Resistance Components of High Speed Small Craft Burkhard MUller-Graf W E G E M T Association Page 2
Small Craft Technology - Athens October 6 - 1 1 1997
Parti
Resistance Components
of
High Speed Small Craft
Dr.-Ing. Burkhard Müller-Graf
WEGEMT Association
SUMMARY
The lecture gives a survey of the total resistance and its numerous components for semi-displacement hulls, planing hulls, fast catamarans, hydrofoil craft, aircushion vehicles (ACVs) surface effect ships (SESs) and SWATH ships in unrestricted and smooth water under trial conditions. The causes of the various resistance components and their subcomponents as v/ell as the procedures for their determination are treated. For each of the seven types of vehicles the special structure of the total resistance is described. Special emphasis is given to the differences in the resistance composition between the theoretically synthesized total resistance and the one which is obtained by model tests.
Resistance Components of High Speed Small Craft Burkhard Müller-Graf WEGEMT Association Page 3
Table of Content Page
SUMMARY 2
1. RESISTANCE COMPONENTS OF HIGH SPEED SMAXU CRAFT 4
1.1 Introduction 4
1.2 Primary Resistance Components 4
1.2.1 Hull resistance Rjj 5
1.2.2 Drag due to lift R L 12
1.2.3 Appendage drag R ^ 14
1.2.4 Air- and wind resistance R ^ 16
1.2.5 Parasitic drag Rp/j^ 17
1.2.6 Trial resistance components Z R J R 18
1.3 Components of the Model Resistance 19
1.4 Composition of the Total Resistance for Different Types of Vessels 20
1.4.1 General considerations 20
1.4.2 Semi-Displacement Round Bilge Hulls 20
1.4.3 Planing Hulls 23
1.4.4 Fast Catamarans 27
1.4.5 Hydrofoil Craft 32
1.4.6 Aircushion Vehicles 35
1.4.7 Surface Effect Ships (SES) 39
1.4.8 SWATH Ships 45
1.5 Added Resistance due to Hull Propulsor Interactions 48
1.6 Added Resistance due to Environmental Effects 49
1.6.1 Added resistance due to shallow water effects 49
1.6.2 Added resistance due to waves 50
1.7 Final Remarks 50
1.8 Nomenclature 51
1.9 Bibliography 57
Resistance Components of High Speed Small Craft Burkhard Müller-Graf WEGEMT Association Page 4
1. RESISTANCE COMPONENTS OF HIGH SPEED SMALL C R A F T 1.1 Introduction
The total resistance of high speed marine vehicles includes more resistance compo-nents than that of slow displacement ships. An optimum design of a fast and uncon-ventional vehicle requires a fundamental knowledge of all the different components and their causes. In order to minimize building costs and to optimize operational costs a reliable power prediction in an early design stage is imperative for these vessels. A correct power prediction can be obtained solely by taking into account each of the oc-curing resistance components carefully. Some of them are amenable to analytical cal-culations, most of them have to be determined by empirical data or semi-empirical es-timates. The use of speed independent allowances as common in the case of the ap-pendage drag or the additional trial resistance is no longer appropriate.
For another reason, the designer of high speed marine vehicles must be familiar with all the occuring resistance components, their causes and their relative contributions to the total resistance. Due to the high specific power of these vessel types, hull and ap-pendages must be designed for minimum resistance within the given design limits. By
selecting proper main dimensions, hull forms and appendage types, the prevailing re-sistance components in the design speed range can be minimized. The values of the resistance components are changing with speed. Due to this fact, optimum hull form
and optimum appendage type can become very different for each of the three main speed regimes of fast marine vehicles, for the semi-displacement region, the pre-planing region and the fally pre-planing region.
The following sections examining the resistance components occuring above the hump speed, i.e. at Froude Numbers related to the waterline length of
Fn = Vs/Vg • LwL > 0,45 (1.1)
\
The considerations are not limited to a special ship length. They are also valid for the super large high speed monohulls which are of interest today.
The symbols used are those given by the ITTC Symbols and Terminology List 1987 and 1993 [1, 2] or they have been developed according to the ITTC recommendations. The definition of the used symbols, i f not explained in the text, is given in section 1.8, in the nomenclature.
1.2 Primary Resistance Components
The total resistance Rj of a hull is the sum of the horizontal forces which are created opposite to the direction of motion when the lower part of the hull moves through the water and the upper part with the super structure through the air. The resistance of high speed marine vehicles is composed of different components. This number is
greater than in the case of slow displacement ships and their relative contribution to the total resistance depends mainly on speed and the type of lift, carrying the weight of the vessel. In general the total resistance of high speed marine vehicles is made up of five primary resistance components as shown by Fig. 1.2.1:
Resistance Components of High Speed Small Craft Burkhard MUIler-Graf W E G E M T Association Page 5
Hull resistance Rp^ kN Drag due to lift Rp kN A.ppendage drag R ^ kN Air- and wind resistance R ^ kN
Parasitic drag RRAR ^
Total resistance RT = R R + RP + I R A P + RA^A + ZRPAJ, kN (1.2)
For vehicle types, which are supported partially or mainly by hydrodynamic lift of the hull surface, the drag due to Uft is considered as a part of the hull resistance. Each primary component includes numerous subcomponents which in turn are composed of the two fundamental resistance elements due to
- pressure and - viscosity.
The first two primary components interact one with the other. The subcomponents of the primary components can interact with each other in a complicated way which will not be treated here.
1.2.1 Hull resistance R^
The hull resistance includes all those resistance components which are generated by direct or indirect contact of the bare or naked hull with the water. Spray rails and
tran-som v/edges or trim^ flaps are considered to be a part of the hull, and not a part of the appendages.
In the hullbome mode the hull resistance RH of a high speed marine monohull is com-posed of five main components as indicated by Fig. 1.2.2:
RH ~ Rw Rs Rv RsR RwE kN (1.3)
The hull resistance of a high speed catamaran includes six main components (Fig 1.2.3):
RH ~ Rw + Rs Ry RsR RwE RiCAT ^
The hull resistance of a Surface Effect Ship is made up of four main components (Fig 1.2.4):
RH " Rw + Rs + Rv RsE kN (1.5)
1*2,1,1 Wavemaking resistance R^y^
This component, caused by the formation of surface waves, includes three subcompo-nents (Fig. 1.2.2-.4):
Resistance Components of High Speed Small Craft Burkhard Müller-Graf WEGENfT Association Page 6
with
Rwp wave pattern resistance due to the generation of free wave systems of
trans-verse and divergent waves. This component is the greatest one in the speed area 0,4 < < 0,8 and diminishes with increasing speed.
RwB wavebreaking resistance caused by energy losses due to the breaking of the bow wave. It disappears at F^ > 0,6.
Rp hull pressure resistance, the horizontal component of the normal force N at the bottom keeping the hull on the inclined pressure niveau (Fig. 1.4.3.3).
Due to the generation of hydrodynamic lift it is defined as the induced resis-tance similar to the induced drag of wings.
wavemakine resistance
and part
If the wavemaking resistance is determined by model tests, this component is included in the residual resistance RR which contains moreover all subcomponents caused by pressure origin like the induced resistance, the pressure resistance due to spray and
spray rails and due to the trim flap.
1.2.1.2 Spray resistance
The spray resistance is caused by the spray formation and consists of a pressure and a viscous subcom.ponent (Fig. L2.2 - .4):
Rs ~ Rsp RsF kN ( 1 . 7 )
with the relationship
Rs = Rsp(Fn) + RsF(Rn, W , )
with the parameters of similitude
Rn = (VsR • LSR)/ V (Reynolds Number) - ( 1 . 8 ) Wn = (VsR^- dsR • p)/a (Weber Number) - ( 1 . 9 )
m/s with
VgR spray velocity
LSR length of the spray at or besides the hull m V kinematic viscosity of water
dsR spray thickness
m^/s m
t/xn
N/m p mass density of the water
a surface tension
Rsp pressure resistance due to the generation of the spray caused by the stagnation pressure at the
Resistance Components of High Speed SmaJi Craft Burichard Müller-Graf W E G E M T Association Page 7
Rsp frictional resistance due to the friction of the spray
sheet at the above water surface of the hull. kN A useful method to calculate the spray pressure resistance component is at present not
available.
The viscous component cannot be computed likewise because:
- the spray wetted area of the hull sides is not accurately definable by visual or pho-tographical observations. This part of the hull is mostly hidden by the spray sheet
[3].
- the velocity of the spray sheet is unknown. In a first approach the velocity can be assumed to 80 per cent of the speed of advance.
- despite the fact, that the spray is fully turbulent after breaking out of the watersur-face, a correct frictional resistance coefficient cannot be determined because the length LSR wetted by the spray is unknown.
- no useful correction method for the frictional spray resistance has been developed taking into account the deviation of this component from the direction of speed. At present this component is neglected for planing hulls and for round bilge hulls [4].
It must be mentioned that the spray cannot generate a classical wave system. There-fore the large spray at the There-forebody of super slender hulls cannot be considered as a hull wave and its resistance is not a component of the wave resistance.
L2.1.3 Viscous resistance Ry
This main component is composed of the fiïctional resistance Rp and the viscous pres-sure resistance Rpy (Fig. 1.2.2 - .4)
Rv - (Rp/cosG) + Rpv kN(l • 10)
1.2.1.3.1 Frictional resistance R F
The frictional or tangential resistance due to shearing forces of the water within the boundary layer of the hull becomes increasing with speed above F^ = 1,0 the largest resistance component of the hull resistance. Rp is assumed to act prallel to the D W L .
Therefore Rp is projected in the direction of motion according to Savitsky [9] by l/cos© as shown by (Fig. 1.4.3.3).
with
0 change of running trim referred to trim at rest ^ deg.
This correction is generally neglected, because with exception of planing hulls, the running trim of fast advanced marine vehicles decreases at speeds Fn > 0,5 and
be-comes smaller than 0 = 3 deg. Therefore the correction gets smaller than 0,13 per cent and is disregarded at model tests. In the follov^ng considerations it is taken into
ac-count for those cases, where a higher running trim can be expected.
Resistance Components of High Speed Small Craft Burkhard Müller-Graf WEGEMT Association Page 8
2
Rp = Sws • (CFS + ACp). Ps/2 .V,V2 k N r i . m
for the full-scale vessel where symbols denote:
m/s
2
m Vg speed of advance of the vessel
SwHS wetted surface of the ship
Cps specific frictional resistance coefficient according to the ITTC-1957-Line Cp = 0,0075/(logioRn - 2)^ _ (1.12) ACp roughness allowance which takes into account the resistance increment
due to structural shell roughness (welds, waviness, fouling, paint rough-ness).
Values of ACp depending on the used hull material are given in Table No. 1 for hulls not longer than approximately 50 m.
Table No. 1
Hull material ACp • 10'^
GR? 0
coDDered wooden hulls 0 plywood hulls covered with epoxy resin 0
plywood painted 0,1
planked wooden hull 0,2 aluminium
steel painted
0,1
0,2 - 0,25
steel painted (tropics) 0,4 At hull lengths L ^ > 50 m the roughness allowance ACp has to be replaced by the
model ship correlation factor C^ which takes into account the scale effects due to vis-cosity.
In most cases, particularly in the design stage the wetted surface at rest S^H without the immersed part of the transom is used. The effective wetted area underway, S^HE?
including the bottom area, spray area and area of wetted sides, can become larger or smaller than the area at rest, depends on the speed and on the hull form respectively of the vessel type. The effective wetted area must be determined with some exceptions
[4] on the basis of model tests by visual and photographical observations of the model or by means of electrical wetness probes [3^.
1.2.1.3.2 Viscous pressure resistance Rpy
The pressure resistance of viscous origin
with
Cpv viscous pressure resistance coefficient _
SwHF wetted surface underwav m is caused by viscous effects of the hull shape and by flow separation and eddymaking.
Because these phenomena disappear at speeds higher than = 0,6 this resistance component can be neglected for F^ > 0,6.
1.2,1.4 Spray rail resistance R^R
If the hull is equipped with spray rails, the hull resistance is increased by (Fig. 1.2.2 -.4):
RsR = RsRP + RsRF kN(1.14) with
RsRp pressure resistance of the spray rails caused by the deflection of the spray sheet in the longitudinal direction,
RsRp frictional resistance of the wetted area of the pressure side of the spray rails.
The deflection of the spray sheet in the transversal direction which generates most of the hydrodynamic lift of the sprayrails, does not cause an additional resistance com-ponent.
The pressure resistance component cannot be computed. For a correct calculation of the frictional resistance component the velocity of the spray at the rail and the specific turbulent frictional resistance coefficient are unknown [5^.
1.2.1.5 Trim flap resistance R^VE
By arranging a trim flap or a transom wedge, the hull resistance rises by (Fig. 1.2.2 -.4)
RwE ~ RwEP RwEF kN(1.15)
with
RwEP pressure resistance or induced drag of the transom flap or wedge due to
the generation of the lift L ^ ,
R ^ p can be calculated according to Savitsky and Brovm [6] by
RwEP = 0,0052 . LwE (5wE + 9) kN(1.16)
with
LwE = 0,046 . Ps • Vs^/2 • I^E • b^E • cosp • S ^ E kN(1.17) IwE chord length of the flap
b^E span of the flap or wedge flap or wedge deflection P deadrise of flap or wedge
m m
deg deg
Page 10
RwEF frictional resistance of the trim flap. In the case of a transom wedge this
component disappears, because the wetted area of the wedge is included in the wetted area of the hull bottom.
1.2.1.6 Hull interference resistance RJCAT
At catamarans the presence of two hulls nearby causes five additional resistance sub-components due to interference effects:
RicAT = ARwpi + ARspi + ARpuw + ARpow - ARpi kN(l. 18)
with
AR^Pj wave pattem resistance increment due to the superposition of the inner
bow and stem waves of the demihuUs.
At speeds > 0,4 the superposition causes an increase of the wave pat-tem resistance. It can be estimated for roimd bilge hull catamarans by means of experimental data [7]. For hard chine planing hull catamarans this resistance component can be found in Ref [27,40,41].
ARspi pressure resistance increment due to the superposition of the inner spray-formations at the centre line of the tunnel.
This component cannot be calculated. At model tests it is included in the residual resistance RR.
ARpijw frictional resistance increment due to the increased velocity at the inner
underwater sides of the demihuUs.
The contribution of this component to the total frictional resistance de-pends on the curvature of the inner waterlines of the demi-huUs and the tunnel width. This increment cannot be calculated. It does not exist at asymmetric demihuUs.
ARpow frictional resistance due to the spray wetting of the tuimel roof and the in-ner above water sides of the demihuUs. As a result of the collision of both inner spray formations and their additional reflection from the water sur-face, the tunnel sides and the tunnel roof are partially wetted. Because the wetted area cannot be determined, this interference resistance is not ame-nable to calculations. At model tests it is included in the residual resis-tance RR . At asymmetric demihuUs it does not exist.
ARpi negative interference drag. It is caused by an increase of the hydrodynamic lift at each demihull due to induced effects of the planing surface of one demihull on the planing surface of the other demihull.
On the basis of model test results, RJCAT is given by the difference between the
cata-maran resistance and the doubled resistance of a solely tested demihull
RicA.T ~ RTCA.T • 2RxDH ( 1 . 1 8 . 1 )
For hard chine planing hull catamarans, RJCAT can be determined by means of the test
results of the VWS Planing Hull Catamaran Series '89 [40,4i;.
1.2.1.7 Seal drag Rgr
and stem compliant seals of SES is build up of a oressure and shown bv Fie. L2.4:
RsE ~ RsEP • RsEF kN(1.19)
with
RsEP pressure drag of the RsEF frictional resistance
wavemaking k N kN
R SE resistance
maining part of the model resistance after deducting the wavemaking re-sistance, frictional resistance of the hull and the aerodynamic resistance
[8].
1.2.1.8 Total hull resistance R H
1.2.1.8.1 Speed range 0,45 < < 0,6
In the semi-displacement region the weight of the hull is supported mainly by hydro-static forces and increasingly with the speed to a small extend by hydrodynamic forces. The resistance of a monohull with spray rails and a transom wedge under trial condition is given by
RR ~ RWP RWB Rp + Rsp RSRP RWEP
+ ARsT + RF/COS0+ Rpv + RsF + RSRF kN(l .20)
The following resistance components are caused by the trial condition: AR^vv added resistance
ARc-p added resistance
kN kN resistance is the larsest resistance
resistance by 70 oer cent at maximum
1.2,1.8.2 Speed range 0,6 < F^ < 1,2
In the pre^planing region where the c ana
namic forces, the wavebreaking resistance Rum and eddymaking resistance creases with V^.
resistance Rvyp decreases with
The hull resistance is made up of
RH " RWP + Rp + Rsp + RSRP RWEP
ARAW + ARsT + RF/CÖS0+ RSF + R^^ kl^l(i.2i)
1.2.1.8.3 Speed range F^ > 1,2
In the fully planing region where the craft is predominantly supported by hydrody-namic forces of the hull bottom, the wave pattem resistance can become negligible
compo-nent, followed by the induced resistance and the spray resistance. The hull resistance is composed of
RH - Rp + RSP + RSR? RWEP
+ ARAW + ARsT + Rp/cos© + Rsp + RSRP kN(l .22)
1.2.2 Drag due to lift R
The m_ost effective way to reduce the hull resistance can be achieved by lifting up the hull partially or completely out of the water. Displaced volume and wetted area are reduced and by this, the ft-ictional resistance Rp and the wave pattem resistance R^^p decrease. The generation of lift causes a pressure resistance or induced drag Rp. Its contribution to the total resistance and its determination denends on the tvne of lift.
1.2.2.1 Induced drag due to hull lift R
At all immersed hull surfaces, mainly at the bottom hydrodynamic normal forces are developed increasingly with speed. The vertical component of the normal force N acts upwards as lift and downwards as suction force (Fig. 1.4.3.3).
The hull lift grows: - with speed,
- with the inclination of the flat bottom area in the direction of motion, - with the camber and
- with the aspect ratio of the bottom area which is given by
-AR = bpB /ApB = bpg/LpB - (1.23)
v^th
bpB span of the plane bottom area LpB length of the plane bottom area Ap3 bottom area bps • Lpg
m m
2
m
The resistance due to lift increases in the same measure as the normal force at the •
bottom increases:
Kp = N • sinx kN(1.24)
The lift component of the normal force at the bottom of the hull decreases with in-creasing deadrise.
If the vessel is supported by the hull lift nearly solely, the induced drag reaches its maximixm [9] with (Fig. 1.4.3.3)
Rp = V . p • g • tgx kN(1.25)
with
V displacement volume p mass density of water
g acceleration due to gravity
m^ t/m^
-2
Resistance Components of High Speed Small Craft Burkhard MUller-Graf WEGEMT Association Page 13
T angle between the mean buttock at 1/4 B
of the afterbody and horizontal plane imderway
X = To -H 0
XQ angle between mean buttock of the
afterbody and horizontal plane at rest 0 running trim
Straight and concave buttock lines or section shapes favour the development of lift. Convex buttock lines and section shapes develop lift in the entrance region and a suc-tion force in the area of maximum curvature. The curvature of the buttocks acts like that of the upper or lower side of a wing section in developing lift or suction forces
[10].
As a result of the convex hull shape and the small aspect ratio of the bottom area, the development of lift of the round-bilge hull is smaller than that of the planing hull having plane surfaces with a greater aspect ratio due to the smaller length to beam ra-tio Lp/Bpx of the vessel. At semi-displacement roimd bilge hulls addira-tional lift can be
generated by arranging spray rails together with a transom wedge. By means of well balanced lift forces, keeping the vessel at optimum running trim, the total hull resis-tance can be reduced at 0,6 < < 1,1 v^th one spray rail at each side by approx. 4 - 6 per cent and by two overlapping spray rails at each side by approx. 7 - 8 per cent [4,5'. The drag due to lift of the spray rails and the transom wedge is considered under item
1.2.1.4 and 1.2.1.5.
1.2,2.2 Induced drag due to foil lift D •
By the hydrodynamic lift of a bow and a rear foil the hull of a hydrofoil craft is lifted out of the water. The drag due to foil lift is given in general by
D L = (CL'/TC) •
X •
psw/2 • Vs' • S with C L lift coefficient C L = Lp /(psw/2 • Vs' • S) Lp foil lift S wing area b • cpsw mass density of seawater b wing span
c foil chord length
X wing length-ratio X = c/h kN(1.26) kN 2 m
t/rn
m m (1.27) The induced drag depends on the dihedral angle, aspect ratio, induced angle of attack, submergence, taper ratio and thickness ratio of the foils. This drag component which amounts to approximately 30 per cent of the total foilbome resistance is manifested by the trough behind the foil units and by the lateral waves originating at or above the foils. The induced drag of the fi-ont foil can be recovered partially i f the rear foil is positioned just under half the wave length behind the former.Resistance Components of High Speed Small Craft Burkhard Müller-Graf W E G E M T Association Page 14
1.2.2.3 Drag due to aerostatic lift Riv,
80 - 85 per cent of the weight of a Surface Effect Ship is supported by the aerostatic an
resistance
ary air around the fan intakes which is called "intake momentum by
RM = P A * Q T - V , kN(1.28)
with
PA density of air
Qx total volume flow entering the lift fans rn/s Vg speed of craft
t/rn
3
m/s
between skirt and watersurface intake momentum drae becomes likewise
122A Drag due to aerodynamic lift Ri A
1 ne bottom oi the wet-deck can generate an aerodynamic lift due to the ram-air pres-sure i f the wet-deck is inclined in the direction of motion. This inclination is caused by hydrostatic and especially by hydrodynamic trim. This lift causes drag= The drag due to lift of flat plates with end plates can be calculated with [11]. A first approxima-tion of can be achived on the basis of the ram-air pressure acting on the wet-deck area projected in the direction of motion.
RLA = p A / 2 - V R ' . B r L x - t g 0 kN(1.29)
with
Bj width of wet-deck
Lx length of wet-deck m m
m
VR hull speed plus v^nd velocity component in the direction m/s
of motion
RLA does not include the lift which is generated at the upperside of
a streamlined superstructure at high speeds. Whilst the lift can be computed in a first approach separately [12], the drag must be determined experimentally. In this case it is included in the aerodynamic profil drag R ^ .
0 inclination of the wetdeck in the direction of speed assumed to
be equal to the runnine trim deg
1.2.3 Appendage drag R ^
The appendage drag is one of the largest primary resistance number and
resistance
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The appendage drag is the sum of all drag subcomponents which are arising due to the presence of
- rudders and rudder shafts, - propeller shafts,
- struts and barrels, - strut palms,
- fins.
- skegs, keel and deadwood, - shaft and nacelle of z-drive, - waterjet inlets.
The drag subcomponents are skin friction drag, profile drag, interference drag, spray drag, induced drag and drag due to ventilation and cavitation. Most of these compo-nents increase with increasing profile thickness ratio and increasing cross-flow angle.
Each component can be calculated on the basis of drag coefficients or approximate formulas as compiled by Hoemer [11], Hadler [13] and Kirkman [14]. A complete review of all these formulas is given in the report of the High Speed Marine Vehicle
Committee of the 17th ITTC [15]. Drag coefficients of the whole shaft and rudder system are presented in Ref [16, 17, 28].
an
take into accoimt change due to the influence
They can be determined bv
thrust resistance
The thickness of the boundary layer 5(x) is defined for5 • 10''<R^<10^ by
5(x) = 0,37 • x f R j '
m (1.30) and for 10^<R„x< 10^ by 5(x) = 0,22 • XIRJ" m (1.31)The used Reynolds Number R^^ is given by
R„, = (X- V)/v (1.32)
The boundary layer profile uA^ has to be calculated by
uA^ - (y/5x)'^^ - (1-33)
with
X distance fi-om the intersection of the stem with the waterline to
Page 16
u velocity of the boundary layer m/s
V speed of advance m/s V kinematic viscosity ni'/s
y distance from the hull surface m If the appendage drag is determined by model tests, it corresponds to the difference of
resistance between the appended and the bare hull at the same running trim. With re-gard to scale effects, the frill scale appendage drag should be scaled up on the basis of
60 - 65 per cent of the measured value.
1.2.4 Air- and wind resistance R AA
hull and the superstructure which is not so streamlined as the under an eddying resistance due to the motion through still air and due tc r- and wind resistance RAA can amount at fast patrol craft approxi nents which are generated by
- the above water hull,
- the superstructure and brie
resistance. is the sum of the resistance
'catamarans and SWATH and the whole hull of hvd - the aerials, radoms, masts and
- the signal spars.
The resistance of each element can be calculated by means of empirical formulas [26], in general by
RAA = PA/2- • Ay • k N ( 1 . 3 4 )
with
PA mass density of air 1,266-10
VD hull speed plus wind velocit
-3
t/xn
V R = V S ± V w m/s
w
V
Ay area exposed to the wind
CAA v ^ d resistance coefficie:
groimd m/s
2
m
The value of CAA changes with the wind direction and reaches its maximum at an an gle between the direction of the aoDroachine wind and the direction of motion of
{|) = 2 0 - 3 0 deg.
The wind resistance coefficient is given in [18] - for corvettes by 0,58 - 0,66,
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for planing pleasure craft without aerials for - zero trim angle by 0,31 - 0,44,
- 4 deg trim angle by 0,39- 0,50.
Special wind resistance coefficients for catamarans have not been published yet. In-vestigations of the Berlin Model Basin in the large v^nd tunnel of the DLR in Braunschweig indicated that with the slope of the front side of deckhouse and bridge the wind coefficient decreases. As an average value can be taken
- for passenger catamarans = 0,42 - 0,45 - for freight catamarans = 0,45 - 0,5.
For hydrofoils in the foilbome mode values of = 0,6 - 0,8 for craft with surface piercing foils and values of = 0,9 for craft with deeply submerged foils have been reported in [19 - 20].
For SESs the aerodynamic coefficient ranges from = 0,4 for a well designed craft to approximately C ^ A ^ 0,8 depending on the size and shape of the superstmc-ture.
For the superstmcuire of the super slender monohulls no wind resistance coefficients have been published up to now.
+
Because the wind velocity V^^ increases with the distance from the water surface,
should be taken at the height of the center of the frontal area of the superstracture. The calculation of the aerodynamic drag does not take into account the wind and wave induced yawing resistance and the wind resistance due to coursekeeping.
1.2.5 Parasitic drag Rp^R
The parasitic drag is the sum of pressure and fiictional resistance components which are caused by protuding exhaust vents, cooling and sanitary water in- and outlet openings, scoops and zinc anodes. The resistance of each element can be calculated by the empirical formula
AR PAR ~ Psw/2 ' u . CDP • Ap kN(1.35) with A C u p DP m m m/s 2
/
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For a first approach the drag coefficient of the inlet openings can be chosen for the condition without any flow through them. In this case the drag coefficient is larger than with flow through the openings [ I T .
1.2.6 Trial resistance comDonents ZR 1.2.6.1 General considerations
under
tank resistance comnonents cannot
dure. These components are:
the air- and wind resistance R the parasitic drag RPAR?
AA5
- the resistance due to coursekeeping AR^-p,
- the resistance due to rippling sea AR^^^.
They are calculated directly for the full scale vessel. They are summarized to the trial resistance comDon(
ZR-pR - RAA ^ ^RPAR A R ^ x A R ^ ^ kN(1.36)
resistance R^s- RAA ^ R p A R
shown by item 1.2.4 - .5. The two rical allowances which can be diff
In the following sections the total resistance includes the trial resistance components.
1.2.6.2 Resistance due to coursekeeping ARg-p
This component is caused by the induced rudder drag, the resistance due to swaying and yawing motions and the additional vAnd resistance. For a conventional round bilge hull up to 50 m length with a twin rudder configuration an allowance of 2 per cent of the resistance of the appended hull is recommended [26]:
ARsx - 0,02 . RxwAP kN(1.37)
with
RTWAP resistance of the hull with appendages kN
1.2.6.3 Resistance due to rippling seas AR^^v
This component arises from the diffraction of small incident waves at the of sea 0 to 1. An allowance of 2 to 3 per cent of the naked hull resistance resistance may be acceptable for conventional round bilge hulls up to dis of approximately A = 5001 [21,26].
Resistance Components of High Speed Small Craft Burkhard Müller-Graf WEGEMT Association Page 19
A R ^ w = 0,02 . R H kN(1.38)
For other vessel types other allowances may be adequate
1.3 Components of the Model Resistance
The theoretically composed resistance includes each arising resistance The model resistance which is the unique basis for all resistance data c two
mine most of the resistance components separately. According to the method of Froude the model resistance can be considered to be composed of the
- residual resistance component R j ^ - frictional resistance component Rpj^
RTM ~ R R RpM N ( 1 . 3 9 )
Because the frictional component can be computed according to expression ( 1 . 1 1 ) , the
residual resistance R^ is given by
RRM ~ RTM • RpM N ( 1 . 4 0 )
with
R-rvf total model resistance of the bare hull N RpM model frictional resistance
RpM - PM/2 • Vjvi^ . S^jvt' C FM
V^t model speed
N ( 1 . 4 1 )
m/s Cpj^ specific frictional resistance
S WM wetted area of the model (exclusively the immersed
transom area) as available, at rest or underway m^ resistance components and those frictional resistance subc(
t accounted for in the main component Rp^^. As shovra resistance of a monohull with spray rails and stem wedge mnrises 8 comuonents. two of them of viscous origin:
RR = RWP + RWB + Rp + RSP + RSRP + RWEP + RSRF + RSF N ( 1 . 4 2 )
The residual resistance of catamarans in Fig. 1.3.2. contains 12 components:
RR ~ RWP RWB + Rp + Rsp + RSRP RWEP RSRF
+ ARwpi + ARSPI + ARpuw + ARpow - ARpj N ( 1 . 4 3 )
For a hull with appendages all frictional and pressure drag components of the append-ages are also included in the residual resistance, i f the appendage drag has not been determined experimentally.
By means of the residual resistance the number of components has been reduced dras-tically. As in the case of slow displacement ships the hull resistance includes two pri-mary components solely,
N (1.45)
IN (l.^O) In addition the residual resistance includes the air resistance of the model RAAM which
becomes meaningful at model speeds Vj^ > 6,0 m/s.
With an increasing number of frictional resistance components in the residual resis-tance RR the power prediction is more and more affected by scale effects. The full scale power becomes too large, because the frictional resistance components and the model air resistance are scaled up by X^-p^/p^, The decrease of the full scale frictional coefficients is not taken into account. By this method the pressure resistance can become overestimated and the frictional resistance underestimated.
1.4 Composition of the Total Resistance for Different Types of Vessels 1.4.1 General considerations
The total resistance of each fast advanced marine vehicle is composed of nearly the same primary components:
R T - Rw + Rv+ R L + R S + 2RAP+ S A R ^ R kN(l .47)
Only the symbol for the resistance component caused by the hull carrying lift changes with the vehicle type.
•ri
To identify the specific resistance characteristics of each vehicle type it is absolutely necessary to breakdown the primary components for each of the three speed ranges of interest in the subcomponents. With regard to the full scale resistance prediction, the subcomponents of the residuary resistance must be known. In the following items a detailed survey of the subcomponents for each advanced vehicle type is given.
1.4.2 Semi-Displacement Round Bilge Hulls 1.4.2.1 Types of semi-displacement vessels
Up to the beginning of the nineties the term semi-displacement hulls designated tv^n-or triple screw monohulls not longer than 60 m and not faster than 38 kn. The hull form was characterized by convex sections, a round bilge, a fine forebody v^th an ex-tremly large deadrise of the sections and a transom stem. The vessels have been used for widespread commercial, para-military and military purposes.
Since some years the category of semi-displacement vessels includes large mono- and twin-hull vessels up to 225 m length [22-25] running at speeds up to 50 kn. Despite their high speeds the Froude Numbers of these designs are comparatively small with
0,5 < Fn < 0,65. Due to the drastic increase in ship length these super slender vessels
RH ~ RR + Rp
with
"^nJ-Resistance Components of High Speed Small Craft Burkhard MUlier-Graf W E G E M T Association Page 21
are operating in the semi-displacement mode. They are characterized by special huU-and bowforms which are designed to pierce the waves at maximum speed at all con-ditions. They should operate as passenger- and car ferries in open sea areas as the Baltic Sea or as container ships in the transpacific or transatlantic traffic. The increase in ship length is imperative
- to increase the sustainable speed in waves,
- to improve the seakeeping behaviour and the ride comfort, - to im.prove the economy
of the designs.
It can be expected that these super slender high speed ships will become an important vessel type within the category of semi-displacement hulls.
1.4.2,2 Theoretical structure of the total resistance under trial conditions
The total resistance of semi-displacement hulls under trial conditions with a stem wedge and sprayrails is given by
Rx = Rw + Rp + Rv+ Rs+ RsR + 2;RAP+ SARXR kN(l .48)
The primary components are composed of the following subcomponents: < 0.6
In the displacement mode, the total resistance is made up of
R T ^ RWP RWB + Rp + Rsp + RSRP RWEP ^RAP RPAR
+ RAA + ARAW + ARsx + Rp + Rpv + RSP + RSRF kN(l .49)
0.6<F^<1.2
In the semi-displacement or preplaning mode the total resistance includes as shown in Fig. 1.4.2.1
R T ~ RWP + Rp + Rsp + RSRP + RWEP + ^RAP + RPAR
+ RAA + ARAW + ARST + Rp + RSF + RSRF k N ( l .50)
Due to the convex section and buttock shape the planing mode cannot be achieved without excessive power requirements. In addition, the lack of sufficient dynamic transversal stability does not allow classical round-bilge hulls to operate safely in the planing mode [26^.
Resistance Components of High Speed Small Craft Burkhard Müller-Graf W E G E M T Association Page 22
For the super slender ships this mode is not attainable due to the lack of planing sur-faces at the bottom of the hull and due to the enormous power requirements.
1.4.2.3 Actual structure of the total resistance under trial conditions on the basis of resistance test results
In the expressions (1.49) and (1.50) m^ost of the pressure resistance components are not amenable for analytical computations. They must be determined by resistance tests. Here they are included in the residual resistance as discussed under item
1.3.1. The number of resistance components decreases with speed.
1.4.2.3.1 Tests without appendages
Resistance tests are often performed without appendages in order to safe time and ex-penses.
The full scale resistance is composed of:
RTS = (RRM • Ps/pM • l'nOOO)+ Rps + ZR^s + ^RTRS kN(1.51)
RM R T M K F M kN(1.52)
R (Rwp + RWB + Rpv Rp RSP RSP^P RWEP RSRF) M kN(L53)
2
Rps = Ps • Vs /2 • SWHES * (Cps + ACp) kN(1.54)
2RTRS ~ (RAA ARAW + ARsp + RPAR)S kN(1.55)
with SWHES R WEP
n
FS ZR APS ZR TRSeffective wetted area underway inclusive the spray wetted area but vdthout the wetted area of the spray rails and the transom
induced drag of transom wedge
specific frictional coefficient of ITTC-1957 Line sum of the appendage drag components
sum of the additional resistance components due to trial condition
2 m kN kN kN Index Index
"M" designates model values
"S" designates full scale values.
1 o
In this speed range RR includes as shown by Fig. 1.4.2.2
Resistance Components of High Speed Small Craft Burkhard Müller-Graf W E G E M T Association Page 23
with
RAA model air resistance N
1.4.2.3.2 Tests with appendages
The total resistance includes the following components:
3
RTS = (RR + 0,6 • RAPM) • Ps/pM • ^ /lOOO +
(Rp + RWEF • cos(SwE + 0) + RAA + RPAR + ARST)S kN(l .57)
with
RRM ^ RTM - [RpM + RAPM + RWEFM " COS(5WE + ©)] N (1.58)
The residual resistance includes at
RRM ~ (Rwp RWB + Rp + Rsp RWEP RSF RSRF
+ RwEF + RAA) M N (1,59)
RRM ~ (RWP + Rp + RSRP RWEB RSF RSRF RWEF
+ RAA) M N (1.60)
1.4.3 Planing Hulls
1.4.3.1 Characteristics of planing hulls
Planing hulls are the worldwide mostly built hull type with lengths up to 45 m. The majority of these craft are recreational boats with lenghts smaller than 18,0 m. For commercial purposes as passenger ferries or mega yachts and for military or para-military purposes as patrol-boat or surveillance craft used, planing hulls show a
con-centration of the hull length in the range of 30,0 - 39,0 m. Most of these large hulls are operating in a speed range of 30 to 35 kn at Froude Numbers F^ = 0,65 - 1,0. Racine boats can reach Froude Numbers of F„ > 2.0.
As in the case of semi-displacement hulls,the length of planing hulls increased during the last 3 years remarkably. Car- and passenger ferries with hull length of 82 - 100 m running at speeds of 35 to 43 kn are now in service in the mediterranean.
Planing hulls are characterized by a hard chine, straight sections and mostly by a con-stant deadrise in the afterbody of 15 < p < 25. Modem planing hulls are equipped v^th spray rails and trim flaps. Longitudinal spray rails at the bottom should reduce the
Resistance Components of High Speed Small Craft Burkhard Müller-Graf W E G E \ f r Association Page 24
wetted area. They should also improve the dynamic transverse stability. The trim flaps at the transom are requisite to diminish the running trim and the resistance at the hump speed region. They are also necessary to increase the running trim at speeds Fn > 1,6 by a negative inclination.
•
1,43.2 Theoretical structure of the total resistance under trial conditi^
In the speed region F^ < 1,2 the total resistance of the planing hull includes the same components as the semi-displacem.ent round bilge hull, increased by the frictional drag of the trim flap. At all speed ranges the wetted area which decreases with running trim does not include the spray wetted area of the bottom and the sides [21].
R T - R^p + R^B + Rp + Rgp + R^^p + R ^ E P Rpv RSF
+ Rp/cos0 + RSRP + RWEF + ^R^p + RAA
+ ARsT + RpAR kN(1.61)
R T = RWP + R ? + RSP + RSRP + RWEP + RF/COS0 + Rgp
+ RSRP + RWEF + ^RAP + RAA + ARST + RPAR kN(l .62)
and
resistance RWD to the hull resistance
with speed. The trial resistance component ARAW is not usefiil at nlanin
resistance ily smaller wetted bottom area.
F . ^ L 2
planing regime the total resistance
R T = Rp + RSP + Rcpp + RwT^p + RCI^T: + Rp/cos© + Rep
+ RSRF + RWEF • COS(5WE + ©) + ^RAP + RAA + ARST + RPAR 1^(1 -63)
The wave pattem resistance R^p disappears in this speed region. Transverse wave systems with lengths of
Lw - ' 271 • LwL m (1.64)
extremely small heights which are proportional to l / L ^ . At F^ = 1,2 the transverse wave length is 9 times and at F^ = 1,4 it is 12,3 times the waterline length of the ve-hicle. At the latter speed acc. to V = 45,0 kn the transverse wave system of a vessel with LwL ^ 28,0 m reaches a length of = 344 m.
Resistance Components of High Speed Small Craft Burkhard MUller-Graf W E G E M T Association
The largest resistance components are frictional resistance Rp, appendage drag Z R ^ , aerodynamic drag R ^ induced resistance Rp and spray resistance Rgp. The contribu-tion of Rp and R^p to the total resistance increases with running trim, whereas the fric-tional resistance, depending on wetted area and speed, decreases and vice versa. The appendage drag, which depends on the type and number of the appendage elements can become in the case of oblique shafts the greatest resistance component. In the case of prop-riders, where the immersed volume and the wetted area can become relatively small, the aerodynamic drag or wind resistance will be the largest resistance compo-nent.
Hydrodynamic speed limits in the planing mode are given by the longitudinal insta-bility depending on the distance between the centre of pressure and the centre of grav-ity and by the transversal instabilgrav-ity depending on the buttock curvature and its angle of incidence.
1.4,3.3 Actual composition of the total resistance on the basis of test results 1.4.3.3,1 Tests without appendages
Due to the Froude method in scahng up the model resistance, the full scale resistance is composed of
RTS = (RR ' Ps/pM ' ^VlOOO) + (Rp/cos© + R « ^ P + ERAP + RAA + RpAR + ARST)S
The residual resistance which is obtained by
includes at
0.6<Fn<1.2
+ RSRF + RSF + RWEF + RAA) M
En^Ll^(Fig. 1.4.3.2)
kN(1.65)
RRM = RTM " [RFM/COSG + RWEFM • COS(5WE + 6)] N (1.66)
RRM ~ (RWP RWB + Rp + Rsp + RSRP + RWEP
+ Rpv + RSRF + RSF + RVVEF)M N (1.67)
RRM ~ (RWP + Rp + Rsp + RSRP + RWEP N (1.68)
Resistance Components of High Speed Small Craft Burkhard Müller-Graf W E G E M T Association Page 26
The frictional resistance Rp of the hull is calculated at > 1,2 in the case of a pris-matic planing hull with the wetted area S^HE ^ft of the spray root line, i.e. with the bottom pressure area which is given in references [6,9,13] by:
SwHE = Im • Bx/cosp m'(1.70) WlLIl
Ijn mean wetted length
^ K L C + L K ) / 2 (1.71)
Lc wetted chine length m
L K wetted keel length m
Bx maximum beam of planing surface m
P mean deadrise angle deg
1.4.3.2.2 Tests with appendages
The total resistance is made up of following components (Fig. 1.4.3.3):
I
J
^
I
RTS = (RR + 0,6 • R^PM) • Ps/pM ' ^'/lOOO + (Rp/cosO +
RWEF • COS(5WE + © ) + RAA + RPAR + ARST)S kN(l .72)
The residual resistance includes at Fn < 0,6
the components of expression 1.65 at 0,6<Fn< 1,2
the components of expression 1.66 atFn>l,2
the components of expression 1.67
1.4.4 Fast Catamarans
1.4.4.1 Characteristics of high speed catamarans
High speed catamarans are used since 15 years as passenger ferries in coastal waters. They are 18 to 40 m long and 28 to 35 kn fast. The majority of these vessels has a length of 32 to 38 m, operates at Froude Numbers of F^ = 0,6 - 0,85 and can carry up to 400 passengers.
The demihuUs of high speed catamarans are characterized by hard chine symmetric, semi-symmetric or asynmietric planing hull sections. In the latter case the inner sides of the hulls are plane, vertical and parallel to the centreline plane. The use of the dif-ferent section forms depends on the required speed range and the sea states of interest. High speed catamaran hulls are equipped with spray rails and transom wedges or trim flaps to control the spray formation and to optimize the running trim.
Resistance Components of High Speed Small Craft Burkhard Müller-Graf W E G E M T Association Page 27
Since the beginning of the nineties the speed and length of catamarans increased. Foil-assisted or foil-supported catamarans are operating at speeds of 40 to 50 kn. Surface piercing catamarans with length of 42 to 98 m are introduced as passenger and car
ferries. Catamarans with lengths of 125 m and speeds of 40 kn for 1500 passengers and 375 cars are under construction.
The slender dernihuUs with length to beam ratios L ^ L / Ö ^ L ^ behave like planing
hulls with very small aspect ratios which are given in the case of symmetrical hulls by:
AR = Bpx/(2 . I J (1.73)
and in the case of asymmetrical hulls by
AR - Bpx/lm (1.74)
with
Bpx maximum breadth over chines m
1^1 mean wetted length
( L K + Lc)/2 m(1.71)
The effects of the main formparameters: - length-displacement ratio
- length to beam ratio
- the half entrance angle of the load waterline
- the ratio of transom area to maximum section area A^R/AX
LWL/(V/2)^''
1 E
on resistance are the same as for planing hulls [28].
I
•
1.4.4.2 Theoretical composition of the total resistance under trial conditions
The total resistance of a hard chine planing hull catamaran with sprayrails and stem wedge includes 8 primary components:
Rx = Rw + Rv + Rp + Rs + RsR + RICAT + 2RAP + SARsx kN(l .75)
The total resistance in the displacement mode is the sum of the following components
RT ~ RWB RWP + Rp + RSP RICAT RSPR RWE Rpv
+ Rp + RSRP + ZR^p + RAA + RPAR + AR^w kN(1.76)
For the symmetrical and the semi-symmetrical hull form the interference resistance includes the following components:
Resistance Components of High Speed Small Craft Burkhard Müller-Graf W E G E M T Association Page 28
C
I
RICAT = ARWPI + ARspi + ARp^w + ARpow kN(l .77)
The symbols are described in item 1.2.1.6.
The symmetrical hull form causes the largest interference drag, which decreases with the hull distance. The maximum of RICAT occurs at = 0,48 as indicated in [7, 27].
For the sm.allest hull distance or tunnel width ratio used at present for high speed catamarans, Bp/LwL = 0,1, the interference factor related to the residual resistance
FjCAT ~ RICAT/(2 • RRDH) (1.78)
with
Bp minimum width between demihuUs m
LwL waterline length m
RRCAT residual resistance of catamaran. kN
RRDH residual resistance of one demihull
infinitely far apart to the other kN
amounts to FICAT ^ and for the largest hull distance ratio of B^/LWL = 0,4 which
can be applied in practice, to FJCAT ~
The interference factor can be calculated for roimd bUge catamarans by means of Fig. ans p • •
Lll
symmetrical section forms the interference factor for a commonly used separation ra-tio of Bp/LwL=0,167 is shown in Fig. 1.4.4.2 for different length to beam ratios of the
demihuUs. For the
semi-symmetrical hull form
RJCAT becomes smaller than for thesymmetrical huU form as shown by Fig. 7.2.1 of reference [27].
At the asymmetrical hull form where all the interference effects due to bow wave and spray disappear, the interference resistance
RICAT ~ ARp^w kN(1.79)
is the smallest. With the length to beam ratio, FJCAT decreases rapidly (Fig. 1.4.4.2).
At 0,3 < Fn < 0,6 the wave pattem resistance Rw? is the largest component for the three hull forms. It must be noticed, that RWP is biggest at the asymmetrical hull form because it increases v^th the second power of the waterline entrance angle i ^ , which is doubled compared with that of the symmetrical hull form.
In expression (1.76) the resistance component which arises by coursekeeping is omit-ted due to the excellent coursekeeping qualities of catamarans.
0.6<F^<1.2
In the pre-planing mode the total resistance is given as seen in Fig. 1.4.4.3 by
Rp - RWP + Rp + Rsp + RJCAT RWEP RSRP
For the symmetrical and semi-symmetrical hull form the interference resistance
con-RICAT = ARwpi + ARgpi - ARpj + ARpuw + ARpow + ARLA kN( 1.81)
w i t h
-ARpi negative interference drag caused by the presence kN of tv^o planing surfaces close side by side.
ARLA resistance due to the generation of aerodynamic lift
at the tunnel deck or wet-deck. kN The wave pattem resistance increment, AR^pi becomes increasingly smaller with
speed, whereas AR^pj, ARpy^ and ARpow are growing rapidly. In addition the interfer-ence resistance includes a negative component ARpi, because the induced resistance of each hull Rp decreases due to the presence of the planing surface of the other demihull nearby. Each planing surface at the tunnel side of the demihuUs induces an upwash velocity on the other one which increases the effective angle of incidence relative to the fi-eestream velocity. Hence the hydrodynamic lift is increaced and by this the running trim and Rp are reduced. The immersed volume and the wetted area become smaller. Therefore the hull resistance of the catamaran is remarkably smaller than that of two single demihuUs (Fig. 1.4.4.2). The negative interference drag AP.pi rises v/ith declining hull distance ratio Bp/L^L due to the rise of lift as shown by model tests
v^th hard chin-planing hull catamerans at the Beriin Model Basis. ARpj cannot be computed at present. A R L ^ can be calculated by Hoemer [11].
For the asymmetrical hull form the interference resistance includes:
RICAT = - ARp, + ARpuw + ARLA kN(l .82)
The wave pattem resistance, which decreases with speed, is in this speed range for the
asymmetrical hull form larger than for the other two huUforms.
In the planing range the total resistance is given by
Rp Rp + Rgp + RICAT + RWEP RSRP ^ Rp
+ RSRF + ZRAP + RAA + RPAR + AR^w k N ( l .83)
For the symmetrical and semi-symmetrical hull form the interference resistance in-cludes:
RICAT = ARspi - ARpi + ARpuw + AR^A kN(l .84)
Due to the increased hydrodynamic lift of the hulls and the aerodynamic lift of the wet-deck, the immersion of the hull is reduced. The inner hull sides are not longer
wetted. From that ARpow disappears and AR^A becomes the largest component of
RICAT-For the asymmetrical hull form the interference resistance includes only two compo-nents:
P = _ AD 4. AT?
^MCAl ^-^^PI ' ^-^^LA 1_XT/1
This explains together with the more effective development of lift due to the tv/o times larger aspect ratio of the planing surface (1.74), the lower resistance of asym-metrical catamarans against symasym-metrical ones at very high speeds. Therefore all off-shore racing catamarans have asymmetrical hulls.
1.4.4.3 Actual composition of the total resistance on the basis of model test results
For catamarans no methodical hull series data have been published until today. For a reliable power prediction specific resistance and propulsion tests are absolutely neces-sary. The presentation and the use of the test data are the same as in the case of plan-ing hulls.
1,4.4.3.1 Tests without appendages
The total full scale resistance is composed of
3
RTS = (RR ' Ps/pM • ^^71000) + (Rp + Z R ^ + R ^
^ RpAR + ARAW)S kN(1.86)
The residual resistance which is calculated by
RRM ~ RTM ' RFM N (1.87)
includes at:
RRM ~ (RWP RWB + Rp + Rsp + RICAT RSRP
*^ RWEP Rvp *^ RSRF)M N (1.88)
with
RICATM = (ARWPI + ARspi + Rpuw + RFOW)M N (1.89)
12 resistance components for the symmetrical and semi-symmetrical hull forms and only one
RICATM ~ (ARPUW)M N (1.90)
Resistance Components of High Speed Small Craft Burkhard Müller-Graf W E G E ^ f ^ Association Page 31
0,6 < F f l ^ l ^ (Fig. 1.4.4.4)
^KM ~ (^WP + K-p + RsP + ^rCAT ^WEP + ^SRP *^ RSRF)M N ( 1 . 9 1 )
with
RICATM = (ARwpi + ARspi - ARpi + AR^A + ARp^w + ARPOW)M N ( 1 . 9 2 )
for symmetrical and semi-symmetrical hull forms and with
RICATM - (~ ARpj + ARpu^ + AR^^ M
for the asymmetrical hull form.
with
for symmetrical and asymmetrical hull forms and with
RICATM - (~ ARpi + ARLA)M
for the asymmetrical hull form.
1.4.4.3.2 Tests with appendages
The total resistance is numbered up by following components
3
RTS = (RRM + 0,6 R ^ ^ ) • PS/PM • ^™00 + (Rp + RAA + RpAR + '^^Aw)s
The model residual resistance which is calculated by
RRM ~ RTM ~ (RAPM RFM)
N (1.93)
RR = Rp + RSP + RSRP + RWEP + RICAT + RSRF N (1.94)
RICATM = (ARSPI - ARpi + ARfuw + ARLA)M N (1.95)
N (1.96)
kN(1.97)
N (1.98)
includes the same resistance components as the hull without appendages. The
compo-nents are enumerated for
by expressions (1.88 - 90)
0.6 < F ^ ^ I ^
Page 32
by expressions (1.94 -96)
The relative contribution of the resistance is given in Fig. 1.4.4.5.
1.4.5 Hydrofoil Craft
1.4.5.1 General considerations
Craft which are supported exclusively by hydrofoil lift are characterized by a total re-sistance which is less than 50 per cent of that of an equivalent displacement vessel. Three types of hydrofoil craft exist:
1. Semi-submerged or surface piercing hydrofoil craft.
They have an inherent static and dynamic pitch, roll and heave stability due to area stabilization. They have been developed by Baron von Schertel of the Supramar AG in Switzerland for offshore service.
2, Shallowly submerged hydrofoil craft.
They have an inherent stabilit}^ due to the effect of the free surface on the liftcun^e slope. They have been developed in the former USSR to operate predominantly in shallow inland waterways. With more than 3000 units, they are the most built type. 3. Deeply submerged hydrofoil craft.
They do not have a natural stability and need an automatic control system. They have been developed by the Boeing company in the USA and offer the best
seakeeping qualities of the three craft types.
i
Hydrofoil craft are used for passenger transportation mainly. They are built with lengths of 20 to 45 m and operate at speeds of 32 to 40 kn for commercial purposes and at speeds up to 50 kn for military purposes. The craft with shallowly submerged foils are the longest ones, the craft with ftilly submerged foils the shortest ones.
1.4.5.2 Theoretical composition of the total resistance under trial conditions
The resistance of the three hydrofoil craft types is composed of the same components and subcomponents [19, 20]. Their particular contribution to the total resistance de-pends on the type of the 3 considered foil systems.
1.4.5.2,1 HuUborne mode ( V < 0,5 V^AX)
In the hullbome mode all three craft types behave like planing boats. The total resis-tance includes the hull resisresis-tance with all its components and additionally the drag of the foil-strut systems (Fig. 1.4.5.1).
Resistance Components of High Speed Small Craft Burkhard Müller-Graf W E G E M T Association Page 33
with
RH hull resistance kN
RSRF frictional resistance of the wave deflectors covering the kN
mounting of the stmts at the forebody
-ZR^P simi of the drag of mdders, shafts, struts, kN
bossings, barrels, pods and inlet opening of waterjets
ZRpR additional resistance components of the hull due kN to trial conditions
2RTR = RAA + RpAR + ARAW + ARgx kN(l .55)
DpL foil drag
DpL = Dp + Dj + D w
oii^j-. —— r w ' i3i3r
kN
kN(l.lOl)
ZDpL sum of the drag of lift generating foil elements kN
DpL = ZDp + ZDi + EDw + EDnsjT + ^DSSP + EDVENT kN(1.102)
STNL drag of nonlift generating strut elements
Dc^. = EDp + EDw + ED.^p + EDi^x + EDVENT kN(l • 103)
EARiHF added resistance due to the mutual interference kN between the wave system of the front and rear foil,
between the spray of.the front and rear foil and the hull,
between the spray of the front stmts and the rear stmts, which can lead to a ventilation of the rear foil reducing its lift and emergence,
between the hull wave systems and the stmts,
between the border of the bow foil through and the rear foil and the rear struts.
The drag of the lift generating foils DpL and the drag of the nonlifting stmts DSTNL are
composed of the following components:
Dp Profile or section drag due to viscous effects. It includes the fiictional and the viscous pressure drag and depends on Rj,, thickness ratio t/c, nose ra-dius, camber ratio f^c, surface roughness, gaps between foil and control surfaces, cavitation condition and angle of attack [11].
Dl Induced drag due to lift which depends on dihedral angle, aspect ration,
induced angle of attack, submergence of the foil, taper ratio, flap deflec-tion, thickness ratio and cavitation condition [ 1 1 , 2 8 , 2 9 , 3 0 ] .
Dw Wave drag of foils and stmts arises by generating gravity waves. It de-creases rapidly at F^^^. > 1,0 and can be neglected at speeds above the takeoff condition, where the Froude Number Fnc based on chord length is very high [11].
D INT boundary junctions of foils with struts
Dssp Spray drag is associated with spray generated by the surface piercin struts. Skin friction due to side wetting by spray sheet is the primary source of drag. Spray drag generally increases with thickness ratio [t/cf and depends upon Reynold's Number [31'.
DvENT Drag due to ventilation is caused by the reduced pressure at the rear side of surface piercing struts or at the upper side of airfed submerged foils.
1.4.5.2.2 Foilborne mode
Above the takeoff speed in the foil-bome mode, when the hull is clear of the water, the total resistance of hvdrofoil craft is mven bv CP\^. 1.4.5 7V
Rx = ZDpL + ZDsxNL + 2RAP + 2RAA + ARAW + ^^^iw kN (1.104)
The component AR^p due to coursekeeping becomes in the foil-bome mode negligible small and can be omitted like the parasitic drag RPAR- Due to the complete emergence
of the hull, the aerodynamic drag is now one of the lareest resistance comnonents as and
craft with deeply submerged foils.
1.4.5.3 Actual composition of the total resistance on the basis of model test results
The stracture of the model resistance shows that at hydrofoil craft the extrapolation of the model resistance to full scale bv means of Froude's Method is stronglv affected bv
and bv surface Hullbome mode. F^^ < 0.6
The residual resistance of the model
RRM "~ RTM " (RFM ^ ^ F ¥ M ) N(1.105)
with
RpM frictional resistance of the hull. N
ZDppivi sum of the skin friction drag of foils and struts N
DFFM = PM/2 - • Cp . SwFM N (1.106)
skin friction coefficient acc. to the standard skin friction line - ( 1 . 1 2 )
Cp skin friction coefficient acc. to
SwFM wetted surface of foils or stmts N
includes the following components:
RRM ~ ( RWP RWB + Rp + Rvp"*" RSP RSRP ^RAP
+ RSF + RSRF + ZARIHF + 2(Dp + Dpp) + ZDj +ZDsw
+ ZDjNx + ZDgsp + ZDYP^X)M N (1.107)
only 5 are pure pressure resistance components:
.cr>n
9 are affected by R^-scale effects:
RyP' RsF5 RSRF? ^RAP) Dp, Dpp, D j , D y ^ ^ , Dggp
3 are affected additionally by surface tension- or Wn-Number effects:
R s F s R s R F s
DSSP-All these components of different origin are scaled up by the third power of the scale ratio X to the full scale resistance. Without special corrections based on the experience
of the towing tank, the use of these values becomes dubious. Foilbome mode. > 0.6
In this condition where the hull is completely out of the water, all resistance nents depend on Reynolds Number. The model resistance includes following compo-nents :
RTM = (ZDpL + ZDSTNL + ^AR^HF + RAP + RAA)M N(1.108)
In this case a residual resistance cannot be determined by Froude's Method. Despite this fact, in a rough estimate the test results are scaled by Froude's Law and by apply-ing empirical correction factors which are based on full scale trial data [19]. On the basis of correlation procedures which determine the profil characteristics for the full scale Rn-Number reliable full scale data can be obtained.
1.4.6 Aircushion vehicles
1.4.6.1 General characteristics of aircushion vehicles
Aircushion vehicles or ACVs are built in lengths of 6 to 57 m up to a maximum dis-placement of A = 300 t. The greatest group of ACVs has lengths of 22 to 29 m and
operates as passenger ferries at service speeds of 33-40 kn. Typical Froude Nimibers
related to the cushion length are F^^q = 0,8 - 1,5. The larger units which are in service as car and passenger ferries are running at remarkably higher speeds of v = 40 - 63 kn
in the region of F^c 2,0. They can carry up to 416 passengers and 67 cars.
Aircushion vehicles are supported by an artificially generated cushion of pressurized air, which is contained by a flexible skirt at the whole perimeter around the craft. Air must be supplied continously to the cushion against the escape of air between
water-surface and skirt. ACVs with flexible skirt are of amphibious type, they can operate over land and water. The only mode of motion is the cushionbome mode. Amphibious air-cushion vehicles are driven by air propulsion [21],
1.4.6.2 Theoretical composition of the total resistance under trial conditions
resistance
nents which interact with each other in a complicated way. In general each component resistance
foUowine resistance
comm resistance
following main components [32,33]:
posed of th
RTS = RAA + Rwc + Rp + RM + RSE - ATcu kN ( 1 . 1 0 9 )
RTS =^ RAA + Rwc + ARp -f- R^ + RSEP + RSEF " A T ^ kN ( 1 . 1 1 0 )
with
RAA aerodynamic or profile drag kN
This component comprises the aerodynamic skin friction and eddymaking resistance. R A ^ becomes the largest resistance component (Fig. 1.4.6.1).
R A A - PA V R /2 • C ^ - Ay kN ( l . l i n
CAA aerodynamic drag coefficient which amounts to - 0,25 for well designed craft, - CAA ^ 0,32 - 0,38 for most of the craft,
" C A A = 0,5 for poorly designed craft,
as reported by Steele [33]
Rwc cushion wavemaking resistance kN The component is due to the generation of surface waves when the
pres-sure field of the cushion moves over the water surface. The wavemaking resistance corresponds to the wavepattem resistance R ^ P of each type of hull operating at the watersurface.
With the increase in speed, R^c rises and falls through a series of humps and hollows until the primary hump at F^c = 0,564 is reached. At higher
speeds the wavemaking resistance decreases and becomes negligible at Froud Numbers related to the cushion length of F^c > 2,0.
Rwc can be calculated by Doctors [34]
Rwc does not include the wavebreaking resistance RWB? and the induced
resistance Rp. In general RWB is not taken into account at ACVs because it is comparatively small and disappears at F^c^ 0,6.
Rp induced resistance
This pressure resistance component keeps the hull on an inclined pressure niveau and depends directly on displacement A and running trim 0 . Rp must be accounted for at a running trim 0 0. At planing speeds, Fnc> 1,2, Rpis given by
