KUNGL TEKNISKA HÖGSKOLAN
Royal Institute of Technology
Department of Naval Architecture
S-100 44 Stockholm
TECHNISCHE UNIVERS1TEIT Laboratorium voor Schoepshydromecharilca Archlef Mekelwog 2, 2628 CD Deift Tel.: 015-786873-Fg,c015-781836Aerodynamic
response of
high-speed monohuHs
by
Anders Olander
AERODYNAMIC RESPONSE OF ifiGH-SPEK
DMONOHUIJS
by Anders OlanderAugust 1991
Royal Institute of Technology Department of Naval Architecture S-10044 Stockholm, Sweden
ABSTRACT
This report deals with the aerodynamic forces actingon high-speed monohulls.
The results presented are based upon wind tunnel measurements, and they are intended to serve as guidelines when the need arises for estimating theaerodynamic forces acting on such hulls. Also presented is a slightly modified performance prediction method ori-ginally formulated by Savitsky, that enables the aerodynamic effects to be included in a simple manner. It is shown that theirpresence has a strong impact on the predicted run-ning trim and total resistance at high speeds.
Key words:
planing hulls, wind tunnel, aerodynamic forces, centre of effort, lift, drag, side force, pitching moment, sheering moment, heelingmoment, performance prediction
Page
1 Introduction
i
2 About the results 5
3 Lift 7 3.1 Lift coefficient 7 3.1.1 Headwind 7 3.1.2 Side wind 10 3.2 Centre of Lift 10 3.2.1 Headwind 12 3.2.2 Side wind 13 4
Drag
15 4.1 Drag coefficient 15 4.1.1 Headwind 15 4.1.2 Side wind 17 4.2 Centre of Drag 19 5 Side force5.1 Side force coefficient
5.2 Centre of Side force Z2
6 Heeling moment 24
7 Performance prediction
7.1 Aerodynamic effects in the Savitsky performance prediction method
7.2 Centre of pressure for triangular planing surfaces 7.3 Adaptable beam
7.4 Example of performance prediction 30
Acknowledgements 35
References
i
INTRODUCTION
Current performance prediction methods for planing hulls include the effects of hydro-dynamic lift and drag due to the hull itself and due to appendages, as well as static boy-ancy, weight of the hull, and thrust forces, see e.g. [1-7]. Aerodynamic effects are nor-mally not included. This model is relevant as long as the speed is moderate and/or the hull-weight is large.
In the case of a light-weight hull in combination with high speed, the influence from the aerodynamic forces is no longer negligible. A more complete design procedure for high-speed monohulls should be able to take into account also the aerodynamic effects. Very little work has been done to assist the designer in this respect.
The aim of this study was to investigate the magnitude and the importance of the aero-dynamic forces, to characterize the aeroaero-dynamicresponse. The intention was to estab-lish some basic aerodynamic data, giving the designer ofhigh-speed monohulls access to an approximative tool for estimating the aerodynamic forces acting on such hulls without having to carry out expensive, time-consuming wind tunnel testing. The calcu-lated aerodynamic effects can easily be included in the performance prediction method formulated by Savitsky, [1].
For this purpose, a series of wind tunnel tests were carried out. Measurements were made of aerodynamic lift, drag, and pitching moment for several values of the vertical angle of attack (trim) t, and the relative horizontal angle of attack a. For relative horizontal
angles of attack a0, additional recordingswere made of side force, sheering moment, and heeling moment. For definitions of trim angle and forces, see figures 1.1 and 1.2 respectively. The relative horizontal angle of attack, as well as the relative speed of the wind, is created by the combination of the true wind and the headwind caused by the speed of the hull. See figure 1.3.
The models used were constant deadrise hulls with =15 or 30 degrees. They had flush decks and no details like sprayrails fitted. The models were equally shaped except for the difference in deadrise, with rather blunt and short foreships as can be seen in figures 1.4 and 1.5. Since the geometric variations were limited, caution is recommended when using the results for hulls of different shape.
All the measurements were carried out in ground effect, to simulate the presence of the water surface.
A more detailed presentation of the experimental work is given in a previous report by the author, [8]. In this report the results have been given a simplified and generalized form, to make them easy to use and applicable, as far as possible, to hulls of varying shapes. The results have also been compared to those presented in [9]. Some comments are inclu-ded regarding the likely influence of different geometries.
Fig 1.2 Definition of forces. The origin of the system is arbitrary.
Relative wind:
speed y, horizontal angle of attack
a
Fig 1.3 Definition of relative wind.
fl
Drag S Side forcek
Lift Hm: Heeling moment Pm: Pitching moment Sm: Sheering moment Headwind:0.325 m I f f I t I f I f I 0 2 4 6 8 10 12 14 16 18 20 Fig. 1.4
Hull model with deadrise 3=30 degrees.
Scale i : 7 20 18 0.22 m pi 1.05 m
0.22 m I I I I I I I I I I I 0 2 4 6 8 10 12 14 16 18 20 1.05 m g. 1.5
HuB model with deadrise =15 degrees.
L
2
ABOUT TILE RESULTS
The results are presented in terms of non-dimensional coefficients, calculated from the measured forces and moments. In order to make the results as general and useful as possible, the areas used when defining the coefficients were not the same in all cases.
Further information will be given in the relevant sections of the presentation, see chap-ters 3-5.
To examine the effect of speed, all the measurements were repeated for wind speeds of 20, 31, and 40 rn/s respectively. The forces/moments were found to be, almost exactly, func-tions of speed squared. This indicates that the systems of vortices are fully developed even at low speeds due to the hard-chine type of hulls, i.e. the calculated coefficients are not dependent on Reynolds number within the speed interval investigated. In the full-scale case, assuming a hull length of 10.0 m, the coefficients are valid down to a relative wind speed of a few knots, far below the speeds where the aerodynamic forces are of inte-rest. The results presented are based on readings obtained using a wind speed of 40 m/s, giving a Reynolds number Re=3.2E6.
The measurements were carried out for 2 different simulated lengths of the "submerged" part of the keel, Lk=0.27 m and Lk=0.67 m respectively, corresponding to relative wetted keel lengths LkJL=0.26 and LkIL'0.64, see figure 2.1. For the latter case (long wetted keel length), only the trim angles t=4 and 8 degreeswere used.
It should be observed that, due to the fact that thepoint of rotation for pitching was fixed for each length of the submerged part, the submerged volumes of the hulls increasedas the the trim angle was increased. This also means that for the trim angle r=0 degrees, there was no submerged volume of the hulls, nor any distinction between short and long wetted keel lengths.
As mentioned earlier, all of the mesurements were carried out in ground effect. The ground plate used was of fixed type.
L=1.O5rn
Lk=0.27m
Lk=0.67m
The presentation is primarily based on the recordings valid for the relative wetted keel length LkIL=O.26, as these measurements were the most comprehensive ones. The cor-responding results are marked x(O.26). The effect of changing the wetted keel length is indicated as x(l)/x(O.26), referring to the results x(026). The results have been assumed to vary linearly between the two tested lengths of the submerged part.
For the case of side wind, the results are presented as xa/x, where x is the corresponding result for a=O, i.e. headwind.
The formulas given in the subsequent chapters can of course be used separately, to predict any aerodynamic force of special interest. In all cases, the relative wind speed and ang-le of attack should be used, see figure 1.3. When calculating the heelingmoment special attention is required, see chapter 6 Heeling moment.
Chapter 7 describes a simple modification that enables the Savitsky performance predic-tion method [1] to take into account also the aerodynamic effects. Inclusion of the aerody-namic forces has a strong impact on the predicted running trim and resistance at higher speeds.
3
LIFT
3.1 Lift coefficient
The results are presented in terms of the non-dimensional lift coefficient Cl. Cl is refer-red to the bottom area between chines projected on the horizontal plane for zero trim, see figure 3.1. This area is considered as governing the magnitude of lift force generated. It is therefore chosen to best enable application of the results on hulls of different geometric proportions.
The aerodynamic lift is calculated according to:
L=O.5pv2a
(Eq.3.1)where L: Lift INI
p: Density of air, 1.3 kg/m3 y: Relative wind speed [in/si
Sb: Projected bottom area [m2] Cl: Lift coefficient
Fig. 3.1 Definition of the bottom area Sb. The projection should be made fort=O degrees.
3.1.1 HeadwiiuI
Figure 3.2 shows the lift coefficient Cl for the relative wetted keel length LkIL=O.26 as function of the trim angle t. The figure includes the results for deadrise angles 3=15 and 30 degrees.
Similarly to the hydrodynamic lift, the aerodynamic lift is producedto a larger extent by hulls with flatter bottoms (less deadrise).
CI(O.26) 0,4 0,3 0,2 0,1 0,0
Fig. 3.2 Lift coefficient, C1(O.26).
CI(I)! CI(O.26) 1,1 1 0 0,9 0,8 o ß=15-30 deg 0,2 0,3 4 0,4 8 0,5 12
06
Fig. 32 Variation of the lift coefficient, C1(1YCI(0.26). t=4-8 degrees.
'r [deg] 16
LkJL
The effect of altering the wetted keel length Lk is indicated in figure 3.3.
This effect is not dramatically pronounced, much of the lift seems to be generated on the "suction" side of the hull. Visualization of the streamlines around the models also show-ed that a substantial system of vortices was built up when the air passshow-ed over the leading edge of the delta shaped part of the deck, much alike the vortices generated by delta wings, [101. See figure 3.4. Another system of vortices, not as strong however, was created at the hard chines, see figure 3.5.
Fig. 3.4 System of vortices built up at the leading edge of the deck.
The models used for these tests had rather blunt and short foreships,as mentioned earli-er. Their relative prismatic length, i.e. the length of constant cross section, was approxi-mately 0.64L. A more realistic high-speed hull would probably have a longer and more slender foreship part, and this is believed to affect the slope of the liftcurve.
The results presented in [9] are based on measurements ofan offshore racing monohull, the Norwegian built Hydrolift T-26. This hull too is of constant deadrisetype, with f3=24 degrees. The lift curve presented for this hull is flatter, more lift is generated for small trim angles, and less for trim angles above 8 degrees.
It seems justified to explain part of this discrepancy by the fact that the Hydrolift hull is more slender. For low trim, the average angle of incidence for the bottom of the hull (not equal to the trim angle as defined here) is larger due to a longer foreship, and this may produce more lift. For higher trim, the increase of theaverage angle of incidence is less pronounced. The sharper leading angle of the deck will probably generate a less effective system of vortices. This may reduce the lift.
However, for trim angles of about 4 to 6 degrees, considered as normal operating angles for these types of hulls, the investigations are in acceptable agreement.
In case the deadrise angle is not constant along the length of the hull, the magnitude of aerodynamic lift generated is affected.
Since the results available do not include studies with warped bottom lines, it is not pos-sible to make any well-founded statements about how these hulls will behave. But, bea-ring in mind that a substantial part of the total lift is createdon the upper suction side of the hull, one may guess that increasing the deadrise in the foreship part will not to a great extent change the situation. For slender hulls and low trim, for which the bottom is rela-tively more important than the deck side according to the discussion above, the effect of warping will probably be more significant. In these cases it might be advantegous to use an average deadrise angle when estimating the lift.
The layout of the deck, and the presence of wind screens etc., will to some extent have an impact on the expected aerodynamic lift.
3.1.2 Sidewind
Figure 3.6 shows the relative effect on the lift coefficient of side wind, for the relative wet-ted keel length LkIL=O.26. It is assumed that the lift coefficient for headwind is already
known.
As can be seen in the figure, the effect of increasedhorizontal angle of attack a is drama-tic, especially for very low trim angles. The lift coefficient for low trim and 20 degrees relative side wind can reach levels 5-10 times as high as for headwind. For higher trim the effect is more moderate, but still significant. In thecase of longer relative wetted keel lengths the situation is similar to that shown in figure3.6.
3.2 Centre of Lift
The position of the centre of lift was calculated from the recorded values of lift and corresponding pitching moments. For certain values of the trim angle, the pitching moment was corrected to minimize the effect of the drag force.
The position of the centre of lift is measured horizontally from the transom, and it is expressed in terms of the relative distance LCLajr/L, see figure 3.7.
CIa(O.26)ICI(O.26)
8
o
LCL.r
lo
20 a [deg]Fig. 3.6 Variation of the lift coefficient, ClaO.26)/Cl(O.26). Deadrise =15-3O degrees.
L
3.2.1
Headwind
Figure 3.8 shows the position of the centre of lift for relative wetted keel length 0.26 as function of the trim angle
t.
The position was found almost independent of deadrise angle in the case of constant deadrise type hulls.For very low trim, the foreship is the only effective lift generating part of the bottom, which gives the centre of lift a position well to the bow. As the trim angle is increased, the point of action moves aft.
LCLaIF(O.26)/L
Fig. 3.8 Centre of lift, LCLair(0.26)/L.
As mentioned earlier, the study does not include cases with more slender hulls, or hulls with warped bottom lines (more deadrise at the bow). The centre of lift for these types of hulls will probably be positioned more aft, especially for very low trim angles, due to
their different distribution of the effective lifting area.
However, as most high-speed hulls operate with short waterline lengths, for normal trim angles, it seems sufficient to position the centre of lift between 0.70L and 0.75L depending on hull form. Normal positions of the centre of gravity (CG) for high-speed monohulls are in the range 0.25L-0.5L forward of the transom, the higher the design speed, the smal-ler the value. Accordingly, the centre of aerodynamic lift is well forward of CG, creating bow-up pitching moments withan accelerating rate of increase. At very high speeds this leads to an unstable condition, when a small pitching motion, e.g. excited by porpoising, can be rapidly amplified and may cause a so called "blow-over"as a result of the unba-lanced hydro- and aerodynamic pitching moments. For dynamic stability, the aerody-namic centre of lift should be positioned aft of CG, [ill, generating a bow-down pitching moment gradient. Additional aerodynamic lifting areas fitted near the transom would be beneficial as far as stability is concerned, creating an aerodynamically more balan-ced craft. 0,9' 0,8 8=15-30 deg 0,7 0,6 'r [deg] o 4 8 12 16
LCLaIr(I)/LCLaIr(O.26) 1,2 1,1 1,0 0,9 ß=15-30 deg LkJL
02
0,3
04
0,506
07
Fig. 3.9 Variation of the centre of lift, LCLairW/LCLair(0.26). t=4-8 degrees.
The effect of changing the wetted keel length Lk is indicated in figure 3.9.
The recorded pitching moments were practically unaffected by changes of Lk. With a larger part of the hull submerged, the lift decreases, but at the same time the centre of lift moves forward creating about the same amount of pitching moment.
3.2.2 Side wind
Figure 3.10 shows the influence on the position of the centre of lift when the relative wind direction is changed from headwind to sidewind. The figure is valid for the relative wet-ted keel length 0.26. It is assumed that the position for headwind is already known. When increasing the horizontal angle of attack a, the centre of lift moves aft. Although not shown here, this effect is somewhat dependent on the trim angle. Low trim will give a more accentuated change of the position. For longer wetted keel lengths, thesituation is similar to that shown in figure 3.7.
Despite the fact that the position of the centre of lift is shifted aft when operating in oblique wind, the resulting pitching moment will increase for low trim due to the dramatic am-plification of the lift coefficient. For trim angles above 4 degrees however, the pitching moments will remain approximately constant.
LCLaI rcx(O.26)/LCLaIr(O.26) 1,2 l'o 0,8 0,6 ß=15-30 deg o 10
Fig. 3.10 Variation of the centre of lift, LCLaira(O.26)fLCLair(O.26).
a [de9]
4
DRAG
4.1 Drag coefficient
The results are presented as the non-dimensional drag coefficient Cd, based on the maximum cross sectional area of the hull, see figure 4.1. This area is considered suit-able to use since it governs the magnitude of drag, at least for very low trim angles. The aerodynamic drag is calculated according to:
D=O.5pv2&Cdk
(Eq.4.1)where D: Drag [N]
p: Density of air, 1.3 kg/m3 y: Relative wind speed [ni's]
Sc: Cross sectional area [m2] Cd: Drag coefficient
k:
Length/cross sectional area factor, see eqs. 4.2, 4.3Note: For higher trim, the ratio between hull length and cross sectional area will affect the slope of the drag curve. Please see the discussion of the factor k below.
Fig. 4.1 Definition of the croes sectionál area Sc. The croes section with the largest gross area
should be used.
4.1.1
Headwind
Figure 4.2 shows the drag coefficient Cd for relative wetted keel lengthLkTL=0.26 as function of the trim angle t. The figure includes the results for deadrise angles 3=15 and 30 degrees.
Cd(O.26) 0,8 0,6 0,4 0,2 0,0 o 4
Fig. 4.2 Drag coefficient, Cd(0.26).
8 12
Fig. 42 Vertical projections of hulls with different lengths.
t[degj
The effect of the ratio hull length to cross sectional area mentioned above is indicated in figure 4.2. The models used were of the same length, but their cross sectional areas were
different. Although giving the same value of Cd for very low trim, the slope of the drag curve for the model with =30 degrees is a little steeper due to the larger ratio between length and cross sectional area.
Comparing two hulls with equal cross sectional area but with different lengths, the
ver-tical projections of the hulls will differ when the trim angle is increased above zero, see figure 4.3. The projected area will of course increase with length.
This is very much the case for the Hydrolift hull referred to earlier, [9]. This hull is con-siderably longer for the same cross sectional area, and the drag curve presented clearly shows the influence of the increased length.
If we assume that there is only a small variation in the distribution of thecross sectional areas, this can be accounted for approximately by comparing the length/'area ratio of the actual hull to the average lengthl'Iarea ratio of the models tested (4.20):
k=1
,for r=O degnes (Eq. 4.2)k=(LJSc)/4.2O
,forc'Odegrees
(Eq.4.3)It is recommended to apply the factor k when calculating the drag force.
Since the drag force for low trim mainly consists of pressure drag, it is believed that for a more slender hull, the values of Cd for very small trim angles will be somewhat lower than shown in figure 4.2. The slope of the drag curve will probably be less steep, due to the more moderate increase in projected area when raising the bow. Also, a sharper leading angle of the deck will probably generate a less effective system of vortices, which is ad-vantageous in this case, cf. chapter 3 Lift.
Drag forces will be affected by the presence of windscreens etc. In such cases, the area of these appendages should be included when calculating the cross sectional area Sc. The effect of changing the submerged keel length Lk is indicated in figure 4.4.
The recorded reduction of drag with increased wetted keel length is a consequence of the smaller projected area of the hull part not submerged.
4.1.2
Sidewind
Figure 4.5 indicates the relative effect of side wind on the drag coefficient, compared to headwind operation. It is assumed that the coefficient for headwindis already known. The drag is always measured parallel with the hull, not parallel with the direction of the incoming wind.
As can be seen in the figure, the influence of side wind is not very pronounced. In case of longer relative wetted keel lengths, the situation is similar to figure 4.5.
Cd(I)/Cd(O.26) 1,1 1,0 0,9 0,8 0,7
Fig. 4.4 Drag coefficient variation, Cd(1)/Cd(0.26).
Cdcx(O.26)/Cd(O.26) 2,0 1,5 0,5 0,0 10
Fig. 4.5 Drag coefficient variation, Cd c«0.26)/Cd(O .26).
LkJL
07
a [deg]
20
4.2 Centre of Drag
The measurements do not permit calculation of the centre of drag. When adjusting the recorded pitching moments in order to calculate the centre of lift, assumed positions had to be used for the centre of drag.
However, the drag force will hardly affect the pitching moment for normal operating va-lues of the trim angle. The force is assumed to act through, or close to CG, and its contri-bution to the pitching moment will then be insignificant.
Naturally, the presence of large superstructures will change the position of the centre of drag. In these cases the drag force may create additional pitching moment.
5
SIDE FORCE
5.1 Side force coefficientThe results are presented as the non-dimensional side force coefficient Cs, related to the longitudinal centreplane sectional area of the hull, see figure 5.1.
The aerodynamic side force is calculated according to:
S=O.5pu2&pC8
(Eq.5.1)where S: Side force [N]
p: Density of air, 1.3 kg/rn3 y: Relative wind speed [inls}
Scp: Centreplane sectional area [m2] Cs: Side force coefficient
Fig. 5.1 Definition of the centreplane sectional area Scp. Only half the hull is shown.
Figure 5.2 shows the side force coefficient Cs for relative wetted keel length 0.26 as func-tion of the relative horizontal angle of attack a.
The side force is always measured as a transverse force on the hull, not perpendicular to the incoming wind direction.
The recorded side forces were not sensitive to the deadrise angle,despite the fact that the size of the vertical parts of the hull sides were different. The trim angle had a minor effect on the side force.
As can be seen in figure 5.2, the side force grows approximately linearly with increasing horizontal angle of attack.
For more slender hulls, it is beleived that the results may be used as presented. The slen-derness is taken into account when calculating the centreplane area.
0,5 0,4 0,3 0,2 0,1 0,0 Cs(O.26)
V
ß=15-30 deg pprA.
r
o 0,2 0,3 0,4 1005
Fig. 5.3 Side force coefficient variation, Cs(1C0.26).
06
a [de9]
20
LkIL
07
Fig. &2 Side force coefficient, Cs(O.26).
Figure 5.3 indicates the effect of changing the wetted keel length Lk. This effect is not very strong for the models tested, but it is larger for larger trim angles. For hulls of lower height T, the influence will probably be somewhat more pronounced due to the larger
re-lative change of exposed centreplane area when altering the wetted keel length.
5.2 Centre of Side force
The position of the centre of side force was calculated from recorded values of side force and corresponding sheering moment.
The position of the centre of side force in the longitudinal direction is presented as the re-lative distance LCSa1r/L, where LCSair is measured horizontally from the transom, cf. figure 3.7.
Figure 5.4 shows the position of the centre of side force for relative wetted keel length 0.26, as fùnction of the relative horizontal angle of attack cx for different trim angles r. The
fi-gure presents the results for the model with deadrise angle 1=30 degrees.
For 3=15 degrees, the relative position of the centre of side force is approximately 5% more forward. LCSaIr(O.26)/L 0,7 0,6 0,5 o 10
Fig. 5.4 Centre of side force, LCSajr(O.26YL. =3O degrees.
The sheering moments, as well as the recorded side forces, showed an almost linear re-lation to the horizontal angle of attack. As a result, the position of the centre of side force is fairly fixed for each value of the trim angle. For lowtrim, the position is a littlemore to the bow than it is for high trim. Despite generating an equal amount of side force, the model with deadrise angle =30 degrees produced less sheering moment. This is
probab-a [de9]
ly an effect of the smaller vertical area of the hull sides at the bow. Although this did not affect the amount of side force generated, it did have an impact on the position of the centre of side force.
For more slender hulls it is believed that the centre of side force will be shifted aft, especi-ally for the combination of low trim and small horizontal angle of attack, due to the dif-ferent shape of the centreplane area.
As is the case for the centre of lift, the position of the centre of side force is not ideal, resul-ting in poor aerodynamic directional stability. To increase stability, additional vertical area fitted near the transom is helpful, [11].
Figure 5.5 indicates the effect on the position of the centre of side force when changing the relative wetted keel length Lk. The figure can be used for =15 degreesas well as for f3=30
degrees.
When increasing the wetted keel length Lk, the position of the centre of side forcemoves
forward. At the same time however, the amount of side force generated decreases, cf. fi-gure 5.3. This makes the resulting sheering moment approximately constant and inde-pendent of Lk. LCSaI r(I)/LCSaIr(Q.26) 1,2 1,1 1,0 0,9 0,2 0,3
04
0,506
Fig. 5.5 Variation of centre of side force, LCSairG)ILCS5jr(0.26).
LkIL
6
HKI4IJNGMOMENT
When operating in relative side wind, heeling moments develop as a result of the acting aerodynamic side and lift forces. The heeling moment strives to heel the hull outwards, i.e. from the wind.
The recorded total heeling moments are not presented here, as they are valid only for hulls of the same shape as the models tested. For all other shapes the relation between side
and lift forces will be different, and their relative centres of effort will probably differ as well. Instead an attempt has been made to separate the effects from the two forces. When operating in side wind, the centre of lift is no longer positioned along the keel line. It is moved in the transverse direction, and accordingly it will contribute to the heeling
mo-ment.
Since the measurements were made only for one fixed position of the connection between the models and the equipment used, there is no way of calculating the true position of the centre of lift (sideways) and of the centre of side force (vertically). But if we assume that the centre of side force is positioned halfway between the keel and the deck, which seems reasonable since the side force was not sensitive to deadrise, an estimate of the position of the centre of lift in the transverse direction can be made.
The result from this analysis is shown in figure 6.1, valid for relative wetted keel length 0.26 and horizontal angle of attack cz=20 degrees. The transverse position of the centre of lift is presented as the relative distance tJ(&2), where t is the transverse distance from the centreplane to the centre of lift and 1il2 is the halfbreadth of the hull.
As can be seen in the figure, for low trim the lift acts at an estimated position close to the side of the hull. For higher trim, the centre of lift is nearer the centre line.
If the horizontal angle of attack is less than 20 degrees, the transverse position of the centre of lift is closer to the centre line. For cz10 degrees, the readings from figure 6.1 should be reduced with approximately 30%.
t(O.26)I(b12) 0,8 0,6 0,4 0,2 0,0 o 4 8 12 t [deg] 16
The reason for this "non-physical" position for low trim may be that the total acting lift force was recorded. It is possible that low pressures giving negative lift were developed at the leeward side of the models. Accordingly, the lift on the wind sidewas larger than recorded.
As both forces generate heeling moments, the effect is that when using the single
recor-ded lift force it has to be positioned far to the side to create an equal amount of moment. For longer relative wetted keel lengths, the situation is not quite as accentuated as shown in figure 6.1.
The immediate question is then around which axle the heeling moment should be calcu-lated. One suggestion is to locate the heeling axle through the centre of hydrodynamicl hydrostatic lift. This point is probably positioned between 113 and 112 of the draught from the water surface, if the true hydrodynamic centre is assumedto be at half the draught. This is the case if the hydrodynamic lift force is assumedto be evenly distributed along the frame at each cross section of the hull. In the longitudinal direction, the centre of hy-drolift is positioned somewhere between the transom and CG, depending on the strength of the aerodynamic lift force acting,see also chapter 7. In lack of further information, it is suggested here that the heeling axle is located at 50% of the draught from the dynamic waterline at the transom.
where
¿:
LCG: LCGe:Ir:
LCLejr: 7PERFORMANCE PREI)ICTION
This section presents a simple way to introduce the effects of aerodynamic lift and drag into the performance prediction method for planing hulls formulated by Savitsky, [1]. An example on the the use of this modified method is included at the end of the chapter. Included is also a modified expression for the calculation of the position of the centre of hydrodynamic lift, applicable to triangular planing surfaces. Planing surfaces of non-constant maximum beam are discussed.
7.1 Aerodynamic effects in the Savitsky performance prediction method
To include the effects of the aerodynamic forces a simple solution, using an effective dis-placement and an effective longitudinal centre of gravity, has been adopted. This is nor-mally the procedure when trim flaps are added.
A certain hull will, at a given speed, produce aerodynamic lift and drag forces mainly governed by the trim angle. The wetted keel length Lk is of minor importance. As the aerodynamic lift is not at all as sensitive to changes in the running conditions,t
exclu-ded, as the hydrodynamic lift, it can be taken into account by calculatingan effective displacement ie and an effective position of the longitudinal centre of gravity LCGe, according to:
= - Loir (Eq. 7.1)
LCGe = ((LCG)- Lajr(LCLair)) ILie (Eq. 7.2)
Total displacement Effective displacement
Longitudinal centre of gravity, measured from the transom Effective longitudinal centre of gravity, from the transom Aerodynamic lift force
Longitudinal centre of aerodynamic lift, from the transom
The effective values, calculated for each trim, representsa hull with reduced weight and CG positioned more aft as a result of the present aerodynamic lift. These effective values are used for the hydrodynamic calculations. The aerodynamic drag is assumed to act through CG, and will add only to the total drag. Figure 7.1 shows the main loop of the
per-formance prediction program after modification.
The aerodynamic lift, drag, and longitudinal centre of lift, are estimated according to equations 3.1 and 4.1, and to figures 3.8 and 3.9. These aerodynamic data can be assum-ed to vary linearly with trim for t=1.O-4.O degrees. To limit the amount of extra input to the prediction program, one set of values for lift, drag, and centre of lift for each of these
two trim angles suffices for interpolating as the iteration proceeds. The solution of inter-polating between two sets of aerodynamic data will probably slightly overestimate the aerodynamic drag and lift for intermediate values of trim, but at the same time position the centre of aerodynamic lift a little too close to the transom.
The Savitsky method starts to iterate at low trim, always producing longkeel lengths Lk and little draught. This indicates that aerodynamic data for long keel lengths are to be used for these values of the trim angle. However, for r=O.1 degrees, the aerodynamic measurements were actually made only for LkIL=O.O, i.e. no parts of the models were
Decrease b r INPUT A CALCU1ATE
LCIr
Dair LCGe Start b.bmaxi
Ir CAT CULATE Cv Start t CALCULATE. Ir CALCULATE:. Find equilibrium trim Run through loop for ñnalt,then Output No
*
*
*
Increase 't OUTPUTFig. 7.1 Main loop of the performance prediction program after modification. The new or
submerged. If increasing the draught above zero, thereby immidiately altering the wet-ted keel length from zero to "LWL', only very small changes will add to the recordings. So, for r=O. i degrees, the aerodynamic results can be considered independent of Lk. For higher trim, the keel length is reduced rapidly as the wetted area becomes more efficient in generating hydrodynamic lift. To get an idea of which keel lengths Lk to expect for different values of the trim angle, it is suggested to start by carrying out the calculations using zero aerodynamic lift. These values of Lk will of course decrease when adding the aerodynamic lift, but they may be used as starting values.
7.2
Centre of pressure for triangular plirning surfas
The original expression for the position of the centre of hydrodynamic lift, reported in [1], was formulated to represent the conditions for a rectangular planing surface, see figure 7.2. The centre of pressure for the rectangular planing area was found to be positioned be-tween 33% and 75% of the mean wetted length Lm forward from the transom, depending on the ratio between hydrostatic and hydrodynamic lift.
When the planing area is triangular the situation is somewhat different, see figure 7.3. The true hydrostatic centre should now be positioned at 33% of the wetted keel length Lic from the transom, i.e. 66% of the mean wetted length Lm. The true hydrodynamic centre should be positioned at O.4Lk, i.e. O.8Lm. For a triangular planing surface, the following expression is suggested:
C'i, = 0.80 - 1
j5.572!
+ 7.14q.
7.3)This expression gives a position of the centre of lift a little more forward, especially for low speeds when the hydrostatic part is dominating. The calculated position will be be-tween O.66Lm and O.8Lm. For a given combination of Cv and X the relative variation is determined by the original expression.
The effect of using this modified expression instead of the original is shown inchapter 7.4. The resulting running trim angle increases due to the new position of the centre of
lift.
7.3 Adaptable beam
The Savitsky method assumes that the shape of the planing area is similar to a rectangle, with a breadth equal to the maximum beam between the chines of the hull. When using the Savitsky method for light-weight hulls, the situation is easily achieved when the actual breadth of the planing area is less than the maximum chinebeam. Thisoccurs when the planing area needed to support the weight is small, and the full beam is not re-quired. The shape of the planing area has become triangular instead of rectangular. If a too large beam is used during the calculations, the calculated value ofX will be too
small, giving negative chine lengths Lc. The calculated planing area will be positioned too far aft, and the computed equilibrium trim angle will be too small. If the input beam is correct, the calculated value of Lc should always be zero or positive. Therefore, for each step of the iteration, the beam should be gradually decreased until the calculated value of LcO. Then, the calculations for the actual trim angle can be carried out using this beam. The procedure is included in figure 7.1. In this way the required beam will be achieved automatically, and the calculated planing area correctly positioned.
bmax Fig. 7.2 b Cp stat Cp dyn
-
I F-O.33Lm O.75Lm Lm=(Lk+Lc)ì2Centre of pressure, rectangular planing area.
Lk
Lm=Lk/2
Fig. 7.3 Centre of pressure, triangular planing are&
q) = 0.75 ÇJ.) = 0.80 5.21 + 2.39
i
i
15.572. + 7.147.4 Example of performance prediction
To illustrate the effect of including the aerodynamic forces in the performance predic-tions, some calculations have been made using the Savitsky method, [1], modified as
discussed earlier.
The predictions were made for a "full-scale" hull based on the J3=30 model used for the aerodynamic measurements, but with smaller cross sectional area. The calculations were made with and without the aerodynamic effects, using the original expression for the centre of pressure as well as the modified version.
Hull characteristics:
Loa: 10.50m Bmax: 3.25 m fI: 30 degrees¿:
1500kg LCG: 2.5 m VCG: 0.5 m f: 0.2m e: O degreesNo appendages were included, i.e. the calculations were "bare hull" calculations. The aerodynamic input were given for the relative submerged keel length LkfL=0.26 for r=1.0 degrees as well as for t=4.0 degrees.
The calculations were performed for different speedsin the interval v30-90 knots. The results are presented in figures 7.4-7.9. The effect of including theaerodynamic forces is obvious. Interesting to note is that this is the case even when the speed is moderate. The higher the speed, the more important is thepresence of the aerodynamic forces, and the calculated running trim and total resistance are strongly affected.
The running trim angle increases due to the different distribution of the total lift, and the total resistance decreases as a result of the smaller weightbeeing hydrosupported. For the highest speed, no results are presented including the aerodynamics, simply because the program was not able to find añ equilibrium trim angle.
One reason for the sudden decrease of the total resistance for speeds exceeding 70 knots, aerodynamic effects included, is that the calculations were made for bare hull. If, more realistically, the drag from appendages had been included, this sudden decrease would probably not have occured. The trim angle is affected in a similar way.
The figures include two sets of results, one using the original Savitsky expression for the centre of hydrodynamic lift, and one using the modified expression (eq. 7.3), also incor-porating the adaptable beam procedure presented. The diferencies between the two sets are mainly due to the alternative expressions for the calculation of thecentre of hydrody-namic lift used, and to a lesser extent due to the adaptable beam procedure. As an examp-le of this, figure 7.10 shows their separate influences on the results.
Aerodynamic input: Cl(1.0): 0.05 Cl(4.0): 0.12 Cd(1.0): 0.22 Cd(4.0): 0.28 LCL8jr/L(1.0): 0.80 LCL«ir/L(4.0): 0.75 Sb: 29.6 m2 Sc: 4.0m2
Trim [deg]
4
3
2
i
Fig. 7.4 Running trim angle, SaVItSky Cp expression.
Trim [deg]
i
Fig. 7.5 Running trim angle, modified Cp expression, adaptable beam.
[knots]
20 40 60 80 1 00
Drag [kN] 12 10 8 6 4 2
Fig. 7.6 Total resistance, Savitsky Cp
expression-Drag[kN] 12 lo 8 6 4 2
V
Fig. 7.7 Total resistance, modified Cp expression, adaptable beam.
U)oJ
pcnotsj
20 40 60 80 1 00
15 Uft [kN] 10 o 15 10 Uft [kN] 5 o
Fig. 7.8 Lift distribution, Savitsky Cp expression.
Fig. 7.9 Lift distribution, modified Cp expression, adaptable beam.
Speed (knots]
20 40 60 80 1 00
Trim [deg] 4,0 3,6 3,2 2,8 2,4 AJt Cp, adapt beam Orig Cp, adapt beam Orig Cp
Fig. 7.10 Separate effects of modi&ations: Cp, adnptable beam.
Speed [knots]
ACKNOWLEDGEMENTS
The experimental part of this project was financed by funds from the National Swedish Board for Technical Development (STU) and the Swedish Shipyard Association (SVF) in cooperation, and by the Gösta Lundeqvist Fund at KTH.
The work has been performed under the supervision of professor Erik Steneroth at the Department of Naval Architecture, KTH. Professor Steneroth has also assisted in rai-sing additional funds making it possible to summarize the project in this report. His contribution is highly appreciated.
REFERENC
Savitsky, D.,
Hydrodynamic Design of Planing Hulls
Marine Technology, Vol 1, No 1, 1964
Blount, D.L., Fox, D.L., Small Craft Power Prediction
Marine Technology, Vol 13, No 1, 1976
Hadler, J.B., Hubble, E.N., Holling, H.D.,
Resistance Characteristics of a Systematic Series of Planing Hull Forms
Series 65
SNAME, Chesapeake Section, May 1974 Hadler, J.B.,
The Prediction of Power Performance on Planing Craft Transactions SNAME, Vol 74, 1966
Hoerner, S.F., Fluid Dynamic Drag
Hoerner Fluid Dynamics, 1965 Mathis, P.B., Gregory, D.L.,
Propeller Slipstream Performance of Four High-Speed Rudders under Cavitating Conditions
NSRDC Report 4361, May 1974
Fridsrna, G.,
A Systematic Study of the Rough-Water Performance of PlaningBoats Davidson Laboratory Report R-1495, March 1971
Olander, A.,
Aerodynamiska egenskaper hos planande fartyglbátar (in Swedish)
Royal Inst. of Technology, Dept. of Naval Architecture, Report TRITA-SKP 1069
December 1990
Wikeby, O.,
Aerodynamics of Offshore Racing Powerboats Ship&Boat International, April 1990
Hoerner, S.F., Fluid Dynamic Lift
Hoerner Fluid Dynamics, 1985
Nangia, R.K.,
Aerodynamic and hydrodynamic aspects of high-speed water surface craft Aeronautical Journal, Vol 91, No 906, June/July 1987
NOMENCLATURE
'r: Vertical angle of attack (trim) Relative horizontal angle of attack
¡3: Deadrise angle
t:
Thrust angle referred to keel linep: Density air, water Displacement
Effective displacement Beam, breadth
bmax: Maximum beam
f: Distance between thrustline and CG (measured normal to the thrustline)
k:
Lengthlcross sectional area factorI:
Relative wetted keel length Lk/Lt: Transverse distance to centre of aerodynamic lift
V: Relative wind speed
D:
Drag
S: Side force
L: Aerodynamic lift, also
L: Length over all
Loir: Aerodynamic lift
Hm: Heeling moment
Pm:
Pitching momentSm: Sheering moment
Lk:
Wetted keel length Le: Wetted chine length L m: Mean wetted length Sb: Projected bottom areaSc: Cross sectional area Scp: Centreplane area Cl: Lift coefficient Cd: Drag coefficient Cs: Side force coefficient
LCLair: Longitudinal centre of aerodynamic lift
LCSajr: Longitudinal centre of aerodynamic side force
LCG: Longitudinal centre of gravity
LCGe: Effective longitudinal centre of gravity
Cp: Ratio of the longitudinal distance from transomto the centre of hydrodynamic pressure divided by the mean wetted length
