High Performance Yacht Design Conference Auckland, 46 Deceniber,2002 THE EFFECT F WATER DEPTH N THE PERFRMANCE F HIGH SPEED CRAFT Ian W Dand', 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 transcritical 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.. INTRDUCTIN 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 in a number of ways, ranging from plain inconvenience to, in the most serious cases, loss of life. In some areas of 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 UK 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. SHALLW WATER AND HIGH SPEED 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) () 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 socalled critical speed) resistance increases markedly and wave wash can reach significant proportions. At speeds yielding Fnh values in excess of unity (supercritical speeds) the wave pattern will have lost its transverse wave system and consist simply of diverging waves. (Reference ). 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 socalled 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; skiboats, leisure craft using waterways of significant natural beauty (the Norfolk Broads in the UK 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. All 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. Director of Hydrodynamics, BMT SeaTech Limited
' \9J0 T7.0 9.0 U,0 Ita 9.0 7.0 S.0 g ^,.0 0 t 4 Double Single u 25 4.5 Fnh Single and Double Hulls h/l = 0.047 5».0 J 7.0 B.0 l U U».0 TJ3 _ : SJi _ Cr.0 3.0 0 4 C o fn 4 0,5 4.5 5J Fnh Double Single single and Double Hulls h/l = 0.25 Figure. Residuary Resistance Coefficients for Catamarans
0 0 0 0 a s u c 0 ««o: \ o" e u c "«no.» o: 0 0 r I t.i 0,3 0,5 0.7 0.9..3 5 7 ) Zl h/l=0.047 h/l=0.25 Fnh 2,3 J.5 Fig 2. Residuary Resistance Ratios for Single (C) and Double (D) Hulls 3. MEASUREMENT AND THERY Measurement has taken place at both model and full 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 now summarised. 3.. Resistance Measurements Figure 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 0.25. 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 demihull of the catamaran, mn in isolaüon. The measurements have been nondimensionalised 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 =.0) a marked increase in residuary resistance coefficient occurs. This has a higher peak value in the shallower of the two water depths in the supercritical speed range, and for this model at least, the residuary resistance coefficient is constant, implying that it varies simply as (speed)^ in the sub and supercritical regimes, the residuary resistance of the demihull is half that of the catamaran; they both have the same coefficient in the critical regime the resistance of the demihull 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 demihull and its catamaran counterpart. It is clear that the resistance of the demihull 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 twinhull counterpart.
0 (C p J I I h/l = Deep h/l = 0.25 Model speed (m/sec) Figure 3. Effective Power for a Catamaran Model in Deep and Shallow Water Figure 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 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.5 m/sec. However, when speed is supercritical, shallow water power is noticeably less than that in deep water up to a speed of about 5 metres/second (Fnh = 3.) after which deep and shallow water measurements show little difference. 3..2 Wash Measurements Comprehensive realworld wash measurements have been made by Whittaker (References and 2) which have demonstrated that: around the critical regime, high speed vessels produce longperiod 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 redirected 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 BMT 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 supercritical regimes and it is clear that, as the full scale measurements suggested, the highest waves occur around the critical Froude Depth Number. Interestingly, the shape of the plot in Figure 4 bears a striking resemblance to those in Figure, 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.
I I I I I I I I ' I l M.0 > 30.0 Po a J I I L J L J l_ h/l = 0.25 o h/l = 0.062 a h/l = 0.047 4.5 5.5 Froude Depth Number 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.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 bystanders by surprise. 3.2 Theory Theoretical methods for predicting free wave patterns in shallow water have met with rather more success than those for predicting resistance. Qualitative predictions of, and explanations for, the sub, trans and supercritical 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 farfield wave forms from nearfield measurements. The wellknown 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). n 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, farfield 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 farfield is an important step forward. Gadd (Reference 8) does this by deducing a singularity distribution for the vessel from nearfield wave measurements and using this to extrapolate to the farfield. The success of this approach was shown in Reference 7 where good predictions were made of the farfield waves of a wavepiercing catamaran. Although the predictions were good (Figure 5) a highfrequency component, present in the real world, was not explained by the mathematical model. It was thought that this wave component may have been due to the jets of water from the waterjets striking the surface of the sea, although no direct evidence for this was available. Subsequent model tests by BMT with a waterjetpropelled 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 in the critical regime.
Surface elevation Eiptrim. 0.4H \ \ 07;05 07:06 07:07 07:08 07:09 07:0 04 T i ] Calculation 0.4! 0 2 3 4 8 Time (miiiulcsl Fig 5. Far Field Waves: Comparison of Prediction and Measurement (ref. 8) displacement vessels are provided with bulbous or ram bows. These vessels are, however, working in the subcritical regime where the wavecancelling and flowimproving abilities of the bulbous bow work weu, especially for those bluff hull forms not wellsuited to efficient progress through water. M3(GÜG2 ol)gia(nja M 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. HULL GEMETRY AND WASH But what about high speed vessels, working in shallow water in the trans and supercritical regimes? Figures 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 0). However, if a high speed vessel must operate in shallow water, especially in or near the transcritical 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? After such research into shallow water behaviour, coupled with the vast amount of work relating to wave resistance and ship waves in deep water carried out over the past century or more, it is fair to ask whether we are in a position to provide designers with guidelines to enable them to minimise problems of excessive wash and resistance in shallow water. Is it possible, by design, to reduce the wavemaking of a hull operating in shallow water form with the double benefit of low residuary resistance and low wash? In deep water, the answer to this question is undoubtedly in the affirmative and is the reason why many large Both approaches have been tried and are now discussed. 4. The Effect of Global Geometry Parameters In this section, the apparent effect of global geometry parameters (block coefficient, displacement/length ratio etc) on wash in the transcritical regime is explored. The results are based on a series of model experiments carried out by BMT in which a number of monohull "displacement" models with simple geometries were tested in the transcritical zone in various water depths. The parameters were varied as shown in Table.
The models with very high L/B ratios were, in 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. In 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 Sharp Bow nly Ceoslm of B3, Twice the Size Figure 7. Lenticular Test Models PARAMETER RANGE Froude Depth Number, Fnh 0.7.2 Water depth/draught, h/t.56.0 Transom area ratio, Aj/BT 0.0.0 Block coefficient, Cb 0.55.0 Prismatic coefficient, C 0.68.0 Displacement/length ratio, 000V/L* 0.093.0 Length/beam, L/B 4.9333 Beam/draught, B/T 0.092.0 Half Angle of entrance, 'Aa^ 3.890 Icb (% from midships) 2.52.5 TABLE The remaining models consisted of a number of socalled 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 demihull 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 in order to determine which were the most significant. This exercise showed that the following parameters were most significant for the generation of wash in the transcritical zone; the most significant is given first. displacement/length ratio Froude Depth Number transom area ratio prismatic coefficient f 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 wellknown 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 nonplaning 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 subcritical speeds for displacement vessels while transom area ratio is also related to residuary resistance of highspeed craft. The wellknown 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. In the extreme, a rowing eight with
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, in order to reduce wash height and resistance in or near the transcritical 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., may lead to a lowwash hull form, but practical considerations have also to be satisfied. If the vessel is to be waterjetpropelled, 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, onboard 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 in large commercial oceangoing vessels moving at comparatively low speeds. ther 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 ). 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 subcritical speeds where their wavecancelling properties can be put to good use; they have in fact been used for energyefficient low speed boat designs for inland waterways (Reference 2) But at supercritical speeds, when the diverging wave system mles supreme, they are unlikely to provide any benefit. Wavecancelling plates are trim and draughtdependent and are therefore of very limited use for most craft; they are also only effective at subcritical speeds and will be of little value to highspeed craft. Changes to the whole hull geometry may also be of limited use at trans or supercritical 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. If 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 in shallow water may be a reduction in transverse stability if long slender hulls are developed. This can be overcome with multihull designs and suggests that catamarans and the like may continue to be in the vanguard of future high speed power craft development. 5. DESIGN GUIDELINES As a result of the recent research earned out by BMT 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 transcritical speed regime keep displacement/length ratio, transom area ratio and prismatic coefficient as low as possible These two simple guidelines, if followed, will see multihull vessels may continue to play their primary role in 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 multihull 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 if high speed is to be combined with passenger comfort and less impact on other waterway users and those ashore. 6. REFERENCES. Whittaker, T. and Elasser, B.: "Coping with the Wash: The Nature of Wash Waves produced by Fast Ferries" Ingenia, February 2002, Issue, p.4044. 2. Whittaker, T.: "An Investigation of Fast Ferry Wash in Confined Waters" International Conference on the Hydrodynamics of High Speed Craft, RINA, London, November 999. 3. May, R.W.P. and Waters C.B.: "Boat Wash Study" April/May 986, BARS 2 report. 4. Dand, I.W., DinhamPeren, T.A. and King, L; "Hydrodynamic Aspects of a Fast Catamaran perating in Shallow Water" RINA Conference on the Hydrodynamics of High Speed Craft, London, November, 999. 5. Dand, I. W.: "The Analysis and Interpretation of Experiment Results obtained with a Series of High Speed Catamaran Models" Report D50 of Brite/Euram SPAN (Safe Passage and Navigation) Study. Document reference number SPAN.BMT.ALL.W.50.I.27/05/99, May 999. 6. Havelock, T.H.: "The Effect of Sliallow Water on Wave Resistance" Proceedings of the Royal Society, A, vol 00, 92. 7. Gadd, G. E.: "High Speed Feny 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 999.
9. Gadd, G. E.: "The Wash of Boats on Recreational Wfltenravi" Transactions of RINA, 994. 0. "The hnpact of High Speed Ferries on the External Environment", Nautical Division, Danish Maritime Authority, 998.. Doctors, L.: "Development of Low Wash Vessels" Ausmarine '98, 3' hiternational Conference, November 998, Fremantle, Australia. 2. Gadd, G. E.: "The Development of an energy efficient low wash Cabin Cniiser Hull Form" EcoBoat '97 Conference, Suffolk, UK, September 997.