Assessing Ship Seaway Perforrnan~e’~
Section 8 Section 8 Design
8.1 Introduction. Sections 2 to 5 have presented procedures whereby predictions can be made of all aspects of the seakeeping performance of ships, both in idealized regular waves and in the irregular patterns actually experienced at sea. Such predictions cover not only motion responses in six degrees of freedom, but derived responses, such as vertical accelerations, ship- ping of water, slamming, added power requirements and wave-induced loads. Section 6 discussed the effects of various motion-control devices. Finally, the preced- ing Section 7 dealt in detail with criteria of seakeeping performance that define acceptable limits of ship re- sponse for specific ship missions or functions. Fur- thermore, it showed that comparing predicted performance over a range of expected sea conditions, ship speeds and headings with the appropriate criteria permits the evaluation of seakeeping performance of a new design in terms of a Seakeeping Performance Index (SPI).
It is the object of this section first to draw upon the earlier sections to offer guidelines that will assist the designer in selecting ship characteristics favorable to good seakeeping behavior. Theory shows (Section 3) that the effects of longitudinal motions (pitch, heave and surge) and of transverse motions (roll, yaw and sway) can, for practical purposes, be considered sep- arately. This will be done here, since design features to reduce motions are generally different for the two cases. The longitudinal motions (particularly heave and pitch) will be considered first, since they are af- fected more by choice of ship dimensions, have a greater effect on attainable speeds in rough seas, and are less amenable to artificial control. Attention will then be given to other design considerations, such as above-water hull form and added power in waves, fol- lowed by the effects of transverse motions (rolling in particular) and discussion of special considerations af- fecting high-performance ships.
Finally, suitable design procedures will be consid-
l 4 Section 8 written by Edward V. Lewis, assisted by Philip Mandel, particularly with sub-section 8.5, High-performance Ships.
ered, including comparative evaluation of the sea- keeping performance of alternative designs and selection of an optimum on the basis of economic con- siderations.
8.2 Factors affecting pitching and heaving. ( a ) Theoretical considerations. Theory, supported by model tests and full-scale observations, provides some good general guidance to the designer. First may be mentioned the dimensional effect of ship size (partic- ularly length) in relation to sea conditions encountered.
Sellars (1983) has pointed out that in general, for con- ventional mono-hulls in head seas, the longer the ship the less the average wave excitation. This is mainly because the probability of encountering waves of near ship length decreases with increasing length, but also because the average height of long waves, and hence wave slope, is less than short waves. Sellars (1983) has calculated the probabilities of encountering con- ditions leading to large heave and pitch excitation in average North Atlantic weather as a function of ship length, as shown in Fig. 119. See also Fig. 74 and discussion in Section 4.7.
The advantage of greater length applies whether overall size, as indicated by displacement, remains the same or increases with length. The favorable effect of increasing all dimensions together is discussed in Sec- tion 4.7, where the non-dimensional plots in Figs. 74 and 75 show clearly the comparative pitching and heav- ing motions of two geometrically similar ships in ir- regular head seas. However, this is an extreme case of a large size difference (ratio of 8 in displacements), while even a modest increase in size would be an ex- pensive way to improve seakeeping qualities. The ef- fects of increasing length with displacement fixed are of greater interest and will be discussed further in this section.
It has been suggested in Section 4.9 that the next consideration is whether the ship is expected to reduce speed in order to operate in sub-critical conditions in rough seas or can remain in a high-speed supercritical state. The first case applies to the majority of normal commercial and naval vessels, while the latter case is characteristic of some of the high-performance craft to be considered separately.
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MOTIONS IN WAVES 161
1.4
1.0, I I I I I , o
- L" /L=l.so
/
i I I L. SHIP ~ N G T H . m' I 1
50
I
100I
150 1200 250 30b 3500
0 200 400 600 800 1000
L, SHIPLENGTH, F l
Fig. 119 Probability of conditions for large pitch and heave excitation, i.e., probability (L, 2 0.75L) (Sellars, 1983)
The problem of attaining sub-critical pitching and heaving behavior of normal ships over as wide a range of speed as possible requires consideration at early stages of design of the relationship of length-the most important dimension-and other hull character- istics to the natural periods of oscillation, as discussed in Section 4.9. This important influence of natural pe- riods of oscillation on motions in waves is often over- looked because of the difficulty in determining natural periods experimentally. A solution to the problem is to plot model test (or calculated) responses on a basis of ship speed or encounter frequency, with wave length constant. The resulting peaks will define an effective natural frequency that is of prime interest.
Fig. 120 is a plot of experimental model data (Stefun, 1958) that illustrates the complex relationships exist- ing between non-dimensional ship motion amplitudes and both wavelength-to-ship length ratio, Lw,L, and tuning factor. A = o,/ on, where o, w e 8 , the frequency of encounter, varies with both wavelength and ship speed ( w , is the natural frequency of pitch or heave.) It can be seen that only the curves plotted for constant values of L,/L (solid lines) have clearly defined max- ima, because w e and hence A here depend only on model speed. Higher speeds would be required to define the maxima for longer waves (L,,, 2 1.25) (Fig. 57). The maxima are shown to occur in this case at a A-value of about 1.1 rather than 1.0 because of approximations made (Section 3.7).
The dashed curves in Fig. 120 drawn for constant Froude Number and varying L,/L do not show distinct peaks because wavelength has a greater direct affect on excitation than indirect affect through changing a,.
All non-dimensional responses go to 1.0 in very long (infinite) waves in which the ship simply follows the wave contour, as shown by a replot of the data in Fig.
121.
Fig. 121 also shows how, with speed constant, the ship response can be separated into a static value- dependent on ship-wave geometry-and a magnifica- tion effect depending mainly on tuning factor.
Another effect of tuning factor is on phase relations.
Szebehely (1955) showed that in waves around ship length the incidence of shipping water over the bow and bow emergence leading to slamming are both as- sociated with synchronous response; bow down into crest, bow up into hollow, with high relative vertical velocity (Lewis, 1955).
Fig. 79 defines in a general way the conditions for critical operation in head seas, which generally give the worst pitching and heaving behavior. It is clear from the figure that the lower the period ratio, T,(IJ/L)"~, the higher the speed before critical condi- tions are reached. Hence, the period ratios for pitching and heaving have a vital effect on ship behavior and on attainable sea speed. The natural periods of pitching and heaving are usually quite close together, but at- tention is focused here on the pitching period,
Tn5,
since it has the greater effect on wetness, slamming, and vertical accelerations. The influence of ship propor- tions and form on T , ~ J / L ) " ~ was discussed in Section 4.9 and general trends shown in Fig. 81.16, 1 4 -
Fn : 0 25 L, k I . 5 1.2
1.0
(\I 0 . 6 .
0.4.
0,2.
a4 0.6 0.8 1.0 1.2 1.4 1.6
TUNINQ F A C T O R , A = W,/W,,
Fig. 120 Pitching and heaving amplitudes for a Series 60, 0.60 black model in head seas (Stefun, 1958)
162 PRINCIPLES OF NAVAL ARCHITECTURE
I I
50 .2 5
HEORETICAL STATIC RESPONSE HEORETICAL STATIC
RESPONSE
1.50
I
F n z 0 2 5 1.25
1.00
$0
IF
>
.75.50
.25
0 ,510 7 5 1.00 1.25 150 1.75 200 L,/L
Fig. 121 Replot of Series 60 (C, = 0.60) motion data on the basis of L , / L
In order to obtain a picture of the possibilities of subcritical operation, Figs. 79 and 81 (Section 4) have been combined in Fig. 122, which shows the relation- ship between ship proportions-as indicated by LIV1’3, W l ( L / 1 0 0 ) 3 or C,T/L-and the Froude num- ber for synchronism with waves of length equal to ship length. Since peak amplitudes for some ships may occur at a tuning factor somewhat below 1.0, a curve for A = 0.9 is also shown. For ships heading directly into irregular seas, with a wide range of wave com- ponents present,the zone above these boundary curves represents conditions for intermittently violent pitch- ing motion, wet decks, bow emergence with possible slamming, and high accelerations. The zone below the curves represents conditions for less severe motions, fairly dry decks, less bow emergence, and moderate accelerations in the same type of sea. Whether slam- ming occurs or not depends on draft and on section shapes. Fig. 122 may be considered as a basic general picture of the conditions for moderate (subcritical) and serious (critical) pitching motions of typical ships head- ing into severe storm seas. I t is apparent that the choice of high LIV’/3 and high L/T, usually adopted for ships intended for high speed in calm water also confers a distinct advantage for speed in rough water-provided that it is not accompanied by exces- sive draft reduction, which might lead to slamming.
It may be of interest to consider a few specific ex- amples of ship performance in heavy seas to illustrate the significance of Fig. 122. James L. Bates (1945) mentions the difficulty experienced by 30-knot destroy- ers in keeping station with the 23-knot Leviathan in rough weather during World War I. In his reply to the discussion of his paper, he points out that the motions of these destroyers were very comfortable when speeds were reduced to about V,lL1/2 = 1.0.
The old destroyer Pruitt, mentioned by Bates, has been plotted in Fig. 122, first at 30 knots-well up in the heavy pitching zone-and then a t 17% knots, which Bates states to have been a comfortable speed. At the reduced speed, the ship may be seen to lie close to the moderate pitching zone.
The Victory-type cargo ship may be considered as an example of a much higher displacement-length ra- tio. At the normal design speed of 16% knots, this ship is shown in Fig. 122 to be well up in the heavy pitching zone. Log data show that, in meeting severe North Atlantic weather, its speeds are reduced to 5 to 9 knots in order to ease the motions. It can be seen in the figure that an average reduced speed of 7 knots brings this ship into the moderate pitching zone.
Another example is furnished by Mockel’s data on typical European trawlers (1953). Like the Victory ship, his trawler “A” lies in the heavy pitching zone at the normal free-running speed of 11 knots. Mockel states that, a t a trawling speed of 3 knots, the ship was comfortable in winds up to force 7 (30 knots) and able to continue normal trawling operations. Both speeds are shown in Fig. 122. (Mockel believes that a somewhat higher speed could have been maintained if sufficient power had been available.) It is clear from the figure that “fat” vessels such as trawlers must be designed for severe motions (high freeboard, V- form sections, and so on) if they are to maintain head- way in rough weather.
Finally, Fig. 122 shows points for the transatlantic liner United States which had a reputation for main- taining high speed in rough weather. The points cor- respond to the good-weather speed of 35 knots and the average (not the minimum) speed of 27 knots reported on a typical rough crossing. Again, a shifting from the heavy to the moderate pitching zone is indicated. The lengthening of T-2 tankers, C-4 type cargo ships, and Libertys would likewise be expected to improve their seakeeping qualities, and this has been found to be the case.
Aertssen (1958-59) plotted all his voyage data on cargo ships obtained up to that time on a graph based on Fig. 122 with the result shown in Fig. 123. This confirms the value of Fig. 123 as a guide to the choice of ship proportions for service in severe sea conditions.
As previous1 noted, there has been a gradual trend hence higher L/Tvalues as ship speeds have increased through the years. This trend undoubtedly has been to higher L I V 1 x (lower displacement-length ratios) and
MOTIONS IN WAVES
1.8
163
TED
-I- ' I TRUXTUN
.
0.5
0.4
* e
d
z 033 0 Y a
3.2
3. I
0
I I I I I
8 7 6 5 4.5
'hi
Fig. 122 Trends of speeds for synchronous pitching, defining zones of serious and moderate motions in irregulor head seas
dictated by calm-water considerations rather than by rough-water performance. I t may be that in many cases seakeeping considerations will encourage this trend.
( b ) Damping. It is normally impossible o r uneco- nomical to design ships for operation in the favorable speed zone only, and therefore an important problem is how to improve ship performance in the critical re- gion of Fig. 123. In this zone, the problem of reducing motions and thereby permitting higher speeds is pre- dominantly one of minimizing near-synchronous re-
sponses, which means increased damping and hence reduced magnificat.ion factor. An increase of damping is effective in an irregular sea in which synchronism with component waves occurs, just as it is under con- ditions of synchronism with regular waves.
Some of the trends of proportions and form that are beneficial to reducing natural periods of pitch and heave are also favorable to increased damping; such as reduced C, and coefficients of other sections, in- creased C, (hence more V-form and reduced C,) and filling the waterlines toward the ends. Work of Grim
164 PRINCIPLES OF NAVAL ARCHITECTURE
(1959) and Porter (1960) show a distinct increase in damping with increasing B/T, although it may not always be favorable for reduced natural preriods. But since the effect of beam increase is felt mostly near midship, this factor may be less important for pitching than filling out the waterplane of the ends (increase in Cwp).
Various writers agree on the importance of increas- ing C,,, which can also be expressed as a decreasing C,,, especially for high-speed ships (Lewis, 1955) (Blok and Buekelmann, 1984). Bales (1980) found that the increase of C, or decrease in C,, using V-sections was more effective in the forebody than in the aftbody.
However, V-form forward may exact a penalty in added resistance in calm water and/or waves.
There is also evidence of the advantage of a wide longitudinal separation of LCF and LCB. (However, supercritical ships such as SWATHS show a strong disadvantage to such separation). With LCF 5.5 per- cent L abaft the LCB, Moor (1970) showed a significant reduction in pitch and heave motions, vertical accel- eration forward, relative bow motion, and speed loss in waves for a series of models of a 770-ft. (250-m), 26-knot passenger ship. However, trial speed was re- duced by 3 percent. Naval vessels with wide transom sterns have been able to take advantage of this fa- vorable effect of LCF and LCB separation. Finally there is the possibility of using fixed fins for damping of pitch (Section 6).
Of course, some of the factors that increase damping will also increase the excitation. However, under con- ditions of severe synchronous responses the damping effect is always at its greatest and hence would be expected t o predominate.
(c) Model test results. Before adopting guidelines derived from simplified theoretical period relation- ships, some confirmation is needed and the best method for that purpose is model tests in waves. Unfortu- nately, comparative model experiments that isolate the effects of specific changes in hull proportions and form are rare. For example, the extensive tests of Series 60 hulls in regular waves (Vossers, et a1 1960), which reveal trends of motions and power with L/T, L / B and C,, include inadvertent effects of changes in dis- placement, LIV‘/3 and B I T as well, and do not com- pare performance under realistic irregular sea conditions.
However, Hamlin and Compton (1966) made use of Vossers’ model data to show the results of calculations on Series 60 models of different L / T (and LIV”3) ratios in a severe irregular sea. Fig. 124 confirms the advantage of a large L/Tvalue for minimum relative bow motion, S / L. Calculations of heave acceleration show a similar advantage. Furthermore, if bow free- board is proportional to length, the shipping of water should decrease with increasing L/T. The situation regarding slamming is somewhat different. Here the more slender ship shows up poorly, because even though the relative bow motion in relation to length is less, the reduced draft would result in more frequent bow emergence and higher relative velocities (Vossers, e t a1 1960). I t should be noted that the model data on which these conclusions were based assumed constant L / B values, which could lead to excessive beam, from a stability viewpoint, in the longest ship.
Subsequent studies have used the same or similar data to calculate and compare the predicted behavior of ships of equal displacement in irregular head seas,
Fig. 123
12 I
ZONE OF SEVERE PITCHING AN0 WET DECKS
10
LIMIT OF SPEED IN BEAUFORT 7
>qeo*
0 6
0 4 .
PITCHING AND DRY DECKS
8 7 6 5 4 8
02, 1 I 1 1 U
100 I50 200 250
(I..)
+-3Trends of attainable speed in different sea conditions, from logbook analysis compared with theoretical trends (Aertssen, 1958 -59)
MOTIONS IN WAVES 165
including the effects of variation in forebody shape, longitudinal radius of gyration, etc. (Swaan, 1961) (Swaan and Vossers, 1961) (Swaan and Rijken, 1964) (Ewing, 1967). St. Denis (1983) has reviewed much of this work and has drawn some general conclusions.
The research confirms that, for moderate to high-speed ships, there are advantages to be gained in pitch and heave-and related responses-by increasing L/T and B/T, reducing C, while increasing C, (more V-shaped sections) and reducing longitudinal radius of gyration.
It also shows that for low-speed ships (Fn < 0.3) some of the above, such as the advantage of high L/T or a low C,, may not apply, especially for large tankers where powering is more of a problem than motions in waves.
A recent model investigation by Schmitke and Mur- dey (1980) and later extended by Murdey and Simoes Ri! (1985) is based on a well-chosen range of hull char- acteristics and again evaluates the models by compar- ing their predicted behavior a t constant displacement in a typical long-crested head sea. Although these re- sults apply specifically to fine frigateldestroyer hull forms (Fig. 125) they are believed to provide useful guidance for other relatively high-speed displacement craft. These studies employed the slenderness param- eter L‘IBT, which indicates length (squared) relative to the area, BT, of the midship circumscribing rectan- gle. Further definition of proportions is given by the ratio B/T, and hull form by C, and C,.
Results showing trends with all these parameters are given in Figs. 126-129 for pairs of models at a constant displacement of 3500 t. In evaluating these results it is important to note that L2/BT and B/T are not independent parameters, since they both involve B. However, the product of L’IBT and B/T is (L/T)‘, and T/L is an independent parameter that has been shown to be important in studying natural periods of pitch and heave (Equation 204d, Section 4.9.) Similarly the ratio C,/ C, = C, may be more significant than the two coefficients considered separately.
The comparative findings in Figs. 126-129 are based on self-propelled experiments on 10 models in regular head waves (with wavelengths varied in about 20 steps from Ll2 to 3L; heights 1/50 L,) at each of four speeds corresponding to Fn = 0.2, 0.3, 0.4, and 0.5. Faired results were used as RAOs to calculate significant responses in irregular head seas, using the ‘ I quadratic regression spectrum” ( Gospodnetic and Miles, 1974) for a significant height of 3.66m (12 ft). Response data were averaged over a wave modal period range of 7.28 to 10.92 see and over a speed range of 15 to 30 knots.
They have been made non-dimensional by dividing by the appropriate response value for the basic hull of the series (No. 6).
First, it may be seen in Fig. 127 that with displace- ment constant there is in all cases a distinct reduction in pitch and heave amplitudes, and in vertical accel- eration a t 0.25L from the bow, as L21BT increases.
This shows the clear value of increasing length and
6 , = 4 2 FT SEVERE STORM
- -.-
X-‘2
.
-1 MOSKOWITZ 3 0 - KNOT RANDOM SEA0.05 I
SERIES 60 HEAD SEAS CB= 0 70
20,400 TONS V=11.28 -=
L / B = 7.0 FED at BOW o,03
LENGTH
,
8 12 16 2 0 2 4 28
L I T
Fig. 124 Relative bow motion trends with L/T ratio in irregular head seas, 500-ft. ships (Hamlin and Compton, 1965)
reducing BT. Furthermore, since L21BT is equal to C,L3/V and C, is held constant, Fig. 127 also implies the same favorable trend with increasing L 3 / V , or L / V1’3, the length-displacement ratio (Froude’s @), as previously suggested (Section 4.9) on the basis of pe- riod considerations.
However, predicted relative bow motion (RBM) shows little change-or even a reverse trend-with increasing L‘IBT. This picture changes if the non- dimensional ratio S I L is used as an index of RBM instead of 3. (See Fig. 126, where S/L reduces signif- icantly with increasing L / T ) . If the RBM data in Fig.
127 are replotted in terms of 31 L it will be found that there is a distinct reduction in response with increasing L21BT in all cases. The question in any specific situ- ation, such as evaluation of probabilities of shipping water or slamming is, which is a more suitable index of performance, S or SIL? In the case of wet decks, it is often feasible to increase bow freeboard in pro- portion to increasing length by simply extending the sheer curve forward. This would mean that S I L is appropriate. On the other hand, an increase in ship length may entail a reduction in draft forward, which would suggest that the absolute value, 3, is significant for consideration of bow emergence and slamming.
Such reduction in draft with increasing L 2 I BT would be expected to increase the probability of bow emerg- ence and slamming, as previously noted. This is not always true, however. Bales (1980) found that “bot- tom slamming per se may be reduced or stabilized by reductions in relative motion attendant to reductions in T/L.”
Fig. 127 (as well as Fig. 126) shows a clear advantage of increasing B/T. This is consistent with the conclu- sion in sub-section 8.2(b) that increases in B/T are favorable for reduced pitching and heaving, because of increased damping. Furthermore, since increasing both L’IBT and B/T is shown to be beneficial, increas- ing their product (L/T)’ should also be beneficial. This is as predicted on the basis of favorable natural periods alone in Equations (204d) and (206), Section 4.9.