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    Computing great circle and rhumb lline courses
    From: Gary LaPook
    Date: 2010 Feb 06, 04:37 -0800

    Posting about Earhart and Wartime navigation in WW II required me to do
    some rhumb line calculations. I had programed my Casio PB-1000
    calculator in about 1989 to do many navigational calculations including
    planning great circle and rhumb line courses. I input the starting and
    ending points and the program computes great circle course and distance
    followed by rhumb line course and distance and the coordinates of the
    vertex. Then I put in the longitude of the first intermediate point and
    the interval of subsequent points and the program returns the latitude
    of the GC at the selected longitude, the rhumb line course and distance
    between the prior point and the new point and the cumulative rhumb line
    distances. I then repeat this for the rest of the intermediate points.
    At the end it also displays the extra distance of this approximation of
    the  GC over a perfect GC course. Bellow is the subroutine that computes
    great circle and rhumb line courses and distances. Line 28 computes
    rhumb line course (RCRS); line 50 rhumb line distance; 60 and 70 the GC
    distance; and 80 and 90 the GC course.
    
    I got the formula for the rhumb line course from AFM 51-40, attached.
    
    It is interesting that an Air Force manual would contain a significant
    typo. The formula given to compute the rhumb line course doesn't work
    because it is missing a pair of parentheses. I remember that it took me
    a while to find this problem. The 180 in the bottom of the formula
    multiplies both terms, not just the first one. (Ln is natural log, log
    base e in AFM 51-40) The problem persists in the current navigation
    manual, AFPAM 11-216.
    
    gl
    
    
    
    
    5 ON ERROR GOTO900
    10 CLS:PRINT"COMPUTING"
    11 IF LT1>=90 THENLT1 =89.9999
    12 IF LT1<=-90 THENLT1=-89.9999
    13 IF LT2>=90 THENLT2 =89.9999
    14 IF LT2<=-90 THENLT2=-89.9999
    15 IF LT1=0 THENLT1=.0001
    16 IF LT2=0 THENLT2=.0001
    20 IF LL1<0 THEN LL1=360+LL1
    21 IF LL2<0 THEN LL2=360+LL2
    23 LHA=LL2-LL1
    24 IF LHA<0 THEN LHA=LHA+360
    25 IF LHA=180 THEN LHA=179.99982
    26 T=LHA
    27 IFT>180 THEN T=360-T
    28
    RCRS=ABS(ATN((PI*(T))/(((LOG(TAN(45+LT2/2)))-(LOG(TAN(45+LT1/2))))*180)))
    30 IF LT1>LT2 THEN RCRS=180-RCRS
    50 RDIST=ABS(((1/(ABS(COSRCRS)))*60)*(LT2-LT1))
    60 ZD=ACS(SINLT1*SINLT2+COSLT1*COSLT2*COS(LHA))
    70 GDIST=60*ZD
    80 AZZ=ACS((COSLT1*SINLT2-SINLT1*COSLT2*COS(LHA))/COS(90-ZD))
    90 GCRS=AZZ:IF LHA<180 THENGCRS=360-AZZ:RCRS=360-RCRS
    800 RETURN
    900 LT2=LT2+.005
    920 RESUME 28
    
    

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