1806457914_1999999096_FAST2001-The_effect_of_bowshape

8/18/2019 1806457914_1999999096_FAST2001-The_effect_of_bowshape

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THE EFFECT OF BOWSHAPE ON THE SEAKEEPING PERFORMANCE OF A FASTMONOHULL

Alexander (J.A.) Keuning , Delft University of Technology, The NetherlandsSerge Toxopeus, Marin, The NetherlandsJakob Pinkster , Delft University of Technology, The Netherlands

SUMMARY

In the earlier publications on the Enlarged Ship Concept (ESC) attention has already been given to the possibilities of improving the seakeeping behaviour of a fast monohull significantly through a thorough change in the bowshape both

below and above the stillwaterline. The aim of this bow modification was to reduce the nonlinear hydrodynamic forcesin particular at the foreship. In the present study this has been taken one step further and the effect of a rather radicalchange in shape of the bow over some 25% of the length is studied. The behaviour ( i.e. heave and pitch motions) in

both head- and following irregular waves of three systematic bowshape variations has been studied. Also themanoeuvring characteristics for these variations are investigated. Because one of the serious concerns about these

proposed bow modifications lies with a possible increased sensitivity of the ships with the sharper and deeper bows to broaching in following waves, this aspect of the behaviour in waves has been studied also.The results of the comparison between these three designs (with this increasing change in bowshape) will be presentedin this paper and the pro’s and con’s of the proposed changes in bowshape will be discussed.

AUTHORS BIOGRAPHY

Alexander (J.A.) Keuning holds the current position of Associate Professor at the Ship HydromechanicsDepartment at the Delft University of Technology, The

Netherlands. He specializes in hydrodynamics of advanced marine vessels including yachts.Serge Toxopeus graduated in 1996 at Delft University of Technology, Faculty of Mechanical Engineering andMarine Technology with a MSc. in Naval Architecture.Since that time, he has been employed at MARIN as aconsultant in the field of ship hydrodynamics,specialising in ship manoeuvring. His previousexperience includes the development and application of the cross flow drag theory for high-speed surface ships.Jakob Pinkster holds the current position of AssistantProfessor at the Ship Hydromechanics Department at theDelft University of Technology, The Netherlands. He iscurrently responsible for setting up new educationcurriculum for ship hydromechanics department, is activein teaching and research and carries out research projectsfor industry. His previous experience includesinvolvement with fast marine vehicles with regard todesign, construction, testing and trouble shooting.

NOMENCLATURE

AX(t) momentaneous submergedtransverse area of crosssection [m]

F’FK Froude-Krilov force [N/m]g Gravitational constant [m/s 2]H1/3 signficant wave height [m]k wave number (2 π/λ) [-]KG height of centre of gravity

(C.o.G) above above keel [m]KM height of metacentre abovekeel [m]

L pp length between perpendiculars[m]

lβ= N β/Yβ lever of application of lateralforce due to drift, forward of CG [m]

lγ = N γ /(Y γ -M') lever of application of lateralforce due to yawing, forwardof CG [m]

M'= M/(0.5 ρL pp2T) sSection added massfor Heave [kg/m]

mYY

sectional added massfor sway [kg/m]

Nβ= N uv/(0.5 ρL pp2T) non-dimensional linear derivative of yaw moment inCG due to drift motion

Nγ = N ur /(0.5 ρL pp 3T) non-dimensional linear derivative of yaw moment inCG due to yaw motion

T p mean zero crossing wave period [s]

u longitudinal (ship-fixed)velocity [m/s]

U ship speed [m/s]

V water velocity componentnormal to the local planningsurface [m/s]

yw(t) momentaneous waterline half beam of cross section [m]

v transverse (ship-fixed)velocity in CG [m/s]

vξ local transverse (ship-fixed)velocity [m/s]

Yβ= Y uv/(0.5 ρL ppT) non-dimensional linear derivative of lateral force dueto drift motion

Yγ = Y ur /(0.5 ρL pp 2T) non-dimensional linear derivative of lateral force dueto yaw motion


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β= arctan(v/u) drift angle [rad]γ = rL pp/U non-dimensional yaw rate

[rad]λ wave length [m]ρ density of water [kg/m 3]ξ distance from the forward

perpendicular, positive in aftdirection [m]

ζ (t) momentaneous wave height[m]

1. INTRODUCTION

The seakeeping behaviour of fast monohulls has a verystrong influence on the actual operability that can beobtained with those ships in particular in the more“exposed” working (sea) areas. Since the application of fast planing monohulls in the role as patrol-, coastguard-,survey- or naval vessels has increased considerably over the last two decades or so, the improvement of this

behaviour of these fast monohulls in waves has been anintense research topic for a long time now. It has beenshown by numerous authors in varies studies, bothanalytical and experimental and in particular also fullscale measurements, that the level of verticalaccelerations in those positions onboard the ship, wherethe crew has to perform its primary duties, is the mostdominant limiting factor for the comfortable and safeoperation of the ship. The voluntary speed reductionapplied by the crew and caused by excessive levels (andmore in particular extreme peaks) in the verticalaccelerations is the prime reason for the loss of fulloperability of the ship in a seaway.Many aspects of the hull design of the planing ship,which could lead to a possible improvement in their seakeeping behaviour, have been investigated. Amongthose parameters are the deadrise-angle of the planning

bottom, the running trim of the ship at speed, the lengthto beam ratio of the hull.In 1995 Keuning and Pinkster, [1], introduced theEnlarged Ship Concept (ESC) as a possible contributionto these improvements. In principle this concept wasaimed at “bringing the length back into the design”. Thedesign practice over the preceding decades had focusedstrongly on minimizing the length of the ships because of its assumed direct relationship with the (building) cost of the ship. Enlarging the length introduced many

possibilities for optimizing the design with respect toresistance and seakeeping.In 1997, [2], Keuning and Pinkster demonstrated that theEnlarged Ship Concept gave even further opportunities

because significant bow shape modifications became possible due to the large amount of available “voidspace” in these designs. These applied bow modificationsimproved the operability of these craft even more.In the present study this is taken even one step further.Based on the obtained insight in the dominanthydrodynamic forces acting on a planning hull in headwaves, a radical bow shape modification is introduced

aimed at minimizing the hydrodynamic (exciting) forcesand by doing so aimed at reducing the peaks in thevertical accelerations. This bow shape has been named“Axe bow” for obvious reasons and its shape and the

philosophy behind it are explained in the following paragraphs. In the present study the seakeeping

behaviour of the ESC with this new bow shape iscompared with the results obtained with the previousESC ships as reported earlier in [1] and [2].In addition a first quick assessment is made of theinfluence of this Axe bow shape on themeanoeuverability of the ESC ship. This has been doneto obtain some insight in the possible draw backs of thisextreme bow shape that may arise when the ship issailing in large and steep following waves, i.e. whenthere is a risk of broaching. Earlier findings with the ESCrevealed a large increase in the course stability whencompared to the shorter “base” ship. For some specificapplications such as patrol boat or navy vessel this

increase in course stability was considered even to be toolarge and hence reducing the manouevrability of thecraft. The local deepening of the forward bow sectionsand the fineness of these sections were thought to bedestabilizing in that respect and therefore increasing themanoeuvrability again.

2. THE ENLARGED SHIP CONCEPT

2.1 INCREASING THE SHIP LENGTH

In the general quest for optimizing the seakeeping behaviour of fast planning monohulls commonly used as patrol- and naval-vessels, Keuning and Pinkster introduced in 1995 the “Enlarged Ship Concept” (ESC)as a possible contribution to the process.This ESC concept was aimed at getting the “length back in the design” of the fast monohull. The general designtrend at that time and applied over the last decennia for fast planing monohulls was to reduce the overall lengthof the ships as much as possible. Many ship ownersstipulated the maximum allowable length of their newdesigns already at the beginning of the design process.This trend was based on the supposed direct relation

between the building cost of the ship and its overalllength. In their first report, [1], Keuning and Pinkster took an existing and quite successful design fromDAMEN SHIPYARDS, the Stan Patrol 2600, as their “base” design and lengthened this ship with 25% and50% respectively, whilst keeping all other design

parameters, such as speed, payload, functions, beam etc.constant. The advantages of the enlarged ship ESC whencompared with the base boat were:

• Increasing the length and so reducing theFroude number for the same forward speed.

• Increasing the Length to Beam ratio, beneficialfor the calm water resistance and reducing the“hump” behaviour and beneficial for the shipmotions in waves.


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• Increasing the Length to Displacement ratio, beneficial for the calm water resistance and theship motions in waves.

• Reducing the pitch gyradius of the ship.• Optimizing the longitudinal position of the

prime working areas on board with respect to

the vertical motions of the ship.

A picture of the general arrangements of these threedesigns is presented in Figure 1.The results obtained from this initial study, which were

based on calculations as far as resistance and motions inwaves were concerned and on data presented byDAMEN SHIPYARD as far as building costs andweights were concerned, showed :

• A significant decrease (around 30%) in therequired installed power to maintain the designspeed of 25 knots.

• A significant reduction of the verticalaccelerations in the wheelhouse and more in

particular of the distributions of the peaks andtheir frequency of occurrence.

• A significant increase in the operability of theship in the Southern North Sea and DutchCoastal waters by some 50%.

• Only a small increase in the calculated buildingcost: for instance only some 6 % for the longestship.

A graphical representation of these results is presented inFigure 2. From these results it was concluded that theEnlarged Ship Concept looked very promising indeed.

2.2 OPTIMAL POSITIONING OF THEWORKING AREAS

A possibility introduced by increasing the length withoutincreasing the number of “functions” on board the ship isthat of optimizing the longitudinal position of the mostimportant working areas aboard the ship with respect tothe vertical motions. In the cases under consideration thishas been the wheelhouse. From motion analyses it isknown that, due to the phase lag between pitch andheave, the minimal vertical motions do occur at roughly30% of the ship length from the stern. Positioning thewheelhouse as close to that position as possible mighteasily reduce the vertical motions at that place by some30% to 50%

Another aspect of this repositioning of theaccommodation etc. is found in a significant shift of thelongitudinal position of the Center of Gravity of the shipto the stern also. This implicates for instance that the

pitch restoring moment with respect to the CoG can bemaintained when the bow is modified, because althoughthe volume forward is reduced its leverage is increased.This aspect will be dealt with in the next paragraph.

2.3 MODIFYING THE BOW

In 1997 Keuning and Pinkster, [2], extended their research on the possibilities with the ESC by using theextra space, the “void” space, that is generated byapplying the ESC, to optimize the hull geometry of the

design with respect to the wave exiting forces and theresulting (vertical) motions in a seaway. This change inhull geometry was in particular applied in the forwardsections of the ship.

From an extensive study analyzing measurements andobservations made onboard real ships, such as Patrol

boats, Search and Rescue vessels etc, it became evidentthat the limiting factor for the safe operation of the shipas applied by the crew aboard of these high speed vesselsis the occurrence (once or maybe twice) of single high

peaks in the vertical acceleration. Once these occur thecrew will voluntary reduce the forward speed of the

vessel to prevent it from happening again. This action of voluntary speed reduction was carried out almostirrespective of the value of the actual significant value of the vertical acceleration at that time. It is known from

both full scale measurements and from modelexperiments and calculations that the relation (or factor)

between the significant value and the extremes (high peaks) in the vertical accelerations is strongly dependenton the non-linearity of the system. The factor betweenthese two, i.e. significant value with roughly 13.5%chance of exceedance and the maximum with circa 0.1%chance of exceedance, is not constant for non-linear systems and increases significantly with the non-linear

behaviour of the system, [3].So evaluating the operability of fast ships on the basis of significant values only is not sufficient or evenmisleading. The distribution of the peaks in the motionsand in particular the vertical accelerations should becompared when comparing fast ships. The aim of anyoptimization of the operability of fast ships in a seawayshould be the reduction of the value of the extremes inthese distributions.

From the results obtained from extensive research on thenonlinear behaviour of fast planing monohulls in headwaves, [3], [4] and [5], it became evident that the most

important components of the exciting (wave) forces on a planing hull, which contribute most to the nonlinear behaviour, are the non-linear Froude-Krilov force and the(non-linear) hydrodynamic lift. So minimizing theseforces therefore should lead to the desired reduction inthe extreme peaks in the vertical accelerations.

The non-linear Froude-Krilov force is found byintegrating the (hydrodynamic) pressure, as found with

potential theory, in the undisturbed wave over the actualmomentaneous submerged volume of the hull, whilst thishull is performing non small relative motions withrespect to the incoming waves. In formula:

)t(gKGA)t(yg2)t(F XWFK ' ρ+ζρ=


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From these formulations its is obvious that minimizingthe change in time of this force should be achieved byreducing the change in the sectional y w(t) and A X (t) whenthe section is carrying out a vertical displacement withrespect to the water surface. Translating this to thegeometry of the shape of the ship sections this means that

the flare of these sections, in particular in the fore ship,should be reduced over the “range” of the instantaneouswaterline.

Since the paper of Von Karman, [4], the theory used for the calculation of the hydrodynamic loads on the hull of a planing boat has been based on the concept of theadded mass. In concept this theory corresponds with the“slender body” theory as it is frequently used to calculatethe hydrodynamic side force on, for instance, low aspectwings and on the underwater part of the hull of surfaceships sailing under oblique flow. This slender bodytheory is therefore also applied in the section of this

paper dealing with the manouevering characteristics of the hulls.Using this theory of Von Karman for the determinationof the normal force on a transverse section of a hull, thisforce is given by the rate of change of the momentum of the oncoming fluid expressed in the terms of added massof the particular cross section under consideration:

( )VmDtD

f a=

The rate of change of momentum of the fluid at a particular section is then further elaborated to:

( )

( )dtd

dVmd

mVVm

VmDtD

aaa

a

ξξ

−+

=

As may be noticed a time dependent added mass of thecross section is introduced which originates also from thenot small relative motions of the sections with respect tothe incoming waves.

From both the analytical and the experimental researchas reported by Keuning in [3] it became apparent that thisnon-linear added mass is much more important for thetime dependent magnitude change of thesehydrodynamic forces (and so for the behaviour of a

planing hull in head waves) than was the frequencydependency of this sectional added mass. Since thechange in the sectional added mass at these relativelyhigh encounter frequencies (fast ship in head waves) may

be considered to be proportional to the change insectional beam y w(t), once again this change in y w(t)should be minimized.

2.3.1 The TUD 4100.

In 1997 this lead to the introduction of the TUD 4100hull shape for the Enlarged Ship Concept, as reported byKeuning and Pinkster in [2] at the FAST 1997.The change in hull shape when compared to the original

hull of the Enlarged Ship is summarized by:• Reducing the flare of the bow sections• Narrowing the waterline• Increasing the waterline length• Deepening the fore foot• Increasing the freeboard

A picture of the lines plan of the modified bow of theTUD 4100 according to these lines of thought is depictedin Figure 3. The change of the hull shape with the moretraditional one of the ESC 4100 is immediately evident.

2.3.2 The Axe bow

A far more radical “elaboration” of this same design philosophy to minimize the nonlinear behaviour of thesystem “fast planing monohull in head waves” isintroduced by what has now been christened the “Axe

bow”.

The most striking features to the eye of this new shapeare:The flare in the bow sections is reduced to almost zerofor minimizing the change in momentaneous added mass(hydrodynamic lift) and momentaneous submergedvolume (Froude-Krilov) whilst the foreship is carryingout relatively large relative motions with respect to thewaves.The stem is placed almost vertical to increase thewaterline length to the maximum and by doing so

bringing “back” volume of displacement in the forward part of the ship and further forward with respect to thecenter of gravity of the ship.The sheer forward is significantly increased, to minimizethe risk of green water on deck and to guaranteesufficient reserve buoyancy.The centerline of the hull has been given a negative slopetowards the bow (downwards or reversed sheer), tominimize the risk of hull emergence when sailing inwaves. The change in momentaneous added mass of asection is obviously most abrupt when a section is re-entering the water (slamming).Great care has been taken to maintain a comparable pitchrestoring moment and reserve buoyancy in the hullforward when compared to the other (parent) hull, i.e. theESC 4100.

Also shown in Figure 3 are the lines plan of the Axe bowhull form derived from the ESC 4100 and also the lines

plan of the TUD 4100. Figure 4 shows a number of 3-Drenderings of the AXE 4100 hull form.

It should be clearly stated at this point that no seriousattempt has been made in this study to generate a


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complete and fully feasible design of this AXE 4100from all points of view. The principal idea of the presentstudy is to investigate the possible benefits of such a newdesign concept on a conceptual level of design only. So a“comparable” design with respect to the other twodesigns, i.e. the ESC 4100 and the TUD 4100, has been

the main objective.

For the sake of clarity all main dimensions of the threedesigns used for the comparison are presented in Table 1.

3. THE COMPUTATIONAL RESULTS

The computations on the three designs to evaluate their hydrodynamic performance have been carried out withtwo different programs: FASTSHIP of the DelftShiphydromechanics Department has been used tocalculate the calm water resistance, the trim and thesinkage of the three designs as well as the motions in

irregular head waves and SURSIM of MARIN inWageningen has been used to assess the maneuveringcharacteristics of the designs.FASTSHIP is extensively described in [3] and is purposemade for predicting the nonlinear behaviour of fast(planing) monohulls in irregular head waves. SURSIM isa simulation program developed at MARIN for the

prediction of the maneuvering characteristics of surfaceships. Both computer codes have been found to yieldreliable results for the applications they have beendesigned for. The Axe bow design however is clearly nota common design and therefore the programs had to beadapted somewhat to accommodate this concept. That is

also the reason for carrying out rather extensive modelexperiments with scale models of these three designs inthe Delft Towing Tank. The results of these testshowever are not available on the time of writing of the

present paper and will therefore be the subject of futurereports.

3.1 CALM WATER RESISTANCE

FASTSHIP predicts the calm water resistance, therunning trim and the sinkage under speed of a planingmonohull based on the results obtained with the DelftSystematic Deadrise Series (DSDS). This DSDS is an

extensive series of model experiments set up as anextension of the original Clement and Blount Series andcarried out at the Delft Shiphydromechanics Laboratorywith some 25 different models each of them towed insome 16 different conditions. The typical speed range is

between Froude number based on volume of displacement from 0.75 to 3.2. For higher speeds themethod of Savitsky is being used.The results of these calculations are presented in Figure5. depicting bare hull calm water resistance versusforward speed.From these results it may be noted that at the designspeed of 25 knots the TUD 4100 has the lowestresistance and the ESC 4100 the highest. The AXE 4100is close to the TUD 4100 but will probably have a

somewhat higher resistance because the total increase inits wetted surface when compared to the other two cannot

be fully accounted for. At higher speeds the resistance of the modified hulls of the Enlarged Concepts, i.e. TUD4100 and AXE 4100, is significantly higher than theoriginal ESC 4100, which may be explained from the

modifications applied to reduce hydrodynamic lift in theforebody.

3.2 MOTIONS IN IRREGULAR HEAD WAVES

The vertical motions of the fast planing monohull inirregular waves are calculated by a solution in the timedomain of the three equations containing the importantforces (X and Z) and moments (M y) working on the hull.The running trim and the sinkage of the planing hull atthe particular forward speed under consideration aredetermined using the procedure mentioned before. Theirregular wave realization, yielding at each time step the

wave profile over the length of the ship, is generatedusing 50 different wave components to describe thegiven sea spectrum.The two seastates used for the present calculations arethe average conditions of Seastate 4 (T p= 6 s and H 1/3=2.25 m) and Seastate 5 (T p= 7.5 s and H 1/3= 3.5 m)respectively. The spectrum formulation used is theBretschneider formulation for the energy distributionover the frequency range. Furthermore, for theseconditions, a vessel speed was taken as being 25 knotsfor all different design concepts.The results are presented as distributions of the peaks of the amplitudes of the heave and pitch motion of the ships

in those conditions in Figure 6 and 7 respectively and asthe distribution of the peaks in the vertical accelerationsat the bow and the wheelhouse in the same conditions inFigure 8 and 9 respectively. For the sake of clarity onlythe negative peaks of the vertical accelerations (i.e.upwards) are presented. The positive peaks remain belowthe value of 10 m/s 2 (i.e. the acceleration, g, due togravity).From these figures it becomes immediately evident thatthe reduction in the vertical accelerations both at the“bow” (i.e. 10%L aft of the forward perpendicular) andat the wheelhouse are already significantly reduced withthe application of the TUD 4100 bow shape and

dramatically reduced with the application of the AXE4100 bow shape when compared with the original(traditional) bow of the ESC 4100. These computationalfindings correspond with the real life observations andexperience obtained so far with the Dutch Coast Guardvessels of the “Jaquar” type (25 knots 42 meter LoaPatrol boats) built along the lines of the TUD 4100. Inthe earlier study on the TUD 4100, [2], thesecomputational results were also validated with modelexperiments in the towing tank. The results obtained for the AXE 4100 indicate that an ever further and verysignificant improvement is to be gained in these seaconditions, because both the significant values of thevertical accelerations and, in particular, the extreme peak


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values are very much reduced with the application of theAxe bow shape.There is only a small increase in the heave and pitchmotion of the AXE 4100 when compared with the other ones, which was to be expected.

3.3 DIRECTIONAL STABILITY

During the project, it was questioned whether the Axe bow concept would be more sensitive to broaching thanthe original TUD4100. Calculations were conducted atMARIN in order to determine the linear horizontal planemanoeuvring coefficients. The aim is to determine thehydrodynamic forces and stability levers for both driftand yaw motions in order to compare the risks of

broaching for the two ships. Although the horizontal plane stability is only one of many factors determining broaching risks, it is thought to be one of the major differences between the two hull forms.

Because of the unconventional hull form and the lack of data published in literature regarding similar hull forms,conventional methods to determine the hydrodynamiccoefficients in the horizontal plane can not be appliedsuccessfully. Therefore, a method recently developed atMARIN was applied during the calculations. Thismethod is based on the slender body strip theory method.

3.3.1 Slender body method

Already in 1966, Jacobs [7] proposed a strip theory alikeapproximation for manoeuvring calculations. This striptheory is based on calculations related to the sectional

added mass. By proper integration of the change of sectional added mass, the required hydrodynamicderivatives can be obtained. A publication of Beukelman,see [8], clearly illustrates the application of this method.

Basically, the strip theory technique says that the lateralforce per slice of the ship is the rate of change of fluidmomentum per slice of the ship. This is expressed as:

+++−=

−=

ξ ξ

ξ

ξ ξ ξ ξ

ξ

d dm

uvd

dvumdt

dmvdt

dvm

Dt

vm D

d dY

YY YY YY YY

YY

in which m YY is the lateral inertia coefficient or the two-dimensional added mass in lateral direction and v ξ thelocal transverse velocity. This formula is used tocalculate the non-dimensional linear manoeuvringcoefficients Y β, Nβ, Y γ and N γ .

Just as with the other potential flow techniques, thecalculation will fail to come up with lateral forces on theship, while the turning moment will come close to theMunk moment. When looking at the lateral force on theship due to a drift angle, the theory states that the force is

equal to the change in sectional added mass between themost forward submerged section and the aftmostsubmerged section. Unless the aft section abruptly endsin a submerged transom, the sectional added masses atthe forward and aft sections are calculated to be zero andtherefore, the lateral force is zero.

Therefore, some modification has to be done to the addedmass distribution in order to arrive at the actual forcedistribution along the length of the ship. Several

proposed modifications are published in literature. For example, Beukelman [8] assumes a constant added massdistribution in the aft ship region up to the section withthe maximum breadth. This actually means that for example the sway coefficient for drift motion Y β is onlyrelated to the sectional added mass of the section withmaximum breadth. With that in mind, the assumptionclearly involves simplifications that result in the samecoefficients for ships with the same section at themaximum breadth position, but different foreships.

Therefore, other corrections to the theory are required inorder to arrive at the realistic hydrodynamic coefficients.

A comparison published in literature between the resultsof segmented model tests and the slender body theory ismade by Clarke, see [9] . The objective of segmentedmodel tests is to obtain insight into the distribution of thelateral forces and yawing moments along the length of the ship. In this comparison, it is found that especially inthe aft ship, deviations occur between the actual resultsand the theoretical estimation.At MARIN, extensive data sets exist concerningsegmented model tests. These test results were used to

verify and "tune" the slender body theory to arrive at therequired values of the linear manoeuvring coefficients.Based on this, a viscous correction formula was obtained,incorporating the full hull form.

3.3.2 Application to the TUD4100 and AXE BOWconcepts

The MARIN slender body method has been applied tothe two hull forms in order to determine the manoeuvringderivatives. By comparison of the results for the twoships, an indication of the relative differences in the

coefficients is obtained. These differences might give anindication about the sensitivity to broaching.As a first step, the method was applied for the designloading condition, i.e. the ship on even keel. Figure 10(a) includes a graph and a table which shows the addedmass distributions along the length of the ships as well asthe derived linear manoeuvring coefficients.In this figure, the peak in the distribution for the Axe

bow is noteworthy. According to MARIN experience, thelinear manoeuvring coefficients are mostly influenced bythe added mass in the forward part of the ship. Therefore,this peak will have a large influence on the results of thecalculations.


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It is seen that the differences in coefficients areconsiderable. It is found that the coefficients for the Axe

bow are in some cases three times larger than theTUD4100 coefficients. The reason for this lies mainly inthe shape of the bow: due to the very slender sectionswith high height to breadth ratio and large draught, the

added mass distribution is considerably higher in theforeship of the Axe bow than for the TUD4100.These results show that during a drift motion, the yawmoment on the Axe bow will be three times as high asfor the TUD4100. The lever of application of the sideforce due to drift l β indicates that the lateral force actsforward of the forward perpendicular. However, it isfound that for the TUD4100, the force also acts veryclose to the forward perpendicular. From this, it can beconcluded that the de-stabilising moments due to drift arelarge for both designs.During yaw motion, the yaw moment on the Axe bow isalso three times as high as for the TUD4100. The lateral

force lever l γ indicates a distance of 34%Lpp forward of the centre of gravity. Due to the bow shape of theTUD4100, the lever for this ship is relatively small.To determine the amount of (in)stability, the difference(lγ - lβ) of the stability levers should be examined. Theabove calculation results show that both the TUD4100and the Axe bow will be directionally unstable, with theTUD4100 more unstable than the Axe bow. Because of the comparative nature of this study, the influence of therudders on the directional stability of the hulls is nottaken into account.

More calculations have been conducted to determine thelinear manoeuvring coefficients for a more realisticattitude of the ships at full speed. Based on tests withsimilar ships, the running trims of both hull forms have

been estimated to be between 1.5° and 2° trim by thestern, combined with almost no sinkage or heave. Thedistribution of the sectional added mass for 2° stern trimand the calculated manoeuvring derivatives are shown inFigure 10 (b).

The change in the stability lever (l γ - lβ) due to the sterntrim is remarkable. It is seen that both the TUD4100 andthe Axe bow are still unstable, but now the TUD4100 isless unstable than the Axe bow. The value for the Axe

bow hardly changed due to the stern trim. Remarkable isthe fact that the "hump" in the distribution of the addedmass for the TUD4100 disappears due to the stern trim,while for the Axe bow, this hump is still existing.

A third condition was investigated, to obtain animpression of the change in directional stability due to

bow trim. This condition can occur when the ship runsinto a wave crest in following seas. The distribution of sectional added mass and the derived manoeuvringcoefficients are shown in Figure 10 (c).

In bow trimmed condition, it is found that the Axe bownow is almost stable. This is mainly caused by therelatively large forward shift of the centre of gravity.

This results in a large reduction of the lever for drift, incombination with a relatively small change of yaw lever.The TUD4100 is found to be unstable, but slightly lessthan in the even keel condition.

3.3.3 Discussion of the risk of broaching

The physics of broaching have often been published inliterature. A recent summary of broaching and capsizingwas described by McTaggart and De Kat [10].

If loss of stability is the reason for broaching infollowing seas, a comparison of the KM values of bothships is of interest. For these hull forms, it is found thatin stern trim or even keel condition, the KM values arealmost the same, but in bow trim condition, the KMvalue for the Axe bow is about 0.6 m smaller than for theTUD4100. This means that when the ship runs into a

wave crest, the transverse stability of the Axe bow isreduced considerably, possibly resulting in capsizing or broaching.

Although the yaw damping moments for the Axe bow arecalculated to be considerably higher than for theTUD4100, the yaw moment due to drift, de-stabilisingthe straight ahead motion of the ship, is thought to be of major importance in the determination of the risk of

broaching. If only a slight drift motion is present, the build up of the lateral forces in the foreship of the Axe bow is considerable, inducing a yaw motion. Combinedwith the inherent straight-line instability of the ship, it is

expected that a risk of broaching is present.

Another aspect of the relatively large yaw moments thatact on the Axe bow lies in the compensating momentsthat are to be generated by the rudders. When themoments on the Axe bow are about three times higher than on the TUD4100, it means that to compensate thismoment by the rudders, a rudder-induced moment of alsoabout three times as high should be generated. Either therudder deflection should be about three times higher thanfor the TUD4100, or the rudder efficiency should bethree times higher. This means that the controllability of the Axe bow is expected to be less than the

controllability of the TUD4100.

Finally, broaching can occur due to an excessive rollmotion due to yaw-roll coupling. Because of the deep

bow of the Axe bow hull form, and the large transverseforces in the bow area of the Axe bow, it is expected thatconsiderable yaw-roll coupling will exist for this hull.With transverse forces about three to four times larger than for the TUD4100, combined with probably a larger vertical lever of application with respect to the centre of gravity, the heeling moment due to drift or yaw might bemore than three times larger than for the TUD4100.


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3.3.4 Considerations

The original slender body theory does not incorporateany viscous or forward speed effects. The modifiedslender body method developed at MARIN to determinethe manoeuvring derivatives based on the added mass

distribution was based on segmented model tests resultswith conventional and naval surface ships. The design of the hull of the Axe bow differs significantly from theships on which the modified theory was based andtherefore, the actual values of the coefficients are likelydifferent from the ones that might be obtained duringmodel tests. Unfortunately, no comparable data wasavailable at the time of writing of this paper. However,

because of the lack of information, the method wasapplied to determine the sensitivity for broaching in aqualitative way.In order to obtain a more reliable prediction of the risk of

broaching model tests with the Axe bow hull form should

be conducted.

4. CONCLUSIONS

Since the introduction of the ESC, the available “space”to modify the bow has been successfully applied to theTUD 4100. The extension into the AXE 4100 leads tofurther improvements in seakeeping capabilities. Theresults obtained for the AXE 4100 indicate that asignificant reduction has been obtained for the verticalaccelerations in the wheelhouse. This is excellent for workability and safe operation of the vessel. This holdstrue for both significant as extreme acceleration values.

Pronounced reductions (50%) have also been found inthe extreme peak values at the bow. The leads to lessslamming and therefore lower slam forces which is

beneficial to the construction of the ship as well as the perception of the crew when sailing her.There is only a small increase in the heave and pitchmotion of the AXE 4100 when compared with the other ones, which was to be expected.

The actual difference in vessel resistance between thethree concepts has yet to be fully examined (i.e. viamodel tests).

In extreme weather conditions (non-applicable for numerous designs) the following may be stated regarding

broaching: Based on the calculations of thehydrodynamic horizontal plane derivatives and additionaldetermination of the metacentre heights in severalattitudes of the hull forms, it is concluded that the Axe

bow may probably be more sensitive to broaching thanthe TUD4100 design. Also, it is expected that yaw-rollcoupling will be more pronounced for the Axe bowdesign, increasing the risk of broaching.The amount of sensitivity and hence the risk of broachingis still subject to further model test investigations.

Broaching tendancy of the axe bow may be considerablyreduced by the application of a center skeg in the sternregion.

5. RECOMMENDATIONS

More calculations and model tests should be undertakento gain a better understanding and quantification of theaspects involved in the determination of the effect of bowshapes on the seakeeping performance of a fastmonohull.

7. REFERENCES

[1] Keuning, J.A., Pinkster, Jakob, "Optimisation of theseakeeping behaviour of a fast monohull". Fast’95conference, October 1995.

[2] Keuning, J.A., Pinkster, Jakob, "Further design and

seakeeping investigations into the “Enlarged ShipConcept”. Fast’97 conference, July 1997.[3] Keuning, J.A., “The Non linear behaviour of fast

monohulls in head waves”. Doctor’s thesis TUDelft, 1994.

[4] Von Karman, W., “A study on Motions of HighSpeed Planing Boats with Controllable Flaps”, Int.Shipbuilding Progress, No 365, January 1985.

[5] Wagner, H. von, “Uber Stoss und Gleitvorgange ander Oberfläche von Flüssigkeiten”, Zeitschrifft für Angewandete Matematik und Mechanik, Band 12,Heft 4, 1932

[6] Velde, J. van der, Pinkster, Jakob, Keuning, J.A.,

“Enlarged Ship Concept applied to a fully planingSAR Rigid Inflatable Lifeboat”, Fast’99 conference,August-September 1999.

[7] Jacobs, W.R., "The Estimation Of StabilityDerivatives And Indices Of Various Ship FormsAnd Comparison Experimental Results", Journal of Ship Research, 1966, Vol. 10, No. 3.

[8] Beukelman, W., "Manoeuvring Derivatives For ALow Aspect-Ratio Surface Piercing Wing-Model InDeep And Shallow Water", Delft University of Technology Ship Hydromechanics Laboratory,Report No. 998, MEMT 35, March 1995. ISBN 90-370-0127-0.

[9] Clarke. D., "A Two-Dimensional Strip Method For Surface Ship Hull Derivatives: Comparison Of Theory With Experiments On A Segmented Model",Journal Mechanical Engineering Science, Vol. 14,

No. 7, 1972.[10] McTaggart, K. and De Kat, J.O.; "Capsize Risk of

Intact Frigates in Irregular Seas", TransactionsSNAME Annual Meeting, Paper No. 8, Vancouver 2001.


9/16

Figure 1. General arrangements of the 26 m. “Base” boat (1.0 L) and Enlarged Ship Concepts (1.25 L and 1.50 L respectively), (taken from [1])

Figure 2. Overall performance indexes for the different design concepts (taken from [2])

Final design resultsOverall performance indexes

00.20.40.6

0.81

1.21.41.61.8

2600 3300 4000

Design concepts

P e r f o r m

a n c e

i n d e x

[ - ]

LengthBuilding costsOperational costs

Transport efficiencyOperability


10/16

Figure 3. The lines plans for respectively ESC 4100, TUD 4100 and AXE 4100

Figure 4. A number of 3-D renderings of the AXE 4100

AXE 4100

ESC 4100

TUD 4100


11/16

Figure 5. The resistance curves for respectively ESC 4100, TUD 4100 and AXE 4100

Table 1. Main dimensions and other relevant data for the ESC 4100, TUD 4100 and AXE 4100.

0

20

40

60

80

100

120

140

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

V (kn.)

R e s

i s t a n c e

( k N )

ESC 4100

TUD4100

AXE4100

ESC 4100 TUD 4100 AXE 4100DimensionsW.L.Length [m] 36.307 38.448 41Length [m] 41 41 41W.L.Beam [m] 5.628 5.662 5.608

Draft [m] 1.425 1.463 2.713DisplacementVolume [m 3] 111.28 111.16 111.57Displ. [kg] 111285 111164 111570LCB [%w.l.] 55.4 59.2 54.9WaterplaneW.P.Area [m 2] 168.24 157.76 162.11LCF [%w.l.] 57.6 61.9 62.5Ctr.Flotn.X [m] 25.619 26.357 25.631Wetted Surface

Wetted S.Area [m2

] 193.87 199.3 222.3Initial StabilityTrans.GM [m] 3.062 2.709 2.543Long.GM [m] 124.352 112.347 134.113CoefficientsWaterplane [-] 0.823 0.725 0.705Prismatic [-] 0.699 0.638 0.699Block [-] 0.382 0.349 0.179Midsection [-] 0.547 0.547 0.256Lwl/(Displ^0.333 [-] 7.56 8.01 8.53


12/16


13/16

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

100 50 20 10 5 2 1 0.5 .2

Pitchseastate 4

pos.ESC 4100

neg.ESC 4100

pos. A XE4100

neg. AXE4100

pos. TUD4100

neg. TUD4100

Pe(X) (%)

P e a

k v a

l u e

X [ r a

d ]

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

100 50 20 10 5 2 1 0.5 .2

file: c:\mijndo~1\jakob\easyplot\epwindow\figpit~1

Pitchseastate 5

pos.ESC 4100

neg.ESC 4100

pos. AXE4100 neg. AXE4100

pos. TUD4100

neg. TUD4100

Pe(X) (%)

P e a

k v a

l u e

X [ r a d ]

Figure 7. The distribution of the peaks of the pitch amplitude for respectively ESC 4100, TUD 4100 andAXE 4100.


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0

20

40

60

80

100

120

140

100 50 20 10 5 2 1 0.5 .2

Negative vertical accelerationBowSeastate 4

ESC 4100

AXE4100

TUD4100

Pe(X) (%)

P e a

k v a

l u e

X [ m / s 2 ]

0

20

40

60

80

100

120

140

100 50 20 10 5 2 1 0.5 .2

file: c:\mijndo~1\jakob\easyplot\epwindow\figbow~1

Negative vertical accelerationBowSeastate 5

ESC 4100

AXE4100

TUD4100

Pe(X) (%)

P e a

k v a

l u e

X [ m / s 2 ]

Figure 8. The distribution of the peaks of the negative vertical acceleration at the bow amplitude for respectively ESC 4100, TUD 4100 and AXE 4100.


15/16

0

10

20

30

40

50

60

100 50 20 10 5 2 1 0.5 .2

Negative vertical accelerationWheelhouseSeastate 4

ESC 4100

AXE4100

TUD4100

Pe(X) (%)

P e a

k v a

l u e

X [ m / s 2 ]

0

10

20

30

40

50

60

100 50 20 10 5 2 1 0.5 .2

file: c:\mijndo~1\jakob\easyplot\epwindow\figwhe~1

Negative vertical accelerationWheelhouseSeastate 5 ESC 4100

AXE4100

TUD4100

Pe(X) (%)

P e a

k v a

l u e

X [ m / s 2 ]

Figure 9. The distribution of the peaks of the negative vertical acceleration in the wheelhouse amplitude for respectively ESC 4100, TUD 4100 and AXE 4100.


16/16

Design loading condition, 0° trim

Even keel condition

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 5 10 15 20 25 30 35 40

aft > front

m

Y Y

[ k g

/ m ]

TUD4100 Axebow

Hull TUD4100 AxebowYβ -0.120 -0.329

Nβ -0.053 -0.178

Yγ 0.003 -0.029 N γ -0.013 -0.042

lβ 0.446 0.540lγ 0.124 0.339lγ -lβ -0.322 -0.201

Figure 10 (a). Added mass distribution and derived linear manoeuvring coefficients(design loading condition, 0° trim).

Full speed condition, 2° trim by the stern

Stern trimmed condition

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 5 10 15 20 25 30 35 40aft > front

m Y Y

[ k g

/ m ]

TUD4100 Axebow


Nβ -0.040 -0.115Yγ 0.028 0.006

N γ -0.007 -0.027lβ 0.237 0.438lγ 0.066 0.238lγ -lβ -0.171 -0.200

Figure 10 (b). Added mass distribution and derived linear manoeuvring coefficients(trimmed condition, 2° trim by stern).

Nose dive condition, 2° trim by the bow

Bow trimmed condition

0

2000

4000

6000

8000

1000012000

14000

16000

18000

20000

0 5 10 15 20 25 30 35 40

aft > front

m Y Y

[ k g / m

]

TUD4100 Axebow


Nβ

-0.082 -0.219Yγ -0.013 -0.058

N γ -0.020 -0.056lβ 0.505 0.457lγ 0.223 0.411lγ -lβ -0.282 -0.046

Figure 10 (c). Added mass distribution and derived linear manoeuvring coefficients(bow trimmed condition, 2° trim by bow).

1806457914_1999999096_FAST2001-The_effect_of_bowshape

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