Islamic University of Gaza Civil Engineering Department Surveying II ECIV 2332 By Belal Almassri

Chapter 9 Route Surveying – Part 5 - Transition Curve Layout Using The Theodolite. - Preliminary work and calculations. - Setting out the curves. - The whole procedure. - Example 9.4.

Transition Curve Layout Using The Theodolite: In order to lay out a combination of circular curve and transition curve, the following procedure is used: 1. Preliminary work and calculations. - Transition Curve. - Circular Curve. 2. Setting out the curve. - Left transition curve. - Right transition curve. - Circular curve. - Common tangent between transition and circular curves.

Transition Curve Equations Length of transition curve (L): - Past experience or uniform rate or equation - a: Rate of change of radial acceleration in m/sec^3 (0.3 – 0.5). - R: Circular curve radius. - V: Design speed in m/sec.

Transition curve shift (S): - The amount of distance that the circular curve is shifted inward to be adopted with the transition curve. - L: Length of transition curve. - R: Circular curve radius.

The total length of the tangent Ts or P-T line: - The total length from the point of the intersection PI to the start point of the transition T can be computed through the following formula: - L: Length of transition curve. - S: Shift of transition curve. - R: Radius of circular curve. - Δ : Central Angle.

Chainage of TS ( T ) and SC ( T 1 ): Chainage of T = Chainage of PI - P T Chainage of T 1 = Chainage of T + L Lengths of partial chords for the left transition curves: - C ≤ R/40 - C 1 to be as computed in circular curves. - C 2 = L – (C 1 + nC), n: intermediate chords.

Deflection angles of the transition curve: - Angle of T 1 (the spiral angle): - Deflection angle of transition curve: - CHECK!.....Sum of d i =

Underground...

The Whole Calculations Procedure: 1. Find R and Δ of the circular curve. 2. Find L, S and PT of the transition curve. 3. Find Chainage of T, T 1, T 2 and T Find the Partial chords and the deflection angles for the following: - Right transition curve. - Circular Curve. - Left Transition Curve.

Example 9.4

Vertical Curves Def: A parabolic curve that is applied to make a smooth and safe transition between two grades on a roadway or a highway. VPC: Vertical Point of Curvature VPI: Vertical Point of Intersection VPT: Vertical Point of Tangency G1, G2: Tangent grades in percent A: Algebraic difference in grades L: Length of vertical curve VPI VPC VPT

There are two kinds of vertical curve: SummetVertical Curves: Type I and Type II. Sag Vertical Curves : Type III and Type IV.

Information needed for vertical curves design: 1. Gradients g1 and g2. 2. Chainage and elevation of VPI. 3. Length of the curve L. Sight Distance: The length of the roadway visible to driver. 1. Stopping sight distance. (S.S.D) 2. Passing sight distance. (P.S.D)

Stopping Sight Distance (SSD) is the viewable distance required for a driver to see so that he or she can make a complete stop in the event of an unforeseen hazard.

V: Velocity in m/s t: Perception and reaction time (2.5 sec) f: coefficient of friction for roads i: gradient (Up is +ve, Down is –ve) g: gravity (9.81m/s^2)

Passing Sight Distance (PSD) is the clear distance that the driver must view in order to be able safely pass the car in front of him. (PSD=2. SSD)

Vertical Curve Calculations Location of Max/Min elevation on the curve: Elevation of any point on the curve:

Chainage and elevation of VPC and VPT:

Length of Vertical Curve: Method 1: K: Rate of curvature. (By Tables) A: Difference of gradients. Method 2: depends on the sight distance, gradient difference: Equations (9.46, 9.47, 9.48, 9.50) from the text book.

Example 9.7