Theory Design Air Cushion Craft 2009 Part 4 doc

106 Steady drag forces inner wetted surface outer wetted surface Fig. 3.20 Sketch of wetted surface of SES. o I o js /"2 TC\ f ^iO ' ^outO -*^out \J.£J) where K out can be obtained from Fig. 3.21, which has been obtained by statistical analysis of photographs on model no. 4 by MARIC. It is found that there are two hollows on the curve of the outer wetted surface area, the first is due to the hump speed, which leads to a large amount of air leakage amidships, and the second is caused by small trim angle at higher craft speed. Method used in Japan [28] Reference 28 introduces the measurement of the inner/outer wetted surface area of a plate-like sidewall of an SES with cushion length beam ratio (IJB C ) of about 2 on the cushion and represented as follows (Fig. 3.22): S = S + (S — S~) e~ Fr + 4h I f (3.26) where S f is the area of the wetted surface of sidewalls (m ), S f30 the area of the wetted surface of sidewalls at high speed (m 2 ) and/ s the correction coefficient for the area of the wetted surface, which can be related to Fr,, as shown in Fig. 3.23 and which is obtained by model test results. In the case of craft at very high speed (higher than twice hump speed), the water surface is almost flat at the inner/outer wave surface and also equal to each other. With respect to the rectangular transverse section of the sidewalls, the wetted area can be written as S*. = [4(A 2 - A eq ) + 2 B,] /, S m is the wetted surface area of the sidewalls of craft hovering statically (m ), (3.27) Sidewall water friction drag 107 Using flexible bow/stern seals 1.0 =._. 0.2 Fig. 3.21 Correction coefficient of outer wetted surface area of SES with flexible bow/stern seals. 11 h eq | > X -r-^ * d T » L / r ts <F= > < I ^ -V / f^ I J * r—i ^ • ^^^* « > X ,h. T T (b) Fig. 3.22 Sketch of SES running attitude at F r = 0(a) and F r = 00(b). B (3.28) where 5 S is the width of the sidewalls with rectangular transverse section (m), / s the length of sidewalls (m), /z c the depth of cushion air water depression, hovering static (m), /z, the vertical distance between the lower tip of skirts and inner water surface, i.e. //! = h 2 ~ T } , as shown in Fig. 3.24, hovering static (m), H 2 the vertical distance between the lower skirt tip and craft baseline (i.e. z b , z s , in Chapter 5) (m), T { the inner sidewall draft, hovering static, and /z eq the equivalent air gap, where Q is the cushion flow rate (m'Vs), p 2 the cushion pressure (N/m), p a the air density (Ns 2 /m 4 ), l } the total length of air leakage at the bow/stern seal (m) and B c the cushion beam (m). 108 Steady drag forces 0.4 - 0.2 - 0.2 0.4 0.6 0.8 h eq lh c Fig. 3.23 Equivalent leakage /? eq compared to the distance from seal lower edge to the cushion inner water surface. 0.8 1.2 2.0 Fr,=v-fgl c 1.0 0.8 0.6 0.4 0.2 0 -0.2 -0.4 Fig. 3.24 Correction coefficient for sidewall wetted surface area. From equations (3.27) and (3.28) the area of wetted surface at any given Fr\, can be interpolated from at Fr { = 0, S ( = S m (max. area of wetted surface) at Fr { = °° S f = S fx (min. area of wetted surface) and Sidewall water friction drag 109 Based on model tests in their towing tank, the following method was obtained by NPL: S t = (S a + AS f ) (1 + 5 5 smax // s ) (3.29) where 5 smax is the max. width of sidewalls at design water line (m), AS f the area cor- rection to the wetted surface due to the speed change (m") and S m the area of wetted surface of sidewalls during static hovering (m ). This expression is suitable for the following conditions: 8</7 c // c <16 and Fr\ > 1.2 Figure 3.25 shows a plot enabling A5" f to be determined within these conditions. B. A. Kolezaev method (USSR) [19] B. A. Kolezaev derived the following expression for sidewall drag: Sf = Kf S m where S f is the area of wetted surface, hovering static (Fig. 3.26), K f the correction coefficient for the wetted surface, related to Fr (Fig. 3.27). S m can also be written as below (see Fig. 3.26): sin/T 21. T (B, COSy? (3.30) -0.5 - Fig. 3.25 Correction coefficient of wetted surface area of sidewall vs Froude Number. [15] 110 Steady drag forces Fig. 3.26 Typical dimensions for wetted surface of sidewalls. Fig. 3.27 Correction coefficient of wetted surface area of sidewalls vs Froude Number. where Tj, T 0 are the inner/outer drafts, hovering static (m), b s the width of the base plate of the sidewalls (m), B s the width of sidewalls at designed outer draft (m) and /? the deadrise angle of sidewalls (°). A number of methods used for predicting the area of the wetted surface have been illustrated in this section. It is important to note that one has to use these expressions consistently with expressions by the same authors to predict the other drag compo- nents, such as skirt drag, residual drag, etc., otherwise errors may result. As a general rule, the methods derived from model tests and particularly photo records from the actual design or a very similar one will be the most accurate. The dif- ferent expressions may also be used to give an idea of the likely spread of values for the various drag components during the early design stage. Sidewall wave-making drag 1 1 1 1,9 SWewall Equivalent cushion beam method SES with thin sidewalls create very little wave-making drag, owing to their high length/beam ratio, which may be up to 3CMO. To simplify calculations this drag may be included in the wave-making drag due to the air cushion and calculated altogether, i.e. take a equivalent cushion beam B c to replace the cushion beam B c for calculating the total wave drag. Thus equation (3.1) may be rewritten as R w =C w p;BJ(p w g) (3.31) where R w is the sum of wave-making drag due to the cushion and sidewalls, C w the coefficient of wave-making drag, C w = f(Fr b \JB C ) and B c the equivalent beam of air cushion including the wave-making due to the sidewalls. The concept of equivalent cushion beam can be explained as the buoyancy of side- walls made equivalent to the lift by an added cushion area with an added cushion beam. The cushion pressure can be written as where W s is the buoyancy provided by sidewalls and W the craft weight. Then the equivalent cushion beam can be written as W W B B c = — = - - - = - ^ - (3.32) Pc i c [(w-wy(i c Bj\i c \-wjw The method mentioned above has been applied widely in China by MARIC to design SES with thinner sidewalls and high craft speed and has proven accurate. Following the trend to wider sidewalls, some discrepancies were obtained between the calcula- tion and experimental results. For this reason, [29] gave some discussion of alternative approaches. Equation (3.31) can be rewritten by substitution of (3.32) into (3.31), as A B r (3.33) C 1 - WW Where R wc is the wave-making drag caused by the air cushion with a beam of B c and without the consideration of wave-making drag caus_ed by sidewalls, C w the coefficient due to the wave-making drag with respect to Fr, IJB C C w = f (Fr b IJB C ) and C w the coefficient due to the wave-making drag with respect to Fr, IJB C C w = f(Fr h lJBJ The total wave-making drag of SESs can now be written as 12 Steady drag forces R wc + R^ w + R m (3.34) where R wc is the wave-making drag caused by the air cushion, R sww the wave-making drag caused by the sidewalls and R m the interference drag caused by the air cushion and sidewalls. Therefore ^sww + ^wi = ^w ~~ ^wc (3.35) as R WC =C W p 2 c BJ^g) (3.36) and Pc =W- WJ(1 C B C ) Therefore * wc = [C w BJ(p w g)][W- WJ(l c B c )f (3.37) If we substitute equations (3.36) and (3.33) into (3.35), we obtain /-> n R + K = ' - R sww W1 c \-wjw wc 1 C, \-WJW - 1 (3.38) If R denotes the buoyancy of sidewalls and equals zero, then the whole weight of the craft will be supported by the air cushion with an area of S c (S c = 1 C B C ) and the wave- making drag could then be written as * W co = [C w BJfa g)} [W/(l c B e ) (3.39) From equations (3.37) and (3.39) we have *wc/* wc o = (1 - WJW} 2 (3.40) Upon substitition of equation (3.40) in (3.38) and using equation (3.39), then equa- tion (3.38) can be written as 7? sw + R^ = * WCO [(C W /C W ) (1 - WJW) - (1 - WJW} 2 } (3.41) The calculation results are shown in Fig. 3.28. It can be seen that the less the WJW, the less the wave-making drag of the sidewalls (R,^ + ^ w ), which is reasonable. The greater the WJW, the more the wave-making drag of the sidewalls. Figure 3.28 also shows that wave-making drag decreases as the WJW exceeds 0.5. This seems unreasonable. The calculation results of [30] and [31] showed that wave- making drag will increase significantly as WJW increases. Reference 32 also showed that the wave-making drag of sidewalls could be neglected in the case of WJW < 15%. The equivalent cushion beam method is therefore only suitable to apply to SES with thinner sidewalls. It is unreasonable to use this method for SES with thick sidewalls or for air cushion catamarans (e.g. WJW ~ 0.3-0.4) and for these craft the wave- making drag of sidewalls has then to be considered separately. Sidewall wave-making drag 113 Yim [30] calculated the wave-making drag due to sidewalls by means of an even simpler method. He considered that the total wave-making of an SES would be equal to that of an ACV with the same cushion length and beam, i.e. it was considered that the sidewalls did not provide any buoyancy, and the total craft weight would be sup- ported only by an air cushion as to lead the same wave-making due to this equivalent air cushion. The effective wave-making drag coefficient of the sidewalls calculated by this method is similar to that for WJW > 0.5 above (see Fig. 3.28). Hiroomi Ozawa method [31] The theoretical calculation and test results of the wave-making drag of air cushion catamarans have been carried out by Hiroomi Ozawa [31]. Based on rewriting his equations found in [29], the final equation for predicting total wave-making drag may be written as (when Fr = 0.8) R», — R,,,, + R c + (3.42) V = [1 - 0.96 WJW + 0.48 (WJW) 2 } [C w B c /(p v gj\ [Wl(l c B c )] : A comparison between the equivalent cushion beam method, the Ozawa method and the Yim method is shown in Fig. 3.28. It can be seen that satisfactory accuracy can be 0.70 - 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 p c S c /W 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 WJW Fig. 3.28 Comparison of calculations for sidewall wave-making drag by means of various methods. 114 Steady drag forces obtained by the equivalent method in the case of WJW < 0.2, but the wave-making drag of sidewalls and its interference drag with the air cushion have to be taken into account as WJW increases. In conclusion, the methods for estimating sidewall drag introduced here are suitable for SES with sidewall displacement up to about 30% of craft total weight. Where a larger proportion of craft weight is borne by the sidewalls, the sidehull wave-making should be considered directly, rather than as a 'correction' to the cushion wave- making. Below 70% contribution to support from the air cushion, the beneficial effect of the cushion itself rapidly dies away, and so it is more likely that optimizing cata- maran hulls will achieve the designer's requirements in the speed range to 40 knots. Above this speed, an air cushion supporting most of the craft weight is most likely to give the optimum design with minimum powering. Calculation method for parabola-shaped sidewalls [33] In the case where the sidewall water lines are slender and close to parabolic shape, then the wave-making drag of sidewalls can be written as (8 Av gin) (B s T 0 // s ) (3.43) where R^ is the wave-making drag of the sidewall (N), C sww the wave-making drag coefficient (Fig. 3.29), p w the density of water (Ns"/m ), B s the max. width of sidewalls (m) and T 0 the outer draft of sidewalls (m). B. A. Kolezaev method [19] Kolezaev defined the residual drag of sidewalls as a function of craft weight: where R^ is the residual drag of sidewalls (N), K fr the coefficient of sidewall residual drag, obtained from Fig. 3.30, and IV the craft weight (N). 1.6 10 12 14 l/2Fr 2 =g/ s /2v 2 Fig. 3.29 Wave-making drag coefficient of slender sidewalls with the parabolic water planes. [39] Underwater appendage drag 115 0 0.5 1.0 1.5 2.0 Fr,=v/Sgl c Fig. 3.30 Residual drag coefficient of sidewall as a function of LJB^ and Froude number. 3.10 Hydrodynamic momentum drag due to engine cooling water In general, the main engines mounted on SES have to be cooled by sea water which is ingested from Kingston valves or sea water scoops mounted at propeller brackets, via the cooling water system, then pumped out from sidewalls in a transverse direc- tion. The hydrodynamic momentum drag due to the cooling water can be written as R™ = /> w V. } G W (3.44) where R mvf is the hydrodynamic momentum drag due to the cooling water for engines (N), Fj the speed of inlet water, in general it can be taken as craft speed (m/s), and g w the flow rate of cooling water (m/s). 3,11 Underwater appendage drag Drag due to rudders, etc. Drag due to rudders and other foil-shaped appendages, such as plates preventing air ingestion, propeller and shafts brackets, etc. can be written as [34]: R t =C f[ (\+Sv/vY(l+r)S I q v (3.45) where R T is the drag due to the rudder and foil-shaped propeller and shaft brackets (N), C fr the friction coefficient, which is a function of Re and the roughness coefficient of the rudder surface. In this case Re = (vc/u) where c is the chord length of rudders or other foil-like appendages (m), dvlv is the factor considering the influence of propeller wake: [...]... the cushion length Effect of cushion pressure-length ratio Wave-making drag increases in proportion to the square of cushion pressure Cushion pressure also affects the craft outer draft, therefore the cushion pressure seriously affects the craft drag The effect of cushion pressure on hump drag will be further increased in the case of poorly designed skirt/seals Figure 3 .47 shows the effect of cushion. .. wetted surface of the sidewalls Figure 3 .49 shows the effect of inner draft change on drag of an SES model running on calm water 1 2 3 4 v,,,(m/s) Fig 3 .47 Influence of cushion length/beam ratio and pj( on total drag of craft models 1, 2, 3: see Fig 3 .44 Effect of various factors on drag 2 3 v(m/s) 4 5 Fig 3 .48 Influence of cushion length/beam ratio on total drag of craft models in different test tanks... the cushion pressure (N/nT), £ the coefficient due to the pressure loss, Q the flow rate (m /s) and S0 the area of outlet of the air duct (m") 2 Flow continuity equation: Q = &b + Qsw sb = Q, + Gb fi = e, + a, + (4. 2) (4. 3) (4. 4) where Qs is the air leakage from under the stern seal (m /s), Qb the air leakage due to bow trim (m /s), and Qsw is the air leakage under the sidewalls Flow rate equation: Air. .. Total ACV and SES drag over water X9.8N 16000 140 00 12000 10000 8000 6000 40 00 2000 20 40 60 80 100 120 140 v(km/h) 20 40 60 80 v(kn) Fig 3.33 The drag and thrust curves of SR.N4 etc.) is included in the air profile drag, because in general the air profile drag coefficient Ca, which can be obtained either by model experimental data or by the data from prototype craft or statistical data, implicitly includes... 0.022 0.02 0.016 0.013 1.0 1.5 6 6 6 6 6 5 4 2 2.5 2 2 40 5 15-30 2-5 2 123 1 24 Steady drag forces 0. 04 Craft speed v,=2m/s Finger type skirt 0.03 0.02 0.01 Firm snow 25 10 15 20 Skirt drag /Craft weight x 100(%) Fig 3.36 Skirt ground interference drag as a function of surface condition and ACV equivalent air gap /?, K [37] Test on concrete surface o o x 4 h 2 - 2 4 6 vs (m/s) 8 10 Fig 3.37 Skirt ground... stability is measured at craft designed speed 4. 2 Static transverse stability of SES on cushion Calculation of static transverse stability of an SES off cushion is similar to that for a conventional catamaran, so we can solve the problem for an SES by extending the calculation method for catamarans As shown in Fig 4. 1, the air cushion force (pc.Sc) will make a heeling moment with craft weight W, and the... valve of the air duct to adjust the running attitude of the craft in order to decrease the water contact drag of the skirt and the craft successfully passed though the hump speed 2 After a time, craft model 711 had been chosen to mount a flexible skirt The takeoff ability of the craft was improved significantly due to the enlarged air cushion area, which reduced the cushion pressure and cushion pressure-length... preliminary design phase, the graph in Fig 4. 3, showing the relation between transverse stability of craft on cushion and key craft geometrical parameters, may be used to ensure satisfactory stability The figure shows that a satisfactory ratio of transverse metacentric height to cushion beam hlBc can be obtained as soon as the relative thickness of sidewalls meets the relations shown in Fig 4. 3 for the cushion. .. volumetric displacement of the craft and pc cushion pressure) [40 ] Figure 4. 4 shows that the relation between the relative thickness of sidewall and cushion length/beam ratio The shaded zone, represents the craft parameters with satisfactory transverse stability [19] The figure was plotted by Kolezaev from statistical data obtained from practical ships The figures are given for designer's reference as a... PJD033 (where D is the volumetric displacement of the craft) 139 140 Stability BJB, 0.25 0.20 0.15 0.10 0.05 1CIBC Fig 4. 4 Craft statistics of relative sidewall thickness and cushion length/beam ratio configuration of sidewalls, characteristic parameters of lift fans, and bow/stern seal clearance, one has to keep in mind that the various craft design parameters have to be similar to that adopted in . A//C = 12 - 54 - ^ = 0 .4, a" = 0.25° Total ACV and SES drag over water 119 X9.8N 16000 140 00 12000 10000 8000 6000 40 00 20 40 60 80 100 120 140 v(km/h) 2000 20 40 60 80 v(kn) Fig. . achieve the designer's requirements in the speed range to 40 knots. Above this speed, an air cushion supporting most of the craft weight is most likely to give the optimum design. the equivalent air gap, where Q is the cushion flow rate (m'Vs), p 2 the cushion pressure (N/m), p a the air density (Ns 2 /m 4 ), l } the total length of air leakage at