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.

aR

vL

3

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.

R

LS

24

2

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.

2)

2tan()(

LSRPT

Chainage of TS ( T ͦ ) and SC ( T1):

Chainage of T ͦ = Chainage of PI - P T ͦ

Chainage of T1 = Chainage of T ͦ + L

Lengths of partial chords for the left

transition curves:

- C ≤ R/40

- C1 to be as computed in circular curves.

- C2 = L – (C1+ nC), n: intermediate

chords.

Deflection angles of the transition curve:

- Angle of T1 (the spiral angle):

- Deflection angle of transition curve:

- CHECK! .....Sum of di =

180.

2R

Ls

180.

6

2

LR

Cd i

i

3

s

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 ͦ , T1, T2 and T3.

4. 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)

)(2.

2

ifg

VtVSSD

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:

A

Lgx 1

maxmin/

2

12

xL

AxgHH VPCM

Chainage and elevation of VPC and VPT:

2

2

2

2

2

1

LCHCH

LgHH

LCHCH

LgHH

VPIVPT

VPIVPT

VPIVPC

VPIVPC

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.

AKL .

Example 9.7