PROSPECTS FOR HARD CHINE? MONOHULL VESSELS

PROSPECTS FOR HARD CHINE? MONOHULL VESSELS Donald L. Blount Donald L. Blount and Associates, Inc. Copyright 1993 Donald L. Blount and Associates, Inc. USA ABSTRACT Applying carefully documented sea trial data from a large number of hard chine vessels up to 68 meters in length, this presentation will quantify transport efficiency achieved through the beginning of 1993. Quantified improvements from 1975 to 1993 are also included to demonstrate technology trends. Other topics derived from the sea trial data base and model tests document achievable, useful load fraction, ride quality in a seaway, minimum calm water drag, and maximum overall propulsive efficiency. 1. INTRODUCTION Evolution in high performance marine vehicles has resulted in new craft concepts. In many cases these new or hybrid vessels were created in order to compensate for perceived deficiencies of more traditional hull forms. While emerging technology is significant, documenting the status and achievements of existing hard chine marine vessels and their maturing technology is also important such that a baseline for measuring future prospects can be established. The less complex structures and systems of hard chine, semi-planing or planing monohulls tend to be relatively low in cost and have high operational reliability relative to their carrying capacity. However, ride quality of hard chine hulls operating at sea is often questioned and sometimes is used to justify the selection of more complex high performance hull concepts. There are complex and interactive factors which must be evaluated to confirm that one hull form is superior to the other alternatives. Economics often become the controlling factor in developing a successful project and must include all vessel development costs, the shore facilities, the number and/or size of the vessels dedicated to the operation, the operational expenses and long term maintenance. The ride quality, maneuverability and control of the vessel in expected sea conditions are significant factors. In addition, the volume and weight of the payload and the ease of loading or off-loading affect the utility of a concept for the specified service. In order to develop a new vessel, the requirements for its intended service must be quantified such that the designer may proceed with a comparative evaluation of various combinations of hull forms and propulsion systems. These requirements must also be considered in light of the operating environment such as sea and atmospheric 1

conditions. It is the intent of this discussion to quantify the state of technology for hard chine, monohull craft influenced by these environmental conditions. The quantification is depicted in Figure 1, the speed-wave height diagram. 2. COMPARISON OF VARIOUS HULL FORMS Documenting the status and achievements for hard chine, semi-planing or planing monohulls is better served when a comparison can be made with other hull concepts. To make credible comparisons among the various configurations, a consistent approach must be adopted to account for hull drag, interactive factors and propulsive characteristics. Gabrielli and von Karman presented a landmark paper for comparing maximum velocity performance for single vehicles in level motion utilizing specific tractive force, E, versus velocity for which they developed a limiting tangent line approximated by E = 0.000155(VhIPH)1.02. The utility of this format is enhanced when velocity is replaced by a dimensionless speed coefficient such as volume Froude number, F,, accounting for vessel size. (A brief discussion of dimensionless speed coefficients is included in Appendix A.) Full-scale trial performance defined by speed, total of propulsive and dynamic lift power and vessel weight may be combined into a transport efficiency, E, = l/e, and a dimensionless speed, F,,. For comparison, preference for E, vice its reciprocal specific tractive force, E, allows the largest numerical value to represent the most efficient mode of transport. This format is useful to discuss relative craft performance as well as the separate trends of bare hull resistance to weight ratio and propulsive efficiency. It is clear that ET increases by improving overall propulsive efficiency, q, and/or reducing the bare hull resistance to weight ratio, (R/W),,. (Amt) (V m/s) rl ET = = (PDLKW) (0.102) ("/w,,, (Metric) (2.1) Figure 2 presents trial data as E, versus F,, for selected hard chine craft to demonstrate the value of this format and significant achievements made by designers and shipbuilders. Typical performance of hard chine craft in service is approximately 70% of the best calm water transport efficiency. Some of the less successful vessels may be the result of inflexible design requirements or constraints which prohibit integration of state-of-the-art technology into various components of a vessel. Thus, early in a project, it is important to identify the sensitivity of design features which may improve overall vehicle efficiency with alteration of requirements. The relative calm water performance of various craft concepts are included for comparison where data for full-scale trial speed power and displacement have been made available. These data relating to craft from 5.5 to 68 meters (18 to 222 feet) in length have been reduced to a dimensionless format, with no Reynolds' corrections applied. The curves of ET for each hull concept in Figure 3 were obtained from fullscale, calm water trial data of numerous military, commercial and recreational craft. These curves represent the upper boundaries of efficient performance for each concept 2

as depicted in the example for hard chine craft in Figure 2. The data depicted in Figure 3, mask the information regarding relative useful load carrying capability but may be considered for selection of a hull concept with minimum power for a single design speed. However, commercial, paramilitary or military vessels seldom have a single speed performance requirement. Thus, selecting a hull solely on that basis could result in an inappropriate choice when other factors or requirements are considered. For design loads typical of planing hulls, round bilge vessels are rarely selected when operational speeds approach FB = 3.0 (2.0 5 F, 5 3.0). It is only at very light hull loadings that round bilge monohull craft operate up to FB = 5.0 (3.0 5 F,, 5 4.5). Hard chine planing craft have a relatively large range of applications for high-speed, load carrying capability. (A discussion of vessel loading relative to its overall dimensions is presented in Appendix B.) Figure 3 represents the upper boundaries of transport efficiency for various hull concepts which represent the best combination of hull and propulsor. Since hull hydrodynamics tend to be closely related to Froude number and propulsors closely related to cavitation number, actual vessel size and speed must be considered when selecting and integrating a hull form with a propulsor concept. The size and speed of various configurations play a significant part in the complex marriage of hull form and propulsion technologies when developing a craft to meet an owner's requirements. This is demonstrated in the upper charts in Figure 3. For example, at F,, = 2.0, those hull hydrodynamic factors sensitive to Froude scaling are the same for 1 MT SES at 12 knots and a 1,000 MT SES at 38 knots. Several propulsors are available for the smaller vessel operating at u, = 5.0. However, a limited number of practical choices exist for the 1,000 MT vessel operating at a, = 0.5. It is worth noting that significant improvements occurred from 1975 to early 1993 in transport efficiency for hard chine monohulls in all speed ranges. This progress is indicated in Figure 4. The results can be seen most clearly by evaluating the percentage improvements in E,. Analysis of the individual craft indicate that reduction in R/W generally contributed to increasing E, for F,, 5 1.5. For F, > 1.5, improved E, was achieved almost entirely by increasing n. Much can be learned from the comparison of calm water transport efficiency for various hull concepts described in Figure 3. These data represent the best performance from carefully conducted sea trials and do not include model experimental or theoretical study results. However, it is important to remember that these data are just one of the considerations with regard to selecting an optimum hull concept. Gabrielli and von Karman indicated that as far as economy is concerned, comparisons are strictly correct only if the useful load to gross weight remains constant. Thus, useful load data are necessary to make unbiased comparisons between several craft concepts. Useful load fraction (ULF) is helpful to evaluate the suitability of different concepts when considering operational requirements: duration, range, payload, personnel and equipment. If the operation requires the transport of a large, low density payload, then the useful load concept should be expanded to include hull volumetric characteristics and/or the available deck area. 3

ULF = (Fuel + Payload)/(Full Load Displacement) (2.2) The curves which represent the best load carrying capability for hard chine, monohulls and SES vessels operating in calm water are shown in Figure 5. The trend for the rapid drop of ULF at high F,, can be observed for most dynamically supported craft. It is likely that ULF will be lower than depicted in Figure 5 for complex craft requiring additional systems for dynamic support and structure related to each concept. These two factors increase the light ship weight fraction for complex craft relative to that achievable by monohulls. Considering the real measure of economy indicated by Gabrielli and von Karman, useful transport efficiency becomes UET = E, (ULF). Comparative data for UE, are given in Figure 6 for hard chine craft and SES indicating a preference for hard chine monohulls over SESs for F,, < 2.3. 3. PROPULSIVE AND RESISTANCE TRENDS Transport efficiency is a ratio of q and (R/W),,. By defining (R/W),, and q separately over the entire operating speed range, the technology associated either with the speed-drag characteristics of a hull concept or the speed-performance of a propulsor may be critically evaluated. It is especially important to be aware of hull drag and thrust characteristics of the propulsors when a craft transitions from displacement speeds to a dynamically supported condition. Dynamically supported craft could have a high thrust loading condition more demanding at transition speed than the operational requirements for maximum speed. When evaluating various propulsor concepts, it is important to apply the appropriate interactive factors such as wake, relative rotative efficiency and propulsor pressure field relative to their impact on bare hull drag and trim. Should a propulsor develop significant vertical or transverse forces, an unfavorable interaction with the hull could alter dynamic stability to an unacceptable level. The majority of hard chine vessels in operation utilize submerged propellers, surface propellers, or waterjets. However, the number and type of thrusters as well as the type of maneuvering system may vary on each craft. Due to a small data base, differences in the efficiency of the propulsors relative to a hull concept cannot be absolutely defined. However, when full-scale power measurements and model test data are available, it is possible to establish reasonable bandwidths of achievable overall propulsive coefficients. Figure I presents the author's experience based on values resulting from instrumented full-scale trials. When efficient performance is the sole criterion, submerged propellers are the preferred choice for applications 25 knots (13 m/s) or less and waterjets the preferred choice for applications 43 knots (22 m/s) or more. Between these speeds, waterjets should be given serious consideration. However, when selecting propulsors other factors must be considered: hull motions in rough seas, thrust production at hump speed, hydro-acoustics, cost and reliability. Experimental series data sources for hard chine hulls provide both trend analysis as well as specific resistance information. Resistance data from Series 62 and 65 for free-to-trim conditions have been analyzed for a displacement of 45 metric tons to 4

define the minimum R/W. Figure 8 depicts the minimum values for R/W within these two data bases for constant F,, as a function of L,/v"~. The merit of this format is to show the important relationship L,/v"~ has on R/W for 1.0 < F,, I 3.0 (semi-planing speeds). The significance of this relationship diminishes considerably for L,/$'3z 7.0. The magnitude of R/W presented is also indicative of the minimum that is most likely to be achieved with hard chine hulls operating in a free-to-trim mode. The minimum values for R/W for Series 62 hulls for free-to-trim conditions are presented in Figure 9. This figure defines lower boundaries for R/W for planing speeds, F,, 2 3.0. Variation in plan form hull geometry is represented by L,/B,. Though not clearly shown by the format in Figure 9, hull loading is important to minimizing R/W at high speed. The equilibrium trim angle is much closer to optimum at high speeds for higher hull loading than for lightly loaded hulls. Aft placement of LCG is significant for these speeds and can result in the dynamic trim angle being near to that which is optimum for minimum R/W. It should also be noted that increasing LJB,, at very high planing speeds, F, 2 4.5, has very little effect on R/W which is important when high speeds in a seaway are part of the operational requirement. 4. RIDE QUAIXTY Characteristics of hard chine craft operating in a seaway have often been questioned and sometimes used to justify selection of more complex high performance hull concepts. Much of the negative experiences relate to craft of very small size with high horsepower to weight ratios and thus operate at very high speeds (F,,) and high wave frequency of encounter. These experiences, though without merit relative to large vessels, tend to bias judgements against hard chine monohulls without proper consideration of mature technology. The 67 meter vessel, DESTRIERO, is one of many whose full-scale seakeeping trial results confirm that within statistical significance, existing experimental and analytical techniques are suitable for making valid design decisions. Utilizing this technology, achievable vertical CG acceleration (contours for 0.06 and 0.20 g RMS) for hard chine monohulls is presented in Figure 10. This figure adds a major quantified boundary to the speed-wave height diagram (Figure 1) which may be used with confidence as a baseline comparison for other vessel concepts or to measure future ride quality improvements. Figure 10 in its dimensionless format highlights the significance of vessel displacement. Increasing displacement reduces both H,,,/v"' and F,, which increases the operational envelope for a vessel. Increasing length-beam ratio further enhances operational opportunities. DESTRIERO is an example of a large hard chine vessels achieving exceptional ride quality at high speed. 5. OTHER FACTORS: SPEED-WAVE HEIGHT DIAGRAM Transport efficiency and ride quality define the major boundaries for unrestricted operation for hard chine monohulls depicted in the speed-wave height diagram. A general state-of-the-art power limit due to rough water is less easily defined as there is a strong interaction between added drag, propulsor and engine characteristics. However, for specific combinations of hull and machinery, the speed 5

characteristics. However, for specific combinations of hull and machinery, the speed limitation in rough water due to waves may be reliably predicted. Though a dynamic stability boundary is shown above the ride quality boundary, it may not necessarily occur outside of the desired operational envelope. The technology and design criteria to assure that a craft will be dynamically stable has evolved through proprietary sources but data have yet to become widely available in the public domain. As speeds increase, dynamic hull pressures and their distribution begin to dominate vertical forces resulting in potential instabilities characterized as being oscillatory and non-oscillatory. Non-oscillatory instabilities usually occur on relatively heavily loaded craft traveling at moderately high speeds. Unstable behavior can occur about the yaw, pitch and roll axes typified by a loss in running trim, increase in the quantity of spray, progressive heeling, bow steering, or a combination of rotations. These motions may result in a new stable orientation; the craft often can be operated with some degree of control for an extended period in this new attitude. Even though the instabilities occur at moderate speeds, the onset may be rapid and without warning, particularly when initiated in a seaway. There also may be secondary results, such as broaching or unpredictable steering response. Finally, loss of stability may occur on craft which would not otherwise require a high degree of operator skill. As a result, these instabilities often create concern among designers and shipbuilders. Oscillatory instabilities include roll oscillations (chine walking), and pitch and heave oscillations (porpoising). There are common factors in these aberrations: both are associated with high-speed, hard-chine planing craft; the amplitude of oscillation is related to boat speed; the oscillations may occur without excitation from environment or operator. In some cases, the oscillations increase while the craft is at constant speed. Design guidelines have proven to be effective in predicting and avoiding porpoising. No accepted guidelines are available for predicting conditions which result in chine walking, but apparent correlation exists with chines dry flow patterns. Typically, oscillatory instabilities occur on boats that require a high degree of operator skill and attention. Except in rare cases, they gradually increase in severity; as a result the operator has an opportunity to adopt corrective measures. A structural boundary is also shown in the speed-wave height diagram with a buffer zone separating it from the ride quality and dynamic stability lines. This depiction is to indicate that vessel integrity has the highest priority. However, as technology advances, the separation between ride quality and structural limits may be reduced so that ULF will increase. As this buffer diminishes strain gauges and accelerometers will be necessary to monitor the condition of the structure rather than trusting to the "feel" of the crew. 6. TRENDS TO THE 21st CENTURY Advanced craft through the beginning of the 21st century will evolve into an ever-increasing number of large, hard chine vessels with waterjet propulsors powered by marine gas turbines. Newly constructed, large advanced craft for commercial service will be designed with speed requirements of 30 to 45 knots. At the same time, military 6

ships are apt to be smaller but with current speed capabilities. Vessels designed for a speed range of 1.8 c F,, 2.8 are likely to set the standards for future development of marine technology. Figures 3, 6 and 10 provide a reference with regard to current competitive craft concepts. For F,, 5 2.3, hard chine hulls represent the superior technology for advanced craft in calm water. Acceptable ride quality with hard chine vessels is also achievable for this same speed range as shown in Figure 10. Even if attaining useful transport efficiencies equal to hard chine craft, round bilge hulls at F,, = 2.0 approach the upper, stable operational limit for that technology. Catamarans with large slenderness ratio hulls offer reduced resistance in this speed range and provide static transverse stability by varying separation between demihulls. Useful transport efficiency, however, is not well documented. Thus, marine operations requiring 100 metric tons or heavier vessels at speeds of 30+ knots will find hard chine hulls preferable unless specialized requirements dominate hull concept selection. A summary of expectations relating to the future of hard chine monohull technology is as follows: Little improvement in R/W is anticipated for hard chine monohulls for 1.8 5 F, I 2.8. This technology has been consistent for some time without demonstrating significant improvement. Ride quality technology for hard chine monohulls is expected to mature. Refined transverse section shapes are expected to yield improvements in pitch, vertical acceleration and roll at high speeds in all headings to the sea. Waterjet propulsive efficiencies (which relate to other advanced craft) will likely improve in the 20 to 40 knot speed range as larger units become widely used. Interactive factors will become better documented; waterjet inlet location and intersection with afterbody hull lines will account for some improvement. The technology for dynamic transverse stability will be defined. Solutions will be evaluated by 3D computational fluid dynamic procedures suitable for arbitrary shapes of hard chine hulls. 9 Hard chine monohulls and catamarans are likely to be the competitive hull forms for 1.8 5 F,, 5 2.8. Large hard chine monohulls may become the economic choice due to the achievable useful load fraction and ride quality. 7. NOMENCLATURE AP BOA BP C* D ET FB F IIL F nv H %3 JT :OA Projected area bounded by the chine and transom Overall beam Projected chine beam v/bp3 - Beam load coefficient Propeller diameter n/(r/w),, - Transport efficiency v/(g BP)'/' - Beam Froude number v/(gl)"z - Length Froude number v/(g v1'3)ln - Volume Froude number Depth of propulsor below water surface Significant wave height Propeller advance coefficient based on thrust measurements Acceleration due to gravity Overall length 7

L LP P DL R t UET V VR w WT E rl tlo 1)A 1)R A V OH OR 8. REFERENCES Waterline length Projected chine length Total shaft power for propulsion and dynamic lift Bare hull resistance Thrust deduction fraction ET (ULF) - Useful transport efficiency Velocity of craft Resultant velocity of flow at tip of propeller Weight of displaced water at rest Thrust wake fraction ~/ET - Specific tractive force Total (overall) propulsive efficiency Efficiency of propulsor in absence of hull influence Appendage drag factor Relative rotative efficiency Displacement of craft at rest Volume of displaced water at rest Cavitation number at a depth of H below the static water surface Cavitation number based on resultant velocity at propeller tip. Allison, J., "Marine Waterjet Propulsion," SNAME Centennial Meeting, September 1993. Blount D.L. and Bjarne E., "Design and Selection of Propulsors for High-Speed Craft," Paper Presented to the 7th Lips Propeller Symposium, Nordwijk, The Netherlands, 1989. Blount D.L. and Codega L.T., "Dynamic Stability of Planing Boats," Marine Technology, January 1992. Blount D.L. and Fox D.L., "Small Craft Power Predictions," Marine Technology, January, 1976. Clement E.P. and Blount D.L., "Resistance Tests of a Systematic Series of Planing Hull Forms," Transactions, SNAME, 1963. Denny S.B. and Feller A.R., "Waterjet Propulsor Performance Prediction in Planing Craft Applications," DTRC Report SPD/0905-01, August 1979. Gabrielli G. and von Karman T., "What Price Speed?" Mechanical Engineering, October 1950. Hadler J.B., "The Prediction of Power Performance on Planing Craft," Transactions, SNAME, 1966. Hadler J.B. and Hubble E.N., "Prediction of Power Performance of the Series 62 Planing Hull Forms," Transactions, SNAME, 1971. Hadler J.B., Model - Its Warships and Hubble E.N., Allen R.G. and Blount D.L., "Planing Hull Feasibility Role in Improving Patrol Craft Design," Symposium on Small Fast Security Vessels, RINA, 1978. Hoggard M., Presentation "Examining Added Drag of Planing Craft Operating in a Seaway," to Hampton Roads Section/SNAME, November, 1979. Hoggard M. and Jones M-P., "Examining Pitch, Heave and Accelerations of Planing Craft Operating in a Seaway,' Presentation to High-Speed Surface Craft Symposium, Brighton, England, June, 1980. Hubble E.N., "Resistance of Hard-Chine, Stepless Planing Craft with Systematic Variation of Hull Form, Longitudinal Center of Gravity, and Loading," DTRC Report 4307, April 1974. Savitsky D., "Hydrodynamic Design of Planing Hulls," Marine Technology, Vol. 1, No. 1, October 1964. 8

Savitsky D. and Brown P-W., "Procedures for Hydrodynamic Evaluation of Planing Hulls in Smooth and Rough Water," Marine Technology, October 1976. Savitsky D. and Koelbel, Jr. J.G., "Seakeeping Considerations in Design and Operation of Hard Chine Planing Hulls," Lecture Notes for NAVSEA Norfolk, May 1978. Savitsky D., Roper J. and Benen L., "Hydrodynamic Development of a High-Speed Planing Hull for Rough Water," 9th Symposium of Naval Hydrodynamics, August 1972. Shuford Jr. C.L., "A Theoretical and Experimental Study of Planing Surfaces Including Effects of Cross Section and Plan Form," NACA Report 1355, 1958. 9

SPEED FIGURE 1 - Speed-Wave Height Diagram XECTED VESSSLS I FE E, r : 33 k I H d Fno FIGURE 2 - Transport Efficiency for Selected Hard Chine Craft 10

- T F nv HARD CHINE ROUND BILGE 0.5 100.0 ----- 0.6 64.5 ----- 0.7 47.5 ---_- 0.8 36.0 _---- 0.9 28.0 31.0 1.0 20.0 26.0 1.2 9.75 20.1 1.4 8.51 16.9 1.6 8.11 10.4 1.8 7.90 7.49 2.0 7.70 6.80 2.2 7.45 6.15 2.4 7.11 5.75 2.6 6.70 5.29 2.8 6.30 4.85 3.0 5.90 4.40 3.2 5.61 3.80 3.4 5.29 -_--- 3.6 4.99 ----- 3.8 4.70 -_- 4.0 4.45 _---- 4.5 3.92 _--_- 5.0 3.50 _---- 5.5 3.15 --_-- 6.0 2.82 _-_-- 7.0 2.40 _- - 8.0 2.09 _---- 9.0 _---- ----- - - ET ( ZATAMARAN SES - - -- - ---_- 10.0 9.59 9.19 8.40 7.85 7.45 7.02 6.75 6.20 5.78 5.36 5.14 5.00 4.85 4.70 4.52 4.33 4.11 3.60 3.26 2.90 - - - - ----_ ----_ 14.9 14.4 13.8 13.0 12.3 11.4 10.2 9.99 10.2 10.4 10.5 10.5 10.2 9.70 9.00 8.11 7.45 6.85 6.35 5.90 5.60 4.80 4.18 3.68 3.20 - - _--- --_- STEPPED HULL -_-_- - -- - 10.0 7.90 6.40 4.75 4.00 3.75 3.62 3.60 3.62 3.65 3.70 3.75 3.80 3.84 3.86 3.88 3.88 3.85 3.72 3.55 3.31 3.05 2.65 2.32 2.08 I... I : f ; f zij- r..yll I I F'nV H-M FIGURE 3 - Upper Boundaries of Calm Water Transport Efficiency

DISFLAEMNT YHI-RANING -I c FiANlNG FIGURE 4 - Increasing Trends in Transport Efficiency for Hard Chine Craft I.0 0.9 0.9 0.7 0.6 0.5 6 ;: 0.4 8 0.3 % FIGURE 5 - Achievable Useful Load Fractions 12

60 I 0.6 0.6 0.7 0.6 FIGURE 6 - Useful Transport Efficiency q(h=o) 0.B 0.7 z ;; k 0.6 # 0.3 20 30 40 50 60 70 SPEED - KNOTS FIGURE 7 - Achievable Overall Propulsive Coefficients for Several Propulsors 13

7 8 9 IO Lp/ p m FIGURE 8 - Minimum R/W from Semi-Planing to Planing Speeds 0.22 Fnv 0.20-6.0 I I I I I 0.18-6.6 a 0.16-5.0 0.14-4*5-0.12-4.0-3.5 0.10-5.0 I I I I I I 2 3 4 6 6 7 LPBPX FIGURE 9 - Minimum R/W for F,, for Planing Speeds o 6- Fnv FIGURE 10 - Achievable Vertical Acceleration with Hard Chine Hulls 14

APPENDIX A Dimensionless SDeed Various dimensionless speed coefficients have been used to document hydrodynamic trends for dynamically supported craft. No dimensionless speed coefficient is universally suitable for all technical analysis; however, one of the following is usually appropriate for the technology being studied. Volume Froude Number - F,, = v/(cjv~/~)~'~ Beam Froude Number - FB = C, = v/(gb,)" Length Froude Number - FnL = v/(gl)'j2 (A-1) (A.2) (A-3) F nv relates speed to volume of displacement and F, and F, respectively relate speed to the hydrodynamic beam and length. Thus, technology comparisons presented as a function of F,,, FB or FnL must account for hull loading and length-beam ratio. The relationships between these coefficients are: FB = F,, (v~'/b~)~' (A-4) F, = F,, (Vl'J/L)ln (A-5) F, seems to best represent hydrodynamic phenomena at high speeds where the forebody is not in contact with the water surface. F,, is often used to represent hydrodynamic phenomena when wetted length varies with speed and FnL when wetted length does not vary with speed. The discussion regarding F,,, FB and FnL relates to dimensionless speed for significant aspects of hydrodynamics related to hull form. For propulsors a cavitation number, CT, must be considered as a significant dimensionless speed coefficient. Cavitation number, a,, based on vessel speed and depth of the propulsor below the water surface is most commonly used in reporting characteristics of propellers. An alternative cavitation number, crr based on the resultant velocity of flow at the tip of a propeller has use whenever heavily loaded applications must be considered. UH = tpa + PgH - P )/1/2 PV2 (A-6) UR = tpa + PW - P )/1/2P VI-t2 (A-7) The relationship between these two cavitation numbers is: CrR = (0~ JT~I/(~-%)~(JT~ + 2) (A.81 Because no analytical relationship exists between Froude and cavitation numbers, the charts at the top of Figure 3 provide a convenient reference for F,, and uh for a range of vessel displacements and speeds. 15

APPENDIX B Relative Hull Loading R/W, seakeeping, stability, and other important performance characteristics of dynamically supported craft are affected by hydrodynamic hull loading. The following dimensionless definitions are used in various references as quantitative expressions of loading for hard chine monohulls: L,/@ = Slenderness ratio C* = Beam load coefficient Ap/+ = Area coefficient (B-1) (B-2) (B-3) It is helpful to determine relative hull loading in order to compare various size vessels to analyze their performance. However, published information may be limited to LOA, BOA and displacement. Figure 11 was prepared to represent constant hydrodynamic hull loading versus LOA by applying the loading criteria from DTRC Series 62 and defined in a simple quantitative form. I,, The majority of commercial and military planing hard chine craft at design full load displacement are concentrated about the heavy line with others distributed between lines identified as light and extremely heavy. FIGURE 11 - Relative Hull Loading 16