Hour Angle at Sunrise and Sunset 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%
✖Tilt Angle is the angle between the inclined slope and the horizontal plane .ⓘ Tilt Angle [β]			+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%

✖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 at Sunrise and Sunset [ω]

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Formula

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Hour Angle at Sunrise and Sunset

Formula

`"ω" = acos(-tan("Φ"-"β")*tan("δ"))`

Example

`"2.09093rad"=acos(-tan("55°"-"5.5°")*tan("23°"))`

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Hour Angle at Sunrise and Sunset Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle))
ω = acos(-tan(Φ-β)*tan(δ))
This formula uses 3 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(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

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.
Latitude Angle - (Measured in Radian) - Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface.
Tilt Angle - (Measured in Radian) - Tilt Angle is the angle between the inclined slope and the horizontal plane .
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.

STEP 1: Convert Input(s) to Base Unit

Latitude Angle: 55 Degree --> 0.959931088596701 Radian (Check conversion here)
Tilt Angle: 5.5 Degree --> 0.0959931088596701 Radian (Check conversion here)
Declination Angle: 23 Degree --> 0.40142572795862 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ω = acos(-tan(Φ-β)*tan(δ)) --> acos(-tan(0.959931088596701-0.0959931088596701)*tan(0.40142572795862))

Evaluating ... ...

ω = 2.09093001937086

STEP 3: Convert Result to Output's Unit

2.09093001937086 Radian --> No Conversion Required

FINAL ANSWER

2.09093001937086 ≈ 2.09093 Radian <-- Hour angle

(Calculation completed in 00.020 seconds)

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Home » Physics » Solar Energy Systems » Basics » Hour Angle at Sunrise and Sunset

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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

Hour Angle at Sunrise and Sunset Formula

Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle))
ω = acos(-tan(Φ-β)*tan(δ))

Hour angle variation

At sunrise the sun rays are parallel to the horizontal surface, hence the angle of incidence and zenith angle is equal and = 90 degrees. At sunset same case occurs only the direction is different.

How to Calculate Hour Angle at Sunrise and Sunset?

Hour Angle at Sunrise and Sunset calculator uses Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle)) to calculate the Hour angle, The Hour Angle at Sunrise and Sunset formula is defined as a measure of the angular distance between the sun at the local solar time and the sun at solar noon. Hour angle is denoted by ω symbol.

How to calculate Hour Angle at Sunrise and Sunset using this online calculator? To use this online calculator for Hour Angle at Sunrise and Sunset, enter Latitude Angle (Φ), Tilt Angle (β) & Declination Angle (δ) and hit the calculate button. Here is how the Hour Angle at Sunrise and Sunset calculation can be explained with given input values -> 2.09093 = acos(-tan(0.959931088596701-0.0959931088596701)*tan(0.40142572795862)).

FAQ

What is Hour Angle at Sunrise and Sunset?

The Hour Angle at Sunrise and Sunset formula is defined as a measure of the angular distance between the sun at the local solar time and the sun at solar noon and is represented as ω = acos(-tan(Φ-β)*tan(δ)) or Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle)). Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface, Tilt Angle is the angle between the inclined slope and the horizontal plane & 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.

How to calculate Hour Angle at Sunrise and Sunset?

The Hour Angle at Sunrise and Sunset formula is defined as a measure of the angular distance between the sun at the local solar time and the sun at solar noon is calculated using Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle)). To calculate Hour Angle at Sunrise and Sunset, you need Latitude Angle (Φ), Tilt Angle (β) & Declination Angle (δ). With our tool, you need to enter the respective value for Latitude Angle, Tilt Angle & Declination Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Hour angle?

In this formula, Hour angle uses Latitude Angle, Tilt Angle & Declination Angle. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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