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.
11l
V lat = Float(input(‘Enter latitude => ’))
V lng = Float(input(‘Enter longitude => ’))
V ref = Float(input(‘Enter legal meridian => ’))
print()
V slat = sin(radians(lat))
print(‘ sine of latitude: #.3’.format(slat))
print(‘ diff longitude: #.3’.format(lng - ref))
print()
print(‘Hour, sun hour angle, dial hour line angle from 6am to 6pm’)
L(h) -6 .. 6
V hra = 15.0 * h
hra -= lng - ref
V hla = degrees(atan(slat * tan(radians(hra))))
print(‘HR=#3; HRA=#3.3; HLA=#3.3’.format(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
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
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
Arturo
degToRad: function [deg]-> deg * pi // 180
radToDeg: function [rad]-> rad * 180 // pi
lat: to :floating input "Enter latitude => "
lng: to :floating input "Enter longitude => "
med: to :floating input "Enter legal meridian => "
print ""
slat: sin degToRad lat
print " sine of latitude: " ++ to :string .format:".3f" slat
print " diff longitude: " ++ to :string .format:".3f" lng-med
print ""
print "Hour, sun hour angle, dial hour line angle from 6am to 6pm"
loop (neg 6)..6 'h [
hra: med + (to :floating 15*h) - lng
hla: radToDeg atan slat * tan degToRad hra
print "HR=" ++ (to :string .format:"3d" h) ++ "; " ++
"HRA=" ++ (to :string .format:"7.3f" hra) ++ "; " ++
"HLA=" ++ (to :string .format:"7.3f" 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
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
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
BASIC
ANSI BASIC
100 REM Horizontal sundial calculations
110 INPUT PROMPT "Enter latitude => ": Lat
120 INPUT PROMPT "Enter longitude => ": Lng
130 INPUT PROMPT "Enter legal meridian => ": Ref
140 PRINT
150 OPTION ANGLE DEGREES
160 LET Slat = SIN(Lat)
170 PRINT " sine of latitude: "; Slat
180 PRINT " diff longitude: "; Lng - Ref
190 PRINT
200 PRINT "Hour, sun hour angle, dial hour line angle from 6am to 6pm"
210 FOR Hour = -6 TO 6
220 LET HourAngle = 15 * Hour
230 LET HourAngle = HourAngle - (Lng - Ref) ! correct for longitude difference
240 LET HourLineAngle = ATN(Slat * TAN(HourAngle))
250 PRINT USING "HR=###; HRA=####.###; HLA=####.###": Hour, HourAngle, HourLineAngle
260 NEXT Hour
270 END
- Output:
Enter latitude => -4.95
Enter longitude => -150.5
Enter legal meridian => -150
sine of latitude: -8.62863657979234E-2
diff longitude: -.5
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= .500; HLA= -.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
Applesoft BASIC
See Minimal BASIC
BASIC256
call SolarhoraAngle(-4.95, -150.5, -150.0)
end
function rad2deg(theta)
return theta * 180 / pi
end function
function deg2rad(theta)
return theta * pi / 180
end function
function sign(x)
if x < 0 then sign = -1
if x > 0 then sign = 1
if x = 0 then sign = 0
end function
subroutine SolarhoraAngle(latitude, longitude, meridian)
print "Latitude = "; latitude
print "Longitude = "; longitude
print "Meridian = "; meridian
print
print "sine of latitude: "; sin(latitude * pi / 180)
print " diff longitude: "; longitude - meridian
print
print " Time Sun hora angle Dial hora line angle"
for hora = 6 to 18
hra = (15 * hora) - longitude + meridian - 180
hla = rad2deg(atan(sin(deg2rad(latitude)) * tan(deg2rad(hra))))
if abs(hra) > 90 then hla += 180 * sign(hra * latitude)
if hora > 12 then time = hora - 12 : ap$ = " p.m." else time = hora : ap$ = " a.m."
print time; ap$; chr(9); hra; chr(9); chr(9); hla
next hora
end subroutineBBC BASIC
INSTALL @lib$+"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
Chipmunk Basic
10 CLS
20 DEF FNR(x) = x * PI/180
30 DEF FND(x) = x * 180/PI
40 INPUT " Enter latitude (degrees): ";latitude
50 INPUT " Enter longitude (degrees): ";longitude
60 INPUT "Enter legal meridian (degrees): ";meridian
70 PRINT
80 PRINT " Time Sun hour angle Dial hour line angle"
90 FOR h = 6 TO 18
100 hra = 15*h-longitude+meridian-180
110 hla = FN D(ARCTAN(SIN(FN R(latitude))*TAN(FN R(hra))))
120 IF ABS(hra) > 90 THEN hla = hla+180*SGN(hra*latitude)
130 PRINT USING "##.##";h;TAB (10)
140 PRINT USING "####.###";hra;TAB (27)
150 PRINT USING "####.###";hla
160 NEXT h
170 END
- Output:
Same as FreeBASIC entry.
FreeBASIC
' 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
window 1
def fn rad2deg( theta as double ) as double = theta * 180 / pi
def fn deg2rad( theta as double ) as double = theta * pi / 180
local fn SolarHourAngle( latitude as double, longitude as double, meridian as double )
long hour
double hra, hla, t
CFStringRef 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 t = hour - 12 : ap = @" a.m." else t = hour : ap = @" p.m."
print using "##"; t; ap, using "####.##"; hra, using "####.###"; hla
next hour
end fn
fn SolarHourAngle( -4.95, -150.5, -150.0 )
HandleEventsOutput:
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
GW-BASIC
10 ' Horizontal sundial calculations
20 PRINT "Enter latitude => ";
30 INPUT LAT
40 PRINT "Enter longitude => ";
50 INPUT LNG
60 PRINT "Enter legal meridian => ";
70 INPUT REF
80 PRINT
90 LET PI = 4 * ATN(1)
100 LET SLAT = SIN(LAT * PI / 180)
110 PRINT " sine of latitude: "; USING "#.##^^^^"; SLAT
120 PRINT " diff longitude: "; USING "####.###"; LNG - REF
130 PRINT
140 PRINT "Hour, sun hour angle, dial hour line angle from 6am to 6pm"
150 FOR H% = -6 TO 6
160 LET HRA = 15 * H%
170 LET HRA = HRA - (LNG - REF): ' correct for longitude difference
180 LET HLA = ATN(SLAT * TAN(HRA * PI / 180)) * 180 / PI
190 PRINT "HR="; USING "+##"; H%;
200 PRINT "; HRA="; USING "+###.###"; HRA;
210 PRINT "; HLA="; USING "+###.###"; HLA
220 NEXT H%
230 END
- Output:
Enter latitude => ? -4.95
Enter longitude => ? -150.5
Enter legal meridian => ? -150
sine of latitude: -.86E-01
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
IS-BASIC
100 PROGRAM "SunDial.bas"
110 OPTION ANGLE RADIANS
120 TEXT 80
130 LET DR=PI/180:LET RD=180/PI
140 INPUT PROMPT "Enter latitude: ":LAT
150 INPUT PROMPT "Enter longitude: ":LNG
160 INPUT PROMPT "Enter legal meridian: ":REF
170 LET S=SIN(LAT*DR)
180 PRINT :PRINT "Sine of latitude :";S
190 PRINT "Diff longitude: ";LNG-REF
200 PRINT " Hour,",,"sun hour angle, dial hour line angle from 6am to 6 pm"
210 FOR H=6 TO 18
220 LET HRA=15*H-LNG+REF
230 LET HLA=ATN(S*TAN(HRA*DR))*RD
240 PRINT "HR = ";H,"HRA =";HRA,"HLA =";HLA
250 NEXTLiberty 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
end
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- Output:
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
Microsoft Small Basic
TextWindow.Write("Enter latitude => ")
lat = TextWindow.ReadNumber()
TextWindow.Write("Enter longitude => ")
lng = TextWindow.ReadNumber()
TextWindow.Write("Enter legal meridian => ")
ref = TextWindow.ReadNumber()
sLat = Math.Sin(Math.GetRadians(lat))
TextWindow.WriteLine("")
TextWindow.Write(" sine of latitude: ")
TextWindow.WriteLine(Math.Round(sLat * 10000) / 10000)
TextWindow.Write(" diff longitude: ")
TextWindow.WriteLine(lng - ref)
TextWindow.WriteLine("")
TextWindow.WriteLine("Hour, sun hour angle, dial hour line angle from 6am to 6pm")
For hour = -6 To 6
hourAngle = 15 * hour
hourAngle = hourAngle - (lng - ref) ' correct for longitude difference
hourLineAngle = math.GetDegrees(Math.ArcTan(sLat * Math.Tan(Math.GetRadians(hourAngle))))
TextWindow.Write("HR=")
TextWindow.CursorLeft = 3 + (3 - Text.GetLength(hour))
TextWindow.Write(hour)
TextWindow.Write("; HRA=")
TextWindow.CursorLeft = 12 + (6 - Text.GetLength(hourAngle))
TextWindow.Write(hourAngle)
TextWindow.Write("; HLA=")
TextWindow.CursorLeft = 24 + (4 - Text.GetLength(Math.Floor(hourLineAngle)))
TextWindow.Write(Math.Round(hourLineAngle * 1000) / 1000)
TextWindow.WriteLine("")
EndFor- Output:
Enter latitude => -4.95
Enter longitude => -150.5
Enter legal meridian => -150
sine of latitude: -0.0863
diff longitude: -0.5
Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA= -89.5; HLA= 84.225
HR= -5; HRA= -74.5; HLA= 17.283
HR= -4; HRA= -59.5; HLA= 8.334
HR= -3; HRA= -44.5; HLA= 4.847
HR= -2; HRA= -29.5; HLA= 2.795
HR= -1; HRA= -14.5; HLA= 1.278
HR= 0; HRA= 0.5; HLA= -0.043
HR= 1; HRA= 15.5; HLA= -1.371
HR= 2; HRA= 30.5; HLA= -2.91
HR= 3; HRA= 45.5; HLA= -5.018
HR= 4; HRA= 60.5; HLA= -8.671
HR= 5; HRA= 75.5; HLA= -18.451
HR= 6; HRA= 90.5; HLA= 84.225
Minimal BASIC
10 REM Horizontal sundial calculations
20 DEF FNM(X) = INT(X*1000+0.5)/1000
30 PRINT "Enter latitude";
40 INPUT L
50 PRINT "Enter longitude";
60 INPUT L1
70 PRINT "Enter legal meridian";
80 INPUT R
90 PRINT
100 LET P = 4*ATN(1)
110 LET S1 = SIN(L*P/180)
120 PRINT " sine of latitude:"; S1
130 PRINT " diff longitude: "; FNM(L1-R)
140 PRINT
150 PRINT "Hour, sun hour angle, dial hour line angle from 6am to 6pm"
160 FOR H = -6 TO 6
170 LET A1 = 15*H
180 REM Correct for longitude difference:
190 LET A1 = A1-(L1-R)
200 LET A2 = ATN(S1*TAN(A1*P/180))*180/P
210 PRINT "HR ="; H;
220 PRINT TAB(9); "HRA ="; FNM(A1);
230 PRINT TAB(24); "HLA ="; FNM(A2)
240 NEXT H
250 END
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
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
True BASIC
FUNCTION rad2deg(theta)
LET rad2deg = theta*180/PI
END FUNCTION
FUNCTION deg2rad(theta)
LET deg2rad = theta*PI/180
END FUNCTION
FUNCTION signo(x)
IF x > 0 THEN LET signo = 1 ELSE LET signo = -1
END FUNCTION
INPUT prompt "Enter latitude (degrees) : ": latitude ! -4.95
INPUT prompt "Enter longitude (degrees) : ": longitude ! -150.5
INPUT prompt "Enter legal meridian (degrees): ": meridian ! -150.0
PRINT
PRINT "Time Sun hora angle Dial hora line angle"
FOR hora = 6 TO 18
LET hra = (15*hora)-longitude+meridian-180
LET hla = rad2deg(ATN(SIN(deg2rad(latitude))*TAN(deg2rad(hra))))
IF abs(hra) > 90 THEN LET hla = hla+180*signo(hra*latitude)
PRINT USING "## ####.## ####.###": hora, hra, hla
NEXT hora
END
XBasic
PROGRAM "sundial"
VERSION "0.0001"
IMPORT "xma"
DECLARE FUNCTION Entry()
FUNCTION Entry()
lat! = SINGLE(INLINE$("Enter latitude => "))
lng! = SINGLE(INLINE$("Enter longitude => "))
ref! = SINGLE(INLINE$("Enter legal meridian => "))
PRINT
slat! = SIN(lat! * $$PI / 180.0)
PRINT " sine of latitude: "; FORMAT$("#.##^^^^", slat!)
PRINT " diff longitude: "; FORMAT$("#.###", lng! - ref!)
PRINT
PRINT "Hour, sun hour angle, dial hour line angle from 6am to 6pm"
FOR hour@ = -6 TO 6
hourAngle! = 15 * hour@
hourAngle! = hourAngle! - (lng! - ref!) ' correct for longitude difference
hourLineAngle! = ATAN(slat! * TAN(hourAngle! * $$PI / 180.0)) * 180.0 / $$PI
PRINT "HR="; FORMAT$("###", hour@);
PRINT "; HRA="; FORMAT$("####.###", hourAngle!);
PRINT "; HLA="; FORMAT$("####.###", hourLineAngle!)
NEXT hour@
END FUNCTION
END PROGRAM
- Output:
Enter latitude => -4.95
Enter longitude => -150.5
Enter legal meridian => -150
sine of latitude: -8.63E-02
diff longitude: -0.500
Hour, sun hour angle, dial hour line angle from 6am to 6pm
HR= -6; HRA= -89.500; HLA= 84.225
HR= -5; HRA= -74.500; HLA= 17.283
HR= -4; HRA= -59.500; HLA= 8.334
HR= -3; HRA= -44.500; HLA= 4.847
HR= -2; HRA= -29.500; HLA= 2.795
HR= -1; HRA= -14.500; HLA= 1.278
HR= 0; HRA= 0.500; HLA= -0.043
HR= 1; HRA= 15.500; HLA= -1.371
HR= 2; HRA= 30.500; HLA= -2.910
HR= 3; HRA= 45.500; HLA= -5.018
HR= 4; HRA= 60.500; HLA= -8.671
HR= 5; HRA= 75.500; HLA= -18.451
HR= 6; HRA= 90.500; HLA= 84.225
Yabasic
SolarHourAngle(-4.95, -150.5, -150.0)
end
sub rad2deg(theta)
return theta * 180 / pi
end sub
sub deg2rad(theta)
return theta * pi / 180
end sub
sub SolarHourAngle(latitude, longitude, meridian)
local long, hour, hra, hla, time, ap$
print "Latitude = ", latitude
print "Longitude = ", longitude
print "Meridian = ", meridian
print "\nsine of latitude: ", sin(latitude * pi / 180)
print " diff longitude: ", longitude - meridian
print "\n Time Sun hour angle Dial hour line angle"
for hour = 6 to 18
hra = (15 * hour) - longitude + meridian - 180
hla = rad2deg(atan(sin(deg2rad(latitude)) * tan(deg2rad(hra))))
if abs(hra) > 90 hla = hla + 180 * sig(hra * latitude)
if hour > 12 then time = hour - 12 : ap$ = " a.m." else time = hour : ap$ = " p.m." : fi
print time using "##", ap$, chr$(9), hra using "####.##", chr$(9), chr$(9), hla using "####.###"
next hour
end subZX Spectrum Basic
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
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;
}
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);
}
}
}
}
C++
#include <cmath>
#include <iostream>
#include <numbers>
// constants used in the calculations
static const double DegreesPerHour = 15.0;
static const double DegreesPerRadian = 180.0 * std::numbers::inv_pi;
// a structure for the calculation results
struct SundialCalculation
{
double HourAngle;
double HourLineAngle;
};
// a class for a sundial at a location
class Sundial
{
// intermediate values used in the caclulations
double m_sinLatitude;
double m_timeZoneCorrection;
public:
Sundial(double latitude, double longitude, double legalMeridian) noexcept
: m_sinLatitude(sin(latitude / DegreesPerRadian))
, m_timeZoneCorrection(legalMeridian - longitude) {}
SundialCalculation CalculateShadow(double hoursSinceNoon) const noexcept
{
double hourAngle = hoursSinceNoon * DegreesPerHour + m_timeZoneCorrection;
double hourAngleRad = hourAngle / DegreesPerRadian;
double hlaRad = atan2(m_sinLatitude * sin(hourAngleRad), cos(hourAngleRad));
double hourLineAngle = hlaRad * DegreesPerRadian;
return SundialCalculation {hourAngle, hourLineAngle};
}
};
int main()
{
double latitude, longitude, legalMeridian;
std::cout << "Enter latitude:";
std::cin >> latitude;
std::cout << "Enter longitude:";
std::cin >> longitude;
std::cout << "Enter legal meridian:";
std::cin >> legalMeridian;
// create a sundial at the user specified location
const Sundial sundial(latitude, longitude, legalMeridian);
for(int hour = -6; hour < 7; ++hour)
{
// cacluate the angles
auto result = sundial.CalculateShadow(hour);
// print the results
auto amOrPm = hour < 0 ? "am" : "pm";
auto hourString = std::to_string(hour < 1 ? 12 + hour : hour);
std::cout << hourString << amOrPm <<
" - sun hour angle:" << result.HourAngle <<
", dial hour line angle:" << result.HourLineAngle << "\n";
}
}
- Output:
Enter latitude:-4.95 Enter longitude:-150.5 Enter legal meridian:-150 6am - sun hour angle:-89.5, dial hour line angle:84.2248 7am - sun hour angle:-74.5, dial hour line angle:17.2829 8am - sun hour angle:-59.5, dial hour line angle:8.33371 9am - sun hour angle:-44.5, dial hour line angle:4.84671 10am - sun hour angle:-29.5, dial hour line angle:2.79487 11am - sun hour angle:-14.5, dial hour line angle:1.27835 12pm - sun hour angle:0.5, dial hour line angle:-0.0431443 1pm - sun hour angle:15.5, dial hour line angle:-1.37079 2pm - sun hour angle:30.5, dial hour line angle:-2.90964 3pm - sun hour angle:45.5, dial hour line angle:-5.01802 4pm - sun hour angle:60.5, dial hour line angle:-8.6714 5pm - sun hour angle:75.5, dial hour line angle:-18.451 6pm - sun hour angle:90.5, dial hour line angle:-95.7752
COBOL
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
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
Delphi
See #Pascal
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
EasyLang
func getn s$ .
write s$
v = number input
print v
return v
.
lat = getn "Enter latitude: "
lng = getn "Enter longitude: "
merid = getn "Enter legal meridian: "
slat = sin lat
diff = lng - merid
print ""
print " sine of latitude: " & slat
print " diff longitude: " & diff
print ""
print "Hour\tSun hour angle\tDial hour line angle"
for h = -6 to 6
hra = 15 * h - diff
hla = atan2 (slat * sin hra) cos hra
print h + 12 & "\t" & hra & "\t\t" & hla
.
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
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#
// 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...
Factor
USING: formatting io kernel locals math math.functions math.libm
math.parser math.ranges math.trig sequences ;
IN: rosetta-code.sundial
: get-num ( str -- x ) write flush readln string>number ;
: get-input ( -- lat lng ref )
"Enter latitude: " "Enter longitude: "
"Enter legal meridian: " [ get-num ] tri@ ;
: .diff ( lat lng ref -- )
- [ deg>rad sin ] dip
"sine of latitude: %.3f\ndiff longitude: %.3f\n" printf ;
: line-angle ( lat hra-rad -- hla )
[ deg>rad sin ] [ [ sin * ] [ cos ] bi ] bi* fatan2 rad>deg
;
:: .angles ( lat lng ref -- )
"Hour, sun hour angle, dial hour line angle from 6am to 6pm"
print
-6 6 [a,b] [
:> h 15.0 h * :> hra!
ref hra lng - + hra!
lat hra deg>rad line-angle :> hla
h hra hla
"HR= %3d; \t HRA=%7.3f; \t HLA= %7.3f\n" printf
] each ;
: sundial-demo ( -- ) get-input nl 3dup .diff nl .angles ;
MAIN: sundial-demo
- 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
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
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
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
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 . unlines)
[ "Latitude " ++ show lat
, "Longitude " ++ show long
, "Legal meridian " ++ show legalMerid
, "Sine of latitude " ++ show (roundDec 6 sinOfLat)
, "Diff longitude " ++ show (-diff)
, "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
- 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 │-89.500 │ 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 │
└──────┴────────────────┴────────────────────┘
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, hraRad;
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
jq
Also works with gojq, the Go implementation of jq.
Adapted from Wren
Generic Utilities
# `prompts` should be an array defining the prompts, variable names, and their types,
# as exemplified below.
# After all values have been gathered, `get` emits an object defining the bindings.
def get($prompts):
label $out
| foreach range(0;infinite) as $_ ({i:null, imax: ($prompts|length)};
if .i == null then .i = 0
elif .i == .imax then break $out
else .help = null
| first(inputs) as $n
| $prompts[.i].type as $type
| if $type == null or $type == "string"
then .result[$prompts[.i].key] = $n
| .i += 1
elif $type == "number"
then (try ($n|tonumber) catch null) as $n
| if $n then .result[$prompts[.i].key] = $n
| .i += 1
else .help = .i
end
elif $type == "integer"
then if ($n|test("^[0-9]+$"))
then .result[$prompts[.i].key] = ($n|tonumber)
| .i += 1
else .help = .i
end
elif $type|type == "object"
then if $type.regex and ($n | test($type.regex))
then .result[$prompts[.i].key] = $n
| .i += 1
else .help = .i
end
else .
end
end;
(select(.help) | $prompts[.help].help // empty),
if .i < .imax then $prompts[.i].prompt
else .result
end )
;
def lpad($len): tostring | ($len - length) as $l | (" " * $l)[:$l] + .;
def rpad($len): tostring | ($len - length) as $l | . + ("0" * $l)[:$l];
# Input: a string of digits with up to one "."
# Output: the corresponding string representation with exactly $n decimal digits
def align_decimal($n):
tostring
| if index(".")
then capture("(?<i>[0-9]*[.])(?<j>[0-9]{0," + ($n|tostring) + "})")
| .i + (.j|rpad($n))
else . + "." + ("0" * $n)
end ;
def pi: 4*(1|atan);The Task
def prompts: [
{ prompt: "Enter latitude: ", key: "lat", type: "number", help: "in degrees"},
{ prompt: "Enter longitude: ", key: "lng", type: "number", help: "in degrees"},
{ prompt: "Enter legal meridian: ", key: "ref", type: "number", help: "in degrees"}
];
def task:
get(prompts)
| if type != "object" then . # the prompts
else
((.lat * pi / 180)|sin) as $slat
| (.lng - .ref) as $diff
| "\n sine of latitude : \($slat)",
" diff longitude : \($diff)",
"\nHour, sun hour angle, dial hour line angle from 6am to 6pm",
(range(-6;7) as $h
| (15*$h - $diff) as $hra
| (($hra * pi /180)|sin) as $s
| (($hra * pi /180)|cos) as $c
| (atan2($slat*$s; $c) * 180 / pi) as $hla
| [$h|lpad(3)] + ([$hra, $hla] | map(align_decimal(3)|lpad(7))) | join(" ") )
end;
taskInvocation: The program handles user input errors provided the -R option is specified:
jq -nRr -f horizontal-sundial-calculations.jq
Transcript
Enter latitude:
-4.95
Enter longitude:
-150.5
Enter legal meridian:
?
in degrees
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 84.224
-5 74.500 17.282
-4 59.500 8.333
-3 44.500 4.846
-2 29.500 2.794
-1 14.500 1.278
0 0.500 0.043
1 15.500 1.370
2 30.500 2.909
3 45.500 5.018
4 60.500 8.671
5 75.500 18.450
6 90.500 95.775
Julia
print("Enter latitude => ")
lat = parse(Float64, readline(STDIN))
print("Enter longitude => ")
lng = parse(Float64, readline(STDIN))
print("Enter legal meridian => ")
ref = parse(Float64, readline(STDIN))
println()
slat = sin(deg2rad(lat))
@printf " sine of latitude: %.3f\n" slat
@printf " diff longitude: %.3f\n" (lng - ref)
println("\nHour, sun hour angle, dial hour line angle from 6am to 6pm\n")
for h in -6:6
hra = 15 * h
hra -= lng - ref
hla = rad2deg(atan(slat * tan(deg2rad(hra))))
@printf "HR = %3d; HRA = %7.3f; HLA = %7.3f\n" 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
Kotlin
import java.lang.Math.atan2
import java.lang.Math.cos
import java.lang.Math.sin
import java.lang.Math.toDegrees
import java.lang.Math.toRadians
// version 1.1.4
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
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 sgnLogo
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)
]Lua
io.write("Enter latitude => ")
lat = tonumber(io.read())
io.write("Enter longitude => ")
lng = tonumber(io.read())
io.write("Enter legal meridian => ")
ref = tonumber(io.read())
print()
slat = math.sin(math.rad(lat))
print(string.format(" sine of latitude: %.3f", slat))
print(string.format(" diff longitude: %.3f", lng-ref))
print()
print("Hour, sun hour angle, dial hour line angle from 6am to 6pm")
for h = -6, 6 do
hra = 15 * h
hra = hra - (lng - ref)
hla = math.deg(math.atan(slat * math.tan(math.rad(hra))))
print(string.format("HR=%3d; HRA=%7.3f; HLA=%7.3f", h, hra, hla))
end
Mathematica / Wolfram Language
lat = Input["latitude", -4.95];
lng = Input["longitude", -150.5];
ref = Input["legal meridian", -150];
slat = Sin[lat Degree];
Table[
hra = 15 h;
hra -= lng - ref;
hla = N@ArcTan[slat Tan[hra Degree]]/Degree;
{h, hra, hla}
,
{h, -6, 6}
] // Prepend[{"Hour", "Sun hour angle",
"Dial hour line angle"}] // Grid
- Output:
Hour Sun hour angle Dial hour line angle -6 -89.5 84.2248 -5 -74.5 17.2829 -4 -59.5 8.33371 -3 -44.5 4.84671 -2 -29.5 2.79487 -1 -14.5 1.27835 0 0.5 -0.0431443 1 15.5 -1.37079 2 30.5 -2.90964 3 45.5 -5.01802 4 60.5 -8.6714 5 75.5 -18.451 6 90.5 84.2248
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.
Modula-2
MODULE SunDial;
FROM STextIO IMPORT
WriteString, WriteLn, SkipLine;
FROM SRealIO IMPORT
ReadReal, WriteFixed, WriteFloat;
FROM SWholeIO IMPORT
WriteInt;
FROM RealMath IMPORT
sin, pi, arctan, tan;
VAR
Lat, Slat, Lng, Ref: REAL;
Hour: INTEGER;
HourAngle, HourLineAngle: REAL;
BEGIN
WriteString("Enter latitude => ");
ReadReal(Lat);
SkipLine;
WriteString("Enter longitude => ");
ReadReal(Lng);
SkipLine;
WriteString("Enter legal meridian => ");
ReadReal(Ref);
SkipLine;
WriteLn;
Slat := sin(Lat * pi / 180.0);
WriteString(" sine of latitude: ");
WriteFloat(Slat, 2, 8);
WriteLn;
WriteString(" diff longitude: ");
WriteFixed(Lng - Ref, 3, 1);
WriteLn;
WriteLn;
WriteString("Hour, sun hour angle, dial hour line angle from 6am to 6pm");
WriteLn;
FOR Hour := -6 TO 6 DO
HourAngle := FLOAT(15 * Hour);
HourAngle := HourAngle - (Lng - Ref); (* correct for longitude difference *)
HourLineAngle := arctan(Slat * tan(HourAngle * pi / 180.0)) * 180.0 / pi;
WriteString("HR=");
WriteInt(Hour, 3);
WriteString("; HRA=");
WriteFixed(HourAngle, 3, 8);
WriteString("; HLA=");
WriteFixed(HourLineAngle, 3, 8);
WriteLn;
END;
END SunDial.
- Output:
Enter latitude => -4.95
Enter longitude => -150.5
Enter legal meridian => -150
sine of latitude: -8.6E-02
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
newLISP
(define pi 3.141592654)
(define (radians degrees) (mul degrees (div pi 180)))
(define (degrees radians) (mul radians (div 180 pi)))
(print "Enter latitude => ")
(set 'lat (float (read-line)))
(print "Enter longitude => ")
(set 'lng (float (read-line)))
(print "Enter legal meridian => ")
(set 'rf (float (read-line)))
(println)
(set 'slat (sin (radians lat)))
(println (format " sine of latitude: %.3f" slat))
(println (format " diff longitude: %.3f" (sub lng rf)))
(println)
(println "Hour, sun hour angle, dial hour line angle from 6am to 6pm")
(for (h -6 6)
(set 'hra (sub (mul 15 h) lng rf))
(set 'hla (degrees (atan (mul slat (tan (radians hra))))))
(println (format "HR=%3d; HRA=%7.3f; HLA=%7.3f" h hra hla))
)
(exit)
Nim
import rdstdin, strutils, math, strformat
let lat = parseFloat readLineFromStdin "Enter latitude => "
let lng = parseFloat readLineFromStdin "Enter longitude => "
let med = parseFloat readLineFromStdin "Enter legal meridian => "
echo ""
let slat = sin lat.degToRad
echo &" sine of latitude: {slat:.3f}"
echo &" diff longitude: {lng-med:.3f}"
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 = arctan(slat * tan(hra.degToRad)).radToDeg
echo &"HR={h:3d}; HRA={hra:7.3f}; HLA={hla:7.3f}"
- 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
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
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
/*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:
Not the same as for REXX anymore as the REXX computer programming example has been updated.
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
use utf8;
binmode STDOUT, ":utf8";
use constant π => 3.14159265;
sub d2r { $_[0] * π / 180 } # degrees to radians
sub r2d { $_[0] * 180 / π } # radians to degrees
print 'Enter latitude => '; $latitude = <>;
print 'Enter longitude => '; $longitude = <>;
print 'Enter legal meridian => '; $meridian = <>;
$lat_sin = sin( d2r($latitude) );
$offset = $meridian - $longitude;
print 'Sine of latitude: ' . sprintf "%.4f\n", $lat_sin;
print 'Longitude offset: ' . $offset . "\n";
print '=' x 48 . "\n";
print " Hour : Sun hour angle°: Dial hour line angle°\n";
for $hour (-6 .. 6) {
my $sun_deg = $hour * 15 + $offset;
my $line_deg = r2d atan2( ( sin(d2r($sun_deg)) * $lat_sin ), cos(d2r($sun_deg)) );
printf "%2d %s %8.3f %8.3f\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
Phix
For better behaviour/proper input on pwa/p2js I suppose this should really be a pGUI app.
with javascript_semantics function prompt(string text, atom v) if platform()!=JS then printf(1,"Enter %s (%g):",{text,v}) object answer = gets(0) puts(1, '\n') if string(answer) then v = to_number(trim(answer),v) end if else printf(1,"%s:%g\n",{text,v}) end if return v end function constant deg2rad = PI/180, rad2deg = 180/PI atom lat = prompt("Latitude",-4.95), lng = prompt("Longitude",-150.5), mer = prompt("Legal Meridian",-150), slat = sin(lat*deg2rad) printf(1,""" Sine of latitude: %g Longitude offset: %g Hour Sun hour angle Dial hour line angle -------- -------------- -------------------- """,{slat,lng-mer}) for hour = -6 to 6 do atom ha = hour * 15 - lng + mer, s = sin(ha*deg2rad), c = cos(ha*deg2rad), hla = atan2(slat*s,c)*rad2deg integer hour12 = iff(hour<=0?hour+12:hour) string am = iff(hour<0?"am":"pm") printf(1,"%3d:00%s %12.3f %17.3f\n",{hour12,am,ha,hla}) end for
- Output:
Enter Latitude (-4.95): Enter Longitude (-150.5): Enter Legal Meridian (-150): Sine of latitude: -0.086286 Longitude offset: -0.5 Hour Sun hour angle Dial hour line angle -------- -------------- -------------------- 6:00am -89.500 84.225 7:00am -74.500 17.283 8:00am -59.500 8.334 9:00am -44.500 4.847 10:00am -29.500 2.795 11:00am -14.500 1.278 12:00pm 0.500 -0.043 1:00pm 15.500 -1.371 2:00pm 30.500 -2.910 3:00pm 45.500 -5.018 4:00pm 60.500 -8.671 5:00pm 75.500 -18.451 6:00pm 90.500 -95.775
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
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
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
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
>
Raku
(formerly 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
REXX
The REXX language doesn't have the usual trigonometric functions, nor for that matter, a sqrt (square root) function,
so these as well as pi were added to this program.
The legal meridian is calculated instead of relying on a specified amount.
The time range was extended (to include quarter─hour times), and to show that the dial hour line angle just doesn't
change its sign when it exceeds ± 90º.
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 length( pi() ) - length(.) /*in case sundial is in polar regions. */
parse arg lat lng . /*obtain optional arguments from the CL*/
/* ┌───────────◄ None specified? Then use the default*/
/* │ of Jules Verne's Lincoln Island, */
$= left('', 30) /* ↓ aka Ernest Legouve Reef. */
if lat=='' | lat=="," then lat= -4.95 /*Not specified? Then use the default.*/
if lng=='' | lng=="," then lng= -150.5 /* " " " " " " */
mer= format(lng/15, , 0) * 15 /*calculate legal meridian longitude. */
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 " */
L= max( length(lat), length(lng), length(mer) ) /*find the maximum length of 3 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 " " " */
say $ center(' ', w1) center("sun hour", w2) center('dial hour' , w3)
say $ center('hour', w1) center(" angle" , w2) center('line angle', w3)
call sep /*to help a one─eyed pirate's eyeball. */
do h=5 to 19 by .25 /*Okey dokey then, now let's show stuff*/
hra= 15 * h - lng + mer - 180 /*calculate sun hour angle (in degrees)*/
hla= r2d( Atan(sineLat * tan(d2r(hra)))) /*this is the heavy lifting calculation*/
if abs(hra)>90 then hla= hla + 180 * sign(hra*lat) /*adjust for negative angle*/
call civil /*convert the time─of─day to civil time*/
say $ center(hc, w1) right(format(hra,,1), w2-2)@ right(format(hla,,1), w3-5)
end /*h*/
call sep /*to help a one─eyed pirate's eyeball. */
exit 0 /*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 $ copies('═', w1) copies("═", w2) copies('═', w3); @= left('',3); 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)
Atan: procedure; parse arg x; if abs(x)=1 then return pi()*x/4; return Asin(x/sqrt(1+x*x))
/*──────────────────────────────────────────────────────────────────────────────────────*/
Asin: procedure; parse arg x; if x<-1 | x>1 then call AsinErr; s= x*x
if abs(x)>=sqrt(2)*.5 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
/*──────────────────────────────────────────────────────────────────────────────────────*/
sin: procedure; parse arg x; x= r2r(x); numeric fuzz min(5, digits() - 3)
if abs(x)=pi then return; 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 #=2 by 2; != -!*x/(#*(#+i)); z= z+!; if z=p then leave; p= z; end; return z
/*──────────────────────────────────────────────────────────────────────────────────────*/
civil: select /* [↓] Maybe below Antarctic circle, */
when h== 0 then hc= 'midnight' /* or above Arctic " */
when h <12 then hc= h 'am' /*convert da hour for human beans (sic)*/
when h==12 then hc= 'noon' /* ··· easier to understand now. */
when h >0 then hc= h 'pm' /* ··· even more meaningful. */
end /*select*/
parse var hc hh ampm .; if \datatype(hh, 'N') then return /*not numeric? */
hh= hh / 1; if hh>12 then hh= hh - 12 /*civil time ? */
if pos(., hh)==0 then do; hc= right(hh, 2)' ' ampm; return; end /*exact hour ? */
parse var hh hr '.' -0 mn; if hr==0 then hr= 12 /*get MN; noon?*/
mn= mn * 60 / 1; hc= right(hr, 2)":"right(mn, 2, 0) ampm; return /*reformat time*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
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
══════════ ══════════ ════════════
5 am -104.5 161.5
5:15 am -100.8 155.6
5:30 am -97.0 144.9
5:45 am -93.3 123.3
6 am -89.5 84.2
6:15 am -85.8 49.3
6:30 am -82.0 31.5
6:45 am -78.3 22.5
7 am -74.5 17.3
7:15 am -70.8 13.9
7:30 am -67.0 11.5
7:45 am -63.3 9.7
8 am -59.5 8.3
8:15 am -55.8 7.2
8:30 am -52.0 6.3
8:45 am -48.3 5.5
9 am -44.5 4.8
9:15 am -40.8 4.3
9:30 am -37.0 3.7
9:45 am -33.3 3.2
10 am -29.5 2.8
10:15 am -25.8 2.4
10:30 am -22.0 2.0
10:45 am -18.3 1.6
11 am -14.5 1.3
11:15 am -10.8 0.9
11:30 am -7.0 0.6
11:45 am -3.3 0.3
12 pm 0.5 0.0
12:15 pm 4.3 -0.4
12:30 pm 8.0 -0.7
12:45 pm 11.8 -1.0
1 pm 15.5 -1.4
1:15 pm 19.3 -1.7
1:30 pm 23.0 -2.1
1:45 pm 26.8 -2.5
2 pm 30.5 -2.9
2:15 pm 34.3 -3.4
2:30 pm 38.0 -3.9
2:45 pm 41.8 -4.4
3 pm 45.5 -5.0
3:15 pm 49.3 -5.7
3:30 pm 53.0 -6.5
3:45 pm 56.8 -7.5
4 pm 60.5 -8.7
4:15 pm 64.3 -10.1
4:30 pm 68.0 -12.1
4:45 pm 71.8 -14.7
5 pm 75.5 -18.5
5:15 pm 79.3 -24.4
5:30 pm 83.0 -35.1
5:45 pm 86.8 -56.7
6 pm 90.5 -95.8
6:15 pm 94.3 -130.7
6:30 pm 98.0 -148.5
6:45 pm 101.8 -157.5
7 pm 105.5 -162.7
══════════ ══════════ ════════════
Ring
# Project : Horizontal sundial calculations
load "stdlib.ring"
pi = 22/7
decimals(3)
latitude = -4.95
longitude = -150.5
meridian = -150.0
see "enter latitude (degrees): " + latitude + nl
see "enter longitude (degrees): " + longitude + nl
see "enter legal meridian (degrees): " + meridian + nl
see "time " + " sun hour angle" + " dial hour line angle" + nl
for hour = 6 to 18
hra = 15*hour - longitude + meridian - 180
hla = 180/pi*(atan(sin(pi/180*latitude) * tan(pi/180*hra)))
if fabs(hra) > 90
hla = hla + 180 * sign(hra * latitude)
ok
see "" + hour + " " + hra + " " + hla + nl
nextOutput:
enter latitude (degrees): -4.950 enter longitude (degrees): -150.500 enter legal meridian (degrees): -150 time sun hour angle dial hour line angle 6 -89.500 84.607 7 -74.500 17.316 8 -59.500 8.342 9 -44.500 4.850 10 -29.500 2.796 11 -14.500 1.279 12 0.500 -0.043 13 15.500 -1.371 14 30.500 -2.911 15 45.500 -5.021 16 60.500 -8.680 17 75.500 -18.488 18 90.500 -96.224
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
Rust
use std::io;
struct SundialCalculation {
hour_angle: f64,
hour_line_angle: f64,
}
fn get_input(prompt: &str) -> Result<f64, Box<dyn std::error::Error>> {
println!("{}", prompt);
let mut input = String::new();
let stdin = io::stdin();
stdin.read_line(&mut input)?;
Ok(input.trim().parse::<f64>()?)
}
fn calculate_sundial(hour: i8, lat: f64, lng: f64, meridian: f64) -> SundialCalculation {
let diff = lng - meridian;
let hour_angle = f64::from(hour) * 15. - diff;
let hour_line_angle = (hour_angle.to_radians().tan() * lat.to_radians().sin())
.atan()
.to_degrees();
SundialCalculation {
hour_angle,
hour_line_angle,
}
}
fn main() -> Result<(), Box<dyn std::error::Error>> {
let lat = get_input("Enter latitude => ")?;
let lng = get_input("Enter longitude => ")?;
let meridian = get_input("Enter legal meridian => ")?;
let diff = lng - meridian;
let sine_lat = lat.to_radians().sin();
println!("Sine of latitude: {:.5}", sine_lat);
println!("Diff longitude: {}", diff);
println!(" Hrs Angle Hour Line Angle");
(-6..=6).for_each(|hour| {
let sd = calculate_sundial(hour, lat, lng, meridian);
println!(
"{:>3}{} {:>5} {:>+15.5}",
if hour == 0 { 12 } else { (hour + 12) % 12 },
if hour <= 6 { "pm" } else { "am" },
sd.hour_angle,
sd.hour_line_angle
);
});
Ok(())
}
- Output:
Enter latitude => -4.95 Enter longitude => -150.5 Enter legal meridian => -150 Sine of latitude: -0.08629 Diff longitude: -0.5 Hrs Angle Hour Line Angle 6pm -89.5 +84.22483 7pm -74.5 +17.28293 8pm -59.5 +8.33371 9pm -44.5 +4.84671 10pm -29.5 +2.79487 11pm -14.5 +1.27835 12pm 0.5 -0.04314 1pm 15.5 -1.37079 2pm 30.5 -2.90964 3pm 45.5 -5.01802 4pm 60.5 -8.67140 5pm 75.5 -18.45100 6pm 90.5 +84.22483
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;Scala
import java.util.Scanner
import scala.math.{atan2, cos, sin, toDegrees, toRadians}
object Sundial extends App {
var lat, slat,lng, ref = .0
val sc = new Scanner(System.in)
print("Enter latitude: ")
lat = sc.nextDouble
print("Enter longitude: ")
lng = sc.nextDouble
print("Enter legal meridian: ")
ref = sc.nextDouble
println()
slat = Math.sin(Math.toRadians(lat))
println(f"sine of latitude: $slat%.3f")
println(f"diff longitude: ${lng - ref}%.3f\n")
println("Hour, sun hour angle, dial hour line angle from 06h00 to 18h00")
for (h <- -6 to 6) {
val hra = 15.0 * h - lng + ref
val hraRad = toRadians(hra)
val hla = toDegrees(atan2(Math.sin(hraRad) * sin(Math.toRadians(lat)), cos(hraRad)))
println(f"HR= $h%3d;\tHRA=$hra%7.3f;\tHLA= $hla%7.3f")
}
}
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
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
|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. $<9> }) displayNl.
]
Tcl
set PI 3.1415927
fconfigure stdout -buffering none
puts -nonewline "Enter latitude => "; gets stdin lat
puts -nonewline "Enter longitude => "; gets stdin lng
puts -nonewline "Enter legal meridian => "; gets stdin ref
puts ""
set slat [expr {sin($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
Wren
import "io" for Stdin, Stdout
import "./fmt" for Fmt
var getNum = Fn.new { |prompt|
while (true) {
System.write(prompt)
Stdout.flush()
var input = Stdin.readLine()
var n = Num.fromString(input)
if (n) return n
System.print("Invalid number, try again.")
}
}
var lat = getNum.call("Enter latitude : ")
var lng = getNum.call("Enter longitude : ")
var ref = getNum.call("Enter legal meridian : ")
var slat = (lat * Num.pi / 180).sin
var diff = lng - ref
System.print("\n sine of latitude : %(slat)")
System.print(" diff longitude : %(diff)")
System.print("\nHour, sun hour angle, dial hour line angle from 6am to 6pm")
for (h in -6..6) {
var hra = 15*h - diff
var s = (hra * Num.pi /180).sin
var c = (hra * Num.pi /180).cos
var hla = (slat*s).atan(c) * 180 / Num.pi
Fmt.print("$2.0f $8.3f $8.3f", h, hra, hla)
}
- Output:
Enter latitude : -4.95
Enter longitude : -150.5
Enter legal meridian : -150
sine of latitude : -0.086286365797923
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
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
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
//(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>
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