Estimates the length of daylight for a given latitude and solar declination using the simple sunrise-equation hour angle.
Published for review. The Founder is checking every card himself; anything he strikes comes down the same hour.
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Inputs
latitude_deg (number, degrees, required) min -90 max 90 : Latitude, positive north, negative south.
declination_deg (number, degrees, required) min -23.45 max 23.45 : Solar declination for the date (see the sun-declination-by-day-of-year card).
Outputs
day_length_hours (hours): Estimated hours of daylight from sunrise to sunset.
Steps
Sunrise equation: cos(H) = -tan(latitude) * tan(declination), where H is the hour angle of sunrise/sunset in degrees.
If the product makes cos(H) <= -1, the location has continuous daylight (midnight sun); if cos(H) >= 1, continuous night (polar night).
Otherwise H = arccos(cos(H)) in degrees.
Day length in hours = 2 * H / 15, because Earth's rotation moves the hour angle 15 degrees per hour.
Round to 2 decimals.
This is the simple, geometric-horizon classroom version (it ignores atmospheric refraction and the sun's angular radius, both of which the estate's own sunrise card handles with the full NOAA method); treat this card's output as an approximation good to a few minutes.
Constants
degrees_per_hour = 15 degrees/hour (source: Solar Engineering of Thermal Processes, 4th ed., the sunrise equation)
Sources
Solar Engineering of Thermal Processes, 4th ed., the sunrise equation (Wiley, 2026-09-30T19:43:00Z) - Standard textbook derivation of cos(H) = -tan(latitude)*tan(declination).