# Solar hour angle

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Solar Expert Posts: 27
Hi!

I need to calculate the Solar hour angle, and I have some doubts. I am using the next formula:

Solar angle=(15*(TST-12h)*pi/180 , [rad]

where TST is the True Solar Time and its calculated as follows:

TST=Hour_legal+(4*(L-Lo)+(9.87*sin(2*c)-7.53*cos(c)-1.5*sin(c)))/60; [hours]

where the factors are:

c = 2*pi*(Year_day-81)/365; where Year day is the day of the year (1 January=1)
L is the longitude of the place and Lo is the reference Longitude (15º*AT), where AT is the difference of the Local Time from Greenwich Mean Time (GMT) in hours.

My doubts are:

- The (L-Lo) factor has to be calculated in degrees or in radians?
- The Legal Hour is the same as the Local Time hour (the time which the watches show)?
- I have the time data in UTC. I have to use this data as Local Time?? Or I should use the UTC Time?? In my case I am at GTM+2h, so the Hour_legal has to be, for example, 14h or 14h+2?? Im not sure because the factor (L-Lo) seems to be used to have this difference of time in account...

I don't know if I have explained well enough...

## Comments

• Solar Expert Posts: 1,913 ✭✭
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Re: Solar hour angle

For all practical purposes, you can drop the correction for the year.

TST=Hour_legal+4*(L-Lo)

L is definitely in degrees, so when multiplied by 4 it gives hours. Your legal time may be 1 hour off because of day-light savings.

If in doubts, you can easily test it - must be noon when the sun is straight South.
• Solar Expert Posts: 10,300 ✭✭✭✭
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Re: Solar hour angle

"If in doubts, you can easily test it - must be noon when the sun is straight South."

be careful with that statement as it is straight sout at solar noon and not necessarily noon. solar noon is directly between sunrise and sunset.
• Solar Expert Posts: 27
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Re: Solar hour angle
NorthGuy wrote: »
For all practical purposes, you can drop the correction for the year.

TST=Hour_legal+4*(L-Lo)

L is definitely in degrees, so when multiplied by 4 it gives hours. Your legal time may be 1 hour off because of day-light savings.

If in doubts, you can easily test it - must be noon when the sun is straight South.

I think that the factor "4" is because of the fact that the Earth rotates 1° every 4 minutes.

And the legal hour, if I am living in a zone that is GMT+2, it should be 2 hours more? or I have to use the Legal Time in UTC??
• Solar Expert Posts: 2,490 ✭✭✭
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Re: Solar hour angle

Will this help ?? You can use the satellite maps and find your exact location.

www.suncalc.net
• Solar Expert Posts: 1,913 ✭✭
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Re: Solar hour angle
JavierOL wrote: »
I think that the factor "4" is because of the fact that the Earth rotates 1° every 4 minutes.

And the legal hour, if I am living in a zone that is GMT+2, it should be 2 hours more? or I have to use the Legal Time in UTC??

You need to use the time for Lo. For example, GMT is time for Lo = 0.
• Solar Expert Posts: 27
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Re: Solar hour angle
Will this help ?? You can use the satellite maps and find your exact location.

www.suncalc.net

Well, not really... because I need to know the hourly angle, and in with this application I only get information about sunrises, twilights, etc... but thanks!
• Solar Expert Posts: 2,490 ✭✭✭
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Re: Solar hour angle
JavierOL wrote: »
Well, not really... because I need to know the hourly angle, and in with this application I only get information about sunrises, twilights, etc... but thanks!
Try this then.

http://www.susdesign.com/sunangle/
• Solar Expert Posts: 27
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Re: Solar hour angle

Yes this is better but I don't get the same results... this application use this formula: LSoT = LST + 4 minutes * (LL - LSTM) + ET

In this link the factors are explained: http://www.susdesign.com/popups/sunangle/time-basis.php

The results dor the Ecuation of Time (ET) are the same, but not for the others. I don't understand... my LST is 14:00 and LL=13.7 East and LSTM is 30º (Im working in Germany, where is GTM+1 with daylight, what means that is like GTM+2 right now).

Im using the same formula in my script. I think that the difference is in the (LL-LSTM) factor, because in the link says: "Note that if the site is east of the LSTM, the (LL - LSTM) factor should be a positive number, and if it is west it should be negative". But (13.7 - 30) is negative, so I don't understand the meaning of this factor...
• Solar Expert Posts: 1,913 ✭✭
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Re: Solar hour angle
JavierOL wrote: »
Im using the same formula in my script. I think that the difference is in the (LL-LSTM) factor, because in the link says: "Note that if the site is east of the LSTM, the (LL - LSTM) factor should be a positive number, and if it is west it should be negative". But (13.7 - 30) is negative

If your LSTM is 30E, you're West of it. 13.7E is West of 30E.
• Solar Expert Posts: 27
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Re: Solar hour angle
NorthGuy wrote: »
If your LSTM is 30E, you're West of it. 13.7E is West of 30E.

Oh I thought it was talking about the E/W of the prime meridian (Greenwich)!