# Wind-Assisted Ship Propulsion of a Series 60 Ship Using a Static Kite Sail

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}kite sail would be sufficient to meet the entire propulsion requirements of the vessel under consideration under appropriate wind conditions.

## 1. Introduction

_{2}emissions by slow steaming was investigated for a typical sailing route of a container ship in the Mediterranean Sea by Degiuli et al. [6]. For engines powered by low sulphur marine gas oil and liquefied natural gas, the reductions in CO

_{2}emissions can reach 286 t and 448 t, respectively.

^{2}kite sail is found to be capable of reducing the fuel consumption of the 50,000 dwt British Bombardier tanker by 10% and more than 50%, respectively. However, the zero-mass model is again used such that the weight of the tether is neglected and the tether is assumed straight. The zero-mass model was also implemented by Bigi et al. [10] in a study investigating the dynamic coupling of a ship and a kite sail for auxiliary propulsion. Apart from concluding that the roll motion of a ship assisted by a kite sail can be lower than the roll motion of a ship that is not, Bigi et al. [10] suggested that the effect of the tether can be significant on the interaction of the kite sail with the ship. Thus, the need for a more accurate representation of the tether is highlighted. Existing literature works making use of the zero-mass model generally consider fixed lift-to-drag ratios for the kites and fixed lengths as inputs for the straight tether. In such cases, the equilibrium condition is satisfied when the resultant aerodynamic force on the kite is collinear to the straight tether and the wind power captured by the kite sail is limited by the input tether length.

^{2}and capable of delivering up to 2 MW of propulsive power while operating at altitudes ranging from 100 m to 300 m [12]. In application for pumping kite generators, kites can even reach 600 m altitudes [13]. By following a figure of eight, the kite sail developed by SkySails is capable of generating as much as 25 times the power per square metre of sail area of conventional sails [14]. The dynamic kite sails developed by SkySails have also been retrofitted on the Beaufort and Beluga SkySails ships. The former is a 55 m long testing ship equipped with an 80 m

^{2}kite sail able to save up to 1200 litre of fuel daily [15] while the latter is 132 m long with a 160 m

^{2}kite sail that can reduce fuel consumption by 20% [16,17].

## 2. Background Theory

#### 2.1. Modelling the Ship Resistance

#### 2.2. Modelling the Wind Profile

#### 2.3. Fundamental Wing Theory for Modelling the Aerodynamic Lift and Drag on a Kite

#### 2.4. Modelling the Catenary Tether of a Kite

#### 2.5. Equilibrium Analysis of the Kite-Tether Assembly

## 3. Numerical Model

## 4. Numerical Simulations

^{3}and 1025 kg/m

^{3}, respectively. Table 2 shows the values for the remaining fixed inputs. Given the likelihood of the kite to be operating in strong winds, ${z}_{0}$ is set to the value stated for a blown sea in Section 2.2. Although this study uses $\u2206z$ to set the kite configuration, its effect is not investigated and thus, it is fixed to a value of 5 m. A high value of 10 is prescribed to $AR$ of the finite wing to allow for the spanwise pressure gradient explained in Section 2.3. While ${C}_{D,t}$ was set as suggested by White [33] for an infinite length-to-diameter ratio, the values of ${d}_{t}$ and ${\mu}_{t}$ were obtained through a separate tether analysis using the same numerical model and fixed parameter values. The tether analysis is explained in further detail below. Also determined from the tether analysis are the maximum ${A}_{k}$ and ${U}_{z,ref}$ considered.

^{2}and 20 m/s was considered reasonable. The maximum ${x}_{k}$ and ${z}_{k}$ observed for these values at $V=4.04\mathrm{m}/\mathrm{s}$ are about 800 m and 420 m, with ${A}_{k}$ and ${z}_{k}$ within the limits from literature already discussed. For $\alpha <30\xb0$, ${c}_{l}$ and ${c}_{d}$ were found through an iteration of the Reynolds Number until its value obtained for $\alpha <30\xb0$ was approximately equal to the Reynolds Number to which the input coefficients correspond. The lift and drag section coefficients used for the NACA-0015 aerofoil for $1\xb0\le \alpha \le 90\xb0$ are plotted in Figure 5 and Figure 6.

^{2}determined for the maximum ${A}_{k}$, the values considered in the parametric analysis for ${A}_{k}$ are of 40 m

^{2}, 80 m

^{2}, 160 m

^{2}and 320 m

^{2}to study the effect of doubling the kite area. The corresponding values of ${c}_{ref}$ are 2.55, 3.60, 5.09 and 7.20 m, while those of the span are 20.00, 28.28, 40.00 and 56.57 m. On the other hand, the values for ${U}_{z,ref}$ are of 10 m/s, 15 m/s and 20 m/s given the maximum value determined from the tether analysis. The reason behind the lower limit of 10 m/s is to ensure a positive relative wind speed for the maximum ship speed of 7.27 m/s determined from the Series 60 Standard Data criteria. The whole speed range determined from the Series 60 Standard Data criteria was considered by repeating each combination for 4.04, 4.85, 5.66, 6.47 and 7.27 m/s, equivalent to 7.85, 9.43, 11.00, 12.58 and 14.13 kn. For the analyses of ${A}_{k}$ and ${U}_{z,ref}$, ${U}_{z,ref}$ and ${A}_{k}$ were set to the corresponding maximum value of 20 m/s and 320 m

^{2}, respectively, to investigate the greatest potential of each of the two parameters. A single run of the Python code explained in Figure 3 generates results for a single $V$ and $1\xb0\le \alpha \le 90\xb0$ with an average computational time of only around 661 ms with an Intel

^{®}Core™ i7-8750H processor.

## 5. Results and Discussion

#### 5.1. Investigating the Influence of the Kite Area

^{2}with all the other variables kept constant, including the reference wind speed, ${U}_{z,ref}$, set to 20 m/s. The plots in this section are those for the highest vessel speed of 7.27 m/s, for which the relative wind speed at the kite elevation, ${W}_{z,k}$, will be the lowest but the ship resistance is the largest. A high vessel speed is often desirable to minimise the voyage time. Hence, these plots will serve to determine the variation in the parameters corresponding to the minimum possible assistance in ship propulsion by a kite sail.

^{2}at an angle of attack 14°. Beyond $\alpha =30\xb0$, another peak, but with a much smaller magnitude, is present at the $\alpha $ of around 35°. The corresponding ${z}_{k}$ values as ${A}_{k}$ is increased from 40 to 320 m

^{2}are 21.1 m, 45.5 m, 106.8 m and 256.4 m. Hence, these values indicate that doubling the kite area increases ${z}_{k}$ by around 140% at an $\alpha $ of 14° and around 130% at 35°. As $\alpha $ approaches 90°, ${z}_{k}$ diminishes to about 5 m for all kite areas. The main contributing factor to this value is the prescription of 5 m to $\u2206z$ since, despite never reaching zero, the elevation of the tether end, ${z}_{t}$, at this $\alpha $ is very low. In relation to the kite area, the convergence to 5 m means that the effect of ${A}_{k}$ also diminishes as $\alpha $ tends to 90°.

^{2}and 160 m

^{2}kite areas. At an $\alpha $ of 90°, ${x}_{k}$ converges to approximately the same value for all four kite areas. Starting at 102.3 m for 40 m

^{2}, ${x}_{k}$ has to be 2%, 4% and 7% higher for each consecutive ${A}_{k}$ up to 320 m

^{2}. With the peak at $\alpha =45\xb0$ for ${A}_{k}=80{\mathrm{m}}^{2}$ being equal to 83.5 m, the maximum value of ${x}_{k}$ that has to be achieved for the smaller two areas is that at $\alpha =90\xb0$. The reason behind the relatively small percentage difference at 90° could be the fact that ${z}_{k}$ is approximately the same for all areas, thus indicating that the aerodynamic effects at this angle of attack have similar effects, irrespective of the area.

^{2}. These percentages indicate that the rates at which ${L}_{k}$ and ${z}_{k}$ increase with ${A}_{k}$ are non-linear, with the rate decreasing for larger kite areas. For a particular $\alpha $, using a kite sail twice the size at a given elevation doubles ${L}_{k}$ which, in turn, calls for an increase in ${z}_{k}$. The increase in ${z}_{k}$ is accompanied by a logarithmic increase in the relative wind speed, ${W}_{z,k}$, which affects ${L}_{k}$ on a quadratic degree. The relationship discussed for ${z}_{k}$ and ${L}_{k}$ is also visible as the angle of attack reaches 90° since both experience a decline. As ${z}_{k}$ at this $\alpha $ is approximately the same for each kite area, the lift is expected to be, in reality, only affected by ${A}_{k}$. In fact, ${L}_{k}$ for a given area is about 100% higher than that for the next smaller area being considered.

^{2}to 320 m

^{2}. The propulsion at these points corresponds to 1.5%, 3.7%, 9.2% and 23.2%, respectively, of the resistance at $V=7.27\mathrm{m}/\mathrm{s}$, with an average increase of about 150% each time the kite is doubled in size. The increase can be attributed to the relationship with ${W}_{z,k}$ in the same manner discussed for ${L}_{k}$. Given that ${z}_{k}$ and ${W}_{z,k}$ at $\alpha =90\xb0$ vary only to a small degree for different kite areas, the propulsive force at this angle mainly depends on ${A}_{k}$. In fact, the increase seen in ${D}_{k}$ each time the kite area is doubled is about 100%. The appendage resistance, ${R}_{App}$, air resistance, ${R}_{Air}$, and resistance due to the power margin, ${R}_{PM}$, contribute towards 3.4%, 3% and 25% of the total ship resistance, respectively, as labelled in Figure 10. Hence, a kite area of 80 m

^{2}is large enough to provide enough thrust to overcome ${R}_{App}$ or ${R}_{Air}$, that of 160 m

^{2}exceeds the two resistances combined by a margin of 43%, while that of 320 m

^{2}can make up for most of ${R}_{PM}$.

^{2}is only 1.0% higher than that for 80 m

^{2}, while that for 80 m

^{2}is only 1.5% lower than the length at the area of 40 m

^{2}. The rapid increase can be a consequence of the kite coordinates at high angles of attack. While ${z}_{k}$ decreases to about 5 m, ${x}_{k}$ is always greater than 100 m. Hence, the horizontal coordinate of the tether end is small such that the high values of ${x}_{k}$ for equilibrium have to be reached by lengthening the bridle lines. With an angle of attack of 60°, ${l}_{f}$ and ${l}_{r}$ need to be set to an average of 10.2 m and 10.8 m, respectively, for maximum thrust.

^{2}and 320 m

^{2}, while the corresponding values of ${T}_{r}$ are equal to 0.6 kN, 1.2 kN, 2.5 kN and 5.1 kN. The percentage increases of about 100% indicate that as $\alpha $ is increased to 90°, the bridle line tensions are mainly affected by the kite area. It is noted that, assuming that the bridle lines are of the same material and diameter of the tether, the safe load of 190 kN is never reached for the ship speed of 7.27 m/s.

#### 5.2. Investigating the Influence of the Wind Speed

^{2}was considered such that the greatest potential of the kite sail in different operating conditions is investigated. The different values considered for the reference wind speed, ${U}_{z,ref}$, are 10, 15 and 20 m/s. The variation in the different parameters with $\alpha $ follows similar trends as those discussed in Section 5.1. Hence, this section focuses on the optimal parameters for different wind and ship speeds. The optimal parameters are the parameter values that correspond to the maximum propulsion and hence, will exploit the full potential of a static kite sail for the conditions considered.

^{2}is lower than the limit of about 800 m. The 800 m limit is the limit prescribed from the tether diameter analysis. However, the maximum ${x}_{k}$ is 254% higher than the maximum ${z}_{k}$ in Figure 13. Hence, the results indicate that for optimal performance, ${x}_{k}$ may be of a greater concern than ${z}_{k}$ due to the relationship between the two coordinates for high angles of attack.

## 6. Conclusions

- The correlations between the aerodynamic forces and output parameters that determine the performance of the kite sail are generally positive.
- The effect of the kite area varies with the angle of attack given that wind shear also comes into effect when the kite elevation has to be changed in response to a different lift force. In fact, doubling the kite area for an angle of attack of 60° increases the kite thrust by about 150%.
- The kite coordinates corresponding to the maximum propulsive drag were found to satisfy practical limits for all the ship and tail wind speeds considered.
- For the highest reference wind speed of 20 m/s, about 80% of the required propulsion can be provided by the kite sail if the 75 m long Series 60 vessel travels at a speed of 5.66 m/s with a tail wind while the angle of attack and coordinates of the kite are set to 60° and (500.9 m, 141.9 m), respectively.
- The modelled ship can be propelled solely by the 320 m
^{2}static kite sail at a speed of about 5.3 m/s when the wind speed is 20 m/s at a height of 90 m. At this wind speed of 20 m/s, the optimal angle of attack leading to maximum thrust was also found to be constant at a value of 60° for all ship speeds considered. However, the optimal angle of attack is expected to vary for low relative wind speeds. - The safe load of 190 kN set for the tether was never reached in the scenarios considered. Additionally, the maximum tether drag as a percentage of the kite thrust as estimated in this study for maximum thrust conditions was found to be only of about 1.5%.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

CFD | Computational Fluid Dynamics |

COP | Centre of pressure |

WASP | Wind-assisted ship propulsion |

${c}_{d}$ | Drag coefficient of a two-dimensional aerofoil (-) |

${c}_{l}$ | Lift coefficient of a two-dimensional aerofoil (-) |

${c}_{m}$ | Moment coefficient of a two-dimensional aerofoil (-) |

${c}_{ref}$ | Reference chord of a finite wing at the midspan (m) |

${d}_{t}$ | Tether diameter (m) |

${l}_{f}$ | Front bridle line length (m) |

${l}_{r}$ | Rear bridle line length (m) |

${l}_{t}$ | Tether length (m) |

${x}_{k}$ | Horizontal coordinate of the kite’s centre of pressure (m) |

${x}_{t}$ | Horizontal coordinate of the tether end (m) |

$z$ | A given elevation above the mean seawater level (m) |

${z}_{0}$ | Surface roughness length of the seawater (m) |

${z}_{k}$ | Kite elevation (m) |

${z}_{ref}$ | Reference height at which the wind speed is known (m) |

${z}_{s}$ | Elevation above sea surface at which the relative wind speed is zero (m) |

${z}_{t}$ | Elevation of the tether end (m) |

${A}_{k}$ | Area of the elliptical kite planform (m^{2}) |

$AR$ | Aspect ratio of the elliptical kite planform (-) |

$B$ | Ship beam (m) |

${C}_{B}$ | Ship block coefficient (-) |

${C}_{D}$ | Drag coefficient of a finite wing (-) |

${C}_{D,i}$ | Induced drag coefficient of a finite wing (-) |

${C}_{D,t}$ | Tether drag coefficient (-) |

${C}_{L}$ | Lift coefficient of a finite wing (-) |

${D}_{k}$ | Drag force on a finite wing (N) |

${D}_{t}$ | Tether drag (N) |

$L$ | Ship length (m) |

$LCB$ | Longitudinal centre of buoyancy (%L) |

${L}_{f}$ | Ship length in feet (ft) |

${L}_{k}$ | Lift force on a finite wing (N) |

${P}_{E}$ | Naked effective power of a ship (kW) |

${R}_{air}$ | Air resistance on a ship (N) |

${R}_{App}$ | Appendage resistance of a ship (N) |

${R}_{Eff}$ | Effective ship resistance (N) |

${R}_{Naked}$ | Naked hull resistance (N) |

${R}_{PM}$ | Ship resistance due to the power margin (N) |

${R}_{T}$ | Total ship resistance (N) |

$T$ | Ship draught (m) |

${T}_{f}$ | Front bridle line tension (N) |

${T}_{H}$ | Horizontal component of the tether end tension (N) |

${T}_{V}$ | Vertical component of the tether end tension (N) |

${T}_{r}$ | Rear bridle line tension (N) |

${T}_{t}$ | Tether end tension (N) |

${U}_{z,k}$ | True wind speed at the kite elevation (m/s) |

${U}_{z,ref}$ | True wind speed at the reference height (m/s) |

$V$ | Ship speed (m/s) |

${V}_{k}$ | Ship speed in knots (kn) |

${W}_{z}$ | Relative wind speed at a given elevation (m/s) |

${W}_{z,k}$ | Relative wind speed at the kite elevation (m/s) |

${\copyright}_{s}$ | Corrected ship resistance coefficient (-) |

$\alpha $ | Kite angle of attack (°) |

${\alpha}_{opt}$ | Kite optimal angle of attack (°) |

$\beta $ | Angle of the rear bridle line with the horizontal (°) |

$\u2206$ | Ship load displacement (t) |

$\u2206z$ | Vertical distance between the tether end and the kite’s centre of pressure (m) |

$\zeta $ | Angle of the front bridle line with the horizontal (°) |

${\mu}_{t}$ | Tether weight per unit length (N/m) |

${\rho}_{a}$ | Air density (kg/m^{3}) |

${\rho}_{w}$ | Water density (kg/m^{3}) |

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**Figure 1.**A two-dimensional representation of the kite system configuration and external forces for the ideal case that the wind and ship direction are the same for a forward relative wind speed, ${W}_{z,k}$.

**Figure 2.**A free body diagram of the bridle lines of the kite sail showing the geometry together with the external and internal forces acting in equilibrium conditions for a given angle of attack, $\alpha $.

**Figure 5.**The lift coefficients of the NACA-0015 aerofoil, obtained by iterations of the average Reynolds Number for $\alpha <30\xb0$ and independent of the Reynolds Number for $\alpha \ge 30\xb0$.

**Figure 6.**The drag coefficients of the NACA-0015 aerofoil, obtained by iterations of the average Reynolds Number for $\alpha <30\xb0$ and independent of the Reynolds Number for $\alpha \ge 30\xb0$.

**Figure 7.**The kite elevations for each kite area and angle of attack at a ship speed of 7.27 m/s and a reference wind speed of 20 m/s.

**Figure 8.**The kite horizontal coordinates for each kite area and angle of attack at a ship speed of 7.27 m/s and a reference wind speed of 20 m/s.

**Figure 9.**The kite lift forces for each kite area and angle of attack at a ship speed of 7.27 m/s and a reference wind speed of 20 m/s.

**Figure 10.**The kite thrust forces compared to the air resistance, appendage resistance and power margin of the Series 60 ship at a ship speed of 7.27 m/s and a reference wind speed of 20 m/s.

**Figure 11.**The front bridle line lengths for each kite area and angle of attack at a ship speed of 7.27 m/s and a reference wind speed of 20 m/s.

**Figure 12.**The front bridle line tensions for each kite area and angle of attack at a ship speed of 7.27 m/s and a reference wind speed of 20 m/s.

**Figure 13.**The optimal kite elevations for different ship and wind speeds and a kite area of 320 m

^{2}.

**Figure 14.**The optimal kite horizontal coordinates for different wind and ship speeds and a kite area of 320 m

^{2}.

**Figure 15.**The maximum kite thrust achieved for different wind and ship speeds and a kite area of 320 m

^{2}as a percentage of the total ship resistance at the corresponding ship speed.

**Figure 16.**The optimal tether lengths for different wind and ship speeds and a kite area of 320 m

^{2}.

**Figure 17.**The tether end tensions exhibited with the optimal parameters for different wind and ship speeds and a kite area of 320 m

^{2}.

**Figure 18.**The estimated tether drag for different wind and ship speeds and a kite area of 320 m

^{2}as a percentage of the kite thrust for the respective combination of ship and wind speed.

Parameter | L (m) | B (m) | T (m) | C_{B} (-) | LCB (%L) |
---|---|---|---|---|---|

Value | 75.23 | 10.75 | 3.58 | 0.70 | 0.50 |

Parameter | z_{ref} (m) | z_{0} (mm) | Δz (m) | AR (-) | d_{t} (mm) | $\mathit{\mu}$ | C_{D,t} (-) |
---|---|---|---|---|---|---|---|

Value | 90 | 0.5 | 5 | 10 | 42 | 64.8 | 1.2 |

V (m/s) | ${\mathit{\alpha}}_{\mathit{o}\mathit{p}\mathit{t}}$$\text{}\mathbf{for}\text{}{\mathit{U}}_{\mathit{z},\mathit{r}\mathit{e}\mathit{f}}=10\mathbf{m}/\mathbf{s}$ (°) | ${\mathit{\alpha}}_{\mathit{o}\mathit{p}\mathit{t}}$$\text{}\mathbf{for}\text{}{\mathit{U}}_{\mathit{z},\mathit{r}\mathit{e}\mathit{f}}=15\mathbf{m}/\mathbf{s}$ (°) | ${\mathit{\alpha}}_{\mathit{o}\mathit{p}\mathit{t}}$$\text{}\mathbf{for}\text{}{\mathit{U}}_{\mathit{z},\mathit{r}\mathit{e}\mathit{f}}=20\mathbf{m}/\mathbf{s}$ (°) |
---|---|---|---|

4.04 | 59 | 60 | 60 |

4.85 | 55 | 60 | 60 |

5.66 | 50 | 59 | 60 |

6.47 | 60 | 55 | 60 |

7.27 | 85 | 54 | 60 |

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## Share and Cite

**MDPI and ACS Style**

Formosa, W.; Sant, T.; De Marco Muscat-Fenech, C.; Figari, M.
Wind-Assisted Ship Propulsion of a Series 60 Ship Using a Static Kite Sail. *J. Mar. Sci. Eng.* **2023**, *11*, 117.
https://doi.org/10.3390/jmse11010117

**AMA Style**

Formosa W, Sant T, De Marco Muscat-Fenech C, Figari M.
Wind-Assisted Ship Propulsion of a Series 60 Ship Using a Static Kite Sail. *Journal of Marine Science and Engineering*. 2023; 11(1):117.
https://doi.org/10.3390/jmse11010117

**Chicago/Turabian Style**

Formosa, Wayne, Tonio Sant, Claire De Marco Muscat-Fenech, and Massimo Figari.
2023. "Wind-Assisted Ship Propulsion of a Series 60 Ship Using a Static Kite Sail" *Journal of Marine Science and Engineering* 11, no. 1: 117.
https://doi.org/10.3390/jmse11010117