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

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)

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Index of Refraction for Common Objects:

Water: 1.33
Ice: 1.309
Glass: 1.52
Diamond: 2.42

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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

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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

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This blog is property of Edward Shore. 2013