Extreme ice thicknesses from freezing rain
Final Report
2.0
Determining extreme ice thicknesses from freezing rain
2.1
Ice accretion models
The CRREL model for the accretion of ice on cylinders (e.g. wires and branches) from freezing
rain is described in Jones (1996). This model determines the amount of ice that freezes both
directly to the wire and as icicles, as any initially unfrozen water starts to drip off the wire. The
Simple model is also introduced in the above report, but is described in more detail in Jones
(1998).
In both models the severity of icing is quantified in terms of the equivalent radial ice thickness t.
A back-of-the envelope formulation of the Simple model that can be used, for example, to
estimate the potential damage to trees and overhead wires in forecasted freezing-rain storms is:
2
⎛V ⎞
t = 0.35P 1 + ⎜ ⎟
(2-1)
⎝ V0 ⎠
where P is the total depth of freezing rain expected and V is the average wind speed
accompanying the freezing rain. The equivalent radial ice thickness t is in the same units as P,
and V0 is 10 for V in mph (or knots) and 5 for V in m/s. Note that t is independent of the wire
diameter. Based on our measurements and observations in the field in freezing rain storms, we
expect significant tree damage when t ≥ 0.25 in.
The mass m of ice with density ρi on a wire with diameter d and length L is calculated from the
equivalent radial ice thickness t:
m = ρiπ L ( dt + t 2 )
(2-2)
The ice mass increases with wire diameter for a given t.
2.2
Equivalent radial ice thickness
The equivalent radial ice thickness that describes the mass or weight of ice on a wire (or other
cylinder) is different from the maximum dimension of the ice accretion provided in Bennett
(1959) and Changnon (2003) and used in various papers by Hay (e.g. Hay 1957). These authors
use the measurements made by the American Railroad Association (ARA) during a 9 year period
in the 1920s and 1930s. According to Stanley Changnon (personal communication, August 2004)
he and William W. Hay were contemporaries at the University of Illinois. Hay had gotten the
ARA to provide him with all the data from the 9 year study. At one point, Hay gave Changnon a
summary list he had compiled from the original data of all the measurements of ice that were
associated with damage. This list is the 1689 point measurements that Changnon refers to in his
2003 paper. The summary (which is not publicly available) lists the location, date, and total ice
thickness, but with no description of how the thickness was measured. Changnon believes the
measurements were made by someone at the depot by climbing up the signal mast ladder with a
September 2004
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