The resurvey of the heartland of the Grand Canyon 1971-1975 was based on two USC & GS survey stations on the North Rim Of the Canyon (Sublime and Obi), one USGS station (Rowe) and one USC & GS station (Middle) on the South Rim — also USC & GS Bench Mark S-61 on the South Rim. Leveling of the USGS along the Bright Angel Trail was used as datum along this trail, as was National Park Service leveling along the lower ten miles of the North Kaibab Trail.
In all, 92 survey stations were used in this new network. Seventy-five of these were positioned by both theodolite and laser observations (see list). Two were unoccupied intersected points; 8 were targeted intersected points; and three were positioned by existing US government coordinates. The azimuth from "Middle" (at Yaki Point) to "Point Sublime" (both USC & GS stations) was assumed as the basic direction on which all others were hung. This direction was also checked by observations at Middle to USC & GS station "Royal" at the southeastern tip of the North Rim, well outside the area being mapped.
Horizontal and vertical angles were measured with a Wild T-3 theodolite. Slope distances were measured with a Laser Ranger II, a Ranger III, and a Rangemaster I, loaned to the project by Laser Systems and Electronics Inc. of Tullahoma, Tennessee, now a division of Keuffel & Esser, Inc. Although most stations were occupied by both theodolite and laser, a small number were not instrument-stations and positioned by intersection of targets set up on them in advance. Two stations (Isis and Osiris) were intersected and not occupied at all.
The helium-neon laser of the Rangers that were used was modulated by a crystal-controlled, electro-optical cell and directed onto an array of retro-prisms positioned at the point to which the distance measurement was to be made. The reflected beam returned from the prisms to the Ranger which is both a transmitter and receiver. Here the light-beam is converted into an electrical signal. The transmitted and reflected beams are compared by the instrument’s self-contained computer which performs a succession of "phase-comparison" measurements, averages them and then converts the result into a direct digital distance readout either in hundreds of a foot or millimeters, as desired.
One problem related to the precision of these distance-measurements remains unresolved, though of little practical importance, because of the relatively short lengths of the lines: This arose from the fact that all "parts-per-million" corrections fed into the Ranger’s computer were based on the average barometric pressures and temperatures, taken at both ends of the line at the time of measurement. Without the costly use of a helicopter to fly a thermometer along the line at the time the measurement is being made, it is clearly impossible to ascertain the true average temperature of the air-mass out in mid-air between the Canyon’s pinnacles.
The stations in the network (see diagram) were distributed as evenly as possible over the area to be mapped, except in the area of the heavily-forested North Rim plateau. However, vertical control was brought into the center of this area by leveling northward up a woodroad from Tiyo Point. The positions and altitudes of four points on the South Rim (Yaki, Yavapai, Hopi, and Pima) precisely linked by both laser and theodolite, anchored near the center on USGS "Rowe" and on the east at USC & GS first order station "Middle" provided a "composite base" for the network. All points out in the Canyon and along its opposite rim were linked by triangulation or trilateration to this South Rim axis, with checks to "Sublime" (slightly beyond the West edge of the map) to the west and "Obi" to the east on the North Rim.
All computations were carried out on the Arizona State Grid System. The laser slope-distances were first reduced to the horizontal and then to sea level and finally to the grid system. Horizontal angles, as measured in the field, were used directly in the grid computations, without change. The theoretical difference between field angles and grid angles was less than one arc/sec and was therefore ignored.
Elevations were based on the altitudes of Yaki and Hopi, tied by closed, precise level-loops to USC & GS Bench Mark S-61 (6876.164 ft.) at the head of the Santa Fe railroad tracks on the South Rim. All other elevations were computed from vertical angles and horizontal distances, the great majority of which were slope-corrected laser-distances. In many cases, reciprocal vertical angles were observed, which gave additional strength to the station involved. It is our belief that all altitudes are accurate within 0.2 foot. Many are within 0.1 foot. Geographical positions are probably accurate to within 0.10 foot. The appended Control Diagram makes clear the distribution of the survey stations and the method used to fix the position of each. Many of these stations were in essence trilaterated and the horizontal angles used for checking only. Tables of Altitudes, Geographical Positions and Laser Data are also appended for reference purposes.
Since this work was completed, a controversy has arisen with regard to the altitude of Bench Mark S-61. This has not yet been resolved, but, if an error does indeed exist at this station as alleged, all altitudes on this map must be adjusted upward by approximately two feet.