The Russo-Japanese War, and particularly the naval battle of Tsushima, have revived the discussion of the value of speed for fighting ships. One can hardly say, however, that much light has been shed on the question, since diametrically opposite conclusions have been drawn from the facts.

On the one hand, a reduction of speed allows giving a ship of fixed dimensions greater offensive and defensive power, or, if the latter remain the same, diminishing her size and in consequence, for the same initial expense, increasing the number of units and putting in the line of battle more gun-power. Considerations as to the accessibility of harbors and the utilization of their workshops; of possible employment of old and less

Speedy units in squadrons without compromising the latter's homogeneousness; of seas or canals in which the squadrons must operate; of the proportions of the engines and of the conditions of installation and service of the magazines, the more favorable as the speed is less, militate in equal degree in favor of low speed.

On the other hand, great speed may be demanded for strategical or tactical reasons.

The question cannot be rigorously treated unless we know the law, in accordance with which the absolute size of large fighting ships varies with their speed, when their offensive and defensive Powers, as well as their radius of action, remain unchanged.

The object of the present note is to find this law.

Let there be a battleship differing little from the English type Commonwealth, the last class of which the results of the trials are known.

Total length of hull (L) 138.00 m.

Maximum width of hull 23.80 m.

Draft 8.15 m.

Height of upper deck above water-line, at middle of length 6.20 m.

Area of immersed part of mid ship section (B^{2}) 180 sq. m.

Displacement with normal coal supply of 1,000 tons (D) 16,600 tons.

Maximum horsepower 18,000 tons

Corresponding speed (V) 19 kts.

Weight of propelling machinery complete, with water 1,800 tons.

Artillery.—Four 30.5 cm., font-24.3 cm., ten 15.2 cm., fourteen 7.5cm., fourteen 4.7 cm. This battery, which is that of the Commonwealth, appears to comprise too many different calibers, but the weight which it represents is about that of the most modern armament of a ship of this kind.

Protection.—This consists of an exterior belt rising in the central part to the upper deck, and of 23 cm. thickness at the waterline, diminishing to 16 cm. at the upper deck. The protection of the ends is weak, especially at the stern.

Let us first determine what increase of available displacement would be given by a reduction in speed of one knot.

This increase is made up of three principal items:

1.THE INCREASE OF DISPLACEMENT RESULTING FROM DIMINUTION OF FINENESS OF LINES.

Considering the formula for maximum normal speed

V= 1.4 (1.026 B^{2} L – D / 1.026 B^{3 }) B^{1/2}

We see that this speed is proportional to the fineness of lines (sharpness), a fractional term, and to the square root of the linear dimensions (B^{1/2}), according to the law of Reech and Froude.

It has been shown, in the table annexed to the note cited, that the speeds thus calculated approach closely the maximum speeds realized, or, at least, that they sensibly follow the same law of variation; the formula, therefore, appears to conform both to theory and to practice.

The coefficient 1.4 is a mean value.

^{2} Approximate rules for the calculation of the propulsive surface (Bulletin de L'Association Technique Maritime, 1899, p. 7).

Let us calculate, for a large ship which has realized a maximum speed V, the coefficient K such that

(1)

We have a right to assume that, if we reduce the speed of this type ship by one knot, B2 and L remaining the same (such are the conditions of our problem), and make the displacement D vary so that K retains the same value, the "coefficient of propulsion" will not vary; in the two cases the water will be displaced in equal times.

Formula (1), differentiated with reference to V and D, the only variables, gives

or, replacing B^{1/2 }by its value from (1), and noting that, the above coefficient being constant, the differentials may be replaced by finite differences,

(2)

From the elements of the battleship type given above, we find for K the value 1.446, which corresponds to great fineness of lines for such a ship, and formula (2) then gives for ?V= — 1,

?D= 468 tons.

The surface, and consequently, the weight of the hull, being slightly increased, we will take as the available increase only 450 tons, or, 2.7 per cent of the original displacement.

For AV= 1, that is to say, for an increase instead of a decrease, of one knot in the speed, the change of displacement is negative and equal to— 450 tons. On account of the necessary increase of fineness, there results a deficiency of displacement of 450 tons.

2.THE DIMINUTION OF WEIGHT DUE TO REDUCED POWER.

The fineness of lines being modified to correspond to the reduced speed, and the two other principal elements of the resistance, area of mid ship section and surface of hull (the latter is not Materially increased) remaining the same, it is very probable that the "coefficient of propulsion" does not vary, and that the powers are proportional to the cubes of the speeds, or, for a reduction of one knot, as

(18/19)^{ 3} = 0.850

If the weight of the propelling apparatus varies as the power, the reduction would be

(1- 0.850) 1800 = 270tons.

This is very nearly the case for the boilers and condensers; the stacks are, it is true, heavier per horsepower, but the relative weight of the tubing is less, and the fuel handling requires a smaller personnel, all proportions considered.

For the machinery, on the contrary, not only does the length of the lines of shafting not change, but, as M. Durand-Viel has shown in a remarkable memoir which has just appeared in the Revue Maritime, for the same ratio of pitch to diameter and the same value of the coefficient of propulsive surface j, the weight of the machinery (about half that of the whole propelling apparatus) varies as V 5/2 instead of Va.

The relative weight of the less powerful propelling apparatus complete is then about

½ ((—18/19)^{3}+ (18/19)^{3} = ½ (0.850 0.875)= 0.8615

and the reduction of weight is

(1— 0.8615) 1800 = 250 tons.

This reduction of weight changes to an increase if the speed of the battleship type, instead of being diminished from 19 to 18 knots, is raised from 19 to 20 knots.

It is interesting to note that the less powerful machinery works under better practical conditions, and will more easily maintain its full power.

M. Durand-Viel shows, as a matter of fact, in the memoir already referred to, that, for the same ratio of pitch to diameter and the same value of the coefficient j, the ratio of the linear dimensions of the engines to those of the hull is independent of the displacement, and varies as V?, that is almost as the speed. Either the stroke is kept the same, which is possible since the dimensions of the hull remain unchanged and the cylinder diameters are diminished, or the piston speeds are notably reduced.

3. THE REDUCTION IN WEIGHT OF THE UPPER WORKS.

It is difficult to accurately estimate this saving, although it undoubtedly occurs; a ship hindered by a seaway behaves better, and is less wet, when her speed is reduced.

The course which makes speed less than the maximum necessary, either to keep the sea without exhaustion or to use the guns, is principally that on which the ship receives the waves from forward or on the bow, the time occupied in rising from the hollow to the crest of the wave being then inversely proportional to the ship's speed increased by the speed of the wave. The most unfavorable sea is that producing short waves, consequently of low speed, such as those of the Mediterranean.

Let 15 knots be the speed of the waves; it may be assumed that the conditions of navigability will be the same for the battleship of eighteen knots and the one of nineteen knots, when, the under- water bodies being the same, the heights of the upper works are in the ratio.

18kn 15kn / 19kn + 15kn = 0.9706.

The height of the upper decks above the water-line at middle length, which is 6.20 m. in the type ship, can therefore be lowered (1—0.9706)6.2= 0.183 m.

The thickness of the outer armor plating being 16 cm. at its Upper part corresponds approximately, taken together with the side supporting it, to 22 cm. of steel, and its total length on the two sides and the transverse bulkheads is 184 meters. This length may without exaggeration be taken as of 22 cm. thickness, taking account of the considerable excess thickness of the turret supports and of the various armored passages whose heights are simultaneously diminished. The saving of weight then would amount to

220 x 0.183 x 0.22 x 7.8 tons = 69.2 tons.

This reduction of 0.183 meters in the height of the upper works does not seem excessive when it is remembered that there are battleships whose freeboards are much less than that of our type ship, the Hood for example—a rather poor sea boat, it is true— of 15400 tons and 173/2 knots, whose freeboard forward is less than 4 meters, an amount at least 2.2 meters less than that of the typeship.

The reduction of 0.183 meters per knot, supposed constant, corresponds, therefore, to a reduction in speed of the typeship of from 10 to 12 knots in order that she may find herself in the same condition as the Hood in the matter of the height of upper works.

The height of the guns ought, it is true, to remain such that their fire shall not be interfered with by the waves under any condition of the sea which would permit fighting; that of our type battleship,8.5 meters, would appear to allow of reduction. Moreover, the height of turret guns can be maintained even while that of the upper works of the ship is reduced; the saving of weight would still be considerable, and the stresses on the deck due to firing the guns would be diminished.

We will take no account of the saving of weight, I, which the space made available by the reduction of the propelling machinery would enable us to make in the superstructures, which we will assume to be reduced to a minimum, as they should be. So, too, we will merely note the reduction of the personnel of the motive power.

It is clear that an increase instead of a reduction of speed of one knot would merely change the sign of the corresponding change of weight.

To sum up, the reduction of the speed of the type battle ship from 19 to 18 knots would furnish an increase of displacement of 450 tons and a saving of weight of 250+ 69= 319tons, or a total availability of 769 tons (4.63 per cent of the initial dis- placement), which can be used to increase either the protection, the artillery, or the radius of action, the ship retaining meanwhile the same draft, length, and beam, and remaining equally seaworthy. The displacement, which was 16,600 tons, would become 17,050 tons.

The availability of 769 tons may be otherwise employed: it may be utilized to reduce the size of a ship.

It is known, as a matter of fact, that any saving of weight ?? realized on a ship, permits reducing her displacement, by an actual decrease of size, by an amount K'?? notably greater than ??, the speed, radius of action, seaworthiness, protection and offensive power remaining the same. If ?? -represents an addition instead of a saving of weight, it is necessary, on the contrary, to increase the displacement, by making the dimensions bigger, by the same quantity K'??.

The coefficient K' varies according to the type of ship. It is approximately equal to

in which a represents the fraction of the total displacement taken up by the weight of the hull and equipment, without armor, artillery, ammunition, or stores, and P is the fixed weight of artillery, turrets, ammunition, and stores, but not the hull armor, which latter varies with the hull surface.

Whether we use this formula, which I gave in 1885, or the slightly modified ones which have been proposed since then, it will be found that, for battleships of the type considered, the value of K’ differs little from 2.5.

If then the available 769 tons be applied to reduce the actual size of the ship, the displacement will be diminished by

769X 2.5= 1922tons

and will become

16,600+ 450— 1922= 15,128tons.

For a reduction in speed of two knots instead of one, the displacement, at 17 knots instead of 19 knots, would be about

16,600+450 x 2—1922 x 2= 13,656 tons.

This figure is too low and ought to be taken rather at 13,800 tons, for the variations corresponding to two knots' difference of speed are too great to be calculated exactly by the differential Coefficient method; moreover, it is necessary to take account of the fact that the fineness of line of the hull ought to be slightly increased for an equal speed with less actual size.

Thus, we see that, if the preceding calculations are correct, in taking as unity the displacement of a battleship of 16,600 tons, 18,000 horsepower and 19 knots, the displacements of similar

Ships having equal offensive and defensive powers, the same radius of action, and the same seaworthiness, and only differing in speed, are approximately at

17 kts. 0.83

18. " 0.91

19 “ 1.00

20 " 1.10

21 " 1.20

At 17 knots the displacement would be about 13,800 tons, and at 21 knots about 20,000 tons.

Since the draft of large battleships cannot without much inconvenience be increased, and since the vertical space available for the machinery is sensibly constant, it will be seen that the proportions of the latter, supposed to be of the reciprocating type, become more and more defective as speed is increased. From this point of view, steam turbines have a serious advantage.

The comparison of the battleships of Kansas type and those of Idaho type now being built for the U.S. Navy seems to confirm the above calculated results.

The very powerful artillery and the protection are almost identical in the two cases, but the displacements are 16,000 and 13,000 tons, and the horse powers 16,500 and 10,000, respectively.

These ships not being yet delivered, their speeds are not exactly known, but admitting an equal propulsive efficiency for the two types, we find that for 18.5 knots, the speed of the Kansas, the Idaho should attain 16.5.

To this difference of two knots corresponds a ratio of displacements equal to 0.814.

This result agrees with the practical rule given above.

The maritime world is greatly preoccupied with the Dreadnought. Whatever may be the differences, still very imperfectly known, between this battleship, celebrated before being born, and the most powerful ships of recent construction, in artillery, protection, and motive power, there ought not to result there from any change in the formula given above. The constants will merely have to be more or less modified.

I am first to recognize that in these calculations a large part is hypothetical.

The problem of which I have attempted to give an approximate solution is of great interest, and merits a more complete study.

COMMENTS ON "THE SIZE OF BATTLESHIPS AS A FUNCTION OF THEIR SPEED."

By NAVAL CONSTRUCTOR D. W. TAYLOR, U.S. Navy.

This very interesting and suggestive article by the late M. Normand bears upon one of the questions in naval architecture which is just now of vital interest. M. Normand has taken the published data for an actual ship and 'developed an approximate formula for the purpose of determining the displacement and power of ships of the same mid ship section and length but greater and less displacements with less and greater speeds. This falls into a class of problems which can be dealt with very directly by model basin experiments, and at the request of the Secretary of the Naval Institute I will indicate the solution of this particular problem, which we obtain from our accumulated data.

We are not able to take up the investigation with knowledge of the actual lines of the Commonwealth, but it happens that we have run at the Model Basin a series of models of ratio of beam to draft very close to that of the Commonwealth, and varying in fullness and displacement. From the results of this series we can determine the effective horsepower for any model within limits upon the parent lines of any size and fullness. To connect this result with the Commonwealth data it is simply necessary to assume an efficiency of propulsion (which happens to be a little over 50 per cent) which will give our ship derived from the series lines and having the same mid ship section area and fineness as the Commonwealth a speed of 19 knots upon 18,000 horsepower. Applying this efficiency of propulsion to the curves of effective horsepower, we are enabled to readily produce the curves of estimated indicated horsepower of Fig. 1 for vessels 452.8 feet long. With 1938 square feet area of mid ship section, and of displacement

{Chart}

{Chart}

ranging from 15,500 to 17,500 tons, for speeds ranging between 15 and 20 knots. While Fig. 1 applies directly to vessels upon the parent lines of the series used, it will represent with very good approximation the nature of the variation of vessels upon other lines. The efficiency of propulsion used is rather low than otherwise, and it is reasonable to suppose that the lines of the series used would drive very much the same as those of the Commonwealth.

Comparing Fig. i with M. Normand's results, it is seen that the latter has, if anything, understated the case as regards the saving of weight and reduction of speed. M. Normand estimates at 15 per cent the reduction of power for a vessel of 17,050 tons and 18 knots speed, making the actual power as thus estimated 15,300. From Fig. i the power for a vessel of 17,000 tons would be about 13,600, or a reduction of nearly 25 per cent. This would make the reduction in machinery weight over 400 tons, instead of the 250 tons as estimated by M. Normand, and would make M. Normand's available displacement due to the change of speed and fullness over 800 tons instead of 769, without allowing anything for the reduction in weight of the upper works, which would be somewhat problematical. On the increase side M. Normand's formula would underestimate the extra weight necessary to put into machinery even more than it underestimates the saving on the side of decreased speed. It would seem then that, for the particular case in hand, M. Normand's formula is very conservative as regards the influence of speed upon available displacements, and that the saving through reduced speed will be in some cases somewhat greater than he indicates.

In this connection attention may be called to the great influence of fineness upon vessels of the dimensions of the Commonwealth when pushed to top speed. The upper curve of Fig. 1 refers to a vessel of the Commonwealth length of 17,500 tons displacement, while the lower curve refers to a vessel of the same dimensions and of 15,500 tons displacement. This increase of 2000 tons is a little under 13 per cent figured on the 15,500 tons, and the cylindrical coefficient increases from .618 for the smallest vessel to .698 for the large stone. At 16 knots the corresponding increase in indicated horsepower is about 14.5 per cent, figured on the power of the smallest vessel, or almost in proportion to the increase of displacement. At 17 knots the increase of power from the smallest to the largest vessel is 17.5 percent. This percentage shows again a moderate rise at 18 knots to 21¾ percent. At 19 knots there has been a rapid increase to 37 per cent, and at 20 knots this increase of 13 per cent in displacement upon the same dimensions involves an increase of 57 percent in power. Nineteen knots is about the extreme limit of economical speed for a vessel 450 feet long, and if such a vessel is to be pushed to a higher speed it is necessary to fine her radically.

The connection between speed and length is very important. Reduction of speed allows length, which is the most objectionable dimension of a man-of-war, to be reduced, as a rule, more than in proportion to the reduction of displacement. Thus, in the case of the Kansas and Idaho, referred to by M. Normand, the displacements are in the ratio of 13/16, or .8125. If all dimensions were reduced similarly to produce this reduction in displacement, the reduction would be in the ratio .933, which would make the length of the Idaho about 420 feet. As a matter of fact, the Idaho could be, and was, reduced in length to 375 feet without exceeding at 17 knots the limit for economical propulsion, and this reduction in length, an indirect result of the reduction in speed, was a very powerful factor in enabling the offensive and defensive power of the Idaho to compare so favorably with those of the vessel of nearly 25 per cent more displacement.

It may be noticed that Fig. 1 illustrates the fact that for vessels of the type under consideration the relative importance of fineness as regards speed increases rapidly with the speed. This fact has a very important result upon the dimensions of high speed battleships. As a practical proposition we cannot afford to make these vessels much longer than is necessary to carry their battery and machinery. Greater length would help somewhat as regards speed, but is forbidden by considerations of protection, handiness, and target area: We must gain speed by adopting the best possible lines and a fineness best adapted to the necessary and unavoidable length and the required speed. This means in practice greater fineness for high speed battleships. Now, with length and displacement fixed, we can gain fineness only by increase of beam or draft. For the near future the easiest and most obvious change is to increase draft. It is to be hoped that the apparently inevitable increase of size and speed of battleships will not compel the naval architect a few years from now to make radical increases of breadth. Already dock entrances 100 feet wide look rather narrow for the most recent battleships building and designed. The present type of battleship is probably threatened today more than at any period of its existence by the submarine. If it survives the competition and is still the dominant type fifteen or twenty years from now, it seems to me quite probable that its maximum breadth will be found 50 per cent greater than at the present day—say 120 feet—unless considerations of sizes of docks and locks restrict the designers of the future.