1. Stopping Sight DistanceV2
S = 1.47 V t +
(30[(a/32.2)"G)])
Note: G in percentage (decimal)

2. Examples (1/2)
2. For a roadway with a 55 mph design speed, a minimum required stopping sight distance of 500 ft, a deceleration rate of 8 f/s2, and driver reaction time of 2 second, the grade will be:
a. 3.0%
b. 4.0%
c. 5.0%
d. 6.0%

3. Examples (2/2)
3. The minimum stopping sight distance for a vertical curve connecting a +3% to a -2% with a deceleration rate of 10 ft/s2, a design speed of 50 mph, and driver reaction time of 2 seconds, will be:
a ft
b ft
c ft
d ft

4. Crest Vertical Curves h2 h1 L S>L L = 2 S - 200(qh1+qh2)2 /|A|
A = G2 – G1
Note: Gi in grade
SSD h2 h1 L
S>L L = 2 S - 200(qh1+qh2)2 /|A|
S#L L = |A| S2 / [200(qh1+ qh2)2]
h1 = 3.5 ft and h2 =2.0 ft
S>L L = 2 S /|A| S# L L = |A| S2/2158

5. Examples
4. The minimum length of a vertical curve with a required 500 ft stopping sight distance, object height of 2 ft, driver’s eye height of 3.5 ft, and connecting a +2% to a -3% grade will be:
a ft
b ft
c ft
d ft

6. Sag Vertical Curves S>L L = 2 S - (400 + 3.5S)/|A|]H
SSD L β
A = G2 – G1
Note: Gi in grade
S>L L = 2 S - ( S)/|A|]
S #L L = |A| S2/( S)
Comfort criteria
L = |A|V2/46.5

7. Examples
6. The stopping sight distance for a 500-ft vertical curve connecting a -3% to a +1% grade and with object height of 2.0 ft and driver’s eye height of 3.5 ft will be:
a ft
b ft
c ft
d ft

8. Horizontal Curves Superelevation Clearance from roadside obstruction
0.01e + f = V2/15R
Clearance from roadside obstruction
HSO = R [1 - cos (28.65 S/R)]

9. Examples (1/2)
7. The required clear distance for a horizontal curve with a radius of 700 ft and stopping sight distance of 215 ft will be:
a. 6.3 ft
b. 7.4 ft
c. 8.2 ft
d. 9.1 ft

10. Examples (2/2)
9. For a 900-foot radius horizontal curve designed for 50 mph and superlevation of 8%, the required side friction should be:
a. 0.04
b. 0.05
c. 0.08
d. 0.10

11. Vertical Curves g1 g2 y x PVI E PVC PVT L/2 y = (g2 - g1)x2/2L
YP= YPVC + g1 x + (g2 - g1)x2/2L
E=a (L/2)2 = (g2 - g1)L/8
Xm = g1 L/(g1-g2)

12. Examples (1/3)
11. The highest point of 500-foot curve connecting a +4% grade to a -2% will be located feet from the PVC.
a. 267
b. 300
c. 333
d. 367

13. Examples (2/3)
12. Given the diagram here, the length of the curve will be:
a ft
b ft
c ft
d ft
-3%
+1%
Sta
Elev
Sta
Elev

14. Examples (3/3)
13. For a point 150 ft to the left of the PVT on a 450-foot curve connecting a -3% to -1% grade, the tangent offset will be:
a. 0.5 ft
b. 2.0 ft
c. 3.5 ft
d. 4.5 ft

15. Horizontal Curves L = π RI/180 T = R tan(I/2) C = 2R sin(I/2)
D = /R
Stake out
d = 0.5(180/π)(x/R)
x = 2 R sin(d)

16. Examples (1/3)
18. The radius for a horizontal curve with a 650-foot long cord and intersection angle of 85o 45’ will be:
a ft
b ft
c ft
d ft

17. Examples (2/3)
20. The deflection angle for a the first whole station of a horizontal curve with the PC station at and a radius of 350 ft will be:
a. 3.9o
b. 4.3o
c. 7.8o
d. 8.6o

18. Examples (3/3)
21. A horizontal curve with an external distance of 5.2 ft and a radius of 800 ft requires for the intersection angle between the tangents.
a. 13o
b. 20o
c. 26o
d. 33ο

19. Angle Measurements Azimuths Deflection angles Bearings
from N 48o or S 228o
Deflection angles
48o R (sometimes left)
Bearings
N 48o E N
48o

20. Example
27.The first sighting(PC-PI) for a horizontal curve is N 62o 30’ E and the next is S 48o 25’ E. The intersection angle for the curve is
a. 27o 30’
b. 41o 35’
c. 69o 05’
d. 110o 55’

21. Earthwork Average end Prismoidal Pyramid V = L (A1+A2)/2
V = L (A1/2 + A2 + A3+…+An-1 + An/2)
Prismoidal
V = L(A1 + 4Am+A2)/6
Pyramid
V= L A/3

22. q-k-u Relationships uf uf
qmax kj
qmax
q=ku
qmax=kj uf/4 kj

23. Example
27. The capacity of a roadway with free flow speed of 50 mph and maximum density of 130 vehicles per mile will be:
a veh/hr
b veh/hr
c veh/hr
d veh/hr

24. Signalized Intersectionsv
y = t +
(2a"64.4 G)
r = (W+l)/v
Note: G in percentage (decimal)

25. Example
29. The required clearance interval for a signalized intersection approach with speeds of 35 mph, approach grade 1%, deceleration rate of 10f/s2, driver reaction time of 2 sec, average vehicle length of 20 ft, and a side street with three 12-foot lanes will be:
a. 1.1 sec
b. 3.0 sec
c. 3.7 sec
d. 4.8 sec

26. Elevation Measurements
Differential leveling
Δh = ΣBS- ΣFS
hi= hi-1 +BSi-1 - FSi

27. Wind Analysis
Determine max
crosswind

28. Wind Analysis (cont’d)23 23 5
Runway 5-23
Use 96%
Runway 23
Use 43%