## 6 Conclusions  
In this study, we analyzed the measured hull girder longitudinal stresses onboard an 8600 TEU container ship to reveal the whipping behavior. We decomposed the longitudinal stresses at the four corners of the midship into the vertical bending, horizontal bending, torsional, and axial force components. Then, the whipping factors were calculated for each one-hour sea state with regard to the vertical bending, torsional, and horizontal bending components. The following findings were drawn from this study:  
1. It was found that the whipping factors in the torsional and horizontal bending components were much smaller than the whipping factors in the vertical longitudinal bending component. In addition, the magnitude of the torsional component was approximately one-third of the vertical bending component, and the magnitude of the horizontal bending stress was approximately one-fifth of the vertical bending stress in terms of raw data extreme values. Thus, it is considered that the torsional and horizontal bending stresses have considerably less influence on the whipping than the vertical longitudinal bending stress.
2. We studied the correlation between the whipping factors of the vertical bending component and the corresponding sea state and ship operational conditions. As a result, it was found that the whipping factor slightly decreased as the wave period increased. In addition, the whipping factor tends to be larger in head seas, and larger ship speeds result in greater whipping factors in head seas. In contrast, a larger ship speed does not affect or even slightly reduces the whipping factor in following seas.
3. Excessively large whipping is sometimes observed due to successive wave impact that accidentally accelerates the existing whipping vibration of the hull girder. Conversely, when whipping works to cancel the vibrational component, the vibrational component may suddenly decrease.  
This study remains a preliminary data analysis. We focused on the response at the midship section, where the longitudinal stress tends to be maximum, and therefore, is the most critical. As  
Figure 12: Time-series stress data during 830–890 s of the vertical longitudinal bending component.  
the next step, we plan to analyze the measured stress data in the fore and aft sections. To precisely reveal the whipping responses and identify their effect on the ultimate strength of the hull girder and hull fatigue strength, it is necessary to analyze an even larger number of measured data points to distinguish between whipping and springing, to examine their effect on the hull strength, and to investigate accurate estimation methods of whipping  
Conceptualization, T.M. and T.O. Resources (measured data preparation), T.M. Software, R.H. and T.M. Validation, R.H., T.O., Y.K., and T.M. Formal analysis, R.H. and T.M. Investigation, R.H. and T.M. Writing--original draft preparation, R.H. Writing--review & editing, T.O. and Y.K. Visualization, R.H. Supervision, T.O. and Y.K. Project Administration, T.O. All authors have read and agreed to the published version of the manuscript.  
This work was partly supported by JSPS KAKENHI, Grant Number 18H01637.  
We would like to thank Editage (www.editage.com) for English language editing.  
The authors declare no conflicts of interest.