If I know the Solar Hour Angle at sunrise, can I calculate twilight by simply -

[IzzaddinR]

At time T(sunrise) the SHA = -81.361029147899785, which makes frac. hours to noon (SHA / 15.0).

Is calculating the time of astronomical twilight to noon as simple as (SHA - 18) / 15.0?

 

[dacruick]

Hi Izzaddin.

I am a little bit confused with what you are trying to find here. Do you want noon or solar noon? and what are your units. If you have SHA - 18, that means you are subtracting 18 degrees from SHA. which is the equivalent of an hour and 12 minutes.

 

[IzzaddinR]

Hi dacruick,

Thanks for your quick reply. What I'm trying to calculate is the time that twilight (sun = 18 degr below horizon) starts, or more generally speaking; I'm trying to calculate the time of day by a given altitude of the sun.

I've been browsing the web and found this: http://stjarnhimlen.se/comp/riset.html
However, I am using an algorithm to calculate solar data (Solar Positioning Algorithm, http://www.nrel.gov/docs/fy08osti/34302.pdf, see p. A-18 for a summary of the values it returns or below) but expierience difficulties calculating the time of day by a given altitude, using the methods described in the first link.

As a solution I'm looking for a way to calculate this using the values that are returned by SPA, notable the Sun Rise Hour Angle, and the Sunset Hour Angle:

T (in hours to noon) = (srha - 18) / 15.0

and

T (in hours from noon) = (ssha + 18) / 15.0

However, as you pointed out, this just simple adds 1 hour and 12 minutes to sunrise/sunset time respectively.

To make a long story short: Is it possible to calculate the time of day by the altitude of the sun to the horizon, using the Sun hour angles at rise, transit, set or any of the other values that are available?

Kind regards,

Izz ad-Din


Values that are available from SPA:

int year; // 4-digit year,    valid range: -2000 to 6000, error code: 1
int month; // 2-digit month,         valid range: 1 to 12, error code: 2
int day; // 2-digit day,           valid range: 1 to 31, error code: 3
int hour; // Observer local hour,   valid range: 0 to 24, error code: 4
int minute; // Observer local minute, valid range: 0 to 59, error code: 5
int second; // Observer local second, valid range: 0 to 59, error code: 6
double delta_t; // Difference between Earth rotation time and terrestrial time
// It is derived from observation only and is reported in this
// bulletin: [PLAIN]http://maia.usno.navy.mil/ser7/ser7.dat,[/PLAIN] 
// where delta_t = 32.184 + (TAI-UTC) + DUT1
// valid range: -8000 to 8000 seconds, error code: 7
double timezone; // Observer time zone (negative west of Greenwich)
A-17// valid range: -12   to   12 hours,   error code: 8
double longitude; // Observer longitude (negative west of Greenwich)
// valid range: -180  to  180 degrees, error code: 9
double latitude; // Observer latitude (negative south of equator)
// valid range: -90   to   90 degrees, error code: 10
double elevation; // Observer elevation [meters]
// valid range: -6500000 or higher meters,    error code: 11
double pressure; // Annual average local pressure [millibars]
// valid range:    0 to 5000 millibars,       error code: 12
double temperature; // Annual average local temperature [degrees Celsius]
// valid range: -273 to 6000 degrees Celsius, error code; 13
double slope; // Surface slope (measured from the horizontal plane)
// valid range: -360 to 360 degrees, error code: 14
double azm_rotation; // Surface azimuth rotation (measured from south to projection of
//     surface normal on horizontal plane, negative west)
// valid range: -360 to 360 degrees, error code: 15
double atmos_refract;// Atmospheric refraction at sunrise and sunset (0.5667 deg is typical)
// valid range: -5   to   5 degrees, error code: 16
int function; // Switch to choose functions for desired output (from enumeration)
//-----------------Intermediate OUTPUT VALUES--------------------
double jd; //Julian day
double jc; //Julian century
double jde; //Julian ephemeris day
double jce; //Julian ephemeris century
double jme; //Julian ephemeris millennium
double l; //earth heliocentric longitude [degrees]
double b; //earth heliocentric latitude [degrees]
double r; //earth radius vector [Astronomical Units, AU]
double theta; //geocentric longitude [degrees]
double beta; //geocentric latitude [degrees]
double x0; //mean elongation (moon-sun) [degrees]
double x1; //mean anomaly (sun) [degrees]
double x2; //mean anomaly (moon) [degrees]
double x3; //argument latitude (moon) [degrees]
double x4; //ascending longitude (moon) [degrees]
double del_psi; //nutation longitude [degrees]
double del_epsilon; //nutation obliquity [degrees]
double epsilon0; //ecliptic mean obliquity [arc seconds]
double epsilon; //ecliptic true obliquity  [degrees]
double del_tau; //aberration correction [degrees]
double lamda; //apparent sun longitude [degrees]
double nu0; //Greenwich mean sidereal time [degrees]
double nu; //Greenwich sidereal time [degrees]
double alpha; //geocentric sun right ascension [degrees]
double delta; //geocentric sun declination [degrees]
double h; //observer hour angle [degrees]
double xi; //sun equatorial horizontal parallax [degrees]
double del_alpha; //sun right ascension parallax [degrees]
double delta_prime; //topocentric sun declination [degrees]
double alpha_prime; //topocentric sun right ascension [degrees]
double h_prime; //topocentric local hour angle [degrees]
double e0; //topocentric elevation angle (uncorrected) [degrees]
double del_e; //atmospheric refraction correction [degrees]
double e; //topocentric elevation angle (corrected) [degrees]
double eot; //equation of time [minutes]
double srha; //sunrise hour angle [degrees]
double ssha; //sunset hour angle [degrees]
double sta; //sun transit altitude [degrees]
//---------------------Final OUTPUT VALUES------------------------
double zenith; //topocentric zenith angle [degrees]
double azimuth180; //topocentric azimuth angle (westward from south) [-180 to 180 degrees]
double azimuth; //topocentric azimuth angle (eastward from north) [   0 to 360 degrees]
double incidence; //surface incidence angle [degrees]
double suntransit; //local sun transit time (or solar noon) [fractional hour]
double sunrise; //local sunrise time (+/- 30 seconds) [fractional hour]
double sunset; //local sunset time (+/- 30 seconds) [fractional hour

 

[dacruick]

It is definitely possible to calculate the time if you have the elevation angle and longitude.

I wrote the exact program that you are trying to write ( I think ), about a year ago.
I input an elevation angle and a date and it outputs the time of the day that the sun is at that elevation.

You need an equation that gives you information on how solar noon changes throughout the year. There are a bunch of approximations out there. I think this is called declination angle.

http://en.wikipedia.org/wiki/Declination#Sun

Check that out.