Horizontal sundial calculations
From Rosetta Code
You are encouraged to solve this task according to the task description, using any language you may know.
A program that calculates the hour, sun hour angle, dial hour line angle from 6am to 6pm for an operator entered location.
As the 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.
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. 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.
[edit] Ada
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
[edit] ALGOL 68
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
[edit] AutoHotkey
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
[edit] 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
[edit] C
#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;
}
[edit] 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);
}
}
}
}
[edit] D
import std.stdio, std.math, std.conv, std.string;
double radians(double x) { return x * (PI/180); }
double degrees(double x) { return x / (PI/180); }
T input(T)(string msg) {
write(msg);
return to!T(readln().strip());
}
void main() {
double lat = input!double("Enter latitude => ");
double lng = input!double("Enter longitude => ");
double lme = input!double("Enter legal meridian => ");
writeln();
double slat = sin(radians(lat));
writefln(" sine of latitude: %.3f", slat);
writefln(" diff longitude: %.3f", lng-lme);
writeln();
writeln("Hour, sun hour angle, dial hour line angle from 6am to 6pm");
foreach (h; -6 .. 7) {
double hra = 15 * h;
hra -= (lng - lme);
double hla = degrees(atan(slat * tan(radians(hra))));
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
[edit] DWScript
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
[edit] F#
// 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...
[edit] 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- ( sin[latitude] longitude )
cr ." Hour : HourAngle , DialAngle"
7 -6 do
cr i . ." : "
fover fover fnegate i 15 * s>d d>f f+
fdup f. ." , "
>radians ftan f* fatan >degrees f.
loop fdrop fdrop ;
[edit] Fortran
with -fbackslash optionprogram 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
[edit] Go
package main
import (
"bufio"
"fmt"
"math"
"os"
"strconv"
"strings"
)
func getnum(prompt string) (r float64) {
in := bufio.NewReader(os.Stdin)
for {
fmt.Print(prompt)
s, err := in.ReadString('\n')
if err != nil {
fmt.Println(err)
os.Exit(-1)
}
r, err = strconv.ParseFloat(strings.TrimSpace(s), 64)
if err == nil {
break
}
fmt.Println(err)
}
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
hla := math.Atan(slat*math.Tan(hra*math.Pi/180)) * 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 84.225
[edit] 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
[edit] 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
[edit] 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 │-89.500 │ 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 │
└──────┴────────────────┴────────────────────┘
[edit] Java
(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
[edit] 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 "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
[edit] Logo
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)
]
[edit] OCaml
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
[edit] 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] );
[edit] 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.
[edit] 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
[edit] PicoLisp
(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
[edit] PureBasic
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
[edit] Python
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
[edit] Racket
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
>
[edit] 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 shows hour/sun hour angle/dial hour line angle, 6am─►6pm.*/
numeric digits 60 /*better overkill then underkill. */
parse arg lat lng mer . /*get the arguments (if any). */
/*If none specified, then use the */
/*default of Jules Verne's Lincoln*/
/*Island, aka Ernest Legouve Reef.*/
if lat=='' | lat==',' then lat=-4.95 /*No argument? Then use default.*/
if lng=='' | lng==',' then lng=-150.5 /*No argument? Then use default.*/
if mer=='' | mer==',' then mer=-150 /*No argument? Then use default.*/
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=sin(d2r(lat))
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 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 separator line for eyeballs*/
do h=-6 to 6 /*Okey dokey then, let's get busy*/
select
when abs(h)==12 then hc='midnight' /*above artic circle ? */
when h<0 then hc=-h 'am' /*convert hour for human beans. */
when h==0 then hc='noon' /* ... easy to understand now. */
when h>0 then hc=h 'pm' /* ... even meaningfull. */
end /*select*/
hra=15*h-lng+mer
hla=r2d(Atan(sineLat*tan(d2r(hra))))
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 done.*/
/*──────────────────────────────────subroutines─────────────────────────*/
/*looking at subroutines is like looking at saugages being made. Don't.*/
sep: say indent copies('═',w1) copies('═',w2) copies('═',w3); return
pi: return, /*a bit of overkill, but hey !! */
3.1415926535897932384626433832795028841971693993751058209749445923078164062862
/*Note: the real PI subroutine returns PI's accuracy that */
/*matches the current NUMERIC DIGITS, up to 1 million digits.*/
/*John Machin's formula is used for calculating more digits. */
d2d: return arg(1)//360 /*normalize degrees►1 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)//(2*pi()) /*normalize radians►1 unit circle*/
tan: procedure; arg x; _=cos(x); if _=0 then call tanErr; return sin(x)/_
tanErr: call tellErr 'tan('||x") causes division by zero, X="||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
sqrtErr: call tellErr "sqrt(x), X can't be negative, X="||x
AcosErr: call tellErr 'Acos(x), X must be in the range of -1 ──► +1, X='||x
Acos: procedure; arg x; if x<-1|x>1 then call AcosErr; return .5*pi()-Asin(x)
Atan: procedure; arg x; if abs(x)=1 then return pi()/4*sign(x)
return Asin(x/sqrt(1+x**2))
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; arg x; x=r2r(x); a=abs(x); numeric fuzz min(9,digits()-9)
if a=pi() then return -1; if a=pi()/2 | a=2*pi() then return 0
if a=pi()/3 then return .5; if a=2*pi()/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
Asin: procedure; parse arg x; if x<-1 | x>1 then call AsinErr; s=x*x
if abs(x)>=.7 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
sqrt: procedure; parse arg x; if x=0 then return 0;d=digits();numeric digits 11
g=.sqrtGuess(); do j=0 while p>9; m.j=p; p=p%2+1; end
do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k; g=.5*(g+x/g); end
numeric digits d; return g/1
.sqrtGuess: if x<0 then call sqrtErr; numeric form scientific; m.=11; p=d+d%4+2
parse value format(x,2,1,,0) 'E0' with g 'E' _ .; return g*.5'E'_%2
- Output:
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
══════════ ══════════ ════════════
[edit] Ruby
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
[edit] 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 "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
[edit] 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;
[edit] 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
[edit] 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. $<9> }) displayNl.
]
[edit] Tcl
set PI 3.1415927
fconfigure stdout -buffering none
puts -nonewline "Enter latitude => "; gets stdin lat
puts -nonewline "Enter longitude => "; gets stdin lng
puts -nonewline "Enter legal meridian => "; gets stdin ref
puts ""
set slat [expr {sin($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
[edit] x86 Assembly
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
