Angle of incidence of sun rays Calculator

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✖Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface.ⓘ Latitude Angle [Φ]			+10% -10%
✖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.ⓘ Declination Angle [δ]			+10% -10%
✖Tilt Angle is the angle between the inclined slope and the horizontal plane .ⓘ Tilt Angle [β]			+10% -10%
✖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.ⓘ Surface Azimuth Angle [γ]			+10% -10%
✖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.ⓘ Hour angle [ω]			+10% -10%

✖Angle Of Incidence is defined as the angle formed between the direction of the sun ray and the line normal to the surface .ⓘ Angle of incidence of sun rays [θ]

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Formula

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Angle of incidence of sun rays

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"))`

Example

`"1.786281rad"=acos(sin("55°")*(sin("23°")*cos("5.5°")+cos("23°")*cos("0.25rad")*cos("10rad")*sin("5.5°"))+cos("55°")*(cos("23°")*cos("10rad")*cos("5.5°")-sin("23°")*cos("0.25rad")*sin("5.5°"))+cos("23°")*sin("0.25rad")*sin("10rad")*sin("5.5°"))`

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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 - Trigonometric sine function, sin(Angle)
cos - Trigonometric cosine function, cos(Angle)
acos - Inverse trigonometric cosine function, 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)
Surface Azimuth Angle: 0.25 Radian --> 0.25 Radian No Conversion Required
Hour angle: 10 Radian --> 10 Radian No Conversion Required

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

FINAL ANSWER

1.78628134488308 ≈ 1.786281 Radian <-- Angle Of Incidence

(Calculation completed in 00.006 seconds)

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Created by ADITYA RAWAT

DIT UNIVERSITY (DITU), Dehradun

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National Institute Of Technology (NIT), Hamirpur

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< 8 Basics Calculators

Angle of incidence of sun rays

Go 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

Go Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle))

Daylight Hours

Go Daylight Hours = 3600*acos(-tan(Latitude Angle)*tan(Declination Angle))

Tilt factor for reflected radiation

Go Tilt factor for reflected radiation = (Reflectivity*(1-cos(Tilt Angle)))/2

Energy Conversion Efficiency of Solar Chimney

Go Max Efficiency of a Solar Chimney = 9.81*Height of Chimney/(1005*Ambient Air Temperature)

Tilt factor for diffused radiation

Go Tilt factor for diffused radiation = (1+cos(Tilt Angle))/2

Declination angle

Go Declination Angle = 23.45*sin(0.9863*(284+Number of days))

Hour angle

Go Hour angle = (Solar time/3600-12)*15*0.0175

Angle of incidence of sun rays Formula

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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