from a solar surface temperature of approximately 6 500 K has passed 1.5 times (AM=1.5) of the atmosphere

<Equation>

The transmission spectrum of the window is as below and

the solar energy weighting factor @AM=1.5 presented in ISO 9050 is follows fig. & Table [S(λ)Δ(λ)]:

When calculating the solar energy transmittance using solar weighting factor and transmittance spectrum:

Weighting factor at 2 500 nm : 1.02

Transmittance at 2 500 nm : 77.723%

T(λ)S(λ)Δλ = 77.723 x 1.02 =79.278

The sum of values calculated in the same way for the entire wavelength is

Σ S(λ)Δλ = 1 027.44

Σ T(λ)S(λ)Δλ = 93 439.186 

Te = Σ S(λ)Δλ / T(λ)S(λ)Δλ = 93 439.186 / 1 027.44 = 90.943 (%)

It can be calculated the Solar [energy] transmittance is 90.94%

For the reference, Analysis results calculated using the program (Solar Transmission 90.94%, @AM=1.5).

Solar Energy distribution

About Solar Energy


The distribution of solar energy reaching the surface consists of ultraviolet (UV), visible (VIS) and near infrared (NIR).

All objects except the absolute temperature of 0 K degree (-273 ℃) emit energy corresponding to that temperature.

The energy emitted from the sum of surface temperature of about 6 500 K is that specific wavelengths are absorbed by ozone, oxygen, nitrogen, carbon dioxide and moisture in the atmosphere, and only the remaining energy is reached to the earth surface.

Generally, solar energy transmitting through a glass window is defined to use only a range of 300 nm to 2 500 nm.

The following Fig. is an solar spectral distribution represent in ISO 13837 norm.

When calculating the solar energy transmittance or reflectance, define the solar spectral distribution based on air mass, AM=1.0 is a vertical entry of the atmosphere, AM=1.5 is an indication of the energy distribution when the sun's light penetrates the thickness equivalent of 1.5 times that of the atmosphere and reaches to the surface.

Most characteristics are defined on the basis of AM=1.5, but some old Norm are described to be calculated on the basis of AM=1.0 or AM=2.0.

Therefore, solar characteristics calculated on the basis of solar energy such as solar energy transmittance, reflectance, total solar energy transmittance or shading coefficient should be checked of air mass(AM) values.

There are two ways in which solar energy enters the room through a glass window.

Some of the light energy of the 300 nm to 2 500 nm range is transmitted directly through glass into the room, but the rest of some energy is absorbed into the window and then re-radiated into the room.

The amount of energy that solar energy directly transmits through glass windows is called the solar radiation transmittance (Te).

The total solar energy transmittance is summation of solar direct transmittance and  the re-emitted energy which is absorbed to the windows that transmitted into the room. (SHGC=Te+qi)

How to calculate CIE L* a* b*

Calculation of CIE L* a* b*


The tristimulus values (X Y Z) can be calculated according to the method mentioned in CIE Y x y calculation method and the CIE L* a* b* color value can be calcu,ated using the following equation.

<Basic equation>



<Calculation>

Example] To calculate tristimulus value X Y Z at D65/2



about the calculation for item 390 nm are

1)  S(λ) ऱ(λ) = 0.0042 x 54.65 = 0.229530
2)  S(λ) ў(λ) = 0.0001 x 54.65 = 0.005465
3)  S(λ) ž(λ) = 0.0201 x 54.65 = 1.098465

The transmittance value of the measured spectrum is 86.261% at 390 nm.

1) S(λ) ऱ(λ) 𝞃(λ) = 0.229530 x 0.86261 = 0.197994
2) S(λ) ў(λ) 𝞃(λ) = 0.005465 x 0.86261 = 0.004714
3) S(λ) ž(λ) 𝞃(λ) = 1.098465 x 0.86261 = 0.947544








The sum of y^(λ) value, denominator value, in the table above is 2133.467, So, k = 100 / 2 133.467 = 0.047 315 611

Therefore, the X Y Z and the color coordinates x and y can be calculated by the above equation.

X = 1773.253 x 0.047315611 = 83.9026
Y = 1884.360 x 0.047315611 = 89.1597
Z = 2042.179 x 0.047315611 = 96.6270




by above equation (24/116)^3 = 0.008 865

1) (X/Xn)^(1/3) = (83.9026 / 95.043)^(1/3) = 0.959294 > 0.008 865
2) (Y/Yn)^(1/3) = (89.1597 / 100.00)^(1/3) = 0.962475 > 0.008 865
3) (Z/Zn)^(1/3) = (96.6270 / 108.879)^(1/3) = 0.960988 > 0.008 865 

Therefore we can use above calculated values as f(X/Xn), f(Y/Yn), f(Z/Zn) 



Using the above equation to calculate L* a* b*,

L* = 116 x 0.962 475 - 16 = 95.647 1
a* = 500 x ( 0.959 294 - 0.962 475 ) = -1.590 6
b* = 200 x ( 0.962 475 - 0.960 988) = 0.297 4

Comparison of L*, a*, b* results between calculated value with EXCEL and by using calculation Program

How to calculate CIE Y x y

Calculation CIE Y x y


To calculate Y x y and L* a* b* values, the tristimulus values (X Y Z) values must first be calculated from the measured spectrum.

<Basic equation>

  where
        S(λ) : Energy distribution of standard illuminate
        ऱ(λ), ў(λ), ž(λ) : weighting factor
        𝞃(λ) : Transmittance

 2 degree                                   10 degree                         Standard illuminate


In the table above, S(λ) belongs to the standard illuminate item and the values ऱ, ў, and ž are two or ten viewing of angle, and this table is only a fraction of them are excerpted.

For the values of the entire wavelength range, you can find the appendix of KS A 0061 or JIS Z 8781-3 standard method.


<Calculation>

Example] For calculation in condition of D65/10 the X Y Z is

about the calculation for item 385nm are

1)  S(λ) ऱ(λ) = 0.0007 x 52.31 = 0.036617
2)  S(λ) ў(λ) = 0.0001 x 52.31 = 0.005231
3)  S(λ) ž(λ) = 0.0029 x 52.31 = 0.151699 


The transmittance value of the measured spectrum is 83.78% at 385 nm.

1) S(λ) ऱ(λ) 𝞃(λ) = 0.036617 x 0.8378 = 0.030679
2) S(λ) ў(λ) 𝞃(λ) = 0.005231 x 0.8378 = 0.004383
3) S(λ) ž(λ) 𝞃(λ) = 0.151699 x 0.8378 = 0.127097 






The sum of y^(λ) value, denominator value, in the table above is 2324.14, So, k = 100 / 2324.14 = 0.043027

Therefore, the X Y Z and the color coordinates x and y can be calculated by the following equation.

X = 1947.202 x 0.043027 = 83.7816
Y = 2072.514 x 0.043027 = 89.1734
Z = 2211.909 x 0.043027 = 95.1715



Y = 89.17
x = X / (X + Y + Z) = 83.7816 / 268.1266 = 0.3125
y = Y / (X + Y + Z) = 89.1734 / 268.1266 = 0.3326


Comparison of Y, x, y results between calculated value with EXCEL and by using calculation Program

How can do you express colors in numbers by measured spectrum?

It is possible to express colors in numbers by measured spectrum?


In general, the color can be expressed by the color coordinates CIE L* a* b* and Y x y.

Y x y (D65/10) : 62.2, 0.292, 0.388



If you know the color distribution as shown the picture, you can imagine what color of this object is by knowing the value of x(0.292), y(0.388) color coordinates which can be calculated  by using transmittance or reflectance spectrum.

So, If we can measure the transmittance or reflectance spectrum, We can calculate the color coordinates and compare them exactly by numbers.

Above color coordinates value is calculated with transmittance spectrum of the actual green glass (thickness 12 mm).


L* a* b* (D65/2) : 83.0, -13.62, -1.80




L* a* b* is another way of expression of color.

L* a* b* (D65/2) : 83.0, -13.62, -1.80 values are calculated by transmittance spectrum for the same green glass as above.

+a* : red
-a* : green
+b* : yellow
-b* : blue

a*, b* values are meaning of the three primary colors (object : red, yellow, blue, light : red green, blue).

Y, L* values range is 0 to 100 which is meaning of bright or dark colors.

Then, What does it mean (D65/2) or (D65/10)?
This means the standard light D65 and observer angle 10 degree.

at first, look at the standard light,

Since the color of an object depend on which light it looks under. In principle, the color of an object should be measured under the reference sunlight.

However, as long as we live on Earth, the sunlight cannot always be the same strength because of the atmosphere.

Solar energy depends on it condition on the weather, such as cloudy and clear day, and its altitude and geographical location.

Therefore, in order to calculate the colorimetric values on the same basis, various kinds of standard illuminate were defined as shown in the table below.



The second reason is that colors look different depending on the viewing angle.

Humans feel different colors depending on the size of the picture in their retina.
This is because the number of cells that can recognize color decreases as they move away from the center of the retina.

When you look at object painted in the same color, the color of a large area, such as a wall, and the color of a small object, such as a coin, look different.

Therefore, when reporting measured values of Y, x, y or L* a* b*, the sort of standard illuminate and viewing angle shall be recorded together.