# Effects of Mooring Compliancy on the Mooring Forces, Power Production, and Dynamics of a Floating Wave Activated Body Energy Converter

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## Abstract

**:**

## 1. Introduction

## 2. The Experimental Set-Up

#### 2.1. Wave Basin

#### 2.2. Wave Energy Converter

#### 2.3. Models

_{C}) varied from 2.0 m (equal to the 80% of the total chain length, pretension of 1 N), to 1.3 m (65%, 3 N), and 1.0 m (50%, 5 N).

#### 2.4. Power Take-Off

_{PTO}is obtained as

- Δt is the time step interval;
- F(t), F(t + Δt) are the forces induced by the device on the PTO at the times t and t + Δt, recorded by the PTO load cell;
- d(t), d(t + Δt) are the relative device displacement at the respective time t and t + Δt, recorded by the displacement sensor.

#### 2.5. Measurements

#### 2.6. Wave States

## 3. Experimental Results: Moorings in Shallow Water

_{W}, θ, and l/L

_{P}, where P

_{W}is the incident wave power per unit width, θ is the main wave direction and l/L

_{P}is the ratio between the device length and the peak wave length. P

_{W}is selected as it is very relevant for power production and summarizes the effect of wave height and period. The choice of l/L

_{P}was suggested by previous studies ([14,23]) showing that the parameter l/L

_{P}affects the overall device behavior, in terms of hydrodynamics, power production, moorings. In fact, the device design length l should be tuned to the local wave climate.

#### 3.1. Power Performance Optimization

_{C}that maximize the average power production P

_{PTO}under regular wave conditions. This investigation is a very common step for R&D of WECs.

_{PTO}(obtained using Equation 1), vs the tested values of l/L

_{P}, for waves given in Table 1. Since the 10 RWs are characterized by variable height and constant steepness, the higher and more energetic waves are longer, so that P

_{W}decreases with l/L

_{P}. The three sub-plots of Figure 4 refer to the three different L

_{C}and include the tests carried out for all the PTO settings (r1 up to r6).

_{PTO}increases rather monotonically by increasing the PTO resistance up to a certain resistance value, either r4 or r5, somewhat lower than the maximum, and then decreases. More precisely, the best PTO configurations correspond to r4 for L

_{C}= 80% (i.e., vertical distance of 0.13 m), and to the r5 (i.e., vertical distance of 0.15 m) for both L

_{C}= 65% and L

_{C}= 50%. For the slack configuration (L

_{C}= 80%) the overall P

_{PTO}increases of 2.4 times from the lower to the best resistance.

_{PTO}for each value of L

_{C}(80%, 65%, and 50%) associated to the optimal r-value (r4, r5, and r5, respectively). The figure shows that P

_{PTO}is mooring dependent, being the highest P

_{PTO}values relative to the slack configuration (i.e., L

_{C}= 80%) for the more energetic RWs. The mooring pre-tension level significantly affects the power production.

#### 3.2. Power Production under Irregular Waves

_{PTO}at prototype scale as function of l/L

_{P}(as in Figure 5). It may be observed that the slack configuration leads to the highest power production performance. The production decreases for waves longer than approximately 100 m (i.e., periods larger than 8 s), which suggests that the designed device is suited to mild wave climates. Note that all irregular waves have a steepness in the range 2.5% to 4%.

_{PTO}around 167 kW may appear too small to justify even the costs of the electrical connections from the device to the shore. Economically feasible installations for DEXA are array schemes [24], or possibly installations in combination with wind turbines ([25,26]) or co-location with other economic activities ([9]).

_{C}= 65% and of 16% for L

_{C}= 50% compared to L

_{C}= 80%. Regardless of L

_{C}, the sets of P

_{PTO}show high values when l/L

_{P}< 0.70.

_{PTO}and the value of the available wave power P

_{W}, based on the expressions

_{g}is the wave group celerity, function of the depth h equal (at full scale) to 27 m and of the energetic wave period T

_{e}≈ 0.9 T

_{p}; b is the device width, equal to 22.8 m. The values of H

_{S}and T

_{p}were derived—for each WG—through a zero-down crossing analysis. In Equation (2), the average values of H

_{S}and T

_{P}recorded at the first seven WGs were considered (see Figure 3).

_{W}, where k is the wave number and C

_{W}is the capture width (also termed capture length, [27]), i.e., the ratio between the power output and the density of power flux of the incident wave front.

_{PTO}, P

_{W}, and η for the three values of L

_{C}. The dependence of η on l/L

_{P}for the three L

_{C}shows pretty well marked peaks around l/L

_{P}= 0.80 or greater (see Table 3). This result highlights the correlation between the device dimensions and the climate at the site of installation, hence the device length l should be approximately equal to the typical wave length L

_{P}to maximize η. Due to the negative correlation with L

_{P}, this device seems ideal for areas with short fetch rather than oceanic wave climates.

_{C}= 80%, the trends of η under oblique WSs are similar to the case of perpendicular waves, i.e., with peaks around l/L

_{P}= 0.80. The effects of different wave obliquities seem to be limited, however η tends to decrease for the largest value of β, confirming the need to design the mooring system to allow an easy device re-orientation to the incoming waves (see Table 3).

_{C}= 80% and the best PTO setting is r4.

#### 3.3. Device Movements

- double integration of the MTi signals to obtain positions from accelerations;
- high-pass filter of the obtained position signals, to remove the linear and eventually second order terms caused by the double integration procedure;
- transposition of the signal from the local to a fixed coordinate system (centered at the hinge position);
- analysis of the LVDT placed on the PTO, in order to derive the time series of the relative pitch angle between the pontoons. Actually, the same information can be obtained as the instantaneous difference between the pitch signals of the two MTi placed on the two pontoons of the same device (see Figure 2). The obtained relative pitch was not as accurate as the LVDT output and therefore the latter was preferred.

_{C}.

_{S}and to decrease with increasing l/L

_{P}. For l/L

_{P}= 1.21 both translations and rotations have the minimum value and appear to be substantially independent from L

_{C}.

_{C}and on l/L

_{P}. In particular, the pretension level L

_{C}has a large influence on the movements for small wavelength, i.e., l/L

_{P}< 0.70.

_{P}< 0.70, and when the mooring is slack, the device easily rides the waves and it has a significant vertical motion (i.e., high heave values), whereas if the mooring is taut the horizontal component is more relevant (i.e., high surge values).

_{C}, whereas the roll movements are larger for the intermediate pretension level L

_{C}.

_{S}, i.e., increasing l/L

_{P}, with the exception of the roll that is almost constant. Roll appears to depend on the plan layout of the chains and on the rigidity to this degree of freedom.

_{C}= 80%. All the translations tend to increase by increasing β especially for higher WSs (i.e., l/L

_{P}< 0.5). The effects of β are more evident for the sway motion, i.e., the greater β the greater the motion, regardless of the l/L

_{P}values.

_{PTO}for the different r settings (from 1 to 5), under the same irregular WS3. The datasets are grouped by the value of the pretension level. The relative pitch ranges from 0.11 to 0.23 rad (i.e., between 6° and 13°) and the P

_{PTO}from 90 kW to 200 kW. Large data scatter can be observed for all WSs, showing that that the value of r and partially the mooring configuration affect the movements and the efficiency.

_{C}= 80, 65, and 50% respectively.

_{PTO}is proportional to the relative pitch motion for a given PTO setting, as it may be argued by observing Equation (1). The proportionality depends also on the wave characteristics, and particularly on the frequency. The larger production is found for L

_{C}= 80% (r = 4), coherently with Figure 5. Under regular waves, the maximum value of the relative pitch is approximately 0.18 rad (10°) whereas the maximum is of order 0.5 rad (28°) under irregular waves.

_{W}. This is a consequence of the correlation between the available wave power and the produced power, for the same PTO setting. Figure 10 shows the almost monotonic trend of the relative pitch (top panel) and of the mean pitch (bottom panel) as a function of P

_{W}. The combination of L

_{C}= 80% and r = 4 gives the larger relative pitch for all conditions. However, the average pitch is the same for the three L

_{C}values. It should be noted that the relative pitch is quite variable, being strongly related to power harvesting. Actually, the relative pitch is larger than the average pitch in case of large production.

_{PTO}and to the PTO setting. It therefore becomes interesting to experimentally relate the motion of the structure under optimal PTO setting to the motion obtained in the absence of the PTO, under the same incident wave conditions.

_{PTO}of the DEXA on the basis of simple experiments, carried out in the absence of the PTO. For example, for L

_{C}= 65%, a relative pitch of 0.16 rad is measured or predicted in absence of PTO. Then, if ones assumes that an optimal PTO is installed, the actual relative pitch would be 80% lower (Figure 11) and the produced power would be just larger than 100 kW (Figure 12).

#### 3.4. Mooring Forces

_{1/50}(i.e., the mean value of the 2% of the highest points) was selected to statistically describe the largest forces during the wave attack.

_{1/50}are given as a function of P

_{W}.

_{1/50}among the four chains, under perpendicular and oblique wave attacks, for L

_{C}= 80%. The maximum loads are within an acceptable limit. For the ordinary WSs the values of F

_{1/50}slightly vary for different wave obliquities β, being slightly lower for perpendicular wave attacks. The lines are mainly slack and the loads are proportional to their elongation, usually very limited. Under oblique waves, yaw rotations induce a greater elongation of the chains with respect to pure surge, therefore larger loads are observed.

_{1/50}increases up to 3.5 times when the waves hit the device perpendicularly to its axis. The larger loads occur when the device reaches its maximum offset and the lines are fully stretched, and the load is proportional to the device deceleration. When the device is forced to yaw before reaching the maximum offset, the device deceleration is slower and the loads are smaller than in case of pure surge.

_{1/50}for different L

_{C}on the same chain as functions of P

_{W}, only available for ordinary WSs. The increase of F

_{1/50}with P

_{W}looks pretty linear for L

_{C}= 80%, indicating a slack reaction. The trend of F

_{1/50}is quadratic for L

_{C}= 50%, while the case with L

_{C}= 65% follows an intermediate trend. Only for L

_{C}= 80%, the load is available also for extreme WSs (see Figure 13, perpendicular case) and it is evident that the linear trend is abandoned.

## 4. Numerical Modeling of Moorings in Deep Waters

#### 4.1. Short Description of the Numerical Model

#### 4.2. Design of the Mooring Schemes

#### 4.3. Mooring Forces and Device Movements

_{W}and β. The force linearly increases with P

_{W}. A different growth rate is observed for ordinary and extreme WSs, since the interaction among the chains is larger in the latter case. The value of β plays a significant role, especially in case of the extreme WSs. The forces for β = 60° have an almost double value with respect to the case of β = 0°. In fact, the WEC oscillates between a fully weathervaning under the larger waves and the initial position under the smaller waves.

_{W}and β. The force-displacement relation is almost perfectly linear, as it is expected due to the elastic characteristic of the connection. The higher values of the forces are found for β = 60°, in agreement with the results in Figure 16.

#### 4.4. Effects of the Rear Mooring

#### 4.5. Cost of the Mooring Layouts

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**3D rendering image showing a single DEXA device at full scale (from www.dexawave.com).

**Figure 2.**Models of the wave activated bodies with spread mooring system, in scale 1:60. H = 0.45 m; L

_{C}≈ 2.00/1.30/1.00 m; L

_{1}≈ L

_{3}≈ 0.15/1.08/1.41 m (measured along their axis); L

_{2}= 0.22 m

**Figure 3.**Scheme of the wave farm line in scale 1:60 (incident waves come from the left side). Black numbers represent the wave gauges (WGs). The distances are in meter.

**Figure 4.**From the left to the right: PTO resistance optimization under 10 RWs for the configuration with L

_{C}= 80, 65, 50%. Five PTO rigidities were analysed for L

_{C}= 80%, and six PTO rigidities were analysed for L

_{C}= 65% and 50%. r1 is the less rigid configuration, r6 is the most rigid one. The optimal PTO resistance is r4 for L

_{C}= 80% and r5 for L

_{C}= 65% and 50%.

**Figure 5.**Mooring pre-tension level optimization based on the best PTO resistance, under 10 RWs (in terms of l/L

_{P}). For an easier comprehension the same symbols and colors adopted in the previous figure were maintained. Values of P

_{PTO}for L

_{C}= 80%, 65%, 50% are with triangles, circles, and squares respectively. Blue color indicates the r4 resistance, whereas red color indicates the r5 resistance.

**Figure 6.**Power production performance in function of l/L

_{P}under IR WSs. Blue triangles, red circles and green squares for L

_{C}= 80%, 65%, and 50% respectively (each with its best PTO resistance). L

_{C}= 80% is confirmed as the best mooring pre-tension level.

**Figure 8.**WS3: Measured relative pitch between the pontoons and power production P

_{PTO}, for all PTO setting and mooring configurations, under the same irregular waves (WS3).

**Figure 9.**Relation between the relative pitch (upper 10% quantile) between the pontoons and the power production P

_{PTO}, (

**a**) using optimal PTO setting: regular waves; (

**b**) irregular waves.

**Figure 10.**Relation between the relative (

**a**) and average (

**b**) pitch and incident wave power P

_{W}(optimal PTO setting, IR).

**Figure 13.**F

_{1/50}of the reliable signals of the force under perpendicular and oblique waves (with L

_{C}= 80%) for ordinary and extreme WSs.

**Figure 15.**(

**a**) Scheme of the first and second mooring configuration. In the first configuration the buoy was moored with the four black lines (from 1a to 4a), whereas in the second configuration the buoy was moored with the eight grey dashed lines (from 1b to 8b); (

**b**) Scheme of the third mooring configuration with the addition of a rear buoy.

**Figure 16.**Relation between the available wave power P

_{W}and the force acting on the most stressed buoy chain.

**Figure 17.**Relation between the available wave power P

_{W}and the force acting on the cable connection.

**Figure 18.**Comparison between the second (one buoy) and third (two buoys) mooring configurations. Dashed lines represent the results of the third mooring layout compared with the second layout (continuous lines). From top to bottom: sway of the rear pontoon, surge of the rear pontoon, surge of the buoy. The addition of the rear buoy avoids the signal drift (visible for the sway motion).

**Table 1.**Regular WSs used to evaluate the best PTO resistance, values in 1:1 scale. H is the wave height, T is the wave period, L is the wave length, l/L is the ratio device–peak wave length, and s

_{o}is the wave steepness.

WS | H (m) | T (s) | L (m) | l/L (-) | s_{o} (-) |
---|---|---|---|---|---|

Regular WSs | |||||

1 | 1.44 | 5.58 | 48 | 1.21 | 0.03 |

2 | 2.16 | 6.82 | 72 | 0.82 | 0.03 |

3 | 2.52 | 7.44 | 84 | 0.70 | 0.03 |

4 | 3.24 | 8.68 | 108 | 0.54 | 0.03 |

5 | 3.60 | 9.30 | 120 | 0.49 | 0.03 |

6 | 3.96 | 9.91 | 132 | 0.45 | 0.03 |

7 | 4.32 | 10.53 | 144 | 0.41 | 0.03 |

8 | 4.68 | 11.23 | 156 | 0.38 | 0.03 |

9 | 5.04 | 11.85 | 168 | 0.35 | 0.03 |

10 | 5.40 | 12.55 | 180 | 0.33 | 0.03 |

**Table 2.**Irregular WSs used to evaluate the device performance, values at prototype scale. H

_{s}is the significant wave height, T

_{P}is the peak wave period, L

_{P}is the peak wave length, l/L

_{P}is the ratio device–peak wave length, and s

_{op}is the wave steepness.

WS | H_{s} (m) | T_{P} (s) | L_{P} (m) | l/L_{P} (-) | s_{op} (-) |
---|---|---|---|---|---|

Ordinary WSs | |||||

1 | 2.0 | 5.58 | 48.6 | 1.21 | 0.041 |

2 | 2.0 | 6.97 | 74.4 | 0.79 | 0.027 |

3 | 3.0 | 7.44 | 83.4 | 0.70 | 0.036 |

4 | 3.0 | 8.37 | 102.0 | 0.58 | 0.03 |

5 | 4.0 | 9.84 | 130.2 | 0.45 | 0.031 |

6 | 5.0 | 11.23 | 156.6 | 0.38 | 0.032 |

Extreme WSs | |||||

7 | 8.0 | 13.09 | 190.8 | 0.31 | 0.042 |

8 | 8.0 | 14.02 | 207.0 | 0.28 | 0.039 |

9 | 8.6 | 13.09 | 190.8 | 0.31 | 0.045 |

10 | 9.0 | 13.79 | 202.8 | 0.29 | 0.044 |

11 | 10.0 | 14.48 | 215.4 | 0.27 | 0.047 |

**Table 3.**Device performance under ordinary IR WSs, values in 1:1 scale. P

_{W}is the available wave power, P

_{PTO}is the generated power by the PTO system, η is the device efficiency, k C

_{W}is the non-dimensional capture width and β is the incoming wave direction.

Direction | Pre Tension Level | WS | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|---|

l/L_{P} | 1.21 | 0.79 | 0.7 | 0.58 | 0.45 | 0.38 | ||

β_{1} = 0° | L_{C} = 80% | P_{W} (kW) | 155.5 | 291.2 | 656.1 | 822.8 | 1250.5 | 2177.9 |

P_{PTO} (kW) | 51.7 | 98.2 | 141.2 | 179 | 124.3 | 128.5 | ||

η | 33.30% | 33.70% | 21.50% | 21.80% | 9.90% | 5.90% | ||

k C_{W} | 1.013 | 0.669 | 0.378 | 0.318 | 0.112 | 0.056 | ||

L_{C} = 65% | P_{W} (kW) | 215.9 | 304.3 | 685 | 719.2 | 1524.6 | 2620.6 | |

P_{PTO} (kW) | 39.5 | 107.2 | 164.1 | 132.2 | 136.4 | 144.2 | ||

H | 24.20% | 26.60% | 21.90% | 17.70% | 9.40% | 5.50% | ||

k C_{W} | 0.736 | 0.528 | 0.385 | 0.258 | 0.106 | 0.053 | ||

L_{C} = 50% | P_{W} (kW) | 169.5 | 251.2 | 592.2 | 737.9 | 1443.6 | 2095.8 | |

P_{PTO} (kW) | 41 | 66.8 | 129.8 | 130.7 | 135.2 | 115.6 | ||

H | 18.30% | 35.20% | 24.00% | 18.40% | 8.94% | 5.50% | ||

k C_{W} | 0.557 | 0.699 | 0.422 | 0.268 | 0.101 | 0.053 | ||

β_{1} = 10° | L_{C} = 80% | P_{W} (kW) | - | 251 | 602.3 | 719.4 | 1422.2 | 2175.1 |

P_{PTO} (kW) | - | 83.7 | 150.6 | 133.9 | 150.6 | 133.9 | ||

H | - | 35.50% | 24.30% | 17.60% | 10.40% | 6.20% | ||

k C_{W} | - | 0.669 | 0.378 | 0.318 | 0.112 | 0.056 | ||

β_{1} = 20° | L_{C} = 80% | P_{W} (kW) | - | 301.2 | 686 | 920.2 | 1438.9 | 2777.4 |

P_{PTO} (kW) | - | 100.4 | 150.6 | 133.9 | 133.9 | 133.9 | ||

H | - | 31.50% | 20.40% | 14.50% | 8.90% | 4.60% | ||

k C_{W} | - | 0.625 | 0.359 | 0.211 | 0.101 | 0.044 |

**Table 4.**Amplitudes of the device motion in full scale. Data, derived from the MTi, were elaborated through a time domain analysis. The data represent the statistical value of the 10% of the highest points for each ordinary WS for the three L

_{C}.

DoF | Pre-Tension | Ordinary Wave States | |||||
---|---|---|---|---|---|---|---|

WS 1 | WS 2 | WS 3 | WS 4 | WS 5 | WS 6 | ||

l/L_{P} = 1.21 | l/L_{P} = 0.79 | l/L_{P} = 0.70 | l/L_{P} = 0.58 | l/L_{P} = 0.45 | l/L_{P} = 0.38 | ||

Surge (m) | L_{C} = 80% | 0.60 | 0.72 | 1.02 | 1.56 | 2.22 | 2.76 |

L_{C} = 65% | 0.54 | 0.72 | 1.08 | 1.68 | 2.46 | 3.06 | |

L_{C} = 50% | 0.60 | 0.72 | 1.26 | 1.92 | 3.00 | 3.66 | |

Heave (m) | L_{C} = 80% | 0.96 | 2.10 | 3.06 | 3.60 | 4.08 | 5.10 |

L_{C} = 65% | 0.78 | 1.80 | 2.58 | 3.30 | 4.02 | 4.74 | |

L_{C} = 50% | 0.90 | 1.32 | 2.28 | 3.30 | 4.38 | 4.86 | |

Sway (m) | L_{C} = 80% | 0.18 | 0.30 | 0.60 | 0.72 | 0.84 | 1.02 |

L_{C} = 65% | 0.24 | 0.30 | 0.42 | 0.66 | 1.38 | 1.02 | |

L_{C} = 50% | 0.18 | 0.30 | 0.48 | 0.84 | 0.90 | 1.26 | |

Roll (°) | L_{C} = 80% | 2.6 | 2.5 | 3.5 | 3.2 | 3.1 | 3.6 |

L_{C} = 65% | 4.7 | 2.6 | 2.8 | 3.3 | 4.1 | 3.6 | |

L_{C} = 50% | 2.6 | 2.0 | 2.8 | 3.2 | 3.3 | 3.9 | |

Yaw (°) | L_{C} = 80% | 5.3 | 7.3 | 11.1 | 12.9 | 14.1 | 15.7 |

L_{C} = 65% | 3.5 | 5.0 | 8.6 | 12.2 | 13.2 | 15.1 | |

L_{C} = 50% | 3.3 | 3.9 | 7.7 | 11.7 | 13.4 | 13.1 |

**Table 5.**Amplitudes of the translations by varying the incoming wave direction β for the slack mooring configuration (L

_{C}= 80%). Values are in full scale.

DoF | Direction | Ordinary Wave States | |||||
---|---|---|---|---|---|---|---|

WS 1 | WS 2 | WS 3 | WS 4 | WS 5 | WS 6 | ||

l/L_{P} = 1.21 | l/L_{P} = 0.79 | l/L_{P} = 0.70 | l/L_{P} = 0.58 | l/L_{P} = 0.45 | l/L_{P} = 0.38 | ||

Surge (m) | β_{1} = 0° | 0.60 | 0.72 | 1.02 | 1.56 | 2.22 | 2.76 |

β_{1} = 10° | - | 0.69 | 1.03 | 1.51 | 3.04 | 4.15 | |

β_{1} = 20° | - | 0.65 | 0.99 | 1.56 | 2.81 | 4.57 | |

Heave (m) | β_{1} = 0° | 0.96 | 2.10 | 3.06 | 3.60 | 4.08 | 5.10 |

β_{1} = 10° | - | 2.09 | 3.10 | 3.59 | 5.39 | 5.56 | |

β_{1} = 20° | - | 2.27 | 3.11 | 3.88 | 4.95 | 6.46 | |

Sway (m) | β_{1} = 0° | 0.18 | 0.30 | 0.60 | 0.72 | 0.84 | 1.02 |

β_{1} = 10° | - | 0.90 | 1.20 | 1.62 | 2.24 | 2.05 | |

β_{1} = 20° | - | 1.21 | 2.01 | 2.22 | 2.85 | 3.77 |

Chain | Length (m) | Mass Unit Length (kg/m) | Equivalent Diameter (m) | Equivalent Cross Section (cm^{2}) | Max Tension (KN) | Stiffness EA (KN) |
---|---|---|---|---|---|---|

1a | 125 | 91 | 0.064 | 32.15 | 3130 | 643072 |

Rear | 406 | 91 | 0.064 | 32.15 | 3130 | 643072 |

2a, 4a | 125 | 70 | 0.056 | 24.61 | 2430 | 492352 |

1b, 2b | 125 | 56 | 0.050 | 19.62 | 1960 | 392500 |

9c | 129.5 | 56 | 0.050 | 19.62 | 1960 | 392500 |

11c, 12c | 134.5 | 56 | 0.050 | 19.62 | 1960 | 392500 |

3b, 8b | 125 | 43.5 | 0.044 | 15.20 | 1540 | 303952 |

3a, 4b, 5b, 6b, 7b, 10c | 125 | 32 | 0.038 | 11.33 | 1160 | 226708 |

**Table 7.**Cost analysis of the three mooring schemes. The total cost does not include the buoys, the elastic rope, and the steel anchors.

Buoy Mooring Configuration | Total Weight Front Chains (kg) | Total weight Rear Chains (m) | Total Weight (kg) | Cost of the Chains (€) | Anchors Total Holding Capacity (KN) | Anchor Cost (€) | Total Cost (€) |
---|---|---|---|---|---|---|---|

4 chains + rear | 32,875 | 36,946 | 69,821 | 350,000 | 12,980 | 130,000 | 480,000 |

8 chains + rear | 40,875 | 36,946 | 77,821 | 390,000 | 14,770 | 150,000 | 540,000 |

8 chains plus a rear buoy with 3 chains | 40,875 | 26,316 | 67,191 | 335,000 | 18,680 | 185,000 | 520,000 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Martinelli, L.; Zanuttigh, B.
Effects of Mooring Compliancy on the Mooring Forces, Power Production, and Dynamics of a Floating Wave Activated Body Energy Converter. *Energies* **2018**, *11*, 3535.
https://doi.org/10.3390/en11123535

**AMA Style**

Martinelli L, Zanuttigh B.
Effects of Mooring Compliancy on the Mooring Forces, Power Production, and Dynamics of a Floating Wave Activated Body Energy Converter. *Energies*. 2018; 11(12):3535.
https://doi.org/10.3390/en11123535

**Chicago/Turabian Style**

Martinelli, Luca, and Barbara Zanuttigh.
2018. "Effects of Mooring Compliancy on the Mooring Forces, Power Production, and Dynamics of a Floating Wave Activated Body Energy Converter" *Energies* 11, no. 12: 3535.
https://doi.org/10.3390/en11123535