Naval Constructor's Office, Navy Yard,
Washington, May 8, 1874.
To the Hon. Geo. M. Robeson, Secretary of the Nary:
Sir: In accordance with a circular from the Navy Department under date of March 17, 1874, I have the honor to respectfully submit a report of an experiment made by me on the United States steamer Shawmut the day before she sailed for Key West, for the purpose of ascertaining the height of her center of gravity.
At the time this experiment was made the Shawmut was lying in the Potomac River, below the Navy Yard, Washington, D.C.
Although the wind blew a little fresh, there was no sea on, thus enabling the draught of water to be taken very correctly.
The ship was complete in every respect and ready for sea; the topsail yards were on the caps, sails- all furled, boats hoisted, and the two broadside 9-inch guns run out; the 11-inch pivot on the main-deck, and the 20-pounder pivot gun on the topgallant forecastle, were amidships and secured for sea.
She had on board a crew of about one hundred men, with provisions for the full complement for three months, 32,295 pounds of water in casks and tanks, 208,320 pounds of coal in the bunkers, both boilers full of water, and steam up, the weight of water in the boilers being 53,000 pounds.
The estimated weight of the articles on board, coming under the Department of Equipment and Recruiting, excepting coal, was 108,160 pounds; the two lower anchors, weighing 6,170 pounds, were down when the experiment was made. . The total weight of ordnance, ordnance stores, and equipments was 117,113 pounds. Total weight of engineers' stores and spare machinery, 4,000 pounds. Total weight of carpenter's stores, 7,068 pounds.
The conclusion that it would not be necessary to employ any other means to incline the ship than that of shifting her guns was arrived at with great satisfaction, on account of the great objection to having a large quantity of rusty pig-iron upon the clean deck of a vessel in commission, the expense attendant on transporting it to and from the yard, and also because of the still further departure from the normal state of the ship which its presence would produce, and the necessity for still greater complexity in the calculations.
As this experiment was made for my own gratification, it was necessary that the consent of the commanding officer, Commander Henry L. Howison, should be first obtained, which was freely given, and all the assistance he could afford was cheerfully accorded, for which to him and his Executive Officer, Lieutenant-Commander Norris, I am greatly indebted.
As this is the only instance that I know of where a United States naval vessel has been experimented upon for this purpose (with the exception of the United States steamer Princeton and the brig Somers, which were inclined by Naval Constructor John Lenthall, late Chief Naval Constructor United States Navy, at the Navy Yard, Philadelphia, in 1844, an account of which was recorded in the Franklin Institute Journal. The Princeton was inclined by moving weights on her decks, the Somers by hanging weights on her lower yard-arms), I consider it necessary, in order that the subsequent portion of my report may be better understood, that I give a rationale of the experiment, which may be found recorded in the "Transactions of the Institution of Naval Architects" for 1860, as made by F. K. Barnes, Esq., member of the Council of Construction, H. B. M.. N. Let ACD, Figure 1, represent the transverse section of a ship, through G, the center of gravity of the hull, and every article on board; WL the load waterline when the ship is floating in upright position; CBGM the middle line, which is therefore perpendicular to, WL, and also contains G, the center of gravity of the ship, and B, the center of buoyancy (or center of gravity of the displacement). Let also P represent a weight or weights on any or all of the decks, such as guns, shot, ballast, etc., capable of being readily transported to the opposite side of the deck or decks.
If the weight or weights, P, be moved across the deck to P', the ship will incline through an angle, WSW', the amplitude of which will depend, cateris paribus, upon the weight or weights moved and the distance through which they have been moved.
When the ship has taken up the new position of equilibrium, the center of buoyancy will have moved from B to B', and the center of gravity of the ship from G to G', so that the line joining B' and G' will be vertical, and, therefore, perpendicular to W' L', the new water-line, and will make the same angle, B M B', with the middle line, BUM, as the water-lines do with each other, and B'G' produced will meet in the middle line in a point, M.
This point, in ships of the usual form, may, without any appreciable error, be assumed to coincide with the metacenter when the inclination does not exceed 40 or 5°.
From a general and well-known property of the center of gravity of a system of bodies, such as a ship, we know that since the weight or weights, P, have been moved in a horizontal direction to P', the center of gravity has also moved in the same direction ; therefore G G', the line joining the original and new center of gravity, will be horizontal. And from another property of the center of gravity we have the weight of the ship x G G' = P x distance through which it has moved; or if W represent the total weight of the ship, and c the distance through which the center of gravity of the weight or weights, P, has been moved,
W x G G’ = Pc and G G’ = (Pc)/(W)
Now, by trigonometry, G G'= GM x tangent of the angle between the middle and the new vertical line B' G' M, i.e. the angle of the ship's inclination from the upright; or, representing the angle of inclination by ?,
G G’ = G M tan ?
G M = (G G’)/(tan ?)
Equating the two values of G G' thus obtained,
(Pc)/(W) = G M tan ? or GM = (Pc)/(W tan ?)
The right hand member of this equation contains all known quantities after the ship has been inclined; and since the metacenter corresponding to any draught of water is easily obtained by calculation from the drawings of the ship, and its position fixed, the distance G M set off below it will give the position of the center of gravity of the ship.
Finally, the angle of inclination (?) is found with the greatest exactness in the following manner:
A T-square above twenty feet in length, with a wide, thick blade, is nailed to the combings in the hatchways in a vertical direction, one in the main and one in the fore hatch. The two squares, being independent of each other, are intended to serve as mutual checks, and also to point out any racking of the ship, which might be occasioned by the movements of the weights on board.
From the upper edge of the head of the square a distance of 20 feet is carefully set off upwards, and at the height thus obtained a nail is driven into the board, and to it is attached a plumb-line, the plummet hanging freely at some distance below the head of the square.
When the vessel is upright, and the experiment about to be commenced, the point where the plumb-line intersects the upper edge of the head of the square is carefully marked; and when the ship has obtained her new position of equilibrium by the movements of the weights, the new point of intersection of the plumb-line and the upper edge of the head of the square is marked in like manner. The distance in feet between the two points marked on the square, divided by twenty, will clearly give the tangent of the angle of the ship's inclination. The first thing done in commencing the experiment was to go to quarters; the powder division having been called on deck, the crew were divided equally on either side of the deck in single file, and along the edge of a seam in the deck equidistant from the center; the marines being divided and placed in a similar manner on the poop-deck.
The two T-squares having been fixed in position, and the draught of water noted, the men were cautioned to note their position, so that they could resume it again when ordered to do so.
When all were again quiet and the ship steady, the points at which the plumb-lines crossed the upper edges of the squares were carefully marked, as already described—an operation which occupied scarcely half a minute, and it is only during these short intervals, when the marks are being made, that the men need be under any constraint.
The men were then ordered to transport the nine-inch gun from the port to the starboard side of the deck, placing it fore and aft the deck, as far out as it could be got, and close to the nine-inch gun on that side. The nine-inch pivot gun was then swung around to starboard and run out. The 20-pounder rifle on the topgallant forecastle was also swung around to starboard and run out. After all the guns had been moved, the men were ordered to resume their stations as before directed. As soon as all were again quiet, the points in which the plumb-lines crossed, the upper edge of the T-squares were marked at the same time; and the deflection of the plumb-line, read off from both squares, was found to be sixteen inches.
The work of the crew here terminated, and by the movement of the guns above mentioned a registered inclination was obtained, and data furnished by which the center of gravity might be found.
The weight of each gun moved was taken, and the distance through which it had been moved in a transverse direction was then very carefully measured and recorded.
Thus ended the work on board the ship. The recorded draught of water at the time of the above experiment was, forward 11 feet 0 inches, aft 18 feet 6 inches.
Displacement to the above line in tons, 1010.84. Center of buoyancy below water-line, 4 feet 6 inches. Center of buoyancy above the lower edge of the keel, 7 feet 6 inches. Metacenter above center of buoyancy, 7 feet 5½ inches. Metacenter above lower edge of the keel, 14 feet 11½ inches.
The sum of the products of each weight, and the distance through which it was moved, was (in tons and feet) 199.32, and the deflection from the upright of the plumb-lines in 20 feet was 16 inches; denoting by ? the corresponding angle, tan ? = (1 1/3)/(20) = (1)/(15), ? = 3 ° 49’ 21”.
Weight of nine-inch gun and carriage 10,437 pounds, moved 20.66 feet. Weight of eleven-inch gun and carriage 24,159 pounds, moved 7 feet. Weight of 20-pounder rifle and carriage 3,793 pounds, moved 3.635 feet.
GM = (Pc)/(W tan ?) = (199.32 x 15)/(1010.84) = 2.958 feet, center of gravity metacenter. The height of the center of gravity above the lower edge of the keel 14.95 feet - 2.96 feet = 11.99 feet. The height of the center of gravity below the mean load-line is, therefore, .26 = 3¼“. Relative stability or displacement, multiplied by the distance between the metacenter and center of gravity 1010.84 x 2.96 = 2992.0864.
The first instance in which this experiment was tried, to determine the position of the center of gravity of a ship experimentally, was on board H.R.M. Sloop Scylla and the Rover, of eighteen guns, in Portsmouth Harbor in May, 1830. The experiment was made by a Mr. Morgan, of the School of Naval Architects, at that time the foreman of the Portsmouth dockyard.
No other experiments are recorded from that time up to 1855 (excepting those made on the Princeton and Somers, before mentioned, in 1844, and found recorded in the Franklin Institute Journal), when, by the upsetting of the steam-transport Perseverance in the dock at Woolwich dockyard, the subject was brought under the serious consideration of naval architects. The determination of the metacenter and center of gravity is now made for every ship added to the English Navy.
The labors of Mr. Froude and of other gentlemen who have devoted their attention to the subject of rolling of ships has resulted in the establishment of two great facts. The first of these is that the principal thing (although not the only one) which influences rolling is the distance between the center of gravity of a ship and the metacenter; the second is that a ship rolling at sea is largely influenced by the period, etc., of the waves she meets with. Experience confirms the accuracy of both of these deductions.
Ships which have a great distance between the center of gravity and the metacenter are technically termed "stiff," and will spread a great amount of canvas, but they usually roll with violence.
On the other hand, ships which have a moderate distance between these points are not so "stiff," and roll moderately; while, if the distance is very short, they will be "crank," and liable, under certain circumstances, to upset.
Very respectfully,
Your Obedient Servant,
(Signed) T. D. Wilson, Naval Constructor U. S. Navy.