Change of Speed Correspgngilnlgpéhange Corre(sp<;n <;Ln g Index I'ypes(x)and(6). Type (I). Type (6). Type (1). Type (6). I 14-16 knots 245 E.H.P. 273 E.H.P. 3-1 3~o

22-23, , 760, , 650, , 5-3 4-9

1 25-26 ', , 890, , 820, , 4-0 4-1

The variation of the rate of growth of I.H.P. (or E.H.P.) with the speed is a result of the interference of the bow and stern wave systems, and is dependent upon the speed-length ratio (vide “ Wave Resistance, ” above). A good illustration is afforded by taking the case of a vessel such-as a torpedo-boat destroyer, which is run over a considerable range of speed. Fig. 37, Plate I I. shows, for such a vessel, three curves plotted to a base of speed, the ordinates being respectivelyesecon ~o t ese iso courseacurveo

IHP lg-JI"-Z;-£3 épfeg), Th d f h f f

resistance, and the rapid rise and fall of the rate of growth of resistance manifests itself in this resistance-curve by a very marked hump between 15 and 25 knots speed. The third curve, that of » is interesting as affording, by its slope at different points, a very good indication of this rate of growth. Up to about 13 knots this curve is not far from being horizontal, indicating that till then the resistance is varying. about as the square of the speed. The rate of growth increases from this point till' it reaches a maximum of 15 knots, and then falls. ofi till at 'about 20 knots the resistance once more"varies as the sqiiare of the speed. From this point onward the resistance increases at a less rate, than the square of the speed. It has been previously noted that the skin friction part of the E.H.P. does not obey the law of comparison; this is on account of variation of f with length, and the index of" the speed .being different from 2. 1 The coefficient f varies much more rapidly-'at the smaller lengths, and hence for these the.skin friction correction is more important for'~a given change in length. For such lengths as are dealt with in ships, e.g. 100 ft. and upwards, and such lengths as we should deal'with iri applying the data that are now given, it has been found possible to express the correction for skin rictionvéry accurately by the curves in fig. 38, PlateII. These indicate the absolute correction that must be applied to the .E.H.P. deduced for .thegiven displacement from the standard curves when interpreted by the law of comparison, and are drawn for a series of displacements on a base of speed; the correction for any odd displacement, can be easily interpolated. An addition must .be made for displacements under, and a deduction for displacements over, the standard 1000 tons.-The following example illustrates this point and the method of using the standard éurvesz- ~ - 1

A vessel 320'><35%'XI?'><2135 tons is being designed; to construct an E.H.P. curve, or speeds I I-22§ l<I1OtS. The proportions B . »

(eam ratio and block coefficient) of the designate most closely, , Draught

approximated to by type 2, group A (320' being the immersed length). First find the length I for a similar vessel of 1000 tons displacement; l'= l=248-5 ft., and then from fig. 41; read off 3,

ordinates representing E.H.P. for the given speedsof the 1000-ton standard ship. These figures are converted into those appropriate for the design, by the law of comparison. If v and e are the speed and E.H.P. for the 1000-ton ship, and V and E corresponding quantities for the design, then';l=(2'-'135)*"¢1-135; and '];=(2;'135)5=2°424“1 using these ratios we get a table thus 1- = 1 . In the results hitherto recorded the depth of water has been supposed sufficient to prevent the disturbance attending the motion of a vessel on the surface from extending to the bottom; in these circumstances the resistance is unaffected by a moderate shsnow change in the depth. Conditions, however, frequently Water arise in which vessels are run at high speeds in comparatively shallow water; anda marked alteration is then observed in the resistance and power corresponding to a particular speed. An investigation of the effect of shallow water on resistance is therefore of im rtance and interest; and a brief account of this part of the subiiect is here appended. ' ~ »,

The change from' deep to shallow water modifies the shape of the stream lines, many of which in deep water are a proximately in planes normal to the surface of the hull; those in siioal water tend to lie more nearly in horizontal planes, owing to the reduced space under the bottom of the § hip. In consequence, the velocity in the stream tubes in the vicinity of the ship is increased, and the chan es of pressure and-the “ statical ” wave heights are exaggerated. This causes an increase in the frictional resistance as the depth of water becomes less; but the 'effect on the residuary resistance is more complicated. » ' » 1

Firstly, the length fl' of the waves corresponding, to a speed 1/ is increased from that expressed by

v2=£§

~ 21r

to be in accordance with the formula

I I ~ 1/”=-'gr tanhwhich

applies to shallow-water waves fora depth h. When the 2

depth h is? equal to 2, the length of wave is infinite, § and the wave becomes of the type investigated by Scott Russell canals, and termed a “solitary wave " or a “ wave of translation.” When the 2 .

depth of water is less than 2 no permanent wave system of speed v can exist. These changes in the wave length considerably affect the wave pattern and alter the speeds at which interference bétween thebow and stern systems' has a favourable or unfavourable effect on the efficiency of propulsion., . ",

In the second place the "amount by which the speed-off travel of the energy of the wave falls short of the speed of the ship is expressed by 2 1; -41th/l . 1 V Y

»~-. ,

smh7- I . ..

f '

In deep water this differencefof speed is 2; in shallow water it diminishes, becoming zero at the critical depth producing a wave of translation., . .. .-. . . i . ~ ' 'T

Thirdly, the local disturbance immediately surrounding the ship is increased in, shallow water, theoretical, , iI1X¢§ ¥lgQl1iQn showing that, at the critical' depth above»referi-ed to, it becomes indefinite or is only lrimngedrby its own viseosit ~and'~eddyingTEsis'tance. #ln still shallower water, the an1ount'of d5isfurl5ance' is reduced as thexleparture from the critical depth becomes greater. 1

Finally the increase of "the frictional resistance due to the higher velocity of rubbirig is further modified by the large 'dimensions of the wave ' accompanying the ship; the particles of a wave in ' very shallow water are moving appreciably in the direction of travel, which might lead to a reduction in the frictional resistance. 5

From these considerations it appears impossible to obtain, a priori, the net effect of shallow water on the resistance, owin to the divergent character of the component effects producing the gnal result. This difficulty is confirmed by the inconsistency of the readings frequently obtained during experiments in shallow A d f A5 Converted bx C . water, pointing to instability in the conditions then existing. S 'ea dmfg Law <>fC0m1>af1- '.C°{Te2u°§ l§ ° C I C I 'A'numl5er of experiments have been carried out in the S?" at S011 for 2 135-TOUS, 0154 of m f' § l"H °P'5 shallow water with both ships and models; the most C““¢S £23 D@51§ l'l- K rgifon' C' ' ' , important are those by Constructor Paulus (Schleswig-Lengt rea. mm Orrecte ' 'Ht1lstein District Club, 1904), Carptain"Rasmus§ en, Mr Yarrow, 2485 Ft' C01, X(;,35=Y)C, ,1, X(, 4,4=E) Flgure' Herr Popper and Major Rota, many of which are recorded 2 ' " ' ', in the {.N.A.hTransactions(dA summary of the conclusions " drawn rom t em is appen e:-

K“0t5~ lE-H~P- Knots' E'H~P° E'H~P' E'H'P' I. The minimum depth of water that has no appreciable I0 15° U35 364 16 342 irffiuence on the resistance increases with the speed and, in 12; 27? ' ""{3'62"' 667 129 ' 63 ' some degree, with the dimensions of the ship. ig f § 2. At constant speed the resistance is, in general, greatest I7 940 19~ 30 2278 61 g 2217 as the critical depth of water . It is concluded, there£8 31 L5 $7 ~.3°4§ folref that the increase of resistance due to the enhanced 23 2 3 22 5O gg g 83 dimensions of the wave then accompanying the ship is more in 59 7 7, than sufficient to counteract the gain resulting rom the The curve shown in fig. 39, Plate ll. results from plotting col. (6) to a base of speed given by col. (3) . Since the propulsive coefficient varies with the speed, it is referable to take the E.H.P. from the curve and convert to l.H.lE., using an appropriate coefficient, than to use a common coefficient by plotting a curve of I.H.P. diminished drairhof. energy frornthe wave ytem astern. 3. At high speeds, when a considerable portionfof the resistance is due to wave-making, the total resistance diminishes at depths lower than the critical depth, and is frequently less in very sha low water than in deep water.

4. The “ humps ” in the curves of resistance, on a base of