Notice that in both the arc definition and the chorddefinition, the radius of curvature is inverselyproportional to the degree of curvature. In otherwords, the larger the degree of curve, the shorter theradius; for example, using the arc definition, the radiusof a 1° curve is 5,729.58 units, and the radius of a 5°curve is 1,145.92 units. Under the chord definition, theradius of a 1° curve is 5,729.65 units, and the radiusof a 5° curve is 1,146.28 units.CURVE FORMULASThe relationship between the elements of a curveis expressed in a variety of formulas. The formulas forradius (R) and degree of curve(D), as they apply toboth the arc and chord definitions, were given in thepreceding discussion of the degree of curvature.Additional formulas you will use in the computationsfor a curve are discussed in the following sections.and solving for T,Chord DistanceBy observing figure 11-7, you can see that thesolution for the length of a chord, either a full chord(C) or the long chord (LC), is also a simpleright-triangle solution. As shown in the figure, C/2 isone side of a right triangle and is opposite angle N2.The radius (R) is the hypotenuse of the same triangle.Therefore,and solving for C:Tangent DistanceLength of CurveBy studying figure 11-6, you can see that thesolution for the tangent distance (T) is a simpleright-triangle solution. In the figure, both T and R aresides of a right triangle, with T being opposite to angleN2.Therefore, from your knowledge of trigonometricfunctions you know thatIn the arc definition of the degree of curvature,length is measured along the arc, as shown in view Aof figure 11-8, In this figure the relationship betweenD, & L, and a 100-foot arc length may be expressedas follows:Figure 11-6.—Tangent distance.Figure 11-7.—Chord distance.11-6

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