CEE 3604: Introduction to Transportation Engineering
Fall 2011
Assignment 7: Geometric Design and Turning Maneuvers
Partial Solutions
Instructor: Trani
Problem 1
a) Calculate the minimum length of a vertical curve designed for an Interstate Highway with a design speed of 70 mph. The
design provides the transition between two grades: 1.95% and 2.45%.
An interstate highway has divided lanes, hence the stopping distance criteria governs the design of the vertical curve. First
determine if the curve is a crest of a sag. Following standard nomenclature used in the handout entitled “Highway Geometric
Design” the transition from a negative slope to a positive slope is a sag curve (see page 6 of the handout).
The formulas to estimate the length of the sag vertical curve are given on page 31 of the handout.
The
stopping sight distance
for a “flat” highway designed for 70 mph according to
AASHTO is 730 feet or 230 meters
(rounded to nearest 10 meters). If we wanted to be conservative we could use the stopping distance considering the downgrade
of 1.95%. However, the stopping distance is combines a downhill section and an uphill section.
AASHTO guidelines assume
h
=0.6 meters and
β
=1 degree. Assume
SSD
≤
L
or
S
≤
L
.
L
=
A
SSD
2
200(0.6
+
SSD
tan(1 deg)
L
=
4.40
230
2
200(0.6
+
230tan(1 deg)
L
=
253 meters
For design purposes we can round to the nearest 10 meter thus resulting in L = 260 meters
.
Since the condition
SSD
≤
L
or
S
≤
L
is true
we use the calculated result for the length of the sag vertical curve.
CEE 3604
A7
Trani
Page 1 of 9
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Alternate method.
Use the rate of vertical curve (K) provided in Table 7.7 on page 33 of the handout. The minimum value of K is 50 for a design
speed of 120 km/hr (closest to 70 mph  upwards).
L
min
=
K
min
A
=
50(4.4)
=
220 meters
L
desirable
=
K
max
A
=
73(4.4)
=
321 meters
Engineers have some decision making in the specification of the sag curve according to the AASHTO table 7.7. The First method
provides a balance between the two solutions provided in the alternate method.
b) Find the elevations of stations along the vertical curve if the VPC is station 2+412.00 (meters) and at an elevation of
102.10 meters above sea level. Create elevations and offsets every 10 meters. Plot the results obtained using Excel or
Matlab.
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 Fall '08
 KATZ
 Electronic toll collection, Toll road, Queueing theory, vertical curve, Trani

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