The Role of an Ellipsoid in a Datum
The semimajor axis and flattening can be used to completely define an ellipsoid of revolution. The ellipsoid is revolved around the minor axis. However, in the traditional approach, six additional elements are required if that ellipsoid is to become a geodetic datum: three to specify its center and three more to clearly indicate its orientation around that center. The Clarke 1866 spheroid is one of many reference ellipsoids. Its shape is completely defined by a semimajor axis, a, of 6378.2064 km and a flattening, f, of 1/294.9786982. It is the reference ellipsoid of the datum known as the North American Datum of 1927 (NAD27), but it is not the datum itself.
For the Clarke 1866 spheroid to become NAD27, the ellipsoid of reference had to be attached at a point and specifically oriented to the actual surface of the earth. However, even this ellipsoid, which fits North America well, could not conform to that surface perfectly. Therefore, the initial point was chosen near the center of the anticipated geodetic network to best distribute the inevitable distortion between the ellipsoid and the actual surface of the earth as the network extended beyond the initial point. The attachment was established at Meades Ranch, Kansas, 39°13'26".686 Nφ, 98°32'30".506 Wλ, and geoidal height was considered to be zero. Those coordinates were not sufficient, however. The establishment of directions from this initial point was required to complete the orientation.
Azimuth from Meades Ranch to Waldo
The azimuth from Meades Ranch to station Waldo was fixed at 75°28'09".64 (from South) and the deflection of the vertical set at zero.
Once the initial point and directions were fixed, the whole orientation of NAD27 was established, including the center of the reference ellipsoid. Its center was imagined to reside somewhere around the center of mass of the earth. However, the two points were certainly not coincident, nor were they intended to be. In short, NAD27 does not use a geocentric ellipsoid.
Measurement Technology and Datum Selection
In the period before space-based geodesy was tenable, a regional datum was not unusual. The Australian Geodetic Datum 1966, the European Datum 1950, and the South American Datum 1969, among others, were also designed as nongeocentric systems. Achievement of the minimum distortion over a particular region was the primary consideration in choosing their ellipsoids, not the relationship of their centers to the center of mass of the earth. For example, in the Conventional Terrestrial System (CTS), the 3-D Cartesian coordinates of the center of the Clarke 1866 spheroid as it was used for NAD27 are about X = –4 m, Y = +166 m, and Z = +183 m. This approach to the design of datums was bolstered by the fact that the vast majority of geodetic measurements they would be expected to support were of the classical variety. That is, the work was done with theodolites, towers, and tapes. They were earth-bound. Even after the advent of electronic distance measurement, the general approach involved the determination of horizontal coordinates by measuring from point to point on the earth’s surface and adding heights, otherwise known as elevations, through a separate leveling operation. As long as this methodological separation existed between the horizontal and vertical coordinates of a station, the difference between the ellipsoid and the true earth’s surface was not an overriding concern. Such circumstances did not require a geocentric datum.