OPERATIONAL APPLICATIONS 

 Requirements, accuracy wise, with respect to geodetic data obviously depend on the particular 

 guidance system employing it. If some guidance, particularly external, is to be provided a missile, 

 its initial launch requirements are not as critical as say for a purely ballistic missile. Since it 

 has yet to be demonstrated that the flight of missiles are geodesic or that the traces of the 

 trajectories upon the ellipsoid of reference are geodesies, distances can be computed by any 

 method which will give results within the capability of the particular system. Since alinement is 

 usually with respect to a local vertical and a "bearing", the normal section azimuth, the angle of 

 depression of the chord below the horizon and the maximum separation between the chord and the 

 surface are all useful associated quantities which can be "integrated" in the computations for 

 distance as will subsequently be shown in the discussion of distance computations along the 

 great elliptic arc. This configuration is shown in Figure 11 as abstracted from Figure 10. 



HYPERBOLIC MEASURING SYSTEMS 



For Loran systems, the earth must be considered an oblate ellipsoid or spheroid, but the 

 nearest hundred feet is probably close enough particularly on long lines. [7], page 170. 

 Hence a computational system is desirable which provides modifications to spherical elements, 

 i.e. functions of spherical arc lengths so that the auxiliary sphere of the particular spheroid of 

 reference can be us'ed since the hyperbolic propagation of systems as Loran may be worldwide 

 as base lines are added or extended. Also to be considered is the use of such computational 

 systems in local areas as for oceanographic surveying and corresponding adaptation to a local 

 sphere of reference. Azimuth computations should be independent, except for dependence on 

 spherical arc length, so that one can have readily the Normal plane section azimuths as well as 

 geodetic azimuths. Finally the system should be easily adapted to local area work in terms of 

 plane coordinates. This can probably best be accomplished through the series of projections, 

 all conformal; spheroid to aposphere, aposphere to sphere, sphere to plane. [8] . 



The present investigation will center about the configuration depicted in Figure 12 which 

 shows the relationships, exaggerated; between the Normal sections. The Great Elliptic Section, 

 The Geodesic, and the Chord between two points Qi, Q2 on the ellipsoid. We begin by deriving 

 the formulae for the Normal Section Azimuths and the Great Elliptic Arc Azimuths. 



NORMAL SECTION AZIMUTHS 

 The normal section azimuths are shown in Figure 13, as extended from Figure 11. The 

 spheroid has been referred to its center as origin of rectangular coordinates, with the refei^ence 

 plane — xz containing the point Q^icf)^, \j) as shown. The z-axis is the polar axis of the spheroid 



40 



