Journal of Surveying Engineering

The finite‐element‐volumes method is a new earthwork volumes technique quite unlike conventional methods. The algorithm provides automatic curvature and prismoidal correction using ordinarily available cross‐section data in conjunction with horizontal baseline geometry. The cross sections are approximated as a series of rectangular elements of equal, user‐specified width. As this width approaches zero, cross‐sectional area and centroid location approach that of the original cross section. Every element is assumed to transition linearly along an offset curve concentric with the baseline to an opposing element upstation or to terminate on a tapered offset curve when an opposing element does not exist. The resulting volume elements are thus curvilinear wedges or frustums of wedges. Linear, circular, and Cornu spiral baseline (clothoidal spline) components are accommodated by the method. Numerical examples show excellent agreement with exact results even when the mass components are not prismoidal. A general formula for the volume of a curvilinear mass component and a new, high‐precision, prismoidal curvature‐correction technique are also presented.

Basic geodetic theory is applied to determine the geodetic azimuth and geodetic altitude required to point dish antennas to geostationary communication satellites. The mathematical treatment presented here takes into consideration the ellipticity of the earth. This generalization contrasts with standard formulas published in technical books in satellite communication engineering where a spherical approximation is implemented. Comparisons between the spherical and more rigorous ellipsoidal methods are discussed. Although the differences between the two approaches are not significant, they should be taken into consideration when very precise pointing to geostationary communication satellites or other space objects is dictated. The suggested method is simple to understand and straightforward to implement, and due to its advantages should replace any spherical alternative currently in use.

The conventional units of surveying distance, the chain and the link, have been in use for about 200 years. Yet, for an important class of survey operations, halving distances, the units become fractional after very few bisections, so that it is impossible to reckon small distances in whole numbers of units. Furthermore, it is recognized that people are loath to adopt new systems of measurements if their units differ conspicuously from the old, familiar ones. The present paper suggests a new system of two units, the new link and the new chain, that are compatible with the old units' magnitudes and that allow much higher accuracy to be expressed solely in terms of integral numbers of units. An additional feature of the new system is a useful binary representation. With the considerable interest in geographic databases and information systems, the ability to compute rapidly with such units is important. The easy binary representation of distance in the new units satisfies this requirement.