A Planing Boat's Thrust and Resistanc

A Planing Boat's Thrust and Resistanc Y Yoshida International Boat Research, Japan concurring Tokyo industrial Technical College of Tsuzuln Integrated Educational Institute,,Japan Abstract This paper is concerned with the balance of planing boat's thrust and resistance at the top speed. As an example the discussion was done about the trial test data of PT having 35 m in overall length, 9 m in width, 1304.3 kn (133.0 tonf) in displacement and three propellers. Thrust 184.0 kn (18.8 ton0 exceed total resistance slightly at the top speed 41.19 kt More difference between thrust and resistance is obtained as decreasing in speed. These show the validity of Attwood's proposition in his "Textbook of Theoretical Naval Architecture". The proposition says that overestimation of thrust by 10 O/o is necessary in case of having no design information. Author analyzed the propeller performance by nomogram based on Gawn's series test data of propellers. The resistance is presumed by empirical equations based on towing tank test data using 3.5 m length models. 1 Introduction A through discussion about resistance, thrust and trial test will be done 2 Resistance 2.1 Diff~culty of presuming resistance Though planing boat's hull is traditional, reasonable design bases is so few that engineers manage to design and make boats by the method of trial and error using their experience and sense. In high-speed range planing boats change their floating position, which enables us to estimate their resistance performance with difficulty. Dynamic lift together with making a tub on transom, which may be considered as the increment of a boat's overall length, should be taken into

consideration in addition to resistance These phenomena make us analvze with much difficulty, by which we will take long time until contribution to design a hull form Also experimental analyses require the tank in which large models can be towed with high speed and long time against damping of wave after a towing test. Few towing tank produce the experimental data. 2.2 Towing tank test Author use data of a series of towing tank tests to presume resistance. The tests were done by using tkeen kinds of 2.5 m length models [l] in Japan Defense Agency's towing tank (Meguro Towing Tank Tokyo). Up to 3.5 in Froude umber FT( =V l( g V' ) ' '') a set of total resistance coefficient C, 2 2 '3 (R i0.5pv V ' ), trim angle chan e A0 and non-dimensional draft change at '8 transom AD(=AD7/b, or AD'/V' ' ) IS obtained by measuring total resistance R, trim angle change A0 and dip of keel at transom AD' at intervals of 0.5 in Froude number.v,g, Vand p mean speed, gravity acceleration, displacement volume and density, respectively. 0 means initial trim angle, which is the angle between water line at rest and the straight line between the points on keel line at Ord. 10 (stem) and 5 (midship). A0 takes positive when bow up. AD takes positive for decreasing draft. bl is half width at stem. A boat having 100 tonf in displacement runs 46 kt, which means about 3.5 in Froude number. One of the examples of the test will be shown as follows. Fig. 1 shows the No. 403 model's hull bottom. The model is set at 0" in initial trim angle 0, having 588.40 N (60 kgf) in displacement. (see Fig.2) Up to about 3.5 in Froude number the model runs as shown figures from 3 through 9. (see from Fig. 3 through 9) 2.3 Resistance performance A planing boat's resistance performance differs from displacement type ships' one. In high-speed range planing boats change their floating position. Keel end point together with rotation of hull form by A9 around this point determines a floating position. Keel end point is obtained by sum of initial draft and AD' whose sign should be considered. C, A0 and AD are expressed by nondimensional form for the law of similarity, showing a pattern as increasing speed [l]. Frictional resistance is obtained by wetted surface area and frictional resistance coefficient. The area under water line, which is based on the floating position, can calculate wetted surface area. 2.4 Boat's resistance '4s an example the resistance of PT having 35 m in overall length, 9 m in width 1304 3 IcN (133.0 ton9 in displacement [2] was obtained. A set of C,, A0 and AD at a Froude number is presumed by the etnpirical equations based on the data of

Figure 1 : Bottom Figure 2 : V = 0.000 m/sec, F, = 0.000 Figure 3 : V = 1.000 dsec, F, = 0.5 1 1

Figure 4 : V = 2.000 dsec, F, = 1.021 Figure 5 : V = 3.000 dsec, F, = 1.53 1 Figure 6 : V = 4 000 dsec, F, = 2.042

Figure 7 : V = 5.141 &sec, F, = 2.623 Figure 8 : V = 6.169 m/sec, F, = 3.1 50 Figure 9 : V = 7.198 dsec, F, = 3.675

the above-mentioned towing tank test, using four hull form parameters LIC''. h2 b2 /V1 and 8. L is length from Ord. 10 (stem) to 0 (bow). h2and b2 are chine height from base line (or keel line ) and half width at 0rd.5 (midship). 8 is trim angle at rest. Two kinds of empirical equations are made by the method of least squares [l]. The one is the linear equation that consists of these four hull form parameters. ( L /V l3 ) and 8 are added to the linear equation, which makes the other equation i.e. the quadratic equation. The total resistances of the boat R, were obtained by these equations. The dotted line in Fig. 10 shows the R, obtained by the linear equation and solid line the quadratic equation. The balance of resistance and thrust of the boat should be discussed. 3 Analysis of propellers First of all, author shows the method of analysis about a propeller. 3.1 Overlay system The method of overlay system [3] is used. The outline of the system is as follows. Inflow velocity into propeller V, and diameter of propeller D are logarithmically scaled on abscissa and ordinate respectively. (see Fig. 11 and 12). Straight lines power (ps) and revolution (rpm) are put on the co- ordinates, which is called A-chart. Curves propeller pitch ratio p/d, propeller Eficiency and critical inflow velocity into propeller against origination of cavitation V,,' together with a base point are written on B-chart, which are based on experimental data of a series of propeller tests such as Gawn's ones etc. [4],[5] and [6]. A set of B-charts for blade area rations BAR=0.50, 0.65, 0.80, 0.95 and l. l0 is provided. This method will be used to analyze PT's propellers at the top speed during trial test. 3.2 Trial test PT has a propeller at center driven by gas turbine together with two side propellers driven by each Diesel engine. Viewed from bow, propeller at center rotates clockwise and two side ones rotate counterclockwise. A series of trial tests of PT was done in Setonaikai sea Japan (E 131" 15' 14", N 33" 57' 9"). Speed V, (kt), propeller shaft revolution N (rpm), propeller shaft horsepower SHP (ps) and trim angle change A8 (deg.) at each engine rate were measured during the test 4 1.19 kt at the top speed was obtained. 3.3 Center propeller at the top speed Center propeller's BAR equals to 0.60. B-chart having BAR=0.65 is selected to analyze. which is close to 0.60. A-chart is overlaid by this B-chart [7].

-K-*++ GAWN +-H.+ CBLAClE AREA RAT 10-1. 1 > ***A-CHART*** Figure 11 : New center propeller

Figure 12 : New propeller of side

A-chart's horizontal lines are put in parallel with B-chart's ones. Consequently, A-chart's and B-chart's vertical lines are put in parallel. Both A-and B-chart have been put in the right position. The intersection of SHP = 4680 ps and N=1704 rpm lines is plotted by "0" mark on A-chart, on which the base point of the B-chart by "0" mark is superposed. Then the superposed point is seen as "@ mark. The intersection of horizontal D=1.040 m and curve p/d=1.196 lines is plotted by "A" mark. V,= 67 kt by this "A" mark, exceeding V, (=4l.l9kt) This means that center propeller has cavitations. During analysis wake fraction o is taken as zero because of high speed. Reforming propeller items is necessary to get new center propeller. 3.4 Propellers of sides at the top speed About one of these propellers discussion will be done. A propeller's BAR equals to 1.10. B-chart having BAR=l. 10 is selected to analyze. A-chart is overlaid by this B-chart [7]. Both A-and B-chart have been put in the right position. The intersection of SHP = 2780 ps and N = 1706 rpm lines is plotted by "0" mark on A-chart, on which the base point of the B-chart by ''0" mark is superposed. Then the superposed point is seen as "Q" mark. The intersection of horizontal D = 0.830 m and curve p/d = 1.000 lines is plotted by "A" mark. V,= 32 kt by this "A" mark, exceeding V,,' ( = 25 kt ). This means that propellers of both sides have cavitation. During analysis wake fraction w is taken as zero because of high speed. Reforming propeller items is necessary to get new propellers of both sides. 3.5 New center propeller at the top speed No cavitation occurrence is important. Although enlarging area of propeller is one of the methods for no cavitation, there are few propellers that exceed 1.10 in BAR. Keeping BAR 1.10 level, a trial will be done by increasing D to 1.100 m 1evel.A-chart is overlaid by this B-chart as Fig. 11.Both A-and B-chart have been put in the right position. The intersection of SHP = 4680 ps and N = 1704 rpm lines is plotted by "0" mark on A-chart, on which the base point of the B-chart mark is superposed. Then the superposed point is seen as mark. by "0" "Q" The intersection of horizontal D = 1.100 m and curve pid = 0.75 lines plotted by "A" mark. By this "A" mark V,, = V,,' = 41 kt and q = 0.49 are obtained. Condition of V,, = V,,' is taken to get propeller having high efficiency. 3.6 New propellers of sides at the top speed About one of these propellers discussion will be done under no cavitation occurrence. Increasing D to 1.000 m level and decreasing BAR to 0.95 one will do a trial. A-chart is overlaid by this B-chart as Fig. 12. Both A- and B-chart have been put in the right position. The intersection of SHP=2780 ps and N = 1706 rpm lines is plotted by ''0" mark on A-chart, on which the base point of the B-chart by "0" mark is superposed. Then the superposed point is seen as "Q"

mark. The intersection of horizontal D = 1.000 m and curve p/d = 0.80 lines is plotted by "A" mark. By this "A" mark V,, = 41 kt, V,,' = 42 kt and q = 0.57 are obtained. V,, 5 V,,', which has no cavitation. Condition of V,, = V,,' is taken to get propeller having high efficiency. 4. Thrust It is difficult to presume thrust of a propeller having cavitation. A little changing propeller items will cause propeller to get no cavitation as the previous section. An approximate value of PT's thrust will be obtained under such a condition. 4.1 Thrust of new center propeller at the top speed Thrust horse power THP will be obtained as THP = DHP q = 4680 X 0.49 = 2293 ps at the top speed V, = 41.19 kt or v, = 21.190 rnisec. Delivered horsepower DHF' equals to shaft horsepower SHP in the present calculation. Using horizontal component of THP, the thrust T, is obtained as follows. T, = (75 THP l v,) cos (12"30' + 3"OO') =(75X2293 121.190) X 0.9636=7821 kgf Angle between water line and shaft lines is 12"30' and trim angle change at the top speed 3 "00' 4.2 Thrust of new propellers of sides at the top speed About one of the propellers discussions will be done. THP = DHP - q = 2780 X 0.57 = 1585 ps at the top speed, the thrust T, is obtained as follows. T,= (75 THPI v,) cos (9"48' + 3-00,) = ( 75X l585/2l.l9o) X 0.9751 = 5471 kgf Angle between water line and shaft lines is 9"48' and trim angle change at the top speed 3"OO'. 4.3 Total thrust at the top speed Total thrust T is obtained by adding these three axes' thrust

5 Study of results Calculation shows that about 97 % of each propeller's THP contribute to horizontal component. This T should be compared with total resistance Rs. Total thrust at V, was obtained against not only at the top speed but also other speed as shown in Fig. 10 by applying the present method to trial test data under constant D and pm. The results are plotted by"o"marks, which should be compared with Rs. Propulsive coefficient 4, (= EHPISHP) shows 0.50 in high-speed range, which is reasonable value. EHP is effective horsepower. T takes larger value than R, up to the top speed. The difference between T and increases as decreasing speed, showing enough thrust. Seeing curves and trial test data in Fig. 10, we can admit Attwood's proposition. Attwood [S] has proposed that overestimation of thrust by 10 % at a design speed is recommendable in case of not having reliable information. Conclusions Synthetic discussion about resistance, thrust and trial test of planing boat were done based on the data from tank tests and trial tests on sea. PT's reasonable balance of resistance and thrust at the top speed was obtained with enough thrust up to the top speed. We can admit Attwood's proposition that overestimation of thrust by 10 % at a design speed is recommendable in case of not having reliable information. References [l] Yoshida, Y Optimum Design of a Planing Boat's hull Form, Marine Technology III, eds. Graczyk, T., Jastrzebski, T. & Brebbia, C.A. WIT Press, 2000. [2] Raymond, V & Blackman, B. (eds). June 's Fighting Ships Londons, p.213. 1975-1976. [j] Tanaka, H., Araki. K.; & Yoshida, Y Study of Nornogram,for Research and Design High-speed-crft 's Propeller ' Hull form and of It's Application, Transactions of The West-Japan Society of Naval Architects, No.61 pp. 113-124, Mar.1981. [4] Gawn, R. W & Burrill, L.C. The Effect of Cavitation on theperformanceofa Series of 16 inch Model Propellers, Trans. INA Vo1.99, 1957. [5] Gawn, R.W.L. The Effect of Pitch and Blade Width on Propeller Performance, INA Vo1.94. pp. 716-8 17, Sep. 1952 [6] Eggert, E.F. Propeller Cavitation, Trans. SNAME, p.58, 1930. [7] Yoshida, Y. An Approximate Value of Planing Boat Thrust, Proc. of 6"' Int. Symp. On Marine Engineering Tokyo Vol.1, pp. 135-142, Oct.23-27 2000. [S] Attwood, E.L. Textbook of Theoretical Naval Architecture, 1922.