I am looking for two mathematical formulas.....any help??????

Question

FORMULA 1: need to calculate the noonday sun angle for given latitude (X) and given date (Y)

FORMULA 2: How to calculate the sun angle in comparison to the equinox and solstice

Answer 1

Direct Angle: (at noon)
Place a straw straight up so it casts a shadow.
Tilt the top of the straw towards the sun until its shadow disappears and a bright spot of light from the sun shines through it.
Measure the angle of the straw with a protractor.
Note the time (standard, not daylight savings), date, and latitude.

Complimentary Angle: (at noon)
Tie a string around the middle of a straw.
Tie a weight at the end of the string.
Tilt the straw towards the sun until the bright spot of sun light shines through it.
Record the angle of the string to the straw.
Subtract this angle from 91.25 degrees to obtain the angle of the sun.
Note the time (standard, not daylight savings), date, and latitude.

Here is the link to a work sheet.
http://www.wgby.org/edu/lessonplans/ntti/1999/ecology.pdf#search='SUN%20ANGLE%20ON%20COMPARISON%20TO%20EQUINOX%20AND%20SOLSTICE'

March 21 (22) is known as the SPRING EQUINOX and September 21 (23) is known as the AUTUMNAL EQUINOX in the Northern Hemisphere. The word EQUINOX comes from two Latin words meaning equal and night.
June 21 is called the SUMMER SOLSTICE, and December 21 is the WINTER SOLSTICE. The word SOLSTICE means "sun stands still".
http://www.madison.k12.wi.us/jmm/isp/U4PDF04.pdf#search='How%20to%20calculate%20the%20sun%20angle%20in%20comparison%20to%20the%20equinox%20and%20solstice'

Axis Tilt and Solar Altitude

The annual change in the relative position of the Earth's axis in relationship to the sun causes the height of the sun (solar altitude) to vary in our skies. The total variation in maximum solar altitude for any location on the Earth over a one year period is 47 degrees (2 x 23.5 = 47). For example, at 50 degrees North maximum solar altitude varies from 63.5 degrees on the summer solstice to 16.5 degrees on the winter solstice. Maximum solar height at the equator goes from 66.5 degrees above the northern end of the horizon during the summer solstice, to directly overhead on the fall equinox, and then down to 66.5 degrees above the southern end of the horizon during the summer solstice.
http://www.scott.k12.ky.us/teacherpages/treed/Reed's%20Stuff/6(h)_%20Earth-Sun%20Geometry.htm

Answer 2

http://www.northwestjournal.ca/dtnav.html
articles V and VI should be good ; and they are interesting from a historical perspective too.