Carved in Stone
And Last Comes XYZ
Cartesian Coordinates can be used to specify the position of any point in three-dimensional space by measuring its distances from three mutually perpendicular planes.
Aggregate operations, or anything else, for that matter, can be located on the earth in a number of ways. When selecting a method, it is important to use unique identifiers. Let’s look at two suburban communities and see how we can differentiate them.
Suburb #1 is called Anthem. Suburb #2 is called Anthem.
Suburb #1 was built by a nationally known developer. Suburb #2 was built by the same developer.
Suburb #1 is located about 15 miles north of a major U.S. metropolitan area. #2 – Ditto.
#1 is located off Exit 229 along the major north/south interstate that serves the area. # 2 – Ditto.
#1 gets much of its aggregate from a nearby river valley. #2 – Ditto.
About 80 percent of the aggregate used by the state in which #1 is located is sand and gravel; about 20 percent is crushed stone. #2 – Ditto.
The annual per capita consumption of aggregate in the state in which Suburb #1 is located is about 6.5 tons. #2 – Ditto.
These identifiers are not helping to distinguish these two suburbs. Fortunately, there are more precise techniques to describe locations. Some people, especially when using geographic information systems (GIS), use three Cartesian coordinates (X, Y, and Z) to specify locations on the earth’s surface, where X is the longitude, Y is the latitude, and Z is the altitude of the point. The coordinates for Suburb #1 are: X = -105° 2′ 30″; Y = 39° 59′ 47″; Z = 5,180 feet. The coordinates for Suburb #2 are: X = -112° 8′ 08″; Y = 33° 51′ 55″; Z = 1,860 feet.
The third Cartesian coordinate – Z – does not always refer to the altitude of the land surface. Sometimes, such as in mine planning software, Z refers to the height above or below the land surface. For example, the alluvial gravels of the river near suburb #2 occur as three distinct alluvial deposits. The upper deposit (Z = 0 to -15 feet) consists of an even mix of sand and gravel and generally meets specification for durability and abrasion resistance after processing.
The middle deposit (Z = -15 to -30 feet) is slightly more clayey with larger sized gravel and slightly more coarse sand than the overlying deposit. It is lower quality than the upper deposit, and waste factors increase by about 3 percent.
The bottom deposit (Z = -30 to about -45 feet) comprises the lowest deposits that can be extracted without extensive inter-burden removal. However, it generally does not make construction-grade aggregate, unless it is blended with other, higher-quality material.