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High Performance Yacht Design Conference Auckland, 4-6 Deceniber,2002

T H E E F F E C T O F W A T E R D E P T H ON T H E P E R F O R M A N C E O F H I G H S P E E D C R A F T

I a n W D a n d ' , ian@bmthaslr.demon.co.uk

Abstract. With the design speeds of some powered leisure craft increasing, the paper explores the relationship between speed, water depth and performance. Particular attention is paid to residuary resistance and the generation of wave wash and the size of the waves in the wash is shown to be greatest in the trans-critical regime. Not unexpectedly, this is in concert with the behaviour of the residuary resistance coefficient which is shown to peak in the same Froude Depth Number range. The relationship between hull design and wash height is then explored to see what hull parameters have the greatest effect. Using model measurements, wash height is shown to depend largely on three global hull geometry parameters, and the reduction of these to as low values as possible, consistent with practical considerations, should help in the quest for low wash hull forms.

1. I N T R O D U C T I O N

The desire to move at speed across water has for many years seized the imagination of naval architects. Whether for the purpose of transporting passengers and goods rapidly from place to place, to outwit or outiun an enemy, or simply to race, the lure of speed has triggered some remarkable advances in ship and boat design.

In recent years, commercial ferry operations have been transformed by the advent of the fast ferry, moving at speeds of 40 knots or more. In the leisure field, power boats and power yachts are capable of greater speeds as boat and propulsor designers combine to produce better hulls and more effective propelling devices.

But speed comes at a price. And that price has been paid i n a number of ways, ranging from plain inconvenience to, i n the most serious cases, loss of life. In some areas o f the world these matters have become so serious that concerned water users and others have caused designers and operators to look carefully at fast vessel design and operation to minimise the problems.

This paper briefly addresses the cause of some of these concerns and presents the results of some work recently earned out by British Maritime Technology Limited (BMT) and others in the U K and elsewhere. The main contention of this work is that many of these problems stem from the apparently innocent combination of vessel speed and the depth of water in which it operates.

2. S H A L L O W W A T E R AND H I G H S P E E D

The relationship between speed and water depth is encapsulated in the Froude Depth Number, Fnh, which gives the ratio between a vessel's speed, u, and the speed of the wave of translation for water of depth h:

Fnh = u/V(gh) (1)

In deep water, or at low speeds, the value of the Froude Depth Number is small or negligible and vessels behave benignly. However, when speed increases so that Fnh approaches unity (the so-called critical speed) resistance increases markedly and wave wash can reach significant proportions. At speeds yielding Fnh values i n excess of unity (super-critical speeds)

the wave pattern will have lost its transverse wave system and consist simply of diverging waves. (Reference 1).

Because modern powered commercial and leisure craft are now able to reach high speeds, they will be able to enter, and pass, the critical regime for waters whose depths were once considered to be "deep". Such waters, for such craft, are now, in effect, shallow.

As a result of this, the so-called wash nuisance has become a feature on the coastlines, beaches and river banks where fast craft operate. Such a feature is not a consequence just of commercial craft operation; ski-boats, leisure craft using waterways of significant natural beauty (the Norfolk Broads i n the U K for example), powered yachts and so on, can all, to a greater or lesser degree, produce excessive wash from excessive speed, aggravated by limited water depth.

In addition to the problems of wash, entry into, and beyond, the critical speed regime may bring with it difficulties in passing through the resistance "hump" in this region. It is not unknown for some vessels to show no apparent change in speed with increasing propeller or waterjet speed, only to accelerate rapidly up to speed, with no apparent warning, after a fmal engine movement.

A l l these topics have been the subject of some active research programmes in recent years. Much of the early work has been aimed at increasing our understanding, by measurement and theory; more recently, the intriguing possibility of reducing the problems by suitable hull design has been investigated.

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Fig 2. Residuary Resistance Ratios for Single (C) and Double (D) Hulls

3. M E A S U R E M E N T AND T H E O R Y

Measurement has taken place at both model and f u l l scale. Theory has concentrated largely on the wash problem and has used surface panel methods (from what is now regarded as classical wave resistance theory) and CFD methods together with coastal wave theory models. The last have been used to explore the nature of wash behaviour in the far field and how it changes with alterations in the course of the vessel (Reference 2).

Recent developments are n o w summarised.

3.1.1 Resistance Measurements

Figure 1 shows measured residuary resistance coefficients for a catamaran model in two water depths. The water was quite shallow, with depth/length (h/L) ratios of 0.047 and 0.125. The speed range was large, starting just below the critical regime and ending well above it. Also shown on the plot are results obtained for a demi-hull of the catamaran, mn i n isolaüon. The measurements have been non-dimensionalised

in the usual way (with respect to (speed)^, wetted surface area and water density) but have not been extrapolated to full scale. They show the following:

• around the critical speed (Fnh = 1.0) a marked increase in residuary resistance coefficient occurs. This has a higher peak value i n the shallower o f the two water depths

• i n the supercritical speed range, and for this model at least, the residuary resistance coefficient is constant, implying that i t varies simply as (speed)^

• in the sub- and supercritical regimes, the residuary resistance of the demi-hull is half that of the catamaran; they both have the same coefficient

• in the critical regime the resistance of the demi-hull is very much less than half that of the catamaran

To illustrate the last observation, Figure 2 shows the ratio of the residuary resistance for the demi-hull and its catamaran counterpart. It is clear that the resistance of the demi-hull drops to a very low comparative value in the critical regime, implying that it expends very much less energy in creating waves here than does its twin-hull counterpart.

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-+ 0

J I I 1

-Model speed ( m / s e c ) h / L = Deep ° h / L = 0.125

Figure 3. Effective Power for a Catamaran Model in Deep and Shallow Water

Figure 1 is fairly typical of what one might expect in shallow water, with much energy being expended to pass

through the main shallow water hump. We have already mentioned possible problems in moving past certain speeds, and Figure 1 begins to indicate why.

However, once past the shallow water hump, some resistance benefits appear. These are illustrated in Figure 3 depicting the effective power measured on a catamaran model at various speeds. The critical regime, where shallow water power is higher than that in deep water, is clearly visible at around 1.5 m/sec. However, when speed is supercritical, shallow water power is noticeably less than that in deep water up to a speed o f about 5 metres/second (Fnh = 3.1) after which deep and shallow water measurements show little difference.

3.1.2 Wash Measurements

Comprehensive real-world wash measurements have been made by Whittaker (References 1 and 2) which have demonstrated that:

• around the critical regime, high speed vessels produce long-period waves which may explain the

• unexpected waves rushing up the beach long after a fast vessel has passed on an otherwise calm day

• large amplitude waves tend to be created around the critical regime

• by suitable route planning, wash nuisance can be re-directed away from vulnerable beaches to those seldom used by the human or animal populations

The study in Reference 3 measured boat wash in an inland waterway system of great natural beauty where it was eroding river banks. Excessive speed was identified as a cause, coupled with boat design, both of which created unacceptable wash. Speed limits reduced the problem, at the expense of some congestion, and strategic planting of reed beds helped protect the river banks from the wash.

Measurements of wash were carried out at model scale by B M T and reported in References 4 and 5. Figure 4, from Reference 5, shows measurements of the maximum measured wash heights for a model moving in three water depths. The speed range encompasses sub-, trans- and super-critical regimes and it is clear that, as the f u l l scale measurements suggested, the highest waves occur around the critical Froude Depth Number. Interestingly, the shape of the plot i n Figure 4 bears a striking resemblance to those i n Figure 1, suggesting, not unexpectedly, that a vessel expends a great deal of energy in the transcritical regime making waves, thereby incurring a residuary resistance (and consequent powering) penalty.

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I I I I I I I I ' I - l M.0 > 30.0 O -Po a J I I L J L - J l _ 4 . 5 5 . 5

Froude Depth Number + h / L = 0.125 o h / L = 0.062 a h / L = 0.047

Figure 4. Measured Maximum Wash Heights for a Catamaran in Various Water Depths In addition to the free waves made by the vessel in shallow

water, solitary waves (or waves of translation) may be formed. These occur over a nan'ow Froude Depth number range from about 0.8 to 1.2. They are usually seen in towing tanks, rivers or canals, but have been observed at model scale in an open water manoeuvring basin (Reference 4). It is fair to say that field measurements have yet to provide conclusive proof of their existence in open shallow water, but they may serve as an additional explanation of the rogue waves which seem to come from nowhere on a calm day, msh up the beach and take by-standers by surprise.

3.2 Theory

Theoretical methods for predicting free wave patterns i n shallow water have met with rather more success than those for predicting resistance. Qualitative predictions of, and explanations for, the sub-, trans- and super-critical wave resistance have been available for many years (Reference 6 for example), but accurate quantitative prediction has been difficult. However, the methods presently available have assumed an important role in predicting far-field wave forms from near-field measurements. The well-known panel method, utilising singularities, has proved most suited to this because it is

possible to predict far field waves a great distance from the track of a vessel (Reference 7). On the other hand, the use of CFD for such predictions is not entirely suitable because of the restricted distance over which wave patterns can be predicted, due to limitations in computing power.

When it comes to considerations of wash nuisance, far-field predictions have the most value because they show what happens when the wash of a high speed vessel reaches the shore. Measurements in towing tanks are limited by tank width and the ability of theory to extrapolate these measurements to the far-field is an important step forward. Gadd (Reference 8) does this by deducing a singularity distribution for the vessel from near-field wave measurements and using this to extrapolate to the far-field. The success of this approach was shown in Reference 7 where good predictions were made of the far-field waves of a wave-piercing catamaran.

Although the predictions were good (Figure 5) a high-frequency component, present i n the real world, was not explained by the mathematical model. It was thought that this wave component may have been due to the jets o f water from the waterjets striking the surface of the sea, although no direct evidence for this was available. Subsequent model tests by B M T with a waterjet-propelled catamaran produced the results in Figure 6. This shows measured wave spectra with and without the waterjets operating and indicates that the jets do in fact have some effect on the free waves produced i n the critical regime.

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Fig 5. Far Field Waves: Comparison of Prediction and Measurement (ref. 8)

— M3(GÜG12 ol)Gia(nja • MO M3lGi.]sig

Figure 6. Effect of Waterjets on Free Wave Spectrum The theoretical work of Gadd was extended to other leisure craft (Reference 9) where good agreement between measured and predicted wash was obtained for a variety of vessels ranging from small boats, typical of those used on the Norfolk Broads, to planing craft of the type used for towing water skiers.

4. H U L L G E O M E T R Y AND W A S H

A f t e r such research into shallow water behaviour, coupled w i t h the vast amount o f w o r k relating to wave resistance and ship waves i n deep water carried out over the past century or more, it is f a i r to ask whether we are i n a position to provide designers w i t h guidelines to enable them to m i n i m i s e problems o f excessive wash and resistance i n shallow water. Is it possible, by design, to reduce the wave-making o f a h u l l operating i n shallow water f o r m w i t h the double benefit o f l o w residuary resistance and l o w wash? I n deep water, the answer to this question is undoubtedly i n the a f f i r m a t i v e and is the reason w h y many large

displacement vessels are provided w i t h bulbous or r a m bows. These vessels are, however, w o r k i n g i n the subcritical regime where the wavecancelling and f l o w -i m p r o v -i n g ab-il-it-ies o f the bulbous b o w w o r k weU, especially f o r those b l u f f h u l l forms not well-suited to e f f i c i e n t progress through water.

But what about high speed vessels, working in shallow water in the trans- and super-critical regimes? Figures 1 and 4 show that the best way to avoid the twin problems of high residuary resistance and excessive wash height is to stay well clear of the transcritical zone. Commercial high speed ferry operators do this and have provided their commanders with guidance as to the speeds they should avoid in a given depth of water. Indeed some marine administrations, in the desire to control wash nuisance, have provided similar guidance (Reference 10).

However, i f a high speed vessel must operate in shallow water, especially i n or near the trans-critical zone, what are the key global hull features which affect wash and, by implication, residuary resistance? Alternatively, is it possible to design a hull shape to provide some wave cancellation in the manner of the bulbous bow?

Both approaches have been tried and are now discussed.

4.1 The Effect of Global Geometry Parameters

In this section, the apparent effect of global geometry parameters (block coefficient, displacement/length ratio etc) on wash i n the trans-critical regime is explored. The results are based on a series of model experiments carried out by B M T i n which a number of mono-hull "displacement" models with simple geometries were tested in the trans-critical zone i n various water depths. The parameters were varied as shown i n Table 1.

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The models with very high L/B ratios were, i n fact, planlcs, used to investigate whether such forms would produce any waves at all in the transcritical zone. This would test whether solitary waves would be triggered by even the smallest water disturbance moving at critical speeds. I n the event they

produced no measurable waves of any sort within the confines of the towing tank. A wave system was observed, but its heights were too small to register on the wave probes used in the experiments.

Sharp Bow and Stern

Sharp Bow, Square Stern

Ceoslm of B3, Twice the Size

Sharp Bow Only

Figure 7. Lenticular Test Models

P A R A M E T E R RANGE

Froude Depth Number, Fnh 0.7-1.2

Water depth/draught, h/T 1.5-6.0

Transom area ratio, A j / B T 0.0-1.0

Block coefficient, C b 0.55-1.0

Prismatic coefficient, C„ 0.68-1.0

Displacement/length ratio, 1000V/L-* 0.09-3.0

Length/beam, L/B 14.9-333

Beam/draught, B/T 0.09-2.0

Half Angle of entrance, 'Aa^ 3.8-90

Icb (% from midships) -12.5-12.5

T A B L E 1

The remaining models consisted of a number of so-called lenticular hulls with a square transom and rectangular sections which could be combined in a number of ways to make various waterline shapes (Figure 7). These models were supplemented by a demi-hull of a catamaran in commercial operation and, for comparison, the catamaran itself.

Wash was measured with all models and resistance for some. Maximum heights in the free wave system were then deduced, as were heights for the solitary waves. Minimum free wave heights were then regressed against the hull geometry parameters of Table 1 in order to determine which

were the most significant. This exercise showed that the following parameters were most significant for the generation of wash i n the trans-critical zone; the most significant is given first.

• displacement/length ratio • Froude Depth Number • transom area ratio • prismatic coefficient

Of these, the Froude Depth Number relates to operating conditions and can be used to limit wash as already discussed. The other three relate, in global terms, to hull shape. They reinforce the well-known conclusion that displacement/length ratio is an important hull parameter when it comes to wash generation (and, of course, residuary resistance)with high speed craft. Transom area

ratio and prismatic coefficient of the non-planing models under test were also important, albeit to a lesser extent, than displacement/length ratio. Again, this is a not altogether surprising result; prismadc coefficient is already well established as an important parameter for residuary resistance at sub-critical speeds for displacement vessels while transom area ratio is also related to residuary resistance of high-speed craft. The well-known slipper stem launches on the River Thames reduced transom area ratio to a minimum while retaining a broad stern and creating little wash nuisance to river users as a result. I n the extreme, a rowing eight with

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negligible transom area (and a very low displacement/length ratio) produces minimal stern waves, and hence wash.

As a result of this investigation, it became clear that, i n order to reduce wash height and resistance in or near the trans-critical zone, the displacement/length ratio, transom area ratio and prismatic coefficient should all be reduced to the lowest possible values.

4.2 Modifications to Hull Geometry

The guidance for designers, given with regard to the three key hull geometry variables in Section 4.1, may lead to a low-wash hull form, but practical considerations have also to be satisfied. I f the vessel is to be waterjet-propelled, a transom will be, in all probability, a necessity and its immersed area will be determined by the waterjet size, number and location. Displacement/length ratio and prismatic coefficient will be determined by the payload, hull mass, on-board equipment, fuel and stores as well as by any limitations on length, beam and draught. Therefore, once the designer has reduced the three key global parameters to values as low as possible, there may still be a need for improvement. This would require some modification to hull geometry in order to cancel (or reduce) some of the wave system. As mentioned above, this has been done,

with some success, using the bulbous bow i n large commercial ocean-going vessels moving at comparatively low speeds. Other devices, (such as a plate to suppress the bow wave) can be used for low speed work, or the shape of the whole hull can be designed for wave cancellation (Reference 11).

These devices have had mixed success, in spite of many claims for the low wash properties of certain designs. Bulbous bows tend to be most successful at sub-critical speeds where their wave-cancelling properties can be put to good use; they have in fact been used for energy-efficient low speed boat designs for inland waterways (Reference 12) But at super-critical speeds, when the diverging wave system mles supreme, they are unlikely to provide any benefit. Wave-cancelling plates are trim- and draught-dependent and are therefore of very limited use for most craft; they are also only effective at sub-critical speeds and w i l l be of little value to high-speed craft. Changes to the whole hull geometry may also be of limited use at trans- or super-critical speeds, but the methodology used, and the hull shapes generated, suggest an intriguing way ahead in the future.

In practice, most effective wash reductions have been obtained using long slender hulls, thereby reducing the first, and most important of the three key parameters, displacement/length ratio. I f this were coupled with a stem having a low, or zero, transom area ratio, wash reduction, coupled with resistance reductions, could be considerable.

A corollary of the quest for low wash at high speed i n shallow water may be a reduction in transverse stability i f long slender hulls are developed. This can be overcome with multi-hull designs and suggests that catamarans and the like may continue to be in the vanguard of future high speed power craft development.

5. D E S I G N G U I D E L I N E S

As a result of the recent research earned out by B M T and others, guidelines for the design and operation of powered craft for high speed in water of limited depth (in relation to the speed) may be stated simply:

• operate outside the trans-critical speed regime

• keep displacement/length ratio, transom area ratio and prismatic coefficient as low as possible

These two simple guidelines, i f followed, will see multi-hull vessels may continue to play their primary role i n the development of high speed craft in shallow water. Such vessels allow slender hulls to be combined with adequate stability and help the wash/speed problem in calm water. In a seaway, however, the multi-hull begins to lose its advantage over the monohull due to its less satisfactory dynamic response. Such matters are, however, beyond the scope of this paper, but hint at the compromises which may be inevitable i f high speed is to be combined with passenger comfort and less impact on other waterway users and those ashore.

6. R E F E R E N C E S

1. Whittaker, T. and Elasser, B.: "Coping with the Wash: The Nature of Wash Waves produced by Fast Ferries" Ingenia, February 2002, Issue 11, p.40-44.

2. Whittaker, T.: " A n Investigation of Fast Ferry Wash i n Confined Waters" International Conference on the Hydrodynamics of High Speed Craft, RINA, London, November 1999.

3. May, R.W.P. and Waters C.B.: "Boat Wash Study" April/May 1986, BARS 12 report.

4. Dand, I.W., Dinham-Peren, T.A. and King, L ; "Hydrodynamic Aspects of a Fast Catamaran Operating in Shallow Water" RINA Conference on the Hydrodynamics of High Speed Craft, London, November, 1999.

5. Dand, I . W.: "The Analysis and Interpretation of Experiment Results obtained with a Series of High Speed Catamaran Models" Report D510 of Brite/Euram SPAN (Safe Passage and Navigation) Study. Document reference number SPAN.BMT.ALL.W.510.I.27/05/99, May 1999.

6. Havelock, T.H.: "The Effect of Sliallow Water on Wave Resistance" Proceedings of the Royal Society, A , vol 100, 1921.

7. Gadd, G. E.: "High Speed Fen-y Wash Prediction" Tlie Naval Architect, September 2000, page 84. 8. Gadd, G. E.; "Far Field Waves made by High

Speed Ferries" International Conference on tlie Hydrodynamics of High Speed Craft, RINA, London, November 1999.

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9. Gadd, G. E.: "The Wash of Boats on Recreational Wfltenravi" Transactions of RINA, 1994.

10. "The hnpact of High Speed Ferries on the External Environment", Nautical Division, Danish Maritime Authority, 1998.

11. Doctors, L.: "Development of Low Wash Vessels" Ausmarine '98, 3' hiternational Conference, November 1998, Fremantle, Australia.

12. Gadd, G. E.: "The Development of an energy efficient low wash Cabin Cniiser Hull Form" EcoBoat '97 Conference, Suffolk, U K , September 1997.

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