On the effect of transom area on the resistance of high-speed catamaran hulls

•/o"' International Conference on Fast Sea Transportation FAST 2009, Athens, Greece, October 2009

ON THE E F F E C T OF TRANSOM AREA ON THE RESISTANCE OF

HIGH-SPEED CATAMARAN HULLS

Jacques B. Hadler\ Kathleen M . Cain^ and Elizabeth M . Singleton^ ' JVebb Institute, Glen Cove, New York, USX

^NAVSEA, Washington, DC, USA

ABSTRACT

This paper is a continuation of the work presented by the first author at FAST'07 on high-speed mono-hulls in which the transom area was varied from 10 to 100 percent of the maximum section. In this paper five of those same hulls were duplicated and tested in the catamaran configuration with hull centeriine spacing's of 0.2, 0.3 and 0.4 of the model length. The result of resistance, heave and trim measurements made on this systematic series of five models are presented. The hulls had a length-to-beam ratio of 12, the same design water plane, the same bow and were tested at the same length-volume ratio over a speed range from FN = 0.2 to 1.1. The hulls used semi-elliptical sections that minimized the wetted surface. The results of the tests showed that stem form has a marked impact on the calm water resistance of hi-speed catamaran hull fomis over the whole speed range, particularly at FN below 0.85. As both mono-hulls and catamarans the base drag of the transom showed a marked effect upon the residuary resistance; affecting both the magnitude and speed where the peak residuary resistance coefficient occurred. Comparison of the resistance of this series of catamarans with a comparable catamaran model designed and tested at the University of Southampton showed a significant reducrion in wave interference resistance, thus reducing the total resistance.

KEYWORDS: Catamaran, Multi-hull, High-Speed, Resistance, Transom NOMENCLATURE

CF = Frictional resistance coefficient based on ITTC 1957 correlation line CR= Residuary resistance coefficient = CT - CF

CT = Total resistance coefficient = Rx/rSV^ Cw = Water plane coefficient

FN = Froude number = ^l^gh L = Model LWL

RR= Residuary resistance RT= Total resistance Sw = Static wetted surface

S/L = Hull Separation Ratio - centeriine to centeriine V = Velocity

r = Density

1. INTRODUCTION

This paper is a continuation of the analytical and experimental work presented by the first author at FAST'07 (Hadler et al. 2007) and FAST'05 (Hadler 2005) on high-speed mono-hulls. The experiments on the hull forms developed in the paper presented at FAST'07 have now been extended to catamarans, since those results clearly showed that the resistance of hull forms with larger transom area had significantly higher resistance over the whole speed range. Eight model configurations were originally developed with transom areas vaiying from 10 to 100 percent of the maximum section. Five of these models were duplicated in fiberglass using the original models as plugs to make the molds and tested with hull centeriine spacing's of 0.2, 0.3 and 0.4 of the model length. The resistance, trim and heave of these models were measured in the Robinson Model Basin at Webb Institute over a Froude number, FN, range of 0.2 to 1.1.

It is the objective of this paper to present the resuhs of these experiments along with an analysis of the results. The results of these experiments have been compared with those conducted by the University of Southampton (USH) on models of comparable size and principal dimensions (Molland 1995).

2. DESCWPTION OF MODELS

The models for this catamaran series were the same as those previously developed for the monohuU series presented at FAST'07 (Hadler et al. 2007). The following is a description, extracted from that paper, of the models and their design process.

"The design of a systematic series with a mathematically derived hull is somewhat different than one derived from a parent hull with specific geometric parameters systematically varied. The mathematically derived hull fonn offers a more flexible means for controlling the hull geometric characteristics in the design of a series to evaluate a specified hull characteristic, such as the subject of this paper.

For this study it was decided to use a 'LN^'^ ratio = 8.5 since that had been used in a previous study (Hadler et al. 2003) and it was one of the values used for thi-ee sets of the models in the University of Southampton catamaran series (Molland 1995). A statistical study of many existing catamaran vessels also indicated that this is a median value.

An L/B ratio of 12 was based on a parametric study utilizing the mathematical model to determine the L/B ratio that produced the minimum wetted surface. This study indicated that L/B variations fi-om 11 to 13 showed only small variations in the minimum wetted surface coefficient, thus a value of 12 was chosen for this study.

Four parameters are required to delineate the DWL; besides the L/B they are, the longitudinal location of maximum beam, Cw, and the half angle of entrance, a). Since this is a transom stem area study and most wateijet propelled catamaran hulls require a wide transom, the maximum beam is located at the transom. The value of Cw was derived by obsei-vation of waterline shape through a parametric study. The qualities desired were an almost constant beam over the last 4 stations, a continuous first derivative of the waterline shape with no inflections and a fme angle of entrance. This was achieved with a Cw = 0.75 and a half angle of entrance = 6.871 degrees. Yeh (1965) recorded in Series 64 the wave profiles along side of the huh at a number of speeds. The half angle of entrance of his hulls varied from 3.7 to 7.8 degrees. Those with the finest angles tended to have the lowest wave profiles, thus it appeared that the value chosen was a good compromise.

The keel line was similar to that of Series 64, a small linear rise of the forefoot starting at station 8. The keel line of the stem had to be different in each model to accommodate the desired transom area and a continuous sectional area curve with minimal inflection at the keel transitional pomts. Two models. Model B and Model C, had the same transom stem area ratio of 0.70 but different slopes of the keel line. The objective was to deteimine if slope was significant. Model B with the steepest slope also had the greatest discontinuity in the sectional area cui-ve due to the use of a straight keel line, which was later modified for Models D and E with the smallest transom areas.

With this hull design approach the forebody of each configuration is identical except for the B/T ratio which of necessity had to be different for each model in order to obtain the desired displacement."

The major characteristics of the demi-hulls of the catamarans are tabulated in Table 1. Also included is a model from the USH catamaran seriés, the results of which will be compared with those obtain from the tests perfomied on the Transom series.

T a b l e 1. - Model Characteristics

Model A Model C Model D Model E Model E

Mod 2 U S H Model 5b L W L ( m ) 1.511 1.511 1.511 1.511 1.511 1.60 At /Ax 1.00 0.70 0.40 0.10 0.25 0.534 L / B 12.0 12.0 12.0 12.0 12.0 11.0 B / T 2.479 2.250 2.151 2.026 2.031 2.0 L A / o l ^ ' ^ 8.50 8.50 8.50 8.50 8.50 8.50 S w / V o l " ^ 7.306 7.421 7.486 7.595 7.595 7.789 Cb 0.581 0.528 0.504 0.475 0.474 0.397 L C B / L W L 0.605 0.579 0.561 0.540 0.542 0.564

The PWL of all of the models is shown in Fig. 1 and the keel line profde of all of the models in Fig. 2. The body plan of Model C is shown in Fig. 3. The others are similar except in the afterbody where the minor axis of the elliptical sections varies depending upon the draft of the section.

Since Models B and C have the same transom areas and the resuhs from the monohull tests did not show a significant difference in the high speed range of interest for catamarans, Model B was dropped from the catamaran series due to its greater discontinuity in the sectional area curve at the keel junction point.

The results of the monohull test on Model E with a hook in the buttock, identified as Model E Mod 2, had shown a significant reduction in resistance over the whole speed range, thus this variation has also been incoiporated into the catamaran series.

7

-1-Statlons

^ 1.0 ^ 0.8 H . 1 0.6 w 0) 0.4 c o \ N Q 0.2 0.0

\

Fig. 2. Non-Dlmensional Profile of Parent Models

D W L

Fig. 3. - Body Plan of Model C 3. TEST CONDITIONS

The model experiments were canied out in the towing tank in the Robinson Model Basin at Webb Institute that has the following characteristics:

Length = 93 ft Breadth = 10 ft Water Depth = 5 ft

Maximum Carriage Speed = 20 ft/sec

The tank is equipped with a single overhead flat-plate rail system with a suspended, lightweight caniage. The model is attached to the caniage by a heave staff equipped with a linear bearing.

Resistance measurements were made with a 5-lb capacity variable reluctance force block dynamometer. In the monohull configuration the resistance dynamometer was attached at the LCB of the models. Trim was measured by means of a rotational variable differential

transformer (RVDT) mounted on the tow fittmg. Sinkage was measured by means of a linear variable differential transfonner (LVDT) also mounted on the towing fitting. The electrical signals from the dynamometer and the differential transfomiers were toansmitted thi-ough

overhead cables on trolley wires to Validyne signal conditioning equipment and ultimately to the computer, where the signals were analyzed to detennine the resistance, trim and heave using a program developed by National Instmment called Lab View. About 2000 signals are recorded over a 10 second measuring period and averaged to obtain the speed, resistance, trim and heave for that run.

For the testmg of catamaran configurations a special towing and cross stmcture apparatus had to be developed.' The apparatus consisted of a heave staff with a force block rigidly attached to a spreader rig as seen in Fig. 4. The spreader rig consists of a towing bar which serves to transfer the force fi-om the models to the force block, and a stabilizing rod that maintains the separation of the hulls along the length. The towing bar is machined to maintain precise S/L ratios for a five-foot model of 0.2, 0.3 0.4 and 0.5. The struts from the towing bar are attached to the model hulls at the longitudinal center of buoyancy and at an effective height of approximately one third of the draft above the keel.

Since the force block is located on the towing bar, it is also measuring the wind resistance of the bar, the attachment to the model hulls and the stabilizing rod, thus a correction to the measured resistance must be made for this effect. A special resistance test was conducted to measure only the wind resistance of the towing bar and the attachments to the model. These measurements were combined with an estimate of the wind resistance of the stabilizing bar resulted in a coiTection factor of 0.000488V^'°'' lbs (V in ft/sec), that was applied to all catamaran model tests.

Calm water total resistance, running trim and sinkage were carried out for all the models. All tests were carried out over a speed range of 0.20 to 1.10 FN.

Calibration of the dynamometer and the potentiometers was perfonned prior to and upon completion of testing. The average of the two calibrations was used to convert the measured voltages to resistance in lbs, the heave in inches and the trim in degrees.

Fig. 4. - Testing configuration of catamaran in Robinson Model Basin

All of the models were fitted with Hama (1956) type triangular turbulence stimulators, which have been shown to be veiy effective in experimental work at Webb Institute (Hadler et al. 2002 & 2003). They were equilateral triangles about 1.9 cm (3/4 inches) on each side composed of 4 layers of electrical tape (0.7 miu thick) placed 11 cm behind the stem of the models. Since the stimulators were within the boundaiy layer, no parasitic drag was assumed.

Uncertainty analysis has been made of the calibration data, which indicates that the resistance data is accurate to about ± 0.019 lbs, the trim data is accurate to about ± 0.125 degrees, and the heave to about ±0.041 inches.

One demihull from each catamaran configui-ation was first tested as a monohull followed by testing as a catamaran with S/L hull spacings of 0.2, 0.3, 0.4. Based on the experimental results from the USH series of catamaran tests (Molland 1995) it did not appear necessary to conduct tests with S/L values of 0.5

4. T E S T RESULTS

The resistance measurements were converted into the total resistance coefficient, C j and residuary resistance coefficient, CR using the ITTC 1957 coirelation line to detennine Cp.. The total resistance coefficient for a typical catamaran model, in this case Model D, is shown in Fig. 5 with the test points identified. More useful are the residuary resistance coefficients. Figs. 6, 7 and 8 present the residuary resistance coefficients vs. FN for the five models with spacings of S/L equal to 0.2, 0.3 and 0.4 respectively. The numerical values of CR for both the monohull and catamaran configurations are presented in Table A-1 of Appendix A along with the accompanying graphs. Figs. A-1 through A-5. The trim measurements are presented in the series of Figs. B-1 through B-5 in Appendix B, also as functions of FN. Similarly, the heave measurement are presented in the series of Figs. C-1 through C-5 in Appendix C.

1 ' 1 I 1 1 " -I 1 1 ] 1 1 1

0-2 0.4 0.6 0.8 1.0 1.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

Not unexpectedly, the comparison of the residuary resistance between catamaran models at any given spacing, as contained in Figs. 6,7 and 8, show trends similar to those when they were tested as monohuhs (Hadler et al. 2007), namely:

1. Stem fonn, particularly transom area, has a marked impact on the calm water resistance over the whole speed range but most particularly at FN below 0.85.

2. The base drag of the transom has a marked effect upon the residuary resistance; affecting both the magnitude and speed where the peak residuary resistance coefficient occui's. The larger the transom area ratio, the greater the magnitude of the residuary resistance coefficient and the lower the speed where it occurs.

3. The introduction of the hook in the buttock of Model E reduced the üim which in tum reduced the resistance despite the increase of transom area, thus control of trim through this feature of stem design is important for vessels with smaller transom areas.

The comparison of the residuary resistance coefficients of the monohulls (Hadler et al. 2007) with their corresponding three catamaran configurations are contained in Appendix A for each of the five fonns tested. In general, the resistance coefficient decreases with increased hull spacing approaching that of the monohull at the higher speeds. The singular exception is Model A, where there is very little difference in resistance due to hull spacing and the coiTcsponding monohull except in a relatively nan-ow speed range at the residuary resistance coefficient hump. These results imply that the base drag of the 100 percent transom is so dominate that it overshadows the wave interference drag.

The other models tend to show that the interference resistance coefficient between the various hull spacings tend to increase the lower the monohull resistance. Thus, for any given hull spacing, mterference resistance becomes a larger percentage of the total as the hull resistance is decreased through design.

The ü-im curves of the five different catamaran hull configurations are shown in Appendix B, Figs. B-1 through B-5 along with those for the con-esponding monohull. A l l of the trim results display the typical rapid rise in trim angle in the region between FN of 0.4 to 0.55 characteristic of high-speed vessels. Above a FN of 0.55 the trim characteristics are different dependent upon the hull configuration and the hull separation. For the monohull, all configurations show a slight increase in trim angle with speed, the magnitude of the increase is an inverse function of the transom area. This suggests that the successful hook in the buttock applied to Model E Mod 2 could be applied m reduced magnitude to the other models with the exception of Model A. What is most notable among all the catamaran configurations is the veiy high trim angle at FN = 0.6 for the hull spacing of S/L = 0.2. This is clearly the result of the wave interference pattern between the hulls. This high trim angle also tends to increase the resistance at the hump speed which is so pronounced in the resistance cui-ves of Appendix A. At the other spacings and at higher speeds the trim angles tend to more closely approximate those of the monohull but usually slightly higher. Thus we must conclude that the interference wave pattern tends to increase the trim.

Similar to the trim cui-ves, the heave curves are contained in Appendix C. A l l of these curves show the typical dip in sinkage at FN about 0.45. Most notable is that the range of variation in heave usually occurs with a hull separation of S/L = 0.2 and tends to decrease in magnitude with greater hull separation minimizing with the monohull.

5. COMPARATIVE RESISTANCE PERFORMANCE

The resuhs of this catamaran series have been compared with the only other published catamaran series, namely that of the University of Southampton (USH) (Molland 1995). Comparison will be made to Model 5b which was tested at the same L/V^'^ ratio and S/L ratios as the models in the Webb series. Two other models. Model 5a and Model 5c, with similar hull fonn but slightly different geometric proportions were tested but they had higher resistance, hence the choice of 5b for this comparison. Perfonnance comparisons will be made using the model resistance-weight ratio at con-esponding speeds. Model 5b has a transom area ratio of 0.534 and will be compared with Models C, D and E Mod2 which have transom area ratios of 0.7, 0.4 and 0.25 respectively. The results are presented in Figs. 9 and 10 for S/L ratios of 0.2 and 0.3 as percent reduction in resistance compared to Model 5b.

Fn F „

Fig. 9. Model R/W Ratio Comparison with USH Model 5b - S/L = 0.2 Fig. 10. Model R W Ratio Comparison with USH Model 5b - S/L = 0.3

Table 2. Percent r e d u c t i o n in R/W ratio in relation t o USHModelSb

M o d e l A T / A X M o n o S/L M o d e l A T / A X M o n o 0.2 0.3 0.4 M o d e l C 0.7 3.6 4.6 7.8 8.4 M o d e l D 0.4 2.0 10.2 12.9 10.0 M o d e l E M o d 2 0.25 8.0 10.5 13.8 10.4

The average percent reduction over the high-speed range of FN from 0.5 to 1.0 is summerized in Table 2 along with those for the mono hull configurations. The results in the table show a marked contrast between the mono hull and the catamaran configurations of the same basic hull fonn. Although the individual hull form has somewhat lower resistance than that of the USH model, but when the hulls are combined into the catamaran configuration the resistance is substantially lower than that of the USH model. This indicates that the Transom series hull forms produce substantially less wave interference resistance between the hulls. This can be shown even more clearly in the Table 3 which shows the average percent reduction in the residuary resistance coefficient over the same speed range of FN from 0.5 to 1.0.

Table 3. Percent r e d u c t i o n in Cr in relation t o U S H M o d e l 5b M o d e l A T / A X M o n o S/L M o d e l A T / A X M o n o 0.2 0.3 0.4 M o d e l C 0.7 2.2 3.8 10.8 12.9 M o d e l D 0.4 - 4 . 1 14.9 21.5 15.1 M o d e l E M o d 2 0.25 16.3 19.4 26.8 23.0

A comparison of tlie running trim between the two series shows that there is very little difference in the trim angles at the coixesponding speeds. Thus it is not believed that loirming trim angles are contributing to this difference in perfonnance.

In an attempt to detennine the reason for this significant reduction in wave interference resistance, the sectional area curves of Models C and D have been compared with USH model 5b as well as the design water plane in Figs. 11 and 12 respectively. From Fig. 12 it is apparent that the half-angle-of- entrance are practically identical. The design water plane of USH model 5b does have a more pronounced shoulder which in conjunction with the small increase in sectional area in this same region, shown in Fig. 11, may be a contributing factor. The other major difference between the Transom series hulls and that of USH is the block coefficient, the values of which have been tabulated in Table 1 and shows that the value for USH model 5b is substantially smaller. Intuhively, one would expect that the finer foim would have lower interference wave resistance in contrast to the results of this comparison, thus it becomes a question of further research to detemiine the cause.

1.0 0.8 0.2 .• "v. • • / / / / / / / '• ^ / / / / / Model C '• ^ / / _{Model E} USH Model 5b 1 0 2 4 6 8 10 12 14 16 18 20 Stations

03 ü E O 2^ 6H O 2 4 6 8 10 12 14 16 18 20 Stations F i g . 1 2 . D e s i g n W a t e r l i n e C o m p a r i s o n 6. CONCLUSIONS

The followmg three conclusions that were determined on the luonohull configurations reported at FAST'07 are equally applicable to the catamaran configurations, namely:

1. Stem form has a marked impact on the calm water resistance of these high-speed slender hull forms over the whole speed range but most particularly at FN below 0.85.

2. The base drag of the transom has a marked effect upon the residuary resistance; affecting both the magnitude and speed where the peak residuaiy resistance coefficient occurs. The larger the transom area ratio, the greater the magnitude of the residuaiy resistance coefficient and the lower the speed where it occurs.

3. The hook in the buttock of Model E reduced the trim and in tum reduced the resistance both the monohull and the catamaran configurations.

In the catamaran configurations the resistance, in general, decreased with increased spacing with the exception of the Model A with 100 percent transom stem area ratio. This implies that base drag was so dominate that it overshadowed the effect of the wave interference resistance.

The comparison of the catamarans of the Transom Series with the comparable USH Model 5b showed a significant reduction in wave interference resistance that is not readily explained by examination of the general hull geometric characteristics. Further research will be required.

ACKNOWLEDGEMENTS

The assistance of Mr. Patrick Doheity in setting up the experiments, assisting in and frequently running the model tests is gratefully appreciated. The contributions of the Webb Institute classes of 2007 and 2008, as part of their naval architecture laboratory experience, is aclmowledged.

References

Bailey, D. (1976) "The NPL high-speed round bilge displacement hull series" Marine Technology Monograph No. 4, Royal Instihition of Naval Architects .

Hadler, J.B., ICliest, .L. and linger, M.l. (2007) " On the Effect of Transom Area on the Resistance of Hi-Speed Mono-Hulls", Proceedings FAST'07.

Hadler, J.B. (2005) " On the Development Of A Hull Form With Minimum Wetted Surface For High-Speed Catamarans And Trimarans", Proceedings FAST'05.

Hadler, J.B. and VanHooff, R.W. (2003) "A Coinparative Analysis of the Resistance Qualities of a Series of Semi-Displacement Hi-Speed Mono-Hull Forms", Proceedings FAST'03.

Hadler, J.B., Gallagher, N.J., VanHooff, R.W. and the Webb Institute Class of 2002 (2002) "Model Resistance Testing in the Robinson Towing Tank at Webb Instimte", Proceedings of the 23rd ATTC .

Hama, F.R., Long, J.D. & Hegarty, J.C. (1956) "On Transition from Laminar to Turbulent Flow", Technical Note BN-81, AFOSR - TN-56-381, AD 95817

Molland, A.F., Wellicome, J.F., Couser, P.R. (1995) "Resistance Experiments on a Systematic Series of High Speed Displacement Catamaran Fonns: Variations of Length-Displacment Ratio and Breadth-Draught Ratio", Transactions of the Royal Instihite of Naval Architects . Vol. 137, 1995.

Yeh, Hugh Y.H. (1965) "Series 64 Resistance Experiments on High-Speed Displaceinent Fonns", Marine Technology, July 1965.