1, 2, 3, 4, 7 and 9. The data fell on nearly a straight
Table 5. Analysis of variance.
line, indicating that they are random and normally
distributed. Bartlett's test for homogeneity of the
Data
Number of
error variance showed that the variances were not
set
observations
Mean
different at the 95% confidence level. A multiple
1
4
0.0207
range test indicated that sets 3 and 9 should not be
2
4
0.0171
included, and Table 5 contains the results of a
3
8
0.0056
series of ANOVA tests to determine which of the
4
12
0.0140
data could be combined.
7
6
0.0199
9
4
0.0378
Between each ANOVA test, a procedure fol-
lowing Grubbs (1969) was used to determine if the
Total
38
extreme values could be considered outlying ob-
servations. This analysis also showed that sets 3
and 9 can be dropped from further analysis on the
For all data sets
basis of statistical arguments. The average rear tire
SS
df
MS
F
ing data sets is 0.0169 with a 95% confidence
TOTAL
0.016013
38
CF
0.01059
1
interval of 0.0138 to 0.0199. These values are shown
TR
0.002986
5
0.000572
graphically on Figure 6. It should be noted that if
RES
0.002437
32
0.0000761
7.516
both sets 3 and 9 are included, the average Rr/Vr
is 0.0167 with a confidence interval of 0.0127 to
Since F0.95 (5,32) = 2.5, there is a difference between data sets.
0.0207, which really isn't much different from the
values obtained from the four data sets, although
For data sets 1,2,3,4 and 7
it is serendipitous that the effects of these two tests
SS
df
MS
F
(3 and 9) average each other out.
From the above analysis, it appears that a trail-
TOTAL
0.009175
34
ing tire in dry snow that is less than 0.22 m deep
CF
0.0002698
1
and that has a density less than about 0.250 Mg/m3
TR
0.0075927
4
0.001898
will have a resistance coefficient of about 0.017,
RES
0.0013125
29
0.000045286
41.92
although values as low as 0.0 and as high as 0.64
Since F0.95(4,29) = 2.7, there is a difference between data sets.
were measured. No data were obtained for snow
densities greater than 0.250 Mg/m3. It should also
be noted that the rear wheels of the CIV carry less
For data sets 1,2,4 and 7
weight than the front wheels, and the effect of a
SS
df
MS
F
trailing tire carrying a higher weight is not known.
TOTAL
0.008817
26
CF
0.007399
1
Deep snow
TR
0.0002128
3
0.00007093
Tests 0125f0125i (data set 5) were done in
RES
0.001205
22
0.00005479
1.295
relatively deep snow compared to the other tests.
These deep snow tests resulted in limited data for
Since F0.95(3,22) = 3.05, there is no difference between data sets.
two different trailing tire configurations. Data were
obtained similar to those described above (all four
wheels of the CIV rolling freely in undisturbed
agree with the other data (Table 4). There was no
snow) and with the front wheels driving while the
apparent reason for this on the basis of test condi-
rear wheels were rolling free. This second condi-
tions or procedure, although data set 9 may have
tion, freely rolling wheel trailing a driven tire, is
been collected in hard "crusty" snow. To legiti-
significantly different from that described earlier.
mately combine these data sets, the data need to be
To tow the CIV through this deep (36 cm) snow,
random and normally distributed and the vari-
a packed path was first made for the lead vehicle.
ances need to be homogeneous. Once this is shown,
Additionally, the snow was deep enough such
an analysis of variance (ANOVA) test or multiple
that the undercarriage of the lead vehicle dis-
range test can be used to determine if the data sets
turbed the snow in which the right side wheels of
can be combined.
the CIV traveled. Thus, in Table 3, for tests 0125f
Figure 5 is a normal probability plot of data sets
and 0125g, data are only presented for the left side
9
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