In this issue of Math in the News we look at the heroic work of salvaging the naval vessels after the bombing at Pearl Harbor. For more media resources go to http://www.media4math.com.

2. USS
California
USS
Arizona
USS
Nevada
Pearl Harbor
The Japanese attacked “Battle Ship Row” in successive waves of attacks. Several
key battle ships are highlighted here.

3. Pearl Harbor
This overhead view shows the arrangement of the battle ships. Note the locations
of the Arizona and the California.

4. Pearl Harbor
The battle ship that suffered the most damage was the USS Arizona. A bomb
ignited explosives on the ship. Over 1000 crewmen perished.

5. Pearl Harbor
Where the Arizona sank would, in time, become the location of a war memorial.
None of the Arizona was salvaged.

6. Pearl Harbor
The California also suffered heavy damage, but not as extensive as the Arizona.

7. Pearl Harbor
In spite of efforts to keep the California afloat, the ship sank three days after the
attack on Pearl Harbor. Only the top-most part of the ship jutted out of the water.

8. Pearl Harbor
But an analysis of the condition of the ship showed that it could possibly be raised.

9. Pearl Harbor
What causes a ship to sink is when water fills the air-filled hull. In the case of the
California, Japanese torpedoes punctured the hull.

10. Pearl Harbor
In other words, a ship floats because it displaces a volume of water equal to at
least the weight of the ship. This gives the ship a density less than water.

11. Pearl Harbor
When a ship takes on water equal to the amount of water it displaces, then its
density is at least twice that of water. Water has a density of 1.

12. Pearl Harbor
Let’s assume that the density of the sunken ship is twice the density of the ship
when it floats.

13. Pearl Harbor
While water is removed from the sunken ship, its density changes, as shown in the
rational function above.

14. Pearl Harbor
A graph of the rational function shows that at c = 1, the density of the ship is equal
to the density of water. The graph of f2(x) = 1 represents the level where the ship’s
density is the same as that of water.

15. Pearl Harbor
To simplify the process, the California had air-tight compartments, allowing the
water to be removed one section at a time.

16. Pearl Harbor
• To help reduce the mass
of the ship, some of its
heavier components
were removed. The
effect was to reduce the
amount of water that
needed to be displaced
in order to raise the
ship.

17. Pearl Harbor
Reducing the mass changes the density equation.

18. Pearl Harbor
As dincreases in value, then the amount of water needed to refloat the ship
decreases.

19. Pearl Harbor
• It took three months to
rescue and raise the
USS California. It had
sustained a great deal
of damage but was still
usable. It would take
close to two years to
retrofit it and get it
battle ready.

20. Pearl Harbor
• When it returned to the
war, the California took
part in these battles:
• Saipan and Guam
• Leyte
• Luzon
• Okinawa
• These were pivotal
battles that led to the
defeat of the Japanese
navy.

21. “All this represented one of history's greatest
salvage jobs. Seeing it to completion
required that Navy and civilian divers spend
about 20,000 hours underwater in about
5000 dives.”
– Naval History and Heritage Command Web Site
Pearl Harbor
We cannot underestimate the heroic efforts to salvage the ships at Pearl Harbor.

22. Pearl Harbor
While the Japanese Imperial Navy may have overestimated the military impact of
Pearl Harbor, they certainly underestimated the resilience of the U.S. Navy.