LCM calculator

Hour Angle at Sunrise and Sunset Calculator

Physics Chemistry Engineering Financial More >>

↳

Mechanical Aerospace Basic Physics Others and Extra

⤿

Solar Energy Systems Automobile Design of Automobile Elements Design of Machine Elements More >>

⤿

Basics Concentrating Collectors Liquid Flat Plate Collectors Other Renewable Energy Sources More >>

✖Latitude Angle is the angle between a line to a point on the surface of the Earth and the equatorial plane.ⓘ Latitude Angle [Φ]			+10% -10%
✖Tilt Angle is the angle between the horizontal plane and the line of sight to an object or a point in the horizontal plane.ⓘ Tilt Angle [β]			+10% -10%
✖Declination Angle is the angle between the magnetic field lines and the horizontal plane at a particular location on the Earth's surface.ⓘ Declination Angle [δ]			+10% -10%

✖Hour angle is the angle between the Sun's apparent position in the sky and the local meridian at a given time and location.ⓘ Hour Angle at Sunrise and Sunset [ω]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Physics Formula PDF PDF Image

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) - Hour angle is the angle between the Sun's apparent position in the sky and the local meridian at a given time and location.
Latitude Angle - (Measured in Radian) - Latitude Angle is the angle between a line to a point on the surface of the Earth and the equatorial plane.
Tilt Angle - (Measured in Radian) - Tilt Angle is the angle between the horizontal plane and the line of sight to an object or a point in the horizontal plane.
Declination Angle - (Measured in Radian) - Declination Angle is the angle between the magnetic field lines and the horizontal plane at a particular location on the Earth's surface.

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: 23.09638 Degree --> 0.403107876291692 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(0.403107876291692))

Evaluating ... ...

ω = 2.09361265775303

STEP 3: Convert Result to Output's Unit

2.09361265775303 Radian -->119.955169224438 Degree (Check conversion here)

FINAL ANSWER

119.955169224438 ≈ 119.9552 Degree <-- Hour angle

(Calculation completed in 00.019 seconds)

You are here -

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

Credits

Created by ADITYA RAWAT

DIT UNIVERSITY (DITU), Dehradun

ADITYA RAWAT has created this Calculator and 50+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< Basics Calculators

Hour Angle at Sunrise and Sunset

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

Tilt factor for reflected radiation

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

Tilt factor for diffused radiation

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

Hour angle

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

Hour Angle at Sunrise and Sunset Formula

LaTeX Go

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

What is Hour Angle Variation?

Hour angle variation refers to the change in the solar hour angle over time, reflecting the Earth's rotation relative to the sun. It increases by 15 degrees for each hour, with zero degrees at solar noon when the sun is highest in the sky. As the day progresses, the hour angle becomes positive in the afternoon and negative in the morning. This variation helps determine the sun's position throughout the day, which is important for solar energy calculations and understanding daylight patterns.

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 -> 6864.118 = acos(-tan(0.959931088596701-0.0959931088596701)*tan(0.403107876291692)).

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 the angle between a line to a point on the surface of the Earth and the equatorial plane, Tilt Angle is the angle between the horizontal plane and the line of sight to an object or a point in the horizontal plane & Declination Angle is the angle between the magnetic field lines and the horizontal plane at a particular location on the Earth's surface.

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

Home

FREE PDFs

🔍 Search