r.ln class 1 f 1 pfi 



Security Classification 



DOCUMENT CONTROL DATA - R&D 



(Security classitication ot title, body of abstract and indexing annotation must be entered when the 



all report is classified) 



1 ORIGINATIN G ACTIVITY (Corporate author) 



U. S. Naval Oceanographic Office 

 Washington, D. C. 20390 



2a. REPORT SECURI TV C L ASS I F I C A T I Oh 



Unclassified 



2b GROUP 



3 REPORT TITLE 



MATHEMATICAL MODELS FOR NAVIGATION SYSTEMS (U) 



4. DESCRIPTIVE NOTES (Type of report and inclusive dates) 



Technical Report 



5. ^UTHOR(S) (Las, name, firs, natr,e. initiaO THOMAS, PaUl D. 



6. REPORT DATE QctobeP 1955 



7a. TOTAL NO. OF PAGES 

 142 



7b. NO. OF REFS 



25 



Ba. CONTRACT OR GRANT NO. 



fa. PROJECT NO. HF- 103-04-02 



9a. ORIGINATOR'S REPORT NUMBERfS; 



Technical Report (TR)-182 



F31-36-ANB 



10. AVAILABILITY/LIMITATION NOTICES 



All distribution of this publication is controlled. Qualified DDC users shall 

 submit requests for copies to the: Commander, U. S. Naval Oceanographic Office, 

 Washington, D. C. 20390, ATTN: Code 4000 



11. SUPPLEMENTARY NOTES 



12. SPONSORING MILITARY ACTIVITY 



U. S. Naval Oceanographic Office 

 Washington, D. C. 20390 



13 ABSTRACT 



The principal objective of this study was an evaluation of the formulas 

 basic to the geodetic inverse solution for distance computations used by the 

 U. S. Naval Oceanographic Office in loran-type charting. The adequacy of the 

 formulas for past requirements was verified but, in anticipation of future 

 requirements, they were modified to give geodesic distances and azimuths 

 between any two points on the reference ellipsoid to uncertainties of less 

 than a meter and a second respectively. 



During the study, associated geometrical configurations were developed or 

 studied: latitudes associated with the auxiliary sphere-spheroid configuration; 

 a spherical rectangular coordinate system on the auxiliary sphere with hyper- 

 bolic loci referenced to it; and geometrical quantities associated with arc 

 distance, such as chord length, dip of the chord, maximum separation of chord 

 and arc, and the geographical position of the point of maximum separation. The 

 formulas with their derivations are presented, (U) 



DD 



1 JAN 64 



1473 



Unclassified 



Security Classification 



