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Hour Angle at Sunrise and Sunset Formula

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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. Check FAQs

ω = a \cos (- \tan (Φ - β) \cdot \tan (δ))

ω - Hour angle?Φ - Latitude Angle?β - Tilt Angle?δ - Declination Angle?

Hour Angle at Sunrise and Sunset Example

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Here is how the Hour Angle at Sunrise and Sunset equation looks like with Values.

Here is how the Hour Angle at Sunrise and Sunset equation looks like with Units.

Here is how the Hour Angle at Sunrise and Sunset equation looks like.

2.0909 = a \cos (- \tan (55 - 5.5) \cdot \tan (23))

2.0909rad = a \cos (- \tan (55° - 5.5°) \cdot \tan (23°))

2.0909 = a \cos (- \tan (55 - 5.5) \cdot \tan (23))

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Hour Angle at Sunrise and Sunset Solution

Follow our step by step solution on how to calculate Hour Angle at Sunrise and Sunset?

FIRST Step Consider the formula

ω = a \cos (- \tan (Φ - β) \cdot \tan (δ))

Next Step Substitute values of Variables

∴

ω = a \cos (- \tan (55° - 5.5°) \cdot \tan (23°))

Next Step Convert Units

∴

ω = a \cos (- \tan (0.9599rad - 0.096rad) \cdot \tan (0.4014rad))

Next Step Prepare to Evaluate

∴

ω = a \cos (- \tan (0.9599 - 0.096) \cdot \tan (0.4014))

Next Step Evaluate

∴

ω = 2.09093001937086rad

LAST Step Rounding Answer

∴

ω = 2.0909rad

Hour Angle at Sunrise and Sunset Formula Elements

Variables

Functions

Hour angle

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.

Symbol: ω

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Hour angle

Latitude Angle

Latitude Angle is defined as the angle between the sun's rays and its projection on the horizontal surface.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Latitude Angle

Tilt Angle

Tilt Angle is the angle between the inclined slope and the horizontal plane .

Symbol: β

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Tilt Angle

Declination Angle

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.

Symbol: δ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Declination Angle

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: 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.

Syntax: acos(Number)

Other Formulas to find Hour angle

Go Hour angle

ω = (\frac{ST}{3600} - 12) \cdot 15 \cdot 0.0175

Other formulas in Basics category

Go Tilt factor for reflected radiation

r r = \frac{ρ \cdot (1 - \cos (β))}{2}

Go Tilt factor for diffused radiation

r d = \frac{1 + \cos (β)}{2}

Go Energy Conversion Efficiency of Solar Chimney

η max = 9.81 \cdot \frac{H}{1005 \cdot T a}

Go Declination angle

δ = 23.45 \cdot \sin (0.9863 \cdot (284 + N))

How to Evaluate Hour Angle at Sunrise and Sunset?

Hour Angle at Sunrise and Sunset evaluator uses Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle)) to evaluate 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 evaluate Hour Angle at Sunrise and Sunset using this online evaluator? To use this online evaluator for Hour Angle at Sunrise and Sunset, enter Latitude Angle (Φ), Tilt Angle (β) & Declination Angle (δ) and hit the calculate button.

FAQs on Hour Angle at Sunrise and Sunset

What is the formula to find Hour Angle at Sunrise and Sunset?

The formula of Hour Angle at Sunrise and Sunset is expressed as Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle)). Here is an example- 2.09093 = acos(-tan(0.959931088596701-0.0959931088596701)*tan(0.40142572795862)).

How to calculate Hour Angle at Sunrise and Sunset?

With Latitude Angle (Φ), Tilt Angle (β) & Declination Angle (δ) we can find Hour Angle at Sunrise and Sunset using the formula - Hour angle = acos(-tan(Latitude Angle-Tilt Angle)*tan(Declination Angle)). This formula also uses CosineTangent, Inverse Cosine function(s).

What are the other ways to Calculate Hour angle?

Here are the different ways to Calculate Hour angle-

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

Can the Hour Angle at Sunrise and Sunset be negative?

Yes, the Hour Angle at Sunrise and Sunset, measured in Angle can be negative.

Which unit is used to measure Hour Angle at Sunrise and Sunset?

Hour Angle at Sunrise and Sunset is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Hour Angle at Sunrise and Sunset can be measured.

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Hour Angle at Sunrise and Sunset Formula

​GoHour angle Formula

Hour Angle at Sunrise and Sunset Example

Hour Angle at Sunrise and Sunset Solution

Hour Angle at Sunrise and Sunset Formula Elements

Other Formulas to find Hour angle

Other formulas in Basics category

How to Evaluate Hour Angle at Sunrise and Sunset?

FAQs on Hour Angle at Sunrise and Sunset

Variable Name

GoHour angle Formula