A curve is a part of the arc of a circle. It is limited at each end by the radii of the circle which form a central angle at the center of the circle. Curves are described by the following terms:

A. Radius is the distance from a point on the curve to the center of the circle.

B. Length of curve is the linear measurement of the curve.

C. Concavity is the inside or indented side of the curve. Conversely, the convex side of a curve is the outside or the side of the curve away from the center of the circle.

D. Direction upon a curve is the general bearing along the curve (such as, northerly, etc.) Direction applied to concavity specifies the bearing from the concave curve at its midpoint to the center of the circle.

E. Tangency occurs when a curve is tangent to a course at a point if the radius of the curve at that point makes an angle of 90° with the course.

F. Radial bearings are furnished if a curve is not tangent to a course at the point of intersection thereof. The length and bearing of the radius must be given to determine the center of the circle.

The following is a list of the types of curves encountered in legal descriptions:

A. A simple curve is the arc of a circle of a given radius.

B. Curves are compound at a point if the curves have a common radial line at the point of contact, different lengths of radius and the centers of the circles are on the same side of the curve.

C. Curves are reverse if they have a common radial line at the point of reverse and the centers of the circles are on opposite sides of the curve.

D. Curves are tangent if they have a common radius or radial line at the point of contact.

The radius of a 1° curve is approximately 5730 feet calculated on a constant chord of arc of 100 feet. To find the radius of any curve described by degrees, divide 5730 by the number of degrees in the curve desired. Thus, a 10° curve has a radius of approximately 573 feet. Curves named by angular descriptions are used principally for railroad surveys.