Radojcic.on High Speed Mono.2010.SYMP

8/20/2019 Radojcic.on High Speed Mono.2010.SYMP

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On High Speed Monohulls in Shallow Water

Dejan Radojcic, University of Belgrade, Faculty of Mech. Engineering, Dept. of Nav. Arch., Serbia

Jeffrey Bowles, Donald L. Blount & Associates, Virginia, USA

ABSTRACT

The hydrodynamic performance of marine craft has

long been known to be influenced by water depth. When

operating in shallow water at subcritical speeds (typical for

displacement vessels), they slow down at constant power.On the contrary, when operating in shallow water at

supercritical speeds (typical for planing vessels), vesselspeeds increase at constant power. Additionally, surface

waves generated by the hull vary radically with vessel

speed and water depth.

In recent years, mega yachts are being designed forlength Froude numbers (FnL) greater than 0.4, with many

operating between 0.5 and 1.0, and some have even higher

non-dimensional speeds. As these modern mega yachts being delivered have overall lengths up to and often

exceeding 100 meters, shallow water effects are being

observed by their captains in relatively deep water. Thus, itis the intent of this paper to refresh, for the mega and high

speed yacht community, what defines shallow water, the

impact on performance and a general discussion on the

responsibilities for hull-generated waves and wake

occurring due to shallow water. A power prediction

procedure applicable in everyday engineering practice isoutlined and an underpinned by a numerical example.

NOTATION (SI Unit System)

B Breadth on DWL

CB Block coefficientD

P Propeller diameter

E Wave energy

Fnh Depth Froude number = V/(gh)1/2

FnL Length Froude number = V/(gL)1/2

Fn Volume Froude number = V/(g1/3)1/2

g Acceleration due to gravity

h Water depthH Wave height

L Length on DWL

LOA Length Overall

L/1/3 Slenderness ration Propulsor shaft speed

PB Brake (installed) power

PE Effective power

PD Delivered power

R T Total resistance

Rw Wave making resistance

R F Frictional resistanceR R Residuary resistance

R T Total resistance

SWPF Ratio of Dh/D

SWRF Ratio of R Wh/R W or R Rh/R R

T Draught

T Wave periodT Thrust of a propulsor

t Thrust deduction fraction

V Speed (velocity) of the vessel

Vw Wave speedw Wake fraction

x Distance from track

Displacement Vol. of water displaced at rest

D Quasi-propulsive efficiency = PE/PD

H Hull efficiency

J Jet efficiency

O Propeller open-water efficiency

P Pump efficiency

R Relative rotative efficiency

w Wavelength

Mass density of water

0.7R Cavitation number at 0.7 propeller radius

Dynamic (running) trim angle

c Thrust loading coefficient

Subscripts:

h - finite water depth

d or - infinite water depth (deep water)

INTRODUCTION

Already a decade or so ago some remarkable (although

probably not all commercially successful) high speedmonohulls, which deserved special attention concerning

THE SECOND CHESAPEAKE POWER BOAT SYMPOSIUM

ANNAPOLIS, MARYLAND, MARCH 2010


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shallow water behavior, were built. For example these

might include Jupiter MDV 3000 (LOA=146 m, V=40+ kts),

Corsair 11000 (LOA=102 m, V=35+ kts), Suzuran

(LOA =187 m, V=30 kts) etc. Their predecessor Destriero

(LOA=67 m, V=60+ kts) was built 15 or so years ago. Inrecent years some outstanding mega yachts have also been

delivered such as A (LOA

=118 m, V=23 kts), Ectasea

(LOA= 86 m, V=35 kts), and Silver (LOA=73 m, V=27 kts).

Both the length and speed of these large monohulls are

growing relative to conventional values; these larger and

faster monohulls have different resistance characteristics as

explained by Blount and McGrath (2009) paper. Further tothese differences, it is likely that operators are noticing that

these vessels behave differently in shallow water when

compared to navigation in deep water. What is beingobserved is a hydrodynamic phenomenon referred to as

shallow water effect.

Various references indicate that shallow water effects

begin to show up at depth Froude numbers greater than0.7, peak at a depth Froude number of about 0.9-1.0 andsubside at a depth Froude number of about 1.2. With thisinformation three regions of depth Froude numbers can be

identified:

Subcritical region (Fnh


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Figure 1 - Surface wave pattern when Fnh = 0.65

Figure 2 - Surface wave pattern when Fnh = 0.90

Figure 3 - Surface wave pattern when Fnh = 1.50(Figures 1 through 3 are from Nwogu, 2003)

Figure 4 - Impact of depth Froude number on diverging

bow wave angle

WAVE WASH

Fast vessels produce wave wash that is different than

that of conventional ships and natural waves; they have

long periods and significant energy. The amplitude of theleading wave produced by high speed craft is not so large

(when compared to storm waves, for instance) but it does

have a relatively long wave period. When these waves

reach (get into) shallow water their height increasesrapidly, often causing large and damaging surges on the

beaches. They also arrive unexpectedly, often long after

the high speed craft has passed out of view. This further

increases the potential danger because the large waves arenot expected by the public when they arrive.

Consequently, wash restrictions were implemented on

several sensitive high speed craft routes. During the last20-years of evolution, wash restrictions were first based on

speed limits, then wave wash heights, and ultimately by the

limitation of energy produced by wash at a certain distance

from the vessel’s track. According to the latest findings both wash height and energy are important; see for instanceCox (2000) and Doyle et al. (2001).

Concerning wash in the sheltered waters, it is only avessel’s divergent waves which are relevant. A visual

indicator of wave wash size is usually its height only;

however the wave period seems to be the critical factor

regarding damage.

Deep Water

As mentioned above, wave wash restrictions are now

based on the energy in the wave train. By using thisapproach the wave height and period are taken into

consideration. For example, the State of Washington

restricts wave wash energy, E, to values of less than 2450

J/m at a distance of 300 m off the vessel’s track, or 2825

J/m at a distance of 200 m off the vessel’s track.

The distances from the vessel are included in the

requirements because wave height diminishes as the lateraldistance from the track increase. The decay rate in far-field

(distances beyond two waterline lengths) may be obtained

from the relation 1/x0.33, where x is distance perpendicular

to ship track. It should be noted, however, that the wave

period is nearly constant as distance x changes.

The calculations of wave wake energy per linear

length of wave front is given by the following equation, in

which the period, T, is associated with the maximum waveheight:

E = (g2H2T2)/16 = 1960H2T2 J/m .

A numerical calculation example is provided in

Appendix 1 for reference.


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Shallow Water

The characterization of shallow water waves is more

complicated because wave period also varies with distance

from the sailing line. Longer and faster waves travel on theoutside of the wash and have a larger Kelvin angle than the

shorter and slower waves. When the waves are in very

shallow water and the supercritical region, the first wave inthe group is usually the highest. However, as depth

increases, the second or third wave typically becomes the

highest.

The appropriate measure of wave wash in shallowwater seems to be both the wave height and wave energy.

As expected, the largest waves occur around Fnh=1 as

shown in Figure 5. Most of the energy is contained in asingle long-period wave with little energy decay at a

distance. The decay rate in shallow water is smaller than in

deep water and is a function of h/L ratio; the hull formitself has very little impact. Further, the decay ratio at

critical speeds is different than that in supercritical region,as shown in Figure 6. This is a contributing factor to

unexpectedly large waves in shallow water at a larger

distance from a vessel’s track. If ratio h/L>0.5, the waves

are more or less the same as in deep water.

Figure 5 - Variation of wave height and energy with depth

Froude number (measurements recorded at xL),(Doyle, 2001)

Low Wash Hulls

Naval architects are nowadays trying to identify low

wave wash hull form characteristics, which is not as simpleas it sounds. Generally, low wash ships have an increased

length and decreased displacement, i.e. far-field wave wash

height is a function of slenderness ratio L/1.3. Byapplying low wash design principles, the wave height

might be reduced but the wave period is not affected (Cox,2000). Moreover, since hull length directly influences

wave period, increasing length is less effective than

reducing displacement. Therefore, deep water wave height

essentially varies directly with displacement, while the period remains essentially constant. Characteristics such as

trim, sinkage, and transom immersion are also influential

on wave wash height, but are secondary to length and

displacement. Hull section shape has little effect, as shownin Figures 7 and 8.

Figure 6 - Decay rate of wave energy and height with

distance from vessel track (Doyle, 2001)


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Figure 7 - Wash wave trace for chine and round bilge hullfor the same vessel design (Phillips and Hook, 2006)

Figure 8 – Wash wave trace from same vessel traveling

forward and in reverse (Phillips and Hook, 2006)

Consequently, for low wash the following is important:

‐ Speeds corresponding to FnL=0.35-0.65 should beavoided

‐ Displacement should be as low as possible whilelength should be as large as possible.

So, if all important parameters are kept the same, so

called low wash hulls produce wave patterns that are not

much different than that of ordinary hull forms.

Furthermore, according to Cox (2000) there is no sufficient

evidence for claims that catamaran, multi-hull vessel, or

any other form is significantly better than monohulls(provided comparison is made between comparable

designs). According to PIANC 2003, high speed craftwave wash cannot be reduced just by optimizing the hull

form and various design ratios since wave period generally

increases with speed and doesn’t decay quickly, which is

particularly important for navigation in shallow water.

SHALLOW WATER INFLUENCE ON RESISTANCE

In shallow water, vessel resistance is very much

different than in deep water, and often may play asignificant role in vessel design. Namely, due to the

phenomena explained above – growth of transverse waves

up to Fnh0.95 (theoretically Fnh=1) which is then followed by a complete loss of transverse waves (Fnh1)– a vessel’sresistance, sinkage and trim (which are all interrelated)

dramatically change compared to that in deep water.

Namely, resistance (R Th) shows a pronounced peak

(maximum) at the critical Fnh of about 0.95, due mainly to a

dramatic increase of wave making resistance (R Wh) evident

by the growth of transverse waves. Operation in the

supercritical region (Fnh1), which is characterized by the

formation of diverging waves only, results in a reduction ofresistance compared to deep water. As the water becomes

shallower for constant speed, or speed increases for

constant depth, the effects explained above become more pronounced. The frictional resistance also changes slightly

due to changes of trim and sinkage, and therefore wetted

surface areas, but these effects are secondary to the changes

in wave making resistance.

It is worthy of noting that in shallow water actually

only one resistance component – the wave making

resistance (R W) – changes dramatically from its deep watercharacteristics. Consequently, this phenomenon may be

well expressed through the ratio of shallow water wave

resistance to deep water wave resistance, i.e.SWRF=R Wh/R Wd. Following this logic, three speed regions

may be detected as shown in Figure 9:

Subcritical region (according to the ITTC Fnh


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simple equations that can be easily calculated on a pocket

calculator for voyage planning or to check specific

operating conditions.

21

/*164.0 hV F nh or 21

**1.6 hF V nh V kts, h m

These equations were used to generate the chart shown in

Figure 14 for quick reference.

Figure 14 - Quick-reference chart indicating region ofoperation

The other and by far the simplest item often used to

consider when determining if shallow water effects are

present is the ratio of the water depth to the vessel overalllength. Shallow water effects may be noticeable when a

vessel is operating in water depths less than h/LOA< 0.80.

SHALLOW WATER INFLUENCE ON PROPULSIVE

COEFFICIENTS

Variations in the quasi-propulsive efficiency, D, inshallow water are exactly opposite to resistance, i.e. around

the critical depth Froude number ηD decreases compared to

the value in deep water. That is, a plot of ηD as a function

of Fnh has a pronounced hollow around the critical speed as

shown in Figure 15. The reduction in d is primarily relatedto increased propulsor loading due to the increased

resistance (resulting in a decrease in O), but is influenced by other factors as well (Hofman and Radojcic, 1997;Radojcic, 1998). Note in the figure that the critical speed

for d occurs slightly sooner than it does for resistance, i.e.it is around Fnh=0.85 for D.

Figure 15 - Quasi propulsive efficiency of a river

fire-fighting boat (shown in Figure 18)

Similar to the variation of resistance due to shallow

water effects, the variation of quasi propulsive efficiency is

also affected by the ratio of vessel length to water depth as

depicted in Figure 16 (from Filipovska, 2004). As withresistance, the ratio of L/h is the most influential parameter

for propulsive efficiency in shallow water.

Figure 16 – Typical surface plot of quasi propulsive

efficiency (Filipovska, 2004)

To expand on the cause for this phenomenon, we must

look at the definition of quasi-propulsive efficiency as

D=OHR , where H=(1-t)/(1-w). Both thrust deductionfraction (t) and wake fraction (w) have pronounced peeks

in the critical region which is shown in Figure 17.Generally, in the critical region, the wake fraction curve

has a hollow while thrust deduction fraction curve has a

peak, resulting in a pronounced hollow in hull efficiency

H. It should be noted, however, that experimental dataregarding the change in propulsive coefficients due to

operation in shallow water are not readily available.

Figure 17 - General trends for w, t, and D in extremelyshallow water

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80 90 100 110

V E S S E L S P E E D

( k t s )

WATER DEPTH (m)

SUPERCRITICAL REGION

CRITICAL REGION

SUBCRITICAL REGION

Fnh = 0.70

Fnh = 1.20

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Fnh

w

0.1

0.2

0.3

0.4

0.5

0.6

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Fnh

t

0.1

0.2

0.3

0.4

0.5

0.6

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 Fnh

n


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SHALLOW WATER INFLUENCE ON POWERING

PREDICTIONS

Figure 18 provides curves (model test data) for

delivered power, shaft speed, vessel trim, and vesselsinkage at various water depths for a 27.5 meter river

vessel propelled by three screw propellers. This

comprehensive figure illustrates the following shallowwater impacts:

The trim () and sinkage of the hull varies withwater depth.

The hump speed (vessel speed at which maximumtrim occurs) is less in shallower water.

The propulsion power significantly increases inthe critical region as water depth decreases.

Propeller shaft speed (n) at a given vessel speedincreases as water depth decreases (indicating areduction in efficiency)

Figure 18 - Power-speed diagram (with RPM, trim andsinkage) of a fire-fighting river boat operating in different

water depths (Heser, 1994)

The net result is that due to both an increase in

resistance and a reduction in quasi-propulsive efficiency, itmight happen that vessel’s speed in the critical region is

substantially lower than is expected and/or that power

demand is substantially increased. This is explained

graphically in Figure 19. However, when operating in thesuper-critical region the reverse occurs; the required power

to achieve a specific speed may be smaller than in deep

water due to smaller resistance and somewhat larger

propulsive efficiency.

Cavitation considerations, which are important for all

propulsors, are especially important when considering

shallow water operation. In the worst-case scenario, thethrust loading, on a propulsor sized for deep water

operation, can increase substantially enough due to shallow

water resistance to cause the onset of excessive cavitation

and thrust breakdown. The achievable shallow water

vessel speeds may be significantly less than in deep watercases because thrust breakdown causes the quasi-

propulsion efficiency to drop dramatically.

Figure 19 - R and T(1-t) versus V in shallow and deepwater showing that the achievable speed in shallow water

might be much lower than in deep water, i.e. V4h vs. V4∞ (Hofman and Radojcic, 1997)

A simple check procedure for the thrust loading limits

of a propeller is presented by Blount and Fox (1978).Equations for several different propeller designs are given

that establish a border representing the maximum thrust

loading limit as a function of cavitation number. Once the propeller operating conditions are calculated they are

plotted on the same axes as the thrust loading limit. If the

propeller operating conditions approach and become

asymptotic to the thrust loading limit, it is indicative thatcavitation is present (See Figure 20).


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Figure 20 - Plot of propeller performance indicating

thrust loading limits

In the case of water jets, a cavitation check is

performed by simply plotting the shallow water resistance

curve on the water jet performance map to determine if the

curve crosses into the cavitation region. Figure 21 shows ageneric performance map with a deep water and shallowwater resistance curve overlaid on it. The contours of

efficiency included in this figure support the claim that the

efficiency decreased in shallow water operation. Threecavitation zones are also shown in the figure:

Zone I - unrestricted operation Zone II – limited operation allowed Zone III – operation not recommended – thrust

breakdown likely.

Figure 21 - Typical water jet performance map (RR-

KaMeWa prospectus, Allison 1993)

From Figure 21 it is obvious that for properly sized

water jet for deep water, in shallow water: a) zone III may

be easily reached, and b) operation at poor efficiencyaround the hump is unavoidable. Therefore, the usual

practice of choosing the smallest water jet size which meets

the thrust design point at high speed, and which operates in

Zone II for a short period of time at lower speeds, has to be

changed for vessels intended to operate in shallow water.Larger water jets with higher cavitation margins must be

chosen which means, that an installation tailored for

shallow water is going to be heavier and more expensive.

In situations where significant cavitation (or thrust breakdown) does not occur when operating in shallow

water (critical region), the vessel’s speed could still be

significantly limited as the main engines often do not have

enough torque available at low engine speeds to allow themto reach rated speed and power, i.e. the engines are then

overloaded. Further discussion of engine loading (or

overloading) is beyond the scope of this paper even though

it is very important for all propulsors in general andespecially for propellers. Blount and Bartee (1997) provide

a good explanation of engine loading and overloading.

FULL SCALE TRIALS

The above conclusions, some of them based on theory,sound good enough provided that the changes explained

actually occur when operating in shallow water. Each ofthe two full scale trial cases presented below represent

different vessel sizes, section shapes, and vessel speeds to

show that the impacts are observed by craft of different

types.

The first vessel is a hard chine, flat bottom planing

craft with an overall length of 10.5 meters that utilizes

submerged propellers for propulsion. Figure 22 (fromBlount and Hankley (1976) shows that when water depth is

less than 80% of LOA, the vessel power demand increases

relative to deep water when operating at displacementspeeds and that the vessel power demand decreases relativeto deep water when operating at planing speeds (note

similarity with Figure 13).

Figure 22 - Ratio of shaft power in shallow water to deepwater for a fast craft operating in different water depths

(Blount and Hankley, 1976)

0.01

0.1

1

0.01 0.1 1

c

0.7R

MAXIMUM THRUST LOADING

LIMIT TAKEN FROM BLOUNT &

FOX (1978)

CALCULATED PROPELLER

OPERATINGCHARACTERISTICS

CURVEINDICATES

INCEPTION

OF

CAVITATION

THRUSTBREAKDOWN

IS PRESENT


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Figure 23 illustrates the low speed performance in the

subcritical region of a water jet propelled, round bilge, 46-

meter motor yacht when operating in shallow water at

maximum power. The data in this case is limited, but

clearly shows increase in resistance associated withoperation in shallow water.

Figure 23 - Plot of the maximum vessel speed versus waterdepth for a displacement yacht

POWERING PREDICTIONS IN SHALLOW WATER

It is well known that a strong interaction exists

between resistance and propulsion, particularly for highspeed craft, so that an integrated approach or even

integration of the whole ship design synthesis would be

desirable, as discussed by, for example, Allison and

Goubault (1975) or Radojcic (1991). Nevertheless,

traditional division into resistance and propulsion

evaluation is accepted here as the data available are not

sufficient to support a one-problem approach. So, deepwater and then shallow water resistance (based on

Radojcic, 1998) should be evaluated first and then thequasi-propulsive efficiency is determined based on the

actual thrust loading of the propulsor in the shallow water

condition. This modular approach, however, allows easier

updating when new information is obtained, which in this

case is surely needed.

A reasonably good estimation of the shallow water

resistance, and in particular of the dominant wave-makingresistance component (in the critical and supercritical

region), may be obtained through the application of theory,

as for instance the Srettenski integral (thin ship

approximation which is similar to well known Michell

integral for deep water) – see Hofman and Radojcic (1997)and Hofman and Kozarski (2000). However, the approach

accepted here is simpler and may be used in everyday

engineering practice as is based on an undemanding

evaluation of SWRF (ratio of residuary resistance inshallow and deep water). Thus final results primarily rely

on deep water data (which are more reliable) and possible

inaccuracies in (unreliable) SWRF should not influence

shallow water power evaluation to a great extent. Besides being intuitive, this approach enables: a) employment of

familiar deep water evaluation methods, and b)

replacement of specific computer routines (when

necessary) either in deep or in shallow water.

It seems, however, that a reliable method for theevaluation of propulsive coefficients (and particularly

quasi-propulsive efficiency) in shallow water does not (yet)

exist. Namely, it is not only that shallow water propulsivecoefficients in critical and supercritical region are rare and

are still missing for fast shallow water hull forms (usually

river vessels with unique form, i.e. extremely low draught

with tunnels and relatively large L/B and B/T ratios), but

they differ considerably from fast sea going vessels. It isobvious, therefore, that the propulsive coefficients of

dissimilar hull forms also differ either in deep or in shallow

water. The above-mentioned is actually the main reasonthat evaluation of SWPF (ratio of quasi-propulsive

coefficients in shallow and deep water) explained in

Radojcic (1988) paper is abandoned here. Instead, the

open water efficiency is calculated for the vessel in the

specific operating condition and the changes on the propulsive factors are ignored. In this manner thedetrimental impact of increased propulsor loading on

propulsor efficiency (the most significant factor) is

calculated relatively accurately.

Resistance Evaluation of High Speed Vessels in Deep

Water

Deep water hull resistance may be obtained in variousways, including use of specific model tests, or appropriate

systematic series model data and regression equations.

Although deep water resistance is not the subject of this

study, for the sake of completeness a few predictionmethods are mentioned here.

Resistance in the planing and semi-planing (or semi-

displacement) regime for the hard chine hulls may becalculated according to Savitsky (1964), Hadler (1966),

Hadler and Hubble (1971), modified Savitsky method

presented by Blount and Fox (1976), Hubble (1981) or the

regression equations by Radojcic (1991). Original NPLseries (Bailey, 1976), or regression equation derived by

Radojcic et al. (1997 and 1999) may be used for hulls with

round bilge, while for double-chine hulls the Radojcic et al.

(2001) paper would be appropriate. The Andersen and

Guldhammer (1986) and Holtrop (1984) methods may beused for fast ships with conventional hull forms. For

slender displacement hull forms, Cassella and Paciolla

(1983) or Fung and Leibman (1995) may be used. The

original data of Series 62, 65, NPL, 64, etc., or theregression equations derived from the data, may also be

used. In this respect, see also the recent Blount and

McGrath (2009) paper. The calculation of factors

secondary to the bare hull resistance, such as the appendage

resistance, wind resistance, added resistance due to waves

etc., is also addressed in some of the papers identified

above.


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Propulsive Efficiency Evaluation of High Speed Vessels

in Deep Water

Vessels Driven by Propellers

For quasi-propulsive efficiency evaluation (D=OR H)

it is important to know the open water efficiency of the

propeller O, relative rotative efficiency R and hullefficiency H (consisting of thrust deduction fraction and

wake fraction). R and H can be evaluated as per Blountand Fox (1976) paper for hard chine craft, per Bailey (1976

or 1982) for round bilge craft, and per Holtrop (1984) for

fast displacement ships. Of course there are other sources

which may be consulted, as well as accurate (but

expensive) model tests. Open water efficiency can beapproximated from characteristics of the propellers with

the segmental type sections (KCA, AEW, MA, etc.) even if

custom fixed pitch or controllable pitch propellers are used.The Wageningen B-Series propeller data can be used for

slower vessels. Regression equations for AEW and KCA

series are respectively given in Blount and Hubble (1981)

and Radojcic (1988), for example.

Vessels Driven by Water Jets

For fast vessels with speeds above 30 knots water jets

may be the preferred choice for propulsor. Quasi- propulsive efficiency for water jets is slightly different than

propellers and is D=PR HJ, where P is pump

efficiency and J is jet efficiency. R and H have the samename and meaning as for propellers, but not the same

values. H and J depend on the specific loading of thewater jet. Reduced efficiency is directly related to

increased loading – a phenomenon which will occur during

shallow water operation (See Figure 24). Note the

reduction in efficiency at the same vessel speed when only

two of the three water jets are used.

Water jet performance data are usually not readily

available, so estimation of the quasi-propulsive efficiencywithout consulting the water jet manufacturer is not

recommended. However, efficiency increases with ship

speed and is typically 0.60 and 0.70 for vessel speeds of 30

and 40 knots respectively, as given for example by

Svensson (1998) for high speed ferries (see Figure 24).

Figure 24 - KaMeWa (now Rolls-Royce) water jet sea trial

results (Svensson, 1998)

The powering performance (prediction of speed) of a

water jet propelled vessel can be determined by finding thespeed at which the resistance curve and the power contour

of interest intersect.

Resistance Evaluation of High Speed Vessels in Shallow

Water

The approach presented here is not new and is based

on the fact that L/h is the dominant factor and that other

parameters (L/T, CB, hull cross-section, etc.) are of

secondary importance. It is also assumed that shallow

water influences only residuary resistance, while frictionalcomponent is essentially unchanged. Shallow water

residuary resistance may be calculated from SWRF given

by R Rh/R Rd = f(Fnh, L/h), which is obtained either frommodel tests, or calculated from linearized wave theory for

the resistance of a ship in deep and shallow water. In both

cases results are expressed in terms of a ratio of shallow to

deep water residuary resistance (i.e. SWRF), rather than theabsolute resistance.

Published model tests for shallow water are rare.

Sturtzel and Graff (1963) describe shallow water model

tests conducted for 15 different round bilge hulls

encompassing a wide range of L/B, B/T, CB, and L/1/3.

However, a single diagram for SWRF is given, shown in

the right side of Figure 25. This diagram is a starting point

for development of the simple resistance prediction method

used here (from Radojcic, 1998), Equations 1 to 3 wereused to develop the graph on the left side of Figure 25.

Figure 25 – Approximated (by EQ 1-3) (left) and original

(right) SWRF of Sturtzel and Graff series

(Radojcic, 1998)


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RRh /RRd = a+b*Fnhc EQ 1

a = EXP [(-0.00370+0.00265*(L/h))/

(1-0.33444*(L/h)+0.03037*(L/h)2)]

b = 1/[-3.5057+0.0312*(L/h)2+14.7440/(L/h)]

c = 2.0306+10.1218*(atan[((L/h)-4.6903)/

0.7741]+/2)/

(RRh /RRd)max = 0.97476+0.01495*(L/h)3 EQ 2(RRh /RRd)critical = (R Rh/R RD)max-(L/h)/20 EQ 2a

(Fnh)max = 0.92226-0.30827/(L/h)1.5 EQ 3

(Fnh)critical = 0.95 EQ 3a

A SWRF could also be obtained from linearized wavetheory with a simplified hull, taken from, for example,

Millward and Sproston (1988), Millward and Bevan

(1985), or it may be calculated separately. SWRF as a

result of these calculations for a T/L=0.03 is illustrated inFigure 26. SWRF for other hull forms would be similar

(Hofman and Radojcic, 1997).

Figure 26 - SWRF obtained from linearized wave theory

with a simplified hull (source: M. Hofman)

The depth of sea route may vary, between say, depth

h1 and hn, or maybe between h1 and deep water (h=), inwhich case resistance curves for several water depths are

required. Using SWRF for ratios L/h1 to L/hn enables

calculation of R h1 to R hn. It is sufficient, however, toconnect the peaks of resistance humps, i.e. to take the

envelope of R h1 to R hn, as shown in Figure 27. This

envelope may be calculated from (R Rh/R Rd)critical and(Fnh)critical, given by equations 2a and 3a. It should be noted

that resistance peaks called critical peaks (denoted "o") do

not coincide with SWRF peaks called maximal peaks

(denoted ""). Both are shown in Figure 27. In the SWRFgraph (Figure 25), the values corresponding to critical

peaks are a bit lower than the maximal peaks. Differences

between critical and maximal peaks (although practicallynegligible) are explained in Hofman (1998) paper.

Obviously, (L/h)/20 in Equation 2a is some form of a

correction factor while (Fnh)critical=0.95 is an approximate

value. The part of the resistance curve for the subcritical

regime for shallowest possible water depth h1 may be

calculated according to Equation 1.

Figure 27 Resistance in various water depths (with

maximal and critical peaks)

The equations are relatively simple and are suitable for

programming enabling approximate evaluation of shallow

water resistance; hence complicated theoretical approaches

(too complex for daily practice) are avoided. It should benoted, however, that the above equations evaluate

resistance increments in the subcritical region only since

the primary problem for a vessel is to overcome the large

resistance hump around the critical speed; resistancedecrements in the supercritical regime are neglected since

they are less important.

Shallow water resistance increments (+) anddecrements (), valid for a particular sea route, areschematically shown in Figure 27. Resistance decrements

in supercritical speed regime will allow a bit higher speedthan in deep water, or the same speed will be maintained

with lower rpm and power consumption. On the other

hand, if propulsors are selected according to deep waterresistance, then resistance increments in the critical region

will pose serious problems, such as reduced service speed,

cavitation, engine overloading, vibrations, etc.

Propulsive Efficiency Evaluation for High Speed

Vessels in Shallow Water

Propulsive coefficients will change in shallow water asdiscussed previously. Obviously, shallow water corrections

to propulsive coefficients are necessary but are not readily

available. There have been some attempts to determine a

general approach for evaluation of SWPF as for instance in

Radojcic (1998) and Filipovska (2004). These approacheswere based on Lyakhovitsky’s idea (see Lakhovitsky

2007), but without success due to insufficient data, so

further research in this area is recommended.

Consequently, due to insufficient data supporting values forSWPF, the recommended approach for predicting powering


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performance is to recalculate the open water efficiency for

the propulsor based on the resistance curve once it has been

adjusted for shallow water. This approach accounts for the

change in open water efficiency due to increased thrust

loading on the propulsor, but does not attempt to address

changes in H or R . For propeller driven vessels, this is

done using the procedure defined in Blount and Fox(1976), using the shallow water resistance without altering

H and R . For water jet propelled vessels, this is done byoverlaying the shallow water resistance curve on the same

performance map provided by the manufacturer for deep

water operation (which includes an assumed H and R ) –see Appendix 3.

CONSIDERATIONS FOR VESSEL DESIGN FOR

SHALLOW WATER OPERATION

As mentioned above, shallow water resistance may bemuch larger around critical speed than is in deep water,

however for supercritical speeds it is only a bit lower.

Therefore, a real problem for vessels intended to sail at

supercritical speeds is to overcome large resistance hump

around the critical speed. An interesting paper on this

subject was presented by Heuser (1994).

According to Hofman and Radojcic (1997), the only

way to avoid the negative influence of water depth onresistance is to avoid the critical region itself (See Figures

10 to 12). Obviously, the largest power increments and

vessel generated waves occur when water is very shallow

(low h/L ratio) and when Fnh0.95 or FnL0.4 and thushaving a design point in (or around) these conditions

should be avoided. As the water becomes deeper and h/L

increases, a somewhat higher FnL becomes critical. Sowhen h/L0.5 (practically deep water) speedscorresponding to FnL0.5 form the wave lengths that areequal to ship length; this is a well known deep water

phenomenon that should be avoided. In other words, when

h/L increases from 0.1 to 0.5, the corresponding high-

resistance Froude numbers1 are FnL=0.3-0.5 and FnL=0.3-

0.7 (with peaks at FnL0.4 and FnL0.5), respectively. So, ahigh-speed vessel which will successfully sail in all water

depths – shallow and deep – must be able to operate in the

supercritical regime, i.e. above FnL0.7. This vessel alsomust be able to accelerate through the critical regime

rapidly. Typical wave pattern of a supercritical vessel (i.e.

intended to operate in the supercritical regime) is depictedin Figure A3.

To reduce wave wash, the depth–critical speed range

to be avoided (Cox, 2000) should be more than 75% andless than 125% of the speed corresponding to a depth

Froude number of 1.0. High-wash speeds generally

correspond to FnL=0.35-0.65.

1 In the context of this paper speed that matches the high-resistanceFroude number might be called sustained speed.

This means that fast littoral and inland vessels should

be designed (matched, adapted) according to the water

depth. Consequently, the right choice of vessel speed and

waterline length should be decided in the very early design

phases, as there isn’t any possibility to improve poor performance later on.

For littoral and inland vessels that operate in shallowwaters, propulsor size selection must be tailored to

operation in these conditions. For a properly sized

propulsor for deep water, when operating in shallow water,

poor efficiency around the hump is unavoidable. In any

case, propulsors that are adaptable to (or are less affected by) changes in resistance should be considered, as for

instance controllable pitch propellers, water jets, or

probably even special shrouded propellers.

If vessels are to operate in shallow water, complex

propulsion plants (engines, gearbox ratios, propellers,

water jets) may be required according to the constraints

dictated by the expected water depth. Flush type water jetshave an advantage of being in the hull and not bellow thehull as are, for instance, various kinds of propellers. This

inherently reduces the vessel’s draught. Low-draught

propellers are typically surface piercing propellers but theyare not “elastic” to cope with large resistance and speed

variations (except if equipped gearboxes with multiple gear

ratios). Particular attention should be paid to intermediate

speeds, i.e. the critical region, and in this respect the

margins suggested by Blount and Bartee (1997) should beconsulted.

Actually, all known “deep water” approaches for

improving performance, and in the first place “the longer,the better” theory, are less effective in shallow water and

are even detrimental in extremely shallow water (as ratio of

h/L becomes the most influential parameter). The only

measure that really “works” in all regimes is to reducedisplacement (weight) as much as possible, but usually that

is easier to say than to achieve.

CONCLUSIONS

The following conclusions can be drawn from the

work contained herein:

Shallow water effects can be noticed whenever

h/LOA0.6-0.7 Three speed regions may be detected:- subcritical region (Fnh


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effects on propulsive factors are not investigated nor

defined accurately enough

By far the largest power increment and vesselgenerated waves occur when h/L ratio is low and

Fnh0.95 or FnL0.4 A high-speed vessel which will successfully operate in

all water depths must be able to operate in thesupercritical regime, i.e. at speeds above FnL0.7.

High speed craft wave wash cannot be reduced just byoptimizing the hull form since wave period generally

increases with speed and doesn’t decay quickly. The

wave wash decay is smaller in shallow than in deepwater and is a function of h/L. The appropriate

measure of wave wash in shallow water is wave height

and wave energy.

Design speed and waterline length, must be carefullyselected for vessels designed for littoral and shallowwater operations. Traditional “deep water thinking”

that “longer is better” might be counter to improving

performance in shallow water. Reduction of displacement (weight) is the onlymeasure that can effectively lower both, resistance and

wave wash.

Propulsor type and size should also be tailored to theshallow water requirements/operation.

ACKNOWLEDGEMENTS

The authors would like to thank Donald L. Blount for

his kind assistance with identifying reference and providing

a keen eye and mind in the editing process.

REFERENCES

Allison, J., "Marine Waterjet Propulsion", SNAME

Transactions, Vol. 101, 1993.

Allison, J., Goubault, P., "Waterjet Propulsion for FastCraft - Optimized Integration of Hull and Propulsor", FAST

1995, Lubeck –Travemunde, 1995.

Andersen, P., Guldhammer, H., "A Computer-Oriented

Power Prediction Procedure", CADMO Conference,

Trieste, 1986.

Bailey, D., "The NPL High Speed Round BilgeDisplacement Hull Series", RINA Maritime Technology

Monograph No 4, 1976.

Bailey, D.,"A Statistical Analysis of Propulsion DataObtained from Models of High Speed Round Bilge Hulls",

RINA Symp. on Small Fast Warships and Security Vessels,

London, 1982.

Blount, D., Fox, D., "Small Craft Power Prediction",

Marine Technology, Vol. 13, No. 1, 1976.

Blount, D., Hankley. D., “Full Scale Trials and Analysis of

High Performance Planing Craft Data”, Trans. SNAME 1976.

Blount, D., Fox, D., "Design Considerations for Propellers

in a Cavitating Environment", Marine Technology, Vol. 15,

No. 2, 1978.

Blount, D., Hubble, N., “Sizing Segmental Section

Commercially Available Propellers for Small Craft”,

SNAME Propellers ’81 Symposium, Virginia Beach, 1981.

Blount, D., Bartee, R., "Design of Propulsion Systems for

High-Speed Craft", Marine Technology, Vol. 34, No. 4,

1997.

Blount, D. L., McGrath, J. A., “Resistance Characteristics

of Semi-Displacement Mega Yacht Hull Forms”, RINA Int.

Conf. On Design, Construction & Operation of Super and

Mega Yachts, Genova, 2009.

Cassella, P., Paciolla, A., "Evaluation of DTMB's Series 64

Hull Power by Means of Regression Analysis", Tecnica

Italiana, No. 3/4, 1983 (in Italian).

Cox, G., “Sex, Lies, and Wave Wake”, RINA Symp.

Hydrodynamics of High Speed Craft: Wake Wash &

Motions Control, London, 2000.

Doyle, R., Whittaker, T., Elsasser, B., “A Study of Fast

Ferry Wash in Shallow Water”, FAST 2001, Southampton,2001.

Filipovska, M., “Analysis of Shallow Water Influence onPropulsive Coefficients”, Diploma thesis, University of

Belgrade, Faculty of Mech. Engng, Dept of Naval

Architecture, Belgrade, 2004 (in Serbian).

Fung, S., Leibman, L., "Revised Speed-DependentPowering Predictions for High-Speed Transom Stern Hull

Forms", FAST 1995, Lubeck-Travemunde, 1995.

Hadler, J., Hubble, N., "Prediction of the Power

Performance of the Series 62 Planing Hull Forms", Trans. SNAME, 1971.

Hadler, J., “The Prediction of Power Performance onPlaning Crafts”, Trans. SNAME, 1966.

Heuser, H., "Inland and Coastal Vessels for Higher

Speeds", 21st WEGEMT, Duisburg, 1994.

Hofman, M., Radojčić, D., “Resistance and Propulsion of

Fast Ships in Shallow Water”, Monograph, University of

Belgrade, Faculty of Mechanical Engineering Dept of

Naval Architecture, Belgrade, 1997 (in Serbian).


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Hofman, M., "On Optimal Dimensions of Fast Vessels for

Shallow Water", PRADS '98, The Hague, 1998.

Hofman, M., Kozarski, V., “Shallow Water Resistance

Charts for Preliminary Vessel Design”, I.S.P. Vol. 47, No.449, 2000.

Holtrop, J., "A Statistical Re-Analysis of Resistance andPropulsion Data", I.S.P. Vol. 31, No. 363, 1984.

Hubble, N., "Planing Hull Feasibility Model", Report of

DTNSRDC/SPD-0840-01, 1981.

Lyakhovitsky, A., “Shallow Water and Supercritical

Ships”, Backbone Publishing Company, Hoboken, NJ,

2007.

Lewthwaite, J., “Wash Measurements on Inland

Waterways using the WAVETECTOR Buoy”, RINA

Conference on Coastal Ships & Inland Waterways 2,

London, 2006.

Millward, A., Bevan, G., "The Behavior of High Speed

Ship Forms when Operating in Water Restricted by a Solid

Boundary", RINA W2 paper issued for written discussion,1985.

Millward, A., Sproston, J., "The Prediction of Resistance of

Fast Displacement Hulls in Shallow Water", RINA Maritime Technology Monograph No. 9, 1988.

Nwogu, O., “Boussinesq Modeling of Ship-Generated

Waves in Shallow Water”, PIANC USA Annual Meeting,

Portland, 2003.

PIANC 2003 – “Guidelines for Managing Wake Wash

from High Speed Vessels”, Report of WG 41 of International Navigation Association, Brussels, Belgium.

Phillips, S., Hook, D., “Wash from Ships as they approach

the Coast”, RINA Conference on Coastal Ships & Inland

Waterway II, London 2006.

Radojcic, D., "Mathematical Model of Segmental Section

Propeller Series for Open-Water and Cavitating Conditions

Applicable in CAD", SNAME Propellers '87 Symposium,

Virginia Beach, 1988.

Radojcic, D., "An Engineering Approach to Predicting the

Hydrodynamic Performance of Planing Craft Using

Computer Techniques", Trans. RINA, Vol. 133, 1991.

Radojcic, D., Rodic, T., Kostic, N., "Resistance and Trim

Predictions for the NPL High Speed Round BilgeDisplacement Hull Series", RINA Conference on Power,

Performance and Operability of Small Craft, Southampton,

1997.

Radojcic, D., “Power Prediction Procedure for Fast Sea-

Going Monohulls Operating in Shallow Water”, The Ship

for Supercritical Speed, 19th Duisburg Colloquium, 1998.

Radojcic, D., Princevac, M. Rodic, T., “Resistance andTrim Predictions for the SKLAD Semidisplacement Hull

Series”, Oceanic Engineering Int., Vol. 3, No. 1, 1999.

Radojcic, D., Grigoropoulos, G. J., Rodic, T., Kuvelic, T.,

Damala, D.P. “The Resistance and Trim of Semi-

Displacement, Double-Chine, Transom-Stern Hull Series”,

FAST 2001, Southampton, 2001.

Savitsky, D. “Hydrodynamic Design of Planing Hulls”,

Marine Technology, Vol. 1, 1964.

Sturtzel, W., Graff, W.,"Investigation of Optimal Form

Design for Round-Bottom Boats", Forschungsbericht des

Landes Nordrhein-Westfalen, Nr. 1137, 1963. (in German).

Svensson, R., "Waterjets Versus Propeller Propulsion inPassenger Ferries", Vocational Training Centre, Hongkong, 1998.

Toro, A., “Shallow-Water Performance of a Planing Boat”,Trans. SNAME , 1969.


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APPENDIX 1 - Wave wake energy evaluation (numerical example)

A generic wave trace measured at 50 m from the vessel’s track is depicted in Figure A1. It shows a maximum waveheight of 0.26 m and an associated period of 6.7 sec.

Figure A1 - Wave wash trace at 50 m off vessel track

At this distance, the wave energy can be calculated as follows:

E = 1960H2T2 = 1960 x 0.262 x 6.72 = 5947 J/m 5950 J/m .

For comparison we can look at the wave energy present at a distance of 200 m off of the vessel’s track. Using the deepwater relationship for decay rate developed by the University of Southampton (Lewthwaite 2006), the wave height at a

distance of 200 m can be calculated as follows:

H200 = HX / (200/x)0.35 = 0.26 / (200/50) 0.35 = 0.16 m .

Consequently, the wave energy at 200 m may be evaluated as

E = 1960H2T2 = 1960 x 0.162 x 6.72 = 2254 J/m 2250 J/m .

Therefore it can be concluded that the energy is below the 2825 J/m restriction of the State of Washington. However,if the same wave would be traveling in the shallow water the decay rate would be different, and definitely smaller than in

deep water (see Figure 6), so wave energy at a distance of 200 m would most probably be higher than the allowable limit.

APPENDIX 2 - Influence of length Froude number and depth Froude number on wave pattern and height

To investigate the combined influence of length Froude number and depth Froude number on wave height, the Michlet

Software - Version 8.07 ( Leo Lazauskas) was employed to calculate surface wave patterns for various length Froude

numbers and depth Froude numbers.

An 86 x 11.5 m NPL hull form, generated with Delft Ship, was used in the calculations. The full scale dimensions

were selected to correspond to the Yacht Ectasea. The results are presented in Figure A2. The images in the center vertical

column are for a constant length Froude number (F nL 0.43), while depth Froude number increases from 0.65 to 1.5

(corresponding to Figures 1 through 3 of main text). On the other hand, the images in the horizontal row have a constantdepth Froude number (Fnh=0.90), while length Froude number increase from 0.26 to 0.61.

The progression from the top to bottom of the vertical figures illustrates the wave pattern changes associated with

transitioning from the subcritical regime to the supercritical regime. Relative to this, the horizontal figures, all evaluated

for the same depth Froude number, depict somewhat different wave patterns and heights with the different length Froudenumbers. Diverging bow wave angle (Kelvin angle) however, is the same for all horizontal figures. The middle figure has

the maximum wave height as Fnh=0.9 and FnL0.4.

Wave pattern of the same hull form as discussed above but for much higher Fnh and FnL (hence the supercritical

regime regardless of water depth) is depicted in Figure A3.


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APPENDIX 3 - Numerical Example

The purpose of this appendix is to provide a numerical example demonstrating the application of the resistance and

powering prediction process recommended in this paper. A powering prediction is provided for water jets. The calculations

are performed for a vessel similar to the yacht Ectasea, but with less installed power . Input parameters for predicting theresistance of the round bilge hull form is as follows:

= 1880 t h = 15 m (shallowest expected on route)LWL = 77 mLCB = 36.3 m PB = 2 x 14 MW

Deep water resistance R Td is calculated from the original NPL systematic series model data using the Froude

extrapolation method. The ITTC 1957 model-ship friction line was used with CA = 0.0000 (see Table Figure A1). The

appendage resistance was calculated according to R APP = (R F + R Rd) * 0.10.

R Rh/R Rd (SWRF) is determined from the Equation 1 in the main text. The equation is used to calculate the shallow

water resistance in subcritical range only for speeds up to F nh = 0.90 for the assumed shallowest expected water depth on

route.

Table A1 - Deep water and subcritical shallow water resistance (shallowest water depth h=15 m, L/h=5.1)

To develop a conservative resistance ‘envelope’, the resistance curve based on shallowest water depth and critical

peaks for other, deeper water depths (h>15 m, corresponding to L/h


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Figure A4 – Resistance envelope curve

Deep water and shallow water resistance curves are plotted on the water jet performance map as shown in Figure A5.A twin water jet application was selected, the maximum predicted speed in each case is identified by the intersection of the

maximum power contour (14 MW) and the relevant resistance curve. The results indicate the speed loss when operating in

shallow water with a depth of 15 m is predicted to be about 7 knots relative to deep water performance! The OPC’sassociated with deep and shallow water operation are 0.54 and 0.42 respectively; representing a 22% reduction in

efficiency! Also note the cavitation margin – the resistance curve lies in the Zone 2 cavitation region and its proximity to

the Zone 3 curve suggests the water jets are on the verge of thrust breakdown at about 23 knots.

Figure A5 – Plot of deep and shallow water resistance on a typical Rolls-Royce water jet performance map

0

200

400

600

800

1000

1200

1400

1600

5 10 15 20 25 30 35 40 45

H U L L R E S I S T A N C E

( k N )

SPEED (kts)

SHALLOW WATERRESISTANCE

DEEP WATER RESISTANCE

CRITICALPEAKS

SUB CRITICALDATA

V (kts) RT (kN )

16.0 246

18.7 452

21.4 1133

22.7 1357

25.4 1462

29.3 1448

35.9 1459

RESISTANCE @L/h = 3

RESISTANCE @L/h = 4

MAXIMAL PEAKS

0

200

400

600

800

1000

1200

1400

1600

5 10 15 20 25 30 35 40 45

N E T T H R U S T

&

H U L L R E S I S T A

N C E

( k N )

3 % m e c h a n i c a l l o s s e s i n c l u d e d

SPEED (kts)

Zone 3 Zone 2Zone 1

2 * 22000 BKW

2 * 16000 BKW

2 * 12000 BKW

2 * 6000 BKW

2 * 14000 BKW

2 * 10000 BKW

2 * 4000 BKW

2 * 2000 BKW

2 * 8000 BKW

2 * 18000 BKW

2 * 20000 BKW

SHALLOW WATER RESISTANCE

DEEP WATER RESISTANCE

P = 2 X 14mwV = 27 KTS

RTd= 1100 KN

d = 0.54

P = 2 X 14mwV = 21 KTS

RTh= 1100 KN

d = 0.42

SHADED AREA REPRESENTSINCREASE IN RESISTANCE

Radojcic.on High Speed Mono.2010.SYMP

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