# Curve Definitions for Land Surveyors

**curve, characteristic—**A curve showing the relationship between exposure and resulting density in a photograph, usually plotted as the density (I)) against the logarithm of the exposure (log E) in candle-meter-seconds.

**curve, circular—**A curve of constant radius. All points on the curve are equal distance from the center of circle.

**curve, compound—**Name for two circular curves of different radius which are tangent at one point with both curves lying on the same side of the common tangent.

**curve, crest**—A vertical curve whose grade undergoes a negative change, i.e., it curves in a downward direction.

**curve, curve spiral point—**The point of tangency common to a circular curve and a spiral where the circular curve ends and the spiral begins. Also called C.S.

**curve, degree of-** The degree of curve (D) defines the radius of a highway or railroad circular curve. There are two definitions: **1 **In railroad and early highway design, the angle subtended at the center of a circle by a chord of 100 feet. **2** The angle subtended at the center of a circle by an arc of 100 feet; used in present day engineering of highway design.

**curve, easement—**See *curve, spiral.*

**curve, horizontal—**A curve connecting two tangents in a horizontal plane.

**curve, length of—**The distance from the point of curvature to the point of tangency. This distance can be measured along the curve for the arc definition, or by 100-foot chords for the chord definition.

**curve, loxodromic—**See *line, rhumb.*

**curve, point of compound curvature **(P.C.C)—The point where a circular curve of one radius is tangent to a circular curve of a different radius, both curves lying on the same side of their common tangent.

**curve, point of curvature—**The point where straight alinement ends and circular alinement begins. Also called the point of curvature (P.C.). See also *chord, long.*

**curve, point of intersection—**The point where the two tangents of a circular curve meet; point of intersection (P I.).

**curve, point of reverse curvature—**The point of tangency common to two circular curves, the curves lying on the opposite side of the common tangent; point of reverse curvature.

**curve, point of tangency—**The point where circular alinement ends and straight alinement begins; point of tangency (P.T.). See also *chord, long.*

**curve, reverse—**Name for two circular curves having a common tangent, the curves lying on opposite sides of the common tangent.

**curve,** **sag—**A vertical curve whose grade undergoes a positive change, i.e. it curves in an upward direction.

**curve, spiral-**^{1}The name for a variable radius curve used to provide a transition from straight alinement to circular alinement, the reverse, or between two circular curves of different radius. Also called transition, taper, or easement curves. Various specific definitions for a spiral have been used in the past, such as the ten-chord spiral (also called the American Railway Association Spiral), the Searles spiral and the cubic spiral. The spiral defined in this *Glossary *is the Euler spiral. This spiral, first investigated by the Swiss mathematician Leonard Euler, is a clothoid. The clothoid with the cubic parabola and the lemniscate have definite mathematical equations; the others, Searles and AREA are empirical. Mathematical simplicity, adaptability, and ease in staking and acceptance make the Euler spiral a standard. It has been accepted and used in publications by Hickerson, Barnett, and Pryor. See also *Euler spiral. *^{2} In route surveying, a curve of varying radius connecting a circular curve and a tangent, or two circular curves whose radii are, respectively, longer and shorter than its own extreme radii.

**curve,** **spiral curve point—**The point of tangency common to a spiral and a circular curve where the spiral ends and circular curvature begins. Also called S.C.

**curve, spiral tangent point—**The point where a spiral ends and straight alinement begins. Also referred to as S.T.

**curve, tangent spiral point—**The point where straight alinement ends and spiral alinement begins. Also called T.S.

**curve, transition—**See *curve, spiral *[ROUTE SURVEYING].

**curve, vertex of—**See *curve, point of intersection.*

**curve, vertical—**A parabolic curve used to connect grades of different slope to avoid the sudden change in direction in passing from one grade to the other. This method of grade change is usually used when there is an algebraic difference of more than 0.2 percent in the two opposing grades.

**curve spiral point—**See *curve, spiral curve point.*

**curves—**Curved rulers, termed irregular curves, or French curves, used for curved lines other than circular arcs. The patterns for these curves are laid out in parts of ellipses and spirals or other mathematical curves in various combinations.

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Source: NSPS “Definitions of Surveying and Related Terms“, used with permission.

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