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Hour Angle at Sunrise and Sunset Calculator

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✖The Latitude Angle is the angular measurement that indicates a location's distance north or south of the equator, influencing solar energy exposure and system performance.ⓘ Latitude Angle [Φ]			+10% -10%
✖The Tilt Angle is the angle at which solar panels are positioned relative to the ground, optimizing sunlight exposure for increased energy efficiency.ⓘ Tilt Angle [β]			+10% -10%
✖The Declination Angle is the angle between the rays of the sun and the plane of the Earth's equator, affecting solar energy collection throughout the year.ⓘ Declination Angle [δ]			+10% -10%

✖The Hour angle is the measure of time since solar noon, expressed in degrees, indicating the position of the sun in the sky relative to an observer.ⓘ Hour Angle at Sunrise and Sunset [ω]

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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 is the measure of time since solar noon, expressed in degrees, indicating the position of the sun in the sky relative to an observer.
Latitude Angle - (Measured in Radian) - The Latitude Angle is the angular measurement that indicates a location's distance north or south of the equator, influencing solar energy exposure and system performance.
Tilt Angle - (Measured in Radian) - The Tilt Angle is the angle at which solar panels are positioned relative to the ground, optimizing sunlight exposure for increased energy efficiency.
Declination Angle - (Measured in Radian) - The Declination Angle is the angle between the rays of the sun and the plane of the Earth's equator, affecting solar energy collection throughout the year.

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 00.004 seconds)

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< 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)). The Latitude Angle is the angular measurement that indicates a location's distance north or south of the equator, influencing solar energy exposure and system performance, The Tilt Angle is the angle at which solar panels are positioned relative to the ground, optimizing sunlight exposure for increased energy efficiency & The Declination Angle is the angle between the rays of the sun and the plane of the Earth's equator, affecting solar energy collection throughout the year.

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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