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Problem 3.61 PP
Overhead electric power lines sometimes experience a low-frequency, highamplitude vertical 
oscillation, or gallop, during winter storms when the line conductors become covered with ice. In 
the presence of wind, this ice can assume aerodynamic lift and drag forces that result in a gallop 
up to several meters In amplitude. Large-amplitude gallop can cause clashing conductors and 
structural damage to the line support structures caused by the large dynamic loads. These 
effects in turn can lead to power outages. Assume that the line conductor Is a rigid rod, 
constrained to vertical motion only, and suspended by springs and dampers as shown in Fig. A 
simple model of this conductor galloping is
(»2+,2)l/2
Where
m = mass of conductor,
ir“fnr’c \/ortinal riicnla^omont
m = mass of conductor, 
y = conductor’s vertical displacement,
D = aerodynamic drag force,
L = aerodynamic lift force,
V = wind velocity,
a = aerodynamic angle of attack = —
T = conductor tension, 
n = number of harmonic frequencies,
/ = length of conductor.
Assume that L(0) = 0 and D(0) =D0 {a constant), and linearize the equation around the value y = 
^ =0. Use Routh’s stability criterion to show that galloping can occur whenever
^ + D b