pmax ≤ 210 kPa
ρf = 0.50 Mg/m3
analysis that is beyond the scope of our initial
ρf = 0.55 Mg/m3
pmax > 210 kPa
models. Further research may show that these
ρf = 0.6 Mg/m3
pmax > 350 kPa
shortcomings can be accounted for by lowering
ρf = 0.65 Mg/m3.
the RCI value used to separate firm from soft sub-
pmax > 700 kPa
strates. We have also ignored the possibility that
shear zones could form between the snow and
The sinkage calculation is also used to esti-
the soil (most likely in shallow snow), which
mate whether the snow is deep or shallow.
would affect both traction and resistance calcula-
Once sinkage z is determined, the value of a
tions.
(contact length) for wheeled vehicles is
Soil sinkage is calculated separately for wheeled
a = r arccos [(rz)/r]
(5)
and tracked vehicles using the sinkage equations
of Willoughby.* The equations for wheeled and
where r is the tire radius (cm or in.). For tracked
tracked vehicles, respectively, are
vehicles the equation is
a = z/sin (θ)
(6)
10 ri
zsoil =
(Wheeled)
5/3
where θ is the angle between the leading edge of
RCI 2 ri bi
the track and the ground surface (Fig. 3b). Since
Wi (1 δ i / hi )3 / 2 s1/ 5
the vehicle database defined for CAMMS and
NRMM does not contain this value, we assume
an average value of 26 for θ for all tracked ve-
zsoil = 0.00443 Li e(5.889 Wi/RCI bi Li) (Tracked) (9)
hicles.
(8)
Undisturbed snow on
(If RCI ≥ 100) (10)
zsoil = 0
a soft substrate
For undisturbed snow over a soft soil, addi-
tional sinkage occurs as a soil rut is formed. This
where RCI = rating cone index
increases motion resistance as the wheel or track
Li = track length (in.)
sinks deeper in the snow and possibly below the
bi = undeflected tire width or track
soil surface.
width (in.)
In this case the total sinkage is estimated to be
ri = tire radius (in.)
the sum of the sinkage of the two materials inde-
Wi = wheel or track load (lb)
pendently. Soil sinkage is calculated ignoring the
δi = tire loaded deflection (in.)
snow cover and is added to the sinkage deter-
hi = tire unloaded section height (in.)
mined for the snow from eq 4. The arc length a,
s = slip in decimal form (chosen to be
0.05 for Cold Regions Models) for
lated based on the combined sinkage:
the running gear element i.
z = zsoil + zmax.
(7)
Combined sinkage less than or
This approach may be naive in its assumption
equal to the snow depth
that the snow and soil can each be treated as
For the situation where sinkage occurs in the
separate entities and that their effects can be
soil (RCI < 100) but z is still less than the snow
added to determine the combined effect on a ve-
depth h, we assume that the motion resistance is
hicle. However, this assumption is probably ad-
only that due to snow. While the combined z from
equate for snow depths greater than about 15 cm
eq 7 is larger than zmax from the snow, the tire or
and soil strengths great enough to suffer less than
track is still contained completely in the snow-
about 10 cm of sinkage. We also recognize that we
pack and thus its resistance to motion is caused
have not accounted for the ability of snow to
primarily by snow deformation. Equations 2 and
spread and attenuate the vehicle's load. In calcu-
3 are used to calculate traction and resistance.
lating soil sinkage using this approach, we have
placed the entire running gear load and contact
pressure on the soil. Although this is clearly in-
correct, an accurate determination of the actual
* Personal communication with W. Willoughby, U.S.
load and pressure would involve a sophisticated
Army Waterways Experiment Station, 1992.
5
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