**Solar Irradiance**

The program
IRRAD will calculate two properties:

(1) The solar angle of incidence given the
angular elevation and azimuth (from south going “counterclockwise”: east-north-west) of both the sun and panel.

(2) The irradiance given by the solar
panel.

**Formulas**

**Angle of Incidence Given Azimuth**

Degree mode is assumed,
the angle of incidence (θ) is found in the following equation:

cos θ =
cos(ep)*sin(es) + sin(ep)*cos(es)*cos(as-ap)

Where:

θ = angle of
incidence

es = elevation
of the sun

ep = elevation
of the panel

as = azimuth of
the sun, from south headed towards east, then north, then west

ap = azimuth of
the panel, from south headed towards east, then north, then west

Angle of Incidence |

Azimuth and Elevation of the Sun and Solar Panel |

**Calculating Flux Density of Solar Radiation on a Surface**

Calculating the
flux density (energy) of solar radiation on a surface, Lambert’s Cosine Law is
used. Lambert’s Cosine Law states that the
relation between the irradiance of the sun and the angle of incidence. The result
is the irradiance of the surface. Irradiance is the rate of energy (power) over
a unit area. In SI units, irradiance is
measured in Watts per square meter (W/m^2).

ls = lb * cos θ

Where:

lb = the sun’s
power or irradiance. Often this is
treated as a constant, which is approximately 1367 W/m^2 for extraterrestrial
solar power, or approximately 1000 W/m^2 when we are dealing with the Earth’s
surface (taking scattering of light into account)

ls = the
panel’s power or irradiance

**Casio Prizm IRRAD**

Deg

“SUN: ELEL, AZI(S)”

?->A:?->B

“PANEL: ELEV, AZI(S)”

?->C:?->D

“IRRADIANCE OF THE
SUN”

“(W÷M²)”

cos C * sin A + cos
A * sin C * cos(B-D)

cos⁻¹ Ans -> θ

I * cos θ -> S

“INCIDENCE ANGLE”

θ ◢

“IRRADIANCE OF SUN”

S

**HP Prime IRRAD**

EXPORT IRRAD()

BEGIN

LOCAL
es,as,ep,ap,θinc;

LOCAL ib,is;

HAngle:=1;

INPUT({es,as},”Sun”,{“Elev.:”,”Azi
(S):”});

INPUT({ep,ap},”Panel”,{“Elev.:”,”Azi
(S):”});

INPUT(ib,”Sun’s
Irradiance”,”I:”,”W/m^2”);

// angle of
incidence

θinc:=ACOS(COS(ep)*SIN(es)+SIN(ep)*COS(es)*COS(as-ap));

MSGBOX(“Incidence
Angle = “+θinc);

// Lambert’s Cosine
Law

Is:=ib*COS(θinc);

MSGBOX(“Surface
Irradiance = “+is);

RETURN {θinc,is};

END;

**Example**

Data:

Sun:

Elevation: 55⁰24’21” ≈ 55.40583⁰

Azimuth: 175⁰15’44” ≈ 175.26222⁰

Panel:

Elevation: 40⁰

Azimuth: 90⁰ (panel is facing due east)

Irradiance of
the Sun: 1000 W/m^2

Output:

Incidence Angle
≈ 48.643169⁰

Surface
Radiance ≈ 660.746510 W/m^2

Sources:

Baldocchi,
Dennis “Lecture 7, Solar Radiation, Part 3, Earth-Sun Geometry” Biometeorogy, ESPM 129 University of California, Berkeley.

Retrieved
February 17, 2015.

Mortimer,
David “Lambert’s Cosine Law” 30 January 2014. The Solar Bucket.

Retrieved March
18, 2015

University of
Oregon Solar Radiation Monitoring Laboratory
“Solar Radiation Basics”
University of Oregon. http://solardat.uoregon.edu/SolarRadiationBasics.html Retrieved February 10, 2015

This blog is
property of Edward Shore – 2015.

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