Page | 15
1.2.3 Distortions in the Ellipsoidal Model As the reader will have surmised, the ellipsoidal model is not an exact fit. The larger the area covered by a datum, the more distortion there is. Height and Elevation – the elevation above MSL is not the same generally as the height above the ellipsoid. Corrections musb md oG ooh s ll d d‘h ghs’o djus hmom ns l l.M su mnsmd nd adjusted to mean sea level by the surveyor may be assumed to lie on the ellipsoid as long as the separation between the two surfaces is relatively small. Related to the previous one, the direction of the local vertical is not the same as the normal to the ellipsoid. This dff nc sknown s h ‘d fl c on n h c l’ ndh s ob mnmz d sp c lly cossl g gon l nd continental datums. This is done using Laplace corrections at regular intervals across the area of interest. Since these corrections vary in a non-regular and non-linear manner, the datum transformation between two datums may vary significantly across larger datums. The EPSG database is a means of identifying where a particular set of parameters should be used. Radius of curvature adjustment (Figure 13) – The ellipsoid has a radius of curvature at a point (varies across the ellipsoid). When measuring distances at heights above or below the ellipsoid of more than about 5000 ft, the distances need to be adjusted to allow for the change in radius of curva u , so h h y ‘m p’ co c ly on o h ll pso d. Measurements made above the ellipsoid need to be reduced and measurements made below the ellipsoid need to be increased respectively, so h m p of h (compu d h ‘ u ’ llpsod dus)m pco clyono h m p in relation to other features. The calculation can be made with the following equation:
Ellipsoidal length = d[1 –( h/(R + h))] where d = measured length
h = mean height above mean sea level (negative if below) R = mean radius of curvature along the measured line
Figure 13: Shows the increase in offset correction with depth and offset distance.
Made with FlippingBook flipbook maker