Figures 18 and 19 show the great elliptic arc formulae for distance arranged with geodetic 

 azimuth formulae and the computations for distance and azimuth over the two lines 

 (1) MOSCOW TO CAPE OF GOOD HOPE and (2) RAMEY AFB to MOUNTAIN HOME AFB. 



No square roots are involved and only eight place tables of trigonometric functions, as 

 Peters, are needed in addition to the constants for a particular spheroid of reference. The 

 comparison with the Helmert rigorous and Andoyer-Lambert approximation is: 

 Line Distance(meters) Method Forward Az. Back hz. 



(1) 10,102,069.91 Great Elliptic Arc 15° 48' 17':519 190° 39' 32':i09 

 10,102,069.06 Helmert 15° 48' 17':674 190° 39' 32'1208 

 10,102,065.28 Andoyer-Lambert 15° 48' 17':518 190° 39' 32'1110 



(2) 5,304,035.439 Great Elliptic Arc 131° 52' 34'1985 285° 10' 06'1870 

 5,304,032.437 Helmert 131° 52' 35':29 285° 10' 06':65 

 5,304,030.844 Andoyer-Lambert 131° 52' 35':043 285° 10' 06':869 



REVIEW OF FORMER STUDIES 



The Air Force Aeronautical Charting and Information Center made an extensive study of 

 the Inverse Problem of Geodesy (1956—1957), over lines 50 to 6000 miles, [12]. A review of 

 this study indicates favorably the use of the so called Andoyer-Lambert Formulae relative 

 to requirements for Hyperbolic Electronic Systems since (1) they give very nearly geodetic 

 distance with about the same error over all lines from 50 to at least 6000 miles, (2) azimuths 

 are within about a second of true geodetic azimuths over all lines, (3) no tabular data for a 

 particular spheroid is needed, (4) the only table of mathematical functions required is a table 

 of the natural trigonometric functions as Peters eight place tables, (5) no root extraction is 

 involved in the computations. The formulae are thus quite adaptable to small electric desk 

 calculators or larger high speed digital machines. However, in review it seemed unnecessary 

 to convert geographic coordinates to parametric before making the computations, hence a 

 series of computations were made over the ACIC chosen lines for direct comparison. A 

 representative group from 50 to 6000 miles was selected and additional comparisons were 

 made against two lines whose true geodetic lengths and azimuths were known. No lines of 

 0° azimuth (meridional sections) were used because this is the trivial or limiting case and 

 extensive tables of meridional distances for all reference ellipsoids are available or quite 

 simple computation formulae are available for computing meridional arcs. The spherical 

 formulae used are: 



61 



