## Angle of incidence of sun rays Solution

STEP 0: Pre-Calculation Summary
Formula Used
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))
θ = acos(sin(Φ)*(sin(δ)*cos(β)+cos(δ)*cos(γ)*cos(ω)*sin(β))+cos(Φ)*(cos(δ)*cos(ω)*cos(β)-sin(δ)*cos(γ)*sin(β))+cos(δ)*sin(γ)*sin(ω)*sin(β))
This formula uses 3 Functions, 6 Variables
Functions Used
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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., acos(Number)
Variables Used
Angle Of Incidence - (Measured in Radian) - Angle Of Incidence is defined as the angle formed between the direction of the sun ray and the line normal to the surface .
Latitude Angle - (Measured in Radian) - Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface.
Declination Angle - (Measured in Radian) - 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.
Tilt Angle - (Measured in Radian) - Tilt Angle is the angle between the inclined slope and the horizontal plane .
Surface Azimuth Angle - (Measured in Radian) - 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.
Hour angle - (Measured in Radian) - 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.
STEP 1: Convert Input(s) to Base Unit
Latitude Angle: 55 Degree --> 0.959931088596701 Radian (Check conversion ​here)
Declination Angle: 23 Degree --> 0.40142572795862 Radian (Check conversion ​here)
Tilt Angle: 5.5 Degree --> 0.0959931088596701 Radian (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
θ = acos(sin(Φ)*(sin(δ)*cos(β)+cos(δ)*cos(γ)*cos(ω)*sin(β))+cos(Φ)*(cos(δ)*cos(ω)*cos(β)-sin(δ)*cos(γ)*sin(β))+cos(δ)*sin(γ)*sin(ω)*sin(β)) --> 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))
Evaluating ... ...
θ = 1.78628134488308
STEP 3: Convert Result to Output's Unit
1.78628134488308 Radian --> No Conversion Required
1.78628134488308 1.786281 Radian <-- Angle Of Incidence
(Calculation completed in 00.004 seconds)
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## < 8 Basics Calculators

Angle of incidence of sun rays
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))
Hour Angle at Sunrise and Sunset
Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle))
Daylight Hours
Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle))
Tilt factor for reflected radiation = (Reflectivity*(1-cos(Tilt Angle)))/2
Energy Conversion Efficiency of Solar Chimney
Max Efficiency of a Solar Chimney = 9.81*Height of Chimney/(1005*Ambient Air Temperature)
Tilt factor for diffused radiation = (1+cos(Tilt Angle))/2
Declination angle
Declination Angle = 23.45*sin(0.9863*(284+Number of days))
Hour angle
Hour angle = (Solar Time/3600-12)*15*0.0175

## Angle of incidence of sun rays 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))
θ = acos(sin(Φ)*(sin(δ)*cos(β)+cos(δ)*cos(γ)*cos(ω)*sin(β))+cos(Φ)*(cos(δ)*cos(ω)*cos(β)-sin(δ)*cos(γ)*sin(β))+cos(δ)*sin(γ)*sin(ω)*sin(β))

## Angle of incidence of sun rays

The angle of incoming solar radiation influences seasonal temperatures of locations at different latitudes.

## How to Calculate Angle of incidence of sun rays?

Angle of incidence of sun rays calculator 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 calculate 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 calculate Angle of incidence of sun rays using this online calculator? To use this online calculator 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. Here is how the Angle of incidence of sun rays calculation can be explained with given input values -> 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)).

### FAQ

What is Angle of incidence of sun rays?
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 and is represented as θ = acos(sin(Φ)*(sin(δ)*cos(β)+cos(δ)*cos(γ)*cos(ω)*sin(β))+cos(Φ)*(cos(δ)*cos(ω)*cos(β)-sin(δ)*cos(γ)*sin(β))+cos(δ)*sin(γ)*sin(ω)*sin(β)) or 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)). Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface, 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, Tilt Angle is the angle between the inclined slope and the horizontal plane , 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 & 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.
How to calculate Angle of incidence of sun rays?
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 is calculated using 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 calculate Angle of incidence of sun rays, you need Latitude Angle (Φ), Declination Angle (δ), Tilt Angle (β), Surface Azimuth Angle (γ) & Hour angle (ω). With our tool, you need to enter the respective value for Latitude Angle, Declination Angle, Tilt Angle, Surface Azimuth Angle & Hour angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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