Figure 60. Parameters used to predict motion resistance us-
ing the NRMM algorithm. (From Richmond 1995.)
snow, since a driven wheel would not likely have
NRMM prediction of motion resistance in snow.
enough traction to overcome the large resistance and
The following method was proposed by CRREL for
would become immobile.
predicting the motion resistance in snow. It was
adopted into the NATO Reference Mobility Model as
For ρ0 > 150 kg/m3 and 2/3 r < z < r,
part of the overall vehicle performance predictions
(32)
scheme. Only the portions of the algorithms related to
Factor = 1.5
motion resistance in snow are stated here. Based on
For ρ0 > 150 kg/m3 and z > r,
Richmond (1995), the motion resistance for the lead-
(33)
ing tire in shallow snow Rs is based on the vehicle
Factor = 2.5.
sinkage z according to
Comparison of measurements, NRMM, and finite
Rs = 13.6041(ρ0 wa)
1.26
element results. In the FEA model the longitudinal
(29)
reaction force at the wheel hub represents the motion
resistance force on the wheel due to deformation of
a = r arcos [(r-z)/r]
(30)
the snow and is directly comparable to the motion
resistance measured with the CRREL Instrumented
Vehicle. Similarly the vertical displacement of the
ρ0
z = h 1 -
hub node is equivalent to the sinkage of the wheel
(31)
0.519 + 0.0023 pmax
into the snow (since the wheel itself is not deforming
in this simulation). Figure 61 shows the resistance
coefficient (the longitudinal load divided by the verti-
where Rs =
motion resistance (leading tire only) (N)
ρ0 =
initial snow density (kg/m3)
cal load on the hub) and vertical displacement for one
of the snow model runs. For this model the vertical
w =
maximum tire width (m)
loading occurs from 0 to 1.5 s, the horizontal accelera-
a =
arc length in contact with snow (m)
tion occurs from 1.5 to 2.0 s, and then constant speed
r =
tire radius (m)
translation is maintained from 2.5 to 5 s at a speed of 8
z =
sinkage (m)
kph (5 mph). The sinkage and motion resistance val-
h =
snow depth (m)
ues are chosen as the average of the values occurring
pmax =
maximum tire contact pressure (kPa).
during the constant speed portion of the simulation.
Comparisons of the measured and modeled sink-
These parameters are illustrated in Figure 60.
age and motion resistance are shown in Figure 62 as
Very little data is available for wheeled vehicles in
a function of snow depth. The model overestimates
deep snow. However, based on numerous observa-
motion resistance, but the trends are consistent with
tions of snow vehicle movement, the following fac-
the measured data and the model falls directly along
tors are applied to the shallow snow equations to es-
the upper edge of the measurements, constituting a
timate the additional motion resistance in deep snow.
conservative prediction. The NRMM predictions of
The factors represent an engineering estimate of the
motion resistance are discontinuous based on the
additional forces due to plowing of the vertical face
snow depth. For this tire, motion resistance for snow
of the wheel and undercarriage drag (Richmond et al.
depths less than 25 cm are calculated using NRMM
1995). The deep snow modifiers would be applicable
eq 29, for depths from 25 to 38 cm using eq 31, and for
to wheels being dragged or towed through deep
46
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