Calculation of sunrise and sunset

Source:

• https://www.esrl.noaa.gov/gmd/grad/solcalc/
• https://en.wikipedia.org/wiki/Sunrise_equation
• http://www.srrb.noaa.gov/highlights/sunrise/calcdetails.html

A script to change settings with MotionEyeOS for day and night settings:

• MotionEyeOS Day and Night Python script

Approximation of solar noon, sunrise and sunset

Input example:

• Date --> vDayOfYear
• Date --> vLeapyear
• ToRads(degs) = degs /360 * 2*Pi
• ToDegs(rads) = rads / (2*Pi) * 360

Fractional year (radians)

 vY = 2 * PI() / (365 + vLeapYear) * (vDayOfYear - 1 )

Equation of time (minutes)

 vEqtime = 229.18 * (0.000075 + 0.001868 * COS( vY ) - 0.032077 * SIN( vY ) - 0.014615 * COS(2 *  vY ) - 0.040849 * SIN(2 *  vY )

Solar declination angle (radians).

 vDecl = 0.006918 - 0.399912 * COS(vY) + 0.070257 * SIN(vY) - 0.006758 * COS(2 * vY) + 0.000907 * SIN(2 * vY) - 0.002697 * COS(3 * vY) + 0.00148 * SIN (3 * vY)

For sunrise or sunset, the zenith is set to 90.833 degrees (the approximate correction for atmospheric refraction at sunrise and sunset, and the size of the solar disk). Hours angle (radians):

Input:

• Latitude --> vLat (corresponds with distance from the equator)

 vHa = ACOS( COS( ToRads(90.833) ) / COS(vLat) * COS(vDecl) - TAN(vLat) * TAN(vDecl) )

Input:

• Longitude --> vLon (corresponds with distance from UTC=0)

Sunrise UTC minutes

 vUtcMinsSunrise = 360 * 2 - 4 * (vLon + ToDegs(vHa) ) - vEqtime

Noon UTC minutes

 vUtcMinsNoon = 360 * 2 - 4 * vLon - vEqtime

Sunset UTC minutes

 vUtcMinsSunset = 360 * 2 - 4 * (vLon - ToDegs(vHa) ) - vEqtime

Sunset local time in fractional day. For Europe/Amsterdam --> vTimezone=+1 or +2 (DST)

 (vUtcMinsSunset / 60 + vTimezone) / 24