ronmental conditions allowed us to construct a
breaker escort in our simulations, but other types
model that predicts NSR passage based on combi-
could easily be modeled. The user may select travel
nations of their probabilities of occurrence. Each
in either the east or west direction, although the
transit scenario can then be programmed to run
results are not significantly different given our cur-
between 1 and 500 times to allow the statistical
rent resolution of environmental data.
distributions in the data to be adequately exer-
The model's cost components are applied as
cised to produce a single mean value each for tran-
three separate inputs: daily cargo ship rates, the
sit time and cost.
daily icebreaker escort rate, and a fixed fee for
Our model lets the environmental conditions
miscellaneous passage charges. Any or all of these
determine a base ship velocity which we then
can be modified by the user. For ship costs, we
modify with slowing factors or the need for ice-
began with standard Corps of Engineers estimates
breaker escort. The base velocity is obtained from
of daily rates for conventional ships plying the
empirical estimates that are stored in lookup tables.
conventional routes and modified these according
This velocity and the slowing factors can easily be
to standard accounting principles to account for
modified for ship types with different capabilities
ice strengthening and Arctic operations. That is,
for sea keeping and ice navigation. The strength of
we increased construction, insurance, and fuel
our model lies in its ability to predict transit speeds
costs. We then discounted these rates to account
for times of the year when few or no voyages have
for the age of the current fleet of cargo ships, its
occurred. Predictions can be made if the modeled
surplus capacity, and to attract first-time foreign
ship's speed is reasonably estimated for the range
involvement. These charter rates can be easily
of conditions encountered on the NSR. These speed
modified as more NSR shipping information be-
estimates can be based on NSR experience or on
comes available. We present sensitivity studies on
sea trials under similar conditions in other polar
the effect that these various cost appications have
regions.
on the results. Our final simulations, however, were
For each voyage, the ice, sea, and atmospheric
obtained by adding the current icebreaker rates as
conditions are used to determine the speed of a
a fixed fee to other miscellaneous fees (i.e., setting
vessel between data and decision nodes along the
the escort daily rate to zero).
route. Data nodes are mesh points where the navi-
The user can select from three choices of output
gation conditions are set for the next trip segment.
formats: 1) a short version that provides only a
These are generally spaced less than 250 nm apart
summary of the mean voyage, 2) a longer version
along the commonly used shipping lanes. Deci-
that provides summary data for each voyage and
sion nodes are similar to data nodes but with the
the mean voyage, and 3) the longest version, which
additional feature of marking where two or more
supplies these two summaries plus a detailed log
route choices exist; for example, where a choice is
showing where each variable changes during ev-
made to follow the coastal route or a more north-
ery voyage. Generating the shortest output, the
erly variant. For each data node, we assembled
program takes approximately 2 min to simulate
probability distributions for ice thickness, concen-
500 voyages on an IBM-PC 486-33 with a math
tration, and pressure, wind speed and direction,
coprocessor, and takes only 21 s for 100 voyages.
wave heights, occurrence of fog, snowstorms, and
Mean transit time and cost for the four months
topside icing. The magnitude of each condition, or
and three ship types were obtained by averaging
its mere existence (in the case of fog, snowstorm,
five repetitions each of 100-voyage simulations.
and icing) is established by random selection, or a
We show these 100-voyage simulations are not sig-
"roll of the die" based on its probability distribu-
nificantly different from simulating 500 voyages.
tion. After a particular set of conditions is set, it is
Results show that nonstop transits from Murmansk
held constant for 8 hours, until sunrise or sunset,
to the Bering Strait during August (the easiest pe-
or until the next node is reached, whichever oc-
riod of navigation) averaged approximately 14
curs first.
days for the three ship classes, with a standard
Four different months were modeled to cover
deviation of about 1.2 days. The mean vessel speed
the easiest (August), intermediate (June and Octo-
was 9.3 knots and for approximately 20% of the
ber), and most difficult (April) transit periods.
time an icebreaker escort was required. The cur-
Three different ice-strengthened ship types were
rent version assumes an icebreaker to be instantly
modeled: a Noril'sk-class multipurpose cargo ship,
available when needed. We also have not pro-
a Strekalovsky-class dry bulk freighter, and a Lunni-
grammed for in-port time or administrative de-
class tanker. We assumed an Arktika-class ice-
lays that may occur. The total cost for a transit in
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