H. O. 229 INTERPOLATION

E. B. Brown and J. J. Speight

Peer Reviewed

Abstract: This paper amplifies and, in some cases, clarifies the instructions for the various interpolation procedures as printed in each volume of H.O. Pub. Ko. 229, Sight Reduction Tables for Marine Navigation. The designs of the special interpolation diagrams and tables are outlined. The relationship of the Interpolation Table with the second and third terms of Bessel’s Interpolation Formula is shown. A graphical correlation of the several manipulations of the interpolation diagrams with the simple alternative procedure described in H.O. 229 for interpolating altitude for hour angle and latitude increments is used to illustrate the principles upon which the design of the diagrams is based. Knowledge of the principles, in turn, enables more expeditious use of diagrams. Also, the latter correlation indicates the relative merits of the two basic procedures. The alternative procedure requiring a simple graphical construction on the plotting sheet or chart is considered more suitable for great-circle solutions. The precisions with which the solutions are determined using the diagrams are not justified when using the assumption that the spheroidal Earth is a perfect sphere; the relative complexity of the use of the diagrams tends to increase the number of blunders. The treatment of interpolation for second differences provides a graphical illustration of why the double second-difference correction is always positive. The coverage of the linear part of the Interpolation Table reveals the inclusion of certain modifying quantities in the tabular values. Their inclusion explains tvhy the values as extracted from the tens part of the table are not always to the nearest tenth of a minute according to the entering arguments.
Published in: NAVIGATION, Journal of the Institute of Navigation, Volume 20, Number 3
Pages: 193 - 207
Cite this article: Brown, E. B., Speight, J. J., "H. O. 229 INTERPOLATION", NAVIGATION, Journal of The Institute of Navigation, Vol. 20, No. 3, Fall 1973, pp. 193-207.
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