Of interest to both the operating personnel and the designers are those elements which affect the Propulsion of ships. Shallow water is one of the least considered and most interesting of these elements and merits attention, I believe, by most of the nautical fraternity.
Nearly everyone is acquainted with the fact that when a body, or more specifically a ship, moves through the water, peculiar disturbances take place in the liquid. These disturbances are most apparent to an observer in the form of waves on the surface, while beneath the surface the movements of the liquid are least apparent. If a ship is in a vast expanse of deep water, the above-mentioned disturbances are of a different nature than if the ship is in water of limited depth and transverse dimensions. The amount of modification depends, of course, upon the proximity of obstacles interfering with the “water disturbances” caused by the ship’s motion.
Previous to the year 1893, and the tests of Captain Rasmussen on the Danish torpedo boat Makralen, no great importance, generally, was attached to the depth of water in which the speed trials of ships were carried out. The results obtained in different depths of water did not agree but, curiously enough, a very different explanation than depth of water was sought for these discrepancies.
Within the last 40 or 50 years various investigations have been undertaken to determine the variations in ship performance under deep and shallow water conditions. Explanations for these differences have in some instances been advanced in conjunction with the published data on the tests. Therefore, I purpose to outline, briefly, the principal variations in ship performance in different depths of water, as determined by these tests, and to relate the generally accepted reasons for these variations.
As previously stated, numerous investigations of this subject have been undertaken. Perhaps the most complete and most enlightening, previous to the year 1900, were carried out at the Experimental Tank of the Royal Dockyard at Spezia, Italy, and described by Major G. Rota, R.I.N., before the Institute of Naval Architects in 1900. These particular experiments
were carried out on models, while in 1909 the speed trials of a full-size ship, the English torpedo boat Cossack, were used as a means of investigating the same subject. I shall deal primarily with the results of these two investigations, which
are in general agreement with other similar tests.
The tests described by Major Rota were carried out using models of different types of ships so that by the application of the laws of dynamical similarity each model might be considered to represent an indefinite series of ships. The models were towed in different depths of water at varying speeds, and curves of the sort shown in Fig. 1 were obtained for each model.
These curves show definitely that in deep water, relatively speaking, the resistance of any one model is definitely less than it is in shallow water at the same speed. For instance, at a speed of 5.92 feet per second the resistance is at least one pound more in water 2 feet deep than in water 10 feet deep.
Pursuing the experiment further, the speed of one model was increased to a range well beyond that shown in Fig. 1. The peculiar fact was now discovered that at a certain speed the model had the same resistance in deep and in shallow water, while at higher speeds the model had a lower resistance in shallow water than in deep water. This is clearly seen in Fig. 2.
In 1909 the speed trials of H.M. torpedo boat destroyer Cossack were described in a paper by Sir Philip Watts and verified the results on models. These trials were carried out at Skelmorlie and again on the Maplin Sands. The Cossack was designed to make 33 knots and she had the following characteristics: length 270 feet, beam 26 feet, and a draft of 8 feet 2 inches on a displacement of 836 tons. The depth of water at Skelmorlie was 40 fathoms and on the Maplins 7.5 fathoms. The shafts were fitted with torsion- meters and horsepower-speed curves were obtained first on the Maplins and afterwards at Skelmorlie. The curves shown in Fig. 3 explain the results.
It will be noted that these curves are power plotted against speed whereas the previous curves were resistance plotted against speed. It is natural to expect power curves to differ somewhat from resistance curves, since the varied stream flow aft in shallow water will affect the propeller action. The differences, however, are not great and do not invalidate the similarity of results.
By studying Fig. 3, it is seen that at Skelmorlie the rate of increase of horsepower in passing from 16 knots to 34 knots is continuous and gradually increasing.
The corresponding rate of increase on the Maplins is at first much more rapid until about 19.5 knots is reached, when it begins to decrease, and at 22 knots it vanishes altogether, the next 2.5 knots being obtained without any increase in power. At 24.5 knots the horsepower again begins to increase, and at about 30 knots the horsepower curve becomes roughly parallel to that at Skelmorlie— but below it. At 26.75 knots the power required at each place is the same. It is evident from the curves that at speeds below 26.75 knots there is advantage in running in deep water but above this speed it is advantageous to run in the shallower water of the Maplins.
Several explanations have been given for these variations in resistance to propulsion as water shoals, and I shall attempt to set forth those features of the explanations upon which most authorities seem to be agreed.
The primary explanation arises out of the fact that, as the depth of water gets less, the streamlines of flow past the ship become more and more of a two-dimensional character. In deep water the disturbances caused by the ship’s motion are free to move in three directions; as the water shoals the motion in a vertical direction is restricted more and more. Approaching the two-dimension condition tends to intensify the streamline velocities past the ship and to intensify the water pressures. Mr. R. E. Froude, F.R.S., advanced the explanation that due to these increased streamline velocities the surface of the ship was in effect augmented and frictional resistance increased. The eddy-making element of the resistance is also increased due to the discontinuous and quite erratic motion set up in the water. Rear Admiral D. W. Taylor (C.C.), U. S. Navy, seemed to be in general agreement with this portion of the explanation, but declared that the intensification of stream velocities in shallow water, its resultant
augmented surface, and subsequent increased resistance, were of relatively small importance.
The dominant factor in the explanations of these phenomena seems to lie in the extra pressures which are set up as the water flow changes from a three-dimensional to a two-dimensional character. These extra pressures cause larger waves in shallow water than would be expected in deep water and, at a given speed, the lengths of the waves accompanying a ship in shallow water are greater than for the same speed in deep water.
The resistance curve of almost any ship shows, at a certain speed in relation to the vessel’s length, a rapid and often rather sudden increase in resistance. If this curve is pursued up to much higher speeds, such as are reached with destroyers, it is found that instead of the curve going on ascending more and more rapidly it begins to fall off, forming a “hump.” According to Mr. R. E. Froude the center of that hump, broadly speaking, coincides with the speed at which the length of wave, proper to that speed, agrees with the length of wave which the vessel tends to form. Now, that wave length proper to that speed becomes increasingly sensitive as the depth diminishes; the effect being that, as the water shallows, the length of a wave at a given speed increases. The effect of this is to lower the speed at which conjunction takes place—conjunction of the wave proper to the ship’s speed, and the wave formed by the hull. The hump is thus pushed down the resistance curve and the result is as indicated in both Figs. 2 and 3—where it is seen that in shallow water, or water of diminished depth, the hump has been pushed to the left. At speeds below the center of the hump the resistance is increased; at speeds above the center of the hump the resistance is decreasing or only gradually increasing and falls below the curve of resistance in deep water. Upon a line of reasoning such as the foregoing rests the explanation for the peculiar phenomena: that up to certain speeds resistance in shallow water is greater than it is in deep water, and beyond these speeds is less than it is in deep water.
The accuracy of the foregoing explanation may in certain respects be questionable but as far as the practical aspects of the phenomena are concerned accuracy is not a prime requisite.
The results of phenomena, such as these, are not only of academic interest but have practical value and application as well. The first practical result was to show, conclusively, that the speed trials of ships were not reliable unless made in deep water so that “shallow water effects” were eliminated. Major Rota stated in his paper in 1900:
Stokes Bay, where British ships used to undergo their speed trials, is only 59 feet deep; the official measured mile at the Gulf of Spezia, Italy, is about 62 feet deep; the measured miles at Cherbourg and Brest are 49 and 59 feet, respectively.
Today, as a practical result of experimentation, these depths are considered entirely inadequate and deep water is specified for the speed trials of ships. In this way discrepancies in results, due to depth of water, are removed. This has been an important factor in minimizing advantage or disadvantage for competitive shipbuilders using trial courses of different depths.
A case of great practical interest concerns that of moderate speed vessels which cannot be pushed beyond the “hump” in the resistance curve and consequently always lose speed in shallow water. For such vessels it is of practical interest to know the least depth of water in which resistance is not measurably increased or the speed appreciably retarded. By using the results described in Major Rota’s paper, Rear Admiral D. W. Taylor has deduced a locus curve which shows the relation between a vessel’s speed and the minimum depth of water at which resistance is not increased.
If M = minimum depth of water for no increase in resistance, in feet,
H = draft of vessel in feet,
V = speed in knots,
L = length of vessel in feet, then M = 10 H(V/√L).
Admiral Taylor states that this formula applies, strictly speaking, only to Rota’s five models, but his models cover the range of usual proportions for models of a fine block coefficient* Quoting Admiral Taylor:
This formula has been found to apply satisfactorily to models of block coefficient higher than 0-5 tested in the United States Model Basin; one model of block coefficient slightly above 0.65 was tried in various depths and the formula found to apply satisfactorily. The above formula may be confidently applied: to vessels not of abnormal form or proportions up to a block coefficient of 0.65 and for speeds for which V/√L is not greater than 0.9.
In applying this formula beyond such limits caution and discretion must be used.
In connection with the above an article appeared in the Nautical Magazine, Glasgow, in May, 1932. This article stated that the minimum depth of water at which there is no increase in resistance can be found by multiplying the cube root of the total displacement in tons by half the speed in knots, i.e.,
M = V 3√ D
2
Using Major Rota’s data as a check for this method I found values which were approximately the same. The differences, however, were sufficient to characterize this formula as a “rule of thumb,” as it no doubt was intended to be.
It is natural to ask what the practical value of increased speed in shallow water is for high speed ships. To take advantage of this phenomenon, except in shallow water of nearly constant depth, would be extremely dangerous. The water might suddenly shoal to a depth less than the vessel’s draft, so slow speed and caution would be paramount in the actions of any captain. The latter part of the curves shown in Figs. 2 and 3 are interesting, therefore, more from an experimental than practical point of view.
Volume of Vessel
* Block coefficient = Length X Beam X Draft
★
BLIGH OF THE BOUNTY
So much has been written about that over-dramatized incident of the Bounty mutiny that one is apt to think of her commander only as an officer whose severe discipline provoked a mutiny on his ship, and that after he was set adrift by the mutineers he navigated an open boat over 3,000 miles in 41 days. But his fame rests on a much more secure foundation, on a career of solid achievement that should not be lost sight of by any one attempting to estimate the qualities of his character. At the early age of 22 Bligh was chosen by the great Captain Cook as the Master of the Resolution. According to Captain Cook he was one of those who “Could usefully be employed in constructing charts, in taking views of the coasts and headlands near which we should pass, and in drawing plans of the bays and harbours in which we should anchor.”
On Bligh’s second voyage to the Pacific he succeeded in transporting breadfruit from Tahiti to the West Indies. At Camperdown he commanded a ship of the line, and at Copenhagen received the thanks of Admiral Nelson himself for the way in which he handled the Glutton. Besides these martial achievements, he charted a new passage through the dangerous Torres Straits, discovered 40 islands in the Fiji Archipelago, and as his last official work, cleaned up the rum traffic in New South Wales. His work and character were such that he retained the confidence of the Admiralty to the end of his career and rose to the rank of Vice Admiral.