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Angle of incidence of sun rays Formula

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Angle Of Incidence is defined as the angle formed between the direction of the sun ray and the line normal to the surface . Check FAQs

θ = a \cos (\sin (Φ) \cdot (\sin (δ) \cdot \cos (β) + \cos (δ) \cdot \cos (γ) \cdot \cos (ω) \cdot \sin (β)) + \cos (Φ) \cdot (\cos (δ) \cdot \cos (ω) \cdot \cos (β) - \sin (δ) \cdot \cos (γ) \cdot \sin (β)) + \cos (δ) \cdot \sin (γ) \cdot \sin (ω) \cdot \sin (β))

θ - Angle Of Incidence?Φ - Latitude Angle?δ - Declination Angle?β - Tilt Angle?γ - Surface Azimuth Angle?ω - Hour angle?

Angle of incidence of sun rays Example

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Here is how the Angle of incidence of sun rays equation looks like with Values.

Here is how the Angle of incidence of sun rays equation looks like with Units.

Here is how the Angle of incidence of sun rays equation looks like.

1.7863 = a \cos (\sin (55) \cdot (\sin (23) \cdot \cos (5.5) + \cos (23) \cdot \cos (0.25) \cdot \cos (10) \cdot \sin (5.5)) + \cos (55) \cdot (\cos (23) \cdot \cos (10) \cdot \cos (5.5) - \sin (23) \cdot \cos (0.25) \cdot \sin (5.5)) + \cos (23) \cdot \sin (0.25) \cdot \sin (10) \cdot \sin (5.5))

1.7863rad = a \cos (\sin (55°) \cdot (\sin (23°) \cdot \cos (5.5°) + \cos (23°) \cdot \cos (0.25rad) \cdot \cos (10rad) \cdot \sin (5.5°)) + \cos (55°) \cdot (\cos (23°) \cdot \cos (10rad) \cdot \cos (5.5°) - \sin (23°) \cdot \cos (0.25rad) \cdot \sin (5.5°)) + \cos (23°) \cdot \sin (0.25rad) \cdot \sin (10rad) \cdot \sin (5.5°))

1.7863 = a \cos (\sin (55) \cdot (\sin (23) \cdot \cos (5.5) + \cos (23) \cdot \cos (0.25) \cdot \cos (10) \cdot \sin (5.5)) + \cos (55) \cdot (\cos (23) \cdot \cos (10) \cdot \cos (5.5) - \sin (23) \cdot \cos (0.25) \cdot \sin (5.5)) + \cos (23) \cdot \sin (0.25) \cdot \sin (10) \cdot \sin (5.5))

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Angle of incidence of sun rays Solution

Follow our step by step solution on how to calculate Angle of incidence of sun rays?

FIRST Step Consider the formula

θ = a \cos (\sin (Φ) \cdot (\sin (δ) \cdot \cos (β) + \cos (δ) \cdot \cos (γ) \cdot \cos (ω) \cdot \sin (β)) + \cos (Φ) \cdot (\cos (δ) \cdot \cos (ω) \cdot \cos (β) - \sin (δ) \cdot \cos (γ) \cdot \sin (β)) + \cos (δ) \cdot \sin (γ) \cdot \sin (ω) \cdot \sin (β))

Next Step Substitute values of Variables

∴

θ = a \cos (\sin (55°) \cdot (\sin (23°) \cdot \cos (5.5°) + \cos (23°) \cdot \cos (0.25rad) \cdot \cos (10rad) \cdot \sin (5.5°)) + \cos (55°) \cdot (\cos (23°) \cdot \cos (10rad) \cdot \cos (5.5°) - \sin (23°) \cdot \cos (0.25rad) \cdot \sin (5.5°)) + \cos (23°) \cdot \sin (0.25rad) \cdot \sin (10rad) \cdot \sin (5.5°))

Next Step Convert Units

∴

θ = a \cos (\sin (0.9599rad) \cdot (\sin (0.4014rad) \cdot \cos (0.096rad) + \cos (0.4014rad) \cdot \cos (0.25rad) \cdot \cos (10rad) \cdot \sin (0.096rad)) + \cos (0.9599rad) \cdot (\cos (0.4014rad) \cdot \cos (10rad) \cdot \cos (0.096rad) - \sin (0.4014rad) \cdot \cos (0.25rad) \cdot \sin (0.096rad)) + \cos (0.4014rad) \cdot \sin (0.25rad) \cdot \sin (10rad) \cdot \sin (0.096rad))

Next Step Prepare to Evaluate

∴

θ = a \cos (\sin (0.9599) \cdot (\sin (0.4014) \cdot \cos (0.096) + \cos (0.4014) \cdot \cos (0.25) \cdot \cos (10) \cdot \sin (0.096)) + \cos (0.9599) \cdot (\cos (0.4014) \cdot \cos (10) \cdot \cos (0.096) - \sin (0.4014) \cdot \cos (0.25) \cdot \sin (0.096)) + \cos (0.4014) \cdot \sin (0.25) \cdot \sin (10) \cdot \sin (0.096))

Next Step Evaluate

∴

θ = 1.78628134488308rad

LAST Step Rounding Answer

∴

θ = 1.7863rad

Angle of incidence of sun rays Formula Elements

Variables

Functions

Angle Of Incidence

Angle Of Incidence is defined as the angle formed between the direction of the sun ray and the line normal to the surface .

Symbol: θ

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Angle Of Incidence

Latitude Angle

Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Latitude Angle

Declination Angle

The declination angle of the sun is the angle between the equator and a line drawn from the centre of the Earth to the centre of the sun.

Symbol: δ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Declination Angle

Tilt Angle

Tilt Angle is the angle between the inclined slope and the horizontal plane .

Symbol: β

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Tilt Angle

Surface Azimuth Angle

Surface Azimuth Angle is the angle in the horizontal plane between the line due south and the horizontal projection of the normal to the inclined plane surface.

Symbol: γ

Measurement: AngleUnit: rad

Note: Value can be positive or negative.

Formulas to find Surface Azimuth Angle

Hour angle

The hour angle at any instant is the angle through which the earth has to turn to bring the meridian of the observer directly in line with the sun's rays.

Symbol: ω

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Hour angle

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

acos

The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: acos(Number)

Other formulas in Basics category

Go Tilt factor for reflected radiation

r r = \frac{ρ \cdot (1 - \cos (β))}{2}

Go Tilt factor for diffused radiation

r d = \frac{1 + \cos (β)}{2}

Go Hour Angle at Sunrise and Sunset

ω = a \cos (- \tan (Φ - β) \cdot \tan (δ))

Go Hour angle

ω = (\frac{ST}{3600} - 12) \cdot 15 \cdot 0.0175

How to Evaluate Angle of incidence of sun rays?

Angle of incidence of sun rays evaluator uses Angle Of Incidence = acos(sin(Latitude Angle)*(sin(Declination Angle)*cos(Tilt Angle)+cos(Declination Angle)*cos(Surface Azimuth Angle)*cos(Hour angle)*sin(Tilt Angle))+cos(Latitude Angle)*(cos(Declination Angle)*cos(Hour angle)*cos(Tilt Angle)-sin(Declination Angle)*cos(Surface Azimuth Angle)*sin(Tilt Angle))+cos(Declination Angle)*sin(Surface Azimuth Angle)*sin(Hour angle)*sin(Tilt Angle)) to evaluate the Angle Of Incidence, The Angle of Incidence Of Sun Rays formula is defined as the angle formed between the direction of the sun ray and the line normal to the surface. Angle Of Incidence is denoted by θ symbol.

How to evaluate Angle of incidence of sun rays using this online evaluator? To use this online evaluator for Angle of incidence of sun rays, enter Latitude Angle (Φ), Declination Angle (δ), Tilt Angle (β), Surface Azimuth Angle (γ) & Hour angle (ω) and hit the calculate button.

FAQs on Angle of incidence of sun rays

What is the formula to find Angle of incidence of sun rays?

The formula of Angle of incidence of sun rays is expressed as Angle Of Incidence = acos(sin(Latitude Angle)*(sin(Declination Angle)*cos(Tilt Angle)+cos(Declination Angle)*cos(Surface Azimuth Angle)*cos(Hour angle)*sin(Tilt Angle))+cos(Latitude Angle)*(cos(Declination Angle)*cos(Hour angle)*cos(Tilt Angle)-sin(Declination Angle)*cos(Surface Azimuth Angle)*sin(Tilt Angle))+cos(Declination Angle)*sin(Surface Azimuth Angle)*sin(Hour angle)*sin(Tilt Angle)). Here is an example- 1.786281 = acos(sin(0.959931088596701)*(sin(0.40142572795862)*cos(0.0959931088596701)+cos(0.40142572795862)*cos(0.25)*cos(10)*sin(0.0959931088596701))+cos(0.959931088596701)*(cos(0.40142572795862)*cos(10)*cos(0.0959931088596701)-sin(0.40142572795862)*cos(0.25)*sin(0.0959931088596701))+cos(0.40142572795862)*sin(0.25)*sin(10)*sin(0.0959931088596701)).

How to calculate Angle of incidence of sun rays?

With Latitude Angle (Φ), Declination Angle (δ), Tilt Angle (β), Surface Azimuth Angle (γ) & Hour angle (ω) we can find Angle of incidence of sun rays using the formula - Angle Of Incidence = acos(sin(Latitude Angle)*(sin(Declination Angle)*cos(Tilt Angle)+cos(Declination Angle)*cos(Surface Azimuth Angle)*cos(Hour angle)*sin(Tilt Angle))+cos(Latitude Angle)*(cos(Declination Angle)*cos(Hour angle)*cos(Tilt Angle)-sin(Declination Angle)*cos(Surface Azimuth Angle)*sin(Tilt Angle))+cos(Declination Angle)*sin(Surface Azimuth Angle)*sin(Hour angle)*sin(Tilt Angle)). This formula also uses SineCosine, Inverse Cosine function(s).

Can the Angle of incidence of sun rays be negative?

No, the Angle of incidence of sun rays, measured in Angle cannot be negative.

Which unit is used to measure Angle of incidence of sun rays?

Angle of incidence of sun rays is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Angle of incidence of sun rays can be measured.

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Angle of incidence of sun rays Formula

Angle of incidence of sun rays Example

Angle of incidence of sun rays Solution

Angle of incidence of sun rays Formula Elements

Other formulas in Basics category

How to Evaluate Angle of incidence of sun rays?

FAQs on Angle of incidence of sun rays

Variable Name