Bungag, Jediann M. October 17, 2015

CE121-C1 Engr. G. Alviento

Route surveying

A route survey is a data collection operation to gather information about the proposed route of a roadway, utility pipe, or railway.

Types of Curves

Simple Curve

A simple arc provided in the road to impose a curve between the two straight lines.

Elements in Simple Curve

PC = Point of curvature. It is the beginning of curve. PT = Point of tangency. It is the end of curve. PI = Point of intersection of the tangents. Also called vertex

T = Length of tangent from PC to PI and from PI to PT. It is known as subtangent.

R = Radius of simple curve, or simply radius. L = Length of chord from PC to PT. Point Q as shown below is the midpoint of L. Lc = Length of curve from PC to PT. Point M in the the figure is the midpoint of

Lc. E = External distance, the nearest distance from PI to the curve. m = Middle ordinate, the distance from midpoint of curve to midpoint of chord. I = Deflection angle (also called angle of intersection and central angle). It is the

angle of intersection of the tangents. The angle subtended by PC and PT at O is also equal to I, where O is the center of the circular curve from the above figure.

x = offset distance from tangent to the curve. Note: x is perpendicular to T. θ = offset angle subtended at PC between PI and any point in the curve D = Degree of curve. It is the central angle subtended by a length of curve equal

to one station. In English system, one station is equal to 100 ft and in SI, one station is equal to 20 m.

Sub chord = chord distance between two adjacent full stations.

Equation to use:

T = R tan 0.5I

E = R sec 0.5I – R

m = R – R cos 0.5I

L = 2R sin 0.5I

LC = πRI / 180o

LC = 20I / D

LC = Sta PT – Sta PC

20 / D = 2πR / 360o

sin 0.5D = 10 / R

Example of Simple Curve

Pan – Philippine Highway (Bocaue, Bulacan)

Subic-Clark-Tarlac Expressway (Angeles, Pampanga)

Route 52 (West Lafayette, IN 47906, USA)

Compound Curve

Combination of two simple curves combined together to curve in the same direction.

Elements of compound curve

PC = point of curvature PT = point of tangency PI = point of intersection PCC = point of compound curve T1 = length of tangent of the first curve T2 = length of tangent of the second curve V1 = vertex of the first curve V2 = vertex of the second curve I1 = central angle of the first curve I2 = central angle of the second curve I = angle of intersection = I1 + I2 Lc1 = length of first curve Lc2 = length of second curve L1 = length of first chord L2 = length of second chord L = length of long chord from PC to PT T1 + T2 = length of common tangent measured from V1 to V2 θ = 180° - I

x and y can be found from triangle V1-V2-PI L can be found from triangle PC-PCC-PT

Finding the stationing of PT

Sta PT = Sta PC + LC1 + LC2

Sta PT = Sta PI – x – T1 + LC1 + LC2

Example of Compound Curve

TPLEx (Cuyapo, Nueva Ecija)

Subic-Clark-Tarlac Expressway

M9 (Linlithgow EH49, UK)

Reverse Curve

Combination of two simple curves combined together to curve in the same direction.

Elements of Reverse Curve

PC = point of curvature PT = point of tangency PRC = point of reversed curvature T1 = length of tangent of the first curve T2 = length of tangent of the second curve V1 = vertex of the first curve

V2 = vertex of the second curve I1 = central angle of the first curve I2 = central angle of the second curve Lc1 = length of first curve Lc2 = length of second curve L1 = length of first chord L2 = length of second chord T1 + T2 = length of common tangent measured from V1 to V2

Finding the stationing of PT

Sta PT = Sta PC + LC1 + LC2

Sta PT = Sta V1 – T1 + LC1 + LC2

Example of Reverse Curve

Marcos Highway (Marikina-Infanta Highway)

Governor’s Drive (Dasmarinas, Cavite)

Highway 401 (Muirkirk, Ontario, Canada)

Transition or Spiral Curve

A curve that has a varying radius. It’s provided with a simple curve and between the simple curves in a compound curve.

Fig: A Spiral Curve Diagram

Elements of Spiral Curve

TS = Tangent to spiral SC = Spiral to curve CS = Curve to spiral ST = Spiral to tangent LT = Long tangent ST = Short tangent R = Radius of simple curve Ts = Spiral tangent distance Tc = Circular curve tangent L = Length of spiral from TS to

any point along the spiral Ls = Length of spiral PI = Point of intersection I = Angle of intersection Ic = Angle of intersection of the

simple curve p = Length of throw or the distance from tangent that the circular curve has

been offset X = Offset distance (right angle distance) from tangent to any point on the

spiral Xc = Offset distance (right angle distance) from tangent to SC Y = Distance along tangent to any point on the spiral Yc = Distance along tangent from TS to point at right angle to SC

Es = External distance of the simple curve θ = Spiral angle from tangent to any point on the spiral θs = Spiral angle from tangent to SC i = Deflection angle from TS to any point on the spiral, it is proportional to the

square of its distance is = Deflection angle from TS to SC D = Degree of spiral curve at any point Dc = Degree of simple curve

Equation to use:

Y = L – L5 / 40R2LS2

X = L3 / 6RLS

p = 0.25XC = LS2 / 24R

θ = L2 / 2RLS

θS = LS / 2R

i = θ / 3 = LS / 6R

iLS2 = isL2

TS = 0.5LS + (R + P)tan 0.5I

IC = I – 2θS

ES = (R + P) / cos 0.5I – R

DLS = DCL

Example of Spiral Curve

Kennon Road (Tuba, Benguet)

Siquijor Circumferential Road (Siquijor)

95 (Al Ahsa, Saudi Arabia)

Symmetrical Vertical Curve

Typically, vertical curves are in the shape of an equal-tangent parabola (aka symmetric). This means the tangent length from VPC to VPI equals the tangent length from VPI to VPT. It is not required for the VPC and the VPT to be at the same elevation to have a symmetrical vertical curve.

Fig: A Symmetrical Vertical Curve Diagram

Equations to use:

A = g2 – g1

K = L / A

r = A / 100L

e = AL / 800

y = 4ex2 / L2 = rx2 / 2 = Ax2 / 200L

Ex = EVPC + g1x + rx2 / 2

x1 = - g1 / r

Et = EVPC - g12 / 2r

Examples of Symmetrical Vertical Curve

Buntun Bridge (Tuguegarao, Cagayan Valley)

Agas Agas Bridge (Southern Leyte)

Rialto Bridge (Venice, Italy)

Unsymmetrical Vertical Curves

An unsymmetrical curve is a curve in which the tangent length from VPC to VPI does not equal the tangent length from VPI to VPT. As already mentioned, symmetrical vertical curves are more common than unsymmetrical vertical curves, but since the designer is likely to encounter both, equations for both situations are provided.

Fig: An Unsymmetrical Vertical Curve Diagram

Equations to use:

A = g2 – g1

K = L / A

r = A / 100L

r1 = Al2 / 100Ll1

r2 = Al1 / 100Ll2

e = Al1l2 / 200L = r1l12 / 2 = r2l22 / 2

Ex1 = EVPC + g2x + r1x2 / 2

Ex2 = EVPC - g2x + r2x2 / 2

xt1 = - g1 / r1

xt1 = - g2 / r2

Et1 = EVPC - g12 / 2r1

Et2 = EVPC – g22 / 2r2

Examples of Unsymmetrical Vertical Curve

Python Bridge (Amsterdam, the Netherlands)