CIVIL ENGINEERING FORMULAS

280 CHAPTER ELEVEN

For crest vertical curves, AASHTO defines the minimum length Lmin, ft (m), of
crest vertical curves based on a required sight distance S, ft (m), as that given by

(11.18)

When eye height is 3.5 ft (1.07 m) and object height is 0.5 ft (0.152 m):

(11.19)

Also, for crest vertical curves:

(11.20)

When eye height is 3.5 ft (1.07 m) and object height 0.5 ft (0.152 m):

(11.21)

where Aalgebraic difference in grades, percent, of the tangents to the verti-
cal curve
H 1 eye height, ft (m), above the pavement
H 2 object height, ft (m), above the pavement

Design controls for vertical curves can be established in terms of the rate of
vertical curvature Kdefined by

(11.22)

whereLlength, ft (m), of vertical curve and Ais defined earlier. Kis useful
in determining the minimum sight distance, the length of a vertical curve from
the PVC to the turning point (maximum point on a crest and minimum on
a sag). This distance is found by multiplying Kby the approach gradient.
Recommended values of Kfor various design velocities and stopping sight
distances for crest and sag vertical curves are published by AASHTO.

K

L

A

Lmin 25 

1329

AS^2

S L

Lmin 25 

200 H 1 H 2 

2

AS^2

S L

Lmin

AS^2

1329

SL

Lmin

AS^2

100  22 H 1  22 H 2 

2 SL

Stopping sight distance S

Vertical curve lengthL

PVI

PVC PVT

H 1 H 2

FIGURE 11.5 Stopping sight distance on a crest vertical curve.