CHAPTER 5 HORIZONTAL ALIGNMENT

1. Horizontal alignment is a combination of circular curves, tangents and transition spirals. 1. Straight distances ( Tangents):  The straight distances in horizontal alignment has to be not exceed 5 km, because of the following reasons: CHAPTER 5 HORIZONTAL ALIGNMENT

2.  - it is difficult to fit the different topography forms with too long alignment;  - the drivers will get tired on long tangents; - the blind danger from the headlights of the opposing vehicles; - it is difficult to estimate the distances between different vehicles.

3. 2.Circular curves:  When a vehicle traveled in a curved path, it is subjected to centrifugal force. This is balanced by an equal and opposite force developed through super-elevation and side friction. for alignment design, sharpness is commonly expressed in terms of degree of curve, which is the central angle subtended by a 100 ft.(30.5 m) length of a circular curve. The degree of curve is defined as: D = 1746.4 / R  1750 / R where: R = radius of the circular curve, m.

5. - Simple curve:  A simple curve is a circular arc adjoining two tangents, its properties are shown in Fig.14.

8. Highway Superelevation When a vehicles moves around a horizontal curve, it is subject to the outward radial force (centrifugal force) and the inward radial force. The inward force is not due to gravity, but rather because of the friction between tires and the roadway. At high speeds, the inward force is inadequate to balance the outward force without some help. That help arises from banking the road, what transportation engineers call superelevation (e). This banking, an inclination into the center of the circle, keeps vehicles on the road at high speed.

9. Centrifugal Force The minimum radius of circular curve (R) for a vehicle traveling at u kph can be found by considering the equilibrium of a vehicle with respect to moving up or down the incline. Let alpha (α) be the angle of incline, the component of weight down the incline is W*sin(α), the frictional force acting down the incline is W*f*cos(α). The "centrifugal" force Fc is

10. Fc =W * ac \ g where – ac = acceleration for curvilinear motion = v2/R – W = weight of the vehicle – g = acceleration due to gravity

12. where – fs = coefficient of side friction and – v2/g = R (tan (α) + fs)

13. Let tan(α)=e, g=9.8 m/sec2, u is in km/hr (and we need R in meters)

14. In rural areas with no snow or ice, a maximum superelevation (e) of 0.10 is used. In urban areas, a maximum of 0.08 is used. Values for fs vary with design speed.

15. Side-Friction (Mn)

17. Transition (Spiral) Curves: Transition or spiral curves are curves introduced between the straight tangent and circular curve on which the radius of curvature decrease gradually from infinity at the tangent-spiral intersection to the radius of the circular curve at the spiral circular curve intersection.

18. -Purposes of spiral curves in horizontal alignment: • 1-To avoid sudden change from straight motion to circular and thus helping the driver to keep his car inside the traffic lane; • 2-It minimizes encroachment of vehicles on adjoining traffic lanes and tends to promote uniformity in speed; •  3-Superelevation can be introduced gradually along transition curve and thus the change in super- elevation will conform to changes in curvature; • 4-It facilitates the transition in width where the • pavement section is to be widened around a circular curve.

19. -Length of transition curve: C.F. acceleration = v2/ Rc time consumed on spiral length = Ls/v rate of change of centrifugal acceleration = C = (v²/Rc) / (Ls/v) = v3 / Rc Ls recommended C = 0.6 m/sec3  Ls = v3 / 0.6 Rc = v3 / (3.6)3 x0.6 x Rc = V3 / 28 Rc

20. where: v = design speed, m/s; Rc = radius of circular curve, m; Ls = spiral length, m; V = design speed, km/h. Another method may be used to calculate the spiral length by using the following formula: Ls = A2 / Rc where: A : spiral parameter, m ( Tab. 18)

21. -Transition curve elements: PI = point of intersection of main tangent; Ts = tangent spiral, common point of tangent and spiral of near transition; SC= spiral curve, common point of spiral and circular curve of near transition; CS = curve spiral, common point of circular curve and spiral of far transition;

22. ST = spiral tangent, common point of spiral and tangent of far transition; Rc = radius of circular curve; Ls = length of spiral between TS and SC; Lc = length of circular curve; Ts = tangent distance PI to TS or ST or tangent distance of complete curve; Es = external distance PI to center of circular curve portion; LT = long tangent distance of spiral only; ST = short tangent distance of spiral only; LC = straight - line chord distance TS to SC; R = offset distance from the tangent to the PC of circular curve produced;

23. K = distance from TS to point on tangent opposite the PC of the circular curve produced = Xm;  = intersecting angle between tangents on entire curve; c= intersection angle between tangents at the SC and CS or central angle of central angle of the circular -curve portion of the curve; s = intersection angle between tangent of the compelete curve and the tangent at the SC, the spiral angle; s = deflection angle from tangent at TS to SC; xc, yc = coordinates of SC from the TS; xm,ym= coordinates of the center of circular curve from the TS.