Here is a nice little program for calculating the suns position and also heliostat position.
I translated it from a QBasic program that can be found here.
https://www.instructables.com/community/heliostat-and-sun-tracker-basic-program/
Thanks to David Williams for original QBasic code.
[code:1:50692aec6e]'Thanks to David Williams for sharing the QBasic version of this program.
'The original QBasic code can be found here:
'https://www.instructables.com/community/heliostat-and-sun-tracker-basic-program/
' SunAlign.BAS (Version for QBasic and similar dialects)
' Calculates position of sun in sky, as azimuth (compass bearing
' measured clockwise from True North) and angle of elevation, as
' seen from any place on earth, on any date and any time.
' Also calculates alignment of a heliostat mirror.
' David Williams
' Initially dated 2007 Jul 07
' This version 2008 Jan 13
' All angles in radians except in i/o routines DegIn and DegOut
'Translated to BASCOM by:
'Dave Carr
'July 14, 2019
$regfile = "m328pdef.dat"
$crystal = 8000000
$baud = 38400
$hwstack = 100
$swstack = 100
$framesize = 100
DECLARE SUB C2P(byref X as single, byref Y as single, byref Z as single, byref AZ as single, byref EL as single)
DECLARE SUB P2C(byval AZ as single, byval EL as single, byref X as single ,byref Y as single ,byref Z as single)
DECLARE FUNCTION Ang(byval X as single ,byval Y as single)as single
DECLARE SUB DegIn(byval P as string,byref X as single)
DECLARE SUB DegOut(byval P as string,byref X as single)
CONST c_PY = 3.1415926536 ' "PI" not assignable in some BASICs
CONST c_DR = 180 / c_PY ' degree / radian factor
const c_W = 2 * c_PY / 365 ' earth's mean orbital angular speed in radians/day
const c_WR = c_PY / 12' earth's speed of rotation relative to sun (radians/hour)
const c_C = -23.45 / c_DR ' reverse angle of earth's axial tilt in radians
const c_ST = SIN(c_C) ' sine of reverse tilt
const c_CT = COS(c_C) ' cosine of reverse tilt
const c_E2 = 2 * .0167 ' twice earth's orbital eccentricity
const c_SN = 10 * c_W ' 10 days from December solstice to New Year (Jan 1)
const c_SP = 12 * c_W ' 12 days from December solstice to perihelion
dim s_C as single
dim st_S as string * 1
dim s_Lt as single
dim s_LG as single
dim i_TZN as integer
dim b_HR, b_MIN as byte
dim b_Mth, b_Day as byte
dim s_CL as single
dim w_D as word
dim s_A, s_B, s_L, s_DC, s_LD, s_SL as single
dim s_tAZ, s_tEL, s_tX, s_tY, s_tZ, s_mAZ, s_mEL as single
dim s_sX, s_sY, s_sZ, s_sAZ, s_sEL as single
dim s_temp1, s_temp2, s_temp3 as single
CLS
Menu:
PRINT "1. Calculate sun's position"
PRINT "2. Calculate mirror orientation"
PRINT "3. Calculate both"
PRINT "4. Quit program"
PRINT
PRINT "Which? (1 - 4)";
DO
st_S = INKEY()
LOOP UNTIL st_S >= "1" AND st_S <= "4"
PRINT st_S
IF st_S ="4" THEN END
' Note: For brevity, no error checks on user inputs
PRINT
PRINT "Use negative numbers for directions opposite to those shown."
PRINT
DegIn "Observer's latitude (degrees North)", s_LT
DegIn "Observer's longitude (degrees East)", s_LG
INPUT "Time Zone (+/- hours from GMT/UT)", i_TZN
INPUT "Hours (24-hr format)", b_HR
input "Minutes ", b_MIN
INPUT "Month ", b_Mth
input "Day of month ", b_Day
PRINT
's_CL = c_PY / 2 - s_LT ' co-latitude
s_CL = c_PY / 2
s_CL = s_CL - s_LT
'print "co-lat ";s_CL
'w_D = INT(30.6 * ((b_Mth + 9) MOD 12) + 58.5 + b_Day) MOD 365
' day of year (D = 0 on Jan 1)
s_C = b_Mth + 9
s_C = s_C mod 12
s_C = 30.6 * s_C
s_C = s_C + 58.5
s_C = s_C + b_Day
s_C = int(s_C)
w_D = s_C mod 365
'print "Day of year = ";w_D
's_A = c_W * w_D + c_SN ' orbit angle since solstice at mean speed
s_A = c_W * w_D
s_A = s_A + c_SN
'print "Orbit angle ";s_A
's_B = s_A + c_E2 * SIN(s_A - c_SP) ' angle with correction for eccentricity
s_C = s_A - c_SP
s_B = sin(s_C)
s_B = s_B * c_E2
s_B = s_B + s_A
'print "Eccentricity ";s_B
's_C = (s_A - ATN(TAN(s_B) / c_CT)) / c_PY
s_C = tan(s_B)
s_C = s_C/c_CT
s_C = atn(s_C)
s_C = s_A - s_C
s_C = s_C/c_PY
's_SL = c_PY * (s_C - INT(s_C + .5))' solar longitude relative to mean position
s_SL = s_C + .5
s_SL = int(s_SL)
s_SL = s_C - s_SL
s_SL = c_PY * s_SL
'print "solar longitude ";s_SL
's_C = c_ST * COS(s_B)
s_C = cos(s_B)
s_C = c_ST * s_C
's_DC = ATN(s_C / SQR(1 - s_C * s_C)) ' solar declination (latitude)
' arcsine of C. ASN not directly available in QBasic
s_DC = s_C * s_C
s_DC = 1 - s_DC
s_DC = sqr(s_DC)
s_DC = s_C / s_DC
s_DC = atn(s_DC)
'print "solar declination ";s_DC
's_LD = (b_HR - i_TZN + b_MIN / 60) * c_WR + s_SL + s_LG ' longitude difference
s_LD = b_MIN / 60
s_C = b_HR - i_TZN
s_LD = s_C + s_LD
s_LD = s_LD * c_WR
s_LD = s_LD + s_SL
s_LD = s_LD + s_LG
'print "longitude difference ";s_LD
CALL P2C(s_LD, s_DC, s_sX, s_sY, s_sZ) ' polar axis (perpend'r to azimuth plane)
CALL C2P(s_sY, s_sZ, s_sX, s_sAZ, s_sEL) ' horizontal axis
s_temp1=s_sAZ - s_CL
CALL P2C(s_temp1, s_sEL, s_sY, s_sZ, s_sX) ' rotate by co-latitude
IF s_sZ < 0 THEN
'BEEP
PRINT "Sun Below Horizon"
PRINT
GOTO NewCalc
END IF
IF st_S <> "2" THEN ' calculate and display sun's position
CALL C2P(s_sX, s_sY, s_sZ, s_sAZ, s_sEL) ' vertical axis
DegOut "Sun's azimuth: ", s_sAZ
DegOut "Sun's elevation: ", s_sEL
PRINT
END IF
IF st_S > "1" THEN ' calculate and display mirror orientation
PRINT "For target direction of light reflected from mirror:"
DegIn "Azimuth of target direction (degrees)", s_tAZ
DegIn "Elevation of target direction (degrees)", s_tEL
PRINT
CALL P2C(s_tAZ, s_tEL, s_tX, s_tY, s_tZ) ' target vector X,Y,Z
s_temp1=s_sX + s_tX
s_temp2=s_sY + s_tY
s_temp3=s_sZ + s_tZ
CALL C2P(s_temp1,s_temp2 ,s_temp3 , s_mAZ, s_mEL)
' angle bisection by vector addition
PRINT "Mirror aim direction (perpendicular to surface):"
DegOut "Azimuth: ", s_mAZ
DegOut "Elevation: ", s_mEL
PRINT
END IF
NewCalc:
PRINT
PRINT "New Calculation"
PRINT
GOTO Menu
FUNCTION Ang (byval X as single,byval Y as single)
' calculates angle from positive X axis to vector to (X,Y)
'SELECT CASE SGN(X)
'CASE 1: Ang = ATN(Y / X)
'CASE -1: Ang = ATN(Y / X) + PY
'CASE ELSE: Ang = SGN(Y) * PY / 2
'END SELECT
local s as single
s = sgn(x)
SELECT CASE s
CASE 1
s=y/x
Ang = ATN(s)
CASE -1
s=y/x
s=atn(s)
Ang = s+c_PY
CASE ELSE
s=sgn(y)
s=s*c_PY
Ang = s/2
END SELECT
END FUNCTION
SUB C2P (byref X as single,byref Y as single,byref Z as single,byref AZ as single,byref EL as single)
' Cartesian to Polar. Convert from X,Y,Z to AZ,EL
local A as single
local s as single
local s2 as single
'EL = Ang(SQR(X * X + Y * Y), Z)
s=x*x
s2=y*y
s=s+s2
s=sqr(s)
el=ang(s,z)
'A = Ang(Y, X)
A = Ang(Y, X)
'IF A < c_PY THEN AZ = A + c_PY ELSE AZ = A - c_PY
IF A < c_PY THEN
AZ = A + c_PY
ELSE
AZ = A - c_PY
end if
END SUB
SUB DegIn (byval P as string,byref X as single)
' Input angle in degrees and convert to radians
local N as single
PRINT P;
INPUT N
X = N / c_DR
END SUB
SUB DegOut (byval P as string,byref X as single)
' converts radians to degrees, rounds to nearest 0.1, and prints
local st as string * 20
local s as single
local i as integer
'S$ = LTRIM$(STR$(INT(10 * ABS(X * c_DR) + .5)))
s=X*c_DR
s=abs(s)
s=s*10
s=s + .5
i=int(s)
st=str(i)
st=ltrim(st)
IF St = "3600" THEN St = "0"
IF LEN(St) = 1 THEN St = "0" + St
'IF X < 0 THEN IF VAL(St) THEN St = "-" + St
IF X < 0 THEN
s=val(st)
IF s>0 THEN St = "-" + St
end if
'PRINT P; LEFT(St, LEN(St) - 1); "."; RIGHT$(St, 1); " degrees"
i=len(st)-1
print P;left(st,i);".";right(st,1);" degrees"
END SUB
SUB P2C (byval AZ as single,byval EL as single,byref X as single,byref Y as single,byref Z as single)
' Polar to Cartesian. Convert from AZ,EL to X,Y,Z
local s as single
Z = SIN(EL)
s_C = COS(EL)
s_C=s_C*-1
X = s_C * SIN(AZ)
Y = s_C * COS(AZ)
END SUB[/code:1:50692aec6e]
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