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Angle of incidence of sun rays Formula

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Angle of Incidence is the angle at which a ray of light or radiation strikes a surface, measured from the 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.

89.9012 = a \cos (\sin (55) \cdot (\sin (23.0964) \cdot \cos (5.5) + \cos (23.0964) \cdot \cos (0.25) \cdot \cos (119.8015) \cdot \sin (5.5)) + \cos (55) \cdot (\cos (23.0964) \cdot \cos (119.8015) \cdot \cos (5.5) - \sin (23.0964) \cdot \cos (0.25) \cdot \sin (5.5)) + \cos (23.0964) \cdot \sin (0.25) \cdot \sin (119.8015) \cdot \sin (5.5))

89.9012° = a \cos (\sin (55°) \cdot (\sin (23.0964°) \cdot \cos (5.5°) + \cos (23.0964°) \cdot \cos (0.25°) \cdot \cos (119.8015°) \cdot \sin (5.5°)) + \cos (55°) \cdot (\cos (23.0964°) \cdot \cos (119.8015°) \cdot \cos (5.5°) - \sin (23.0964°) \cdot \cos (0.25°) \cdot \sin (5.5°)) + \cos (23.0964°) \cdot \sin (0.25°) \cdot \sin (119.8015°) \cdot \sin (5.5°))

89.9012 = a \cos (\sin (55) \cdot (\sin (23.0964) \cdot \cos (5.5) + \cos (23.0964) \cdot \cos (0.25) \cdot \cos (119.8015) \cdot \sin (5.5)) + \cos (55) \cdot (\cos (23.0964) \cdot \cos (119.8015) \cdot \cos (5.5) - \sin (23.0964) \cdot \cos (0.25) \cdot \sin (5.5)) + \cos (23.0964) \cdot \sin (0.25) \cdot \sin (119.8015) \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 (23.0964°) \cdot \cos (5.5°) + \cos (23.0964°) \cdot \cos (0.25°) \cdot \cos (119.8015°) \cdot \sin (5.5°)) + \cos (55°) \cdot (\cos (23.0964°) \cdot \cos (119.8015°) \cdot \cos (5.5°) - \sin (23.0964°) \cdot \cos (0.25°) \cdot \sin (5.5°)) + \cos (23.0964°) \cdot \sin (0.25°) \cdot \sin (119.8015°) \cdot \sin (5.5°))

Next Step Convert Units

∴

θ = a \cos (\sin (0.9599rad) \cdot (\sin (0.4031rad) \cdot \cos (0.096rad) + \cos (0.4031rad) \cdot \cos (0.0044rad) \cdot \cos (2.0909rad) \cdot \sin (0.096rad)) + \cos (0.9599rad) \cdot (\cos (0.4031rad) \cdot \cos (2.0909rad) \cdot \cos (0.096rad) - \sin (0.4031rad) \cdot \cos (0.0044rad) \cdot \sin (0.096rad)) + \cos (0.4031rad) \cdot \sin (0.0044rad) \cdot \sin (2.0909rad) \cdot \sin (0.096rad))

Next Step Prepare to Evaluate

∴

θ = a \cos (\sin (0.9599) \cdot (\sin (0.4031) \cdot \cos (0.096) + \cos (0.4031) \cdot \cos (0.0044) \cdot \cos (2.0909) \cdot \sin (0.096)) + \cos (0.9599) \cdot (\cos (0.4031) \cdot \cos (2.0909) \cdot \cos (0.096) - \sin (0.4031) \cdot \cos (0.0044) \cdot \sin (0.096)) + \cos (0.4031) \cdot \sin (0.0044) \cdot \sin (2.0909) \cdot \sin (0.096))

Next Step Evaluate

∴

θ = 1.56907270195998rad

Next Step Convert to Output's Unit

∴

θ = 89.9012435715125°

LAST Step Rounding Answer

∴

θ = 89.9012°

Angle of incidence of sun rays Formula Elements

Variables

Functions

Angle Of Incidence

Angle of Incidence is the angle at which a ray of light or radiation strikes a surface, measured from the normal to the surface.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle Of Incidence

Latitude Angle

Latitude Angle is the angle between a line to a point on the surface of the Earth and the equatorial plane.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Latitude Angle

Declination Angle

Declination Angle is the angle between the magnetic field lines and the horizontal plane at a particular location on the Earth's surface.

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 horizontal plane and the line of sight to an object or a point in 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 horizontal angle measured clockwise from the north direction to a line that passes through a point on the Earth's surface.

Symbol: γ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Surface Azimuth Angle

Hour angle

Hour angle is the angle between the Sun's apparent position in the sky and the local meridian at a given time and location.

Symbol: ω

Measurement: AngleUnit: °

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- 5150.962 = acos(sin(0.959931088596701)*(sin(0.403107876291692)*cos(0.0959931088596701)+cos(0.403107876291692)*cos(0.004363323129985)*cos(2.09093062382759)*sin(0.0959931088596701))+cos(0.959931088596701)*(cos(0.403107876291692)*cos(2.09093062382759)*cos(0.0959931088596701)-sin(0.403107876291692)*cos(0.004363323129985)*sin(0.0959931088596701))+cos(0.403107876291692)*sin(0.004363323129985)*sin(2.09093062382759)*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 Sine (sin)Cosine (cos), Inverse Cosine (acos) 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 Degree[°] for Angle. Radian[°], Minute[°], Second[°] 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