Revisiting the Serçe Limanı Sail Plan

Abstract

The reconstruction of the Serçe Limanı ship proposed a double-masted rig consisting of two sails with a total combined area of 100 m². That proposal considered provenance evidence and appraised hydrodynamic and hydrostatic conditions. The current paper proposes an alternative rig consisting of a single sail. By applying computational fluid analysis and hydrostatic stability software to evaluate hull resistance, sail propulsion, and heeling moments, it has been demonstrated that a sail of no less than 150 m² was suited to propel the Serçe Limanı. One of the two suitable alternative sails tested has been selected.

1. Introduction

The Serçe Limanı ship was discovered in the Serçe Limanı Bay, on the southwest coast of Turkey, opposite Rhodes, and excavated in 1977–1979 by an expedition of the Institute of Nautical Archaeology and Texas A&M University, headed by George F. Bass. The ship, also known as the ‘Glass Wreck’ because of the large quantities of broken glassware visible on the site, was dated to 1025 CE [1]. Until recent years, it was considered the first ship to have been constructed purely skeleton-first. Its reconstructed dimensions were 15.66 m long and 5.2 m wide, with an estimated burden of 35 tons [2], and it was a small two-masted vessel with lateen sails. This article aims to revisit and re-evaluate the reconstructed sail plan of the Serçe Limanı shipwreck [3]. The locomotion of a sailboat in water is a study in fluid mechanics, a dynamic interplay between hull resistance to water and the propulsive capacity of wind to supply forward thrust on a sail. By examining the hull and sail reconstruction plans of the Serçe Limanı, a numerical analysis was conducted, applying the disciplines of computational fluid dynamics (CFD) based on the Navier–Stokes equations (Equations (1)–(4)). The CFD software platforms were Orca3D^® V3, a Rhinoceros 8 plug-in, and SolidWorks^® 2023 Flow Simulation. The governing Navier–Stokes equations implemented for the numerical calculation of incompressible flow with constant viscosity (real viscous fluids) describe all the actions and forces acting upon a fluid. The fluid is assumed to be Newtonian, meaning that the linear shear stress is directly related to the velocity gradient. Both the pressure force and the viscous force are those which act at the surface of a fluid particle. The partial differential equations are given with the following coordinate system:

• Continuity equation (conservation of mass), expressed in a differential volume in the flow:

  $$\frac{\partial \rho }{\partial t}+\frac{\partial }{\partial x}\left(\rho u\right)+\frac{\partial }{\partial y}\left(\rho v\right)+\frac{\partial }{\partial z}\left(\rho w\right)$$

  (1)

• Navier–Stokes Equations (conservation of momentum)

x-momentum:

$$\rho \left(\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}+w\frac{\partial u}{\partial z}\right)=-\frac{\partial p}{\partial x}+\mu \left(\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}+\frac{{\partial }^{2}u}{\partial z^2}\right)+\rho g_x$$

(2)

y-momentum:

$$\rho \left(\frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}+w\frac{\partial v}{\partial z}\right)=-\frac{\partial p}{\partial y}+\mu \left(\frac{{\partial }^{2}v}{\partial x^2}+\frac{{\partial }^{2}v}{\partial y^2}+\frac{{\partial }^{2}v}{\partial z^2}\right)+\rho g_y$$

(3)

z-momentum:

$$\rho \left(\frac{\partial w}{\partial t}+u\frac{\partial w}{\partial x}+v\frac{\partial w}{\partial y}+w\frac{\partial w}{\partial z}\right)=-\frac{\partial p}{\partial z}+\mu \left(\frac{{\partial }^{2}w}{\partial x^2}+\frac{{\partial }^{2}w}{\partial y^2}+\frac{{\partial }^{2}w}{\partial z^2}\right)+\rho g_z$$

(4)

where: g = gravity, ρ = density, p = pressure, µ = dynamic viscosity, the x component of velocity is u, the y component of velocity is v, and the z component of velocity is w.

In Volume 1 of the Serçe Limanı shipwreck final report [1], in Chapter 11 by S. Matthews dealing with the rigging reconstruction, it was noted that the absence of a full-length keelson and rigging attachments impeded the ability to establish a plausible rigging plan in the Serçe Limanı shipwreck [3]. If only an exemplary remnant of the keelson had been revealed, it would have sufficed to locate the recess into which the mast heel would have resided to reconstruct a sail plan. Matthews, however, relied on indirect evidence consisting of the provenance of halyard blocks and sheaves: the two-sail rigging plan was hence devised. Provenance evidence is indeed essential in developing maritime reconstructions. However, in heeding Bass’s guidance in the same volume describing site documentation, “readers should exercise caution before concluding the seemingly anomalous location of any single object on the site” [1]. As required, Matthews then proceeded to calculate the hydrostatics and resistance properties, from which the geometry of a double sail propulsion system was conceived (Figure 1). However, these findings, as the authors indicated, “cannot discount the possibility that Serçe Limanı ship carried only one mast” [3].

In deriving an alternative sail plan, the authors resourced the archaeological reconstructions of the hull, keelson, and keel [1]. Hence, the mast step was assumed to be located vertically aligned with the center of least resistance (CLR), slightly forward of the center of effort (CE). This fundamental design concept, which ensured minimal weather helm, has been employed by ancient shipwrights and contemporary marine architects alike [4,5]. This basic architectural principle served the authors in locating the mast step.

2. Methodology

2.1. Serçe Limanı’s Architectural and Nautical Specifications

The analyses conducted on the Serçe Limanı ship were based on a model developed from a line drawing provided by Steffy [6]. Applying the ‘lofting’ functionality provided in the CAD software SolidWorks^®2023, a framing shell was developed upon which the hull skin was swept. Ignoring surface friction, the hull was faired and then imported into the Orca3D V3 Marine Design for Rhinoceros^® 8 program for CFD hull resistance and hydrostatic stability analyses. In its simplest terms, CFD processes a physical flow problem while applying the basic Newtonian equations of conservation of mass and the second law of motion. The Orca3D^® marine design software provides an interface dedicated to generating the mass properties and floated ship properties used in the CFD ship hull analysis. The results of this preprocessing closely matched the data presented by Steffy [6] (

Table 1. Mass and floated properties of the Serçe Limanı ship.

Source	Displacement at Waterline (Metric Tons)	Length at Load Waterline (LWL) (m)
Steffy	57.27	14.93
Orca3D®	57.24	14.94

).

2.2. Hull Resistance

CFD and hydraulic stability analyses require specific dimensional and physical input data generated by the preprocessor and applied to governing fluid dynamics equations. The prevailing Eastern Mediterranean maritime conditions between the months of April and October determined wind velocity when computing lift and drag sail forces.

When possible, an analytical methodology was implemented. This involved initially solving a given formula or equation to arrive at a calculated value. This was indeed valuable in setting orders of magnitude and a generalized direction to complex problems of fluid dynamics. The solution was verified by applying numerical analysis, which iteratively ‘converges’ on the solution of a fixed value [7]. This method was particularly useful in modeling the CFD aerodynamic analysis of the sail forces where more detailed and specific aerodynamic input parameters were required [8]. The forward movement sailing vessel, rigged with a single lateen sail, is dependent on the forward thrust propulsion system of the vessel. The forward thrust of the vessel relies on the capacity of the sail to develop the power to overcome the wave and hull-side resistance forces, as illustrated in Figure 2.

The choice of a single sail the length of the ship was supported by CFD resistance testing of the Serçe Limanı, which compared ‘with-keel’ and ‘without keel’ configurations [9]. It was demonstrated that the keel of the Serçe Limanı, as reconstructed, provided enough side-force and yawing moment, which increased the proximity between the center of effort (CE) and the center of least resistance (CLR). Thus, the vessel without the keel would have necessitated a sail that would extend forward beyond the bow, similar to Nile dhows [9].

Hence, the CFD analysis simulated a vessel being towed directly through the water while the software continuously sampled and iteratively calculated the development of the resistant forces on the hull, while heeling and yawing angles were neglected as not being relevant to the research. The simulation was a generalized symmetrical system of resistance and thrust regimes upon which the geometry of the sail was configured (Figure 3). The validity of this approach has been demonstrated in a study that revealed that the primary factor influencing resistance on the hull of the Serçe Limanı was its forward velocity through the water [9]. The system essentially emulated a hydraulic towing tank. The CFD setup parameters were set at the following:

• Hull type: displacement;
• Forward velocity: 3.08 m/s;
• Mesh type: 3D; number of cells—3,513,022; number of faces—10,816,738; number of nodes—3,760,396;
• Analysis type: Resistance/Powering;
• Time definition: Time steps with five iterations; 800 times steps; frequency-200;
• Dynamic option: Pitch and heave;
• Wave: no wave.

There is a direct relationship between the speed of a displacement boat and the length of the wave the hull generates [10], p. 10. Resistance to the water on the hull increases to the square of the hull’s velocity. The Serçe Limanı, a displacement ship, moves through the water while creating small waves that progress towards the aft along the side of the ship. As the speed of the vessel increases, the waves generated at the bow increase their wavelengths (the distance from crest to crest) until only one wave is created, the length of the entire watercraft. With any additional increase in speed, the wave becomes longer, driving the stern of the vessel into a trough and causing the vessel to ‘climb an inclined plane’. Forward motion is resisted until the vessel reaches its natural limit [10]. This is designated as the ‘hull speed’, a parameter required for the calculation of hull resistance. The velocity value for a displacement vessel can be calculated using the equation:

$$v=\sqrt{\frac{g\lambda }{2\pi }}$$

(5)

where v = velocity, g = gravitational acceleration, λ = wavelength at the waterline (14.93 m). Hence, based on Equation (5), the hull speed of the Serçe Limanı equals approximately 4.8 m/s or 9.3 knots under maximum conditions. The velocity on the simulations was held at 6.0 knots (3.08 m/s) under the assumption that a sail that would overcome resistance at 6.0 knots would be sufficient to propel the vessel at lower hull speeds.

A related input value when calculating the resistance on the hull is the generation of waves caused by the longitudinal motion of the vessel in the water. This can be simplified by assuming that the water is moving and that the hull is stationary. The flow around the hull would be the same as if it were moving over still water [5]. As the speed increases, the resistance increases exponentially (Figure 4). Longer wavelengths are generated along the hull, while concomitantly, the phenomenon of wave interference occurs. If the crests of the bow and stern coincide, large waves result. If the bow wave crests coincide with the troughs of the stern, wave attenuation occurs [11]. This is expressed in the Froude number (Equation (2)), which was employed when conducting a resistance analysis on the digital model of the Serçe Limanı. The resistance was relative to diverging hull wave amplifications and attenuations; the ‘humps and hollows’ are indicative of this phenomenon (Figure 5). The dimensionless value is expressed in Equation (6)

$$F_{n=}\frac{v}{\sqrt{g{L}_{WL}}}$$

(6)

where F_n = Froude number, v = velocity (m/s), g = gravity, and $L$ = wavelength at waterline (m).

Further, it can be demonstrated that there is a relationship between wavelength and traveling speed. Given the relationship wave speed in Equation (7):

$$\sqrt{\frac{g\lambda }{2\pi }}=1.25\sqrt{\lambda }$$

(7)

where λ = wavelength, an 8 m long wave will have a speed of 3.5 m/s. The wave travels longitudinally with the ship; hence, the length of the waves generated depends on the ship’s speed. As per Equation (3), if the speed is 1.25 times the square root of the water line length, a vessel with wave crests simultaneously at the bow and the stern will have a speed of 3.5 m/s. As per Equation (2), the Froude number is 0.39.

2.3. Sail Power

2.3.1. The 11th Century Prevailing Wind Speed

The Eastern Mediterranean experienced a warm phase in the period between 1000 and 1200 CE, otherwise known as the ‘Medieval Climate Anomaly’ [12], a fact that would necessarily impact wind velocity regimes. This period overlaps and is inclusive of the period when the Serçe Limanı ship plied the seas. Adding to the complexity of adjusting current wind conditions to the 11th-century prevailing winds, demonstrated that there have been significant warming episodes over the last 150 years. Thus, the complexity of gauging the 11th-century conditions to contemporaneous wind velocities prevented a reliable extrapolation. Assuming a tolerable range of error, the authors opted to apply the current prevailing conditions to the Serçe Limanı ship.

The determination of the driving force generated by the sail is directly dependent on the sail area and wind velocity. Pre-CFD analytical calculations to determine orders of magnitude and range were evaluated by applying Equation (8):

$$F_D=C_R\times \rho \times v^2\times A$$

(8)

where F_D = driving force, C_R = aspect ratio coefficient, ρ = air density, v = velocity, A= area [5]. Other relevant parameters include shape and cloth roughness. Preprocessing fluid CFD parameters were set at the following:

• Flow type—both laminar and turbulent;
• Surface roughness—12 µm;
• Wind velocity 3.08 (m/s);
• Angle of attack—25° (0.436 radians);
• Semi-dense meshing regime;
• Sail canvas roughness—12.0 µm;
• Wind velocities were based on the survey conducted by the Turkish National Committee of the World Energy Council, as the average offshore wind speed was measured in wind classes higher than 4.0 m/s [12], p. 34. Wind velocities were set as a variable parameter at 6.0 knots (3.08 m/s).

Sail propulsive force was determined by employing aerodynamical CFD SolidWorks^® 2023 Flow Simulation. The preprocessor was set to evaluate both the lift (F_Y) and the drag forces (F_X) on the sail samples, yielding the total force, F_T. The product of the F_T and wind velocity yields power in terms of Watts in Equation (9):

$$P=v\times F_T$$

(9)

where P = Power [W], v = velocity [m/s], and F = force [N], where the force is the product of the sail area pressure multiplied by its projected area.

Determining the shape of a medieval sail is problematic [2]; hence, as a single sail configuration, two different triangular-shaped sails were proposed for CFD aerodynamic velocity-pressure simulations: one resembling a right-angle triangle and the other, a scalene triangle. In rigging the sails, care was taken in the design of the sails to place the CE forward of the CLR to reduce weather helm (Figure 6).

A sampling of 100 m², 150 m², and 200 m² triangular sails was processed as airfoils, such that the apparent wind velocity was kept constant at 6.0 knots (3.08 m/s) at an attack angle of 25° (Figure 7). The F_Total, the resultant of the drag and crosswind forces, was subsequently converted to a power-based equation Equation (9). The results were compared to the effective hull power (resistance) [W] derived from the CFD Orca3D^® V3: The sail power had to be greater than the hull resistance. In both sail types, the yard was removed, thereby ignoring turbulence eddies developed along the luff.

2.3.2. Optimizing Mesh: Convergence Analyses

Verification of CFD results involves an iterative process of optimizing meshing refinement until differences between the results are reduced and converge to an optimal value. The process begins at a base line to which subsequent runs are compared. The integrity of the analysis is enhanced with the addition of finite elements, their specific type, and the number of time-steps and iterations. The objective of the analysis is to achieve maximum result consistency at minimal analysis run-time.

A convergence process was conducted on the aerodynamic analysis of the scalene triangle sail by repetitively evaluating a force–power scenario; the sail was fixed in its domain while refining the meshing. The ‘global mesh’, which is a relatively coarse foundational mesh, was kept constant while the ‘equidistance refinement’, which builds layers of increasingly refined ‘local mesh’, was varied. The number of elements can be increased on a sliding-scale functionality known as ‘maximum equidistant level’. Up to three variable offset distances can be manipulated. The convergence was achieved at a foundation layer of 0.5 m offset from the surface of the sail and 0.8 m offset for the less refined layer. The results of the convergence are presented in

Table 2. Computational fluid dynamics (CFD) convergence values.

No.	Base Offset [m]	Secondary Offset [m]	Refinement Value	Number of Elements	Iterations	Total Force Result [N]	Time [s]
1.	0.061	0.0244	4	116,968	146	834.92	395
2.	0.2	0.4	4	374,993	157	1004.70	1016
3.	0.2	0.4	4	274,792	144	1003.20	880
4.	0.5	0.8	5	4,254,403	181	1010.62	22,881

.

There was an appearance of convergence between analyses 1, 2, and 3. Upon significantly raising the refinement level and run time in analysis number 4, it was apparent that any refinement of the mesh beyond level 3 did not contribute to the convergence. The analysis appearing in Figure 7, which was run at level 3, is the analysis of the scalene triangle sail displaying the wind velocity differential between the windward and leeward sides. The windward side has characteristically higher pressure and an attack angle of 25°, providing forward propulsion.

2.4. Stability

If a ship returns to its initial position after heeling, the condition of equilibrium is stable. If the ship continues to heel, the equilibrium is unstable, causing it to capsize [13]. Matthew noted that the two-sail design was constructed such that the CE was lowered to prevent large heeling motions and stability [3]. This was, however, difficult to verify due to the lack of quantitative data: height and fore-aft positioning. To perform the calculation, several quantities must be known, among others:

• The estimated displacement of the ship, which included its cargo and distribution;
• The ship’s dimensions: length, beam, overall depth, heeling arm;
• Sail dimensions;
• Forces on the sail resulting from wind velocity.

The stability of the vessel under beam wind conditions is governed by the critical value known as the vertical center of gravity (VCG), otherwise known as the keel gravity (KG). The basic equation for identifying the VCG is Equation (10):

$$VCG=\frac{W_{hull}\times d_{hull}+W_{cargo}\times d_{cargo}}{W_{hull}+W_{cargo}}$$

(10)

where W_hull = weight of the hull, d_hull = the distance of the gravity of the reference point, W_cargo = cargo weight, d_cargo = cargo weight. d_cargo = the distance of the cargo’s center of gravity from the same reference point. This calculation resulted in a value of 1.2 m, applying the sinkage, as reported by the Orca3D^® CFD application, as 1.21 m. Lacking any evidence otherwise, it is assumed that the cargo was evenly distributed over the length of the ship at a depth of 1.2 m.

The VCG is an axis about which a heeling moment, caused by the wind on the sail, tends to roll the ship. The heeling moment is countered by the righting moment, which is dependent on the distance between the center of buoyancy and the center of gravity [5], p. 338. This calculation assumes a static condition where dynamic factors such as wave action and wind can affect stability, requiring highly complex computation. When evaluating the stability of a vessel, its righting arm is calculated over a range of heeling angles. Figure 8 is a generalized ‘stability curve’, which shows two graphs of static equilibrium where point A is the angle of the steady heel or angle equilibrium, point B is the point of maximum stability, and point C is the angle of vanishing stability. Hence, the plots display the relationship of the righting moment to the heeling moment where positive stability persists from 0° to 80°.

The calculation of the heeling arm relates to force Fy = pyAy, where py is the wind pressure, and Ay is the area of the sail (Figure 9). The force Fy tends to heel and drift the ship but is opposed by force R, which is equal to Fy. R acts at the half-draft T/2, where torque is developed until the heeling moment equals the righting moment. The heeling arm varies with the heeling angle where the area exposed to the wind varies proportionally to cosϕ parallel to the inclined plane W_θL_θ and is expressed in the Equation (11):

$$L_y\left(\varphi \right)=\frac{P_y{A}_y\left(h_y+\frac{T}{2}\right)}{g∆}{cos}^2\varphi$$

(11)

where L_y = wind heeling arm, h_y = height of sail area centroid above W₀L₀ [13]. This is the governing equation, in addition to a set of criteria for sea and structural conditions, which are set before running a stability analysis (Figure 10 and Figure 11).

3. Results and Discussion

The objective of this study was to offer an alternative solution to the sail plan of the Serçe Limanı ship based on the results applying rigorous methodologies of computational fluid dynamics and hydrodynamics stabilities software. This kind of research is not experimental in the sense of collecting populations or samples of statistical data to be tested for significance, averaged, or trend tested. The results rely on the intense iterative computations of complex partial differential equations partitioned into time steps, which generate moving averages. Each hydrodynamic and aerodynamic result was unique and verified by repeating the computations at least twice. Care was taken, when possible, to precede numerical solutions with analytical methods by calculating governing equations. The results were sufficient to generate range and orders of magnitude, providing direction and continuity.

The computational results were from three categories: analysis of hull hydrodynamic resistance, aerodynamic sail propulsion, and wind-heeling stability. The hull and sail results were translated into power values [W], while the heeling results were given in degrees of heeling as a function of a statical arm [m].

The values displayed in

Table 3. Hydrodynamic computational fluid dynamics (CFD) simulation evaluating the resistance force translated to power (Orca3D^®/SimericsMP).

Simulation Speed [m/s]	Resistance Force [N]	Power [W]
3.08	712.76	2195.31

present the resistance force and, hence, the effective power of the ship’s hull. This served as a baseline for the minimum power required by a given sail to propel the ship forward to a velocity of 3.08 m/s (6.0 knots).

Table 4. Aerodynamic computational fluid dynamics (CFD) simulations evaluating propulsion power of a scalene triangle sail (SolidWorks^® Computational Fluid Dynamics).

	Sail Area	Velocity-Apparent Wind [m/s]	Total Force [N]	Power [W]
	100 m2	3.08	682.4	2101.8
	150 m2	3.08	1004.7	3094.5
	200 m2	3.08	1341.7	4132.4

and

Table 5. Aerodynamic computational fluid dynamics (CFD) simulations evaluating propulsion power of a right-angle lateen sail.

	Sail Area	Velocity–Apparent Wind [m/s]	Total Force [N]	Power [W]
	100 m2	3.08	627.2	1931.8
	150 m2	3.08	893.4	2751.6
	200 m2	3.08	1218.4	3752.7

present the results of triangular lateen sails of two different geometries: an acute angle and a right-angle sail, comparing the propulsion capacities of each by varying their projected area. Each sail type was re-scaled to 100 m², 150 m², and 200 m², analyzed for forward thrust power, and then compared to the effective hull resistance power. The scalene triangle sail, although performing slightly better than the right-angle sail, was selected as the most suitable single sail configuration due to its shorter ‘hy’ distance (Figure 9), which would provide greater stability. The oversized 200 m² sail, which produced twice the power required, was dismissed.

The single sail concept gains credence based on the excavated finds of the Ma‘agan Mikhael B shipwreck (7th–8th century CE) found off the coast of Israel in 2005. This 25-m-long merchantman possessed unequivocal evidence of a hook-shaped masthead fitting with sheaves, a single mast step, and mast support indicative of a single lateen sail rig [14]. A digital 3D model of the Ma‘agan Mikhael B ship was developed by resourcing excavation data, iconographic representations, and relevant documentation. A standard maritime engineering analysis of stability and strength, and CFD analyses were performed on the digital model to evaluate hull resistance and the power of the ship’s single lateen sail. The simulations demonstrated that the fully loaded merchantman was seaworthy and made satisfactory speed over the ground with a sail area of 200 m² [15].

Stability Results

The aerodynamic results, as displayed in Table 3 and Table 4, demonstrated almost identical power output [W] for both sail configurations. The mast heights CLR to CE of the ‘right angle’ and the ‘acute angle’ sails were 9.35 m and 7.90 m, respectively. Agreeing with Matthews that a lower center of gravity would provide greater heeling stability [3], the stability analysis was conducted on the ‘acute angle’ sail. The method of calculation conformed to the standards set by the Netherlands Regulatory Framework (NeRF)—Maritime [16] for vessels exceeding 12 m. As per the standard, two basic qualifying tests were performed: stability with struck sails (Figure 9) and stability under sail (Figure 10). The equations prescribed by NeRF for calculating both heeling moment conditions are as follows:

For vessels with struck sails: stationary wind load = 51.4 kg/m²;

gust = 77.1 kg/m²

Moment 1 = 51.4 × (Orl × Arl + Otuig × Atuig)

Moment 2 = 77.1 × (Orl × Arl + Otuig × Atuig)

For a ship under sail (basic rigging): stationary wind load = 7.0 kg/m²;

gust = 10.5 kg/m²

Moment 1 = 7.0 × (Orl × Arl + Osail × Asail)

Moment 2 = 10.5 × (Orl × Arl + Osail × Asail)

where Orl = lateral surface of the hull (m²), Arl = distance between the center of gravity of Orl (m), Otuig = total rigging (m²), Atuig = one-half the height of the highest mast to the lateral point (m), Osail = the total area of the sails (m²), Asail = distance of composed center of effort to the lateral point (m).

In both evaluations, area ‘A’ must be equal to area ‘B’, where φ0 = the vessel’s angle of heel under the influence of the stationary wind load with lowered sails, φA = the roll amplitude due to a resonant roll movement caused by the wave load, and φC = the vessel angle of heel due to a gust [16]. The calculations performed demonstrated a high degree of stability based on the NerRF standards, such that φA = 17.68°, φ0 = 2.00° < 20°, φC = 23° < 45.00°, φC = 25.6° < 50.00°.

4. Conclusions

Matthews proposed a dual sail rigging configuration with a combined sail area of 100 m² for the Serçe Limanı ship. In this paper, an alternative single lateen sail rig has been proposed while analyzing the power required to propel the Serçe Limanı ship. Applying Orca3D V3 CFD software to evaluate the resistance of the ship’s hull at 6.0 knots, it became apparent that a sail area of 100 m² was incapable of propelling the vessel.

Two lateen sail options were selected for inquiry: a right-angle and an acute-angle sail. Both sails, though markedly different in their appearance, demonstrated that, to generate the power to propel the Serçe Limanı, at least 150 m² was required. Both sails could be rigged within the boundaries of the ship’s hull, their only difference being their heights: 7.9 m (acute angle) versus 9.35 m (right angle). The 7.9 m long mast was selected for testing, assuming a lower center of gravity and, therefore, less vulnerability to capsizing. Applying hydrostatic stability testing, it was thus demonstrated that the single sail Serçe Limanı, with a 7.9 m mast, faired extremely well, even under gust conditions.

It was demonstrated that the acute angle sail configuration robustly produced sufficient power to propel the Serçe Limanı while meeting standard stability criteria. Thus, a single acute triangular sail met the challenge of the dual sail rigging as proposed by Matthews. In the spirit of further research, a challenge is welcome.

In the strictest sense, CFD results should be validated either by employing towing tanks or wind tunnels. These types of validations were not performed, but their absence provides an opportunity for future research in other variable parameters, such as hull shape and construction methods. Further, in addition to towing tanks and wind tunnels, future research should involve the application of a Velocity Prediction Program (VPP), a program used in yacht design that predicts heel, speed, leeway, and apparent wind quantities.