Celebrating 130 years

NAVAL ENGINEERS JOURNAL

March 2018 | Vol. 130 | No. 1

Celebrating 130 years

In This Issue: Using the Design Reference Mission for Framing Naval Ship Design Problems 53 Understanding the Dynamics of Program Productivity to Drive Towards Labor “Should-Cost” 65 Optimal Design of Spanish Navy F-110 Frigates Combat Information Center 79 A Comparative Structural Analysis of Shell-first and Frame-based Ship Hulls of the 1st Millennium AD 91 Comparison of Different Approaches for Calculation of Propeller Open Water Characteristic Using RANSE Method 105

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DEPARTMENTS 5 President’s Page 6 Code of Ethics 7 Secretary’s Notes 11 Committee Directory 12 Contributors 14 New Members 16 Letter to the Editor 18 In Memoriam 50 Section Directory 51 Upcoming Events 52 Corporate Supporters 64 Advertising Rates 144 Know Brainer

FEATURES & NEWS 9 All Students Need Engineers ASNE Educator in Residence Michael Briscoe issues a call to action to support STEM outreach programs with an update on the work ASNE Sections are doing across the country.

20 Book Review—Neglected Skies: The Demise of British Naval Power in the Far East, 1922-1942 CAPT Barry Tibbits, USN (Ret.) reviews this history of the inter-war development of naval aviation by the British and the Japanese navies by Australian author Angus Britts.

22 From the Archives: Seakeeping By Design The U.S. Navy is on the eve of recapitalizing the surface combatant fleet with the beginning of Future Surface Combatants (FSC) design studies. This paper from April 1980 is an example of how rapidly progress can be made with intensive collaboration between the fleet operator, the Navy’s technical community, industry and academia.

46 NATO SeaSparrow Missile Consortium Continues to Deliver Combat Relevant Capability

145 Membership Application

2 | March 2018 | No. 130-1

This year marks the 50th anniversary of the NATO SeaSparrow Missile Consortium, initially a creature of the Cold War that launched an international weapon development and acquisition program that has delivered a highly capable ship defense system.


March 2018 | Vol. 130 | No. 1

113

TECHNICAL PAPERS 53 Using the Design Reference Mission for Framing Naval Ship Design Problems Kristin Giammarco, Spencer Hunt, Clifford Whitcomb

65 Understanding the Dynamics of Program Productivity to Drive Towards Labor “Should-Cost” CAPT Chris Mercer USN, David Barksdale, Christopher S. Trost, Donna D. Mayo

79 Optimal Design of Spanish Navy F-110 Frigates Combat Information Center Gerardo González-Cela, Roberto Bellas, Javier Martínez, Ramón Touza, Rafael Carreño

91 A Comparative Structural Analysis of Shell-first and Frame-based Ship Hulls of the 1st Millennium AD Nathan Helfman, Boaz Nishri, Deborah Cvikel


105 Comparison Of Different Approaches For Calculation Of Propeller Open Water Characteristic Using RANSE Method PhD. Tran Ngoc Tu, Msc. Nguyen Manh Chien

113 An Experimentally Validated Dynamical Model of a Single-Track Hydrofoil Boat G. P. van Marrewijk, J. K. Schonebaum, A.L. Schwab

135 A Low-Voltage Test-Bed for Development and Validation of Control Strategies for Electric Propulsion Systems with Hybrid Energy Storage Jun Hou, David M. Reed, Heath F. Hofmann, Jing Sun

ON THE COVER As part of the celebration of ASNE’s 130th year, Naval Engineers Journal covers in 2018 will feature photos from ASNE’s history. To view full-size versions of the photos and captions, visit http:// www.weareasne.org and click on the images in the banner. Add photos of your own by tweeting with #WeAreASNE.

March 2018 | No. 130-1 | 3

TECHNICAL PAPER

A Comparative Structural Analysis of Shell-first and Frame-based Ship Hulls of the 1st Millennium AD Nathan Helfman1, Boaz Nishri2, Deborah Cvikel1

Abstract The 1st millennium AD experienced a significant change in ship construction. A slow transition evolved where ships built ‘shell-first’ were ultimately supplanted by ‘frame-based’ ships. Shell-first ships were constructed with strakes edge-jointed using pegged and later unpegged mortise-and-tenons joints, dowels or coaks, and at times, sewing, which resulted in a strong and rigid hull. The strakes were then fitted with transverse frames independent of the keel. Frame-based ships were characterized by transverse frames; most of the frames were fixed to the keel and reinforced by longitudinal components. The hull planks were later fastened to the pre-existing frames. The objective of this study was to examine whether mechanical factors contributed to the transition in ship construction. An initial comparative linear static FEA global comparison analysis was conducted on CAD models reconstructed from two archaeological shipwreck findings: Ma‘agan Mikhael (400 BC) and Dor 2001/1 (6th century AD). The Ma‘agan Mikhael shipwreck was representative of the shell-first technique and the Dor 2001/1 shipwreck represented the frame-based technique. The application of standard global stillwater criteria revealed that both ships possessed high degrees of rigidity and low von Mises stress values. Further controlled analyses were performed on two symmetrically identical archetypal quarter hulls while varying load and construction parameters. In all the archetypal load scenarios, the shell-first samples exhibited higher rigidity and less extreme von Mises stress differences than the framebased samples. Frame-based rigidity and stress levels were directly dependent on the number of frames added to the structure. Further to be researched are

the ancillary economic, social and ecological issues intertwined with engineering factors which contributed to the transition.

Introduction The 1st millennium AD witnessed a protracted methodological transition in the construction of wooden sailing vessels from ‘shell-first’ to that which supplanted it, the ‘frame-based’ method. In the shell-first construction “the vessel materializes gradually in the assembly of the planking” (Pomey, 2004, p. 27). The hull was conceived longitudinally, and the only assembly components that initially defined the structure of the hull before applying the planking were the keel, stem, and sternpost. Sequentially, the garboard and the adjacent strakes were installed and joined by pegged or unpegged mortise-and-tenon joints (or by other edge-fasteners such as dowels or coaks, or by sewing). Frames were installed later and connected to the pre-existing hull planks. Generally, this process was conducted in stages: first some strakes, then floor-timbers, more strakes, and then more framing timbers such as futtocks. Planks always preceded the frames. Exemplary of this technique are the Ma‘agan Mikhael ship dated to c. 400 BC (Linder, 2003, p. 45; Kahanov & Pomey, 2004), and the Kyrenia ship dated to the end of the 4th/beginning of 3rd century BC (Kahanov & Pomey, 2004; Pomey et al., 2012, p. 293), both discovered in the Eastern Mediterranean. The transition to the ‘frame-based’ method signaled the abandonment of edge-jointed planking in favor of planks which were fastened directly to the pre-erected transverse frames of the vessel (Steffy, 1994, p. 84). Most of the frames were fixed directly to the keel, creating a spinal-skeletal structure. The transition process was hardly linear, and probably started from several different origins throughout the Mediterranean basin. Though the evolution was initially prolific, the transition from

1 Department of Maritime Civilizations and the Leon Recanati Institute for Maritime Studies, University of Haifa, Haifa 3498838, Israel. 2 CorFlow Ltd. aerodynamic and flow technologies, Israel


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A Comparative Structural Analysis of Shell-first and Frame-based Ship Hulls of the 1st Millennium AD

FIGURE 1: The relative time-lines of hull construction and features in the Mediterranean (Whitewright, 2008, p. 174. Reproduced with permission) shell-first to frame-based was completed as early as the 6th–7th centuries (Pomey et al., 2012, p. 308) (Fig. 1). Conjectures and inferences abound attributing the 1,000-year-long technological transition as part of larger phenomena of socio-economic, geographic and environmental factors (Kreutz, 1976, p. 89; van Doorninck, 1972, p. 130). Other factors possibly impacting the transition included ‘Barbarian’ invaders of the Western Mediterranean such as Vandals, Burgundians, Visigoths and Ostrogoths. Climate change and the ecological effects on forests must also be weighed as factors (Pomey et al., 2012, p. 236). Technologies undergo periods of development and change until reaching a point of stabilization. Once accepted by a society, they reach what has been termed ‘closure’ (Whitewright, 2009, p 103). Hocker recognized the need for a generalized conceptualization of the transition in terms of ‘shell/skeleton’ transition, but rejected its oversimplification. He expanded shipbuilding concepts into three main aspects: design, assembly sequence and structural philosophy. In his view, the structural philosophy was central in that it involved specific intent: “the way in which the shipwright intends the component timbers to distribute the different working stresses the vessel can be expected to encounter” (2004, p. 6). Hence, for a given maritime application, a thick edge-joined shell with light reinforcement would provide the dominance of strength and rigidity. Indeed, under other circumstances, a combination of both methods would be optimal. Steffy took a broader and more evolutionary perspective at this holistic progression when asserting: “The demise of edge joinery and the introduction of standing frames were fruits of that progression. And they did not evolve suddenly in the medieval period; they were in the making since the first human pushed away from shore” (1994, p. 85). The first elements of technological change were identified

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FIGURE 2. CAD reconstructions: a) Ma‘agan Mikhael ship; b) Dor 2001/1 shipwreck in the increased spacing between mortise-and-tenon-joints (van Doorninck, 1982, pp. 139–140). Shipwrecks such as those from the 4th century AD site at Yassi Ada (Bass & Van Doorninck, 1984, p. 182), or the mid-4th century AD Dramont E (Santamaria, 1995, pp. 149–150), having joint spaces measuring 20 cm, about twice those of earlier vessels. The evolution of the mortise-and-tenon-joint produced a variety of versions as detailed by Pomey et al. (2012, p. 295), until the process ultimately abandoned edge-joined planking in favor of pre-erected frames of the vessel as represented by the Dor 2001/1 (Kahanov & Mor, 2014, p. 41) and the Serçe Limanı (Steffy, 1994, p. 85) shipwrecks. Though structurally distinct, both the shell-first and frame-based construction methods were manufactured with the design intent of bearing external loads and internal stresses. Furthermore, the contemporary longevity of these two mechanical approaches indicated that both techniques were successful by any structural criteria. Hence, Steffy posed the question ‘Why was it necessary to change from shell-first to frame-based forms of construction – what was wrong with the system as it existed in any period?’ (Steffy, 1994, p. 84). Steffy’s question served as the impetus for this research, which was conducted with the application of engineering methodologies.

Means and materials The ships In order to address the question: ‘To what extent did structural-mechanical factors contribute to the transition from shell-first to frame-based?’, two candidates for comparison


Ma‘agan Mikhael

Dor 2001/1

Length (m)

14.4

16.9

Length on waterline (m)

11.9

14.6

Beam (m)

4.2

5.4

Maximum Depth (m)

2.6

2.4

Draft (m)

1.4

1.5

Freeboard amidships (m)

1.2

0.9

Displacement—weight including cargo (ton)

23.0

32.5–CAD calculation

Cargo Capacity (ton)

16.0

25.0–CAD calculation

Height of center of gravity above bottom of keel (m)

1.50

1.50

Sail Area (m2)

46.0

73.0

Maximum angle of heel (degrees)

60.0

23.0

Hull wall thickness (cm)

4.7

2.8

Parameter

TABLE 1. Results of analytical calculations and CAD generated calculations made for Ma‘agan Mikhael and Dor 2001/1 (Ben Zeev et al., 2009, p. 2; Kahanov & Mor 2014: p. 63) were selected for global finite element analysis (FEA): the Ma‘agan Mikhael ship and the Dor 2001/1 shipwreck. The Ma‘agan Mikhael ship was built exclusively by the shell-first technique (Kahanov, 2003, p. 53), while the Dor 2001/1 shipwreck was constructed by using a frame-based method (Kahanov & Mor, 2014, p. 41). Both shipwrecks were discovered and excavated close to the coast of Israel at depths of less than 5 meters of water and within approximately 2.5 NM of each other. 14C analysis of short-living organic specimens and typing of pottery date their constructions as spanning about 1000 years: the Ma‘agan Mikhael ship dated to 400 BC (Linder, 2003, p. 45) and the Dor 2001/1 shipwreck dated to the first third of 6th century AD (Kahanov & Mor, 2014, p. 41). Both ships represent milestones on the transition timeline in that while being dimensionally similar in length, beam and volumes, their methods of construction and hull shapes are distinctly dissimilar, thus justifying their choice as candidates for analysis. Their re-constructed CAD models used for this research appear in Figure 2. As candidates for mechanical analysis, a comparison of the maritime and physical properties of both ships’ similarities and differences is in order. There were distinct differences in their amidships sectional geometry: The Ma‘agan Mikhael was built with a ‘wine-glass’ cross-section, while the Dor 2001/1 was constructed in a flat-bottomed riverine tradition with flat frames about amidships, a hard chine and straight sides (Kahanov & Mor, 2014, p. 64) (Fig. 3). As can be discerned by Table 1, the lengths, beams, and


FIGURE 3. Comparative cross-sections of the ships: a) Ma‘agan Mikhael drawing (Kahanov, 2003, fig. 4:); b) Ma‘agan Mikhael ‘wine-glass’ CAD reconstruction; c) Dor 2001/1 cross-section midships drawing near Frame E20 (Kahanov & Mor, 2014, fig. 13); d) Dor 2001/riverine CAD reconstruction volumes of both ships bore dimensional similarities attesting to their apparent designs as merchantman ships plying the Levant coast, albeit at different extremes of a millennium period. The principal differentiator between the hulls of the two vessels types is the relationship between their keels and frames. McGrail (1997) indicated that transitional ship hulls were of predominantly mixed construction, using the terms ‘plank-oriented’ and ‘frame-oriented’ or ‘frame-based’. Pomey et al. (2012, p. 236) emphasized that the variations are ‘more than merely technical’, manifesting fundamental changes in ship design, construction methods and hull structure. This difference was described by Basch (1972, pp. 15–49) as ‘active’ or ‘passive’ when referring to the framebased and shell-first construction method. He characterized shell-first as ‘passive’ frames and ‘active’ for the frame-based ships. The ‘passive’ frames were not connected to the keel, while the ‘active’ frames were. Basch’s interpretation bears

FIGURE 4. Comparative cross-sectional view of the frame-keel differentiator used in the analysis: a) Ma‘agan Mikhael—floating frame; b) Dor 2001/1—frame fastened to the keel (Author’s CAD depiction)

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credence in the FEA analyses performed in this study, witnessed by the increase of rigidity relative to the addition of keel-connected frames in the frame-based archetype. Figure 4 is a comparative cross-sectional view of the CAD models of the Ma‘agan Mikhael and Dor 2001/1 used in the analyses, where care was taken in treatment of the relationship between the frames and the keel.

Structural analysis Shipbuilders of antiquity did not develop a structured technological knowledge based on a profound understanding of the science underlying the technological processes (Olaberria, 2014, p. 3). However, the Mediterranean Sea served as a baseline, an initial stepping stone, justifying the assumption that both the Ma‘agan Mikhael and Dor 2001/1 shipwrecks, and all of those of their classes, encountered and experienced similar, if not identical, load environments. These loads were the bases of the comparative global analyses. When material is loaded by an external force, a deformation occurs. If it does not return to the mechanical properties that existed during its resting state, the material has failed; the material has lost its bearing capacity (Callister, 2000, p. 151). The criteria by which rigid bodies fail under the actions of external loads is known as rigid body failure analysis, where the concept of the design factor or the factor of safety is expressed in the following generic equation: Allowable stress (strength) S = σ Calculated stress

(1)

Analyzing these stress conditions underpins the analyses and the choice of the failure theories to be applied. The type of material, and its mechanical behavior drive that choice. The distortion energy theory, also known as the von Mises-Hencky theory, Eq. (2), represents stress due to angular distortion. It is the preferred theory to be used for analyzing ductile materials, and indicates failure at the beginning of yield (Shigley et al., 2004, p. 193). ½

(σ1 – σ2)2 + (σ2 – σ3)2 + (σ3 – σ1)2 = σVM 2

(2)

where σn = principal stress. The stresses σ1, σ2, and σ3 are principal stresses, i.e., in the direction where there are no shear stresses and as such, on the bases of von Mises stress, σVM ≥ σy

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(3)

Relative change in property from 12% MC At 6% MC (%)

At 20% MC (%)

Modulus of elasticity parallel-to-the-grain

+9

-13

Tensile strength parallel-to-the-grain

+8

-15

Compressive strength parallel-to-the-grain

+35

-35

Property

TABLE 2. Effects of moisture content (MC) on mechanical properties of clear wood at 20o C (Gerhards, 1982) If the von Mises stress induced in the material is greater than the yield stress, the material has exceeded ‘Y’, the allowable stress.

Wood material properties Performing a comparative structural analysis on two ancient wooden vessels posed several formidable engineering challenges, primarily with the setting of mechanical properties of wood. The elastic behavior of wood can be described by twelve constants: three moduli of elasticity, E, three moduli of rigidity, G, and six Poisson ratios, μ. Wood rigidity/ stiffness is also significantly influenced over time by moisture, temperature, chemical exposure, and the cross-section configuration of growth rings, among other contributing factors (Forest Products Laboratory, 2002, p. 5-2). Ultimately, the choice of mechanical property values parallel to the grain was based on the wide industrial usage of empirically derived moduli of elasticity (MOE) and moduli of rupture (MOR) which are shown to have correlative values, both based on center-loaded beam failure testing (Gutekin et al., 2012). This linearity of the mechanical properties enabled standardized linear static testing. Of the factors that most significantly influence mechanical behavior of wood, emphasis was placed on moisture content. Most of the mechanical properties of wood vary inversely with the moisture content below a fiber saturation point (Gutekin & Aydin, 2013, p. 878). In a systematic series of tests performed on the Ma‘agan Mikhael II (the replica ship) during its initial trial immersions at the Israel Shipyards, the moisture content varied widely, from 15% to 60%, averaging 25% at about 23oC (Tresman, personal communication, 2016). Accordingly, this required calibration of the relevant mechanical properties of all the wood species involved in the analysis. These included the elastic modulus, mass density, compressive strength and yield strength inserted into the FEA Simulations materials tables. The modulus and strength


extrapolated values were based on research conducted by the U.S. Forest Service (Gerhards, 1982) as per Table 2. Linearity is assumed and consistent in the ranges relevant to this study. There were five different wood species where all mechanical properties were calibrated for moisture (Table 2): Pinus brutia (Calabrian pine), Cupressus sempervirens (Mediterranean cypress), Quercus petraea (Sessile oak), Ulmus campestris (Elm), and a hybrid weighted average type composed of three other species used in the Dor 2001/1 framing timbers. Density, , being subject to moisture content, was calculated based on empirically generated equations (Eqs. 4, 5) by the United States Forest Service. Initially (specific gravity based on volume at moisture content) is calculated, where is volume at moisture content, and , ‘basic specific gravity’ or ‘green volume’ extracted from the tables provided (Ross, 2010): Gm = Gb /(1 – 0.265Gb)

(4)

ρ = Gm (1 + M /100)

(5)

Static analyses paradigms Global A comparative FEA structural analysis approach was adopted based on the guidelines of the DNV GL for yachts and boats (Lloyd, 2003), an international certification body. It was assumed that the Ma‘agan Mikhael and the Dor 2001/1 shipwrecks experienced the load regimes similar to those of modern yachts, with the exception of keel weight and rudder forces (ISSC Committee, 2007, fig. 1). The initial analyses were ‘global’, labeled by the standard as ‘strength assessment criteria for hull design loads’ which served as guidelines. The purpose of the global analysis was to place the structures under typical loads in order to reveal mechanical failures. The global analysis was performed on both loaded vessels under global contact-bonding and as single contiguous bodies (Parunov et al., 2010). Thus, the initial global CAD and FEA models, which were developed to accommodate hydrostatic loads, gravitational loads (cargo, dead weight), torsion loads, wind and transverse, longitudinal stresses due to rigging, mast compression, and midship bending moments. The vessels were restrained on the upper faces of their fore and aft end posts, canceling six degrees of freedom. All forces were loaded simultaneously during each run, only to be varied during sagging and hogging scenarios. Table 3 summarizes the multiple load configuration.


Load Type

Ma’agan Mikhael

Dor 2001/1

Gravity (selfweight) (N) Hydrostatic (still-water + hogging and sagging) Cargo + Ballast (N)

48,500.0*

51,050.0*

-Draft lines -trochoidal wave curves

-Draft lines -trochoidal wave curves

174327.0**

202176.0**

4,830.0***

6,300.0***

±20,000.0

±40,000.0

Wind-73ostarboard beam (N) Longitudinal Torsion (two directions about central axis) (N.m)

TABLE 3. Multiple Static Loads of the Ma‘agan Mikhael and Dor 2001/1 Shipwrecks *CAD Material Properties **Result of equilibrium testing with draft line at 1.0 m ***Beaufort 5, 21 knots—standard parameter used for calculating wind pressure strength on small sailing yachts (Ben Zeev et al., 2009, p. 68).

External loads The DNV GL yacht design criteria for vessels less than 30 feet long require a global analysis which includes rig loads from headstay and backstay, stillwater and wave loads. The loads and strength assessment is “undertaken for all load scenarios (global and local) and the final assessment shall be made on the most onerous strength requirement” (DNV GL, 2015, p. 5). These ‘onerous’ load scenarios as prescribed by the DNV GL certification are manifested as stress-strain yields as revealed by the von Mises FEA results. The Dor 2001/1 model (Fig. 5) is representative of both vessels, which were loaded with identical load regimes for FEA testing.

Static equilibrium An analysis in linear static paradigm requires that the system be in a state of equilibrium, that is, eliminating accelerations while balancing all forces and moments in static equilibrium. Initial balancing a stillwater ship is an iterative process done by adjusting the draft line with respect to the vertical Y axis until the resultants ideally equal (nearly) zero. This task, however, is further complicated given the composite of loads, such as the application of torsion around the longitudinal axis or loads such as wave sagging and hogging. Iterations may in fact influence previously achieved equilibrium states. This equilibrium challenge was resolved by using a technique known as ‘inertial relief’. This option facilitates static analysis in aircraft, ship and satellite designs based on the D’Alembert principle. It calculates the accelerations that counter-balance the net applied loads so that the analysis becomes equivalent to a free-body or unrestrained analysis.

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FIGURE 6. Stillwater hogging and sagging treatment: Dor 2001/1 sagging; Ma’agan Mikhael hogging

FIGURE 5. Multiple static external loads impacting both ships’ hulls as represented by Dor 2001/1: a) superimposed wind force; b) gravity; c) torsion; d) rigging force; e) cargo load; f) stillwater hydrostatic The following equation describes the process where {F}t = Applied external forces; {a}t = Translation acceleration due to inertia (calculated); ρ = Material density; v = material volume. {F}t + ∫V {a}t ρdv = 0

(6)

The above equation can be represented as: Fx Fy Fz

+ t

Mxx

0

0

ax

0

Myy

0

ay

0

0

Mzz

az

0 = t

0

(7)

0

where Mxx , Myy , Mzz are total masses in x, y, and z directions, and are evaluated by a row-by-row summation of the elemental mass matrices over the translational degrees of freedom. Once Mxx, Myy, Mzz are evaluated, the equation yields the induced accelerations ax, ay, and az which are applied as an acceleration field to the solution (Dassault Systemes Corporation, 2015, p. 155).

Data sampling and evaluation methods For both von Mises stress and stiffness/rigidity analyses, a standard sampling method was employed for the global and archetypal studies. The FEA software was configured to display the loci of maximum values for the von Mises stresses and displacements. At maximum von Mises stressed loci, a

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random sample of 10 nodal probes within a 20 cm radius was collected and then averaged. This sampling method is based on a standard FEA method recommended by the American Bureau of Shipping (2014, p. 29). Global displacement levels were similarly evaluated. Stiffness/rigidity was calculated based on the quotient of the directional (vectoral) maximum external load applied, divided by the resulting maximum displacement: the lower the displacement, the higher the stiffness/rigidity.

Stillwater hogging and sagging The global analysis included calculation of bending moments resulting from stillwater hogging and sagging loads. Longitudinal stress effects vary slowly (typically 5–15 seconds for large open waves). These wave-induced loads, causing hogging and sagging, fall in the realm of ‘quasi-static’ and are evaluated with linear static analysis. They are considered ‘snapshots in time’ (Miller, 2009, p. 12). When the ship is subjected to hogging, the midsection is lifted on a wave, while the bow and stern are not supported. In sagging, the bow and stern are lifted, while the midsection is not supported. Sagging therefore creates compressive stresses in the deck and tensile stresses in the bottom (Fagerberg & Zenkert, 2005, p. D8). For purposes of modeling hogging and sagging to represent the pressure conditions on the hull surface (Johny et al., 2012, p. 120), an inert wave was employed using the equations: x=

L H + sinφ 2π 2

(8)

H 1 – cosφ 2

(9)

y=

The wave-length equaling the ships’ lengths and its wave height equaling: H=

L ; L < 50 m 9

(10)

where H = wave height and L = ship length.


FIGURE 7. Archetype models of shell-first and frame-based: a) shell-first meshed; b) frame-based meshed; c) exploded shell-first model; d) exploded frame-based model With the purpose of concentrating specifically on the hulls’ structural compression and tension loads in the hogging and sagging scenarios, the rigging, wind pressure and torsion loads were removed, as illustrated in Figure 6.

Archetypical paradigm Though representative of their periods, juxtaposing the Ma‘agan Mikhael ship opposite the Dor 2001/1 shipwreck possessed inherent limitations. At a global level, one could comparatively calculate the strengths and rigidities. However, because of their structural, material and geometric dissimilarities, it would be impossible to isolate contributing factors to the transition. Significantly, the global testing of the FEA models exhibited high degrees of structural integrity: both ships met DNV GL criteria and did not reveal any structural failures. As a result, an experimental environment was devised with the intent of isolating and manipulating the variables involved in the shell-first/frame-based transition. Moreover, the global analysis results gave impetus to formulating a null hypothesis: ‘The inherent mechanical advantages of the frame-based technique contributed to the transition from shell-first to frame-based’. A FEA simulation experiment was designed to maintain the hull geometry and materials constant, employing the same data sampling methods as in the global testing. The hull construction varied in terms of wall thickness, the number of frames, frame cross-sections, and the frame to keel connection. Selection of materials was intended to neither augment nor diminish mechanical properties. The frame material chosen was Quercus patraea at 25% moisture content, representing the averaged mechanical properties


of the nine different species employed on both the Ma‘agan Mikhael ship and the Dor 2001/1 shipwreck. Hull planking material selected for both ships was Pinus brutia. Under this paradigm, each archetype, shell-first and frame-based, was given characteristic properties and calculated as symmetrical quarters 5 meters in length (Fig. 7). Symmetrical analysis is a common practice in FEA analysis under conditions where loads, restraints, geometries and materials are completely symmetrical. The original hull lengths of the Ma‘agan Mikhael and the Dor 2006/1, were 14.4 m and 16.0 respectively (Table 1). The length of the archetypal model, representing both types of construction, was reduced to 10 m in length, requiring a proportionate reduction in the number frames per vessel. The Ma‘agan Mikhael (shell-first), was reduced from 14 to 12 frames and the Dor 2006/1 (frame-based) was reduced from 43 to 32. Frames were not linearly reduced, but molded and sided to average values (based on Kahanov, 2003, p. 93; Kahanov & Mor, 2014, p. 48), and were adjusted to accommodate area moment of inertia section properties. The shell-first frames were 105 mm molded and 80 mm sided, while the framebased was 100 mm molded and 80 sides. The frames of the shell-first were not connected to the keel while the framebased model was characteristically contact-bonded to the keel. The shell-first was a single contiguous solid body which simulated a hull consisting of planking mortise-and-tenon edge-joined. Planking thickness was 4.5 cm (as in the original ship). The frame-based was composed of 10 separate strakes contact-bonded to the frames while the edges were bonded by ‘no-penetration’ with a friction factor of 0.37. The strake thickness was 2.7 cm (as in the original model).

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FIGURE 8. Models used for justifying the use of contiguous wooden hulls simulating mortise-and-tenon joints: a) assembly model employing mortise-and-tenon joints; b) single plank; c) exploded detail of assembly mortise-and-tenon joint The archetype scenarios, in principle, were designed to test the null-hypothesis, while concentrating on the number of frames in the frame-based method as the differentiator in establishing strength and rigidity approaching that of the shell-first method. Both the shell-first and the frame-based archetype samples were meshed using a convergence process to determine optimal values for element size. Optimizing the element size served to calculate stress concentration with greater resolution and therefore higher accuracy. The result was a high quality tetrahedral mesh with an average element size of 10 cm and an a/b ratio of 1.5 (Fig. 7).

Hull model contiguity The use of a contiguous hull model was compelled by the protracted and painstaking modeling, joining and then computing of more than 5,000 individual joints and contact elements. Moreover, it would have resulted in millions of degrees of freedom and nodes, much beyond the capacity of a high end engineering station. Hence a simulated validation test was devised to comparatively measure the equivalence and exchangeability of contiguous and edge-jointed models. Displacements and stress levels were measured on two constructs, 2 m in length, 40 cm wide, and 5 cm thick. They were modeled to simulate an extraction from a ship’s hull; one represented a contiguous body and the other an edge-jointed body. The contiguous body was represented by a single plank, while the other was an assembly of two

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FIGURE 9. Cantilever simulation comparing contiguous beam to edge-joint beam: (I a,b), beam structure; (II a,b), von Mises results: almost identical stress levels edge-joined 20 cm wide rectangular planks (Fig. 8). The analysis consisted of restraining the two structures and cantilevers while applying 10,000 N and then comparing both von Mises stresses and displacements (Fig. 9). The edge-jointed assembly experienced 4.7 mm more displacement in the Y-direction than the single plank, which could be considered negligible (Table 4). Thus, the choice of a contiguous hull model was assumed valid for purposes of FEA analysis.

Scheduling and load schemes Global The global schedule commenced with a ‘multiple load’ which included wind forces, hydrostatic pressures, cargo and gravity. This was followed by stillwater testing using a flat draft line, while hogging and sagging were represented by trochoidal waves, as prescribed by the DNV GL. Equilibrium for the flat draft lines scenarios was established by maintaining a 1 m draft line while adjusting the cargo values accordingly. Hogging and sagging equilibrium was established relative to trochoidal waves and iterative modifications of the cargo loads based on static equilibrium calculations.

Archetypal The objective of the archetypal FEA linear-static studies was to measure and compare stress, displacement and rigidity of two symmetrical ships with identical hull geometries (see the ‘Archetypical Paradigm’ section). The archetype


Max. von Mises Stress* (N/mm2)**

Max. Displacement (mm)

Single Plank

1.5

4.9

Edge-jointed Planks

1.1

9.6

Test Sample

TABLE 4. Comparative simulation results: single plank vs. edge-jointed planks * Average of 15 samples taken on the length of the models **yield values: Quercus petraea = 74.7 N/mm2; Pinus brutia = 41.5 N/mm2

Load Direction

Load Value (N)

+X

50,000

Schematic Representation

configurations were keel-connected and equally distributed on the inside of the hull. The number of keel-disconnected frames on the shell-first symmetrical quarter archetype was kept constant at 6, also distributed equally, and approaching the 14 frames of the Ma‘agan Mikhael ship. The loading conditions were not intended to simulate specific sea or hydrostatic conditions, but rather to apply a set of multidirectional forces, both concentrated and distributed onto the construct. The load levels were established for each scenario through interpolated runs, keeping them below the realm of ‘very large displacements’, a loading regime which would negate linear static analysis. The schematics of the loads are shown in Table 5. The archetypal FEA analyses commenced with the shell-first configurations, progressed through the frame-based 16 frame configurations, and concluded on the frame-based 6 frames.

Results Global analysis -Y

20,000

+Y

20,000

+Z

100,000

TABLE 5. Applied Archetypal Loads Scheme scenarios, in principle, were designed to test the null-hypothesis, while concentrating on the number of frames in the frame-based method as the differentiator in establishing rigidity approaching that of the shell-first method. In order to examine the contribution of frames to the hull of the frame-based archetypes, two configurations were employed: 6 and 16 frames. As a symmetrical quarter representation, 6 frames represented an arbitrary baseline of 12 frames and 16 represented 32 frames, approaching the number of frame stations in the Dor 2001/1 shipwreck. Both


The Ma‘agan Mikhael and the Dor 2001/1 shipwrecks were subjected to two loading regimes: multiple loads and stillwater loads; stillwater loads consisted of draft line, sagging and hogging. For our purposes, the relevant data for investigation were von Mises stress and displacement, two key indicators which reveal states of strength and rigidity of body under loads. The global testing revealed that both ships, built within a 1000-year span, were on a par and exhibited high degrees of structural integrity based on DNV GL standardization for yachts and von Mises allowable stress criteria.

Global von Mises The comparative global von Mises results of both ships were, under all loading conditions, below the yield stress of 41.5 MPa of Pinus brutia. These results indicated no failure levels and were consistent with allowable stress criteria. The highest stresses on both ships were concentrated stresses located at the mast-steps, caused by rigging subjected to simulated loads of Beaufort 5 wind conditions. These stresses were also well below the yield stress (Fig.10).

Global Displacement In displacement testing, as prescribed by the DNV GL criteria, the averaged maximum values on both ships’ multiple load scheme, were also on a par. Likewise, all the other loading categories revealed negligible displacement differences. Remarkably, each category for both ships was in the

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approaching yield values for the Quercus petraea while exceeding yield for Pinus brutia. Indeed, as frames were added, stress levels decreased accordingly (Table 6).

Archetypal Displacement

FIGURE 10. Global comparative analysis: von Misses stresses

Here too a pattern was apparent (Table 7): the rigidity values were consistently higher on the shell-first archetypes. The rigidity value of the shell-first +Z archetype scheme was approximately 40 times higher than that of the frame-based 6 frames +Z scheme. Also, correlative to the von Mises stress values, rigidity was increased with the addition of frames, as witnessed by the fact that the frame-based 16 frames +X archetype was 86% the rigidness of the +X shell-first archetype.

Discussion

FIGURE 11. Global comparative displacement results same range and varied by not more than 3 mm. As in the case of stress levels, there were relatively high displacements occurring on the masts and the mast-assemblages, apparently due to wind conditions of Beaufort 5. These extreme mast displacement results were not averaged into the global hull displacement calculations. The relatively low overall displacement values were correlative to the high rigidity/ stiffness levels for both ships (Fig. 11).

Archetypal analysis Archetypal von Mises The archetypal analyses revealed a general pattern of structural behavior: the shell-first archetype consistently exhibited the greater structural robustness, as manifested in its comparatively low von Mises stress values, all of which were well below yield values. At the other extreme, 6 framebased archetypes consistently exhibited high stress levels,

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The transition from shell-first to frame-based construction could be characterized as an evolutionary and experimental process of compromise between strength and stiffness. In the Uluburun shipwreck (ca 14th century BC), a high degree of lateral and longitudinal stiffening was transferred to the hull planking by employing extraordinarily deep mortise-and-tenon joints which resisted shear forces, bending and torsional moments exerted on the joints. The Uluburun’s widely spaced stiffening end-joints acted as internal ‘frames’ (Pulak, 1999, p. 220). A Roman war galley designed for ramming would require both strength and stiffness which was accomplished by fashioning closely spaced mortise-and-tenon joints (McGrail, 2004, p. 154). At the other end of the strength-stiffness spectrum, one finds the Viking Skuldelev ships (around 1000 AD) where experimental trials confirmed that the ships were constructed to avoid stiffness. This allowed controlled movements of the hull, especially twisting in the response to external loads (Hocker, 2004, p. 53). Though lacking Newtonian physics upon which modern engineering analysis is grounded, the ancient engineer, similarly to his modern counterpart, was also required to control strength and stiffness design parameters. Based on a variety of requirements for a particular application, the end-product could vary from a robust warship to a coastal merchantman. Instead of standardization, precision tools and experimental procedures, the designer most likely relied upon what is known in engineering as the ‘ignorance factor’, as opposed to allowable stress criteria. Without knowing the precise limits of material and mechanical properties, the ignorance factor resulted in a ‘design overshoot’, a very safe overreach of failure parameters in order to insure structural integrity: thick hull walls, closely spaced joints, etc. Interlocked with


+X

-Y

+Y

+Z

Shell-first

18.06

10.05

8.38

3.40

Frame-based (16 frames) Frame-base (6 frames)

20.24

22.54

29.06

11.80

43.10

40.72

38.13

18.70

TABLE 6. Archetypal comparative von Mises results of all the loading schemes (N/mm2) +X

-Y

+Y

+Z

Shell-first

1083.89

540.50

540.00

19739.00

Frame-based (16 frames) Frame-base (6 frames)

931.10

189.00

218.00

1192.00

368.80

101.32

110.20

542.53

TABLE 7. Comparative archetypal rigidity values of all loading schemes (N/mm) environmental, economic, and social stresses, the process of compromising between stiffness and strength ultimately brought about an evolving ‘best design’ (Pomey et al., 2012, p. 236). The results of global analyses in this study, given the diverse material content and mechanical configurations of both ships, would seem to synthesize a design and manufacturing evolution. The archetypal study shows that the effort achieving a close equivalence between the Ma‘agan Mikhael ship and the Dor 2001/1 ship must have been an extended and arduous process. Indeed, though no simple linear development can be postulated (Pomey et al., 2012, p. 296), a millennium of pragmatic design modification and refinement produced hulls seaworthy and strong enough to supplant the shell-first technique. The results of the archetypal studies run counter to the null-hypothesis which stated that the transition from shellfirst to frame-based ships was the result of enhanced structural advantages. The results of this study cannot affirm the null-hypothesis, and thus may be rejected. Indeed, the global testing demonstrated a par between the two contemporaneous methods, with no structural advantage to be attributed to either technique. The archetypal testing, however, seems to have contradicted the equivalence between the two ships in the global analyses: findings on both von Mises stress rigidity testing demonstrated that the overall structural integrity of the frame-based technology was significantly inferior to the shell-first technology. However, it was revealed that by adding more frames, the mechanical integrity improved, though only barely closing the gap in rigidity. Further, it would be challenging to explore the role of


frames in other ships built by the shell-first technique, such as the Kyrenia ship. The Kyrenia, contemporaneous with the Ma‘agan Mikhael ship, was approximately the same length and beam as the Ma‘agan Mikhael. The Kyrenia, however, with a hull thickness of 3.7 cm, contained almost three times as many frames and a different framing pattern; cross-sectional dimensions were similar to those of the Ma‘agan Mikhael (Steffy, 1985, p. 87; Pomey et al., 2012, p. 294). Steffy, in recounting the progress of Mediterranean wooden vessels into the 11th century AD, noted that the ships of the period were strikingly different from their early millennium Roman counterparts. Though approximately the same length as their predecessors, their frame-based pine hulls were fuller and flat-bottomed with sharp bilges, enabling them to hold more cargo with less draft. They were strengthened longitudinally with stringers, possessed heavy keelsons, and had both longitudinal and transverse ceiling planks. Above all, they lacked the hulls constructed of thick walled planking edge-joined by mortise-and-tenon (Steffy, 1994, pp. 77, 84). This would further be supported by Kahanov & Mor’s Dor 2001/1 shipwreck description (2014, p. 214): “… large amounts of interior and exterior longitudinal reinforcement such as chines, stringers, foot wales, and ceiling strakes, to insure stiffness…” as visualized in a cross-sectional view (Fig. 4). The Dor 2001/1 shipwreck, a 6th century AD vessel, seems exemplary of the transition construct as described by Steffy. Its global robustness requires investigating the mechanical significance of additional keel-connected frames, and the strengthening role of reinforcing longitudinal and transverse structures. The question would be, therefore, not if technology contributed to the transition, but what were the contributing mechanical factors which ultimately enabled the adoption of frame-based ships, thereby completing the transition? There is a need for further research, returning us to Steffy’s seminal question: “Why was it necessary to change from the shell-first to the frame-based—what was wrong with the system as it existed in any period?” (Steffy, 1994, p. 84). It just may be, as the late Professor Kahanov posited, “Because the frame-based was good enough.”

Conclusions The comparative global multi-load and stillwater FEA analyses performed on CAD models of both the Ma‘agan Mikhael ship and the Dor 2001/1 shipwreck passed DNV GL and allowable-stress criteria. These included von Mises levels that never exceeded 26.33 N/mm2 (MPa), well

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below the yield levels for the materials tested. Rigidity and stiffness levels were likewise high, as shown by the very low displacement values. The archetypal analyses, simulating shell-first and framebased hull and frame configurations, were performed on two geometrically identical CAD models. Frame and hull wood species were also identical for both models, and were kept constant. The frames of the frame-based models were characteristically joined to the keel. Identical +X, -Y, +Y, and +Z vectoral loads, concentrated and distributed, were applied to both archetypes. The results revealed a consistent and significant advantage in withstanding plastic deformation and failure of the shell-first method over the frame-based method. Regarding frame-based models, the addition of frames consistently decreased von Mises stress levels while increasing rigidity. The global simulations demonstrated that the end-product, a vessel constructed using the frame-based system, achieved equivalence to its predecessor, the shell-first system. The archetypal simulations, however, emphasized that the process of adopting of the frame-based system required overcoming a degraded and structurally inferior design. This result is counter-intuitive to our modern ‘upgrading’ mentality, and the driving motivations and advantages pursued by the engineers of the transition remains a conundrum. In light of these results, more research is required with an alternative hypothesis: the transition from shell-first to frame-based was an evolving process of constructing

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structurally inferior frame-based vessels which were improved by acquiring skills and applying the means of production to achieve a satisfactory end-product. Further to be researched are the ancillary economic (e.g. Kahanov et al., 2015), production engineering, social and ecological issues intertwined with mechanical engineering factors which contributed to the transition.

Acknowledgments This study was supported by a Sir Maurice Hatter Fellowship. The authors are grateful to J. Tresman for his skillful English editing. This article is dedicated to the memory of Professor Yaacov Kahanov, our mentor and friend.

AUTHOR BIOGRAPHIES NATHAN HELFMAN is a mechanical engineer, currently pursuing his Doctoral degree at the Department of Maritime Civilizations, University of Haifa. He has been concentrating on the application and development of mechanical engineering methodologies in researching ancient shipbuilding. DR. BOAZ NISHRI is the CTO at CorFlow Ltd., a company specializing in CFD (Computational Fluid Dynamics and FEA (Finite Element Analysis). Prior to Dr. Nishri’s work at Corflow, he was a research associate at the Faculty of Engineering, Tel Aviv University. DR. DEBORAH CVIKEL is a researcher at the Leon Recanati Institute for Maritime Studies, and a senior lecturer in the Department of Maritime Civilizations, both at the University of Haifa. She concentrates on ancient shipwrecks and shipbuilding and the maritime history of the region.


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