Journal of Sailing Technology 2020, Volume 5, Issue 1, pp. 47 – 60. The Society of Naval Architects and Marine Engineers.

A Performance Depowering Investigation for Wind Powered Cargo Ships Along a Route

Fredrik Olsson [email protected]

Laura Marimon Giovannetti SSPA Sweden AB, Sweden, [email protected]

Sofia Werner SSPA Sweden AB, Sweden. Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021 Christian Finnsgård SSPA Sweden AB, Sweden.

Manuscript received September 30, 2020; revision received November 10, 2020; accepted November 26, 2020.

Abstract. For a sailing yacht, depowering is a set of strategies used to limit the sail force magnitude by intentionally moving away from the point of maximum forward driving force, potentially reducing the ship speed. The reasons for doing this includes among others; reduction of quasi-static heeling angle, structural integrity of masts and sails and crew comfort. For a wind powered cargo ship, time spent on a route is of utmost importance. This leads to the question whether there is a performance difference between different depowering strategies and if so, how large. In this research, a wind-powered cargo vessel with rigid wings is described in a Velocity Prediction Program (VPP) with four-degrees of freedom, namely surge, sway, roll and yaw, with a maximum heel angle constraint. The resulting ship speed performance for different depowering strategies are investigated and the implications in roll and pitch-moments are discussed. The wind conditions when depowering is needed are identified. A statistical analysis on the probability of occurrence of these conditions and the impact of the different depowering strategies on the required number of days for a round-trip on a Transatlantic route is performed.

Keywords: Velocity Prediction Program; Wind Powered Ships; Depowering; Routing.

NOMENCLATURE

�,, Forces in x,y,z direction [N] �,, Moments in x,y,z direction [Nm] � Ship speed [kts] � Reefing factor [-] � Wind speed [m s-1] -1 � Wind speed at 10m [m s ] � Height above mean sea level [m] � Angle of attack [°] β Leeway angle [°] δ Rudder angle [°] φ Heel angle [°]

47 1. INTRODUCTION

New targets on reduction of greenhouse gas emission from global shipping originating from the International Maritime Organization (IMO) drives development of innovative design concepts as well as retrofits to existing vessels of a range of different wind propulsion systems. With more and more of the propulsion power harvested from wind propulsion systems, design considerations from the 1800s re-emerges in the merchant shipbuilding industry. Examples of this is quasi-static heel angle constraints and wind propulsion depowering options to keep within the specified limits.

When sailing a yacht in strong winds, if the righting moment of the crew and movable loads is not enough to counteract the aerodynamic heeling moment, it is possible to depower the sails initially via “flattening”, then “twisting” and “easing” sheet and finally “reefing” in order to maximize overall performance of the yacht (Day, 2017). However, once considering commercially operating cargo ships, the limitations in maximum permitted heel angle are much stricter than in sailing yachts, as cargo security and reliability, crew safety and comfort and structural integrity are of great

importance. Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021

The current research aims at studying the effect on performance of a wind powered cargo ship due to different depowering strategies. Three different depowering strategies are investigated using a methodology involving a Velocity Prediction Program (VPP) and a statistical route analysis. The heeling angle constraint criteria itself is not studied and for the purpose of this research, the numeric value on the heel angle criteria has simply been set to 5°.

Velocity Prediction Programs (VPPs) to assess sailing yacht’s behaviours were initially developed at the end of 1970s (Kerwin, 1978). Since then, they have been developed to account for transient behaviours (Dynamic VPP), that can describe motions such as tacking (Ridder et.al., 2004), gybing (Battistin & Ledri, 2007) and body motions of sailors (Banks et.al., 2016).

For sailing yachts, results from VPPs are usually presented in the form of polar curves, showing the performance over a range of wind speeds and wind angles. Performance differences between different yacht designs and sail wardrobes can be readily studied simply by comparing performance polar curves. What the performance differences entails in terms of how much time is spent on the course is of little importance as long as less time is spent than the opponents.

Entering the realm of commercial shipping, time spent on the shipping route, i.e. the time for transporting goods from A to B is of utmost importance, as is the spread around the expected time on route. In terms of wind powered cargo ships, this introduces a necessity of comparing not only performance polar curves but also the actual performance on the planned route early in the design phase.

2. TEST CASE

The investigated test case consists of a wind powered cargo ship and a generic Transatlantic route.

2.1 Vessel

The vessel is a wind powered cargo ship based on the Wallenius Marine Sailing Car Carrier that is currently being developed under a grant from the Swedish Transport Agency.

For this study, the ship is equipped with 4 identical, rigid (i.e. non-twistable), single element wing sails, each with a planform area of 1844 m2, totalling a sail area of 7376 m2 for the ship. Each wing sail has a span of 80 m and a mean chord length of 23 m resulting in an aspect ratio of 3.47.

48 The wings are placed along the centreline of the ship with spacing of approximately 42 m and 27 m above the mean water line. The wings are free to rotate 360° and the spacing allows for independent rotation.

2.2 Route and Wind Conditions

The performance impacts of the different depowering techniques are evaluated on a round-trip on a single generic Transatlantic route defined by a great circle between waypoints A and B, as seen in Figure 1:

�: 49° 30’ � 4° � �: 36° � 74° �

The route travels a total distance of 3081nm (5706km).

Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021

Figure 1: Generic Great Circle Transatlantic route used for performance evaluation.

The route is divided into 10 equidistant legs. For each leg, hourly wind speeds and directions are fetched for the leg midpoint for the full year of 2019, corresponding to 8760 measurements for each leg. The 10m wind from the ERA5 reanalysis dataset available in the Copernicus Climate Data Store (https://cds.climate.copernicus.eu) is used as source. The data is shown in an aggregated form in Figures 2 and 3. Upwind conditions (0-90°) are predominant on the westbound route (A to B) whereas tailwinds (90-180°) are predominant on the eastbound route (B to A) suggesting that westerly winds are predominant in the area.

49 Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021

Figure 2: Discrete, joint probability distribution of 10 m True Wind Speeds and True Wind Angles relative Course over Ground (COG) on westbound route (A to B), 0° is headwind. Numbers in boxes are probability expressed in %. All wind angles are mapped onto a single side of the vessel. Aggregated data for the full year of 2019 based on the ERA5 reanalysis dataset available at Copernicus Climate Data Store.

Figure 3: Discrete, joint probability distribution of 10 m True Wind Speeds and True Wind Angles relative COG on eastbound route (B to A), 0° is headwind. Numbers in boxes are probability expressed in %. All wind angles are mapped onto a single side of the vessel. Aggregated data for the full year of 2019 based on the ERA5 reanalysis dataset available at Copernicus Climate Data Store.

50 The wind is modelled with an atmospheric boundary layer in the vertical direction which, at all ship speeds above 0 knots, will create a twisted inflow to the wing sails. The boundary layer profile is defined as � �(�) = � ∗ , (1) 10 for a reference height of 10m, where z is the height above the mean sea surface.

2.3 Depowering Strategies

In order to depower the aerodynamic load on a cargo vessel with rigid wing sails, two techniques are assumed to be possible: • “easing” of the wing sheet angle, therefore effectively reducing the angle of attack on the wings and hence reducing the lift and drag forces on the wing which translates to reductions of side force and thrust force on the vessel. At closed-haul conditions in particular, it results in a substantial reduction of side force experienced by the vessel. Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021 • “reefing”, reducing the planform area of the wings by lowering the top sections of the wings in a telescopic arrangement.

In this paper, three specific depowering strategies are investigated and compared, namely: • Only “easing” is allowed. • Continuous “reefing and “easing” is allowed. • Discrete “reefing” and “easing” is allowed.

For “reefing” two different approaches are compared. One where only discrete adjustment of the sail area in three steps is allowed, similar to regular soft sails and another where the sail area is allowed to be changed continuously. Discrete “reefing” is performed in pre-determined steps of 100%-75%-50% of the original wing span. Also note that “easing” is always allowed, even in combination with any of the “reefing” approaches.

In addition to the three depowering strategies, a reference result is also presented for a case with no-heeling angle constraint.

3. METHOD

The methods used for investigating the performance differences from the different depowering strategies is two-fold: • Use of a VPP to predict the ship maximum speed at a range of different true wind speeds and true wind angles. The output from the VPP calculations is in the form of performance polar curves. These are analysed and compared as-is but are also used as input into the next step, namely • A route performance prediction methodology, whereby the performance differences of the different depowering strategies are applied to a specific route with associated wind statistics using a Monte Carlo simulation technique. This enables a statistical evaluation of the operational importance of the performance differences.

These two methods are further described in detail below.

3.1 Velocity Prediction Program

The VPP finds the maximum speed of the wind-assisted ship while enforcing force equilibrium in 4 degrees of freedom (DOF), namely surge, sway, roll and yaw.

The generic optimization problem may be formulated as:

51 max �(�) � �. �. (2) �(�) = � � ≤ � ≤ �

Where � is the vector of decision variables, ��(�) is the objective function to be optimized (the ship speed), �(�) is the equality constraints (force residuals) and � and � are minimum and maximum bounds of the decision variables respectively.

A sequential least squares quadratic programming algorithm (SLSQP) is utilized at the heart of the VPP to perform the optimization. The algorithm is a gradient-based algorithm and therefore requires both the objective function and any constraint functions to be smooth and differentiable. Great care has been taken to ensure that the force model for calculating the force residuals adhere to these requirements. Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021 3.1.1 Decision Variables and Bounds

The decision variables are chosen as

� = [�, �, �, �, �], (3)

where � is the rudder angle, � is the heel angle, � is the leeway angle, � is the vector of angle of attack of the wings and � is the reefing fraction of the wings. Minimum and maximum bounds have been applied as follows:

−35° ≤ � ≤ 35° −5° ≤ � ≤ 5° −10° ≤ � ≤ 10° (4) −20° ≤ � ≤ 20° 0.2 ≤ � ≤ 1.0

In words, these bounds entail the following: • Maximum 35° of rudder deflection is allowed to either side • Maximum 5° of heel angle is allowed to either side • Maximum 10° of leeway angle is allowed to either side • Maximum 20° of angle of attack is allowed on the root section of the wing • Reefing between 100% to 20% of the original wing span is allowed. Reefing is performed by removing top sections of the wing, with corresponding changes to the centre of effort.

Each wing is sheeted individually whereas the same reefing factor is applied to all wings.

3.1.2 Coordinate System

The static force model in the VPP is defined in a right-handed cartesian coordinate system with origin at Lpp/2, at centreline of the hull and in the mean waterline.

52 Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021

Figure 4: Definition of the coordinate system

3.1.3 Force Modules

The VPP relies on a modular setup of static force modules to calculate the force residuals during each iteration of the optimization algorithm. These force modules are part of SSPAs Seaman software (Ottosson & Byström, 1991) and is extensively used for all kinds of static as well as dynamic simulations. Below is a brief introduction of the two most prominent modules for this specific research: hull and rudder hydrodynamics and wing aerodynamics.

Hull and rudder forces due to drift and rudder angles are modelled based on slow-motion hydrodynamic derivatives. The hydrodynamic derivatives are found through CFD, so called Virtual Captive Test (VCT). The methodology is further described in Marimon Giovanetti et.al. (2020).

A simple, yet highly performing, aerodynamic model, denoted as ‘SILL’ in Persson et.al. (2019), is used. The model uses 2D aerofoil lift and drag curves from RANS CFD, accounts for planform shape and wind twist by a vertical integration procedure and corrects for 3D effect, assuming an elliptic lift distribution, to determine the global forces on the whole wing.

The ‘SILL’ force module has been extended with functionality for reefing, allowing for the wing span (and subsequently the wing area) to be reduced in a telescopic arrangement. For example, a reefing fraction of 0.9 means that the wing span is reduced by removing wing sections from the top until 90% of the original wing span remains. Depending on the planform shape, this does not necessarily correspond to a reduction of 10% in planform area.

In this comparative study focused on the wind powering, added resistance due to waves have been neglected completely for all investigated cases.

53 3.2 Route Performance Prediction

The ship performance on a route is evaluated using a Monte Carlo simulation technique, allowing for quick estimations of performance distributions, enabling answers to be given, to some degree of accuracy, to questions such as: • What will the average speed along this route be? • What is the 95 % confidence interval of total time spent on this route? • How long travel time should be planned for if the probability of arriving on time (or earlier) should be at least 95%?

In this research, the Monte Carlo simulation technique is used, for each investigated configuration, to estimate the distribution of the total time spent on the route.

3.2.1 Monte Carlo Simulation

Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021 The route is divided into a set of legs, each leg treated independently. For each leg on the route, a discrete joint weather distribution (True wind speeds and True wind angles) is defined based on the hourly wind data. The leg-wise distributions are assumed uncorrelated.

A Monte Carlo simulation is then performed according to the following steps:

1. For each iteration in the MC simulation a. For each leg on the route i. Find the average azimuth and distance that the ship will travel on this leg ii. Draw a sample weather condition from the discrete, joint weather distribution. The sample is randomly chosen based on its probability of occurrence, i.e. a weather condition with 2% probability of occurring has a 2% probability of being sampled. iii. Evaluate ship performance for this specific weather condition using the performance polar curves from the VPP, linearly interpolating where necessary. b. Calculate aggregate results for the route based on sub-results for each leg 2. Combine aggregate route results from all iterations into a single cumulative performance distribution

When evaluating the ship performance for a specific weather condition, a tacking/gybing algorithm is included such that the ship always sails on the largest attainable Velocity Made Good on Course (VMC).

The Monte Carlo simulations were performed over 1 Million iterations, effectively traversing the route 1 Million times in different, sampled wind conditions. A Monte Carlo simulation with 1 Million iterations for one depowering strategy takes about 10 minutes to complete on a standard laptop running on a single-core run-time environment.

4. RESULTS

4.1 VPP Results

The VPP results are presented in the form of performance polar diagrams. The radial axis shows the ship speed in knots, the angular axis shows true wind angle relative to the direction of motion of the ship.

54 Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021

Figure 5: Performance at True Wind Speed 8 m/s. No heeling angle constraint is active for any wind angle which gives identical performance (all curves placed on top of each other) for all investigated strategies.

At 8 m/s, as presented in Figure 5, the heeling angle constraint is not active, i.e. all wind conditions result in absolute heeling angles less than 5 degrees, resulting in identical performance for all the four investigated strategies.

At 12 m/s (seen in Figure 6), the heeling angle constraint is active for true wind angles ranging from approximately 40° to 90°, i.e. close-hauled conditions. At beam and following winds, the performance is identical for all strategies. For the upwind conditions, all of the cases where heeling is constrained shows a clear decrease in upwind performance in comparison with the reference case with smaller differences in between the three depowering strategies. “Continuous reefing” gives the overall best performance whereas “Easing” gives the worst. “Discrete reefing” performs in the middle of the two other strategies, having the same performance as “easing” from approximately 75°-90°. At about 75°, the algorithm choses to activate the first, discrete reef and so the performance resembles that of “Continuous reefing” from approximately 40°-70°.

55 Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021

Figure 6: Performance at True Wind Speed 12 m/s. Heeling angle constraint is active for close-hauled wind conditions.

Figure 7 shows that at 16 m/s, the heeling angle constraint is active for true wind angles from approximately 40° to 110°, also including beam winds. The general observations from the 12 m/s case still holds even though the differences are larger, this is especially obvious comparing with the reference case. One can also see that the “Discrete reefing” curve now has two bumps, the first at approximately 100° and the other at approximately 75°, signalling the wind conditions where the algorithm choses to activate the first and second discrete reef respectively. This can also be seen more clearly in figure 8 where the utilization of the reefing factor � is shown at 16 m/s.

The VPP is limited to 4 Degrees of Freedom, thus force equilibrium of the vessel is not required in neither heave nor pitch. In order to confirm that the pitching angle is small enough to be ignored, a single sample case has been evaluated. At 14 m/s the maximum pitching moment from the wings on the ship is found at approximately 100° true wind angle. The experienced pitching moment is such that approximately 18 cm of vessel trim change is expected. This is considered well within bounds of what will be noticeable by the crew and is also not expected to affect the resistance significantly.

56 Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021

Figure 7: Performance at True Wind Speed 16 m/s. Heeling angle constraint is active for close-hauled as well as beam wind conditions.

Figure 8: Reefing factor at True Wind Speed 16 m/s.

57

4.2 Route Analysis Result

The results from the route analysis is presented as the average and the median describing the estimated distribution of the number of days needed to complete a round-trip.

Table 1: Round-trip durations in days on a generic Transatlantic route Unconstrained Easing Continuous Discrete heeling angle reefing reefing Average 37.2 37.8 37.7 37.7 Median 30.6 31.2 31.0 31.1

The required number of days to complete a round-trip for the reference case is on average 37.2 days, as seen in Table 1. For the cases where heeling is constrained, the average number of days required to complete the round-trip is 37.7-37.8 days. The difference to the reference case is Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021 approximately 0.5 days (12 hours) which corresponds to a 1% increase. The differences in between the depowering strategies are in the order of magnitude of 0.1 days or approximately 2 hours.

The median of the required number of days is significantly smaller than the average (approximately 7 days), suggesting that the distribution is highly skewed, with a relatively long tail towards a larger amount of days. Also, the median shows a difference of approximately 0.5 days in between the reference case and the three cases with constrained heel angle.

The probability of encountering weather conditions which requires depowering in order to adhere to the constraint on heel angle is approximately 20%, i.e. about a fifth of the time.

5. CONCLUSIONS

Depowering strategies for a wind powered cargo ship have been investigated from a performance perspective under a heel angle constraint using a two-fold methodology utilizing a VPP for generic performance assessments and a route analysis methodology allowing for estimating the impact of the performance differences. The presented method is used to evaluate three different depowering strategies; “Easing”, “Continuous reefing” and “Discrete reefing”, as well as a reference case (without a heel angle constraint).

The performance polar curves obtained from the VPP show that a depowering strategy is needed from wind speeds above about 10 m/s in close-hauled conditions to avoid too large heeling angles. All the depowering strategies show, as expected, a performance decrease in relation to the reference case which increases with increasing wind speed. The VPP results also show that “Continuous reefing” is the best performing depowering strategy and “Easing” is the worst. “Discrete reefing” performs somewhere in between, also as expected, as it is essentially a mix between the two. The differences in between the different strategies are however relatively small.

Perhaps counterintuitively, “easing” is allowed also in combination with continuous “reefing” in the VPP model. In a strict sense, this should not be needed as “reefing” is expected and is shown to be a more efficient means of depowering than “easing” and thus should be preferred by the optimization algorithm at all times. However, in order to exploit this knowledge and “simplify” the optimization problem for the case with continuous “reefing”, we need to know the optimal angle of attacks of all the wings for the range of allowable reefing factors. This would have to be solved in separate optimization problems, since it is a non-trivial problem for 4 interacting wing sails, for discrete values of the reefing factor. As such, it was chosen to include the angle of attack directly in the formulation of the full optimization problem also for the case with continuous “reefing”, thus implicitly allowing for “easing”, effectively changing the sheeting angle.

58

The route analysis shows that even though the performance differences are highly noticeable in the VPP results, the required number of days to complete a round-trip is less sensitive. This is somewhat unexpected since the probability of accounting weather conditions requiring depowering is as large as 20%. It should be noted, however, that a relatively large share of these 20% are wind conditions where the vessel is tacking in sub gale wind speeds (10-14 m/s), i.e. where the performance differences in relation to the reference case are quite small, on the order of a couple of percent.

The route analysis methodology includes several simplifications, most notably; the exclusion of weather routing and the exclusion of voluntary/involuntary speed reductions.

By using weather routing algorithms instead of a great circle route, the influence of depowering strategies is expected to decrease even further. The reason to expect this is two-fold; the amount of time spent tacking is expected to decrease and harsh wind conditions requiring depowering will

be avoided to a greater extent. Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021

Voluntary/involuntary speed reductions, in excess of a heel angle constraint, are, as of now, excluded from the route analysis tool. This includes effects like slamming and added resistance in waves, effects that worsen with increasing ship speed. Therefore, all of these are expected to further decrease the difference with regards to the reference case.

Even with the simplifications introduced by using a great circle route and excluding weather routing, the tooling used for the comparison is found to be very practical indeed to probabilistically answer questions about the impact of performance differences evaluated on a route. One of the main benefits being the low computation times in comparison with weather routing which is important in the early design stage where many concepts and/or strategies needs to be evaluated.

6. FUTURE WORK

The set of tools used for this research should be further developed and its strengths and limits further explored in the future. Specifically, the following are identified as interesting areas of suggested future efforts: • The inclusion of weather routing as part of the route simulation methodology should be investigated. Since the methodology is primarily aimed for use in the design phase and leverages a frequency domain algorithm as a base, neither the benefits nor the implementation details are, however, obvious. • The accuracy of the Monte Carlo route simulation approach should be further assessed. Specifically, the assumption about independent weather distributions on each leg should be investigated in detail to understand its implications on the simulated performance distributions on route level, taking into consideration the trade-offs between required accuracy and algorithmic complexity/computation time. A study on this topic would probably also include in-depth research on step-size (i.e. leg length) and its dependency on meteorological timescales.

7. ACKNOWLEDGEMENTS

This work was supported by the Swedish Transport Agency under grant TRV 2018/96451.

8. REFERENCES

Banks, J., Marimon Giovannetti, L., Taylor, J. C. & Turnock, S. R. (2016). Assessing Human-Fluid- Structure Interaction for the International Moth. Procedia Engineering.

59 Battistin, D. & Ledri, M. (2007). A Tool for Time Dependent Performance Prediction and Optimization of Sailing Yachts, Proceedings of the 18th Chesapeake Sailing Yacht Symposium, Annapolis, Maryland, USA.

Day, A. H. (2017). Performance Prediction for Sailing Dinghies. Ocean Engineering.

Kerwin, J. E. (1978). A Velocity Prediction Program for Ocean Racing Yachts. SNAME report 75- 17.

Marimon Giovanetti, L., Olsson, F., Alexandersson, M., Werner, S., Finnsgård, C. (2020). The Effects of Hydrodynamic Forces on Manoeuvrability Coefficients for Wind-Assisted Ships. Proceedings of the ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering.

Ottosson, P., & Bystrom, L. (1991). Simulation of the Dynamics of a Ship Maneuvring in Waves.

SNAME transactions. Downloaded from http://onepetro.org/jst/article-pdf/5/01/47/2478413/sname-jst-2020-03.pdf by guest on 24 September 2021

Persson, A., Li, D.-Q., Olsson, F., & Werner, S. (2019., Performance Predictions of Wind Propulsion Systems Using 3D CFD and Route Simulations. Proceedings of the International Conference on Wind Propulsion, London.

Ridder, E. J., Vermeulen, K. J. & A., K. J. (2004). ‘A Mathematical Model for the Tacking Maneuver of a Sailing Yach., 18th International HISWA Symposium on Yacht Design and Yacht Construction, HISWA, Amsterdam.

60