Follow-up to Part 1Part 1 of this series described “early” geodetic leveling and the resolution of the International Geodetic Association in 1912. As a follow-up to that article, I read History of Geodetic Leveling in the United States by Ralph Moore Berry. To quote one short paragraph, “A distinction has been made between geodetic leveling and precise leveling in which the point is made that in geodetic leveling, all known imperfections in the instrument system (collimation, rod calibration, temperature, imbalance between foresight and back-distances, etc.) are compensated by the application of computed corrections, whereas in precise leveling it is attempted to reduce the magnitude of the observational errors to tolerable limits by careful and frequent adjustment and calibration of the instrument system, by which process the calculation of systematic corrections is minimized or totally eliminated.” Professor Berry starts his article by stating that geodetic leveling has been defined as “leveling of a high order of accuracy, usually extended over large areas, to furnish accurate vertical control for all surveying and mapping operations.”
The purpose of this series is to describe the standards and specifications that were used to establish the vertical control we use today. This is a history article, and I say history because, as I’ve been told, the U.S. National Geodetic Survey (NGS) has only one leveling crew for the entire United States. In the future, much of the vertical control will have to be established by other means.
BenchmarksBenchmarks are the monuments used to denote vertical control. The Manual of First-Order Leveling, Special Publication 140 refers to them as “Permanent Benchmarks.” The publication states, “The benchmarks are the only visible evidence of the work, and the necessary time and money should be spent to perpetuate the line by making the marks of a substantial character and by placing them in locations where they will be free from the usual causes of disturbance.”
The brass markers we see on benchmarks are called benchmark tablets (see Figure 1). These tablets have been set on both horizontal and vertical surfaces. When set in a vertical surface, it is less likely to be disturbed but most difficult to use by the surveying community. It used to be common practice to place the tablets in public buildings such as schools and courthouses. If placed on the steps of a building, it had to be on steps where the foundation extended below frost line.
Standard Concrete BenchmarksMost benchmark tablets were set in concrete posts, and there was a procedure for doing this. This procedure described the shape, material, and size and depth.
Shape The benchmark shall be larger at the base than at the surface of the ground. It may take the form of the frustum of a pyramid or cone or be a post with an enlarged base. If it is built in the form of a frustum, there should be a batter of not less than 1" to 1'. It is believed that a post with an enlarged base will offer just as great a resistance to the lifting effect of freezing and thawing as a conical post. The base should be not less than 4" larger in horizontal cross section than the post itself, and the enlarged portion should be at least 6" thick vertically. Care should be taken that the outside edges of the base are not rounded, as to prevent any change in elevation due to a sifting of sand particles or dirt around the edges during a thawing period. The portion of the mark above the frost line should be molded to lessen the lifting effect of the surface layers of the ground when freezing. These molds may be of sheet iron or wood and should have a slope of at least 1" to 1'. The sheet iron may be cut to proper size and shape, bent for a lock seam and carried flat until needed.
Material The main consideration in making concrete is to have clean materials. Mix the materials thoroughly before adding water. Make sure the mixture is not too wet and tamp well into the form. Each streak of dirt in concrete means a line of cleavage. Where rough aggregate is available, the proportions may vary from 1-2-3 to 1-3-5, but the top 12" of the mark should be of considerable richer mixture. When only cement and sand are available, the lower part of the mark should be proportioned one part of cement to three parts of sand. The upper part should be one part of cement to two parts of sand.
With a mark of the proper size, it will not be necessary to reinforce the concrete with metal rods or wire. To avoid cracking of the concrete due to rapid drying, it should be covered with paper or cloth and then with earth or other material for at least 48 hours.
Size and Depth Where lack of transportation does not make the cost prohibitive, the post should be not less than 12" in least cross-section dimension except at the top, where it is shaped by the mold, and that should not be less than 10". The top should extend from 2" to 4" above the surface. It should not be placed in a line of traffic.
The marks should extend below frost depth except where the frost penetrates to a greater depth than 4'. The minimum depth of any benchmark should be 36" below the surface, and the maximum depth should be 48". It is believed that with a mushroom base, a mark extending 48" below the surface will not be elevated by the action of frost, even though frost should extend below that depth. The instructions to the chief of the leveling party will in all cases specify the depth to which benchmarks should be set.
Descriptions of BenchmarksThe description of the permanent benchmarks was one of the most important tasks for leveling parties. The description had to explain, exactly, how a person could find the mark. I’m going to save description for the next column, where I’ll give instructions to find data sheets in the NGS database.
Geodetic LevelingThe following is copied from the publication Standards and Specifications for Geodetic Control Networks (Federal Geodetic Control Committee, 1984). Only the parts pertaining to vertical control are reproduced. Because of the large amount of space needed to describe the specifications, only the standards will be described in this article. Also, some of the terms used will need an explanation; I’ll do that in the next column. These standards and specifications are the ones in use today; early surveys did not have sophisticated instruments with optical micrometers. Also, NGS is the agency under the Federal Geodetic Control Committee that certifies order and class. (Note: Today the name Federal Geodetic Control Committee has been changed to Federal Geodetic Control Subcommittee.)
Vertical Control Network StandardsVertical control points are classified by order and class. When a vertical control point is classified with a particular order and class, NGS certifies that the orthometric elevation at that point bears a relation of specific accuracy to the elevations of all other points in the vertical control network. That relation is expressed as an elevation difference accuracy, b. An elevation difference accuracy is the relative elevation error between a pair of control points that is scaled by the square root of their horizontal separation traced along existing level routes. An elevation difference accuracy, b, is computed from a minimally constrained, correctly weighted, least squares adjustment by B = S/ (d)1/2 where d = approximate horizontal distance in kilometers between control points traced along existing level routes and S = propagated standard deviation of elevation difference in millimeters between survey control points obtained from the least squares adjustment. Note that the units of b are (mm)/ (km)1/2.
The elevation difference accuracy pertains to all pairs of points (but in practice is computed for a sample). The worst elevation difference accuracy (largest value) is taken as the provisional accuracy. If this is substantially larger or smaller than the intended accuracy, then the provisional accuracy takes precedence.
Geodetic leveling is a laborious task; not only do you have to make accurate observations, you also have to establish concrete monuments in remote locations. The next article in the series (September 2000) will address specifications.