The maximum comfortable speed on a horizontal curve is primarily dependent upon

# The maximum comfortable speed on a horizontal curve

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The maximum comfortable speed on a horizontal curve is primarily dependent upon the radius of the curve and the super-elevation of the carriageway. In addition, vehicle speeds and safety on high-speed roads are aided by extra- carriageway widths at curves themselves and the insertion of transition curves between straights and curves. In design of horizontal curves look out for MIN. RADIUS, SUPERELEVATION and CURVE WIDENING
Horizontal Alignment Lecture 4 13/04/14 11 Properties of Simple Circular Curve A simple curve is defined as a circular curve of single radius connecting two tangents. A circular curve joining two road tangents can be described either by its radius or by its degree of curvature. The degree of curve is defined as the central angle which subtends a 100m arc of the curve. (see sketch) The principal properties of a simple horizontal curve include PI, PC, PT, respectively known as points of intersection, curvature and tangency. Useful formulae for such a curve (see derivation in survey book): R= 50/sin (D/2); D= 5729.6/R ; T = R tan ( /2); L c = 2Rsin ( /2); L= 2 R /360; E= T tan ( /4), M= R[1-cos( /2 )] where, D= degree of curvature, E= external distance, L=length of curve, Lc =long chord length, M= chord- to-curve length, T= length of tangent, R= radius of curve
Horizontal Alignment Lecture 4 13/04/14 12 Minimum Radius of Horizontal Curve It can be shown that the minimum radius of a horizontal curve depends on the design speed (V), the superelevation (e), and the coefficient of side friction (f). 2 2 (tan ) 127( ) V V R g f e f
Horizontal Alignment Lecture 4 13/04/14 13 Superelevation In order to resist the outward-acting centrifugal force, it is customary to superelevate or slope the carriageway cross-section of curved sections of modern highways. Along a tangent section of a horizontal alignment both sides of the pavement crown slope away from the centerline of the highway. When this type of pavement crown (normal crown/camber) is carried along a curved section, the tendency to slip is retarded on the inside of the curve because of the banking effect of the crown. Conversely, the hazard of slipping is increased on the outside of the curve due to the outward sloping or negative crown of the pavement.
Horizontal Alignment Lecture 4 13/04/14 14 For every combination of radius of curvature and highway design speed, there is a particular rate of superelevation that exactly balances the centrifugal force. When f =0, and forces are in equilibrium, then the centrifugal force is entirely counteracted by superelevation. When the superelevation is insufficient to balance the outward force, it is necessary for some frictional force to be developed between the tyres and the road surface in order to keep the vehicle from sliding laterally. IN PRACTICE Superelevation is combined with Friction to ensure vehicle stability Good practice with respect to superelevation envisages a situation of one negotiating a curve at about the average speed of the road. This results in more gentle superelevation.

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• Fall '08
• Devine,D
• Slope, Osculating circle, Sag Curves

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