May

27

 Was the Vasa was the greatest warship of her time? By the time Samuel Pepys (great gossip, even greater Gilbert & Sullivan head of the Queen's Navy) became Secretary, the Stuart Navy was successfully challenging the Dutch and the French and offering its protection the Swedish merchant marine ships in their trade in the West Indies.

In his Miscellany Pepys lists the following classes of ship:

Rate          Name        Length     Beam     Draft    Tons  Men  Guns
First          Sovereign      127         46         19     1141  600  100
Second      Fairfax          116         34         17     745    260  52
Third         Worcester      112         32         16     661   180  46
Fourth       Ruby             105         31         15     556   150  40
Fifth          Nightingale      88         25         12     300   90   24
Sixth         Greyhound       60         20        10     120    80  18

A comparison of the Sovereign with the Vasa is dispiriting. The Vasa was roughly the same size - 1200 tons; but it was nearly twice as long - 230 ft. - and its beam was 8 ft narrower (38 ft.). That is a length to beam ratio of 6 to 1.

That was asking for trouble. The rough rule of thumb since people first started sailing and capsizing boats is that a monohull should be three times as long as she is broad. This should not have been news to the Vasa's architects. The Mary Rose (built 90 years before the Vasa) had a ratio of 3 to 1.

There is a reason for the Vasa's builders to have wanted it to be so long. There is even an explanation of why they thought they could build to such an extreme ratio. The longer a boat is, the less beam she needs proportionately. A boat's resistance to being overturned varies as the fourth power of her waterline length, the heeling moment of the wind pressure on the sails or the waves and swells against the hull in an engine powered ship varies as a cube of her length. Length is desirable in itself because the maximum speed of a vessel is - roughly - 1.2 times the square root of its length at the water level.

The Vasa's builders were trying to achieve the same results that American naval architects produced with the Iowa class battleships — the last ones ever built by the U.S. and the last battleships to operate on the high seas. The Iowas had to fit through the Panama canal and be able to keep up with the carriers (which were much lighter and, therefore, faster for the same propulsive power). As a result, they had an extreme beam to length ratio (8 to 1).

Then, why did Iowas survive typhoons while the Vasa sank literally in port? The answer is that the added stability of length can be horribly offset by increases in height. The Vasa had a height of 172 ft. - 75% of its length. For the Iowas to have had the same proportion, their hulls would have had to be 500 ft. high! Adding another 3+ ft. and a great deal more ballast kept the Vasa's sister ship from sinking in the Baltic, but it could never have survived the North Sea. Even using the 3.5 to 1 length-to-beam ratio that the smaller rated ships in Pepys' fleet (the Worcester, for example) would have required the Vasa and its sister to have beams of at least 65 ft; and, in the age of sail, there was no way for them to reduce its height to the dimensions of the Iowas.

The analogy with financial engineering is certainly appropriate. Somewhere in Stockholm in 1630 there must have been some bright young men who looked at the extraordinary success of the ancient Viking long ship designs thought "leverage can only lead to greater glory." But, the little matter of the Viking long boat's limited sail height seems to have be ignored. There are no surviving rigs for the long ships, but the best estimate for a 30 meter boat is that it had a mast height of 12 meters or roughly 40% of its length.

Phil McDonnell writes:

 I visited the Vasa Museum. It is a fascinating story of the greatest warship of her time that heeled over and sank within minutes of first setting sail in moderate conditions. In many ways it is the story of man's attempts to master engineering, be it naval or financial. The ship was only raised in the last century with modern engineering and is over 90% preserved due to salinity conditions in the Baltic. The interesting sequel to the Vasa disaster is that her sister ship which was completed two years later was only one meter wider but had significantly improved ballast engineering. The redesigned ship actively served Sweden in the war against the King's cousin, the King of Poland. Highly recommended tour.

Dr. McDonnell is the author of Optimal Portfolio Modeling, Wiley, 2008

Paolo Pezzutti comments:

 Maybe the ship was top-heavy.  If the ballast, for example, is not enough, the metacentric height (distance between the center of gravity and the metacenter) is too low, the ship would be unstable.  
 
From the thesaurus:

"metacenter - (shipbuilding) the point of intersection between two vertical lines, one line through the center of buoyancy of the hull of a ship in equilibrium and the other line through the center of buoyancy of the hull when the ship is inclined to one side; the distance of this intersection above the center of gravity is an indication of the stability of the ship".
(The center of buoyancy is the line of action of the resultant of all buoyant forces of the immersed portion of the ship).
(The center of gravity is a function of the distribution of the weights on board the ship and the ships itself).

There could have been different problems. An initial instability because of low metacentric height. Shifting of weights on board the ship may have altered the center of gravity. Or both.

Is how to calculate the metacentric height of a market a silly question?


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