Vertical AlignmentVertical Alignment

TS4447 Highway GeometricTS4447 Highway Geometric

Horizontal Alignment

Vertical Alignment

Bad Combinations of Bad Combinations of Horizontal and Vertical CurvatureHorizontal and Vertical Curvature

Good Combinations of Good Combinations of Horizontal and Vertical CurvatureHorizontal and Vertical Curvature

Bad Combinations of Bad Combinations of Horizontal and Vertical CurvatureHorizontal and Vertical Curvature

Vertical AlignmentVertical Alignment

• Maximum Grade• Critical Length of Climbing Lane• Property of Simple Parabolic Curve• Vertical Curve

• Crest • Sag

• Minimum Length of Vertical Curve

Typical MassTypical Mass--Haul DiagramHaul Diagram

STA.4+200 STA.4+300 STA.4+400 STA.4+500 STA.4+600 STA.4+700

20,00

25,00

30,00

35,00

40,00

45,00

20,00

25,00

30,00

35,00

40,00

45,00

Gambar 2 Profil Elevasi Tanah

Existing Ground ProfileExisting Ground Profile

STA.4+200 STA.4+300 STA.4+400 STA.4+500 STA.4+600 STA.4+700

20,00

25,00

30,00

35,00

40,00

45,00

20,00

25,00

30,00

35,00

40,00

45,00

Gambar 2 Profil Elevasi Tanah

Existing Ground ProfileExisting Ground Profile

STA.4+200 STA.4+300 STA.4+400 STA.4+500 STA.4+600 STA.4+700

20,00

25,00

30,00

35,00

40,00

45,00

20,00

25,00

30,00

35,00

40,00

45,00

Gambar 2 Profil Elevasi Tanah

Existing Ground ProfileExisting Ground Profile MAXIMUM GRADE (G)MAXIMUM GRADE (G)

Grade (%) = ( H / L )Grade (%) = ( H / L ) x 100x 100Slope Ratio = H : LSlope Ratio = H : L

Tan Tan α α ((oo) = H / L) = H / L

ααGG

LL

HH

850

760

670

680

590

5100

Maximum Grade (%)

Design Speed (km/h)

RSNI 2004 Table 19 p. 41 MAXIMUM CRITICAL LENGTH OF MAXIMUM CRITICAL LENGTH OF GRADE WITHOUT CLIMBING LANEGRADE WITHOUT CLIMBING LANE

Critical Length of Up Grade Slope

G %

Properties of ParabolaProperties of Parabola

1. The line joining the midpoint C of a chord AB of a parabola with the intersection D of the tangents at the ends of the chords is bisected by the parabola it self at E. Thus DE = EC.

2. Offsets from the tangent to the parabola vary as the square of the distance from the point of tangency.

3. The rate of change of curvature of the parabola varies directly as the distance.

Source: Barry, B. Austin (1988)

11STST Property of ParabolaProperty of Parabola

Source: Barry, B. Austin (1988)

D E C

B

A

D

E

CA

B

22ndnd Property of ParabolaProperty of Parabola

Tangent to ParabolaParabola

(2/3)2 10.00 = 4.44

(1/3)2 10.00 = 1.11

10.00

1/3 T2/3 T

T

33rdrd Property of ParabolaProperty of Parabola

The initial gradient changes uniformly with the distance: the rate of change of gradient in percent per station (r) is constant between the initial gradient (g1) and the final gradient (g2):

Lggr 12 −

=

33rdrd Property of Parabola Property of Parabola (cont(cont’’d)d)

For,g1 = -2.00%g2 = +4.00%L = 6 Sta.

r = (-2.00% - (+4.00%))/6 Sta.= -1.00%/Sta.

33rdrd Property of Parabola Property of Parabola (cont(cont’’d)d)

The initial gradient = + 4.00% will run out to 0% at this constant rate in four stations, thus giving the high point at Sta. 61:

g1 + r(n’) = 0%;n’ = -g1/r

= -4.00%/-1.00% = 4.00 Sta. From PVC

A Simple Computation of Parabolic A Simple Computation of Parabolic Vertical CurveVertical Curve

80

84

88

92

96

100

55 56 57 58 59 60 61 62 63 64 65

STATIONING OF ROUTE

ELE

VA

TIO

N O

F R

OU

TE

Tangent Elevation Curve Elevation Chord Elevation

PV

C

PV

I

PV

T

g1 = + 4.00%

g2 = - 2.00%

El. 100.00D

E

C

A

B

El. 88.00

El. 94.00

Parabolic Vertical Curve

Forward Tangent

Following Tangent

El. = 1/2 (100+91) = 95.50

El. = 1/2 (94+88) = 91.00

Finding offsets at any point Finding offsets at any point for a vertical parabolic curvefor a vertical parabolic curve

Offset at Sta. 58 = offset at Sta. 62= (1/3)2 4.50 = 0.50

Offset at Sta. 59 = offset at Sta. 61= (2/3)2 4.50 = 2.00

L = ( A x SL = ( A x S22 ) / 658 ) / 658 S < LS < LL = 2S L = 2S –– ( 658 / A )( 658 / A ) S > LS > L

L crest curve length (m)A algebraic difference in grade (%)S stopping sight distance (m)

Standard Minimum Crest Vertical Curve Standard Minimum Crest Vertical Curve Length for Stopping Sight DistanceLength for Stopping Sight Distance

RSNI 2004 p.41 & Table 20 p.42

Z = AS / 800Z = AS / 800

A algebraic difference in grade (%)S stopping sight distance (m)

Z > h1 Z > h1 S < LS < LZ < h1 Z < h1 S > LS > L

S < L or S > L ?S < L or S > L ? Standard Minimum Crest Vertical Curve Standard Minimum Crest Vertical Curve Length for Stopping Sight DistanceLength for Stopping Sight Distance

Standard Minimum Crest Vertical Curve Standard Minimum Crest Vertical Curve Length for Stopping Sight DistanceLength for Stopping Sight Distance

Standard Minimum Crest Vertical Curve Standard Minimum Crest Vertical Curve Length for Stopping Sight DistanceLength for Stopping Sight Distance

L = ( A x SL = ( A x S22 ) / (120 + 3,5S)) / (120 + 3,5S) S < LS < LL = 2S L = 2S –– [ (120 + 3,5S) / A ][ (120 + 3,5S) / A ] S > LS > L

L sag curve length (m)A algebraic difference in grade (%)S stopping sight distance (m)

Standard Minimum Sag Vertical Curve Length Standard Minimum Sag Vertical Curve Length for Stopping Sight Distancefor Stopping Sight Distance

RSNI 2004 p.42 & Table 21 p.43

Standard Minimum Sag Vertical Standard Minimum Sag Vertical Curve Length for Stopping Sight Curve Length for Stopping Sight

DistanceDistance

STOPPING SIGHT DISTANCESTOPPING SIGHT DISTANCE

( )gfVVDSSD ±

+=254

7,02

PASSING SIGHT DISTANCEPASSING SIGHT DISTANCE

4321 ddddDPSD +++= 432min 32 dddDPSD ++=

[SSGDUR 1992 p.33 or p.123-125]

Calculated Stopping Sight DistanceCalculated Stopping Sight Distance

Source:Standar Specification for Geometric Design of Urban Roads, 1992

( )gfVVSSD+

+=2

00394.0694.0

V = running speed (kph)f = friction coefficientg = grade (%)

Calculated Stopping Sight Distance Calculated Stopping Sight Distance (cont(cont’’d)d)

0.440.44202020200.440.44303030300.380.38363640400.350.35454550500.330.33545460600.310.31686880800.300.3085851001000.290.29102102120120

Friction Friction CoefficientCoefficient

Running SpeedRunning Speed((kphkph))

Design Speed Design Speed ((kphkph))

Source:Standar Specification for Geometric Design of Urban Roads, 1992

STOPPING SIGHT DISTANCE CHART FOR DESIGN SPEED 20 - 50 kph

10

20

30

40

50

60

70

10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Grade (%)

Stop

ping

Sig

ht D

ista

nce

(m)

V=50kph

V=40kph

V=30kph

V=20kph

( )gfVVSSD+

+=2

00394.0694.0

V = running speed (kph)f = friction coefficientg = grade

STOPPING SIGHT DISTANCE CHART FOR DESIGN SPEED 60 - 100 kph

50

100

150

200

250

300

10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Grade (%)St

oppi

ng S

ight

Dis

tanc

e (m

)

V=120kph

V=100kph

V=80kph

V=60kph

( )gfVVSSD+

+=2

00394.0694.0

V = running speed (kph)f = friction coefficientg = grade

L = ( A x SL = ( A x S22 ) / [ 800 (C) / [ 800 (C--1,5) ] 1,5) ] S < LS < LL = 2S L = 2S –– [ 800 (C[ 800 (C--1,5) / A ] 1,5) / A ] S > LS > L

L sag curve length (m)A algebraic difference in grade (%)S stopping sight distance (m)C vertical clearance (m)

Standard Minimum Sag Vertical Curve Standard Minimum Sag Vertical Curve Length for Underpass Sight DistanceLength for Underpass Sight Distance

RSNI 2004 p.43 & Table 21 p.43

Standard Minimum Sag Vertical Standard Minimum Sag Vertical Curve Length for Underpass Sight Curve Length for Underpass Sight

DistanceDistance

L = K x A L = K x A

K Crest Curve Table 20 page 42Sag Curve Table 21 page 43

L crest curve length (m)A algebraic difference in grade (%)

Standard Minimum Vertical Curve Length Standard Minimum Vertical Curve Length for Kfor K--ValueValue

RSNI 2004 Table 20 p.42 & Table 21 p.43

ym

xm

TugasTugas MingguMinggu DepanDepan

1. Elevasi rencana2. Maximum Grade3. Lengkung Vertikal

Dikumpulkan 29 April 2009 sebelum jam 12:00 wib (via email & CDRW)