Design, manufacture and full scale trial of high performance surface-piercing-propellers

Design, Manufacture and Full Scale Trial of High

Performance Surface-Piercing Propeller

Hwang, J-L(l); Wang, S-Y(2); Kouh, J-S(*); Wang, W-S(3); Yeh, T-C(4)l

An integrated design and geomet~ definition program is developed for surface-piercing-propeller (SPP). The design method is based on the basic SUS series data @om the Technische

University Berlin in Germany with correction of the expanded area ratio efect on pitch ratio. From the design program, the diameter, pitch, gear ratio, shafi angle, immersion ratio and stern jlap arrangement are determined with considerations on both the macimum speed and hump speed with maximum eficiency at maximum speed. The propeller surface geometry is defined by BAspline curve and spiine surface with speciai considerations on the blending surface of the jZlets. The fZlets must be careful~~nished for high speed propeller. Then, the well designed and developed geometry are preparing for manufacture. Two s-p propellers have been designed and manufactured for this stu~.

The first propeller is designed for a catamaran with draft only 50. 8cm(20’~, twin screw, 1100ps x 2100RPM, gear ratio 2.0, maximum speed of 30 knots only. SPP is the best choice for this special shallow draft vessel. The triai results are 30 knots with 2050 RPM and the cruising speed is 4 knots more than that of the original propeller.

The second propeller is than designed for a 55 knots fast patrol boat (UFPB-01) with

Lw x Bm xTXA =11.82m x 3.30m x 0.68m x 12 Tons, 735 ps x 2300 RPMx 2, gear ratio 1.12. The

final design of the SPP is 67.31cm x 99.06cm x 6 x 0.5 with eji?ciency of 0.71 estimated at propeller immersion ratio of 0.40. But the trial speed is only 47 knots at 2300 RPM After analyzing the sea trial results, it shows that the SUS propeller develops too large vertical force to change the optimum design running time angle. Vertical force efects must be carejidly considered during ship design. Rake eflect on vertical force is an important topic to be studied. The cooperation of university, propeller manufacture and ship yard will continue to develop high performance surface-piercing propeller.

(l)Department of Naval Architecture and Ocean Engineering, National Taiwan University, Taipei, Taiwan, R.O.C.

(2)Chung-Shan Institute of Science and Technology. (3)FASTER PROPULSION SYSTEM Co., LTD. (4)Lung-Teh Shipbuilding Co., LTD.

Introduction

Surface-piercing propeller applications for high-speed crafts and shallow draft vessels are steadily increasing within recent year. Not only pleasure crafts but also high-speed patrol boats are equipped with this ~pe of propulsor. Major advantages are little appendage drag, little danger of cavitation erosion and high propulsion efficiency. Inadequate propeller thrust to get over the hump resistance in transient state is still a big problem. Therefore, steerable transom gear to increase the propeller immersion or controllable pitch propeller application are the two ideas for SPP application.

The flow field around SPP is similar to that of super-cavitating propeller, but with more complications of water entrance and gas-vapor mixing problems. Especially, the secondary forces of SPP are also very important to be solved. Theoretical performance analysis and prediction have been attemped[ 1][2], but not been success for engineering applications, Individual model test and experience are still the design tools for SPP application. Up to now, some individual model test data or small propeller series data have been published (as in ref.[3-1l])for solving some independent problems. The SUS (~chnelle ~nkonventionelle Schiffe) is the most complete and useful test data base for SPP[ 12]. Not only the steady forces but also the secondary forces of SPP are included.

Design, model test, manufacture and sea trial analysis are the important ways for ship industry development. The secondary force has a crucial effect on high speed vessel performance. Sea trial analysis and feedback into design data base are the important works for SPP development. Two typical s-p propellers are in this study. One is for a shallow draft vessel, and the other is for a high speed patrol boat.

SUS Series

Characteristics

SUS propeller series is a complete eftlcient surface-piercing propeller series, which was developed by Kruppa & Wang [12] in the Technische Universitaet Berlin, ( T U Berline ). The main geometry parameters in the series are pitch ratio ( P/D ), expended area ratio ( EAR), hub ratio ( d~ ), maximum camber ratio ( f.u/c ) and skew, while the number of blade of six and zero rake angle are fixed. The geometry data of the model propeller is shown in table 1.

All the test were run in the famous fi-ee surface cavitation tunnel of ISM ( Institute fhr schiffs-und-Meerestechnik ). The main performance parameters considered are immersion ratio ( hP /I) ), shaft angle ( a ), pitch ratio ( P/D ) and cavitation number ( c ). The test parameter matrix is shown in table 2..

Geometry Characteristic

Surface-piercing propellers are usually designed with the same sense as fully cavitating propellers. Blade section is usual in sharp leading edge, blunt trailing edge and positive pressure side camber. High performance section forms are developed with the following principles in this series and shown in Fig. 1.

(1) The pressure side camber is concentrated near trailing edge and the maximum camber is at 80°A chord length from leading edge.

(2) The leading edge is very thin through the whole blade, while trailing edge is in blunt shape from root section to 0.5 radius and in sharp trailing edge from 0.5 radius to tip end.

(3) The thickness line is circular arc shape and the maximum thickness is determined from required section modulus.

Design Methodology

The design of SPP is more complex than that of the conventional submerged propellers. At least, three more parameters must be considered during design process, those are the cavitation number, shaft angle and immersion ratio. Due to the complicated flow field around SPP, systematic test results are still the most reliable design data base for SPP. From analyzing the valuable systematic test results of SUS series, the typical design chart is shown in Fig, 2, representing the following relationships.

Estimation of propeller diameter, pitch ratio and efficiency could be done quickly from this chart. The correction of pitch and diameter due to EAR effect is also got fi-om analyzing the test results as follows.

(~+~).,a? = ~ ()-(0 1475)(EAR-O.50) ₍₃₎

(~+ Ill,, ‘ “

The design program for SPP has been developed and the flow chart is shown in Fig. 4. The design is based on power option, same as that of subcavitation propellers, but with more design constraints to be satisfied, as shown in the followings.

(1) The propulsive thrust at hump speed must be calculated and a suitable thrust margin must be

considered for good acceleration [13].

(2) Stern gear arrangement and propeller immersion ratio must be considered during the vessel in transient condition.

(3) In general, 5% thrust margin is required at design speed.

Design Examples.

Two typical design cases of SPP are included in this study. The first one was designed for a 30 knots catamaran with draft only 50.8 cm (20”) and the second one was designed for a 55 knots fast patrol craft (UFPB-O 1) which was designed and manufactured by Lung-Teh Shipbuilding Co.

Table 3 lists the design parameters of the catamaran. Table 4 represents the hull resistance components and EHP for the vessel. The propeller geometry is designed with the necessary information of table 3 and table 4. Table 5 represents the design geometry data of SPP. The strength calculation is based on the DNV society rule with cyclical loading factor of 1.0, The propeller geometry is also shown in Fig. 5.

Table 6 lists the main particulars of high speed patrol boat. Table 7 represents the dynamical trim angle, hull resistance and EHP of the vessel by the method of Blount[14]. The final propeller geometry data are shown in table 8 and table 9. The propeller geometry is also shown in Fig. 6.

Representation of an expanded blade

geometry

To define the sectional curves and the outer contour of a propeller blade, the so-called B 1.-spline curves [15]

are chosen. A B Aspline curve is an extension from a B -spline curve which is defined by[16] :

Zj(”) = fJNi+*,k(u);j+l u E[0,1]lsj<m-(k-1) (4)

$=0 ;( :1=1...rn

where ~,(u) is the j-th parametric curve segment, jjj+l are the position vectors of the control points and Ni+l,~(u) are the normalized B -sphne basis functions of order k (degree k-1). A B A-spline curve is generated by subdividing asegment ofa B -spline curve into 1 segment (see Fig. 6)

If m data points (~,... ~m) are given, they are to be interpolated by means of a B A-spline curve. As shown in Fig. 7, by confining the curve through the data points, the following boundary conditions can be written:

{-Z-,)+, (0) = ~f i=l... m ₍₅₎

QA(~-,J(1)= pm

Because the number of segments of a B A-spline curve is increased from (m-1) to A (m-1), the number of

the total control points is also increased correspondingly, Woodward has proposed an implicit conversion algorithm to determine the contro 1 points for B2-splines [17]. The key idea of the method is as follows: Because a B -spline curve has an order of (k-1), it is everywhere Ck-2 continuous. This means equivalently that the (k- 1)-th differentiation of a B A-spline curve definition results in a constant vector.

Applying this property at the internal joints of the B -spline curve segments, yields:

Z:::)+r O) = 6:;:)+,+, (0) i=l...l-l r=l...l-l (6)

Similar to the definition of a B spline curve, a B

-spline surface is defined in tensor-product by:

~,,j(U,V) = ‘~’k~’Na+,,kU (U)kfb+,,kV(V)~i+a,,+b u, v E[0,1]

0=0 b.11

lsism-(k”-1) l<j<~-(~v-l)

~:t’=1,..m S=l... n (7)

where Q,,, (u, v) is the (i, j). th biparametric B -spline patch. ~i+.,j+~ are the control points of a defining polygon net. m and n are the control points in the u and V directions, respectively. k“ and ~ are the order in the u and V directions. Na+l,k”(u) and M~+l,k,(v) are the normalized basis fictions of order k,,(degree

k“-1) and ~(degree ~-1) in the u and Vdirections. If rnxn data points ~i,j(i= l... rn,j=n).. n) are given as shown in Fig. 9 and are interpolated by adopting a B -spline surface. Under the constraints that all data points have to be passed through, yields the following equations: [ Gi,j(0,0)=7/,j i=l... ]-] j=l...l–l ~n,_,,j(l,o)= Fmi,, j=l...l–l (8) QI,..I(oJ)= 7,,. i=I...m -1 dn,_,,n_,(l,l)= Fm,n

With the eqs. (8) and also the additional conditions proposed as [18] at the four boundary curves of a B

-spline surface, the control points of a B --spline surface can then be determined and the whole surface shape is thus defined completely by the eq. (7).

If the defined surface shape is not acceptable and needs some modification, the only way to complete the

task is to move the control points. Since the relationship between the control points and the given data points is

unique, the modified surface will not pass through all the data points any more. This drawback can be removed by subdividing a B -spline patch into au x 2, sub-patches, It

is namely a B 1 -spline surface as shown in Fig. 9. If a B A-spline surface is used to interpolate the same data points Fj,jti=l...m j=l...n) as before,

~(~-1) x ~@-1) sub-patches ~J(i=l..i@O,j=l. .~(n--l) have to be f~stly defined. To this end, it needs totally [Ati(m-1)+ (k. - 1)]x [Zv(n - 1) + (kv - 1)] control points. They are determined by an equation-system resulted tlom the following interpolation requirements:

QA(,-I)+I,AO-I)+I(OYO)=-pj.j i=l.,. m–1, j=l...n -Q~C~-,J,IuU-,J+I(l,O)‘PM.J j=l,..n _

~L(i-l)+l,~~.-iJ(O,l)‘-pin (=1...l–l

Q4(m-l),A(.-l)(LU= pm

(9)

9the same implicit conversion algorithms as used in the

case of a B A-spline curve as well as conditions at the four boundary curves of aB A-spline surface.

Fig. 11 shows a blade surface represented by the B A

-spline surface as described above.

Definition of a fillet surface

A fillet surface is to be constructed to blend the hub

and the blade surfaces. In this paper, the hub surface, denoted by 00, is defined in an implicit surface expression:

f(;) = o (lo)

where ~ is a vector, ~ = [x y Z], x, Y and Z are the Cartesian coordinates. On the other hand, the blade surface, denoted by YO, is defined by a parametric B A-spline surface:

; =&u, v) (11)

The mathematical model of the fillet surface is adopted from the method proposed by Hartmann [19]. In the method, classes of offset surfaces are defined for each to be blended surface. The offset surfaces corresponding to the hub, denoted by m=, are defined by

f(;) = c (12)

where os c s CO with CO> (). o, is thus a surface with a normal offset of c from @O. In a similar way, the offset surfaces corresponding to the blade, denoted by

Yd, are defined by

; = F(u,v,d) = ~(u, v) + d;(u,v) (13)

where Os ds dO with dO >0 and ;(u, v) is the unit surface normal vector of the blade surface D(u, V) and is

defined by

;(U,V)= y@u(u,v)x z. (w v) (14)

where 7 is a positive real value which may depend on

(u, V)(for example y = 1 or ~= @u. @p“). Similarly,

Yd is thus a surface with a normal offset of d from Y,. The both offset surfaces o ~ and Vd are combined by points of the correlation curve implicitly given by fimction:

h(c, d) = O (15)

)z(c, cl)= O contains the points (CO,O) and (O,dO). There the curve has contact with the c-axis and d-axis respectively of at least fust order (The axes are tangent to the curve (Fig. 12).). It means

hC(CO,O) =

O,

hd(cO

,o)

* 0,

hC(O,dO) #O, h~(O,dO)=O (17)

Each point (c, d) of the correlation curve

h(c, d) =o determinesa pair@c and ‘Ydof offset

surfaces, which should have a nontrivial intersection. If we consider the intersection curve @~n Yd of such a fixed pair, we get the equation

F’(z4,v,d)= y(~(u,v,d)) = c (18)

which implicitly describes the intersection curve in the u – v – parameter space. Substituting c in eq. (18) in the correlation curveh(c, d) = O, yields an implicit equation with u, v and d as variables:

G(u,v,d) =h(F’(u,v, d),d) = O (19)

Solving the eq. (19) for the unknown d, the fillet surface is then defined by substituting d in eq. (14).

In regarding to the correlation curve, different types can be considered [19]. In this paper, an ellipse-type (a special type of a superellipse) is chosen:

h(c,d)= (c/cO–l)2+(d/d0 –1)2- 1=0 (20)

The complete geometrical model of a surface-piercing-propeller after blending the hub and blade with a fillet surface is shown in Fig. 13, while Fig. 14 shows the same model with rendering.

Manufacture

The propeller blade surface and fillet are defined by BLspline surface. Casting, three-axis NC machining, polishing and balancing test are the normal standard procedures of FASTER propeller manufacture, The propellers are made of Ni-Al Bronze and the manufacture accuracy is 1S0 484/2-S class.

Sea-Trial Analysis

Sea trial results of the catamaran ffom shipyard is 30 knots with 2050 RPM and the cruising speed is 4 knots more than that of the their original propeller. It is a successful design.

The trial results of “UFPB-01” were carefi.dly run by us with DGPS system. Two different types of SPP were designed for this vessel. One is the SUS series propeller for research purpose, while the other one is an original design, with cupped section and DXP0,7~XZXEARof 0.6223 mX0.9266mX5X1.0. The comparisons of the blade section of 0.7R are shown in Fig. 15. The rake angle of SUS propeller is zero, while that of the cupped propeller is 10 degree.

“UFPB-O 1“ with cupped propeller gets a wondertld speed of 56 knots, while with SUS propeller gets only 47 knots. During the transient stage, the cupped propeller should change the immersion ratio through transom gear to get over the hump resistance, while the SUS propeller can accelerate easily to reach the maximum speed. The

trial results areshown in Fig. 16 for comparison.

The trim effect on hull resistance of “UFPB-O 1“ are great as shown in Fig. 17. IF the trim angle reduce 0.5 degree, the resistance may increase from 11% to 14’?40for speed within 45 knots to 55 knots. So, the trial speed of 8Kts less may be due to resistance increase (5.5Kts) and propeller efficiency loss (2.5Kts) as shown in Fig. 17. Running trim off the design condition due to vertical force of SUS propeller may be the real reason for the maximum speed only 47Kts. The test results of Prof. Kruppa also reveal the same trend that the higher the rake angle of propeller, the less the vertical force is [20].

The running trim effects on hull resistance increase must be carefully considered for the high speed vessel with SPP, especial to that with transom gear system. The

design of general arrangement should include the vertical force effect of propeller to get an optimum running trim state. Rake effect on vertical force of SPP is an interesting and important topic to be clarified for SPP application.

Concluding Remarks

From the above descriptions of this study, the following conclusions and suggestions are got.

1. The design methodology and design program developed from SUS-series model test data are reliable and usefid. 2. The Bk-spline surface definition is suitable for propeller

blade surface and fillet description.

3. The vertical force of surface-piercing propeller must be incorporated into hull form design to get an optimum running trim angle of high-speed vessel.

4. Rake effect on vertical force of surface-piercing propeller is an important topic to be studied.

Acknowledgement

We are acknowledged the supports from the Industry Development Bureau, R.O.C. We are also indebted to Prof. Dr.ing Kruppa. C.F.L for his comments and encouragement.

Reference

1. Furuya, 0,, “A Performance Prediction Theory for Partially Submerged Ventilated Propellers,” J. Fluid Mech., Vol. 151, 1985, pp. 311-335.

2. Vorus, W.s., “Forces on Surface-Piercing Propellers with Inclination,” J. of Ship Research, Vol, 35, No.3, Sep. 1991, pp.210-218.

3. Rose, J.C. and Kruppa, C.F.L., “Surface Piercing Propellers - Methodical Series Model Test Results,” FAST’91, June 1991, Norway.

4. Rose, J.C., Kmppa, C.F.L. and Koushan, K., “Surface Piercing Propellers - Propeller/Hull Interaction,” FAST’93, Dec. 1993, Japan.

5. Hadler, J.B. and Hecker, R., “Performance of Partially Submerged Propellers,” 7* Symposium on Naval Hydrodynamics, Aug. 1968, pp. 1449-1496.

6. Hecker, R., “Experimental Performance of a Partially Submerged Propeller in Inclined Flow;’ SNAME Spring Meeting, April 1973.

7. Brandt, H., “Modellversuche mit Schiffspropellem an der Wasseroberflaeche,” Dissertation der Technischen Universitaet Berlin (D83), Schiff und Hafen, Jahrgang 25, Heft 5,6, Juni 1973.

8. Bath, A., “Experimentelle Untersuchungen zur Frage der hydrodynamischen Fluegel-belastung teilgetauchter Schiffspropeller; Dissertation der Technischen Universitaet Berlin (D83), 1976.

9. Kruppa, C,F.L. and Radhi, M,, “Einfluss von Fluegelhang und - ruecklage bei teilgetauchten Hochgeschwindigkeitspropellem,” 2. Zwischen-bericht,

TUWISM Bericht Nr. 81/6, Berlin, 1981 (not Propellers, ” (Not published). published).

10. Krupp% C.F.L. and Radhi, M., “Einfluss von Fluegelhang und - ruecklage bei teilgetauchten Hochgeschwindigkeitspropellem,” TUB/ISM Bericht Nr. 84/6, Berlin, 1984 (not published).

11. Krupp% C.F.L., “Testing Surface Piercing Propeller,” Marin Jubilee Meeting, Workshop A: Advanced Vessels, May 1992, Wageningen, The Netherlands.

12. Wang, S.Y., “Systematische Analyse von Modellversuchen mit teilgetauchten Propelled,” Dissertation der Technischen Universitaet Berlin (D83), 1995.

13. Blount, D.L. and Fox, D.L., “Design of Propulsion Systems for High-Speed Craft Predictions,” Marine Technology , vol. 34, Oct. 1997.

14. Blount, D.L. and Bartee, R.J., “Small Craft Power Predictions,” Marine Technology, Jan. 1976.

15. M.A.Krokes and M. Slater: “Interactive Shape Control of Interpolation B-splines,” EUROGRAPHICS, Vol. 11, (1992).

16. D,F. Rogers and J.A. Adams: “Mathematics Element for Computer graphics;’ McGRAW Hill Publ., 2ndEd, pp. 333-335, (1989).

17. C. Woodward: “B2splines: A Local Representation for Cubic Spline Inter-polation~ The Visual Computer, VO1.3,pp. 152-161, (1987).

18. B.A. Barsky, “End Condition and Boundary Condition for Uniform B-Spline Curve and Surface Representations,” Computer in Industry, VO1.3,pp. 17-29, (1982).

19. Hartmann, E., “Blending an implicit with a parametric surface,” Computer-Aided Design 12,825-835, (1995).

20. Kruppa, C.F.L, “Testing Surface Piercing

144

Table 1 Geometry of Model Propellers(SUS)

Prop. D z PID A~Ao skew rake [”] d#D (fmJc)o.,

No. (mm) [01 (%) 1440 250 6 1.5 0.5 8 0 0.25 2.4 1441 250 6 1.5 0.79 0 0 0.25 1.4 1442 250 6 1.5 0.79 0 0 0.25 2.1 1443 250 6 1.5 0,79 15 0 0.25 1.4 1445 250 6 1.5 0,65 8 0 0.25 1.8 1446 250 6 1.2 0.5 8 0 0.25 2.4 1447 250 6 1.5 0,44 8 0 0.35 2.4

Table 2 Test condition Matrix

Flow velocity [m/s] 8 (in special case :6,5and 4.5) Cavitationnumbel u (0.1),0.2,0.5&u.,~ (V=4.5,c,,~=9.8; V=6.5, a,,~=4.7;

H

change) +5(1.8) ,0

(1.5), -5 (1.23), -10 V=8.0, u,m=3.1) 40,50,60 (1.0)

Table 3 Main ship parameters of CAT

LW (M) 24.0 M A(Tons) 60 Tons BHP(ps) 11OO(X2) RPM 2300 G.R. 2.0 Max. Draft (M) 0.508 Max Vel. (Kts) 30 No. of blade (Z) 5 FnD 2.5 + Fn Vs(kts) 1.25 37.27 1.20 35,78 1.15 34.29 1.10 32,80 1.05 31,30 1.00 29,81 0.95 28,32 0.90 26.83 0.80 23,85 Table 4 Resistance& E cR*~03cFs*lOJRTo(kgS) 1.255 1.728 9127 1.313 1,737 8583 1.375 1,747 8060 1.443 1.758 7545 1.518 1.769 7043 1.598 1.780 6558 1.698 1.792 6099 1.820 1.805 5669 2.130 1.834 4874 iP of CI Rfi(kgs) 417 384 353 323 294 267 241 216 171 T RTS(kgs) EHP(ps) 9544 2439 8967 2200 8413 1979 7868 1770 7337 1575 6825 1396 6340 1232 5885 1083 5045 825

Table 5 Geometry of SPP(I) for CAT

PropellerDesign SPP(I) D= 1016mm P= 927.1 mm Pm= 0.9125 z= 5 Lo~~/IE 0.4631 EAR= 0.95 Strengthchecked by DNV Rule r/R I(mm) ~(mm) t.Jmm) SK(mm) BL(mm) “ 0.165 182.0 2.11 56.4 0.0 29,0 0.20 214,0 2.95 53.6 0.0 26,0 0.25 263,3 4.04 49.9 -2.34 21,7 0.30 306.3 5.09 45.8 -7.01 17,7 0.35 348.5 6.14 41.8 -14.72 13.9 0.40 383,6 7.15 37.7 -20.12 10.4 0.50 440,7 8.95 30.0 -26.82 4,5 0.60 470,5 10,36 23.0 -28.14 1.0 0.70 465,2 10,88 16.8 -21.79 0.0 0.80 411,7 10.01 11.7 -4.01 0,0 0.90 316,9 7.55 7.0 23.47 0,0 0.95 230.0 5.79 4.7 40.23 0.0 1,0 0.0 0.00 2.5 54.31 0,0

Table 6 Main ship parameters of “UFPB-O 1“

h.(m) 13,50 LW1(m) 11,82 BPX(m) 3,30 @Transon 3.07m @F13 Draft(m) 0,68 l,c.g(m) 3.889 AP(mz) 34.26 S(m2) 36.20 A(Trial)(tons) 12.0ton Engine BHP/RPM 735 HP*212,300 EngineDHP 705 HP*2 Gear Ratio 1.12:1 Max. velocity(kts) 55.0 Fn ~ 5.99

Table 7 Resistance& Ehp of “UFPB-O 1“ Vs(kts)r(trim angles) R~O(kgs) Rflkgs) EHPO EHP(ps)

35 5.202 1771 1904 426.7 458.7 40 4.455 1811 1989 496.8 545.5 45 3.877 1903 2128 587.3 656.6 50 3.425 2044 2338 700.8 801.7 55 3.065 2226 3602 839.6 981.5 60 2.773 2443 2912 1005.6 1198,7

Table 8 Propeller Particulars of SPP(II) for “UFPB-O 1“

PropellerNo,1440 v [kts] 55.0 J 1.228 rl 0.705 ‘QJ’ 5.273”103 K~ K~(%) 8.5 Km/ K~(%) 25.6 CavitationNo. a 0.248 D(m) 0.673 Pm 1.472 I& m(%) 40 d@ 0.15 z 6 EAR 0.5

Table 9 Geometry of SPP(II) for “UFPB-O 1“

PropellerDesign SPP(II)

D= 6730 mm Pm= 1.472 P= 9907 mm z= 6 Lo,,@W= 02147 EAR= 0.50

Strength checkedby DNV Rule

r/R l(mm) ~(mm) ~(mm) SK(mm) 0.25 80.88 1.24 32.21 0.0 0.30 94.09 1.53 29.61 -2,66 0.35 107.03 1.85 27.05 -4,52 0.40 117.82 2.16 24.50 -5.52 0.50 135.34 2.75 19.51 -6.19 0.60 144.51 3.18 16,23 -5.36 0.70 142.89 3.34 13.46 -3.46 0.80 126.44 3.07 9.99 -0.53 0.90 97.33 2.32 7.04 3.26 0.95 70.50 1.78 5.73 5.52 1,0 0.00 0.00 2.48 8,0 At

1-

I

+

‘(’’’Q=’

,&

_.

..

Fig. 1 Blade section components & Geometry of SUS-Propeller

(“..I . ..*.*..*,

Fig. 2 SUS Design charts

Y“ t

Fig. 3 Design flow chart of SPP

A+J

<(0)?

.---

_&.,)ro

4

_E

Fig. 6 A B A-spline curve

Fig. 7 Subdividing of a B -spline curve segment

r —---+

‘B

\

Fig. 8 Expanded blade drawing

,,

Fig. 9 Interpolation of given data points by a B -spline surface -’J Z.@,).,,l., %! _d .--- < / --- , --. / --/ /. . Q+1,l., / /, I+ ---A-~. / ‘.,*, / \ / -.<’ \ / / .< --- L /, -.. /’ ./‘

“<

‘G7

.

“

Fig. 10 Subdivision of a B A-spline surface

dt

.__&

__.__c

o

Fig. 12 The correlation curve h(c,d) = O

Fig. 13 Complete geometrical model of a sp-prope :ller

o 20 40 60 80 100 120 140

X(nlm)

o 40 80 120 160 200 240

X(mm)

Fig. 15 Comparisons of cupped-prop section and SUS-prop, Section ( 0.7J

Fig. 14A sp-propeller with rendering

1400 1600 1800 2000 2200 240

NS( RPM)

Fig. 16 Sea trial results of “UFPB-01”

3000 2600 22CKI 2cxxl 18Wil I I I I I I I I 1 I 1 I k 44 46 48 50 52 54 56 58 6 Vs( knots)

I

S)DE MAXIM,). R0T4r40N PITCH EXPAI.DED r/R CVCL.. TIOM ‘HCKNESS D15TRIBUTIDN OUTLINE

RAD(. S

}-

—-—-—-—-—-J

2!2’

Fig.4 Geometry of SPP(I) for CAT

SIDE . ....”. _,,,.,,0. PITCH ,.,..0,0

EVE. V4TION ‘HICK NESS — “5’’’ 5””0” OLIT. !NE ,,0.5 ,,,

w

,0, “,,.