66 PRINCIPLES OF N A V A L ARCHITECTURE
g R T L G I . = w1/2
The well known (but outdated) admiralty constants by are defined bv
and
c,
= -.C, is related to the power-displacement coefficient C,, PE
C, is related to the resistance-displacement coefficient CTV by
Section 8
RESISTANCE 67 on the effects of changes in dimensions, hull form,
machinery types, and so on. This is an area in which the high-speed computer can play an important role, enabling the designer to consider a f a r greater number of possible solutions than could ever be made in the past.
8.2 Choice of Form Coefficients. The approximate relation between the block coefficient C, and the Froude number Fn can be expressed by formulas orig- inally given by Alexander (van Lammeren, et al, 1948),
- 0.595 (1.08 - C,) for trial speed V
Z P -
_ _ _ - - 0.595 (1.05 - C,) for service speed
G P
V
Troost (1955) has given a similar formula for sus- tained sea speed in terms of the prismatic coefficient C,, which is more in line with design practice:
(65)
_ _ -
’’
JgL,
- 0.55 - 0.48 C,where the trial speed is taken as
V , = 1.06 V, (66) This sustained sea speed, V,, lies very close to that a t which the C,-curve begins to rise steeply; i.e., to the speed a t which the power begins to increase more rapidly than V3. If the power over the first part of the rise is assumed to vary a s V4 then Equation (66) is equivalent to saying that the power a t the trial speed is about 25 percent greater than that a t the sustained sea speed under trial conditions. This is in keeping with the general design practice that the service speed should be attained under trial conditions a t 80 percent of the maximum continuous power.
The above relationships are intended a s rough guides to the designer and do not take the place of a careful analysis and comparison of alternative designs.
For passenger liners, cross-channel ships and other craft in which high speed is important the relations in Equations (65) and (66) no longer apply. Comparative economic evaluations a r e essential in these cases.
Napier (1865) was one of the first who used a cost equation which he differentiated to find the optimum speed. Compared to this direct approach an iterative procedure is more versatile, requiring less simplifying assumptions and showing the penalties for departure from optimum configurations. Benford (1966,1967) has presented a n optimization method in which the costs have been split up into components making up the building and operating costs. The revenues are deter- mined on the basis of the transport capacity with due allowances made for the bunker capacities required.
Using appropriate economic criteria, the relative prof- itability of competing ship designs can be determined.
Fisher (1972) has presented such an optimization
procedure applied to the Australian ore trade. In this paper the economic criterion used is the Required Freight Rate. He also investigated the impact of var- iations of fuel costs, interest rates, insurance costs and construction costs on the Required Freight Rate.
The above-mentioned procedures are valid and use- ful when costs (capital and operational) are known a s general functions of the primary design parameters.
These are, however, most often not known with enough accuracy. Fisher (1973) introduced a method based on the existence of a good (basic) design for which the full details are known. Optimization is car- ried out by varying the main parameters of this design, introducing errors of much smaller magnitude.
Economic optimization studies can yield valuable in- formation concerning the relative merits of a design.
However, a s the results of these methods rely heavily on hydrodynamic knowledge, information concerning cost levels and predictions of the future economic and political situation (amount of freight, insurance rates, shipping routes and so on), care should be taken in the interpretation of the results.
The final decision on length and fullness should not be taken without considering the sea-going qualities of the ship. A short, full ship may well suffer such loss of speed in bad weather as to justify the extra cost of a longer, finer ship. The choice depends on many things, including the ocean conditions on the trade routes in question, particularly the length of the pre- dominant waves and the frequency of their occurrence.
Thus to maintain a weekly service on the North At- lantic in winter, requiring speeds of 28 or 29 knots, the length of express liners cannot well be less than 950 f t (See Chapter VIII).
Excessive fullness also promotes a tendency to bot- tom damage due to slamming. Flat areas on the bottom forward should be avoided. The floor lines should begin to lift immediately the parallel body ends, so a s to give a V-shape which will allow the hull to enter the water smoothly when the ship is pitching (Todd, 1945). The relative qualities of U and V-sections in avoiding bot- tom damage have been analyzed by Townsend (1960) of the U. S. Salvage Association, who showed the dan- gers in vertical stems and too-pronounced U-sections forward. These questions are discussed further in Chapter VIII, but it is essential to have in mind the importance of seagoing behavior from the very incep- tion of a new design.
Fig. 61 shows typical @-curves for different types of ships (Todd, 1963). The wave-making resistance humps occur approximately at values of Fn equal to 0.24, 0.30 and 0.48, and their importance depends upon the speed and fullness of the ship. The coaster, with a prismatic coefficient C, = 0.83 cannot be driven above Fn = 0.158 without an excessive increase in resistance, and a s shown in Fig. 61 this coincides with Troost’s definition of sustained sea speed. These speeds for the cargo ship and tanker also indicate the points where the resistance begins to increase rapidly.
68 PRINCIPLES OF NAVAL ARCHITECTURE
. .
0 0.12 0.18 0.24 0.30 0.36 0.42 0.48 0.54 0.60 0.66
Fn
Fig. 61 Typical @ curves
In the trawler, with a finer hull form of C, = 0.57, the lower humps are not very marked, and a Fn value of 0.24 can be reached before the rise in the
0
curve begins. However, speed has great significance in these ships, to get to the fishing grounds quickly and to get home to market afterwards, and they are usually over- driven up to values of Fn = 0.30.The cross-channel ship, of C, = 0.58, can be driven to Fn = 0.33 without excessive resistance, for al- though the C, is the same as in the trawler, the length is perhaps twice as great, showing the advantage of length in delaying the onset of heavy wave-making.
The destroyer, in which economy in the commercial sense is not paramount, normally has a top speed of Fn = 0.6 or more, well beyond the last hump a t about Fn = 0.48.
When the principal dimensions and fullness coeffi- cients have been chosen, the resistance then depends chiefly upon the following elements of ship form:
(a) Distribution of displacement along the length, as typified by the curve of cross-sectional areas and the LCB.
(b) Shape of the LWL, particularly in the fore body.
(c) Shape of the transverse sections, especially (d) Midship-section area coefficient.
(e) Type of stern; i.e., raised counter, cruiser, tran- som, and so on.
The midship-section coefficient C, varies with full- ness. In merchant ships with block coefficients around 0.80, it may be as high as 0.995. As the fullness de- creases and the length of parallel body becomes shorter, it is necessary to ease the midship-section area near the ends.
somewhat to avoid too pronounced shoulders in the lower waterlines. In Series 60 the relation between C,, C,, and C, is as follows:
CB 0.800 0.750 0.700 0.650 0.600
C, 0.994 0.990 0.986 0.982 0.978
C p 0.805 0.758 0.710 0.661 0.614 With still finer ships, C, is still smaller, being about 0.93 on fast passenger liners, trawlers and tugs, and 0.90 on cross-channel ships.
The choice of the shape of section area and LWL curves depends upon the values of Fn and C,, and will also be influenced by the need to provide adequate stability. Naval architects must draw upon their own experience, with recourse to published design data, where there is much information on the best values or shapes for these elements of form for different kinds of ships. General guidance in this field has been given by Taylor, D.W. (1943), Lindblad (1961) and Todd (1945). The recommendations from the two last-named sources are summarized in Table 17. The ship types are arranged in order of decreasing block coefficients, from 0.80 for a slow-speed cargo ship to 0.52 for a cross-channel ship. As already mentioned, there is a corresponding reduction in C,, and with the finest ships this will approximately compensate for the re- duction in C,, so that C, tends to reach a steady value of around 0.59. Indeed, a t the very highest Fn values, the C, can be increased with advantage, as first pointed out by Taylor, and in destroyers it may be as high as 0.65. These points are illustrated in a chart given by Saunders (1957) showing the relations between speed- length ratio, prismatic coefficient, and displacement-
RESISTANCE 69 length ratio. This is reproduced in Fig. 62. The curves
were based upon data from a variety of sources, and result in two pairs of empirical curves which define two “design lanes.” These apply to merchant and com- batant vessels of orthodox form, and not to special
types such as fishing vessels and tugs.
The load waterplane coefficient C , decreases with decreasing fullness, its value depending also to a con- siderable extent upon the type of transverse sections.
For Series 60 it is related to the C, by the approximate formula
C , = 0.18
+
0.86CpIn general C , will depend also on the stability re- quirements and sea keeping.
In full ships considerable parallel body can be worked in with advantage, and the entrance can be short, the run being long and fine to minimize sepa- ration and form resistance. As C, decreases, so does parallel body, and the entrance is made longer to re-
duce the increase in wave-making resistance, the LCB moving aft in consequence. Most of the reduction in
C,
is thus accomplished by fining the entrance, the change in the coefficient of the run being much less.The sectional area curve and load waterline follow a similar pattern. At low Fn values and high prismatic coefficients, both are slightly convex forward and aft.
As Fn increases, they become straight and eventually S-shaped with a hollow near the stern. At Fn values of 0.45 and above, the hollow should disappear in the LWL, which should be straight or even slightly convex in destroyers and other high-speed types. In such ships, too, the onset of high wave-making resistance calls for as long a length as is compatible with the other design requirements.
The information given in Table 17 can only be used for general guidance in the preliminary design stage.
In any particular ship design, more detailed analyses, based upon model and full-scale data for closely similar ships, must later be made to determine the most suit-
7.0
5.0
% A 0 1.0 2
$.
-
I- z 1.0w
0
LL LL Y 0 0
L w I- I 3
>
8.0
- ”
.O 6
.O
0
SPEED-LENGTH RATIO
L I I I I I I I I I I I I I I I ~ ~ I I I I I I I I ~ J
012 016 0 2 0 0 2 4 0 2 8 0 3 2 0 3 6 0 4 0 0 4 4 0 4 8 0 5 2 056 060 FROUDE NUMBER F, = V / K L
Fig. 62 Design lanes for prismatic coefficient and displacement-length ratio (Saunders, 1957) (English units).
Table 17-Variation of Form Coefficients and Elements of Hull Shape, Based on Lindblad (1961) and Todd (1945) Slow speed Medium speed
Type of ship cargo ship cargo ship Cargo liners
0.80 0.75 0.70
0.99-0.995 0.985-0.99 0.98 0.809-0.805 0.762-0.758 0.715
0.88 0.84 0.81
0.15-0.18 0.18-0.19 0.21 L ercent
trom rr
J,p_pJ,-
0.7 35 250.8 12
0.9
E i y e c e n t 35 25 12
0.7 0.8 0.9
LEB
percent L~~ 1.5-2.5 fwd 1.0-2.0 fwd 0-1.0 aftfrom PP
a
Fwd Straight with U sections, slightly con- vex with V sections and raked stem Aft Straight or
slightly con- vex with easy shoul- der Sectional area
curve shape
Straight with Straight with slight hollow some hollow a t extreme forward giv- fore end ing S-shape
Straight or Straight ex- slightly con- cept a t ex-
vex treme aft
end
Passenger and cargo, fruit
ships 0.65 0.98 0.664 0.78 0.24 1
.o
5 1.0-2.0 aft S-Shape-fineentrance es- sential with
ronounced
K
ollow for- ward Straight ex-cept a t ex- treme aft end
Fwd Slightly con- Slightly con- Sli htly hollow S-Shaped, hol- vex through- vex'or grward, or low forward
out straight strai ht
with7onger entrance
I
Half-angle of entrance on LWL (id
Aft, Slightly con- Slightly con- Slightly con- Slightly con-
vex. If possi- vex vex vex
ble the slope should not exceed 20 deg
35 deg 27 deg 12 deg with 10 deg
hollow L WL, 16 dee if
High-speed passenger liners,
ferries, etc.
0.60 0.97 0.62 0.71 0.24-0.30
n 1 .OLl. 1 1.5-2.0 aft
Fast passenger liners, trawlers,
tugs 0.55 0.93 0.59 0.69 0.24 -0.36
1.1-1.2 0 2.0-2.8 aft
Cross-channel ships 0.54 -0.52 0.9 15-0.905 0.59 -0.575 0.69 -0.675 0.36 -0.45
0 2.0-3.0 1.2 a f t
v 0
Destroyers 0.46-0.54 0.76-0.85 0.56-0.64 0.68-0.76 0.45 and above
0 0.55 0.5-2.0 a f t S-Shape for Fn S-Shape at Fn S-Sha e with Maximum area
= 0.24, becom- = 0.24 holEw for- aft of mid- -D above this above Fn = = 0.36 be- Straight or z
value, with ad- 0.27 comin slightly con- G
vex area I- straigater curve for- v, in
dition of bulb
for 0.45
ward
Straight except S-Shape Strai ht with Good buttock
2
ing straight straight ward a t Fn ships. E
V
a t extreme aft hofow a t ex- lines a f t and
end treme aft transom
z
P
z
slight hollow Fn = 0.30 with hollow, midshi s. 4
value ings fuller quite W
end stern
Fine WL, almost Fine WL, S- Up to Fn = Maximum 9
straight with shaped below 0.30 fine WL beam aft of
3
straight above Fn = Waterfne
above this 0.3, WL end- forward c and straight, straight or
or hollow even a little with bulb convex Full WL, nearly Full, straight Full WL, con- WL aft very
transom stern and cover screws
straight or convex vex full to su1t
6 deg 8%-10 deg 6-7 deg below 4-11 deg Fn = 0.30.
Above this speed, 9 deg with
straight WL, 6 deg with hollow and bulb L W L ~ S
straight
RESISTANCE 71
-a G
B
c
-
E G a, mW
oil) w e
Q O
C Ld
Y m
able form together with estimates of the probable ef- fective and shaft powers.
8.3 Design Data. Naval architects in designing a new ship must study the effects upon power of a num- ber of choices of hull form and proportions. Data for such comparisons are available in the publications of the technical societies and the technical press, to which they will add their own experience from past designs.
Many of these data are derived from model experi- ments, and it is quite impossible to describe other than representative examples.
8.4 Model Resistance Data Sheets, SNAME. A val- uable source of information exists in the data sheets published by The Society of Naval Architects and Ma- rine Engineers (1953-1966). These have been compiled for some 150 ships from the results of model experi- ments carried out in various towing tanks. All types of ships are included, it being one of the objects of the collection to give a variety of data for the benefit of those naval architects not having access to other sources or engaging in a new basic field of design. The sheets give all the principal form coefficients, the basic model data, and predicted values of RR/W and
0
to bases of VK/$ and0,
respectively. Area curves and lines plans are included.8.5 Methodical Series Experiments. The data given in the Society’s sheets and in many pubished papers are valuable guides in the design of closely similar ships. On the other hand, they refer to a group of completely unrelated forms, and it is difficult to de- termine the trends in resistance values with changes in proportions and coefficients or, what is equally im- portant, the penalties involved in specific changes.
Information of this kind is obtained by running a series of models in which the principal characteristics are changed in a systematic manner. The results of such methodical series can be used to plot design charts which are of inestimable value to the designer.
Such a series may be based upon a single parent form or upon a number of parents related to one an- other in some graphical or mathematical pattern. The prismatic coefficient can be changed by systematic var- iations in the curve of areas, while the proportions such as L/B and B/T can be varied by straight geo- metrical methods.
8.6 Taylor’s Standard Series. A complete investi- gation of the effects of altering proportions using a single parent form was made by Admiral Taylor in the Experimental Model Basin (EMB), Washington, giving rise to the well-known Taylor’s Standard Series (Tay- lor, D.W., 1943).
The original parent was patterned after the British cruiser Leviathan of 1900, which had a ram bow and twin-screw, cruiser stern. For the series parent, the ram was eliminated, the maximum section was moved to midlength, and a 3 percent bulb was adopted at the bow. The sectional-area curves and body lines for the other models were derived from the parent partly by mathematical means. The models were run a t various
72 PRINCIPLES OF NAVAL ARCHITECTURE
L
A.F! 39'4 39 38 37 36 35 34
m
B L
4 3 2 I F'P
Fig. 63 Lines for the parent form of Taylor's Standard Series
periods up to 1914, and the first full presentation of results was in the 1933 edition of Speed and Power of Ships. The data appeared as contours of residual resistance per tonne of displacement against prismatic coefficient and displacement-length ratio, each chart being for particular values of
B/T
and VK/$.These contours were derived by the methods in use a t EMB in 1910; the model frictional resistance was determined by the use of frictional coefficients mea-
sured on 20-ft planks in the Washington tank and the full-scale frictional resistance was calculated by using Tideman's ship coefficients. After some intermediate changes, the ATTC standard method was adopted in 1947, the ship PE being increased by a model-ship cor- relation allowance of
+
0.0004, as already described (Section 3.5). In view of this change, the Taylor data were reanalyzed, and the new contours based on the ATTC coefficients were published by Gertler (1954).V FROUDE N U M B E R F
9 L
3 0 x 10':
[L 0 ri
(L
w 0 0
:
2.0 x 10-3z
;I 2 a a
e
a
u) w
-J 2 v) w
I 0 x 10-3
C
(
Fig. 64 Typical Taylor's Stondord Series contours
RESISTANCE 73 The lines of the parent form are shown in Fig. 63.
The midship-section area coefficient was 0.925. The prismatic coefficients of the fore-and-aft bodies were equal, and the LCB was always amidships. The quan- tities varied were C,, B/T and W/(L/100)3, the mid- ship-section area coefficient C, remaining constant.
The variations in L/B, B/T, and W/(L/100)3 were obtained by selecting different ratios of B/T and L/B and varying the offsets geometrically.
The ranges of the variables covered in the Taylor’s Standard Series are:
C,
...
0.48 to 0.86 B/T.....
2.25, 3.00 and 3.75 W/(LwJ100)3 (English)...
20 to 250 C,...
.0.925 V/(LwL)3...
0.70 to 8.75 x In presenting the reanalyzed results, Gertler used the nondimensional volumetric coefficient V/(LwL)3 in preference to W/(L/100)3. Contours of the wetted sur- face coefficientc,
=s / J G
were derived and given for three different values of B/T.
In converting the Series results to the ATTC pre- sentation, Gertler went back to the original model data.
In doing so, he took the opportunity of making certain corrections to the data, which had been omitted in the original Standard Series presentation, including the effects of temperature, the absence of turbulence stim- ulation and the interference between model and tank boundaries upon the measured resistance.
To facilitate the calculation of PE for specific ships, Gertler gave charts of CR to a base of V/& C,,
is nondimensional in any consistent equal to ___
system of units, as is V / z . An auxiliary scale of V/& in units of knots and feet was incorporated on the charts.
The design charts give contours of C, against V/& for various values of V/LwL3, each chart being for a particular value of C, and B/T, Fig. 64.
For merit comparisons, Gertler used the @ -
0
presentation for a ship of standard length of 121.92 m (400 ft) on the L, in water of 3.5 percent salinity at 15 deg C (59 F). The values of C, for this ship can be found from Fig. 21 of the publication by Gertler (1954), as a function of
0,
VK/& or Fn. C, is obtained from the charts, so that C, = C,+
C,, with theaddition of the model-ship correlation allowance of +0.0004 if desired.
RR XPSV’
@ can then be found from the equation
@ = 39.78 @ CT (45) Gertler gives charts for the conversion of C, and Fn (or V K / d L ) to @ and
0.
For a ship designed to carryB
v) Lu
3 4
>
5
W PI u1 Y
u- 0 PI
9
z
1.60
1.40
1.20
1.00
0‘
t5
1.20;
PI
1.00
Fig. 65 Variation in Taylor’s Standard Series P, with change of C, for a ship with L/V” = 8.7
a given displacement a t a given speed, curves of @ to a base of @ will give a merit comparison between various choices of dimensions, as described in Section 7. Merit comparisons can also be obtained from the
C,
presentation for any particular design by calculating and plotting curves of the ratio of PE to that of the model used for reference. Such curves can also be used to find the effects of major changes in design param- eters.
Such a comparison for ships of the destroyer type is shown in Fig. 65, taken from Gertler (1954). In this case, the displacement volume is 2720 m3 and the value of L/V‘ is 8.7. For values of Fn less than 0.30, the lowest PE is realized by using the smallest
C,
value of 0.50. At high speeds, the picture is different, and at Fn = 0.60, corresponding to 40 knots, the bestC,
is about 0.65 to 0.67.Figure 65 also shows that an increase in B/T causes a moderate increase in PE, but the effect may be larger in rough water than in smooth.
In some other experiments, Taylor, D.W. (1908) in- vestigated the effects of shape of midship section on resistance. The models all had a Cp = 0.56, the same curve of areas, and the same maximum section area,