Stability in a ship

[Davide Pastore]

Being a brief, simple, raw, inaccurate and confusing depiction of stability in a ship.

(Note: I started writing something about this topic in the thread "8 inch guns". Since it has nothing at all to do with such weapons, I expanded it here. I hope it can be of some use)

"To the naval architect, stability is a measure of the moment of force trying to bring the ship upward from a heeled position." [D. K. Brown]

We will analyse three warship designed by Messrs. von Pastor & Le Pasteur, of the award-winning Germagnano Imperial Yard:

- the monitor HMS Impossible (shallow draught, extra broad beam)
- the aircraft carrier USS Nevertown (a "midrange" ship)
- the cruiser IJN Everykaze (narrow beam, plus the tallest pagoda tower ever)

each of them has a displacement of 10,000 tons.



Figure 1 shows the three ships (transversal section view) in a flat calm.

G = centre of Gravity. The weight of the ship (W=10,000 tons of iron) acts downward through this point. We will consider G as a fixed point, although in the real world it will slightly change position when the ship is heeled (due to the movement of fuel, and as a rule of anything not bolted to the hull). The yellow area represent the amount of ship above surface.

B = centre of Buoyancy. The buoyancy force (equal to W since, according to Archimedes, it is the weight of the 10,000 cubic meters of water dislocated by the hull) acts upward through this point. This point clearly moves as the ship is heeled. The blue area represent the amount of ship above surface. We will consider the ship as impermeable, although in the real world the sea will actively try to fill the interior of the hull through any opening.

Note that, to show the variations, I tried (being a not simple task!) to make blue areas of same size in all conditions and all ships.

[Davide Pastore]

Figure 2 shows the three ships with a slight angle of heel (10 degrees for clarity's sake).

M = the point where the vertical line passing through point G crosses the central axis of the ship

Z = the orthogonal distance between said line and point G

The Righting Moment is measured by: W x GZ

At small angles of heel (A) the righting moment can be approximated as: W x GM x sin(A)

where GM is called Metacentric Height. Most of you will have met this term, haven't you?

For our three ships, W and A are the same, so the stability is given by their respective GM.

- HMS Impossible has a great GM, i.e. a great righting moment. So, if heeled by wave or wind action, she will try to right herself in a very brusque and lively manner. This is unpleasant for the crew, and negative for gunnery precision.

- IJN Everykaze has a small GM. Her righting force is small, and so her roll movement will be slow and fluid. The crew will love her, and she is also a perfect gun platform.

- USS Nevertown is a middle solution between the other two.

[Davide Pastore]

Figure 3 shows the three ships at their respective "range" (defined by Brown as "the extreme angle at which there is a positive righting moment"). This is a very critical position, since the smallest increase in the angle of heel will cause the vertical line passing through G to fall on the left of B (plainly speaking, the ship will instantaneously capsize).

- HMS Impossible has an immense 80 degree range. It's practically impossible that even a tsunami wave will ever cause her to heel so much. She has a great stability (in fact, she has too much stability to be an efficient warship).

- IJN Everykaze has a pitiful 30 degrees range. This ship will be in positive danger in anything above a gentle breeze. She has insufficient stability.

- USS Nevertown is a middle solution between the other two. She has the right amount of stability.

[Davide Pastore]

Chapter 4

A diagram showing A and GZ along its X and Y axis is called "Curve of Stability" by naval architects. It shows that GZ starts from zero (when A=0), ends at zero (when A=range) and reaches a maximum somewhere midway, called "Maximum Stability Lever". The angle of heel at which such maximum happens is a most important value, since if a wave causes the ship to heel above it, chances are than the ship will continue to heel until capsizing (since from then on the righting force will steadily decline).

The curve depicted below is somewhat conjectural (since I identified just three points for each curve) but nonetheless shows the pattern.

Davide

[Davide Pastore]

Below there is a somewhat more scholastic curve, by D. K. Brown

Note: I keep adding pieces of post, since I haven't discovered yet how to mix images and text

Davide

[Davide Pastore]

Chapter 5

Below we can see one of the most famous case in history of a ship with insufficient stability: HMS Captain (capsized off Cape Finisterre in 1870) compared with her contemporary HMS Monarch.

Shown are the two respective curves of stability.

It interesting to note that both ships had the same GM (2.8 feet, Captain actually being a bit higher than Monarch), but the righting moment fell away once her (very low) deck edge was immersed.


Davide

[Davide Pastore]

Chapter 6

In the real world, the metacentric height GM will be first of all calculated by the naval architect at the design stage. After building, the theory will be verified by subjecting the ship to an "inclining experiment" (any naval aficionado would probably have seen one or more photo of some of them), where known weights (w) are moved a specified distance (d) across the deck and the heel (A) measured. Then:

w x d = W x GM x sin(A)

Since the position of M can be (tediously) calculated with precision, G can be deduced.

If required, Metacentric height can be modified on an existing ship:

- positioning lower weights (by ballasting) raises GM
- positioning higher weights (by adding antennae, masts, etc.) lowers GM
- broadening the beam (by inserting a blister along the sides of the hull) raises GM

Example: the Pearl Harbour battleships were reconstructed with a vast increase of their AA panoply (more higher weights, raising GM) and this in turn required blistering the hull (to lower GM) to balance and neutralize the former effect.

Source: D. K. Brown (ed.), The Design and Construction of British Warships 1939-1945: The Official Record (Conway maritime Press 1995)


Note: having been pleasantly surprised by the success of this thread (at least, judging from the number of views) I had laboriously written a long dissertation about historical GMs compared to ships' behavior (mainly based on Norman Friedman's books). Unfortunately a single wrong click was sufficient to send it all out of cyberspace. I'm totally demoralized and unable to start it all again. Isn't there any way to save your work mid-way during the writing phase?

Davide

[tommy303]

I usually start out by writing a long message in note pad and they when it is ready copy it to the message box.

[SM79Sparviero]

Definition of concepts is conclusive, in life.
I think I was wrong when I spoke about "stability" .I meant that a "stable" ship is a ship which is hardly moved by the waves , not a ship which is moved by the waves and quickly turns back thanks to its righting moment.I think that the concept "not influenceable" would be better than "instable" for expressing my ideas.
According to your thread I agree that a ship wich turns right too quickly makes more troubles than a ship wich turns slowly.

I wonder:Is really the righting moment the trouble?

1) A wide ship quickly turns back right I agree, but which is the starting angle?It is much more difficult for the waves to turn a wide ship from the right position, she would be howewer turned by a lower angle than a ship with a narrow hull.The righting moment could become futile for aiming a target if the ship is so "not influenceable" that she always ( or often) she keeps right by herself.

my scanner is off by now, I would like to send a picture of USS Massachussets close to an aircraft carrier in a storm, just to compare the tilting angle of the battleship with the one of the carrier.......

2) Are you sure that a higher righting moment with a narrow tilting angle is such disavantadgeous if compared to a broad tilting angle , if you shoot by an high-speed gun at long range?

[Davide Pastore]

a picture of USS Massachussets close to an aircraft carrier in a storm, just to compare the tilting angle of the battleship with the one of the carrier

This by itself proves nothing, the movemente of the two ships are not necessarily "in phase". It is just a frozen instant.

Data for the two classes (I suppose the CV is an Essex) are:

- South Dakota
GM 8.84'-8.94' normal load, 9.36'-9.51' full load
max GZ 4.95'-5.06' at 33.7°-34.2°
range 66.2°-68.8°

- Essex
GM 8.95' normal load, 9.59' full load
max GZ 7.46'-7.94' at 42.5°-42.7°
range 81.5°-84.8°

The two ships seems more or less to exhibit the same behavior up to 34°, the BB worsening afterward (of course, to heel such a behemot by 34° requires a king-size tornado).

2) Are you sure that a higher righting moment with a narrow tilting angle is such disavantadgeous

Yes, I am. One of the most famous cases of ships with too much stability were the USN DEs. The Royal Navy received a number, below are a couple of excerpts from their captains:

"Since this report is written at sea it is difficult to describe with reticence the nauseating movement of these vessels in the open sea [...]. As gun platform these ships are satisfactory only under the most favourable weather. [...] The Hedgehog is inaccurate in a short head swell on account of the unpredictable roll and the resultant tilt. [...] It is infleneced by excessive and incontrollable rolling which is a factor which obscures every virtue these ships may possess."

"Commanding officers [...] are unanimous in their complaints about the rapid rolling of these ships. The quickness of the recovery not only causes physical exhaustion but makes the efficient operating of weapons and instruments most difficult. [...] The motion in s seaway, though not excessive in extent, is so violent in character as to be a menace to life and limb, to equipment and property, to seasoned stomachs, and to normally equable nerves and tempers. Morale cannot fail to be affected. Fighting efficiency will certainly suffer."

OTH a couple of Farragut class DD (a ship with GM about 50% of DEs) capsized in the famous 1944 hurricane (also portraited in "The Caine Mutiny"), and two others survived only through ballasting their fuel tanks with salt water. A DE would have never experienced such fate.

Source: Norman Friedman, U.S. Aircraft Carrier / U.S. Battleships / U.S. Destroyers, Annapolis (various years)

Davide

[David C. Clarke]

Awesome discussion gentlemen!!! Way over my head!

By the way, I thought a major factor in the capsizing of the American DDs in the typhoon was that their fuel supplies were critically low and the lack of fuel weight made them less stable.

Best,
David

[varjag]

Davide's description is quite correct. In an older 'tramp-steamer' it was possible to
experience all THREE conditions in the same ship, depening on the cargo.
1) Scandinavian Iron Ore (65% iron) - and stable as hell but violent in roll.
2) Coal loading - superb. Fills normally to just under the hatches.
3) Sawn timber load - with a 2-4 meter high deck-load and the ship becomes 'weak'.
(Especially with breaking seas that waterlog the deckload......... :roll: ) Varjag

[Davide Pastore]

By the way, I thought a major factor in the capsizing of the American DDs in the typhoon was that their fuel supplies were critically low and the lack of fuel weight made them less stable.

Friedman specifies that the lost Farraguts had 75% fuel. However, they could well have been critically low regarding stability, just the same. He notes that the captains of the two capsized Farraguts (Hull and Monaghan) were the more junior (Annapolis class 1937 & 1938) and less experienced ones, while the two surviving units (Dewey and Aylwin) were commanded respectively by former Nimitz's assistant chief of staff, and by the leader of Third Fleet logistics group. Friedman argues that the two junior captains preferred not to contaminate their fuel tanks, the subsequent cleaning taking as long as six hours. The two senior captains added that critical last 25% of weight, and got safe.

In the same hurricane also Spence (Fletcher class) capsized. She was a ship with higher GM (near as high as the DEs, which however were much smaller) but her tanks were nearly empty (just 15% fuel). "Again, there was great reluctance to fill tanks with salt water"

"The destroyer escorts showed superior seaworthiness in both Atlantic and Pacific storms, riding them out like corks, although they rolled heavily and could hardly be described as confortable."

(Friedman, U.S. Destroyers, pp. 188-189).

Friedman adds that, according to USN powers-that-be, the unpleasantness of RN DEs was due to the removal of their torpedo tubes (a big load high over the hull), which the USN units retained. However RN calculated that the difference would have been minimal. (Friedman, p. 161)

Stability data for both class (Source is the usual Friedman. Fantastic books):

Farragut class (beam 34.3'):
GM (1934) 2.76' (normal load - 1,583.9t) / 2.37' (full load - 2,063.8t)
GM (1944, after AAA modification) 1.67' (full load and then a bit more - 2,307.2t)

DEs (beam 35'-37'):
GM - 3.87' (TE - 1,147.7t) to 4.51' (DET - 1,518t) normal load / 3.96' (TE - 1,652.4t) to 4.69' (DET - 1,623t) full load

Davide

[David C. Clarke]

Hi Davide! The only reason I brought it up was because I thought the weight of fuel was calculated as a normal part of a ship's displacement and therefore an integral factor in a ship's stability which was taken into account by the designers of a vessel.

Best,
David

[Davide Pastore]

Hi Davide! The only reason I brought it up was because I thought the weight of fuel was calculated as a normal part of a ship's displacement and therefore an integral factor in a ship's stability which was taken into account by the designers of a vessel.

Consuming the fuel altered the stability (as did, for example, launching torpedoes and consuming ammo). The designer would have calculated the stability in each condition (full, empty, etc.) and derived the respective data. The captain should have known that his ship becomes dangerous when, with X tons of fuel, she meets waves of force Y (and so on).

Davide