Horizontal sundial calculations

From Rosetta Code
Task
Horizontal sundial calculations
You are encouraged to solve this task according to the task description, using any language you may know.
Task

Create a program that calculates the hour, sun hour angle, dial hour line angle from 6am to 6pm for an operator entered location.


For example, the user is prompted for a location and inputs the latitude and longitude 4°57′S 150°30′W (4.95°S 150.5°W of Jules Verne's Lincoln Island, aka Ernest Legouve Reef), with a legal meridian of 150°W.

(Note: the "meridian" is approximately the same concept as the "longitude" - the distinction is that the meridian is used to determine when it is "noon" for official purposes. This will typically be slightly different from when the sun appears at its highest location, because of the structure of time zones. For most, but not all, time zones (hour wide zones with hour zero centred on Greenwich), the legal meridian will be an even multiple of 15 degrees.)

Wikipedia: A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style (also called its Gnomon, a thin rod or a sharp, straight edge) onto a flat surface marked with lines indicating the hours of the day (also called the dial face or dial plate). As the sun moves across the sky, the shadow-edge progressively aligns with different hour-lines on the plate. Such designs rely on the style being aligned with the axis of the Earth's rotation. Hence, if such a sundial is to tell the correct time, the style must point towards true north (not the north or south magnetic pole) and the style's angle with horizontal must equal the sundial's geographical latitude.

Ada

Translation of: ALGOL 68

sundial.adb:

with Ada.Text_IO;
with Ada.Numerics.Elementary_Functions;
procedure Sundial is
use Ada.Numerics.Elementary_Functions;
use Ada.Numerics;
package Float_IO is new Ada.Text_IO.Float_IO (Float);
 
Latitude, Longitude, Meridian : Float;
Latitude_Sine  : Float;
begin
Ada.Text_IO.Put ("Enter latitude: ");
Float_IO.Get (Latitude);
Ada.Text_IO.Put ("Enter longitude: ");
Float_IO.Get (Longitude);
Ada.Text_IO.Put ("Enter legal meridian: ");
Float_IO.Get (Meridian);
Ada.Text_IO.New_Line;
 
Latitude_Sine := Sin (Latitude * Pi / 180.0);
Ada.Text_IO.Put_Line
(" sine of latitude:" & Float'Image (Latitude_Sine));
Ada.Text_IO.Put_Line
(" diff longitude:" & Float'Image (Longitude - Meridian));
Ada.Text_IO.New_Line;
 
Ada.Text_IO.Put_Line
("hour, sun hour angle, dial hour line angle from 6am to 6pm");
for H in -6 .. 6 loop
declare
Hour_Angle : constant Float :=
15.0 * Float (H) - (Longitude - Meridian);
Line_Angle : constant Float :=
Arctan (Latitude_Sine * Tan (Hour_Angle * Pi / 180.0)) * 180.0 /
Pi;
begin
Ada.Text_IO.Put_Line
("HR=" &
Integer'Image (H) &
"; HRA=" &
Float'Image (Hour_Angle) &
"; HLA=" &
Float'Image (Line_Angle));
end;
end loop;
end Sundial;
Output:
Enter latitude:       -4.95
Enter longitude:      -150.5
Enter legal meridian: -150

   sine of latitude:-8.62864E-02
   diff longitude:-5.00000E-01

hour, sun hour angle, dial hour line angle from 6am to 6pm
HR=-6; HRA=-8.95000E+01; HLA= 8.42248E+01
HR=-5; HRA=-7.45000E+01; HLA= 1.72829E+01
HR=-4; HRA=-5.95000E+01; HLA= 8.33371E+00
HR=-3; HRA=-4.45000E+01; HLA= 4.84671E+00
HR=-2; HRA=-2.95000E+01; HLA= 2.79487E+00
HR=-1; HRA=-1.45000E+01; HLA= 1.27835E+00
HR= 0; HRA= 5.00000E-01; HLA=-4.31443E-02
HR= 1; HRA= 1.55000E+01; HLA=-1.37079E+00
HR= 2; HRA= 3.05000E+01; HLA=-2.90964E+00
HR= 3; HRA= 4.55000E+01; HLA=-5.01802E+00
HR= 4; HRA= 6.05000E+01; HLA=-8.67140E+00
HR= 5; HRA= 7.55000E+01; HLA=-1.84510E+01
HR= 6; HRA= 9.05000E+01; HLA= 8.42248E+01

ALGOL 68

Works with: ALGOL 68 version Revision 1 - no extensions to language used
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny
Works with: ELLA ALGOL 68 version Any (with appropriate job cards) - tested with release 1.8-8d

Example extracted - with permission for a GPL - from Simon Wheaton-Smith's Illustrating Time's Shadow web page.

BEGIN
REAL lat, slat, lng, ref;
print ( "Enter latitude => " ); read (lat);
print ( "Enter longitude => " ); read (lng);
print ( "Enter legal meridian => " ); read (ref);
new line(stand out);
 
slat := sin(lat*2*pi/360) ;
print ( (" sine of latitude: ", float(slat,8,2,1), new line ) );
print ( (" diff longitude: ", fixed((lng - ref),0,3), new line, new line ) );
 
print ( ("Hour, sun hour angle, dial hour line angle from 6am to 6pm", new line ));
 
FOR h FROM -6 TO 6
DO
REAL hra , hla ; # define hour angle and hour line angle #
hra := 15 * h ; # hour angle is 15 times the hour #
hra := hra - (lng - ref); # but correct for longitude difference #
hla := arc tan ( slat * tan(hra*2*pi/360) ) * 360 / ( 2*pi) ;
# page 132 of a68gdoc.pdf documentationfile #
print ("HR="+whole(h,3)+"; HRA="+fixed(hra,8,3)+"; HLA="+fixed(hla,8,3));
new line(stand out)
OD
END
Output:
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150  

    sine of latitude:   -86.3e-3
    diff longitude:     -.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA= -89.500; HLA= +84.225
HR= -5; HRA= -74.500; HLA= +17.283
HR= -4; HRA= -59.500; HLA=  +8.334
HR= -3; HRA= -44.500; HLA=  +4.847
HR= -2; HRA= -29.500; HLA=  +2.795
HR= -1; HRA= -14.500; HLA=  +1.278
HR= +0; HRA=  +0.500; HLA=  -0.043
HR= +1; HRA= +15.500; HLA=  -1.371
HR= +2; HRA= +30.500; HLA=  -2.910
HR= +3; HRA= +45.500; HLA=  -5.018
HR= +4; HRA= +60.500; HLA=  -8.671
HR= +5; HRA= +75.500; HLA= -18.451
HR= +6; HRA= +90.500; HLA= +84.225

AutoHotkey

Translation of: F#

AutoHotkey is not a command-line programming language, let me make that clear. However, in translating the F# I found that the command line really is best for this type of app. The first 3 comments in the script describe the workarounds used to interface with the commandline.

DllCall("AllocConsole")  ; Open a console window for this application
Pi := 4*ATan(1)
,Degrees := Pi/180
 
FileAppend, Enter Latitude: , CONOUT$ ; write to stdout
FileReadLine, latitude, CONIN$, 1 ; read from stdin
 
FileAppend, Enter Longitude: , CONOUT$
FileReadLine, longitude, CONIN$, 1
 
FileAppend, Enter Legal meridian: , CONOUT$
FileReadLine, meridian, CONIN$, 1
 
sineLatitude := Sin(latitude*Degrees)
FileAppend, `n, CONOUT$
FileAppend, Sine of latitude: %sineLatitude%`n, CONOUT$
FileAppend, % "Difference of Longitudes (given longitude - meridian): " . longitude-meridian . "`n", CONOUT$
FileAppend, `n, CONOUT$
 
FileAppend, Numbers from 6 AM to 6 PM:`n, CONOUT$
FileAppend, Hour`t`tSun Hour Angle`t Dial hour line angle`n, CONOUT$
 
 
hour := -7
While (++hour < 7)
{
clockHour := hour < 0 ? abs(hour) . "AM" : hour . "PM"
shr := RTrim("" . (15.0*hour - (longitude-meridian)), "0") ; RTrim() removes trailing zeroes
dhla := Atan(sineLatitude*Tan(shr*degrees))/Degrees
FileAppend, %clockhour%`t`t%shr%`t`t%dhla%`n, CONOUT$
}
MsgBox close me when done.
Output:
Enter Latitude:-4.95
Enter Longitude:-150.5
Enter Legal meridian:-150

Sine of latitude: -0.086286
Difference of Longitudes (given longitude - meridian): -0.500000

Numbers from 6 AM to 6 PM:
Hour            Sun Hour Angle   Dial hour line angle
6AM             -89.5           84.224833
5AM             -74.5           17.282934
4AM             -59.5           8.333712
3AM             -44.5           4.846709
2AM             -29.5           2.794874
1AM             -14.5           1.278353
0PM             0.5             -0.043144
1PM             15.5            -1.370788
2PM             30.5            -2.909643
3PM             45.5            -5.018023
4PM             60.5            -8.671397
5PM             75.5            -18.450999
6PM             90.5            84.224833

AWK

 
# syntax: GAWK -f HORIZONTAL_SUNDIAL_CALCULATIONS.AWK
BEGIN {
printf("enter latitude (degrees): ") ; getline latitude
printf("enter longitude (degrees): ") ; getline longitude
printf("enter legal meridian (degrees): ") ; getline meridian
printf("\nhour sun hour angle dial hour line angle\n")
slat = sin(dr(latitude))
for (hour=-6; hour<=6; hour++) { # 6AM-6PM
hra = 15 * hour - longitude + meridian
hraRad = dr(hra)
hla = rd(atan2(sin(hraRad)*slat,cos(hraRad)))
printf("%4d %15.3f %21.3f\n",hour+12,hra,hla)
}
exit(0)
}
function dr(x) { return x * 3.14159265 / 180 } # degrees to radians
function rd(x) { return x * 180 / 3.14159265 } # radians to degrees
 

output:

enter latitude (degrees): -4.95
enter longitude (degrees): -150.5
enter legal meridian (degrees): -150

hour  sun hour angle  dial hour line angle
   6         -89.500                84.225
   7         -74.500                17.283
   8         -59.500                 8.334
   9         -44.500                 4.847
  10         -29.500                 2.795
  11         -14.500                 1.278
  12           0.500                -0.043
  13          15.500                -1.371
  14          30.500                -2.910
  15          45.500                -5.018
  16          60.500                -8.671
  17          75.500               -18.451
  18          90.500               -95.775

BBC BASIC

      INSTALL @lib$+"FNUSING"
 
INPUT "Enter latitude (degrees)  : " latitude
INPUT "Enter longitude (degrees)  : " longitude
INPUT "Enter legal meridian (degrees): " meridian
 
PRINT '" Time", "Sun hour angle", "Dial hour line angle"
 
FOR hour = 6 TO 18
hra = 15*hour - longitude + meridian - 180
hla = DEG(ATN(SIN(RAD(latitude)) * TAN(RAD(hra))))
IF ABS(hra) > 90 hla += 180 * SGN(hra * latitude)
PRINT FNusing("##.##", hour), FNusing(" ####.### ", hra), FNusing(" ####.###", hla)
NEXT hour
Output:

(note the correct negative value for time 18:00)

Enter latitude (degrees)      : -4.95
Enter longitude (degrees)     : -150.5
Enter legal meridian (degrees): -150.0

 Time     Sun hour angle      Dial hour line angle
 6.00        -89.500              84.225
 7.00        -74.500              17.283
 8.00        -59.500               8.334
 9.00        -44.500               4.847
10.00        -29.500               2.795
11.00        -14.500               1.278
12.00          0.500              -0.043
13.00         15.500              -1.371
14.00         30.500              -2.910
15.00         45.500              -5.018
16.00         60.500              -8.671
17.00         75.500             -18.451
18.00         90.500             -95.775

C

Translation of: ALGOL 68
#include <stdio.h>
#include <math.h>
 
#define PICKVALUE(TXT, VM) do { \
printf("%s: ", TXT); \
scanf("%lf", &VM); \
} while(0);

 
#if !defined(M_PI)
#define M_PI 3.14159265358979323846
#endif
 
#define DR(X) ((X)*M_PI/180.0)
#define RD(X) ((X)*180.0/M_PI)
 
int main()
{
double lat, slat, lng, ref;
int h;
 
PICKVALUE("Enter latitude", lat);
PICKVALUE("Enter longitude", lng);
PICKVALUE("Enter legal meridian", ref);
printf("\n");
 
slat = sin(DR(lat));
printf("sine of latitude: %.3f\n", slat);
printf("diff longitude: %.3f\n\n", lng - ref);
 
printf("Hour, sun hour angle, dial hour line angle from 6am to 6pm\n");
 
for(h = -6; h <= 6; h++)
{
double hla, hra;
hra = 15.0*h;
hra = hra - lng + ref;
hla = RD(atan(slat * tan(DR(hra))));
printf("HR= %3d; \t HRA=%7.3f; \t HLA= %7.3f\n",
h, hra, hla);
}
 
return 0;
}

C#

using System;
 
namespace RosettaCode
{
internal sealed class Program
{
private static void Main()
{
Func<double> getDouble = () => Convert.ToDouble(Console.ReadLine());
double h = 0, lat, lng, lme, slat, hra, hla;
 
Console.Write("Enter latitude => ");
lat = getDouble();
Console.Write("Enter longitude => ");
lng = getDouble();
Console.Write("Enter legal meridian => ");
lme = getDouble();
 
slat = Math.Sin(lat*2*Math.PI/360);
Console.WriteLine("\n sine of latitude: {0:0.000}", slat);
Console.WriteLine(" diff longitude: {0:0.000}\n", lng-lme);
Console.WriteLine("Hour, sun hour angle, dial hour line angle from 6am to 6pm");
for (h = -6; h<6; h++)
{
hra = 15*h;
hra -= lng-lme;
hla = Math.Atan(slat*Math.Tan(hra*2*Math.PI/360))*360/(2*Math.PI);
Console.WriteLine("HR= {0,7:0.000}; HRA {1,7:0.000}; HLA= {2,7:0.000}", h, hra, hla);
}
}
}
}

COBOL

Works with: OpenCOBOL
PROGRAM-ID. horizontal-sundial-calc.
 
DATA DIVISION.
WORKING-STORAGE SECTION.
01 latitude PIC S9(3)V9(5) COMP.
01 longitude PIC S9(3)V9(5) COMP.
01 legal-meridian PIC S9(3)V9(5) COMP.
 
01 lat-sine PIC S9(3)V9(5) COMP.
01 diff-longitude PIC S9(3)V9(5) COMP.
 
01 lat-sine-disp PIC -(3)9.9(5).
01 diff-longitude-disp PIC -(3)9.9(5).
 
01 hour PIC S9 COMP.
01 sun-hour-angle PIC S9(3)V9(5) COMP.
01 dial-hour-line-angle PIC S9(3)V9(5) COMP.
 
01 hour-disp PIC 99.
01 sun-hour-angle-disp PIC -(3)9.9(5).
01 dial-hour-line-angle-disp PIC -(3)9.9(5).
 
PROCEDURE DIVISION.
DISPLAY "Enter latitude: " NO ADVANCING
ACCEPT latitude
DISPLAY "Enter longitude: " NO ADVANCING
ACCEPT longitude
DISPLAY "Enter legal meridian: " NO ADVANCING
ACCEPT legal-meridian
DISPLAY SPACE
 
COMPUTE lat-sine, lat-sine-disp ROUNDED =
FUNCTION SIN(latitude * 2 * FUNCTION PI / 360)
DISPLAY "Sine of latitude: " FUNCTION TRIM(lat-sine-disp)
 
SUBTRACT legal-meridian FROM longitude
GIVING diff-longitude, diff-longitude-disp
DISPLAY "Diff longitude: " FUNCTION TRIM(diff-longitude-disp)
DISPLAY SPACE
 
DISPLAY "Time Sun hour angle Dial hour line angle"
PERFORM VARYING hour FROM -6 BY 1 UNTIL hour > 6
COMPUTE sun-hour-angle ROUNDED = hour * 15 - diff-longitude
COMPUTE dial-hour-line-angle ROUNDED = FUNCTION ATAN(lat-sine
* FUNCTION TAN(sun-hour-angle * 2 * FUNCTION PI / 360))
* 360 / (2 * FUNCTION PI)
 
ADD 12 TO hour GIVING hour-disp
MOVE sun-hour-angle TO sun-hour-angle-disp
MOVE dial-hour-line-angle TO dial-hour-line-angle-disp
DISPLAY hour-disp ":00 " sun-hour-angle-disp " "
dial-hour-line-angle-disp
END-PERFORM
.
Output:
Enter latitude: -4.95
Enter longitude: -150.5
Enter legal meridian: -150
 
Sine of latitude: -0.08629
Diff longitude: -0.50000
 
Time   Sun hour angle  Dial hour line angle
06:00  -89.50000        84.22441
07:00  -74.50000        17.28173
08:00  -59.50000         8.33311
09:00  -44.50000         4.84635
10:00  -29.50000         2.79467
11:00  -14.50000         1.27826
12:00    0.50000        -0.04314
13:00   15.50000        -1.37069
14:00   30.50000        -2.90943
15:00   45.50000        -5.01765
16:00   60.50000        -8.67077
17:00   75.50000       -18.44973
18:00   90.50000        84.22441

D

Translation of: Python
import std.stdio, std.math, std.conv, std.string;
 
double radians(in double x) pure nothrow { return x * (PI / 180); }
double degrees(in double x) pure nothrow { return x / (PI / 180); }
 
T input(T)(in string msg) {
msg.write;
return readln.strip.to!T;
}
 
void main() {
immutable lat = input!double("Enter latitude => ");
immutable lng = input!double("Enter longitude => ");
immutable lme = input!double("Enter legal meridian => ");
writeln;
 
double slat = lat.radians.sin;
writefln(" sine of latitude:  %.3f", slat);
writefln(" diff longitude:  %.3f", lng - lme);
writeln;
"Hour, sun hour angle, dial hour line angle from 6am to 6pm".writeln;
 
foreach (immutable h; -6 .. 7) {
immutable double hra = 15 * h - (lng - lme);
immutable double hla = atan(slat * hra.radians.tan).degrees;
writefln("HR=%3d; HRA=%7.3f; HLA=%7.3f", h, hra, hla);
}
}
Example run:
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150

    sine of latitude:   -0.086
    diff longitude:     -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA=-89.500; HLA= 84.225
HR= -5; HRA=-74.500; HLA= 17.283
HR= -4; HRA=-59.500; HLA=  8.334
HR= -3; HRA=-44.500; HLA=  4.847
HR= -2; HRA=-29.500; HLA=  2.795
HR= -1; HRA=-14.500; HLA=  1.278
HR=  0; HRA=  0.500; HLA= -0.043
HR=  1; HRA= 15.500; HLA= -1.371
HR=  2; HRA= 30.500; HLA= -2.910
HR=  3; HRA= 45.500; HLA= -5.018
HR=  4; HRA= 60.500; HLA= -8.671
HR=  5; HRA= 75.500; HLA=-18.451
HR=  6; HRA= 90.500; HLA= 84.225

DWScript

Translation of: Java
procedure PrintSundial(lat, lng, lme : Float);
begin
PrintLn(Format('latitude:  %7.2f', [lat]));
PrintLn(Format('longitude:  %7.2f', [lng]));
PrintLn(Format('legal meridian:  %7.2f', [lme]));
 
var slat := Sin(DegToRad(lat));
 
PrintLn(Format('sine of latitude: %.3f', [slat]));
PrintLn(Format('diff longitude:  %.3f', [lng-lme]));
PrintLn('');
PrintLn('Hour, sun hour angle, dial hour line angle from 6am to 6pm');
 
var h : Integer;
for h:=-6 to 6 do begin
var hra := 15 * h - (lng - lme);
var hraRad := DegToRad(hra);
var hla :=RadToDeg(ArcTan2(Sin(hraRad)*slat, Cos(hraRad)));
PrintLn(Format('HR=%3d; HRA=%7.3f; HLA=%7.3f', [h, hra, hla]));
end
end;
 
PrintSundial(-4.95, -150.5, -150);
Output:
latitude:          -4.95
longitude:       -150.50
legal meridian:  -150.00
sine of latitude: -0.086
diff longitude:   -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA=-89.500; HLA= 84.225
HR= -5; HRA=-74.500; HLA= 17.283
HR= -4; HRA=-59.500; HLA=  8.334
HR= -3; HRA=-44.500; HLA=  4.847
HR= -2; HRA=-29.500; HLA=  2.795
HR= -1; HRA=-14.500; HLA=  1.278
HR=  0; HRA=  0.500; HLA= -0.043
HR=  1; HRA= 15.500; HLA= -1.371
HR=  2; HRA= 30.500; HLA= -2.910
HR=  3; HRA= 45.500; HLA= -5.018
HR=  4; HRA= 60.500; HLA= -8.671
HR=  5; HRA= 75.500; HLA=-18.451
HR=  6; HRA= 90.500; HLA=-95.775

ERRE

PROGRAM SUN_DIAL
 
FUNCTION RAD(X)
RAD=X*π/180
END FUNCTION
 
FUNCTION DEG(X)
DEG=X*180/π
END FUNCTION
 
BEGIN
 
INPUT("Enter latitude (degrees)  : ",latitude)
INPUT("Enter longitude (degrees)  : ",longitude)
INPUT("Enter legal meridian (degrees): ",meridian)
 
PRINT
PRINT(" Time Sun hour angle Dial hour line angle")
PRINT("---------------------------------------------")
 
FOR HOUR=6 TO 18 DO
HRA=15*HOUR-LONGITUDE+MERIDIAN-180
HLA=DEG(ATN(SIN(RAD(LATITUDE))*TAN(RAD(HRA))))
IF ABS(HRA)>90 THEN HLA+=180*SGN(HRA*LATITUDE) END IF
WRITE("##.## ####.### ####.###";HOUR;HRA;HLA)
END FOR
 
END PROGRAM
 
Output:
Enter latitude (degrees)      : ? -4.95
Enter longitude (degrees)     : ? -150.5
Enter legal meridian (degrees): ? -150

 Time    Sun hour angle  Dial hour line angle
---------------------------------------------
 6.00          -89.500         84.225
 7.00          -74.500         17.283
 8.00          -59.500          8.334
 9.00          -44.500          4.847
10.00          -29.500          2.795
11.00          -14.500          1.278
12.00            0.500         -0.043
13.00           15.500         -1.371
14.00           30.500         -2.910
15.00           45.500         -5.018
16.00           60.500         -8.671
17.00           75.500        -18.451
18.00           90.500        -95.775

Euphoria

Works with: OpenEuphoria
 
include std/console.e
include std/mathcons.e
 
atom lat = prompt_number("Enter Latitude: ",{})
atom lng = prompt_number("Enter Longitude: ",{})
atom lm = prompt_number("Enter Legal Meridian: ",{})
puts(1,'\n')
 
atom ha, hla
 
function D2R(atom degrees)
return degrees * PI / 180
end function
 
function R2D(atom radians)
return radians * 180 / PI
end function
 
function atan2(atom y, atom x)
return 2*arctan((sqrt(power(x,2)+power(y,2)) - x)/y)
end function
 
atom s_lat = sin(D2R(lat))
 
puts(1,"Hour, Sun Hour Angle, Dial Hour Line Angle\n")
 
for hour = -6 to 6 do
ha = hour * 15 - lng + lm
atom s = sin(D2R(ha))
atom c = cos(D2R(ha))
hla = R2D(atan2(s_lat*s,c))
printf(1,"%3d\t\t\t%7.3f\t\t\t%7.3f\n",{hour+12,ha,hla})
end for
 
if getc(0) then end if
 
Output:
Enter Latitude: -4.95
Enter Longitude: -150.5
Enter Legal Meridian: -150

Hour,  Sun Hour Angle, Dial Hour Line Angle
  6	-89.500			 84.225
  7	-74.500			 17.283
  8	-59.500			  8.334
  9	-44.500			  4.847
 10	-29.500			  2.795
 11	-14.500			  1.278
 12	  0.500			 -0.043
 13	 15.500			 -1.371
 14	 30.500			 -2.910
 15	 45.500			 -5.018
 16	 60.500			 -8.671
 17	 75.500			-18.451
 18	 90.500			-95.775

F#

Translation of: C#
// Learn more about F# at http://fsharp.net
 
open System
 
//(degree measure)*Degrees => Radian measure
//(radian measure)/Degrees => Degree measure
let Degrees = Math.PI / 180.0
 
Console.Write("Enter latitude: ")
let latitude = Console.ReadLine() |> Double.Parse
 
Console.Write("Enter longitude: ")
let longitude = Console.ReadLine() |> Double.Parse
 
Console.Write("Enter legal meridian: ")
let meridian = Console.ReadLine() |> Double.Parse
 
let sineLatitude = Math.Sin(latitude * Degrees)
Console.WriteLine()
Console.WriteLine("Sine of latitude: {0}",sineLatitude)
Console.WriteLine("Difference of Longitudes (given longitude - meridian): {0}",longitude-meridian)
Console.WriteLine()
 
printfn "Numbers from 6 AM to 6 PM: "
printfn "Hour\t\tSun hour angle\t Dial hour line angle"
 
for hour in -6..6 do
let clockHour = if hour < 0 then String.Format("{0}AM",Math.Abs(hour)) else String.Format("{0}PM",hour)
let shr = 15.0*(float)hour - (longitude - meridian)
let dhla = Math.Atan(sineLatitude*Math.Tan(shr*Degrees))/Degrees;
Console.WriteLine("{0}\t\t{1}\t\t{2:0.000}",clockHour,shr,dhla)
done
 
//To keep the console window open, can be omitted with block comment (" (* comment *) ")
Console.WriteLine("Press any key to continue...")
Console.ReadKey() |> ignore
Example output:
Enter latitude: -4.95
Enter longitude: -150.5
Enter legal meridian: -150

Sine of latitude: -0.0862863657979234
Difference of Longitudes (given longitude - meridian): -0.5

Numbers from 6 AM to 6 PM:
Hour            Sun hour angle   Dial hour line angle
6AM             -89.5           84.225
5AM             -74.5           17.283
4AM             -59.5           8.334
3AM             -44.5           4.847
2AM             -29.5           2.795
1AM             -14.5           1.278
0PM             0.5             -0.043
1PM             15.5            -1.371
2PM             30.5            -2.910
3PM             45.5            -5.018
4PM             60.5            -8.671
5PM             75.5            -18.451
6PM             90.5            84.225
Press any key to continue...

Forth

: faccept ( -- f )
pad 32 accept pad swap >float 0= throw ;
: >radians ( deg -- rad ) 180e f/ pi f* ;
: >degrees ( rad -- deg ) pi f/ 180e f* ;
: sundial
cr ." Enter latitude: "
faccept >radians fsin
cr ." Enter longitude: "
faccept
cr ." Enter legal meridian: "
faccept f- fnegate ( sin[latitude] -longitude )
 
cr ." Hour : HourAngle , DialAngle"
7 -6 do
cr i 4 .r ." : "
fover fover i 15 * s>d d>f f+
fdup f. ." , "
>radians fsincos fswap frot f* fswap fatan2 >degrees f.
loop fdrop fdrop ;

Fortran

Works with: gfortran
with -fbackslash option
program SunDial
 
real :: lat, slat, lng, ref
real :: hra, hla
integer :: h
 
real, parameter :: pi = 3.14159265358979323846
 
print *, "Enter latitude"
read *, lat
print *, "Enter longitude"
read *, lng
print *, "Enter legal meridian"
read *, ref
 
print *
 
slat = sin(dr(lat))
write(*, '(A,1F6.3)') "sine of latitude: ", slat
write(*, '(A,1F6.3)') "diff longitude: ", lng - ref
 
print *, "Hour, sun hour angle, dial hour line angle from 6am to 6pm"
 
do h = -6, 6
hra = 15.0*h
hra = hra - lng + ref
hla = rd( atan( slat * tan( dr(hra) ) ) )
write(*, '(" HR= ",I3,"; \t HRA=",F7.3,"; \t HLA= ", F7.3)'), h, hra, hla
end do
 
contains
 
function dr(angle)
real :: dr
real, intent(in) :: angle
dr = angle*pi/180.0
end function dr
 
function rd(angle)
real :: rd
real, intent(in) :: angle
rd = angle*180.0/pi
end function rd
 
end program SunDial

freeBASIC

Translation of: BBC BASIC
' version 04-11-2016
' compile with: fbc -s console
 
#Macro deg2rad (x)
(x) * Atn(1) / 45
#EndMacro
 
#Macro rad2deg (x)
(x) * 45 / Atn(1)
#EndMacro
 
' ------=< MAIN >=------
 
Dim As Double latitude, longitude, meridian, hra, hla
Dim As ULong h
 
Input " Enter latitude (degrees): ", latitude
Input " Enter longitude (degrees): ", longitude
Input "Enter legal meridian (degrees): ", meridian
 
Print
Print " Time Sun hour angle Dial hour line angle"
 
For h = 6 To 18
hra = h * 15 - longitude + meridian - 180
hla = rad2deg(Atn(Sin(deg2rad(latitude)) * Tan(deg2rad(hra))))
If Abs(hra) > 90 Then hla += 180 * Sgn(hra * latitude)
Print Using "##.## ####.### ####.###"; h; hra; hla
Next
 
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
Output:
      Enter latitude (degrees): -4.95
     Enter longitude (degrees): -150.5
Enter legal meridian (degrees): -150

 Time  Sun hour angle  Dial hour line angle
 6.00      -89.500           84.225
 7.00      -74.500           17.283
 8.00      -59.500            8.334
 9.00      -44.500            4.847
10.00      -29.500            2.795
11.00      -14.500            1.278
12.00        0.500           -0.043
13.00       15.500           -1.371
14.00       30.500           -2.910
15.00       45.500           -5.018
16.00       60.500           -8.671
17.00       75.500          -18.451
18.00       90.500          -95.775

FutureBasic

 
include "ConsoleWindow"
 
local fn rad2deg( theta as double ) as double
end fn = theta * 180 / pi
 
local fn deg2rad( theta as double ) as double
end fn = theta * pi / 180
 
local fn SolarHourAngle( latitude as double, longitude as double, meridian as double )
dim as long hour
dim as double hra, hla, time
dim as Str15 ap
 
print "Latitude = "; latitude; chr$(13); "Longitude = "; longitude; chr$(13); "Meridian = "; meridian
print : print "sine of latitude: "; sin(latitude * pi / 180 ); chr$(13); " diff longitude: "; longitude - meridian
print : print "Time", "Sun hour angle", "Dial hour line angle"
for hour = 6 to 18
hra = ( 15 * hour ) - longitude + meridian - 180
hla = fn rad2deg( atn( sin( fn deg2rad( latitude ) ) * tan( fn deg2rad( hra ) )))
if abs( hra ) > 90 then hla = hla + 180 * sgn( hra * latitude )
if hour > 12 then time = hour - 12 : ap = " a.m." else time = hour : ap = " p.m."
print using "##"; time; ap, using "####.##"; hra, using "####.###"; hla
next hour
end fn
 
fn SolarHourAngle( -4.95, -150.5, -150.0 )
 

Output:

Latitude  = -4.95
Longitude = -150.5
Meridian  = -150

sine of latitude: -0.0862863658
  diff longitude: -0.5

Time            Sun hour angle  Dial hour line angle
 6 p.m.          -89.50           84.225
 7 p.m.          -74.50           17.283
 8 p.m.          -59.50            8.334
 9 p.m.          -44.50            4.847
10 p.m.          -29.50            2.795
11 p.m.          -14.50            1.278
12 p.m.            0.50           -0.043
 1 a.m.           15.50           -1.371
 2 a.m.           30.50           -2.910
 3 a.m.           45.50           -5.018
 4 a.m.           60.50           -8.671
 5 a.m.           75.50          -18.451
 6 a.m.           90.50          -95.775

Go

package main
 
import (
"fmt"
"math"
"os"
)
 
func getnum(prompt string) (r float64) {
fmt.Print(prompt)
if _, err := fmt.Scan(&r); err != nil {
fmt.Println(err)
os.Exit(-1)
}
return
}
 
func main() {
lat := getnum("Enter latitude => ")
lng := getnum("Enter longitude => ")
ref := getnum("Enter legal meridian => ")
slat := math.Sin(lat * math.Pi / 180)
diff := lng - ref
fmt.Println("\n sine of latitude: ", slat)
fmt.Println(" diff longitude: ", diff)
fmt.Println("\nHour, sun hour angle, dial hour line angle from 6am to 6pm")
for h := -6.; h <= 6; h++ {
hra := 15*h - diff
s, c := math.Sincos(hra * math.Pi / 180)
hla := math.Atan2(slat*s, c) * 180 / math.Pi
fmt.Printf("%2.0f %8.3f %8.3f\n", h, hra, hla)
}
}
Output:
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150

    sine of latitude:    -0.08628636579792338
    diff longitude:      -0.5

Hour, sun hour angle, dial hour line angle from 6am to 6pm
-6  -89.500   84.225
-5  -74.500   17.283
-4  -59.500    8.334
-3  -44.500    4.847
-2  -29.500    2.795
-1  -14.500    1.278
 0    0.500   -0.043
 1   15.500   -1.371
 2   30.500   -2.910
 3   45.500   -5.018
 4   60.500   -8.671
 5   75.500  -18.451
 6   90.500  -95.775

Haskell

module Rosetta.HorSunDial where
 
roundDec :: Int -> Double -> Double
roundDec d = (/10.0^d). fromIntegral. round. (*10.0^d)
 
radToDegr = ((180/pi)*)
degrToRad = ((pi/180)*)
 
main = do
let lat = -4.95
long = -150.5
legalMerid = -150
sinOfLat = sin $ degrToRad lat
diff = legalMerid - long
 
putStrLn $ "Latitude " ++ show lat
putStrLn $ "Longitude " ++ show long
putStrLn $ "Legal meridian " ++ show legalMerid
putStrLn $ "Sine of latitude " ++ show (roundDec 6 sinOfLat)
putStrLn $ "Diff longitude " ++ show (-diff)
putStrLn "hour sun hour angle dial hour line angle"
mapM_ (\h ->
let sha = diff + 15*h
dhla = radToDegr . atan. (sinOfLat *). tan $ degrToRad sha
in putStrLn $ take 7 (show h ++ repeat ' ')
++ take 16 (show (roundDec 3 sha) ++ repeat ' ' )
++ " " ++ show (roundDec 3 dhla)
) [-6,-5..6]
Output:
*Rosetta.HorSunDial> main
Latitude         -4.95
Longitude        -150.5
Legal meridian   -150.0
Sine of latitude -8.6286e-2
Diff longitude   -0.5
hour   sun hour angle   dial hour  line angle
-6.0   -89.5            84.225
-5.0   -74.5            17.283
-4.0   -59.5            8.334
-3.0   -44.5            4.847
-2.0   -29.5            2.795
-1.0   -14.5            1.278
0.0    0.5              -4.3e-2
1.0    15.5             -1.371
2.0    30.5             -2.91
3.0    45.5             -5.018
4.0    60.5             -8.671
5.0    75.5             -18.451
6.0    90.5             84.225

Icon and Unicon

procedure main()
PrintSundial(-4.95, -150.5, -150);
end
 
procedure PrintSundial(lat, lng, mer )
write("latitude: ", lat,
"\nlongitude: ", lng,
"\nlegal meridian: ", mer)
 
slat := sin(dtor(lat))
 
write("sine of latitude: ",slat,
"\ndiff longitude: ", lng-mer)
write("\nHour, sun hour angle, dial hour line angle from 6am to 6pm")
 
every h := -6 to 6 do {
hraRad := dtor(hra := 15 * h - (lng - mer))
hla :=rtod(atan(sin(hraRad)*slat, cos(hraRad)))
write("HR=",
right(if h <= 0 then 12+h else h,2),
if h < 0 then "am" else "pm",
" HRA=",hra,", HLA=",hla)
}
end
Output:
latitude:        -4.95
longitude:       -150.5
legal meridian:  -150
sine of latitude: -0.08628636579792337
diff longitude:   -0.5

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= 6am HRA=-89.5, HLA=84.22483260136025
HR= 7am HRA=-74.5, HLA=17.2829335027853
HR= 8am HRA=-59.5, HLA=8.333711921468083
HR= 9am HRA=-44.5, HLA=4.846708924373172
HR=10am HRA=-29.5, HLA=2.794873809318642
HR=11am HRA=-14.5, HLA=1.278352980919063
HR=12pm HRA=0.5, HLA=-0.04314426995813971
HR= 1pm HRA=15.5, HLA=-1.370787843187052
HR= 2pm HRA=30.5, HLA=-2.909643210076617
HR= 3pm HRA=45.5, HLA=-5.018023174356126
HR= 4pm HRA=60.5, HLA=-8.671396957302381
HR= 5pm HRA=75.5, HLA=-18.45099922256532
HR= 6pm HRA=90.5, HLA=-95.77516739863968

J

require 'trig'
atan2=: {:@*.@j. NB. arc tangent of y divided by x
 
horiz=: verb define
'lat lng ref'=. y
out=. smoutput@,&":
'Latitude ' out lat
'Longitude ' out lng
'Legal meridian ' out ref
'Sine of latitude ' out slat=. sin rfd lat
'Diff longitude ' out -diff=. ref - lng
lbl=.'hour ';'sun hour angle ';'dial hour line angle'
r=.((,. (,. (atan2 *&slat)/@+.@r.&.rfd)) diff + 15&*) i:6
smoutput lbl ,: ('3.0';'7.3';'7.3') 8!:1 r
)
Example:
   horiz _4.95 _150.5 _150
Latitude _4.95
Longitude _150.5
Legal meridian _150
Sine of latitude _0.0862864
Diff longitude _0.5
┌──────┬────────────────┬────────────────────┐
│hour │sun hour angle │dial hour line angle│
├──────┼────────────────┼────────────────────┤
│ -6 │-89.50084.225
│ -5 │-74.50017.283
│ -4 │-59.5008.334
│ -3 │-44.5004.847
│ -2 │-29.5002.795
│ -1 │-14.5001.278
00.500 │ -0.043
115.500 │ -1.371
230.500 │ -2.910
345.500 │ -5.018
460.500 │ -8.671
575.500 │-18.451
690.500 │-95.775
└──────┴────────────────┴────────────────────┘

Java

Translation of: C
(Substitutes in atan2 for the hour line angle calculation)
import java.util.Scanner;
public class Sundial {
public static void main(String[] args) {
double lat, slat, lng, ref;
Scanner sc = new Scanner(System.in);
 
System.out.print("Enter latitude: ");
lat = sc.nextDouble();
System.out.print("Enter longitude: ");
lng = sc.nextDouble();
System.out.print("Enter legal meridian: ");
ref = sc.nextDouble();
System.out.println();
 
slat = Math.sin(Math.toRadians(lat));
System.out.printf("sine of latitude: %.3f\n", slat);
System.out.printf("diff longitude: %.3f\n\n", lng - ref);
 
System.out.printf("Hour, sun hour angle, dial hour line angle from 6am to 6pm\n");
 
for (int h = -6; h <= 6; h++) {
double hla, hra;
hra = 15.0 * h;
hra = hra - lng + ref;
hraRad = Math.toRadians(hra);
hla = Math.toDegrees(Math.atan2(Math.sin(hraRad)*Math.sin(Math.toRadians(lat)), Math.cos(hraRad)));
System.out.printf("HR= %3d; \t HRA=%7.3f; \t HLA= %7.3f\n",
h, hra, hla);
}
}
}
Output:
Enter latitude: -4.95
Enter longitude: -150.5
Enter legal meridian: -150

sine of latitude: -0.086
diff longitude: -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR=  -6;  	  HRA=-89.500;  	  HLA=  84.225
HR=  -5;  	  HRA=-74.500;  	  HLA=  17.283
HR=  -4;  	  HRA=-59.500;  	  HLA=   8.334
HR=  -3;  	  HRA=-44.500;  	  HLA=   4.847
HR=  -2;  	  HRA=-29.500;  	  HLA=   2.795
HR=  -1;  	  HRA=-14.500;  	  HLA=   1.278
HR=   0;  	  HRA=  0.500;  	  HLA=  -0.043
HR=   1;  	  HRA= 15.500;  	  HLA=  -1.371
HR=   2;  	  HRA= 30.500;  	  HLA=  -2.910
HR=   3;  	  HRA= 45.500;  	  HLA=  -5.018
HR=   4;  	  HRA= 60.500;  	  HLA=  -8.671
HR=   5;  	  HRA= 75.500;  	  HLA= -18.451
HR=   6;  	  HRA= 90.500;  	  HLA= -95.775

Kotlin

import java.lang.Math.*
 
// version 1.1.2
 
fun main(args: Array<String>) {
println("Please enter the following in degrees:")
print(" Latitude  : ")
val lat = readLine()!!.toDouble()
print(" Longitude  : ")
val lng = readLine()!!.toDouble()
print(" Legal Meridian : ")
val mer = readLine()!!.toDouble()
 
val slat = sin(toRadians(lat))
val diff = lng - mer
println("\nSine of latitude = ${"%.6f".format(slat)}")
println("Longitude - Meridian = ${"%.3f".format(diff)}\n")
println("Hour Sun Hour Angle Dial Hour Line Angle")
println("----- -------------- --------------------")
println(" ° °")
for (h in -6..6) {
var hr = h + 12
val am = if (hr < 12) "AM" else "PM"
if (hr > 12) hr -= 12
val sha = 15.0 * h - diff
val dhla = toDegrees(atan2(slat * sin(toRadians(sha)), cos(toRadians(sha))))
println("%2d %s  %+7.3f  %+7.3f".format(hr, am, sha, dhla))
}
}

Sample input/output:

Output:
Please enter the following in degrees:
  Latitude       : -4.95
  Longitude      : -150.5
  Legal Meridian : -150

Sine of latitude     = -0.086286
Longitude - Meridian = -0.500

Hour   Sun Hour Angle  Dial Hour Line Angle
-----  --------------  --------------------
              °               °
 6 AM      -89.500         +84.225
 7 AM      -74.500         +17.283
 8 AM      -59.500          +8.334
 9 AM      -44.500          +4.847
10 AM      -29.500          +2.795
11 AM      -14.500          +1.278
12 PM       +0.500          -0.043
 1 PM      +15.500          -1.371
 2 PM      +30.500          -2.910
 3 PM      +45.500          -5.018
 4 PM      +60.500          -8.671
 5 PM      +75.500         -18.451
 6 PM      +90.500         -95.775

Liberty BASIC

Based on Algol & BBC BASIC versions. Note Liberty BASIC works in radians.

global pi
pi =3.14159265
 
input "Enter latitude (degrees)  : "; latitude ' -4.95
input "Enter longitude (degrees)  : "; longitude ' -150.5
input "Enter legal meridian (degrees): "; meridian ' -150.0
 
print
print "Time Sun hour angle Dial hour line angle"
 
for hour = 6 TO 18
hra =15 *hour - longitude +meridian -180
hla =rad2deg( atn( sin( deg2rad( latitude)) *tan( deg2rad( hra))))
if abs( hra) >90 then hla =hla +180 *sgn( hra *latitude)
print using( "##.##", hour), using("####.### ", hra), using("####.###", hla)
next hour
 
function rad2deg( theta)
rad2deg =theta *180 /pi
end function
 
function deg2rad( theta)
deg2rad =theta *pi /180
end function
 
function sgn( x)
if x >0 then sgn =1 else sgn =-1
end function
 
end

LiveCode

Translation of BASIC versions.

on mouseUp
ask "Enter lng,lat,meridian"
if it is empty then exit mouseup
// -150.5, -4.95, -150.0
put item 1 of it into longitude
put item 2 of it into latitude
put item 3 of it into meridian
 
repeat with hour = 6 TO 18
put 15 *hour - longitude + meridian - 180 into hra
put rad2deg(atan(sin(deg2rad(latitude)) * tan(deg2rad(hra)))) into hla
if abs(hra) > 90 then put hla + 180 * sgn(hra *latitude) into hla
put hour && hra && hla & cr after sunhours
end repeat
put sunhours
end mouseUp
 
function rad2deg theta
return theta * (180 / pi)
end rad2deg
 
function deg2rad theta
return theta * (pi / 180)
end deg2rad
 
function sgn x
if x >0 then return 1 else return -1
end sgn


type "|Enter latitude: |
make "lat readword
type "|Enter longitude: |
make "long readword
type "|Enter legal meridian: |
make "long :long - readword
 
print [Hour : HourAngle , DialAngle]
for [hour -6 6] [
make "hra 15 * :hour - :long
make "hla arctan product sin :lat quotient sin :hra cos :hra
print (sentence "hour :hour ": :hra ", :hla)
]

МК-61/52

МГ	П2	->	МГ	П1	->	МГ	sin	П0
6 /-/ П3
ИП3 1 5 * ИП1 ИП2 - - П4
tg ИП0 * arctg ИП4 ИП3 С/П
ИП3 1 + П3 7 - x=0 12
Сx С/П

Input: latitude ^ longitude ^ legal meridian С/П ... С/П ...; switch of the angle measure set to Г.

Example: -4,57 ^ -150,3 ^ -150 С/П.

Output: hour in РX, sun hour angle in РY, dial hour line angle in РZ.

Nim

Translation of: Python
import rdstdin, strutils, math, strfmt
 
proc radians(x): float = x * Pi / 180
proc degrees(x): float = x * 180 / Pi
 
let lat = parseFloat readLineFromStdin "Enter latitude => "
let lng = parseFloat readLineFromStdin "Enter longitude => "
let med = parseFloat readLineFromStdin "Enter legal meridian => "
echo ""
 
let slat = sin radians lat
echo " sine of latitude: {:.3f}".fmt(slat)
echo " diff longitude: {:.3f}".fmt(lng-med)
echo ""
echo "Hour, sun hour angle, dial hour line angle from 6am to 6pm"
 
for h in -6..6:
let hra = float(15 * h) - lng + med
let hla = degrees arctan(slat * tan radians hra)
echo "HR={:3d}; HRA={:7.3f}; HLA={:7.3f}".fmt(h, hra, hla)

Output:

Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150

    sine of latitude:   -0.086
    diff longitude:     -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA=-89.500; HLA= 84.225
HR= -5; HRA=-74.500; HLA= 17.283
HR= -4; HRA=-59.500; HLA=  8.334
HR= -3; HRA=-44.500; HLA=  4.847
HR= -2; HRA=-29.500; HLA=  2.795
HR= -1; HRA=-14.500; HLA=  1.278
HR=  0; HRA=  0.500; HLA= -0.043
HR=  1; HRA= 15.500; HLA= -1.371
HR=  2; HRA= 30.500; HLA= -2.910
HR=  3; HRA= 45.500; HLA= -5.018
HR=  4; HRA= 60.500; HLA= -8.671
HR=  5; HRA= 75.500; HLA=-18.451
HR=  6; HRA= 90.500; HLA= 84.225

Objeck

Translation of: C#
 
class Sundial {
function : Main(args : String[]) ~ Nil {
"Enter latitude: "->Print();
lat := System.IO.Console->ReadString()->ToFloat();
"Enter longitude: "->Print();
lng := System.IO.Console->ReadString()->ToFloat();
"Enter legal meridian: "->Print();
ref := System.IO.Console->ReadString()->ToFloat();
'\n'->PrintLine();
 
slat := lat->ToRadians()->Sin();
"sine of latitude: {$slat}"->PrintLine();
value := lng - ref;
"diff longitude: {$value}"->PrintLine();
'\n'->PrintLine();
 
"Hour\t\tsun hour angle\t\tdial hour line angle from 6am to 6pm"->PrintLine();
for (h := -6; h <= 6; h+=1;) {
hra := 15.0 * h;
hra -= lng - ref;
hla := (slat* (hra*2*Float->Pi()/360.0)->Tan())->ArcTan() * 360.0 / (2*Float->Pi());
"HR={$h}\t\tHRA={$hra}\t\tHLA={$hla}"->PrintLine();
};
}
}
 

OCaml

Translation of: ALGOL 68
let () =
let pi = 4. *. atan 1. in
print_endline "Enter latitude => ";
let lat = read_float () in
print_endline "Enter longitude => ";
let lng = read_float () in
print_endline "Enter legal meridian => ";
let ref = read_float () in
print_newline ();
 
let slat = sin (lat *. 2. *. pi /. 360.) in
Printf.printf " sine of latitude:  %.3f\n" slat;
Printf.printf " diff longitude:  %.3f\n" (lng -. ref);
print_newline ();
 
print_endline "Hour, sun hour angle, dial hour line angle from 6am to 6pm";
 
for h = -6 to 6 do
let hra = 15. *. float h in
let hra = hra -. (lng -. ref) in
let hla = atan (slat *. tan (hra *. 2. *. pi /. 360.)) *. 360. /. (2. *. pi) in
Printf.printf "HR= %3d; \t HRA=%7.3f; \t HLA= %7.3f\n" h hra hla;
done
 
Output:
Enter latitude		=> 
-4.95
Enter longitude	=> 
-150.5
Enter legal meridian	=> 
-150.

    sine of latitude:   -0.086
    diff longitude:     -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR=  -6;  	  HRA=-89.500;  	  HLA=  84.225
HR=  -5;  	  HRA=-74.500;  	  HLA=  17.283
HR=  -4;  	  HRA=-59.500;  	  HLA=   8.334
HR=  -3;  	  HRA=-44.500;  	  HLA=   4.847
HR=  -2;  	  HRA=-29.500;  	  HLA=   2.795
HR=  -1;  	  HRA=-14.500;  	  HLA=   1.278
HR=   0;  	  HRA=  0.500;  	  HLA=  -0.043
HR=   1;  	  HRA= 15.500;  	  HLA=  -1.371
HR=   2;  	  HRA= 30.500;  	  HLA=  -2.910
HR=   3;  	  HRA= 45.500;  	  HLA=  -5.018
HR=   4;  	  HRA= 60.500;  	  HLA=  -8.671
HR=   5;  	  HRA= 75.500;  	  HLA= -18.451
HR=   6;  	  HRA= 90.500;  	  HLA=  84.225

Octave

lat = input("Enter latitude: ");
lng = input("Enter longitude: ");
ref = input("Enter legal meridian: ");
slat = sind(lat);
printf("sine of latitude: %.3f\n", slat);
printf("diff longitude: %.3f\n\n", lng - ref);
printf("Hour, sun hour angle, dial hour line angle from 6am to 6pm\n");
 
hras = [-6:6] .* 15.0 .- lng .+ ref;
hlas = atand( tand(hras) .* slat );
printf("HR= %3d; \t HRA=%7.3f; \t HLA= %7.3f\n",
[ [-6:6]; hras; hlas] );

OoRexx

Translation of: REXX
/*REXX pgm shows:  hour,  sun hour angle,  dial hour line angle,  6am ---> 6pm*/
/* Use trigonometric functions provided by rxCalc */
parse arg lat lng mer . /*get the optional arguments from the CL*/
/*None specified? Then use the default of Jules */
/*Verne's Lincoln Island, aka Ernest Legouve Reef.*/
 
if lat=='' | lat==',' then lat=-4.95 /*Not specified? Then use the default.*/
if lng=='' | lng==',' then lng=-150.5 /* " " " " " " */
if mer=='' | mer==',' then mer=-150 /* " " " " " " */
L=max(length(lat), length(lng), length(mer))
say ' latitude:' right(lat,L)
say ' longitude:' right(lng,L)
say ' legal meridian:' right(mer,L)
sineLat=rxCalcSin(lat,,'D')
w1=max(length('hour') ,length('midnight'))+2
w2=max(length('sun hour') ,length('angle'))+2
w3=max(length('dial hour'),length('line angle'))+2
indent=left('',30) /*make the presentation prettier. */
say indent center(' ',w1) center('sun hour',w2) center('dial hour' ,w3)
say indent center('hour',w1) center('angle' ,w2) center('line angle',w3)
call sep /*add a separator line for the eyeballs*/
 
do h=-6 to 6 /*Okey dokey then, let's get busy. */
select
when abs(h)==12 then hc='midnight' /*above the arctic circle? */
when h<0 then hc=-h 'am' /*convert the hour for human beans. */
when h==0 then hc='noon' /* ... easier to understand now. */
when h>0 then hc=h 'pm' /* ... even more meaningful. */
end /*select*/
hra=15*h-lng+mer
hla=rxCalcArctan(sineLat*rxCalctan(hra,,'D'),,'D')
say indent center(hc,w1) right(format(hra,,1),w2) right(format(hla,,1),w3)
end
call sep
Exit
sep: say indent copies('-',w1) copies('-',w2) copies('-',w3)
Return
::Requires rxMath Library
Output:

Same as for REXX.

Pascal

Program SunDial;
 
Const
pi = 3.14159265358979323846;
dr = pi/180.0;
rd = 180.0/pi;
tab = chr(9);
 
Var
lat, slat, lng, ref : Real;
hla, hra : Real;
h : Integer;
 
function tan(val : Real) : Real;
begin
tan := sin(val)/cos(val)
end;
 
Begin
Write('Enter latitude: '); Read(lat);
Write('Enter longitude: '); Read(lng);
Write('Enter legal meridian: '); Read(ref);
WriteLn;
slat := sin(lat * dr);
WriteLn('sine of latitude: ', slat);
WriteLn('diff longitude: ', lng - ref);
WriteLn('Hour, sun hour angle, dial hour line angle from 6am to 6pm');
for h := -6 to 6 do begin
hra := 15.0 * h;
hra := hra - lng + ref;
hla := arctan(slat * tan(hra * dr)) * rd;
WriteLn('HR= ', h:3, '; ',
tab, ' HRA= ', hra:7:3, '; ',
tab, ' HLA= ', hla:7:3)
end
end.

Perl 6

sub postfix:<°> ($a) { $a * pi / 180 } # degrees to radians
sub postfix:<®> ($a) { $a * 180 / pi } # radians to degrees
 
my $latitude = prompt 'Enter latitude => ';
my $longitude = prompt 'Enter longitude => ';
my $meridian = prompt 'Enter legal meridian => ';
 
my $lat_sin = sin( $latitude° );
say 'Sine of latitude: ', $lat_sin.fmt("%.4f");
say 'Longitude offset: ', my $offset = $meridian - $longitude;
say '=' x 48;
say ' Hour  : Sun hour angle° : Dial hour line angle°';
 
for -6 .. 6 -> $hour {
my $sun_deg = $hour * 15 + $offset;
my $line_deg = atan2( ( sin($sun_deg°) * $lat_sin ), cos($sun_deg°) )®;
printf "%2d %s  %7.3f  %7.3f\n",
($hour + 12) % 12 || 12, ($hour < 0 ?? 'AM' !! 'PM'), $sun_deg, $line_deg;
}
Example output:
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150
Sine of latitude: -0.0863
Longitude offset: 0.5
================================================
 Hour  : Sun hour angle° : Dial hour line angle°
 6 AM      -89.500              84.225
 7 AM      -74.500              17.283
 8 AM      -59.500               8.334
 9 AM      -44.500               4.847
10 AM      -29.500               2.795
11 AM      -14.500               1.278
12 PM        0.500              -0.043
 1 PM       15.500              -1.371
 2 PM       30.500              -2.910
 3 PM       45.500              -5.018
 4 PM       60.500              -8.671
 5 PM       75.500             -18.451
 6 PM       90.500             -95.775

Phix

Copy of Euphoria

atom lat = prompt_number("Enter Latitude: ",{})
atom lng = prompt_number("Enter Longitude: ",{})
atom lm = prompt_number("Enter Legal Meridian: ",{})
puts(1,'\n')
 
atom ha, hla
 
function Deg2Rad(atom degrees)
return degrees * PI / 180
end function
 
function Rad2Deg(atom radians)
return radians * 180 / PI
end function
 
function atan2(atom y, atom x)
return 2*arctan((sqrt(power(x,2)+power(y,2)) - x)/y)
end function
 
atom s_lat = sin(Deg2Rad(lat))
 
puts(1,"Hour, Sun Hour Angle, Dial Hour Line Angle\n")
 
for hour = -6 to 6 do
ha = hour * 15 - lng + lm
atom s = sin(Deg2Rad(ha))
atom c = cos(Deg2Rad(ha))
hla = Rad2Deg(atan2(s_lat*s,c))
printf(1,"%3d  %7.3f  %7.3f\n",{hour+12,ha,hla})
end for
 
{} = wait_key()
Output:
Enter Latitude: -4.95
Enter Longitude: -150.5
Enter Legal Meridian: -150

Hour,  Sun Hour Angle, Dial Hour Line Angle
  6       -89.500           84.225
  7       -74.500           17.283
  8       -59.500            8.334
  9       -44.500            4.847
 10       -29.500            2.795
 11       -14.500            1.278
 12         0.500           -0.043
 13        15.500           -1.371
 14        30.500           -2.910
 15        45.500           -5.018
 16        60.500           -8.671
 17        75.500          -18.451
 18        90.500          -95.775

PicoLisp

Translation of: ALGOL 68
(load "@lib/math.l")
 
(de prompt (Str . Arg)
(prin Str " => ")
(set (car Arg) (in NIL (read))) )
 
(use (Lat Lng Ref)
(prompt "Enter latitude " Lat)
(prompt "Enter longitude " Lng)
(prompt "Enter legal meridian" Ref)
(prinl)
(let Slat (sin (*/ Lat pi 180.0))
(prinl " sine of latitude: " (round Slat))
(prinl " diff longitude: " (round (- Lng Ref)))
(prinl)
(prinl "Hour, sun hour angle, dial hour line angle from 6am to 6pm")
(for H (range -6 6)
(let Hra (- (* 15.0 H) (- Lng Ref))
(let Hla (*/ (atan (*/ Slat (tan (*/ Hra pi 180.0)) 1.0)) 180.0 pi)
(prinl
"HR="
(align 3 H)
"; HRA="
(align 8 (round Hra))
"; HLA="
(align 8 (round Hla)) ) ) ) ) ) )
Output:
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150.          # Don't omit the '.' here

    sine of latitude:   -0.086
    diff longitude:     -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA= -89.500; HLA=  84.225
HR= -5; HRA= -74.500; HLA=  17.283
HR= -4; HRA= -59.500; HLA=   8.334
HR= -3; HRA= -44.500; HLA=   4.847
HR= -2; HRA= -29.500; HLA=   2.795
HR= -1; HRA= -14.500; HLA=   1.278
HR=  0; HRA=   0.500; HLA=  -0.043
HR=  1; HRA=  15.500; HLA=  -1.371
HR=  2; HRA=  30.500; HLA=  -2.910
HR=  3; HRA=  45.500; HLA=  -5.018
HR=  4; HRA=  60.500; HLA=  -8.671
HR=  5; HRA=  75.500; HLA= -18.451
HR=  6; HRA=  90.500; HLA=  84.225

PowerShell

 
function Get-Sundial
{
[CmdletBinding()]
[OutputType([PSCustomObject])]
Param
(
[Parameter(Mandatory=$true)]
[ValidateRange(-90,90)]
[double]
$Latitude,
 
 
[Parameter(Mandatory=$true)]
[ValidateRange(-180,180)]
[double]
$Longitude,
 
 
[Parameter(Mandatory=$true)]
[ValidateRange(-180,180)]
[double]
$Meridian
)
 
[double]$sinLat = [Math]::Sin($Latitude*2*[Math]::PI/360)
 
$object = [PSCustomObject]@{
"Sine of Latitude" = [Math]::Round($sinLat,3)
"Longitude Difference" = $Longitude - $Meridian
}
 
[int[]]$hours = -6..6
 
$hoursArray = foreach ($hour in $hours)
{
[double]$hra = (15 * $hour) - ($Longitude - $Meridian)
[double]$hla = [Math]::Atan($sinLat*[Math]::Tan($hra*2*[Math]::PI/360))*360/(2*[Math]::PI)
[PSCustomObject]@{
"Hour" = "{0,8}" -f ((Get-Date -Hour ($hour + 12) -Minute 0).ToString("t"))
"Sun Hour Angle" = [Math]::Round($hra,3)
"Dial Hour Line Angle" = [Math]::Round($hla,3)
}
}
 
$object | Add-Member -MemberType NoteProperty -Name Hours -Value $hoursArray -PassThru
}
 
$sundial = Get-Sundial -Latitude -4.95 -Longitude -150.5 -Meridian -150
$sundial | Select-Object -Property "Sine of Latitude", "Longitude Difference" | Format-List
$sundial.Hours | Format-Table -AutoSize
 
Output:

Sine of Latitude     : -0.086
Longitude Difference : -0.5




Hour     Sun Hour Angle Dial Hour Line Angle
----     -------------- --------------------
 6:00 AM          -89.5               84.225
 7:00 AM          -74.5               17.283
 8:00 AM          -59.5                8.334
 9:00 AM          -44.5                4.847
10:00 AM          -29.5                2.795
11:00 AM          -14.5                1.278
12:00 PM            0.5               -0.043
 1:00 PM           15.5               -1.371
 2:00 PM           30.5                -2.91
 3:00 PM           45.5               -5.018
 4:00 PM           60.5               -8.671
 5:00 PM           75.5              -18.451
 6:00 PM           90.5               84.225

PureBasic

Translation of: ALGOL 68
If OpenConsole()
Define.f lat, slat, lng, ref
Define.i h
Print("Enter latitude => "): lat=ValF(Input())
Print("Enter longitude => "): lng=ValF(Input())
Print("Enter legal meridian => "): ref=ValF(Input())
PrintN("")
 
slat=Sin(lat*2*#PI/360)
PrintN(" sine of latitude: "+StrF(slat,3))
PrintN(" diff longitude: "+StrF((lng-ref),3)+#CRLF$)
PrintN("Hour, sun hour angle, dial hour line angle from 6am to 6pm")
 
For h=-6 To 6
Define.f hra, hla
hra=15*h
hra=hra-(lng-ref)
hla=ATan(slat*Tan(hra*2*#PI/360))*360/(2*#PI)
PrintN("HR="+RSet(Str(h),3)+"; HRA="+RSet(StrF(hra,3),7)+"; HLA="+RSet(StrF(hla,3),7))
Next
 
EndIf
Output:
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150

    sine of latitude:   -0.086
    diff longitude:     -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA=-89.500; HLA= 84.225
HR= -5; HRA=-74.500; HLA= 17.283
HR= -4; HRA=-59.500; HLA=  8.334
HR= -3; HRA=-44.500; HLA=  4.847
HR= -2; HRA=-29.500; HLA=  2.795
HR= -1; HRA=-14.500; HLA=  1.278
HR=  0; HRA=  0.500; HLA= -0.043
HR=  1; HRA= 15.500; HLA= -1.371
HR=  2; HRA= 30.500; HLA= -2.910
HR=  3; HRA= 45.500; HLA= -5.018
HR=  4; HRA= 60.500; HLA= -8.671
HR=  5; HRA= 75.500; HLA=-18.451
HR=  6; HRA= 90.500; HLA= 84.225

Python

Translation of: ALGOL 68
from __future__ import print_function
import math
try: raw_input
except: raw_input = input
 
lat = float(raw_input("Enter latitude => "))
lng = float(raw_input("Enter longitude => "))
ref = float(raw_input("Enter legal meridian => "))
print()
 
slat = math.sin(math.radians(lat))
print(" sine of latitude:  %.3f" % slat)
print(" diff longitude:  %.3f" % (lng-ref))
print()
print("Hour, sun hour angle, dial hour line angle from 6am to 6pm")
 
for h in range(-6, 7):
hra = 15 * h
hra -= lng - ref
hla = math.degrees(math.atan(slat * math.tan(math.radians(hra))))
print("HR=%3d; HRA=%7.3f; HLA=%7.3f" % (h, hra, hla))
Output:
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150

    sine of latitude:   -0.086
    diff longitude:     -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA=-89.500; HLA= 84.225
HR= -5; HRA=-74.500; HLA= 17.283
HR= -4; HRA=-59.500; HLA=  8.334
HR= -3; HRA=-44.500; HLA=  4.847
HR= -2; HRA=-29.500; HLA=  2.795
HR= -1; HRA=-14.500; HLA=  1.278
HR=  0; HRA=  0.500; HLA= -0.043
HR=  1; HRA= 15.500; HLA= -1.371
HR=  2; HRA= 30.500; HLA= -2.910
HR=  3; HRA= 45.500; HLA= -5.018
HR=  4; HRA= 60.500; HLA= -8.671
HR=  5; HRA= 75.500; HLA=-18.451
HR=  6; HRA= 90.500; HLA= 84.225

Racket

Translation of: ALGOL 68

I must say, I'm a bit astonished by the fact that no one is bothered by the atan problem (HLA=84.225) that appears in the ALGOL 68 solution and all of the ones derived from it. Composing tan & atan produces the identity only in the range [-90,90], and you have to correct for angles outside of this.

Also, I apologize for the length; I added quite a bit of commenting, and I peeled things out into functions so I could test them. Hopefully, the result--though longer--is also more readable.

#lang racket
 
;; print the table for a given latitude and longitude-offset,
;; given in degrees
(define (print-table lat long-offset)
 ;; print the table header
(display
(~a " sine of latitude: "
(~r (sin (deg->rad lat)) #:precision '(= 3))
"\n"
" diff longitude: "
(~r long-offset #:precision '(= 3))
"\n\nHour, sun hour angle, dial hour line angle "
"from 6am to 6pm\n"))
 ;; print the table
(for ([h (in-range -6 7)])
(define hra (- (* 15 h) long-offset))
(define hla (to-hla lat hra))
(display (~a "HR="(pad-to 3 (~a h))"; "
"HRA="(pad-to 7 (~r hra #:precision '(= 3)))"; "
"HLA="(pad-to 7 (~r hla #:precision '(= 3)))"\n"))))
 
 
;; compute the angle on the gnomon corresponding to a
;; given angle of the sun (angles given and returned in degrees)
(define (to-hla lat ang)
(define lat-sign (cond [(< lat 0) -1] [else 1]))
 ;; move to the right quadrant for
 ;; angles outside [-90,90]
(define correction (* (cond [(< ang -90) -180]
[(> ang 90) 180]
[else 0])
lat-sign))
(+ (rad->deg (atan (* (sin (deg->rad lat))
(tan (deg->rad ang)))))
correction))
 
;; write the prompt, return the entered number
(define (prompt->num p)
(printf "~a" p)
(string->number (read-line)))
 
;; translate degrees to radians
(define (deg->rad d) (* 2 pi (/ d 360)))
 
;; translate radians to degrees
(define (rad->deg r) (* 360 (/ r (* 2 pi))))
 
;; add spaces to reach given length
(define (pad-to cols str)
(define spaces-needed (max 0 (- cols (string-length str))))
(string-append
(list->string (for/list ([i spaces-needed]) #\space))
str))
 
 
;; INPUT PARAMETERS, PRINT TABLE:
(define lat (prompt->num "Enter latitude => "))
(define lng (prompt->num "Enter longitude => "))
(define ref (prompt->num "Enter legal meridian => "))
 
(print-table lat (- lng ref))
 
;; test cases for angle conversion
(require rackunit)
(check < (to-hla 30 89) 90)
(check-= (to-hla 30 90) 90 1e-5)
(check > (to-hla 30 91) 90)
(check > (to-hla 30 -89) -90)
(check-= (to-hla 30 90) 90 1e-5)
(check < (to-hla 30 -91) -90)
(check < (to-hla -30 -89) 90)
(check-= (to-hla -30 -90) 90 1e-5)
(check > (to-hla -30 -91) 90)
(check > (to-hla -30 89) -90)
(check-= (to-hla -30 90) -90 1e-5)
(check < (to-hla -30 91) -90)
 
Output:
Welcome to DrRacket, version 5.3.3.5--2013-02-20(5eddac74/d) [3m].
Language: racket; memory limit: 512 MB.
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150
    sine of latitude: -0.086
    diff longitude:   -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA=-89.500; HLA= 84.225
HR= -5; HRA=-74.500; HLA= 17.283
HR= -4; HRA=-59.500; HLA=  8.334
HR= -3; HRA=-44.500; HLA=  4.847
HR= -2; HRA=-29.500; HLA=  2.795
HR= -1; HRA=-14.500; HLA=  1.278
HR=  0; HRA=  0.500; HLA= -0.043
HR=  1; HRA= 15.500; HLA= -1.371
HR=  2; HRA= 30.500; HLA= -2.910
HR=  3; HRA= 45.500; HLA= -5.018
HR=  4; HRA= 60.500; HLA= -8.671
HR=  5; HRA= 75.500; HLA=-18.451
HR=  6; HRA= 90.500; HLA=-95.775
> 

REXX

REXX doesn't have the usual trig functions, nor for that matter, a SQRT (square root) function, so these as well as PI were added to this program.

No attempt was made to explain the inner workings of the trigonometric functions.

/*REXX program displays:   hour,  sun hour angle,  dial hour line angle,  6am ───► 6pm. */
numeric digits 60 /*better digit overkill then underkill.*/
parse arg lat lng mer . /*obtain optional arguments from the CL*/
/* ┌───────────◄ None specified? Then use the default*/
/* │ of Jules Verne's Lincoln Island, */
/* ↓ aka Ernest Legouve Reed. */
if lat=='' | lat=="," then lat= -4.95 /*Not specified? Then use the default.*/
if lng=='' | lng=="," then lng= -150.5 /* " " " " " " */
if mer=='' | mer=="," then mer= -150 /* " " " " " " */
L=max(length(lat), length(lng), length(mer) ) /*find maximum length of three numbers.*/
say ' latitude:' right(lat, L) /*display the latitude to the terminal*/
say ' longitude:' right(lng, L) /* " " longitude " " " */
say ' legal meridian:' right(mer, L) /* " legal meridian " " " */
sineLat=sin( d2r(lat) ) /*calculate sine of (radian) latitude. */
w1=max(length('hour') , length("midnight")) + 2 /*compute the max hour width. */
w2=max(length('sun hour') , length("angle")) + 2 /* " " " angle " */
w3=max(length('dial hour'), length("line angle")) + 2 /* " " " lineº " */
indent=left('', 30) /*make the presentation a bit prettier.*/
say indent center(' ',w1) center("sun hour",w2) center('dial hour' ,w3)
say indent center('hour',w1) center("angle" ,w2) center('line angle',w3)
call sep /*add a separator line for the eyeballs*/
do h=-6 to 6 /*Okey dokey then, now let's get busy.*/
select
when abs(h)==12 then hc='midnight' /*Holy smokes! Above the arctic circle.*/
when h <0 then hc=-h 'am' /*convert da hour for human beans (sic)*/
when h==0 then hc='noon' /* ··· easier to understand now. */
when h >0 then hc=h 'pm' /* ··· even more meaningful. */
end /*select*/
hra=15 * h - lng + mer /*calculate sun hour angle (in degrees)*/
hla=r2d(Atan(sineLat * tan( d2r(hra)))) /*this is the heavy lifting calculation*/
say indent center(hc, w1) right(format(hra, ,1), w2) right(format(hla, ,1), w3)
end /*h*/
call sep
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078; return pi
d2d: return arg(1) // 360 /*normalize degrees ──► a unit circle. */
d2r: return r2r( arg(1) * pi() / 180) /*convert degrees ──► radians. */
r2d: return d2d( (arg(1) * 180 / pi() ) ) /*convert radians ──► degrees. */
r2r: return arg(1) //(pi() * 2) /*normalize radians ──► a unit circle. */
sep: say indent copies('═', w1) copies("═",w2) copies('═',w3); return
tan: procedure; parse arg x; _=cos(x); if _=0 then call tanErr; return sin(x)/_
tellErr: say; say '*** error ***'; say; say arg(1); say; exit 13
AsinErr: call tellErr 'Asin(x), X must be in the range of -1 ──► +1, X=' x
AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X=' x
tanErr: call tellErr 'tan(' || x") causes division by zero, X=" x
Acos: procedure; arg x; if x<-1 | x>1 then call AcosErr; return .5 * pi() - Asin(x)
/*──────────────────────────────────────────────────────────────────────────────────────*/
Asin: procedure; parse arg x; if x<-1 | x>1 then call AsinErr; s=x*x
if abs(x)>=sqrt(2)*.4 then return sign(x) * Acos(sqrt(1-s)); z=x; o=x; p=z
do j=2 by 2; o=o*s*(j-1)/j; z=z+o/(j+1); if z=p then leave; p=z; end; return z
/*──────────────────────────────────────────────────────────────────────────────────────*/
Atan: procedure; arg x; if abs(x)=1 then return pi() / 4 * sign(x)
return Asin(x / sqrt(1 + x*x) )
/*──────────────────────────────────────────────────────────────────────────────────────*/
sin: procedure; arg x; x=r2r(x); numeric fuzz min(5, digits() - 3)
if abs(x)=pi() then return 0; return .sinCos(x,x,1)
/*──────────────────────────────────────────────────────────────────────────────────────*/
cos: procedure; parse arg x; x=r2r(x); a=abs(x); hpi=pi*.5
numeric fuzz min(6, digits() - 3); if a=pi() then return -1
if a=hpi | a=hpi*3 then return 0; if a=pi()/3 then return .5
if a=pi() * 2 / 3 then return -.5; return .sinCos(1,1,-1)
/*──────────────────────────────────────────────────────────────────────────────────────*/
.sinCos: parse arg z,_,i; x=x*x; p=z
do k=2 by 2; _= -_ * x / (k*(k+i)); z=z+_; if z=p then leave; p=z; end; return z
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); numeric digits; h=d+6
m.=9; numeric form; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_ % 2
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g
output   when using the default inputs:
       latitude:  -4.95
      longitude: -150.5
 legal meridian:   -150
                                           sun hour   dial hour
                                  hour      angle     line angle
                               ══════════ ══════════ ════════════
                                  6 am         -89.5         84.2
                                  5 am         -74.5         17.3
                                  4 am         -59.5          8.3
                                  3 am         -44.5          4.8
                                  2 am         -29.5          2.8
                                  1 am         -14.5          1.3
                                  noon           0.5          0.0
                                  1 pm          15.5         -1.4
                                  2 pm          30.5         -2.9
                                  3 pm          45.5         -5.0
                                  4 pm          60.5         -8.7
                                  5 pm          75.5        -18.5
                                  6 pm          90.5         84.2
                               ══════════ ══════════ ════════════

Ruby

Translation of: ALGOL 68
Translation of: Python
include Math
DtoR = PI/180
 
print 'Enter latitude: '
lat = Float( gets )
print 'Enter longitude: '
lng = Float( gets )
print 'Enter legal meridian: '
ref = Float( gets )
puts
 
slat = sin( lat * DtoR )
 
puts " sine of latitude:  %.3f"% slat
puts " diff longitude:  %.3f"% (lng-ref)
puts
puts 'Hour, sun hour angle, dial hour line angle from 6am to 6pm'
-6.upto(6) do |h|
hra = 15 * h
hra -= lng - ref
hla = atan( slat * tan( hra * DtoR ))/ DtoR
puts "HR =%3d; HRA =%7.3f; HLA =%7.3f" % [h, hra, hla]
end
Output:
Enter latitude: -4.95
Enter longitude: -150.5
Enter legal meridian: -150

    sine of latitude:  -0.086
    diff longitude:    -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR = -6; HRA =-89.500; HLA = 84.225
HR = -5; HRA =-74.500; HLA = 17.283
HR = -4; HRA =-59.500; HLA =  8.334
HR = -3; HRA =-44.500; HLA =  4.847
HR = -2; HRA =-29.500; HLA =  2.795
HR = -1; HRA =-14.500; HLA =  1.278
HR =  0; HRA =  0.500; HLA = -0.043
HR =  1; HRA = 15.500; HLA = -1.371
HR =  2; HRA = 30.500; HLA = -2.910
HR =  3; HRA = 45.500; HLA = -5.018
HR =  4; HRA = 60.500; HLA = -8.671
HR =  5; HRA = 75.500; HLA =-18.451
HR =  6; HRA = 90.500; HLA = 84.225

Run BASIC

global pi
pi = 22 / 7
 
print "Enter latitude (degrees)  : "; :input latitude ' -4.95
print "Enter longitude (degrees)  : "; :input longitude ' -150.5
print "Enter legal meridian (degrees): "; :input meridian ' -150.0
 
print
print "Time Sun hour angle Dial hour line angle"
 
for hour = 6 TO 18
hra = (15 * hour) - longitude + meridian -180
hla =rad2deg( atn( sin( deg2rad( latitude)) *tan( deg2rad( hra))))
if abs( hra) >90 then hla =hla +180 *sgn( hra *latitude)
print using( "##", hour);" ";using("####.##", hra);" ";using("####.###", hla)
next hour
 
function rad2deg( theta)
rad2deg =theta *180 /pi
end function
 
function deg2rad( theta)
deg2rad =theta *pi /180
end function
 
function sgn( x)
if x >0 then sgn =1 else sgn =-1
end function
end
Output:
Enter latitude: -4.95
Enter longitude: -150.5
Enter legal meridian: -150

Time     Sun hour angle   Dial hour line angle
 6          -89.50           84.606
 7          -74.50           17.316
 8          -59.50            8.342
 9          -44.50            4.850
10          -29.50            2.796
11          -14.50            1.279
12            0.50           -0.043
13           15.50           -1.371
14           30.50           -2.911
15           45.50           -5.021
16           60.50           -8.680
17           75.50          -18.488
18           90.50          -96.224

Sather

class MAIN is
 
getvalue(s:STR):FLT is
#OUT + s + ": ";
return #FLT(#IN.get_line.str);
end;
 
dr(a:FLT):FLT is
return a * FLT::pi / 180.0;
end;
 
rd(a:FLT):FLT is
return a * 180.0 / FLT::pi;
end;
 
main is
lat ::= getvalue("Enter latitude");
lng ::= getvalue("Enter longitude");
ref ::= getvalue("Enter legal meridian");
#OUT + "\n";
slat ::= dr(lat).sin;
#OUT + "sine of latitude: " + #FMT("%.3f\n", slat);
#OUT + "diff longitude: " + #FMT("%.3f\n\n", lng - ref);
#OUT + "Hour, sun hour angle, dial hour line angle from 6am to 6pm\n";
loop h ::= (-6).upto!(6);
hra ::= 15.0 * h.flt;
hra := hra - lng + ref;
hla ::= rd((dr(hra).tan * slat).atan);
#OUT + #FMT("HR = %3d; \t HRA=%7.3f; \t HLA= %7.3f\n", h, hra, hla);
end;
end;
end;

Seed7

$ include "seed7_05.s7i";
include "float.s7i";
include "math.s7i";
 
const float: radianToDegrees is 57.295779513082320876798154814114;
const float: degreesToRadian is 0.017453292519943295769236907684883;
 
const proc: main is func
local
var float: lat is 0.0;
var float: slat is 0.0;
var float: lng is 0.0;
var float: meridian is 0.0;
var float: hla is 0.0;
var float: hra is 0.0;
var integer: h is 0;
begin
write("Enter latitude: ");
readln(lat);
write("Enter longitude: ");
readln(lng);
write("Enter legal meridian: ");
readln(meridian);
writeln;
slat := sin(degreesToRadian * lat);
writeln("sine of latitude: " <& slat digits 3);
writeln("diff longitude: " <& lng - meridian digits 3);
writeln;
writeln("Hour, sun hour angle, dial hour line angle from 6am to 6pm");
for h range -6 to 6 do
hra := 15.0 * flt(h);
hra := hra - lng + meridian;
hla := radianToDegrees * atan(slat * tan(degreesToRadian * hra));
writeln("HR= " <& h lpad 2 <& "; HRA= " <& hra digits 3 lpad 7 <&
"; HLA= " <& hla digits 3 lpad 7);
end for;
end func;
Output:
Enter latitude: -4.95
Enter longitude: -150.5
Enter legal meridian: -150

sine of latitude: -0.086
diff longitude: -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA= -89.500; HLA=  84.225
HR= -5; HRA= -74.500; HLA=  17.283
HR= -4; HRA= -59.500; HLA=   8.334
HR= -3; HRA= -44.500; HLA=   4.847
HR= -2; HRA= -29.500; HLA=   2.795
HR= -1; HRA= -14.500; HLA=   1.278
HR=  0; HRA=   0.500; HLA=  -0.043
HR=  1; HRA=  15.500; HLA=  -1.371
HR=  2; HRA=  30.500; HLA=  -2.910
HR=  3; HRA=  45.500; HLA=  -5.018
HR=  4; HRA=  60.500; HLA=  -8.671
HR=  5; HRA=  75.500; HLA= -18.451
HR=  6; HRA=  90.500; HLA=  84.225

Sidef

Translation of: Perl 6
var latitude  = read('Enter latitude       => ', Number)
var longitude = read('Enter longitude => ', Number)
var meridian = read('Enter legal meridian => ', Number)
 
var lat_sin = latitude.deg2rad.sin
var offset = (meridian - longitude)
 
say('Sine of latitude: ', "%.4f" % lat_sin)
say('Longitude offset: ', offset)
say('=' * 48)
say(' Hour  : Sun hour angle° : Dial hour line angle°')
 
for hour (-6 .. 6) {
var sun_deg = (15*hour + offset)
var line_deg = rad2deg(
atan2(
sin(deg2rad(sun_deg)) * lat_sin,
cos(deg2rad(sun_deg))
)
)
printf("%2d %s  %7.3f  %7.3f\n",
(hour + 12) % 12 || 12, (hour < 0 ? 'AM' : 'PM'), sun_deg, line_deg)
}
Output:
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150
Sine of latitude: -0.0863
Longitude offset: 0.5
================================================
 Hour  : Sun hour angle° : Dial hour line angle°
 6 AM      -89.500              84.225
 7 AM      -74.500              17.283
 8 AM      -59.500               8.334
 9 AM      -44.500               4.847
10 AM      -29.500               2.795
11 AM      -14.500               1.278
12 PM        0.500              -0.043
 1 PM       15.500              -1.371
 2 PM       30.500              -2.910
 3 PM       45.500              -5.018
 4 PM       60.500              -8.671
 5 PM       75.500             -18.451
 6 PM       90.500             -95.775

Smalltalk

Works with: GNU Smalltalk
|lat slat lng ref hra hla pi|
pi := 1 arcTan * 4.
'Enter latitude: ' display. lat := stdin nextLine asNumber.
'Enter longitude: ' display. lng := stdin nextLine asNumber.
'Enter legal meridian: ' display. ref := stdin nextLine asNumber.
slat := lat degreesToRadians sin.
('sine of latitude: %1' % { slat }) displayNl.
('diff longitude: %1' % { lng - ref }) displayNl.
 
'Hour, sun hour angle, dial hour line angle from 6am to 6pm' displayNl.
 
-6 to: 6 do: [ :h |
hra := 15.0 * h.
hra := hra - lng + ref.
hla := (hra degreesToRadians tan * slat) arcTan radiansToDegrees.
('HR= %1;  %4 HRA=%2;  %4 HLA= %3' % { h. hra. hla. $<9> }) displayNl.
]

Tcl

Translation of: ALGOL 68
set PI 3.1415927
fconfigure stdout -buffering none
puts -nonewline "Enter latitude => "; gets stdin lat
puts -nonewline "Enter longitude => "; gets stdin lng
puts -nonewline "Enter legal meridian => "; gets stdin ref
puts ""
 
set slat [expr {sin($lat*$PI/180)}]
puts [format " sine of latitude:  %8g" $slat]
puts [format " diff longitude:  %3.3f" [expr {$lng - $ref}]]
puts ""
puts "Hour, sun hour angle, dial hour line angle from 6am to 6pm"
 
for {set h -6} {$h<=6} {incr h} {
set hra [expr {15.0 * $h}]; # hour angle is 15 times the hour #
set hra [expr {$hra-$lng+$ref}]; # but correct for longitude difference #
set hla [expr {atan($slat * tan($hra*$PI/180)) * 180/$PI}]
puts [format "HR=%+3d; HRA=%+8.3f; HLA=%+8.3f" $h $hra $hla]
}
Sample output:
Enter latitude       => -4.95
Enter longitude      => -150.5
Enter legal meridian => -150

    sine of latitude:   -0.0862864
    diff longitude:     -0.500

Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA= -89.500; HLA= +84.225
HR= -5; HRA= -74.500; HLA= +17.283
HR= -4; HRA= -59.500; HLA=  +8.334
HR= -3; HRA= -44.500; HLA=  +4.847
HR= -2; HRA= -29.500; HLA=  +2.795
HR= -1; HRA= -14.500; HLA=  +1.278
HR= +0; HRA=  +0.500; HLA=  -0.043
HR= +1; HRA= +15.500; HLA=  -1.371
HR= +2; HRA= +30.500; HLA=  -2.910
HR= +3; HRA= +45.500; HLA=  -5.018
HR= +4; HRA= +60.500; HLA=  -8.671
HR= +5; HRA= +75.500; HLA= -18.451
HR= +6; HRA= +90.500; HLA= +84.225

x86 Assembly

Works with: nasm
Library: libc

It must be linked with the C standard library and startup code.

	global main
extern printf, scanf
 
section .text
 
getvalue:
push edx
push eax
call printf
add esp, 4
push in_ft
call scanf
add esp, 8
ret
 
st0dr:
fld qword [drfact]
fmul
ret
 
 
main:
lea eax, [lat_t]
lea edx, [lat]
call getvalue
lea eax, [lng_t]
lea edx, [lng]
call getvalue
lea eax, [ref_t]
lea edx, [ref]
call getvalue
 
push newline
call printf
add esp, 4
 
fld qword [lat]
call st0dr
fsin
fst qword [slat]
 
sub esp, 8
fstp qword [esp]
push sin_ft
call printf
add esp, 12
 
fld qword [lng]
fld qword [ref]
fsubr st0, st1
sub esp, 8
fstp qword [esp]
push diff_ft
call printf
add esp, 12
 
push tab_t
call printf
add esp, 4
 
mov ecx, -6
.loop:
cmp ecx, 6
jg .endloop
 
push ecx
fild dword [esp]
fld qword [xv]
fmulp
fld qword [lng]
fsubp
fld qword [ref]
faddp
pop ecx
 
sub esp, 20
mov dword [esp], ecx
fst qword [esp+4]
 
call st0dr
 
fptan
fxch
fld qword [slat]
fmulp
fxch
fpatan
 
fld qword [rdinv]
fmul
 
fstp qword [esp+12]
 
push o_ft
call printf
mov ecx, [esp+4]
add esp, 24
 
inc ecx
jmp .loop
.endloop:
 
xor eax, eax
ret
 
 
section .data
 
lat: dq 0.0
lng: dq 0.0
ref: dq 0.0
xv: dq 15.0
slat: dq 0.0
drfact: dq 0.01745329251994329576
rdinv: dq 57.29577951308232090712
 
 
section .rodata
 
lat_t: db "Enter latitude: ", 0
lng_t: db "Enter longitude: ", 0
ref_t: db "Enter legal meridian: ", 0
 
in_ft: db "%lf", 0
newline:
db 10, 0
 
sin_ft:
db "sine of latitude: %.3f", 10, 0
diff_ft:
db "diff longitude: %.3f", 10, 10, 0
 
tab_t:
db "Hour, sun hour angle, dial hour line angle from 6am to 6pm", 10, 0
 
o_ft:
db "HR= %3d; ",9," HRA=%7.3f; ",9," HLA= %7.3f", 10, 0

XPL0

inc  c:\cxpl\codes;
def Pi = 3.14159265358979323846,
Deg2Rad = Pi/180.0,
Rad2Deg = 180.0/Pi,
Tab = $09;
real Lat, SinLat, Long, Mer;
real HA, HLA; \hour angle and hour line angle
int H, T; \hour, time
[Text(0, "Latitude: "); Lat:= RlIn(0);
Text(0, "Longitude: "); Long:= RlIn(0);
Text(0, "Legal meridian: "); Mer:= RlIn(0);
Text(0, "
Hour Sun hour angle Dial hour line angle
");
Format(4, 3);
SinLat:= Sin(Lat*Deg2Rad);
for H:= -6 to 6 do
[HA:= float(15 * H); \hour angle is 15 times the hour
HA:= HA - (Long-Mer); \ but corrected for longitude difference
HLA:= ATan2( SinLat * Sin(HA*Deg2Rad), Cos(HA*Deg2Rad) ) * Rad2Deg;
T:= H+12; if T>12 then T:= T-12;
if T<10 then ChOut(0, ^ ); IntOut(0, T);
Text(0, if H>=0 then "pm " else "am ");
RlOut(0, HA); ChOut(0, Tab); RlOut(0, HLA); CrLf(0);
];
]
Output:
Latitude:       -4.95
Longitude:      -150.5
Legal meridian: -150

Hour  Sun hour angle   Dial hour line angle
 6am     -89.500          84.225
 7am     -74.500          17.283
 8am     -59.500           8.334
 9am     -44.500           4.847
10am     -29.500           2.795
11am     -14.500           1.278
12pm       0.500          -0.043
 1pm      15.500          -1.371
 2pm      30.500          -2.910
 3pm      45.500          -5.018
 4pm      60.500          -8.671
 5pm      75.500         -18.451
 6pm      90.500         -95.775

zkl

Translation of: F#
//(degree measure)*Degrees => Radian measure
//(radian measure)/Degrees => Degree measure
const pi=(0.0).pi, toDeg=(0.0).pi/180;
 
latitude :=ask(0,"Enter latitude: ").toFloat();
longitude:=ask(1,"Enter longitude: ").toFloat();
meridian :=ask(2,"Enter legal meridian: ").toFloat();
 
sineLatitude:=(latitude * toDeg).sin();
Console.writeln();
Console.writeln("Sine of latitude: ",sineLatitude);
Console.writeln("Difference of Longitudes (given longitude - meridian): ",longitude-meridian);
Console.writeln();
 
println("Numbers from 6 AM to 6 PM: ");
println("Hour\t\tSun hour angle\t Dial hour line angle");
 
foreach hour in ([-6..6]){
clockHour:=( if(hour < 0) "%sAM".fmt(hour.abs()) else "%sPM".fmt(hour) );
shr  :=15.0*hour - (longitude - meridian);
dhla  :=(sineLatitude*(shr*toDeg).tan()).atan()/toDeg;
Console.writeln("%s\t\t%5.1f\t\t%+7.3f".fmt(clockHour,shr,dhla));
}
Output:
$ zkl bbb -4.95 -150.5 -150

Sine of latitude: -0.0862864
Difference of Longitudes (given longitude - meridian): -0.5

Numbers from 6 AM to 6 PM: 
Hour		Sun hour angle	 Dial hour line angle
6AM		-89.5		+84.225
5AM		-74.5		+17.283
4AM		-59.5		 +8.334
3AM		-44.5		 +4.847
2AM		-29.5		 +2.795
1AM		-14.5		 +1.278
0PM		  0.5		 -0.043
1PM		 15.5		 -1.371
2PM		 30.5		 -2.910
3PM		 45.5		 -5.018
4PM		 60.5		 -8.671
5PM		 75.5		-18.451
6PM		 90.5		+84.225
Output:
$ zkl bbb -4.95 
Enter longitude: -150.5
Enter legal meridian: -150
<as above>

ZX Spectrum Basic

Translation of: ERRE
10 DEF FN r(x)=x*PI/180
20 DEF FN d(x)=x*180/PI
30 INPUT "Enter latitude (degrees): ";latitude
40 INPUT "Enter longitude (degrees): ";longitude
50 INPUT "Enter legal meridian (degrees): ";meridian
60 PRINT "Latitude: ";latitude
70 PRINT "Longitude:";longitude
80 PRINT "Legal meridian: ";meridian
90 PRINT '" Sun Dial"
100 PRINT "Time hour angle hour line ang."
110 PRINT "________________________________"
120 FOR h=6 TO 18
130 LET hra=15*h-longitude+meridian-180
140 LET hla=FN d(ATN (SIN (FN r(latitude))*TAN (FN r(hra))))
150 IF ABS (hra)>90 THEN LET hla=hla+180*SGN (hra*latitude)
160 PRINT h;" ";hra;" ";hla
170 NEXT h