great.gms : Great Circle Distances

**Description**

The coordinates of points (airports) on the globe are given in degrees latitude and longitude. The shortest distance (great circle distance) between pairs of points is desired. First, the spheric coordinates are translated into Cartesian coordinates. Second, the straight line distance between points on the unit sphere are calculated. Third, the great circle distances are computed.

**Reference**

- Brooke, A, Kendrick, D, and Meeraus, A, GAMS: A User's Guide. The Scientific Press, Redwood City, California, 1988.

**Small Model of Type :** GAMS

**Category :** GAMS Model library

**Main file :** great.gms

$Title Great Circle Distances (GREAT,SEQ=73) $Ontext The coordinates of points (airports) on the globe are given in degrees latitude and longitude. The shortest distance (great circle distance) between pairs of points is desired. First, the spheric coordinates are translated into Cartesian coordinates. Second, the straight line distance between points on the unit sphere are calculated. Third, the great circle distances are computed. Brooke, A, Kendrick, D, and Meeraus, A, GAMS: A User's Guide. The Scientific Press, Redwood City, California, 1988. The center of the earth is the origin for all coordinate systems. Spheric coordinates latitude angle north positive south negative longitude angle east positive west negative Cartesian coordinates x-axis 0 N 0 E y-axis 0 N 90 E z-axis 90 N $Offtext Sets k coordinates / x-axis, y-axis, z-axis / a airports / sfo san francisco mia miami jfk new york iah houston iad washington dc khi karachi - pakistan nnn north pole sss south pole / Alias (a,ap) Table loc(a,*) location on map lat-deg lat-min long-deg long-min sfo 37 37 -122 -23 mia 25 48 - 80 -17 jfk 40 38 - 73 -47 iah 29 58 - 95 -20 iad 38 57 - 77 -25 khi 24 40 67 10 nnn 90 sss -90 Scalar pi trigonometric constant / 3.141592653 / r radius of earth (miles) / 3959 / Parameters lat(a) latitude angle (radians) long(a) longitude angle (radians) uk(a,k) point in cartesian coordinates (unit sphere) useg(a,ap) straight line distance between points (unit sphere) udis(a,ap) great circle distances (unit sphere) dis(a,ap) great circle distances (miles); lat (a) = (loc(a,"lat-deg") + loc(a,"lat-min") /60)*pi/180; long(a) = (loc(a,"long-deg") + loc(a,"long-min")/60)*pi/180; uk(a,"x-axis") = cos(long(a))*cos(lat(a)); uk(a,"y-axis") = sin(long(a))*cos(lat(a)); uk(a,"z-axis") = sin(lat(a)); useg(a,ap) = sqrt(sum(k, sqr(uk(a,k)-uk(ap,k)) )); udis(a,ap) = pi; udis(a,ap)$(useg(a,ap) lt 1.99999) = 2*arctan(useg(a,ap)/2 /sqrt(1-sqr(useg(a,ap)/2))); dis(a,ap) = r*udis(a,ap); Options lat:5, long:5, uk:5, useg:5, udis:5, dis:0; Display loc, lat, long, uk, useg, udis, dis;