From:Alexandre GRIES <agries@planete.net>Organization:Pressimage, FranceDate:13 Oct 95 01:30:21References:1 2 3

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Dear Captain Barnett, As I understood you're looking for the formulae to calculate great circle course and distance while having departure and destination coordinates. We, in France, call it "orthodromie" computation. The formulae following are giving the distance and the departure azimuth for the great circle ride. Definitions: A is the departure point B is the destination point M is the distance LA is the departure latitude LB is the destination latitude GA is the departure longitude GB is the destination longitude P is the longitude difference ZA is the departure azimuth 1. Distance computation. Cos M = Sin(LA).SIN(LB) + Cos(LA).Cos(LB).Cos(P) Cos M = a + b a has a negative value when latitudes have a different sign b has a negative value when P>90° if a+b is positive M<90° if a+b is negative M>90° Use the acos function. M is given in degree and minute of arc. It has to be converted in nautical miles. 2. Departure azimuth. The azimuth is the the angle between the local meridian and the great circle computed. The two formulae are efficient: Sin(ZA) = (Cos(LB).Sin(P))/Sin(M) Cotg(ZA) = (((Tg(LB).Cos(LA))/Sin(P)) - Sin(LA).Cotg(P) Cotg(ZA) = a - b a has the LB sign. b is positive when Sin(LA) and Cotg(P) have the same sign. use the asin or acotg functions. 3. Example. LA = 33.00 S GA = 91.55 W LB = 14.30 N GB = 100.39 E Distance computation. P = 167.26 Cos(M) = 0.92887 a is negative, b is negative, a+b is negative => M>90° M = -21°44 = 180 - 21.44 = 158°16 = 9496 Nm Departure azimuth. Sin(ZA) = 0.56888 ZA = 34.40 = 180 + 34.40 = 214.40 (215°) Cotg(ZA) = 1.44640 ZA = 214.40 (215°) The destination azimuth can be found by replacing LA by LB in the formula. I hope that these few elements will be interesting for your demand. Sorry for my "french pilot" way of speeking english (I am an Airbus 320 Air France pilot, ATR 42/72 Captain and French ATPL instructor) Alexandre GRIES - agries@planete.net - Tel/Fax 33 (1) 42 57 15 80 38 Avenue JUNOt - F75018 PARIS - FRANCE