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Computer program calculates great circle bearings & distances If you want to point your beam to Recife on the eastern-most tip of Brazil, what bearing would you use? A map based on Mercator's projection would suggest a few degrees north of east but of course you know better than that. By PHILIP WATSON, VK2ZPW But what bearing would you use? If you are lucky enough to have a great circle map based on your city, that's fine. But if not, or you live somewhere between Woop Woop and Bulamakanka, finding the correct bearing is not always easy. This program will calculate the distance and bearing between any two points on earth. All you have to do is feed in the latitude and longitude of each. It was written by J. Hall and C. Hutchinson of ARRL headquarters and published in several editions of the ARRL Antenna Book. The ARRL has waived any copyright restrictions on the program. The program was originally written for a Radio Shack TRS-80 Level II computer using a form of BASIC suited to that machine. This differs slightly from GW BASIC and the version given here has been modified to suit the latter. Also, the original was written to accept degrees and decimals of a degree. Since most references quote degrees and minutes, the program has been modified to accept data in this form. Another modification has been to write the user's location permanently into the program. This is shown at line 260 which lists the location for Sydney. All you have to do is substitute your own location and the corresponding latitude and longitude figures where appropriate. The most practical way to use the program is to compile a list of major world centres, plus any special localities the you frequently contact. This can be kept at the operating position. Using the software is easy. First boot up your computer in GW BASIC, then load and run the program in the usual manner. Fig.2 shows the program listing while Fig.1 shows a sample readout. You simply enter the name of the distant location, the latitude and longitude of your own location, and the latitute and longitude of the distant location. The program then displays the required information and asks Sample Printout PROGRAM TO CALCULATE GREAT CIRCLE DISTANCES~ BEARINGS BY J. HALL~ C HUTCHINSON, ARRL HQ, JULY 1981 ARRL PROGRAM IS NOT COPYRIGHTED~ MAY BE REPRODUCED FREELY <MODIFIED BY P. WATSON, VK2ZPW> ENTER NEGATIVE VALUES FOR LATITUDES SOUTH OF THE EQUATOR ENTER NEGATIVE VALUES FOR LONGITUDES EAST OF GREENWICH <MAX 180) SYDNEY:LAT.-33DEG.55MIN. LON.-151DEG.13MIN. ENTER NAME OF DISTANT LOCATION (OPTIONAL) SAN FRANCISCO THIS LOCATION LATITUDE (DEGREES AND MINUTES)? -33.55 THIS LOCATION LONGITUDE <DEGREES AND MINUTES)? -152.13 OTHER LOCATION LATITUDE (DEGREES AND MINUTES>? 37.45 OTHER LOCATION LONGITUDE (DEGREES AND MINUTES>? 122.27 DISTANT LOCALITY: SAN FRANCISCO THE FORWARD BEARING IS 55.385 DEGREES THE GREAT CIRCLE DISTANCE IS 11861.15 KILOMETRES 6405.08 NAUTICAL MILES 7370.22 STATUTE MILES TO CALCULATE NEW BEARING PRESS ENTER? Fig.1: this sample printout shows the hearing and distance from Sydney to San Francisco, USA. You simply enter in the latitude and longitude of each location. 78 SILICON CHIP Program Listing 10 REM*** BEARING/BAS*** 20 REM A=YOUR LAT. 30 REM B=OTHER STATION LAT. 40 REM C=BEARING ANGLE 50 REM D=DEGREES OF ARC 60 REM E=INTERMEDIATE VALUE 70 REM K=CONVERSION CONSTANT,ARC TO KILOMETRES 80 REM L=DIFF IN LONGITUDES 90 REM Ll=YOUR LONG 100 REM L2=0THER STATION LONG 110 REM M=CONVERSION CONSTANT, DEGREES TO RADIANS 120 REM N=CONVERSION CONST, ARC TO NAUT MI. 130 REM S=CONVERSION CONST, ARC TO STATUTE MI. 140 CLS:KEY OFF 150 PRINT"PROGRAM TO CALCULATE GREAT CIRCLE DISTANCES~ BEARINGS" 160 PRINT 170 PRINT"BY J. HALL~ C HUTCHINSON, ARRL HQ, JULY 1981 180 PRINT"ARRL PROGRAM IS NOT COPYRIGHTED~ MAY BE REPRODUCED FREELY " 185 PRINT"(MODIFIED BY P. WATSON, VK2ZPW>" 190 DEFDBL A,A,C,D,E,L,M: 200 D=1:K=111.11:M=57.29577951308238#:N=60:S=69.041: 210 PRINT 220 PRINT"ENTER NEGATIVE VALUES FOR LATITUDES SOUTH OF THE EQUATOR" 230 PRINT"ENTER NEGATIVE VALUES FOR LONGITUDES EAST OF GREENWICH <MAX 180)" 240 IF D<>l THEN 320 250 PRINT 260 PRINT"SYDNEY:LAT.-33DEG.55MIN. LON.-151DEG.13MIN." 270 INPUT"ENTER NAME OF DISTANT LOCATION (OPTIONAL> ", N$ 280 INPUT"THIS·LOCATION LATITUD£ (DEGREES AND MINUTES>";A: 290 A1=(A-FIX<A>>:A2=A-A1:A=A2+(A1/,6):A=A/M 300 INPUT"THIS LOCATION LONGITUDE (DEGREES AND MINUTES>";Lt 310 L11=(L1-FIX(L1)):L12=L1-L11:L1=L12+(L11/.6): 320 INPUT"OTHER LOCATION LATITUDE (DEGREES AND MINUTES>";B: 330 B1=(B-FIX<B>>:B2=B-B1:B=B2+(B1/.6):B=B/M 340 INPUT"OTHER LOCATION LONGITUDE (DEGREES AND MINUTES)";L2 350 L21=(L2-FIX<L2)):L22=L2-L21:L2=L22+(L21/,6): 360 L=!L1-L2>/M 370 E=SIN<A>*SIN!B)+COS(A>*COS<B>*COS<L> 380 D=-ATNCE/SQR(l-E*E))+!.57079 390 C=(SIN(B)-SIN<A>*E)/(COS(A)*SIN(D>> 400 IF C>=l THEN C=O:GOTO 420ELSE IF C<=-1 THEN C=180/M:GOT0310 410 C=-ATN(C/SQR(l-C*C>)+!.57079 420 C=C*M 430 IF SIN(L><O THEN C=360-C 440 PRINT"DISTANT LOCALITY: "JN$ 450 PRINT "THE FORWARD BEARING IS";:PRINT TAB(36)USING"#####,###";C ; 455 PRINT" DEGREES" 460 PRINT"THE GREAT CIRCLE DISTANCE IS"; 470 PRINT TAB(35)USING"######.##";K*D*M;:PRINT" KILOMETRES" 480 PRINT TAB(35)USING"######.##";N*D*M;:PRINT" NAUTICAL MILES" 490 PRINT TAB<35)USING"######.##";S*D*M;:PRINT" STATUTE MILES":PRINT 500 INPUT"TO CALCULATE NEW BEARING PRESS ENTER ";D:GOTO 260: Fig.2: the program is written is GWBASIC but conversion to other BASICs should pose no problem. Note that you will have to customise line 260 to suit your particular location. if you want to calculate another bearing. To exit the program, you simply hit Ctrl Break. You can then exit to DOS by typing SYSTEM and pressing the Enter key And the bearing for Recife'? Oh yes - around 170 degrees, or over Antartica, close to the South Pole.~ FEBRUARY1990 79