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Vertical alignment (GRD, Part 3 Chpt. 8)

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• topography of the area

• geotechnical conditions

• earthworks

• existing features to be crossed (roads, railways, rivers, utility services)

• clearances, protection depth requirements

• property entrances and threshold levels

• pedestrian access

• median openings

• visibility requirements

Vertical alignment is profile of centreline

Issues that can govern the level of the road:

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3Vertical grades Aim for grades as flat as possible ( > 1%)

Exaggerate speed differences (less than 3% minimises speed differential)

Enable storm water to drain to run‐off points ( > 1% provides adequate drainage)

Maximum grades (Table 8.3) Minimum grades (Table 8.5)

Steep grades can cause some vehicles to slow down (some vehicles cannot climb > 15%). (Refer to Table 8.2 on effect of grade on vehicle type)

Avoid long steep grades because of adverse effects on vehicle performance.

(Refer to Table 8.4 on desirable lengths of grades)

Operating speed (km/h)

TerrainFlat Rolling Mountainous

60 6 – 8 7 – 9 9 – 10

80 4 – 6 5 – 7 7 – 9

100 3 – 5 4 – 6 6 – 8

120 3 – 5 4 – 6 –

130 3 – 5 4 – 6 –

Location Minimum grade

Roads with kerb and channel

Des = 1%Abs. min = 0.3%

Roads in cutUnlined drainsLined drains

0.5%(1)

0.3%

Roads without kerb and channel and not in cut

0%(2)

4Vehicle speeds on Grades Table 8.2

Grade

Reduction in vehicle speed as compared to flat grade %

Road type suitabilityUphill Downhill

Light vehicle

Heavy vehicleLight

vehicleHeavy vehicle

0 – 3% Minimal Minimal Minimal Minimal For use on all roads

3 – 6 % Minimal

Somereduction on high speed

roads

Minimal MinimalFor use on low-moderate speed roads (incl. high traffic

volume roads)

6 – 9%Largely

unaffectedSignificantly

slowerMinimal

Minimal for straight alignment. Substantial for

winding alignment

For use on roads in mountainous terrain. Usually need to provide auxiliary lanes if high traffic volumes

9 – 12% Slower Much slower Slower

Significantly slower for straight alignment. Much

slower for winding alignment

Need to provide auxiliary lanes for moderate – high traffic volumes. Need to consider run-away vehicle facilities if

proportion of commercial vehicles is high

12 – 15%10 – 15

km/h slower

15% max. Negotiable

10 – 15 km/h

SlowerExtremely slow

Satisfactory on low volume roads (very few or no commercial vehicles)

15 – 33% Very slow Not negotiable Very slow Not negotiableOnly to be used in extreme cases and be of short lengths

(no commercial vehicles)

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Location Minimum clearance (m)

Urban and rural freeways 5.4Main and arterial roads 5.4Other roads 4.6High clearance routes 5.9Very high clearance routes (with no alternative) 6.5Pedestrian bridges • At lease 0.2 m greater than adjacent bridges, but no less than 5.4 m

• 5.5 m where there are no adjacent bridges• 6.0 m on designated high clearance routes

Major overhead sign structures • 5.4 m above any moving traffic lane to the lowest edge of the sign, supporting structure or lighting mounted below the sign

• 5.9 m for high clearance routes• 6.0 m where future lighting is considered

Pedestrian footpaths/subways 2.4Bicycle paths 2.5Railways(4) – measured from top of rail Freight routes (non-electrified)Suburban lines (electrified)

4.8 – 7.15.75 – 5.9

Tramways(5) – measured from top of railUnder structuresTrolley wire

5.35.07 to 5.64

Electricity Cables(6)

500 kV220 kV

17.014.5

Typical minimum vertical clearances over roadways and pedestrian/cycle paths (Table 8.1)

6Vertical alignmentMade up of:

• Series of straight grades (complying with maximum and minimum criteria) and vertical curves (complying with forward visibility, safety, comfort and appearance criteria)

• Grades can be positive or negative (going up or down in the direction being considered)

• Curves can be concave or convex (sag or crest)

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7Vertical curves• Usually based on the parabola, with gradually reducing radius starting from infinity

• Parabolic curve provides for constant vertical acceleration

• The change of grade is proportional to the length of the curve

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A

LK

Vertical alignment

K is the length of parabolic curve required to generate a 1% change of grade

It determines:

• the adequacy of the sight distance over a crest

• the feeling of discomfort on a sharp crest or sag curve

• the sight distance under a bridge on a sag curve

K is a value that defines the size of a parabolic curve

The value of K can be used to determine the radius of the apex of a parabolic curve: R =100K

= curve length

= algebraic differencein grades

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KAL

221

2

200 hh

SK

when S < L

and

2

2

212002

A

hh

A

SK

when S > L

where

L = length of vertical curve (m)

K = is the length of vertical curve in meters for 1% change in grade

A = algebraic grade change (%)

S = sight distance (m)

h1 = driver eye height, as used to establish sight distance (m)

h2 = object height, as used to establish sight distance (m)

• Crest Curves - must provide at least stopping sight distance for horizontal design speed

• Use SSD formula from previous session

• Sag curves - must meet comfort criteria, headlight performance

• Minimum vertical curves detract from appearance

• Avoid unnecessarily long crest curves in cut situations for drainage reasons

Vertical curve

10Length of crest vertical curves (Table 8.6)

Operatingspeed(km/h)

Min. grade change

requiring a crest

vertical curve% (1, 2)

Minimum length of

crest vertical

curve m (3)

Minimum K value (4)

S < L

40 1.0 20 – 30 20 – 30

50 0.9 30 – 40 33 – 44

60 0.8 40 – 50 50 – 62

70 0.7 50 – 60 71 – 86

80 0.6 60 – 80 100 – 133

90 0.5 80 – 100 160 – 200

100 0.4 80 – 100 200 – 250

110 0.3 100 – 150 333 – 500

120 0.2 100 – 150 333 – 500

130 0.1 100 – 150 333 – 500

1. In practice, crest vertical curves are frequently provided at all changes of grade.

2. VicRoads (2002a).3. RTA (1989).4. Round resultant L values up to nearest 5 m.

(Values determined with SSD for reaction time = 2 sec and d = 0.36).

Length of crest vertical curves – appearance criterion when S < L

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11Minimum crest vertical curve (Table 8.7)

Design speed(km/h)

Based on stopping sight distance for a car (1)

h1 = 1.1m h2 = 0.2m

Absolute minimum values for specific road types and situations(2)

based on d = 0.46(3) (4)

Desirable minimum values for most urban and rural road types

based on d = 0.36

Values for major highways and freeways in flat terrain

based on d = 0.26

RT = 1.5s (5) RT = 2.0s RT = 2.5s RT = 1.5s (5) RT = 2.0s RT = 2.5s RT = 2.0s RT = 2.5s

40 2.1 2.9 – 2.6 3.5 – 4.8 –

50 4.0 5.4 – 5.2 6.8 – 9.6 –

60 7.0 9.2 – 9.3 11.8 – 17.2 –

70 11.3 14.6 – 15.3 19.1 – 28.6 –

80 17.3 22.0 – 23.9 29.3 – 44.6 –

90 25.5 31.8 38.8 35.5 42.9 51.0 66.6 76.6

100 – 44.5 53.7 – 60.8 71.4 95.7 109.0

110 – 60.6 72.3 – 83.6 97.3 133.4 150.6

120 – 80.6 95.3 – 112.2 129.6 181.1 202.9

130 – 105.1 123.3 – 147.6 169.1 240.5 267.7

Minimum capability provided by the

crest vertical curve size(6)

Car stopping at night(7)

d = 0.61 (dry road braking), h1 = 0.65 m, h2 = 0.3 m.

d = 0.46, h1 = 0.65 m, h2 = 0.5 m.

d = 0.53 (dry road braking), h1 = 0.65 m, h2 = 0.2 m.

d = 0.46, h1 = 0.65 m, h2 = 0.3 m.

d = 0.37, h1 = 0.65 m, h2 = 0.2 m.

Truck stopping

Truck stopping at night(7)

d = 0.29, h1 = 2.4 m, h2 = 0.3 m.

d = 0.29, h1 = 1.05 m, h2 = 1.25 m.

d = 0.25, h1 = 2.4 m, h2 = 0.2 m.

d = 0.29, h1 = 1.05 m, h2 = 0.6 m.

d = 0.18, h1 = 2.4 m, h2 = 0.2 m.

d = 0.26, h1 = 1.05 m,h2 = 0.2 m.

Minimum size crest vertical curve (K value) for sealed roads (S<L)

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0

50

100

150

200

250

300

40 50 60 70 80 90 100 110 120 130

K v

alue

Speed km/h

d 0.46 T 1.5d 0.46 T 2.0d 0.46 T 2.5d 0.36 T 1.5d 0.36 T 2.0d 0.36 T 2.5d 0.26 T 2.0d 0.26 T 2.5

Crest K Values

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13K values for Trucks Table 8.9

Design speed(km/h)

Truck stopping sight distance h1 = 2.4m & h2 = 0.2m d = 0.29

RT = 1.5s RT = 2.0s RT = 2.5s

40 2 2 3

50 4 5 6

60 7 8 10

70 11 14 17

80 18 22 25

90 27 32 37

100 – 46 53

110 – 64 73

14Sag curves• Appearance and comfort are generally the limiting criteria

• Curves should not produce more than 0.05 g

(0.1 g on low standard roads and at intersections)• On unlit roads, design should consider headlight sight distance of

150 m• On two-way roads long sag curves >750 m should be avoided for

roadside drainage reasons

K

where

K = length of vertical curve in metres for 1% change in grade

a = vertical acceleration (m/sec2) = 0.05g (max)

V = speed of the vehicle (km/h)

g = gravitation force m/sec2 = 9.81 m/sec2.

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• Headlight sight distance

Sag curves sight distance criteria

1o

K

when S < L

𝐾2𝑆𝐴

200 ℎ 𝑠 tan 𝑞𝐴2 when S < L

and

where

h = mounting height of headlights (m)

S = stopping sight distance (m), in Table 5.4

q = elevation angle of beam 1° (+ upwards) (tan 1° = 0.01746)

A = algebraic grade change (%)

L = length of curve (m)

The minimum acceptable sag curve K values for a headlight mounting height of 0.65 m and one degree of light beam elevation.

16K values for sag curves (Figure 8.9)

Criteria for minimumsize sag vertical curves

Adapted from VicRoads Road Design Guidelines – Figure 2.5.10

Use of ‘K’ values exclusively through the guides

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17K Values for Sags

Speed Not Used Low Standard Comfort Headlights Aesthetics

40 1 3 4 7 7

50 2 4 7 11 11

60 3 6 10 16 16

70 4 8 13 21 21

80 5 10 17 28 28

90 6 13 21 35 43

100 8 16 26 42 61

110 10 19 31 51 84

120 11 23 37 60 112

130 13 27 43 69 148

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0

20

40

60

80

100

120

140

160

40 50 60 70 80 90 100 110 120 130

K v

alue

Speed km/h

Not Used Low Standard Comfort Headlights Aesthetics

K Values for Sags

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19Questions ?

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QUESTIONS?

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