Quoting CoolGuy (Reply 2):
*That would be fine; however is there a way to find out my position throughout the flight? For example, JFK-LHR, after 1000 miles elapsed (if it were following the great circle path).* |

JFK (40 degrees 38'23"N 73 degrees 46'44"W)

LHR (51 degrees 28'39"N 0 degrees 27'41"W)

In radians

JFK is

lat1=(40.639751)*pi/180=0.709297462, lon1=(73.778926)*pi/180=1.287685177 and

LHR is (lat2=0.898451866,lon2=1.287762)

The distance from

JFK to

LHR is

d = 2*asin(sqrt((sin((lat1-lat2)/2))^2+cos(lat1)*cos(lat2)*(sin((lon1-lon2)/2)^2))

= 2*asin(sqrt((sin(0.709297462-0.898451866)/2))^2+cos(0.709297462)*cos(0.898451866)*(sin((1.287685177-0.008052757)/2)^2))

= 0.869478789 radians

= 0.869478789*180*60/pi=2989nm

or

d = acos(sin(lat1)*sin(lat2)+cos(lat1)*cos(lat2)*cos(lon1-lon2))

= acos(sin(0.709297462)*sin(0.898451866)+cos(0.709297462)*cos(0.898451866)*cos(1.287685177-0.008052757))

= 0.869478789 radians

= 0.869478789*180*60/pi=2989nm

The initial true course out of

JFK is:

sin(0.008052757-1.287685177) < 0 so

tc = acos((sin(lat2)-sin(lat1)*cos(d))/(sin(d)*cos(lat1)))

= acos((sin(0.898451866)-sin(0.709297462)*cos(0.869478789))/(sin(0.869478789)*cos(0.709297462))

= 0.896117182 radians

= 51.3437 degrees

An enroute waypoint 100nm from

JFK on the 51.3437 degree radial (100nm along the

GC to

LHR) has lat and long given by:

100nm = 100*pi/(180*60)=0.029088821 radians

lat = asin(sin(lat1)*cos(d)+cos(lat1)*sin(d)*cos(tc))

= asin(sin(0.709297462)*cos(0.0290888)+cos(0.709297462)*sin(0.0290888)*cos(1.150035))

= 0.727241168 radians

= 41.667850 N

lon = mod(lon1-asin(sin(tc)*sin(d)/cos(lat))+pi,2*pi)-pi

= mod(1.287685177- asin(sin(0.896117182)*sin(0.869478789)/cos(0.727241168))+pi,2*pi)-pi

= 1.257276036 radians

= 72.036611 W

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