Degree of Curve (Chord Definition) - 14071_243

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By studying figure 11-4, you can see that the ratio design  speed  and  allowable  superelevation.  Then  the between the degree of curvature (D) and 360° is the radius is calculated. same  as  the  ratio  between  100  feet  of  arc  and  the circumference (C) of a circle having the same radius. That may be expressed as follows: Since  the  circumference  of  a  circle  equals above expression can be written as: the Solving this expression for  R: and also  D: Degree of Curve (Chord Definition) The  chord  definition  (fig.  11-5)  is  used  in  railway practice and in some highway work. This definition states that the degree of curve is the central angle formed by two radii drawn from the center of the circle to the ends of a chord 100 feet (or 100 meters) long. If you take a flat curve, mark a 100-foot chord, and determine the central angle to be 0°30’, then you have a 30-minute curve (chord definition). From observation of figure 11-5, you can see the following   trigonometric   relationship: Then, solving for  R: For a 1° curve, D = 1; therefore R = 5,729.58 feet, or meters, depending upon the system of units you are using. For a 10 curve (chord definition), D = 1; therefore R = In practice the design engineer usually selects the 5,729.65  feet,  or  meters,  depending  upon  the  system  of degree of curvature on the basis of such factors as the units you are using. Figure  11-5.—Degree  of  curve  (chord  definition). 11-5

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