Resistance characteristics of small and fast monohull vessels M. Rezaul Abid, C.C. Hsiung Department of Mechanical Engineering, Technical University of Nova Scotia, Halifax, Nova Scotia, Canada B3J 2X4 Abstract In this paper, resistance results of three models, each representing a typical hull form of a category, are examined with respect to their resistance, sinkage and trim characteristics. The three hull forms concerned are of the categories: displacement, semi-displacement or semi-planing, and fullyplaning with transom sterns. Parameters varied and studied include the longitudinal position of the centre of gravity and the loading conditions over a range of speeds corresponding to the maximum operating volume Froude numbers of Fny ~ 1.75 for the displacement hull, Fny % 2.5 for the semi-planing hull and Fny % 3.9 for the fully-planing hull. Hull forms were developed and hydrostatics were calculated with the aid of a computer aided ship design package run at the Centre for Marine Vessel Design and Research (CMVDR) and all tank experiments were conducted in the 30-m towing tank of the Technical University of Nova Scotia (TUNS). The experimental results along with the non-dimensional trends of the performance of each type based on resistance characteristics, sinkage and trim attitude have been made and presented. Nomenclature B Breadth Moulded of Midship Section Bmax Maximum Breadth at LCG CA Correlation Allowance Cf Fractional Resistance Coefficient C'r Residuary Resistance Coefficient Ct Total Resistance Coefficient A, Disp Weight Displacement (general)
94 Advances in Fluid Mechanics Am As Fn, FNL» Fn Fnb, FNB, Fnb Fnv, Fnv, FNV Fs g H LOA, LOA LCGI LCG L*i, LWL LT V R Rn, Rn RT, Rt p S TAO, a V Vcg, VCG Model Weight Displacement in Tank Water Ship Weight Displacement in Salt Water Froude Number Based on Waterline Length Froude Number Based on Beam Froude Number Based on Displaced Volume Net Skin-Friction Force on the Wetted Hull Acceleration due to Gravity Sinkage, Heave, Hydrodynamic Centre Length Overall Longitudinal Position of the Centre of Gravity Length of the Water Plane Long ton Volume Displacement Horizontal Dynamic Force, Drag Reynolds Number Based on Waterline Length Total Resistance Force Density of Water Wetted Surface Area Trim Angle Forward Velocity Vertical Position of the Centre of Gravity Subscripts model ship 1 Introduction The ever-increasing demands for speed in marine craft have led to the evolution of high-speed craft like semi-planing^ and planing hulls^ that part of their weight is supported by dynamic forces to overcome the inherent hydrodynamic limitations associated with high-speed operation of the conventional displacement hull. The present work is the result of a research project* that was undertaken with the main objective of finding a replacement of hull form for the traditional fishing vessels of the Canadian Eastern Seaboard^. The so-called Cape Islander displacement hulls suffer heavily from excessive resistance increase* at speed higher than 9-10 knots as the dynamic pressure on the longitudinally and transversely curved convex surfaces at the stern and bilges of such a hull operating at high speed is negative. The new hull shape would be fuel efficient and would operate at a higher speed range of 15-20 knots without much increase of the total resistance. This was accomplished in two ways: first, by suitably refining the lines of the existing hull form, the hydrodynamic forces developed during forward motion would be sufficient enough to support a substantial proportion of the craft's weight by pushing a portion of the hull out of the water, thus reducing the wetted area; the other is by developing a new hull form. Model RGP-3042 is the result of thefirstapproach and Model T-3012 is of the second.
Advances in Fluid Mechanics 95 2 Selection of Hull Shapes and Test Conditions 2.1 Displacement Hull: Linda M.C. Table 1: Test Conditions for Model Linda M.C. LCG (%LQA Fwd. Transom) As (LT SW) Speed Range (knots) Am (gms FW) Condition 40 45 50 13.72 13.72 13.72 2129 2129 2129 45 50 Load I Load I 45 50 21.69 21.69 3365 3365 Load II load II Linda M.C. is a 42 foot fishing vessel (Figure 1). It has a length/beam (L/B) ratio of 2.88. The test model of Linda M.C. was built to a linear scale of 1:18.533. Table 1 shows the test conditions and speed range for the model Linda M.C. to be tested at three longitudinal centre of gravity (LCG) locations. LCG position of 40%LoA was later discarded* at two of the loading conditions. Figure 1: Lines Plan of Linda M.C. 2.2 Semi-Planing Hull: RGP-3042 RGP-3042 is a 42 foot double-chine semi-planing hull with an L/B ratio of 2.85 (Figure 2). It was developed mainly by flattening the after-body
96 Advances in Fluid Mechanics Figure 2: Lines Plan of RGP-3042 buttock lines of Linda M.C. and raising them to an effective deadrise angle (measured at mid-chine length) of 12.5. The test-model of RGP-3042 was built to a linear scale ratio of 1:18.533. The hull form with developable surfaces from the lines plan is shown in Figure 2. The test conditions for RGP-3042 are given in Table 2. Table 2: Test Conditions for Model RGP-3042 (%LQA LCG As Fwd. Transom) (LT SW) Speed Range (knots) Am (gms FW) Condition 37.5 40.0 425 45.0 37.5 40.0 42.5 45.0 10.01 10.01 10.01 10.01 1553 1553 1553 1553 Load Load Load Load 2.3 Fully-Planing Hull: T-3012 T-3012 is a 43 foot hard-chine (single chine) fully-planing hull with an L/B ratio of 3.0 and a deadrise angle of 12" (Figure 3). It has an integral chine spray strake extending over the total chine length and having a width equal to 7% of maximum beam. A linear scale ratio of 1:19.287 was used to build the test-model of T-3012. The model was to be tested at three LCG locations each for a set of four arbitrarily chosen displacement conditions and upto a maximum full scale speed of 34 knots as given in Table 3.
Advances in Fluid Mechanics 97 Figure 3: Lines Plan of T-3012 Modelling Theory and Resistance Calculation Table 3: Test Conditions for Model T-3012 LCG (%LQA Fwd. Transom) As (LT SW) Speed Range (knots) Am (gms FW) Condition 25 30 35 9.62 8.83 8.83 6-33 1324 1216 1216 25 30 35 25 30 35 13.26 13.26 13.26 17.66 17.66 17.66 6-33 6-31 1825 1825 1825 2432 2432 2432 Load I Load I Load I Load II Load II Load II 25 30 35 22.09 22.09 22.09 6-31 6-33 3042 3042 3042 Load III Load III Load III Based on the dimensional analysis, the total resistance coefficient (Ct) of a marine vessel is a function of Froude number, (F^), and Reynolds number, where, Ct 1^,25 ^ the residuary resistance coefficient including wave making resistance, form drag and other resistance components except the skin friction, and Cf is the frictional resistance coefficient of an equivalent flat plate with equal length and equal wetted area of a vessel. In practice, Cf (1)
98 Advances in Fluid Mechanics is determined either by the ATTC line or the ITTC line which are experimentally fitted frictional resistance coefficient curves for the turbulent flow. In the present study Cf(Rn) is computed by the ITTC 1957 Model-Ship Correlation Line: 0-075,ox 2 (2) (logiokn-2) The model resistance test is conducted in a water basin by towing the model at a velocity determined by Froude's Law of Similitude, as (Fn) = (Fn), then (C^ = (C,)., where, C, = T^. There are several definitions of the Froude number for the semi-planing and planing vessel experiment. Since the wetted length of such a vessel is not always constant. The beam Froude number is defined as FnB = ~r, and the volumetric Froude number is defined as F^v = / nr k this work, y g9% Fnv is adopted as the speed parameter. The total resistance coefficient of the full-scale vessel can be found by extrapolating the model test results as follows: or, where, (!).- +. Ct, = Cr, + Cf, 4- CA (4) Cfs = frictional resistance coefficient of the smooth ship calculated following equation (2) CA = correlation allowance that must be added to account the roughness of hull surface. A constant value of 0.0004 was used in all the full scale prediction calculation regardless of the hull type Therefore, we have, Ct, = Cm + Cf, + 0.0004 (5) as the expression for the extrapolation of model resistance data to full scale ships. 4 Results and Discussion 4.1 Model Test Results Calm water resistance tests had been conducted for three models of different hydrodynamic properties but with comparable slenderness (L/B ratio) and loading conditions for a set of 27 test conditions with different LCG locations and speeds. The non-dimensiorialised results of one set of such
Advances in Fluid Mechanics 99 i i " i " i i rr ' ' ' _' _' ' ' v.\- 0.0 0.4 0.8 1.2 1.6 2.0 Volume Fraud* No. Fnv -r-r-r-!/. _L_L_L # '» -. r-r L _ L _ ~ri 0.0 0.4 0.8 Volume Freud* 0.0 0.4 0.8 1.2 1.6 2.0 Volume Freud* No. Fnv <^ :ir:c3cu: ^f-rjrr'r m&ffrr-r Volume Froude No. Fnv 0.0 0.4 0.8 1.2 1.6 Volume Freud* No. Fnv LCG = 45% LOA Fwd. Transom O Tank water temp. - 23.0 de*(c) LCG = 50% LOA Fwd. Transom O Tank water temp. - 22.9 dej(c) Model : Linda M C. Disp. = 2.789 kg Figure 4: Non-dimensional test results plotted against F^v for model Linda M.C. Disp.=2.789 kg tests are given herein as a series of curves of, TAO, Ctm, model ( ^ ) plotted against F^v (Figures 4,5 and 6). They have shown a \ ** / model definite qualitative pattern in the performance for each vehicle type. 4.2 Comparison of Full- Scale Results Based on ITTC 1957 Ship-Model Frictional Resistance Coefficient Line a scheme* was taken to compute and compare the extrapolated full scale resistance per unit displacement and effective horsepower requirements of the three hull forms under investigation. The results for one of the loading conditions are shown as Figures 7 and 8. It is evident from the plots that the planing hull performs very well in the high speed (above 25 knots) region; while the results are not that promising within the slow (upto 10 knots) and medium (from 10 to 20 knots) operating speeds regions. It can be easily perceived that the semi-planing hull has the lowest resistance per unit displacement values and lesser power requirements for speed up to 20 knots for the same kind of displacement and loading condition. Although, in the low volume Froude number region there is not much difference in the
100 Advances in Fluid Mechanics Volume Froude No. fm LCG = 42.5% LOA Fwd. Transom ' Tuxk w»ur t.mp. -21.6 *«c<c) LCG - 45.0% LOA Fwd. Transom Tank w.ur t.mp. - 22.7 «Uf(C) Model : RGP-3042 Dlsp. = 2.769 kg Figure 5: Non-dimensional test results plotted against F^v for model RGP- 3042 Disp.=2.789 kg Volume Froude No. Fi Figure 6: Non-dimensional test results plotted against 3042 LCG=30%LOA for model T-
Advances in Fluid Mechanics 101 Full Scolo Displacement = 18 LT (opprpn.) «0.15 - rreuda No. For ICC 46.0% LOA Fvd. LCC A^O.OX LOA LCO J7.6X LOA f*d. T LCC - 40.0X U>A LOG «2.6X LOA f»d- LCC J6.0X LOA f^ LCC - ^5.0% LOA Nd. Tr LCC 90.0X LOA f»d. Tr LCC - &8.0X LOA r i. Figure 7: Plot of Rt/A as a function of Fnv for a displacement of 18 LT; various LOG positions * Figure 8: Plot of EHP LCG positions Ship Sp««d (KooU) as a function of ship speed for A = 18 LT; various
102 Advances in Fluid Mechanics performance among the hulls in terms of ^ and EHP values. A comparison of the performances of Linda M.C., RGP-3042 and T -3012 based on the predicted results together with the model test results of six inshore fishing vessels*'^ has been done and presented as Tables 5.1 and 5.2 of [1], Similar trends as above were observed, that is, RGP-3042 fulfils the objective of finding a replacement hull form for the Eastern Canadian Inshore Fishing Vessel Fleet and operates efficiently at higher speed range of 18-20 knots with much less EHP requirements than the existing ones. Acknowledgements The first author acknowledges thefinancialsupport provided by the Canadian Commonwealth Scholarship and Fellowship Committee while the research work was conducted. He also appreciates Professor Matiur Rahman's suggestions and encouragements which led to the submission of this paper for AFM 96 conference. References 1. Abid, Rezaul M., An Experimental Investigation of Resistance Characteristics of Planing, Semi-Planing and Displacement Hulls, MASc. thesis, Technical University of Nova Scotia (TUNS), March 1994. 2. Compton, Roger H., Resistance of a systematic series of semiplaning transom-stern hulls, Marine Technology, Vol. 23, No. 4, October 1986. 3. Fridsma, G., A systematic study of the rough water performance of planing boats, Davidson Laboratory, Stevens Institute of Technology, Report 1275, November 1969. 4. Model tests of six eastern Canadian inshore fishing vessels, Project Report No. 119, Fisheries Development Branch, Scotia-Fundy Region, Nova Scotia, Canada. 5. Project Report No. 140, Fisheries Development Branch, Scotia-Fundy Region, Nova Scotia, Canada.