CFD Analysis of the Survivability of a Square- Rigged Sailing Vessel

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1 Engineering Applications of Computational Fluid Mechanics ISSN: (Print) X (Online) Journal homepage: CFD Analysis of the Survivability of a Square- Rigged Sailing Vessel William C. Lasher & Logan S. Flaherty To cite this article: William C. Lasher & Logan S. Flaherty (2009) CFD Analysis of the Survivability of a Square-Rigged Sailing Vessel, Engineering Applications of Computational Fluid Mechanics, 3:1, 71-83, DOI: / To link to this article: Copyright 2009 Taylor and Francis Group LLC Published online: 19 Nov Submit your article to this journal Article views: 343 View related articles Citing articles: 1 View citing articles Full Terms & Conditions of access and use can be found at

2 Engineering Applications of Computational Fluid Mechanics Vol. 3, No. 1, pp (2009) CFD ANALYSIS OF THE SURVIVABILITY OF A SQUARE-RIGGED SAILING VESSEL William C. Lasher* and Logan S. Flaherty Penn State Erie, The Behrend College, School of Engineering, 5101 Jordan Road, Erie, PA , USA * lasher@psu.edu (Corresponding Author) ABSTRACT: A CFD-based model has been developed for predicting the aerodynamic forces on the rig and sails of the U.S. Brig Niagara. Wind tunnel tests and full-scale experiments were performed to validate the model. The model was then used to predict the heel angle for different wind speeds and sail configurations, with a focus on determining whether the ship would be able to survive a storm. The results show that the Captain s practice of not allowing the ship to heel greater than 10 degrees is prudent, and that one of the sail configurations examined should be safe for any reasonably expected wind conditions on the Great Lakes. These results are useful for providing guidance to the Niagara s officers regarding survivability of the ship. Keywords: sailing, stability, survivability, square-rigged 1. INTRODUCTION For several hundred years wooden traditionallyrigged sailing ships were the dominant form of ocean transportation. Even though fuel power replaced sail as the primary mode of propulsion long ago, there are still an estimated 300 traditionally-rigged sailing vessels world-wide. These vessels, which are also known as tall ships or square-rigged ships, are used today primarily for historical reasons. One example of such a vessel is the U.S. Brig Niagara (Fig. 1). Niagara is a re-construction of a sailing warship built for the War of 1812 between the U.S. and England. She has a dual mission of historic interpretation as well as skills preservation. Within this historic interpretation mission there are two main tracks. The ship is interpreted as representing a warship from an important battle in the War of 1812, a story of naval history. The ship also represents seafaring as an industrial process. The other, and dominant, aspect of the mission is a skills preservation program carried out through the active sailing of the ship on 60 to 75 days each summer. Niagara sails today with a crew of up to forty people, half professional, half trainee. As a comparison, during the time that the Niagara was commissioned as a U.S. Naval Vessel, she carried a crew of 155. Due to the difference in both size and experience, today s crew is less able to respond to sudden changes in weather conditions, such as squalls that can quickly appear on the Great Lakes. As a result, they are very concerned about survivability that is, how much sail she can carry and still remains upright during a storm. One might think that a question such as what it would take to capsize a square-rigged sailing ship would have been answered in the historical record; after all, these vessels were around for hundreds of years and sailed through almost every imaginable condition. There is, in fact, a small body of literature describing practical seamanship in sailing vessels, but it is largely anecdotal and the information is spotty (for example, Harland and Myers, 1984). In many cases the information only applies to specific vessels; in some cases it is simply wrong. Fig. 1 Niagara under partial sail. Received: 20 May 2008; Revised: 31 Jul. 2008; Accepted: 7 Aug

3 There is a significant body of published work (both experimental and computational) on sail aerodynamics, most of which applies to sailboat racing. For example, there are several wind tunnels that specialize in sail aerodynamics research. Most of these tunnels have capabilities that are important to studying sail aerodynamics, such as the tunnel at the Wolfson Unit at the Southampton University (Deakin, 1991). This tunnel has been involved in wind tunnel tests on sailing vessels since the late 1960 s, and is capable of producing an atmospheric boundary layer, which will be described later. Deakin investigated the wind heeling characteristics of sailing vessels in both steady winds and in gusts a problem similar to that investigated here, but under different conditions. Flay (1996) described the development of a twisted flow wind tunnel at the Yacht Research Unit at the University of Auckland. Twisted flow occurs due to the combination of the atmospheric boundary layer and the motion of the boat relative to the wind. This tunnel has been used for a number of studies for grand-prix racing yachts, such as those described by Fallow (1996). Ranzenbach and Mairs (1997) implemented advanced blockage correction techniques at the Glenn L. Martin Wind Tunnel at the University of Maryland and used these techniques for a variety of studies, such as the investigation of forces on downwind (sailing in the direction of the wind) sails (Ranzenbach and Mairs, 1999). Blockage correction is especially important when the flow over the sails is separated, which occurs when a vessel is sailing downwind, or in conditions that are examined in this paper. Computational techniques have also been used for sail aerodynamics research for some time. Milgram (1968) first employed panel techniques to sail aerodynamics with some success, and Charvet and Huberson (1992) used vortex particle methods on this problem. These inviscid techniques work reasonably well for upwind sailing (sailing towards the wind), where the sails are flat and separation is at a minimum; however, they cannot be applied to downwind sails due to large areas of separated flow (Richards, 1997). Hedges, Richards and Mallinson (1996) were among the first to used Reynolds-Averaged Navier Stokes (RANS) simulation for downwind sail aerodynamics. Lasher and Richards (2007) compared the results from RANS simulations to wind tunnel data for spinnakers (a special type of downwind sail) in an untwisted atmospheric boundary layer, and in general the lift and drag coefficients were predicted with reasonable accuracy. Sail forces have also been found through fullscale testing. One of the most noted publications on full-scale testing is by Gerritsma, Kerwin and Moeyes (1975), who used equilibrium concepts and data from model tests of the hull to estimate the sail forces. Recognizing the limitations of this approach, Milgram, Peters and Eckhouse (1993) built a sailing dynamometer, which is a specially constructed boat where the mast and rigging are attached to a rigid frame that is structurally separate from the hull. This allows for direct measurement of the sail forces without having to estimate the hull hydrodynamic forces. Other sailing dynamometers have been built as reported by Masuyama and Fukasawa (1997) and by Hochkirch and Brandt (1999). While a sailing dynamometer is a major improvement over the force-balance approach, there are still significant problems determining accurate force coefficients. Due to problems associated with accurately measuring boat speed, wind speed near the boat (the sails influence the incoming free stream), sail shape, and the inherent fluctuations in both wind speed and direction, there is a tremendous amount of scatter in the data. For example, Milgram, Peters and Eckhouse (1993) showed drag coefficient vs. lift coefficient for upwind sailing. At a lift coefficient of 1.0, the mean experimental drag coefficient is near 0.19, with a standard deviation of and a range from 0.14 to While the stability limits of square-rigged vessels can be found through on-the-water experimentation, such an approach is risky, as it may result in the loss of the ship. The value of a science-based approach to predicting these limits, such as those described above, is clear. As a result of this need, two teams of researchers began investigating the stability of two different squarerigged vessels (Lasher et al., 2007; Miles et al., 2007). Lasher et al. (2007) developed a CFDbased model using Fluent 6.3 (Fluent, 2006) for predicting the stability of the Niagara, and Miles et al. (2007) began an experimental program to record wind and stability data during sailing conditions on the Pride of Baltimore II. The present work is an outgrowth of the computational work of Lasher et al. (2007), and is part of a larger program on square-rigged vessel stability. The two teams mentioned above have begun collaborating on a joint computational/experimental program to develop and validate models of square-rigged ship stability, and use these models to provide guidance to naval architects for design purposes, 72

4 as well as ship operators for decision making purposes. This paper focuses on one aspect of the stability question survival in a storm. During heavy weather the ship s captain may decide to go hoveto, which is a state where just enough sail is hoisted to keep the ship pointed in the desired direction, and forward motion is minimized. In the following sections an explanation of sailing aerodynamics and terminology will first be presented. The mathematical model used to predict stability will then be explained, including a discussion of model validation. The particular cases (or hove-to configurations) that were analyzed will be described, followed by a presentation of results and discussion. 2. A PRIMER ON SAILING AND SQUARE RIG TERMINOLOGY When a ship is sailing, the wind as seen from the ship s reference is a vector combination of the true (or actual) wind and the wind generated by the forward motion of the ship. This wind is known as the apparent wind, and the angle that the wind makes with the bow (or front) of the ship is known as the apparent wind angle (AWA). The sails act as airfoils, and the apparent wind generates aerodynamic lift and drag forces as shown in Fig. 2. These forces can be resolved into drive and side forces. The drive force propels the ship forward, and the side force has two effects it makes the ship slide sideways, and also causes a heeling moment, which makes the ship heel, or tip sideways. The side force is resisted by an equal and opposite hydrodynamic force on the ship s hull, and the heeling moment is resisted by a righting moment, which is generated by a shift in the ship s center of buoyancy. The main challenge in assessing stability is to determine the heeling moment due to the sails and rig (the rig consists of spars, such as the masts and yard arms; and rigging, which are lines that hold the masts up). The righting moment of the hull as a function of heel angle (or tipping angle) can be determined by the naval architect through hydrostatic analysis of the ship s hull shape and an on-the-water inclining experiment, from which the ship s vertical center of gravity can be found. The actual heel angle can then be determined by setting the heeling moment equal to the righting moment. The sailor s primary goal is to select the combination of sails and sail settings (angle of attack of the sails) to produce the desired effect, which is normally to maximize the drive force and minimize the side force and heeling moment. This is a complex process which is made even more complicated in Niagara s case by the large number of sails and possible combinations. Fig. 3 shows a sail plan for Niagara, along with the names of the different sails. The sails shown in white are square sails; those shown in grey are known as fore and aft sails. To the novice the names of these sails appear to be a foreign language, but to an experienced sailor they have very specific meanings. For simplicity, references to specific sail names will generally be followed by the letter shown in the legend for Fig. 3. A. Spanker H. Main Topgallant Staysail B. Mainsail I. Fore Topsail C. Main Topsail J. Main Topmast Staysail D. Main Topgallant K. Foresail E. Main Royal L. Foretopmast Staysail F. Fore Royal M. Jib G. Fore Topgallant N. Flying jib Fig. 3 Niagara s sail plan. Fig. 2 Aerodynamic forces acting on a sailing vessel. AWA is the apparent wind angle. The angle of attack of each of these sails to the wind can be adjusted on the ship by various lines. When sailing the angle of the sail is referenced to 73

5 the centerline of the ship rather than to the wind, and on square-rigged vessels this angle is known as the bracing angle (the term bracing angle technically only applies to the square-rigged sails, but for simplicity the term will be used for all sails). For example, if a sail is set so that the chord is parallel to the centerline of the ship, then the bracing angle would be zero; if it were eased out square to the ship its bracing angle would be 90. In Fig. 2 the bracing angle of the sail is 35 degrees. 3. MATHEMATICAL MODEL 3.1 Overview of the aerodynamic model Due to geometric complexity, the computation of the heeling moment was broken into two parts the moment due to the sails, and the moment due to the rig (spars and rigging). The moment due to the sails was determined through CFD computation, and the moment due to the spars and rigging was determined using a simple drag coefficient approach. Interaction between the sails, spars and rigging was neglected, and the two moments were summed to find the total heeling moment. This moment was then used in conjunction with the righting moment curve to find the heel angle. All analyses were done using a reference wind speed of 40 knots (20.6 m/sec), and the resulting heeling moments were then scaled to different wind speeds assuming that the moments varied with the square of the wind velocity. While wind speeds of 40 knots are not common on the Great Lakes, they do occur, especially during thunderstorms. It is also known that ships sail in an atmospheric boundary layer, so a velocity profile appropriate for the open ocean was used (Kerwin, 1978): V( y) = 1.96 ln(1000y+ 1) (1) In Eq. (1), y is the vertical distance from the water surface measured in meters and V the wind velocity in meters per second. This produces the reference wind speed of 40 knots at the head of the mainmast on Niagara, which is where the anemometer is located. Since the wind seen by the anemometer can be influenced by the presence of the ship and sails, the CFD analysis was used to determine what velocity would be measured by the anemometer when Eq. (1) was used as an inlet boundary condition. In the present analysis this was very close to the reference velocity (typically within 1%), since all of the sails analyzed were low on the rig and far from the anemometer. The forces on each of the spars and rigging were calculated using a drag coefficient of 1.13 (Kerwin, 1978). The lateral components of these forces were then multiplied by the distance to the center of lateral resistance of underwater portion of the ship s hull, which was assumed to be 40% of the ship s draft below the waterline. The value of 40% is used because this represents the location of the center of lift on an ellipticallyloaded airfoil. While the hull is not acting strictly as an airfoil this is a reasonable approximation, and any error introduced by this assumption will be small due to the large height of the rig compared to the draft of the ship. The calculated heeling moment was then added to the heeling moment due to the sails as predicted by CFD. 3.2 CFD model for sails Flow equations The equations governing incompressible turbulent flow are the well-known Reynolds-Averaged Navier Stokes (RANS) equations, written in Cartesian tensor notation as: Du 1 u i p = + ν i uu ' ' Dt ρ x x x i j i j j and (2) u i = 0 (3) x i Equation (2) is derived from the momentum equation, where the velocities u i are the timeaveraged velocities and u i ' are the fluctuating velocities caused by the turbulence, so the equation represents a time-averaged balance of momentum. Eq. (3) is the continuity equation, representing conservation of mass. The above equations do not form a closed set (i.e., there are not enough equations for the number of unknowns) due to the last term in Eq. (2), which is called the Reynolds stress. Various models for this term have been proposed. Lasher and Sonnenmeier (2008) performed simulations using six different turbulence models on a series of sail models that had been previously tested in a wind tunnel, and compared the simulations to experimental data. They showed that the Realizable k-ε model (developed by Shih et al., 1995) was the best of the six models tested in terms of accuracy and stability. This model was therefore used for the present work. The Realizable k-ε model is based on the Boussinesq eddy-viscosity hypothesis, which 74

6 relates the Reynolds stress to the mean flow strain rate tensor s ij, the turbulent kinetic energy k, and a turbulent viscosity v t by: ' ' 2 uu = kδ + 2ν s i j 3 ij t ij and 1 u u = j s i + ij 2 x x j i (4) (5) If the turbulent kinetic energy k and turbulent viscosity v t can be defined as a function of the mean flow variables u i and p, then the set of Eqs. (2) through (5) can be solved. In the Realizable k-ε model the turbulent viscosity is determined from the turbulent kinetic energy k and turbulent dissipation ε from 2 ν = c k t μ ε (6) The turbulence quantities k and ε are determined from modeled differential Eqs. (7) and (8): Dk ν = ν+ t k + G ε (7) Dt x σ x j k j Dε ν ε 2 = ν+ t ε + DSε D (8) Dt x σ x 1 2 k + νε j ε j G in Eq. (7) is the generation rate of turbulent kinetic energy, and is given by u u =ν j u G i + i t x x x j i j (9) The term S in Eq. (8) is based on the magnitude of the mean vorticity and is given by S = 2Ω Ω ij ij (10) where Ω ij is the mean rate-of-rotation tensor given by 1 u u Ω = i j ij 2 x x j i (11) The constants in this model generally take on the following values (Fluent, 2006): σ k = 1.00, σ ε = 1.20, D 2 = The coefficient D 1 in Eq. (8) is a function of S, k and ε, and the coefficient c μ in Eq. (6) is a function of the turbulent kinetic energy and dissipation, as well as the mean strain rate s ij Domain and boundary conditions The ship was placed in the center of a rectangular domain measuring 305 m 183 m (with the 305 m dimension in the streamwise direction), and a vertical height of 137 m (Fig. 4). The overall length of the ship is approximately 60 m, and the top of the mainmast is approximately 37 m above the water. To verify that the domain was large enough to not influence the results, a sample simulation was performed using a domain that was 33% smaller in each direction. The resulting predicted heeling moment was 2% larger, indicating that the domain size is appropriate. Z Fig. 4 Y X Computational domain shown in isometric perspective. Wind is in the positive x-direction. Equation (1) was used as a boundary condition on velocity at the domain inlet. Turbulence boundary conditions at the inlet were determined by comparing Eq. (1) to a generalized model for atmospheric boundary layers (Cook, 1985): ( ) u * y V y = ln κ y0 (12) In Eq. (12), u * is the friction velocity, κ is von Karman s constant (taken as 0.41), and y 0 is the surface roughness. Eqs. (1) and (12) produce identical velocity profiles but are in different forms. Equation (1) assumes an average surface roughness of m that is independent of wind velocity, whereas Eq. (12) allows for surface roughness that varies with wind speed. At the reference velocity selected for this paper, the friction velocity determined by comparing the two equations is m/s. The turbulent kinetic energy for an atmospheric boundary layer can be found from Eq. (13) 2 * k = 5.5u (13) 75

7 and the turbulent dissipation rate ε can be found from Eq. (14). u ε = * (14) κ( y+ y ) 0 Equations (13) and (14) were determined by a balance of the standard k-ε model using Eq. (12) as the velocity profile (Richards and Hoxey, 1993). A wall boundary condition with wall functions was used for the water s surface. With this boundary condition one specifies the velocity at the wall (zero in this case) as well as the turbulent shear stress, which determines the near-wall dissipation rate and kinetic energy. The shear stress on the water s surface τ w is given by Eq. (15): 2 τ w = ρu * (15) In Eq. 15, ρ is the density of the air. The surface roughness in Fluent is defined by the product of two constants: a roughness height K s and a roughness constant C s. A comparison of Fluent s roughness model with Eq. (12) shows that the product of the two constants must be approximately 10 times the surface roughness y 0 used in Eq. (12) to produce the same velocity profile, so the default constant of 0.5 was used for C s along with a surface roughness of 0.02 m for K s. A moving wall boundary condition was also used for the upper surface, with the wall velocity set to the velocity computed from Eq. (1). A symmetry condition was applied to the sides of the domain, and a uniform reference pressure of zero was applied to the outlet. Since the intent of being hove-to is to produce no motion, the velocity of the ship was set to zero. All of the sail shapes used in the CFD model were fixed (that is, it was assumed that the sails were rigid, with the only variable being the bracing angle). The sail shape used for the square sails was based on photographs taken from the deck. Since these sails are the largest and high in the rig, they are the most critical in terms of matching predicted performance with actual performance. Fore and aft sail shapes were based both on photographic evidence as well as commonly accepted values for the actual camber. The crosssection shape used for all sails was a circular arc Solution procedure The transport equations described above were solved using the finite volume method with the SIMPLE technique for determining pressure (Patankar, 1980) as implemented in Fluent (Fluent, 2006). The convective terms were calculated using a QUICK-type scheme (Leonard, 1979), which is second-order accurate as implemented in Fluent for unstructured grids. Both the normalized residuals and the aerodynamic lift and drag coefficients were monitored, and the solution was iterated until either the normalized residuals were less than , or the force coefficients changed by less than 0.5% after several time steps. The number of time steps required for convergence depended on the angle of attack of the sails. The solutions took between 2 to 6 hours on a 3 GHz Pentium Processor. Two grids were used to assess numerical error due to grid spacing. The coarse grid used an initial grid spacing of 0.6 m on the sail surfaces, increasing at a geometric expansion ratio of 1.08, with a maximum grid spacing of 9 m. The fine grid used initial and maximum grid spacings of 0.3 m and 4.5 m, respectively, with the same expansion ratio. It was not possible to obtain a converged solution using the fine grid for all of the angles of attack due to the unsteady nature of separated flow, so the coarse grid was used for all subsequent computations to provide a consistent basis for comparison. Using Richardson extrapolation (Roache, 1998) the error in predicted force coefficients on the coarse grid was estimated to be approximately 5%. A fundamental problem in computing separated flows such as those seen in the present work is that they are inherently unsteady. Technically, the simulations should be transient with the results time-averaged to fully capture large-scale coherent structures such as vortex shedding. This would require a much finer mesh than is practical for this type of problem, especially given the uncertainty in the computed rigging drag, the actual sail shape, and the actual wind velocity profile (which can vary greatly, especially during storm conditions). In addition, the simulations technically should be performed using an unsteady turbulence model, which is currently not available in Fluent. The grid parameters used in the present work probably under-resolve the flow; however, a detailed study on the simulation of separated flow over sails by Lasher and Sonnenmeier (2008) showed that these grid parameters produced results which reasonably agreed with wind tunnel tests. When using wall functions the distance of the first point from the sail surface is important. This distance is measured using the variable y + =u τ y/υ, where u τ is the shear velocity at the sail surface 76

8 (τ wall /ρ) 0.5. It is generally recommended that y + for the first grid points should be no less than 30 but as close to 30 as possible. In the present case most of the first points had y + values between 30 and 120, with a few less than 30 and some as high as 200 (depending on the sail shape and angle of attack). Given the highly complex nature of this flow this is a reasonable range of values for y +, as it is not practical to have a constant value. Further, Lasher and Richards (2007) showed that the predicted force coefficients for sail aerodynamics are not sensitive to either the near-wall grid spacing or the type of wall function used. 3.3 Heel calculation The righting moment for the ship (Fig. 5) was determined by the naval architect based on hydrostatics and the results of an inclining experiment. A 5th-order polynomial was fit to the data. The maximum righting moment for Niagara occurs at 30 degrees, and the ship would capsize if the heel exceeds this amount. As mentioned above, the total heeling moment was calculated by adding the heeling moment due to the sails to that due to the spars and rigging. Since all calculations were done at a reference velocity of 40 knots, the heeling moment was scaled to other wind speeds by assuming that it was proportional to the square of the velocity. creates a downward force and additional heeling moment. The magnitude of this additional moment is uncertain; however, Deakin (1991) showed in wind tunnel tests that the heeling moment for sailing yachts decreases by cos 1.3 (θ). At 30 degrees heel the difference between using cos(θ) and cos 1.3 (θ) is about 4%, so cos(θ) was used to make the model conservative. The reduced heeling moment was set equal to the righting moment, and the resulting nonlinear equation was solved for the heel angle using Newton-Rhapson. 4. MODEL VALIDATION 4.1 Wind tunnel tests Since the square sails are a major contributor to both driving force and heeling moment, it is especially important to know how accurate the CFD simulations are for these sails. To assess the accuracy of the simulations, a rigid scale model of a topsail (C or I) was built and tested in a wind tunnel using the procedure described by Lasher et al. (2003). Lift and drag coefficients (the force coefficients perpendicular and parallel to the free stream) were measured at angles of attack (defined as the angle between the incoming free stream and the chord of the sail) ranging from 20 to 90 in 10 increments. CFD analysis was also performed for this sail using the conditions in the wind tunnel. The experimental and predicted force coefficients are shown in Fig. 6. Fig. 5 Niagara s righting moment determined from inclining experiments and hydrostatics. All calculations were performed with the ship at zero degrees heel, so it was necessary to correct the heeling moment due to the reduction in projected area as the ship heels. In the present work the heeling moment was reduced by cos(θ), where θ is the heel angle. It can be argued that the heeling moment should decrease by cos 2 (θ), since both the projected area and the heeling arm are reduced; however, as the ship heels the sails become tilted horizontally to the free stream, causing the flow to be deflected upwards, which Fig. 6 Comparison of wind tunnel data and results from CFD simulation for a single rigid topsail. The predicted force coefficients are always larger than the experimental values. Over the range of angles tested, the average predicted lift and drag are 11% and 15% greater than the experimentally measured lift and drag, respectively. At 50, the predicted lift and drag are 24% and 28% higher than the measured lift and drag, respectively. These results suggest that the heeling moment predicted by the model will be higher than what is 77

9 experienced by the ship, depending on the influence of the other factors. This means that the model will most likely provide a conservative estimate of the heel angle; that is, the actual heel angle is likely to be less than that predicted by the model. 4.2 Full-scale validation It is extremely difficult to obtain accurate heel measurements on the ship to compare with predictions from the model. One must have a relatively long period of steady wind conditions with low waves to allow the ship to reach equilibrium. The wind speed must also be high enough to generate a measurable heel angle (on the order of 3 5 ) and/or consistent ship speed, yet not so high that the master becomes concerned with the ship s and crew s safety. Finally, it is difficult to measure the actual sail trim, so this must be estimated, introducing additional error. Due to both Niagara s schedule and the wind conditions on the Great Lakes, only a few measurements were taken that are useful for validation; however, these measurements do provide some illuminating information. Three different cases for validating the predicted heel angle are presented. In each of these cases the wind speed was measured using the anemometer and the heel angle was measured using an inclinometer. Sail trim was estimated by observation. CFD simulations were performed to match the recorded conditions and sail trim. In the first case the ship was hove-to with the foretopmast staysail (L) aback (set backwards) and single reefed (reduced area) topsails (C, I) with the fore topsail aback (see Fig. 7). The wind was 17 knots on the beam (i.e., at an AWA of 90 degrees). The heel angle was measured to be 1.8 degrees using the dinghy davits on the photograph and the water surface as a reference. In the second case the ship was sailing at about 60 degrees AWA in knots of wind. The ship was carrying the jib (M), foretopmast staysail (L), maintopmast staysail (J), both topsails (C, I), and a single reef in the spanker (A). The measured heel angle was approximately 4 degrees. In the third case the ship had been sailing close to the wind when a front came through. She was carrying both topsails (C, I) with a single reef, the jib (M), foretopmast staysail (L), and maintopmast staysail (J). The sails were trimmed appropriately for the apparent wind direction when the master had the ship turned away from the wind. When the wind was on the beam, the heel angle was approximately 5 degrees, and the wind speed was approximately knots (due to the rapidly changing situation there is some uncertainty as to what the actual wind speed was at the time the heel angle was recorded). Fig. 7 Niagara practices going hove-to in moderate winds. Notice the two topsails (square sails) are pointed in opposite directions; the forwardmost topsail is backed. The measured and predicted heel angles for all three cases are shown in Fig. 8. Error bars of ± 0.5 are shown on the measured values; these represent an estimate of the error in measuring the heel angle due to the resolution of the inclinometer as well as the fact that the ship may have had an initial unmeasured heel. In all three cases the predicted heel angle is greater than the measured heel angle by degrees. For cases 2 and 3, the predicted heel angle is approximately 15% higher than what was measured. The heel angle for case 1 is too small to calculate a meaningful percent error. Fig. 8 Comparison of predicted and measured heel angles. 78

10 While these results cannot be considered definitive, they do indicate that the model is reasonably accurate. The overprediction of heel angle is consistent with what was found comparing the wind tunnel data with CFD simulations, and suggests that the other assumptions made in the model are not contributing significantly to the total error. As mentioned in the introduction, a large scale program is currently under way to measure and record wind conditions and heel angle on both Niagara and the Pride of Baltimore II. These data will be used for further validation of the mathematical model. 5. DESCRIPTION OF HOVE-TO CONFIGURATIONS A ship will go hove-to when the wind is too high to maneuver safely. This process consists of setting a small number of sails, sometimes reversed (or backed), with the rudder positioned to keep the ship pointed in the desired direction relative to the wind. Different hove-to configurations can be used in different conditions, as explained below. The goal of being hove-to is to minimize drift of the ship while riding out the storm with minimum strain on the vessel. The Captain of the Niagara was most interested in four specific hove-to configurations, which are summarized in Table 1 and shown in Fig. 9. A brief note on each of these configurations is provided below: Configuration 1 Since the wind is on the beam and waves will cause the ship to roll, this is only used in light to moderate weather for man overboard recovery, fire drills, abandon ship drills, etc. The Captain is interested in knowing the upper wind limit of this tactic. Configuration 2 Niagara has resorted to this on several occasions but not in wind velocities of over 30 knots, or wave heights greater than 5 feet. This is historically the preferred method of heavingto in a square rigged ship, and is considered to be safe to ride out in a major storm. The Captain wants to know whether this configuration would be safe for Niagara in very heavy winds. Configuration 3 This has been tried on Niagara but found to be uncomfortable, primarily because it was undercanvassed (i.e., did not provide enough force) in the winds in which it was tested (25 knots). The Captain wants to know whether this approach might work in higher winds. Configuration 4 This would be for extreme conditions and used in combination with a sea anchor, which is a drogue that reduces drift of the ship and helps keep her headed in the proper direction. 45 degrees AWA is the most likely orientation, but 70 degrees is the worst case (i.e., maximum heeling moment), so both of these apparent wind angles were analyzed. Table 1 Summary of hove-to sail configurations. Configuration AWA, degrees Sails Sail bracing angle, degrees (a) 70 (b) 45 Fore topsail (I) Fore topgallant (G) Main topsail (C) Main topgallant (D) Spanker (A) Jib (M) Fore topmast staysail (L) Fore topsail (I), double reef Main topsail (C), double reef Fore topmast staysail (L) Spanker (A), double reef Fore topmast staysail (L) Main topmast staysail (J) Backed (-30) Backed (-30) Backed (-15) 5 Backed (-15) 20 Spanker (A), triple reef 5 79

11 Configuration 1 Y Z Y X Z X Configuration 2 Z Y X Y Z X Configuration 3 Z Y X Configuration 4a (Configuration 4b is not shown; same geometry at different apparent wind angle) Z Y X Fig. 9 The four hove-to sail configurations. (The apparent wind is in the direction of the postitive axis.) 6. RESULTS AND DISCUSSION The forces and moments calculated by the CFD simulations for the sails and the force coefficient calculations for the spars and rigging are summarized in Table 2. All of the results in Table 2 are computed at a reference velocity of 40 knots. A number of conclusions can be drawn from this table: As expected, the total heeling moment decreases with decreasing sail area. 80

12 With the exception of configuration 2, the driving force for all cases is quite small compared to the side force. This is generally the desired effect, as the goal in heaving-to is to minimize forward motion. The large lateral area of the underwater portion of the hull creates a significant reactive force, which will restrict sideways motion due to the side force. The larger relative driving force for configuration 2 is due to the fact that the two topsails (C, I) are set in the normal driving position, and these sails are large compared to the backed fore topmast staysail (L). The contribution to the total heeling moment from the spars and rigging increases from 17% for configuration 1 to 87% for configuration 4(a). This means that the accuracy of the model for calculating the heeling moment due to the spars and rigging becomes more important as sail is reduced; for configurations 4(a) and (b) the ultimate stability of the vessel is almost entirely determined by windage on the rig. This suggests that further full-scale experimental verification of the rig model is critical for determining the safety of the ship in these configurations. The heeling moment due to the spars and rigging is not the same for all configurations because the apparent wind angle is different, and this changes the direction of the drag vector. In addition, there are differences in the exposed area of the spars, as some of the spars have different bracing angles and some of them are lowered, depending on the configuration. Table 2 Forces and heeling moments at a reference velocity of 40 knots. Force or moment Configuration number (a) 4(b) Driving force, m 2,331 28,263 7,339 1,139 1,321 Side force, m 178,583 63,117 57,806 11,133 11,947 Heel moment from sails, N-m 2,830, , ,774 77,862 83,764 Heel moment from rig, N-m 584, , , , ,074 Total heeling moment, N-m 3,415,409 1,481,501 1, , ,838 Fig. 10 Heel angle vs. wind speed for all four configurations. The heeling moments from Table 2 were scaled by the square of the wind velocity (i.e., it was assumed that the heeling moment coefficient was constant), and this scaled moment was used to calculate the heel angle as described earlier. The predicted heeling angles vs. wind speed are shown in Fig. 10. It should be noted that the validation discussed earlier indicates that the model overpredicts the heel angle by approximately 15%, which provides a small safety factor. Since the heeling moment varies with the square of the wind speed, this reduces the underprediction of wind speed that would cause a particular heel angle to about 7%. For example, the wind speed predicted by the model to produce a heel angle of 30 degrees for configuration 1 is about 39 knots; a 15% overprediction of the heel angle means that the actual wind speed required to produce this heel angle would be approximately 42 knots a difference on the order of the accuracy of the anemometer. Also, since the validation was done using wind tunnel testing of a sail only (no rig), and the full-scale validation was performed using configurations with a large amount of sail area, there is a higher uncertainty in the results that have smaller sail area configurations. This uncertainty needs to be further explored by fullscale on-the-water testing. 81

13 In addition to the general trends, the captain of Niagara is interested in two specific wind velocities those which create heel angles of 10 and 30 degrees. Ten degrees is the comfortable limit of heel due to the importance of safety, the captain does not want to exceed this heel angle as a matter of practice. At 30 degrees the ship will capsize and be lost, so the captain does not want to get even close to that limit. An examination of Fig. 10 shows the wisdom of not wanting to exceed 10 degrees of heel. For example, for configuration 1 the wind speed required to produce a heel angle of 10 degrees is approximately 25 knots, and the maximum wind speed for survivability of the vessel is 39 knots. In wind conditions with mean wind speeds of 25 knots it is not uncommon to have temporary gusts in excess of 40 knots. While it will take time for the ship to respond to a gust of short duration, the possibility that the ship will capsize must be avoided. Wind speeds in excess of 60 knots are infrequent on the Great Lakes, so it is doubtful that the Captain would have to be concerned about configuration 4 while sailing in home waters. The only concern in this case would be if the ship were to be on an extended ocean voyage, which has not been attempted in her history. Configuration 4 can be considered safe for essentially any weather condition that the ship is likely to experience. It was previously mentioned that configuration 3 was uncomfortable because it was undercanvassed in winds of 25 knots. Figure 10 shows that this configuration should produce a heel angle of approximately 4 degrees at 25 knots, and is better suited for wind speeds of knots, thus supporting the Captain s original observations. Finally, the Captain has noted that the wind speeds that would capsize the ship are somewhat lower than what he expected. Niagara does not have a very deep draft due to the fact that it had to be moved over a sandbar to get from the harbor where it was built into Lake Erie. As a result of this low draft the ship does not have the same stability as other ships of that era with similar size and mission. The low relative stability of Niagara makes the results of this work even more important. 7. CONCLUSIONS A CFD-based model for predicting stability for the U.S. Brig Niagara was developed. Results from the model were shown to be in good agreement with full-scale experimental data. Some of the more important results from this analysis are: The model overpredicts the heel angle of the ship by about 15%. Although the data set is small and further verification is warranted, these results are consistent with a comparison between the CFD simulations of the sails and wind tunnel tests of a small, rigid sail. The results provide useful guidance for the crew that confirms some of their standard practices. These results will help the Captain make decisions such as whether is it better, when caught on a lee shore (a shore closely downwind from the ship), to try to sail away from the shore and risk capsize, or to head directly to the shore and risk beaching. The relative importance of the heeling moment created by the rig for the smaller sail area configurations indicates that experimental verification of the rig model is warranted, so that the accuracy of the predictions for these cases can be determined. A program is currently in progress to further develop and validate this model, and will be an important step towards providing naval architects and sailors with methodologies for designing and operating traditionally-rigged vessels safely. ACKNOWLEDGEMENTS This work was supported by grants from the Behrend College Undergraduate Student Research Programs. The authors also wish to express their thanks to sailmaker David Bierig for originally suggesting the line of inquiry, and to Niagara Captains Walter Rybka and Wesley Heerssen for their assistance in collecting full scale experimental data. REFERENCES 1. Charvet T, Huberson S (1992). Numerical Calculation of the Flow around Sails. European Journal of Mechanics, B/Fluids 11(5): Cook NJ (1985). The Designer's Guide to Wind Loading of Building Structures, Part 1. Butterworth. 3. Deakin B (1991). Model Test Techniques Developed to Investigate the Wind Heeling Characteristics of Sailing Vessels and their Response to Gusts. Proceedings of the Tenth 82

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