1. Vertical alignment controls how the road follows the existing terrain.
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
VERTICAL ALIGNMENT
Vertical alignment controls how the road follows the existing terrain.
Grades are connected with parabolic vertical curves calculated using the stopping sight distance and grade difference.

2. If NO Vertical Alignment is provided . . . . .
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
If NO Vertical Alignment is provided

3. If Vertical Alignment is provided . . . . .
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
If Vertical Alignment is provided

4. Suggested maximum grades for Tolled Expressways (LLM)
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
GRADES
Maximum Grade
Roadway grades have a direct correlation with the uniform operation of vehicles.
Vehicle weight and the steepness of the grade have a direct relationship on the ability of the driver to maintain a uniform speed.
Flatter grades should be used where possible.
The following are the suggested maximum grades based on design speed.
Suggested maximum grades for Tolled Expressways (LLM)
Design speed (km/h)
140
120
100 80
Maximum grade (%) 3 4 5 6

5. Desired maximum grade (%)
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
Suggested maximum grades for roads (JKR)
Design speed (km/h)
Desired maximum grade (%)
Maximum grade (%)
120 2 5
100 3 6 80 4 7 60 8 50 9 40 10 30 12 20 15
Minimum Grade
The minimum grade (Malaysia road practice)
0.2 – 0.3% (LLM) and 0.35 – 0.5% (JKR)
Minimum grades is mainly in the removal of water from the pavement surface.

6. Critical Grade Length (m)
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
Critical Grade Length
The performance of a vehicle on a grade is not only influenced by maximum grade but also the grade length.
The critical grade length is the maximum length a loaded truck can traverse a climbing lane without significantly reducing its speed.
Suggested critical grade  lengths (JKR)
Design speed (km/h)
Grade (%)
Critical Grade Length (m)
120 3 4 5
500
400
300
100 6 80 7 60 8
250
200 50 9
170 40 10
150

7. Warrant for climbing lane:
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
Climbing Lane
Climbing lanes are introduced on steep upgrades to provide a lane for trucks and other slow moving vehicles whose speed drop as the result of the grade.
Warrant for climbing lane:
A climbing lane is required if all three of the following criteria are met:
1) A speed reduction of 15 km/h for a 300 lb/hp truck.
2) Upgrade traffic flow exceeds 200 veh/h.
3) Upgrade truck traffic flow exceeds 20 veh/h.

8. Design of climbing lane according to JKR specifications:
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
Design of climbing lane according to JKR specifications:
Climbing lane must end at least 60 m beyond the crest of the curve, or when safe passing sight distance is achieved. The desired end taper length is 100 m.
Adequate traffic signs and pavement markings must be provided to ensure drivers are aware of the limitations of movements.
Shoulder width must not be less than 1.25 m. Desirably, shoulder length must be equal to the normal lane width.
Climbing lane starts at the foot of the grade with taper length not less than 50 m.
Climbing lane width is 3.25 m or equal to the normal travel lane width.

9. Suggested minimum k values for vertical curves (JKR)
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
Vertical Curve Length
The minimum vertical curve length is given by the formula L = kA, where A is the algebraic difference between the grades and k is the horizontal distance required to influence a 1% change in gradient.
k is also the measure of curvature for vertical curves.
Suggested minimum k values for vertical curves (JKR)
Design speed km/h
Minimum k value
Sag Curve
Crest curve
120 60
100 40 80 28 30 15 50 12 10 8 5 20

10. Crest Curves Sag Curves
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
VERTICAL CURVES
Vertical curves are employed to provide gradual change between roadway grades.
Vertical curves should be simple in application and should result in a design that is safe and comfortable in operation, pleasing in appearance, and adequate for drainage.
Types of curves:
Crest Curves Sag Curves

11. Elements of a Vertical Curve
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
Elements of a Vertical Curve
BVC
VIP
EVC
A% = G1 – G2 G1 G2 E y Y x
L (vertical curve length)
L/2
VIP = vertical intersection point
x = horizontal distance from a point on the curve, measured from BVC
G1 and G2 = tangent grades
BVC = beginning of vertical curve
EVC = end of vertical curve
E = elevation of minimum/maximum point on the curve, measured from BVC
algebraic difference between grades G2 and G1

12. Maximum/minimum point on the curve:
Therefore,
where,
At maximum/minimum point,

13. Elevation of a point on the curve:
LPn = G1*(Interval) + LPn-1
yn =
where e =
LPn yn Lx xn
Note : the elevation at any point on the curve can be obtained using the following equations

14. Example of Vertical Curve Design:
Given,
G1 = +2.0%
G2 = -3.0%
L = 300 m
Interval = 25 m
Elevation at BVC = m
VIP = m
EVC = m
Design the crest vertical curve and determine the location of the maximum point on the curve.

15. Solution: A = 2 – (-3) = 5 e = AL/800 = 5(300)/800 = 1.875
G1 x Interval = 0.02 x 25 = 0.50 m x LP
x/L
(x/L)2
yn = 4e(x/L)2
Lx = LP - yn
Remarks
18.00
0.0000
18.000
BVC 25
18.50
0.0833
0.0069
0.0521
18.448 50
19.00
0.1667
0.0278
0.2083
18.792 75
19.50
0.2500
0.0625
0.4688
19.031
100
20.00
0.3333
0.1111
0.8333
19.167
125
20.50
0.4167
0.1736
1.3021
19.198
150
21.00
0.5000
1.8750
19.125
175
21.50
0.5833
0.3403
2.5521
18.948
200
22.00
0.6667
0.4444
3.3333
18.667
225
22.50
0.7500
0.5625
4.2188
18.281
250
23.00
0.6944
5.2083
17.792
275
23.50
0.9167
0.8403
6.3021
17.198
300
24.00
1.0000
7.5000
16.500
EVC

16. Determination of the maximum point on the curve:
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
Determination of the maximum point on the curve:
ymax = + Ymax = = 19.2 m

17. Sketching of the vertical curve:
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
Sketching of the vertical curve:

18. BFC3082 Traffic and Road Safety Engineering Lecturer: Mr
BFC3082 Traffic and Road Safety Engineering Lecturer: Mr. Basil David Daniel
That’s all !