# A Measurement System for the Environmental Load Assessment of a Scale Ship Model—Part II

^{*}

## Abstract

**:**

## 1. Introduction

- a slowly varying component, loaded with a bias component, which is responsible for the wave drift of the vessel;
- a fast varying component, which consists of irregular oscillations with zero mean value, called wave frequency (WF) motions.

## 2. Spectral Wave Representation in Estimation of Ship Forces

## 3. Device for Wave Measurement

#### Measurement Hardware Characteristics

## 4. Results

- raw data extraction and calculation of the deviations from the slow-changing component;
- frequency calculation of mean value;
- computation of the wave significant height and estimation of their probability distribution functions;
- analysis of the correlation of wind speed and wave height as well as wave spectrum assessment.

#### 4.1. Wind Force and Wave Height Correlation

#### 4.2. Significant Height Analysis of the Wind Induced Waves

#### 4.3. Measurements and Wave Statistics

#### 4.4. Measured Wave Spectra Modeling

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BFT | Beaufort wind scale |

DP | dynamic ship positioning |

ITTC | International Towing Tank Conference |

JONSWAP | Joint North Sea Wave Project |

PEF | peak enhancement factor |

PM | Pierson–Moskowitz spectrum |

PSD | power spectral density |

RAO | response amplitude operator |

RMSE | root mean square error |

SSC | sea state code |

SWAN | Simulation of WAves in Near shore areas |

USV | unmanned surface vehicle |

WF | wave frequency |

WW3 | WaveWatch III |

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**Figure 1.**Experiment of wavemeter scaling in a pool: (

**a**) wavemeter and (

**b**) zoomed-in wavemeter part with two electrodes (A and B) indicated.

**Figure 4.**Wind speed and wave height correlation for 4 BFT: (

**a**) wind speed and wave height measurements; (

**b**) wind speed and wave height correlation.

**Figure 5.**Wind speed and wave height correlation for 5 BFT: (

**a**) wind speed and wave height measurements; (

**b**) wind speed and wave height correlation.

**Figure 6.**Wind speed and wave height correlation for 6 BFT: (

**a**) wind speed and wave height measurements; (

**b**) wind speed and wave height correlation.

**Figure 7.**Wind speed and wave height correlation for 7 BFT: (

**a**) wind speed and wave height measurements; (

**b**) wind speed and wave height correlation.

**Figure 8.**Wind speed and wave height correlation for 9 BFT: (

**a**) wind speed and wave height measurements; (

**b**) wind speed and wave height correlation.

**Figure 9.**Significant wave height for the fully developed sea and for the lake as a function of the wind force in BFT.

**Figure 10.**Statistical analysis of the wave height corresponding to 4 BFT wind force in ship scale: (

**a**) deviations from the slow-changing component; (

**b**) probability distribution of wave height deviations from mean value; (

**c**) recorded wave amplitudes; (

**d**) probability distribution of wave height amplitudes.

**Figure 11.**Statistical analysis of the wave height corresponding to 5 BFT wind force in ship scale: (

**a**) deviations from the slow-changing component; (

**b**) probability distribution of wave height deviations from mean value; (

**c**) recorded wave amplitudes; (

**d**) probability distribution of wave height amplitudes.

**Figure 12.**Statistical analysis of the wave height corresponding to 6 BFT wind force in ship scale: (

**a**) deviations from the slow-changing component; (

**b**) probability distribution of wave height deviations from mean value; (

**c**) recorded wave amplitudes; (

**d**) probability distribution of wave height amplitudes.

**Figure 13.**Statistical analysis of the wave height corresponding to 7 BFT wind force in ship scale: (

**a**) deviations from the slow-changing component; (

**b**) probability distribution of wave height deviations from mean value; (

**c**) recorded wave amplitudes; (

**d**) probability distribution of wave height amplitudes.

**Figure 14.**Statistical analysis of the wave height corresponding to 9 BFT wind force in ship scale: (

**a**) deviations from the slow-changing component; (

**b**) probability distribution of wave height deviations from mean value; (

**c**) recorded wave amplitudes; (

**d**) probability distribution of wave height amplitudes.

**Figure 16.**Comparison of the empirical wave spectrum evaluated for 4 BFT wind force in ship scale and the modified ITTC model.

**Figure 17.**Comparison of the empirical wave spectrum evaluated for 5 BFT wind force in ship scale and the modified ITTC model.

**Figure 18.**Comparison of the empirical wave spectrum evaluated for 6 BFT wind force in ship scale and the modified ITTC model.

**Figure 19.**Comparison of the empirical wave spectrum evaluated for 7 BFT wind force in ship scale and the modified ITTC model.

**Figure 20.**Comparison of the empirical wave spectrum evaluated for 9 BFT wind force in ship scale and the modified ITTC model.

**Table 1.**Sea state codes [20].

Code | Description | ${\mathit{H}}_{1/3}$ [m] | Percentage of Occurrence | ||
---|---|---|---|---|---|

World Wide | North Atlantic | Northern North Atlantic | |||

0 | Calm (glassy) | 0.00 | |||

1 | Calm (rippled) | 0.00–0.10 | 11.2486 ^{1} | 8.3103 | 6.0616 |

2 | Smooth (wavelets) | 0.00–0.50 | |||

3 | Slight | 0.50–1.25 | 31.6851 | 28.1996 | 21.5683 |

4 | Moderate | 1.25–2.50 | 40.1944 | 42.0273 | 40.9915 |

5 | Rough | 2.50–4.00 | 12.8005 | 15.4435 | 21.2383 |

6 | Very rough | 4.00–6.00 | 3.0253 | 4.2938 | 7.0101 |

7 | High | 6.00–9.00 | 0.9263 | 1.4968 | 2.6931 |

8 | Very high | 9.00–14.00 | 0.1190 | 0.2263 | 0.4346 |

9 | Phenomenal | over 14.00 | 0.0009 | 0.0016 | 0.0035 |

^{1}Percentage for codes 0, 1 and 2 is summarized.

Immersion Depth $\mathbf{\Delta}\mathit{h}$ [mm] | Digital Value $\mathit{DV}$ | Fit | Fit Error | |
---|---|---|---|---|

Absolute [–] | Relative [%] | |||

0.0 | 43,790 | 43,941 | −150.78 | −0.34 |

−16.5 | 42,380 | 42,357 | 22.67 | 0.05 |

−38.5 | 40,200 | 40,246 | −46.05 | −0.11 |

−60.5 | 38,130 | 38,135 | −4.78 | −0.01 |

−95.0 | 34,760 | 34,824 | −43.92 | −0.13 |

−115.0 | 33,330 | 32,857 | 473.40 | 1.42 |

−133.5 | 31,230 | 31,129 | 100.81 | 0.32 |

−155.5 | 29,190 | 29,018 | 172.08 | 0.59 |

−183.0 | 26,100 | 26,379 | −278.82 | −1.07 |

−199.5 | 24,590 | 24,795 | −205.37 | −0.84 |

−221.5 | 22,520 | 22,684 | −164.10 | −0.73 |

−243.5 | 20,470 | 20,573 | −102.82 | −0.50 |

−273.0 | 17,870 | 17,742 | 128.20 | 0.72 |

−295.0 | 15,730 | 15,631 | 99.48 | 0.63 |

Mean Digital Value | Min. Digital Value | Max. Digital Value | Standard Deviation $\mathit{\sigma}$ | Max Discrepancy of Water Level Measurement $\mathbf{\Delta}\mathit{h}$ [mm] |
---|---|---|---|---|

43,790 | 43,710 | 43,880 | 26.32 | 1.77 |

42,380 | 42,300 | 42,460 | 28.52 | 1.67 |

40,200 | 40,100 | 40,280 | 28.73 | 1.88 |

38,130 | 38,040 | 38,260 | 29.5 | 2.29 |

34,780 | 34,690 | 34,880 | 26.92 | 1.98 |

33,330 | 33,260 | 33,420 | 29.22 | 1.67 |

31,230 | 31,160 | 31,300 | 27.82 | 1.46 |

29,190 | 29,100 | 29,270 | 29.05 | 1.77 |

26,100 | 26,040 | 26,150 | 19.02 | 1.15 |

24,590 | 24,520 | 24,660 | 24.39 | 1.46 |

22,520 | 22,470 | 22,560 | 17.65 | 0.94 |

20,470 | 20,410 | 20,550 | 20.42 | 1.46 |

17,870 | 17,810 | 17,910 | 14.57 | 1.04 |

15,730 | 15,670 | 15,780 | 13.93 | 1.15 |

BFT in Scale Ship | Estimated Significant Wave Height ${\mathit{H}}_{1/3\mathit{e}\mathit{s}\mathit{t}}$ [mm] | Measured Significant Wave Height ${\mathit{H}}_{1/3}$ [mm] | Significant Wave Height Error [%] | Measured Wave Height Variance $({\mathit{D}}_{\mathit{\zeta}}^{2})$ |
---|---|---|---|---|

4 | 10.50 | 9.24 | 13.65 | 6.89 |

5 | 14.62 | 14.00 | 4.42 | 13.37 |

6 | 23.62 | 22.23 | 6.26 | 34.88 |

7 | 29.05 | 26.07 | 11.42 | 52.75 |

9 | 32.30 | 29.50 | 9.48 | 65.20 |

Sea State Code | Description | Open Sea Wave Height ${\mathit{H}}_{1/3}$ [m] | Scaled Lake Wave Height ${\mathit{H}}_{1/3}$ [mm] | Corresponding Scaled Lake Wind Force [BFT] |
---|---|---|---|---|

0 | Calm (glassy) | 0.00 | 0.00 | 0 |

1 | Calm (rippled) | 0.00–0.10 | 0.00–4.2 | 0–3 |

2 | Smooth (wavelets) | 0.00–0.50 | 0.00–20.8 | 3–6 |

3 | Slight | 0.50–1.25 | 20.8–52.0 | 6–9 |

4 | Moderate | 1.25–2.50 | 52.0–104.2 | 9–10 |

5 | Rough | 2.50–4.00 | 104.2–166.7 | 10–11 |

6 | Very rough | 4.00–6.00 | 166.7–250.0 | 12 |

7 | High | 6.00–9.00 | 250.0–375.0 | – |

8 | Very high | 9.00–14.00 | 375.0–583.3 | – |

9 | Phenomenal | over 14.00 | over 583 | – |

BFT in Ship Scale | RMSE | Estimated Peak Frequency ${\mathit{f}}_{\mathit{pest}}$ [rad] | Observed Peak Frequency ${\mathit{f}}_{\mathit{p}}$ [rad] | Max. Estimated Spectrum Value $\left[{\mathbf{mm}}^{2}\mathbf{s}\right]$ | Max. Observed Spectrum Value $\left[{\mathbf{mm}}^{2}\mathbf{s}\right]$ |
---|---|---|---|---|---|

4 | 0.02 | 1.07 | 1.19 | 0.07 | 0.08 |

5 | 0.03 | 0.90 | 1.00 | 0.17 | 0.20 |

6 | 0.05 | 0.89 | 0.93 | 0.42 | 0.50 |

7 | 0.07 | 0.83 | 0.78 | 0.74 | 0.76 |

9 | 0.10 | 0.78 | 0.69 | 0.99 | 0.99 |

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**MDPI and ACS Style**

Miller, A.; Rak, A.
A Measurement System for the Environmental Load Assessment of a Scale Ship Model—Part II. *Sensors* **2023**, *23*, 3415.
https://doi.org/10.3390/s23073415

**AMA Style**

Miller A, Rak A.
A Measurement System for the Environmental Load Assessment of a Scale Ship Model—Part II. *Sensors*. 2023; 23(7):3415.
https://doi.org/10.3390/s23073415

**Chicago/Turabian Style**

Miller, Anna, and Andrzej Rak.
2023. "A Measurement System for the Environmental Load Assessment of a Scale Ship Model—Part II" *Sensors* 23, no. 7: 3415.
https://doi.org/10.3390/s23073415