sun’s altitude and azimut calculation

sun’s altitude and azimut calculation:

Hc = Sun’s calculated altitude = sun’s calculated height

Zv = Sun’s azimuth

sun's altitude and azimut calculation, image azimuth (Zv) and height of the sun (Hc)
Screenshot
sun's altitude and azimut calculation, formulas azimuth et calculated height


Overall, please consider that the website’s overarching context commences with the La Rochelle exercise, leading you to an interactive worksheet.

Furthermore, The primary goal is to acquire the skill of determining your line of position at sea through a series of eight identical exercises.

Windy day by the Sea. Author image: Susanne Nilsson

Remember, You need to calculate the sun’s height Hc first before proceeding with the azimuth calculation Zv

In summary, the first exercise has been fully explained, and for the second exercise, you will need to complete it on your own.

To access the explanation and answer for the second exercise, click the provided hyperlink.


sun’s altitude and azimut calculation: First exercise for calculation Hc/zv

exercise for calculated height and true azimuth

calculated height

sun's altitude and azimut calculation, formula calculated height
Formula Hc

P is always positive in these formulas.

L and D positive if North

L and D negative if South

The entries obtained on our worksheet:

L = 31° 29‘, 5 N

D = 23 ° 18 ‘, 0 N

P = 32 ° 23 ‘, 8 NE

P = NE: The Northern Hemisphere and the sun is in the East which means the sun is still rising. (Attention: Do not confuse with East longitude.)

Hc =

𝑠𝑖𝑛 ¯¹ (𝑠𝑖𝑛(31°29′,5)

sin(23°18′)

➕ cos(31°29′,5)

✕ 𝑐𝑜𝑠(23°18′)

✕ 𝑐𝑜𝑠(32°23′,8))

Hc = 60 ° 13 ‘, 0

sextant height and sun's azimut calculation solution calculated height
example of how to use the scientific calculator type CASIO

Indeed, after finding Hc, we are going to calculate Zv.


Norman Beach, Tidal River, Author image: Emmanuele.ancona

sun’s altitude and azimut calculation:

True azimuth Zv

sun's altitude and azimut calculation, formula azimuth (Z)
Formula Z

L = 31° 29‘, 5 N

D = 23 ° 18 ‘, 0 N

Hc = 60 ° 13 ‘, 0

cos ¯¹ ( ( sin (23 ° 18 ‘, 0)

ー sin ( 31° 29‘, 5)

✕ sin (60 ° 13 ‘, 0) )

➗( cos (31° 29‘, 5)

✕ cos (60 ° 13 ‘, 0) ) )

Z = 97,8° 

ロP = NE ou SE  ⟹Sun in the East ⟹ Zv = Z

ロP = NW ou SW ⟹Sun in the West ⟹ Zv = 360°- Z

P = 32 ° 23 ‘, 8 NE Zv = Z

Zv = 97,8°  98°

sextant height and sun's azimut calculation solution azimuth calculation
soleil à l’est: translation Sun in the East/ example casio calculator

Crimea, Black Sea.  Author image: Vyacheslav Argenberg

sun’s altitude and azimut calculation: second exercise for calculation Hc/Zv

You need to complete it on your own. To access the explanation and answer for this second exercise, click the provided hyperlink.

calculated height Hc

sun's altitude and azimut calculation, formula calculated height (Hc)

L = 19° 46′ N

D = 21 ° 09′,1 S

P = 39 ° 06‘, 2 (NE)

𝑠𝑖𝑛 ¯¹ ( 𝑠𝑖𝑛(𝐿)

sin(𝐷)

➕ cos(𝐿)

✕ 𝑐𝑜𝑠(𝐷)

✕ 𝑐𝑜𝑠(𝑃))

Hc = _ _ ,° _

Indeed, after finding Hc, we are going to calculate Zv.


Vashishti river joins Arabian sea at Dhabol. Author image: Pradeep717

sun’s altitude and azimut calculation:

Zv

sun's altitude and azimut calculation, formula azimuth

L = 19° 46′ N

D = 21 ° 09′,1 S

Hc = _ _ ° _ _ ‘, _  (Hc we found above)

cos ¯¹ ( ( sin (D)

ー sin (L)

✕ sin (Hc) )

➗( cos (L)

✕ cos (Hc) ) )

Z = _ _ _ , _° 

ロP = NE ou SE  ⟹Sun in the East ⟹ Zv = Z

ロP = NW ou SW ⟹Sun in the West ⟹ Zv = 360°- Z

Zv = _ _ _,°_