I hope you had a great weekend and a great Thanksgiving. For those of you in the United States, hopefully Friday was peaceful and not crazy.

**HP Prime: Approximating the Length of Daylight in Hours**

This time, we are taking a slightly more complex formula. The inputs are:

lat = Earth's latitude of the observer. (from -90° (South) to 90° (North))

day = the number of days since the

**December solstice**(around December 21-22). Note that is different from many approximate formulas which used the vernal equinox as a starting point.
The formula used is a simplification of the Final Formula presented by Herbert Glarner (http://www.gandraxa.com/). For the complete article and the derivation, please click on link:

http://www.gandraxa.com/length_of_day.xml (Retrieved November 23, 2015)

The algorithm used in the DAYLIGHT is:

With the inputs lat and day:

m = 1 – tan(lat°) * tan(23.439° * cos(480/487 * day))

If m > 2, let m = 2.
If m < 0, let m = 0.

Then:

b = acos(1 – m)/180 *24

Where b is the length of daylight in hours.

I adjusted the formula to allow for all inputs to be in
degrees. Glamer had mixed inputs for the
trigonometric functions.

Here is the program:

Program DAYLIGHT:

EXPORT DAYLIGHT(lat,day)

BEGIN

// latitude, days from

// December solstice

LOCAL m,b,a:=HAngle;

HAngle:=1; // Degrees

m:=1-TAN(lat)*TAN(23.439*COS(

480/487*day));

IF m<0 THEN

m:=0;

END;

IF m>2 THEN

m:=2;

END;

b:=ACOS(1-m)/180*24; // hours

RETURN b;

HAngle:=a;

// www.grandraxa.com

END;

Examples:

Let’s assume a 365 day and the December solstice was
December 22.

Latitude: -60°, March
1 (day = 69)

Result: Approx.
16.67808 hours

Latitude: 54°,
July 24 (day = 214)

Result: Approx.
16.03426 hours

For another approximate formula, I wrote on one for the HP 35S here: http://edspi31415.blogspot.com/2013/05/hp-35s-approximate-length-of-sunlight.html

Have a great day,

Eddie

This blog is property of Edward Shore. 2015