Metacentric Height

The following appeared on MARHST-L in June 1999, and appears by permission of the author, Maxwell Mulholland (BlauerMax@AOL.COM)), who is a Qualified US Navy Chief Engineer and Former Damage Control Officer, USS Arkansas.

This is a follow-on to my note from yesterday on metacentric height (referred to as "GM" among naval architects) and its effect on gunnery. Consider this a second short primer on the subject.

The standard relationship is basically:
Larger metacentric height (GM) = larger Righting Arm (RA) = greater stability

As I mentioned before, GM is a design characteristic of ships. A ship impacted by external forces basically behaves as a pendulum of length GM. The value of GM is determined by a huge number of factors, including a vessel's length-beam ratio, underwater cross-sectional profile, waterplane coefficient, bilge and keel shape, the placement of specific weights (which determines the location of the center of gravity), the amount of freeboard, and others. Naval architects have considerable leeway in setting the GM of the ships they design through the various choices and design trade-offs they make. Every newly built ship, and every ship leaving a shipyard after a significant alteration to its original design condition, undergoes what is known as an "inclining experiment" while dockside to validate the GM value.

Less stable ships have smaller GMs and a longer ("softer") roll period, which as I mentioned earlier normally results in easier fire control solutions and better accuracy - not to mention more comfortable sailing characteristics and better living conditions for crew and passengers! British-American battleships and today's modern cruise ships were purposefully designed to have moderate-sized GMs for these reasons. My comment that German WW1-era battleships and battlecruisers were better gun platforms in the North Sea (with its unsettled waters and choppy seas) had to do with the fact that they were inherently more stable than their Royal Navy counterparts and thus better able to handle the conditions they faced in this somewhat enclosed body of water.

Just a quick comment: there is no explicit relationship between a ship's stability and its inherent buoyancy - HOWEVER, as weight is added to a vessel (either deliberately through periodic updating or conversion, or inadvertently as a result of flooding from battle damage) this situation will tend to reduce the ship's design RA curve (the plot of the magnitude of righting moment versus the ship's angle of heel or list) which is considered to be the best indicator of stability. As a sinking ship fills up more and more with water, her effective displacement goes up and her metacentric height goes down. This results in her roll period getting longer and longer, and she tends to feel increasingly "loggy" (meaning that her RA is getting smaller and smaller, therefore reducing her ability to right herself) -- until the final catastrophic moment arrives when she rolls completely over and doesn't recover.

Counterflooding is a vital damage control countermeasure that will help reduce a ship's list (thus ensuring that munitions hoists can continue to operate properly, and that guns and FC systems can be brought to bear on the enemy) but this action will also reduce the GM and thus tend to make a ship LESS stable. While conventional thinking leads to the belief that any amount of flooding below a ship's center of gravity is good, in reality this is only true if the compartment in question is COMPLETELY filled, for any partially filled space -- regardless of where it is located -- will lower a ship's stability through what is known as the free surface effect, which has a severe negative impact on the size of the GM (clearly, any flooding above a ship's center of gravity is BAD).

I hope that this note helps people achieve some more understanding on this somewhat arcane topic!

This is a quick response to some questions and commentaries posted by others on this thread:

1) SMS NASSAU was considered by the Imperial German Navy staff as being "too stiff" after her delivery into the fleet. As a result of the fast period of roll she demonstrated during sea trials, she was sent back to the dockyards to have additional bilge keels and hull strakes put on to dampen down the speed of her pendular motion in a moderate seaway. According to Norman Friedman in his book "Battleship Design and Development 1906-1945" (Mayflower Books, 1978), NASSAU's stability and performance were adversely affected while sailing in the North Sea because her period of roll was resonant with that of waves commonly found in these waters. Friedman also states that additional counter-measures were tried on her sister ships, to include the use of surge tanks and gyro-stabilizers (but none of these was successfully, not surprising for WW1-era vessels given the level of engineering sophistication these demanding systems require...although aren't these devices really meant more to reduce the MAGNITUDE of a ship's roll rather than the actual roll PERIOD?)

2) The Royal Navy's REVENGE-class ships were the first British dreadnoughts purposefully designed with a very low metacentric height (GM), the intent being to build battleships with a slower roll period, an easier gunlaying capability, and therefore more accurate long-range accuracy. This was done to this class by raising the height of their armored deck to the top of the main belt. While this design alteration also resulted in better protection against shell-fire, the change at the same time greatly reduced these ships' resistance to underwater damage and made them ominously unstable when subjected to only moderate amounts of flooding (in the maddening way that adding one good feature usually results in a trade-off requiring creation of a bad one).

In general, British dreadnoughts of the pre-WW1 age were designed with GMs of around 1.4 - 1.8 meters. This was, as I had mentioned before, a fairly moderate metacentric height for capital ships. In comparison, REVENGE's GM was an astonishingly low 1.0 meters (as was the wartime-designed HOOD's as well) -- a dramatic drop in value from the previous norm of Britain's big ships! Imperial Germany's dreadnoughts had GMs in the range of 2.3 - 2.6 meters, while some particular battlecruisers had even larger metacentric heights (such as MOLTKE with a GM of 3 meters, and SEYDLITZ with a GM of an incredible 3.12 meters - another key to her ability to return to the Jade after Jutland/Skaggerak carrying over 4,000 tons of saltwater in her hull).

(PS - data on GM values comes from the appendix in Friedman's book).

Last Updated: 12 July, 1999.

 Return to WWI The Maritime War

 Return to WWI Archive main page.