HP 35S: Sun Altitude, Azimuth, Solar Pond Absorption

Source: Sun Altitude, Azimuth, Solar Pond Absorption, HP 67/97 Energy Conservation December 1978, Author: HP

Input:

This program asks for:

D = days after March 21 (later will be sun's declination : 23.45 sin (D * .9856°) )

L = latitude given in D.MMSS (degrees minutes seconds) format (avoid ±90°)

T = time before solar noon (12:00 PM), if the time is after noon, enter hours as a negative (example: 3:00 PM → -3)

N = index of refraction of surface/fluid (see below)

Index of Refraction for Common Objects:

Water: 1.33

Ice: 1.309

Glass: 1.52

Diamond: 2.42

Formulas: (Degrees Mode)

Sun Declination

D = 23.45 * sin( days after March 21 * .9856°)

Altitude of the Sun (H):

H = asin (cos L * cos D * cos (15 * T) + sin L * sin D)

Azimuth of the Sun (A): (degree from latitude ground wise north)

A = acos ( (sin H * sin L - sin D) ÷ (cos L * cos H) )

Fraction of the surface penetrated by the sun that hour (T):

T = 2 * n * (x^2 + y^2) * sin H * cos R

Where

R = asin (cos H ÷ n)

x = (cos R + n * sin H)^-1

y = (sin H + n * cos R)^-1

Example 1:

Input:

D = 68 (May 28), L = 46°, T = 4 (8:00 AM), N = 1.33 (water)

Output:

H (altitude) = 35.98991°

A (azimuth) = 84.40835°

F (fraction of coverage) = 0.95943

Example 2:

Input:

D = 90 (June 19), L = 23°, T = -3 (3:00 PM), N = 2.42 (diamond)

Output:

H = 48.81756°

A = 99.85903°

F = 0.82156

Program:

U001 LBL U

U002 INPUT D \\ declination

U003 DEG

U004 0.9856

U005 *

U006 SIN

U007 23.45

U008 *

U009 STO D \\ altitude

U010 COS

U011 INPUT L

U012 HMS→ \\ or → H

U013 STO L

U014 COS

U015 *

U016 INPUT T

U017 15

U018 *

U019 COS

U020 *

U021 RCL L

U022 SIN

U023 RCL D

U024 SIN

U025 *

U026 +

U027 ASIN

U028 STO H

U029 VIEW H \\ azimuth

U030 SIN

U031 RCL L

U032 SIN

U033 *

U034 RCL D

U035 SIN

U036 -

U037 RCL L

U038 COS

U039 RCL H

U040 COS

U041 *

U042 ÷

U043 ACOS

U044 STO A

U045 VIEW A

U046 RCL H \\ fraction

U047 COS

U048 INPUT N

U049 ÷

U050 ASIN

U051 STO R

U052 COS

U053 RCL H

U054 SIN

U055 RCL* N

U056 +

U057 1/x

U058 x^2

U059 RCL H

U060 SIN

U061 RCL R

U062 COS

U063 RCL* N

U064 +

U065 1/x

U066 x^2

U067 +

U068 RCL* N

U069 2

U070 *

U071 RCL H

U072 SIN

U073 *

U074 RCL R

U075 COS

U076 *

U077 STO F

U078 VIEW F

U079 RTN

This blog is property of Edward Shore. 2013