VERTICAL ALIGNMENT
y = ax
2
+ bx + c
dy / dx = 2ax + b = slope (rise / run)
dy/dx = b = G1 (initial slope when x=0)
d
2
y/dx
2
= 2a
d
2
y/dx
2
= (G
2
 G
1
) / L
a = (G
2
 G
1
) / 2L
a = coefficient in the parabolic curve
equation
L = KA
x
hl
= KG
1
(x is the high/low point)
Y = offset at distance, x, from PVC (ft)
Y
m
= midcurve offset (ft)
Y
f
= offset at end of vertical curve (ft)
A = absolute value of difference in
grades ( G1  G2 ) (%)
SSD =
V
1
2
+ V
1
*t
r
2g[(a/g) ± G]
SSD = stopping sight distance (ft)
V
1
= initial vehicle speed (ft/sec)
g = gravitational constant (32.2 ft/sec2)
a = deceleration rate (ft/s
2
)
Equation 3.1
Equation 3.2
Equation 3.3
Equation 3.4
Equation 3.5
Equation 3.6
b = coefficient in the parabolic curve
equation
c = elevation of PVC
Equation 3.7
Equation 3.8
Equation 3.9
Equation 3.10
Equation 3.11
L = length of vertical curve (ft)
x = distance from the PVC (ft)
K = horizontal distance (ft) to affect
a 1% change in slope.
x
hl
= distance from PVC to high/low
point (ft)
Equation 3.12
G = roadway grade (+ for uphill and 
for downhill) in percent/100
t
r
= perception reaction time
200
AL
Y
f
=
2
200
x
L
A
Y
=
800
AL
Y
m
=
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 Fall '02
 Petrucha
 sight distance, Underpass Sight Distance

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