temperature or humidity, atmospheric pressure, and solar radiation to determine how much of the
available precipitation actually freezes to the structure.
The simplest case of ice accreting in freezing rain occurs if all the precipitation impinging on
a flat horizontal plate freezes in a uniformly thick accretion. When that happens the amount of
ice on the structure is directly related to the amount of rain that falls. For example, if 1 cm of
freezing rain falls on a 2-cm-wide flat plate and freezes in place, then a layer of ice 1(rw/ri) = 1.1
cm thick would form. On a 4-cm-wide plate nearby, the same thickness of ice would form with
twice the mass. A 2-cm-diameter circular cylinder would intercept the same depth of rain as the
2-cm-wide flat plate. If that water depth is then spread uniformly around the cylinder's circum-
ference and frozen, forming a uniform accretion, then the layer of ice would be 1(rw/ri)/p = 0.35
cm thick. The factor of p is the ratio between the circumference and the diameter of the circular
cylinder. Actual ice accretion shapes may vary significantly, from a crescent on the top or wind-
ward side of a wire, to little ice on the wire with long icicles underneath. However, the shape
of the ice accretion does not have a significant effect on the accreted ice load.
This simple model shows that, at least to first order, the thicknesses of ice on components
with the same shape cross section but different dimensions are the same. A slightly more com-
plex model takes the increased flux of water due to the horizontal velocity of the raindrops in the
wind into account. Using the flux of precipitation from the falling rain and the wind-blown rain,
{(0.1P ρ )
}
(
)
2 1/ 2
1
2
t=
+ 0.36 Wj Vj
∆T
∑
(3)
jw
πρi
where Pj
=
precipitation amount in the jth hour (mm/hr)
Vj
=
wind speed in the jth hour (m/s)
0.067Pj0.846 (g/m3)
Wj
=
DT
=
1 hour.
The summation is over the number of hours in the freezing-rain storm. W is the liquid water con-
tent of the air containing raindrops. This formula for W as a function of the precipitation rate is
from Best (1959).
Detailed models for ice accretion include a heat balance calculation to determine the fraction
of the impinging precipitation that actually freezes, either directly to the structure, or as icicles as
the water begins to drip off. The CRREL model uses temperature, dew point, and solar radiation
data with empirical heat transfer coefficients to calculate the heat balance at the accretion sur-
face. As there may not be sufficient cooling to freeze all the available precipitation, the amount
of ice accreted by the CRREL model is often less than that calculated by the simple model for
the same weather conditions. The CRREL model determines the ice load at the location where
the weather data are measured, and the simple model determines the ice load at some hypotheti-
cal nearby location with the same amount of precipitation, but colder conditions. These two mod-
els are described in more detail and compared with other ice load models in Jones (1996a and b).
In freezing-rain storms other types of precipitation may be mixed with freezing rain. In
applying the models we make the conservative assumption that snow and ice pellets mixed with
freezing rain freeze to structures as if they were freezing rain. This ignores a) the probably lower
collision efficiency and smaller sticking fraction of snow and b) ice pellets bouncing when they
hit and thus not sticking to branches and wires.
10
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