Development of Frigate Designs with good Seakeeping Characteristics

Thomas Eefsen1), Frans van Walree2), Daniele Peri3), Peter van Terwisga4), Hans Otto Kristensen5), Roberto Dattola6),

Marcel Visser7) 1)FORCE Technology, Lyngby, Denmark, 2)MARIN, Wageningen, the Netherlands, 3)INSEAN, Rome, Italy,

4)Royal Netherlands Navy, the Hague, the Netherlands, 5)Danish Naval Materiel Command, Copenhagen, Denmark, 6)Italian Navy, Rome, Italy, 7) Royal Netherlands Navy, the Hague, the Netherlands.

Abstract Heading The paper summarises a design study of advanced mono-hull frigate concepts. Based on the parent design of a 120 m frigate, seven different alternatives of hull forms and concepts have been developed. The concepts have been evaluated according to their performance as regards a) ship motions in head, following and stern sea, b) linear operability for the North Atlantic and c) bare hull resistance and added power in head seas. The work was done as part of the THALES programme, which is a project with the Danish Naval Materiel Command (Denmark), FORCE Technology (Denmark), INSEAN (Italy), Italian Navy (Italy), MARIN (the Netherlands), Royal Netherlands Navy (the Netherlands) and Delft University of Technology (the Netherlands). The THALES programme has been completed in the period 2000-2004.

Keywords Frigate; hull design; seakeeping; model tests; numerical optimization.

Introduction The aim of the study was to develop new mono-hull concepts to be considered for the next generation of surface combatants and to explore the hydrodynamic performance and risks of these concepts. Compared to conventional mono-hull combatants, the concepts should provide improvements as regards resistance in the high-speed range and as regards operability in a seaway. The evaluation was based on model tests com-bined with numerical calculations. In order to evaluate the applicability of numerical design tools in the design process, comparisons between model tests and numeri-cal calculations have also been made. Furthermore a numerical optimization technique has been applied for development of the best compromise between good still water performance and good seakeeping characteristics.

Description of Concepts Seven alternative designs have been made based on a parent design. The design of the parent hull form (PHF) has been developed under the framework program of ‘The Future Reduced Cost Combatant Study (MO2015)’, ref. Keizer, E.H.W. (1998). The hull lines are illustrated in Figure 1. The main dimensions of the hull and the alternative designs are listed in Table 1.

Figure 1 : Bodyplan of Parent Hull Form (PHF).

All design alternatives have been designed to have the same deadweight and internal volume. Furthermore all designs have been designed to meet the navy intact stability requirements. The GMT has been calculated to satisfy the ‘Stability and Buoyancy Criteria for U.S. Naval Surface Ships’, ref. Sarchin and Goldberg (1962). In order to have a fair comparison of the seakeeping characteristics, a GMT of 1.5m has been selected for all concepts, except the PHF-TH and PHF-TH-WP, which were tested with GMT=2.48m because of the said stabil-ity requirements compared to the other concepts. The COFEA concept (Center of Floatation Extreme Aft) is a mono-hull with the center of floatation shifted aft. The fore body is of SWATH type with reduced water plane area. The hull form has been developed in a previous study, ref. Kapsenberg G.K. and Brouwer R.

9th Symposium on Practical Design of Ships and Other Floating StructuresLuebeck-Travemuende, Germany© 2004 Schiffbautechnische Gesellschaft e.V.

(1998). The hull lines of the concept are illustrated in Figure 2.

Figure 2 : Bodyplan of COFEA hull form.

The PHF20 concept is an enlarged version of PHF. The PHF20 hull form has been lengthened 20% com-pared to PHF, maintaining the same beam. The dis-placement has been balanced to have the same payload as PHF. Thus the additional volume in the hull due the additional length is mainly used for void spaces. The Enlarged Ship Concept follows the ideas of J.A. Keun-ing and Jakob Pinkster (1995 and 1997). The hull lines of the concept are illustrated in Figure 3.

Figure 3 : Bodyplan of PHF20.

The hull lines of AXE20 are based on PHF20. The fore ship has been modified with a deep vertical V-shaped bow and less flare. The hull lines of the concept are illustrated in Figure 4.

Figure 4 : Bodyplan of AXE20.

The ESC40DV (Enlarged Ship Concept) is an even more enlarged version of PHF with a deep V-shaped bow, as for AXE20. Compared to PHF, the length of the hull is 40% increased (Lpp=168 m). The hull lines of the concept are illustrated in Figure 5.

Figure 5 : Bodyplan of ESC40DV.

The PHF-TH is as PHF, but with 10 degrees tumble-home from the waterline to the deck line. The beam of the hull has been increased to allow for the same vol-ume in the hull as PHF. PHF-TH-WP is a variant of the above-mentioned hull form with a wave piercing type of bow. The hull lines of PHF-TH and PHF-TH-WP are illustrated in Figure 6 and Figure 7.

Figure 6 : Bodyplan of PHF-TH.

Figure 7. Bodyplan of PHF-TH-WP.

Table 1: Main dimensions and hull parameters of the parent hull form and the alternative hull form de-signs.

Concept Lpp [m]

Bwl [m]

T [m]

Vol. [m3]

PHF 120.0 15.89 4.83 4561 COFEA 120.0 18.77 4.60 4138 ESC40DV 168.0 15.45 4.10 5116 PHF20 144.0 15.80 4.43 4760 AXE20 144.0 15.71 4.19 4520 PHF-TH 120.0 16.92 4.60 4357 PHF-TH-WP 120.0 16.92 4.60 4465

Seakeeping Performance The seakeeping performance in head and following seas of the alternative concepts has been evaluated by means of model tests and linear strip theory calcula-tions. The model test program was divided between FORCE Technology and MARIN to the extent of an equal workshare and to meet the possibilities and re-strictions of the facilities. Both FORCE Technology and MARIN have done performance analysis on the design variants. The concepts were evaluated for two sea states selected as a) Hs=2.5m / Tp=8.4s and b) Hs=5.5m / Tp=13.6s. The selected wave conditions correspond to

approximately a 20% probability of exceedence for the Mediterranean and the North Atlantic respectively. The concepts were evaluated for ship speeds of 18 knots and 25 knots. The measured and calculated motions in the two sea states have been compared to the criteria given by STANAG 4154, ref. NATO (1998) A limited number of critical motions and events have been selected based on initial studies of the motions. The critical motions and the corresponding criteria are listed in Table 2.

Table 2: Performance Criteria Values.

Location Pos1 Type of motion Criterion2 1. COG 0 m Pitch 3 deg 2. Bridge 30 m Vert. acc. 4 m/s2 3. Gun 42 m Vert. vel. 1 m/s 4. Helideck -51 m Vert. acc. 4 m/s2 5. Helideck -51 m Heave 1.4 m 6. Helideck -51 m Vert. vel. 2 m/s 7. Bow - Green water 30 occ/hr 8. Bow - Emergence 20 occ/hr 9. Propeller - Emergence 90 occ/hr

The locations listed in Table 2 have been defined such that the horizontal distance to midship is identical for all alternative designs. This implies that the helicopter deck on the enlarged hull forms is positioned relatively closer to midship than for the PHF. The performance in head seas of the concepts for the four combinations of wave height and speed has been evaluated using a weighted average of significant ampli-tudes of all six motions listed in Table 2. For the four combinations of speed and wave height it has been assumed that the relative probability of a 2.5 m wave height is 2.63 times that of a 5.5 m wave height (accord-ing to wave statistics data) and it has been assumed that the relative probability of 18 knots vessel speed is twice the probability of 25 knots vessel speed. The results for some of the motions are illustrated in Figure 8. Here it is seen that the weighted average of pitch motions are highest for the PHF concept and low-est for the ESC40DV concepts. It should be noted that the largest differences occur for the 2.5 m wave. For the same length of the ship it is seen that the COFEA hull form reduces pitch motions compared to the conven-tional hull form of PHF. Furthermore it is seen that, when comparing the performance of AXE20 and PHF20, the axe bow concept does not improve pitch motions. For the vertical heave motions at the helideck, it is seen that PHF has the highest motions and the ESC40DV has the lowest motions. Furthermore it seen that the heave motions on the helideck are reduced for the COFEA compared to PHF. The results indicate that 1 Longitudinal distance relative to midship. 2 Significant amplitude (2*RMS) or occurrence per hour

this effect is most significant for the 5.5 m waves. The low heave motion for the ESC40DV is due to the posi-tion of the helideck, being relatively closer to the mid-ship than for the other concepts. Comparing the results of AXE20 and PHF20 it is seen that the axe bow has only a marginal positive effect on the heave motions on the helideck.

Figure 8. Weighted average of selected ship motions.

For vertical accelerations at the bridge, it is seen that PHF has the highest accelerations and that ESC40DV has the lowest. Furthermore, it seen that the weighted average of accelerations of the COFEA concept is re-duced compared to the PHF concept. However, it should be noted that for the 5.5 m waves the accelerations are actually higher for the COFEA concept than for PHF. This apparent contradiction is due to the weighted aver-age of motions where the low waves and low speeds have the highest probability. Comparing the results of the AXE20 with the PHF20 concept, it is seen that the axe bow increases the accelerations at the bridge. For the vertical velocity at the gun, conclusions are similar as for the vertical accelerations at the bridge.

Figure 9: Weighted average of selected events.

In Figure 9 the weighted average of occurrence of the events (green water, bow emergence and propeller emergence) are documented. As regards green water, it is seen that the PHF and COFEA concepts have the highest probability of green water, with the COFEA concept being the worst of the two. For all the enlarged

ship concepts the probability of green water is negligi-ble, which is due to the raised foredeck of these con-cepts. As regards bow emergence, it is seen that the PHF and PHF20 concepts have the highest probability, with the PHF concept being the worst of the two. For all concepts the probability of propeller emergence is neg-ligible. In order to evaluate the concepts relative to the criteria specified in Table 2 the seakeeping performance of the concepts have also been evaluated by two score assign-ment methods, which are described as follows:

1

1 for v<c

0 for v > cS =

⎧⎨⎩

(1)

( )22

31

c

vS e−

= − (2)

where v is the performance (2*RMS) and c is the crite-rion (2*RMS). The performance of the concepts as regards ship mo-tions has been evaluated according to the criteria de-fined in Table 2. The total score for a concept in a cer-tain condition is calculated as Sc =(∑S)/nc (3)

where nc is the number of criteria. The total score over all conditions is calculated as Stotal=∑Sc pcd (4) where pcd is the relative probability of occurrence of the condition. For both methods a higher Stotal corresponds to a better performance. The score assignment method S1 is a zero-one calcula-tion method, whereas the calculation method S3 gradu-ates the criteria values. Therefore the calculation method S1 is the most stringent of the two methods. As regards the relative probability of the condition, it has again been determined on basis of the wave scatter diagram that the relative probability of a 2.5 m wave height is 2.63 times that of a 5.5 m wave height, and it has been assumed that the relative probability of 18 knots vessel speed is twice the probability of 25 knots vessel speed. Equal probability of head and following seas has been assumed. In Table 3 the calculated performance values for the different design alternatives are listed. Performance values are presented using criteria 1-6 (no events) and criteria 1-9 (including events). From the table it is seen that the seakeeping performance of PHF and COFEA is almost identical. Also it is seen that the enlarged hull forms generally have slightly higher seakeeping per-formance with ESC40DV having the highest score val-ues. This indicates that for most of the concepts the

critical motions are not significantly changed due to changes of the hull forms, whereas increased length results in improved performance. It should be noted though, that the tumble home hull forms rank lower.

Table 3: Seakeeping performance for PHF and al-ternative concepts.

Concept Criteria 1 -6 Criteria 1-9 S1 S3 S1 S3 PHF 0.85 0.92 0.89 0.94 COFEA 0.86 0.94 0.89 0.94 ESC40DV 0.93 0.96 0.94 0.96 PHF20 0.86 0.95 0.89 0.95 AXE20 0.87 0.94 0.91 0.96 PHF-TH 0.82 0.91 0.84 0.92 PHF-TH-WP 0.84 0.92 0.79 0.86 When comparing results of PHF20 and AXE20, it is seen that for the same length of the ship, the axe bow does not significantly improve performance of motions. However, when considering all criteria 1-9, it is seen that the AXE20 has an improved performance compared to PHF20. This is due to the relatively larger probability of bow emergence for the PHF20, which is not present for the AXE20 concept. The tumble home concepts rank low here because of higher probability of green water. These concepts do not have increased shear forward. In order to compare experimental and calculated re-sults the seakeeping performance has also been calcu-lated by means of linear strip theory calculations. In Table 4 the calculated performance values has been compared to the same values determined by means of model tests, see Table 3. For S3 the trend of the calcula-tions is almost the same as in the experimental results, except for the tumble home hull forms since the linear analysis tools cannot predict the relatively high number of occasions that green water appears on the forward deck.

Table 4: Seakeeping performance calculated by means of linear strip theory (all criteria)

Concept S1 S3 Exp Calc Exp Calc PHF 0.89 0.89 0.94 0.93 COFEA 0.89 0.88 0.94 0.93 ESC40DV 0.94 0.93 0.96 0.96 PHF20 0.89 0.91 0.95 0.95 AXE20 0.91 0.92 0.96 0.96 PHF-TH 0.84 0.84 0.92 0.89 PHF-TH-WP 0.79 0.84 0.86 0.89

Stability and Course Keeping in Stern Seas In order to evaluate dynamic stability and course sta-bility of the tumble home hull forms, additional test in bi-chromatic waves have been performed for these hull forms. Bi-chromatic waves consist of two regular waves with the same amplitude but a slightly varying period. The resulting wave appears as a regular wave with slowly varying amplitude. By performing tests in such waves the limiting wave height with respect to course keeping and roll in stern quartering waves can be estab-lished. The wave direction was stern quartering for all cases (315 deg). Table 5 and Table 6 show the roll and yaw extremes for the PHF-TH and PHF-TH-WP con-cepts.

Table 5: Roll and yaw responses for PHF-TH in stern quartering seas.

Hs [m]

T [s]

V [kn]

ϕa/H [deg/m]

ϕmax

[deg] ψa/H

[deg/m]ψmax

[deg] 4.0 8-9 23 13.7 29.0 2.7 6.9 6.0 8-9 23 15.7 50.0 3.0 12.7 4.0 9-10 18 7.2 16.3 1.7 3.9 4.0 9-10 23 10.8 23.1 2.0 4.8 6.0 9-10 18 8.2 27.0 1.5 6.7 8.0 9-10 18 8.7 41.1 2.0 11.7

Table 6: Roll and yaw responses for PHF-TH-WP in stern quartering seas.

Hs [m]

T [s]

V [kn]

ϕa/H [deg/m]

ϕmax

[deg] ψa/H

[deg/m]ψmax

[deg] 4.0 8-9 23 6.5 14.4 2.7 6.9 6.0 8-9 23 7.8 26.6 3.2 12.7 4.0 9-10 18 3.6 7.7 1.8 4.6 4.0 9-10 23 2.6 6.4 1.3 2.6 6.0 9-10 18 3.8 13.3 2.0 8.2 8.0 9-10 18 4.4 20.9 2.1 11.3

In these tables definitions are as follows: • φa/H denotes the maximum roll excursion (maxi-

mum minus consecutive minimum) divided by the maximum wave height (crest to trough values),

• φmax denotes the maximum single amplitude roll angle, either positive or negative,

• ψa/H denotes the maximum yaw excursion (maxi-mum minus consecutive minimum) divided by the maximum wave height (crest to trough values),

• ψmax denotes the maximum single amplitude yaw angle, either positive or negative.

The tables show that the conventional bow tumble-home concept PHF-TH rolls substantially more than the wave piercer bow PHF-TH-WP. Yaw responses are

approximately the same. This result is quite remarkable. Considering the differences in bow shape one would have expected larger differences in yaw and lower dif-ferences in roll. Similar tests were made for the enlarged hull concepts PHF20 and AXE20 in a number of regular waves. Tests were made with active fin stabilizers at identical GMT of 1.5 m. The results are summarized in Table 7 and Table 8.

Table 7: Roll and yaw responses for PHF20 in stern quartering seas.

Hs [m]

T [s]

V [kn]

ϕa/H [deg/m]

ϕmax

[deg] ψa/H

[deg/m]ψmax

[deg] 3.0 6.3 23 4.4 7.94 3.1 5.9 4.0 6.3 23 6.5 18.5 3.8 12.3 4.0 5.7 23 4.7 13.4 3.9 11.3 5.5 9.5 23 9.8 31.4 1.9 8.4 5.5 11.4 23 8.5 26.2 1.7 6.0

Table 8: Roll and yaw responses for AXE20 in stern quartering seas.

Hs [m]

T [s]

V [kn]

ϕa/H [deg/m]

ϕmax

[deg] ψa/H

[deg/m]ψmax

[deg] 3.0 6.3 23 3.5 5.4 1.9 3.8 4.0 6.3 23 4.6 12.9 1.5 4.6 4.0 5.7 23 3.4 9.4 2.9 8.6 5.5 9.5 23 9.2 27.8 1.8 7.1 5.5 11.4 23 7.6 20.9 1.4 4.7

Table 9: Roll and yaw responses for PHF20 and AXE20 in stern quartering seas at 23 knots. Hs=4.0m and T=5.7s. Concept Fins ϕa/H

[deg/m] ϕmax

[deg] ψa/H

[deg/m]ψmax

[deg] PHF20 A 6.8 22.2 4.7 15.7 PHF20 P 7.7 22.4 3.0 10.9 AXE20 A 3.8 10.9 2.9 7.8 AXE20 P 3.7 9.6 2.9 8.3

According to the results AXE20 performs better than PHF20 in roll. The sharp bow probably results in an increased roll damping, although under the conditions considered here stability is of more importance than roll damping. This is illustrated by the fact that the roll re-sponse with passive fins is only slightly higher for the PHF20 and even lower for the AXE20. Active fins were used that reacted on the roll velocity and not on the roll angle. As such the fins provided roll damping and did not increase stability.

The better course stability for the AXE20 is again somewhat surprising. In view of the sharp bow of the AXE20 one might have expected course-keeping prob-lems. It is furthermore noted that using passive fins for the PHF20 reduces the yaw motions.

Still Water Performance In order to evaluate the still water performance of the alternative concepts, the bare hull resistance has been measured for all concepts. The results show that the PHF and PHF-TH have the highest wave resistance in the speed range 18-25 kn. Furthermore, it is seen that the wave-piercer bow of PHF-TH-WP reduces the wave resistance slightly, and it is seen that the COFEA hull form has a significantly reduced wave resistance coeffi-cient compared to the PHF. For the enlarged ship con-cepts ESC40DV, PHF20 and AXE20 it is seen that these have a reduced wave resistance coefficient com-pared to the PHF, which is due to the increased length of these concepts. When comparing the results for the PHF20 and the AXE20, it is seen that the axe bow does not have a significant influence on the wave resistance.

Figure 10: Effective Power for the different concepts (based on bare hull resistance).

The measured effective power (bare hull resistance) for all concepts is illustrated in Figure 10. At 25 knots the total power is as follows, relative to that of the PHF :

• COFEA : - 13 % • ESC40DV : - 23 % • PHF20 : - 19 % • AXE20 : - 17 % • PHF-TH : + 3 % • PHF-TH-WP : + 2 %

At 18 knots there is no significant difference between the concepts. The still water resistance and powering of the differ-ent concepts has been estimated using a combined method of empirical data and potential flow calculations (SHIPFLOW XPAN, version 2.4). First the wave resis-tance coefficient of the PHF was estimated based on an

empirical database method. Thereafter the wave resis-tance coefficients of the non-conventional alternative hull designs were estimated using results of non-linear potential flow calculations relative to the PHF hull form. The wave resistance of the PHF hull form was esti-mated by FORCE Technology based on the hull pa-rameters. By comparing the estimated wave resistance with the later measurements of bare hull resistance tests, it is seen that the accuracy of the estimated wave resis-tance coefficient based on empirical data is within 5%, which is considered as a fine result. Based on non-linear potential flow calculations the wave resistance coefficient of the alternative hull con-cepts was estimated based on the relative difference to PHF. The results of the estimated and measured wave resistance at 18 and 25 knots relative to PHF are docu-mented in Figure 11 and Figure 12. From the figures it is seen that some deviations of the calculations com-pared to the measurements exist. For 18 knots it is seen that the procedure is not able to derive the ranking of the alternative hull forms, caused mainly by a too high prediction of the wave resistance coefficient of the COFEA. However, for 25 knots it is seen that the calcu-lations derive the correct ranking of the hull forms.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

PHF PHF20 COFEA AXE20 ESC40DV

Rel

ativ

e C

w c

ompa

red

to P

HF

MeasuredEstimated

Figure 11: Measured and estimated wave resistance at 18 knots. Figures are relative to PHF.

Even though the procedure does not result in very accu-rate estimates of the wave resistance, the procedure is considered as good for alternatives of ‘non-conventional’ hull forms. The non-conventional hull forms may not be well predicted by normal database methods and therefore the combined approach with non-linear potential flow calculations is considered to be feasible in the early design.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

PHF PHF20 COFEA AXE20 ESC40DV

Rel

ativ

e C

w c

ompa

red

to P

HF

MeasuredEstimated

Figure 12: Measured and estimated wave resistance at 25 knots. Figures are relative to PHF.

Speed Loss in Head Sea As part of the seakeeping tests the speed loss in head seas were measured. For both sea states the speed loss relative to the reference speed of 25 knots in still water was determined. The results are documented in Table 10. From this figure it is seen that all concepts have less speed loss compared to PHF. Furthermore it is seen that the COFEA concept has the lowest speed loss for the 2.5 m wave and that the AXE20 concept has the lowest speed loss for the 5.5 m wave.

Table 10 : Speed Loss in Knots Relative to Still Wa-ter Speed of 25 knots.

Concept 2.5 m wave 5.5 m wave PHF 1.20 kn 3.50 kn

COFEA 0.25 kn 2.50 kn ESC40DV 0.31 kn 2.60 kn

PHF20 0.33 kn 2.30 kn AXE20 0.35 kn 1.65 kn

Numerical Optimization Technique In order to identify the margin for improvements of the PHF, a numerical optimization technique has been applied by INSEAN. The optimization technique has been performed with respect to two objective functions: a compound of total resistance at two speeds, emphasiz-ing the top speed qualities, and a compound of the verti-cal motion response of the ship for three different speeds in head seas. The optimization technique uses in-house INSEAN CFD codes to estimate the behavior of the candidate hulls - as a consequence, since no database or statistical tools are applied, this approach is useful when new concepts are examined. The optimization tool is fully automatic. It contains a tool for hull geometry manipu-lation and modification and different algorithms for the solution of the constrained optimization problem. Every CFD solver is considered as plug-in, and the optimizer contains all the interfaces for connecting the CFD solver

to the optimizer. Here a strip-theory code is applied for the seakeeping problem, and a linear potential solver is applied for the evaluation of total resistance in calm water. An example of application of the same optimizer with higher level solvers, i.e. a RANSE solver, is re-ported in Ref. Peri, D. and Campana, E.F. (2004). Hu-man interaction is possible in addressing the process: deeper analysis could be performed in the vicinity of interesting solutions. Among the possible alternatives, a PSI (Parameter Space Investigation) approach has been adopted for the solution of the optimization problem. Details are given in Refs. Peri, D. and Campana E.F. (2001) and Peri, D. and Campana E.F. (2003), 1-3. The global minimum of a multi-objective constrained optimization problem is found. Due to the multi-objective nature of the problem, a single optimum does not exist. As a consequence, a set of alternatives is pro-duced as the output of the process, and the design team is free in giving a preference on the best solution. Post-processing on other objective functions, evaluated by the CFD solvers but not considered in the optimization, or different aggregation of the considered objective functions is also possible, since all the produced data are organized and stored, and the designer is not forced by a single solution of the problem. No explicit limitations on the number of the objective functions is present by the way, since the evaluation of the objective function is connected with the results of a CFD simulation, the amount of time needed for the solution of the problem is connected with the number of calls to the CFD solver. In order to validate the optimization technique, two hull forms have been made by the technique based on a variant of PHF with a sonar dome. Models were made of the design alternatives, and model tests were per-formed for experimental verification of the optimization technique. The optimized hull forms are illustrated in Figure 13 and Figure 14. Both designs have unchanged length of Lpp = 120 m. From the body plans it is seen that the most noticeable difference compared to PHF are in the aftship, where the water plane area has been slightly reduced.

Figure 13 : Bodyplan of PHF-OPT-1.

Figure 14 : Bodyplan of PHF-OPT-2.

Two more models have been produced optimizing an enlarged PHF (Lpp = 126 m). New length comes from a parametric study in which seakeeping characteristics have been optimized enforcing a constraint on the total resistance at top speed, assuming a new (augmented) displacement evaluated avoiding void spaces. Details are reported in Peri, D. and Dattola, R. (2003). The seakeeping performance relative to PHF has been calculated using equations (1) and (2). The results are listed in Table 11, where a comparison with other con-cepts is also shown. A limited number of criteria has been applied, since onsly head seas tests have been performed on the optimized hulls. Furthermore the wave resistance coefficient has been measured by model tests, and the results are illustrated in Figure 15 The results show that when using S1 the seakeeping performance of the two optimized hull forms with re-spect to PHF are unchanged, while only for enlarged ships, like AXE20 and PHF20, there is a significant increase in the operability. However, when using the gradual calculation method S3, differences comes to light, and the optimized hull forms perform better in head seas. In particular, the improvement of the enlarged optimized hulls is comparable with that of the largest concepts here reported (144 meters long), al-though these optimized hulls are only 126 meters long. Furthermore, it is seen from Figure 15 that the wave resistance coefficient for PHF-OPT-1 with respect to PHF has been reduced - especially for the higher speeds.

Table 11: Seakeeping performance of the optimized PHF and other concepts for a reduced number of criteria (head seas only).

Concept S1 S3 PHF 0.57 0.71

PHF-OPT-1 0.57 0.81 PHF-OPT-2 0.57 0.81

PHF-5-OPT1 0.55 0.83 PHF-5-OPT2 0.57 0.83

PHF-TH 0.57 0.71 PHF-TH-WP 0.58 0.72

PHF20 0.65 0.86 AXE20 0.65 0.83

Figure 15: Measured Wave Resistance Coefficient for PHF and optimized hull forms.

Conclusions The seakeeping performance of a series of hull forms has been evaluated on basis of experimental data and a limited set of motion criteria. Considering head and following seas only, the most enlarged hull concept ESC40DV shows the best seakeeping performance. Second best are the AXE20 and PHF20. The study showed that for hull forms of equal length (PHF20 and AXE20) the use of an axe bow form does not improve the seakeeping performance for the ship design charac-teristics and the conditions and criteria taken into con-sideration in this study. The operability of the tumble home hull forms PHF-TH and PHF-TH-WP suffers from green water on the deck, and therefore a higher forward freeboard is required for these hull forms. In oblique seas enlarged hull forms show a similar performance as conventional hull forms. The use of lengthened hull forms does in general not lead to stabil-ity or course keeping problems. The use of the axe bow does not deteriorate the dynamic stability or the course keeping ability. Tumble home hull forms show a suffi-cient stability and course keeping as well. In stern quar-tering seas some favorable differences in roll perform-ance appear for the tumble home hull form with a wave- piercing bow when compared to the other hull forms. When the strip theory results are used instead of ex-perimental results for assessing the seakeeping perform-ance of concepts, an almost similar ranking is found. Thus strip theory tools can be applied with some confi-dence. The use of a gradual ranking system is to be preferred above a zero-one ranking system. For all concepts, the calm water resistance has been obtained from model tests. The increased length con-cepts show the lowest wave making resistance, whereas the tumble home concepts show the highest wave mak-ing resistance due to their increased beam. The speed loss in head seas is lower as well for the enlarged con-cepts while the AXE20 is shows a lower speed loss than the PHF20. The resistance prediction tool applied by FORCE Technology yields reasonable results when ranking the wave making resistance of unconventional hull forms. The numerical hull form optimization method devel-

oped by INSEAN is capable of delivering hull forms with improved resistance and seakeeping characteristics.

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