Civil Engineering Reference
In-Depth Information
Centerline of bridge
Centerline of track
CF
h
cg
e
W
e
s
e
c
d
S
/2
S/2
FIGURE 3.6
Railway track superelevation.
the superelevation can be expressed as
dV
2
gR
,
e
=
(3.25)
where
d
is the horizontal projection of track contact point distance, which may be
taken as 4.9 ft for North American standard gage tracks; CF is the centrifugal force;
W
is the weight of the train;
m
W
/
g
is the mass of the train (
g
is the acceleration
due to gravity);
V
is the speed of the train.
Substitution of
R
=
32.17 ft/s
2
=
5730
/D
,
d
=
4.9 ft, and
g
=
into Equation
3.25 yields
0.0007
DV
2
,
e
≈
(3.26)
where
e
is the equilibrium superelevation, inches, and
D
is the degree of the curve.
Transition curves are required between tangent and curved tracks to gradually
vary the change in the lateral train direction. The cubic parabola is used by many
freight railroads as a transition from the tangent track to an offset simple curve. The
length of the transition curve is based on the rate of change of superelevation. Safe
rates of superelevation “run-in” are prescribed by regulatory authorities and railroad
companies. For example, with a rate of change of superelevation that is equal to
1.25 in/sec, the length of the transition curve,
L
s
,is
L
s
=
1.17 eV,
(3.27)
where
e
is the equilibrium superelevation, inches, and
V
is the speed of the train, mph.
