Table 2. Tire deflection data.
Maximum
Maximum
Nominal
Deformed
undeformed
section
load
radius
radius
width
Wheel location
(N)
(cm)
(cm)
(cm)
Inflation pressure 103 kPa
left front
6800
30.5
36.5
27.2
right front
30.0
36.5
27.2
left rear
5510
31.5
37.0
27.2
right rear
32.5
37.0
27.2
Inflation pressure 179 kPa
left front
6800
33.0
36.7
25.6
right front
32.4
37.5
26.3
left rear
5510
33.5
37.5
25.5
right rear
34.2
38.0
25.5
where h is the snow depth, and ρf is the theoretical
following in the ruts made by the tow vehicle.
After each test run, the undisturbed snow depths
final density, which is determined from the fol-
along both the left and right wheel ruts were
lowing with pmax the maximum contact pressure:
measured at 1-m intervals. These data were later
ρf = 0.50 Mg/m3
for pmax ≤ 210 kPa
averaged to obtain an undisturbed snow depth
ρf = 0.55 Mg/m3
for pmax > 210 kPa
value for each side of the vehicle. At the conclusion
ρf = 0.60 Mg/m3
for pmax > 350 kPa
of a series of tests, several snow pits were used to
ρf = 0.65 Mg/m3
for pmax > 700 kPa.
characterize the snow and to determine an aver-
age density for each test.
A value of 0.50 Mg/m3 is used for the CIV with the
inflation pressure and tires used in these tests.
Three equations are plotted on Figure 3. These
RESULTS AND ANALYSIS
are
Table 3 contains a summary of the data col-
Rs = 15.62 (ρ0aw)1.2676
lected. The data are separated into sets based on
(2)
the day of the test and the tire inflation pressure.
Initial snow depths ranged between 10 and 37 cm
which is a fit of the data collected during the CIV
and average initial snow densities ranged from
tests reported herein
0.11 to 0.25 Mg/m3. All of the snow data collected
Rs = 11.25 (ρ0aw)1.58
are given in Appendix A.
(3)
which was obtained for the CIV alone in 1988 and
Leading tire resistance
The leading tire data from Table 3 are plotted in
1989 (Richmond et al. 1990) and
Rs = 68.083 (ρ0aw)0.9135
kilograms per meter, developed by Richmond et
(4)
al. (1990). The variables in this parameter are illus-
trated in Figure 4; ρ0 is the average initial undis-
which is the currently used shallow snow resis-
turbed density of the snow, a is the arc length of the
tance equation (Richmond et al. 1990). Rs is the
tire in contact with the snow, and w is the maxi-
resistance per wheel (in Newtons) for a vehicle
mum tire width in meters. The arc length a is
traveling through primarily undisturbed snow.
determined from the sinkage z and the tire radius,
Combining the old and new CIV data yields the
where the sinkage is determined from
following equation
Rs = 21.313 (ρ0aw)1.1918
(5)
ρ
z = h 1 0
(1)
ρf
which has an r2 value of 0.58 compared to 0.76 for
4
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