CAE419 Final Exam Review Problems
Part 1: Horizontal Curve Design
Problem 1
: A two-lane highway (two 12-ft lanes) has a posted speed limit of 50 mph and, on one segment,
has horizontal curve as shown below. A recent day time accident (driver traveling east bound and striking
a stationary roadway object) resulted in a fatality and a lawsuit alleging that the 50 mph posted speed
limit was an unsafe speed for the curves in question and a major cause of the accident. Assuming a
perception-reaction time of 2.5 sec and a deceleration rate of 12.9 ft/sec
2
. Evaluate and comment on the
roadway design.
Hint: Compute SSD, derive maximum speed allowed, and then compare it with the speed limit.
Horizontal curve length: L=ST32+75 – ST16+00 = 1,675ft.
2
π
R
CL
/360
0
= L/80
0
R
CL
= (L/80
0
)x (360
0
/2
π
)= (1,675ft /80
0
)x (360
0
/2
π
)= 1,198.65ft.
R
V
= R
CL
– 12/2 = 1,198.65– 6 = 1,192.65ft.
D
S
= 5,729.58/R
V
= 5,729.58/1,192.65 = 4.804
0
M
S
= 18 + 12/2 = 24ft
Assuming that the terrain is level,
α
= 0.
Then
479.34 = 1.075 x V
0
2
/12.9 + 1.466 x V
0
x 2.5
V
0
= 56.98 mph > speed limit = 50mph.
D
58
729
5
R
.
,
=
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
⋅
=
−
v
s
1
s
s
s
R
M
1
cos
D
200
D
Δ
100
S
ft
34
.
479
1,192.65
24
1
cos
4.804
200
R
M
1
cos
D
200
S
1
v
s
1
s
=
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
−
=
⎥
⎦
⎤
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
=
−
−
α
⋅
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⋅
+
=
cos
466
.
1
075
.
1
0
2
0
r
t
V
a
V
S
r
t
V
a
V
S
⋅
+
=
0
2
0
466
.
1
075
.
1

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Problem 2
:
A level, rural, two-lane highway has a 10
0
curved section as it passes by a large building. The
obstructing corner of the building is 24.5 feet away from the central line of the highway. Assuming
vehicle deceleration rate of 12.9 ft/s
2
and driver’s perception-reaction time of 2.5 seconds.
(a)
If the lanes of highway are 11 feet wide, what is the stopping sight distance on this section?
(b)
What is the safe operating speed on the section in case the corner is only 17 feet away from the
center line of the highway?

Problem 3
: A parabolic vertical curve connects a +4.5% grade with a -4.0% grade on a rural highway at
section 875+25.4 and elevation 512.6 feet above the sea level. The length of the curve is 550 feet.
Calculate the location and elevation of the PVC and PVT, and elevations at stations 870+50 and 876+50.

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