Ice ( and some maths)

88.4 degrees lattitude

At 88.7 degrees, the minimum latitude at which our cruising speed 18 knot Arktika could travel in order that it circumnavigate in twenty-four hours, we need to understand specific geographic conditions in order that its path be properly calculated. Below is a map showing the ice thickness for January 2011 from satellite data. This is at the height of winter when we can expect the ice to be its absolute coldest and thickest. There's very little snowfall at this level of the arctic and it is in fact classified as one of the driest places on the earth in terms of rainfall.
Ice thickness
So, even accounting for the fact that global warming is predicted to halve the ice density of the Arctic Sea in the next hundred years, the ice is still very definitely manageable. And this is perhaps a key point - the Arktika, circumnavigating on average every twenty-four hours will only have to cut the channel once, because the time it takes the ice to refreeze is far greater than the twenty-four hours it takes to pass around again. There's both scientific and qualitative data to prove this. Below is a chart that shows the sea temperatures for the arctic for 2011.


Sea ice, because of salt content, freezes at -1.8 centigrade. At this temperature, the 'frazil' - the smallest ice crystals - can shed the salt content of the water. So from around day 250 on the chart ice is forming all year round in the arctic sea. What remains is to estimate how long it takes for a certain amount of ice to grow. This formula is a combination of the formula for Freezing Degree Days - a variable of the temperature over time - and a conversion formula to turn this into a spatial measure developed by Lebedev in 1938. So, where p is the freezing point of the ice, x is the average temperature and d is the number of days:

Formula for ice growth.

So for 4 days at an average of -5 degrees we might expect sea ice to grow as such.

Applied formula for ice growth

4.009187 cm.

This formula is entirely holistic however and depends on the idea that there is no ice already, that weather does not affect the growth, that changes in current keep the water stable and so and so forth. More usefully and from a more empirical standpoint, we could look at the yearly level and note the four to eight weeks it takes for ice growth to begin between August and October and guess that for ice to reach normal levels again takes weeks, rather than days.

It's pretty easy to conclude from this that as long as the vessel stays on course every 24 hours, it will almost definitely be in a clear channel all the time. So although breaking through the ice will initially limit it's speed to around 10-15 knots, once the channel is cleared, it can reach it's maximum of around 21 knots.

In addition, the simple way that the Arktika is used gives us an insight: It's used to clear channels across the Siberian coast that are used by other ships. We have to assume that an icebreaker can't accompany every single one of the hundreds of ships that travel these routes; the icebreaker is so much slower and there are only nine of them. This prohibitive behaviour would draw trade to a near standstill. It's clear that the ice must take a week or so to become impassable to standard hulls and a few weeks to fully reform.