ion. The effect that each had on total cost for 500-
TC = 23.402 CSR + 6,448
voyage Noril'sk-class runs during the months of
for April transits, as the r2 statistic is 0.9989. The
April and August (representing the two extremes
in total cost) are presented below.
slope of this line shows that for every
||content||
change in
First, CSR was varied while holding IBR and
the vessel's daily rate, there is a resulting change
MF constant. IBR was held at zero and MF was
of .40 in the total cost. The difference values in
held at 7,000 for April and 6,000 for August.
column D show that the simple equation slightly
These values represented the fixed miscellane-
underpredicts the numerical model.
ous fees that we used in our final simulations for
For August transits, the linear fit to the numeri-
those months. The total transit time (TT) for April
cally modeled results was
was 566.11 hours, or 23.588 days, and for August it
was 326.43 hours, or 13.601 days (see Transit Time,
TC = 14.173 CSR + 3,827
under Final simulations below). Equation 5 then
becomes:
and the corresponding r2 statistic is also 0.9989.
The change in total cost is 14.173 times the change
TC = (CSR 23.588 days) + 7,000
in the cargo ship rate. The difference between the
simple prediction equation and the numerical re-
for April transits and
sult is only slightly greater but can still be well
approximated for any value of CSR once the total
TC = (CSR 13.601 days) + 6,000
transit and icebreaker escort times have been ob-
tained from the numerical model.
for August transits. The results of varying CSR are
IBR was then varied while holding CSR and
presented in Table 17 and Figure 13. The values
MF constant. MF was held at zero and CSR was
appearing in column B are those predicted using
held at ,450/day. The average amount of time
the simple equation above. Those appearing in col-
an escort was required for April transits was 518.96
umn C are modeled results. The least-squares lin-
hr, which gets rounded up to 22 days by our model.
ear fit to the modeled results is well represented
For August, ET was 77.02 hr, rounded to 4 days.
by the equation
Table 17. Tabular results from varying cargo ship rates for Noril'sk
multipurpose cargo ship transits.
Total cost ($)
A
B
C
D
Ship rate
Simple
Model
Difference*
Linear fit to
($/day)
prediction
results
(%)
model results
April transits
14,000
467,231
474,120
1.47
15,000
490,818
497,366
1.33
16,000
514,407
522,564
1.59
TC = 23.402 (CSR) + 146,448
r2 = 0.9989
16,450
525,021
528,850
0.73
17,000
537,995
544,728
1.25
(see Fig. 13a)
18,000
561,582
568,388
.21
19,000
585,170
590,834
0.97
August transits
14,000
306,418
312,168
1.88
15,000
320,019
325,220
1.63
16,000
333,620
341,120
2.25
TC = 14.173 (CSR) + 113,827
r2 = 0.9989
16,450
339,741
347,945
2.41
17,000
347,221
355,291
2.32
(see Fig. 13b)
18,000
360,822
369,116
2.30
19,000
374,424
382,228
2.08
* The difference between the simple model derived from eq 5 and the numerical model
output is calculated by subtracting the model results (col. C) from the predicted results
(col. B) and dividing by the predicted value (i.e., [BC]/B). Multiplying by 100 then
gives the percentage difference shown in col. D.
38
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