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## Natural Arch Components

When we describe or discuss natural arches, it is frequently necessary to refer to the different parts or components that a natural arch comprises. This is especially true when either classifying or measuring natural arches. Most classification schemes are based, at least in part, on the shapes of various natural arch components and their spatial relationships with each other. It would be very difficult to define different types of natural arches without being able to refer to natural arch components by name. Attempts to define the dimensions of a natural arch without precise definitions for its components would face similar difficulties.

Most sources that describe natural arch components identify or define essentially the same set of components. Unfortunately, these sources use different words to label the same component. We present here a standard set of component names as well as definitions. Furthermore, most sources only describe components for one or two basic morphologies. The labels and definitions presented here cover all natural arch morphologies. Finally, no other source uses mathematical concepts to define natural arch components. We present here two sets of component definitions – a rigorous, mathematical set for use in classifying and measuring natural arches, and a simplified set for most other uses, e.g., general reference.

We start with a set of simplified definitions for the basic five components of a natural arch. The labels we will use for these five components are "opening," "entrance," "lintel," "base," and "abutment." We recommend the use of these terms as standards, even though, as stated above, other sources use different terms to refer to essentially the same components. The simplified definitions for these components follow. The reader may want to review the definition of a natural arch for context.

Definitions:

• The opening of a natural arch is the volume (of air or loose boulders) that fills the hole of the natural arch.

• An entrance to the opening of a natural arch is either of the two end surfaces of the opening that bound it (conceptually) from the rest of the atmosphere.

• The lintel of a natural arch is the volume of rock in the rock frame that is unsupported except at two ends by the remainder of the rock frame.

• The base of a natural arch is the surface (rock frame, soil, or water, but not loose boulders) that is under the opening or the lintel.

• An abutment of a natural arch is any volume of the rock frame that supports the lintel but is not part of the base.

Note that where soil or water partially fill the hole such filler material is not considered part of the opening, but is considered as part of the base. However, where loose boulders lie within the hole, they are ignored for purposes of measurement or classification, i.e., they are considered to be part of the opening as if they did not exist.

A natural arch with a single opening can have either one or two abutments, depending on its morphology. Generally, this depends on the orientation of the lintel. Horizontal lintels are usually supported above the base by two abutments (one on each end), while vertical lintels are supported by an abutment from above, and the base from below.

Some of these definitions are too ambiguous for classification and measurement purposes. We need to know more precisely where the entrances are and where the lintel starts and ends. To achieve this, we resort to mathematics. We begin by defining some new terms that will help us gain precision. These terms will also be of great importance when we discuss Natural Arch Dimensions.

Definition:

• An orbit is any closed loop on the surface of the natural arch that cannot be shrunk to a point. An orbit that encircles only air (loose boulders may be imbedded in the area encircled) is called an opening orbit. An orbit that encircles only rock is called a lintel orbit. Further, a planar orbit is an orbit that is confined to a plane, a vertical orbit is an orbit confined to a vertical plane, and a horizontal orbit is an orbit confined to a horizontal plane. Opening orbits and lintel orbits can be vertical, horizontal, planar, or non-planar. [See basic terminology for additional explanation and examples.]

Using these terms, we can now present rigorous definitions for three of the five natural arch components:

Definitions:

• The opening of a natural arch is the volume defined by the set of points interior to all planar opening orbits that exist on the surface of that natural arch. Should part of the rock frame intersect the area interior to any planar opening orbit, such rock is not included.

• An entrance to the opening of a natural arch is either of the two segments of the surface of the opening volume that are not also part of the surface of the natural arch.

• The lintel of a natural arch is the volume defined by the set of points interior to all vertical and horizontal lintel orbits that exist on the surface of that natural arch. If there are no vertical or horizontal lintel orbits, then the lintel is the volume of rock in the rock frame that is above the opening volume. [Should the lintel be pierced by a secondary natural arch, this secondary opening is ignored for purposes of defining the lintel of the primary natural arch.]

The definitions for base and abutment do not need to be refined.

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