## 2 Materials & Methods  
### The Numerical Model  
For the purposes of securing non-standardized cargo on board, the CSS Code from the IMO is mostly followed by the industry as the default methodology for calculating the accelerations sustained by the cargo during the sea passage. As a consequence, the stowage position and the final design of the securing arrangement carried out to support all these forces are influenced by this mentioned international code. Many Cargo Securing Manuals of ships are prepared following this guidance. However, we can find cases of ships or lashing companies where other guidelines issued by different classification societies, such as the DNV, are followed instead. Although in the new CSS Code the mathematical models of the accelerations are included, they can be laborious to apply unless they are programmed in a suitable spreadsheet, and it is still considered more useful and intuitive to use the basic acceleration data and then apply the corresponding correction factors. Therefore, from Table 2 of Annex 13 of the CSS Code are obtained the transverse, longitudinal, and vertical basic accelerations acting on cargo, which depend on the stowage position of the cargo from two baselines. The first one is the height of the stowage about the keel (high deck, main deck, tween deck, and lower hold), which determines the longitudinal acceleration (ax), shown in Figure 1.  
The longitudinal position of the stowage from the aft perpendicular determines the vertical acceleration (az), which is graphically represented in Figure 2. Finally, the combination of the position from the aft perpendicular together with height above the keel gives the transverse acceleration (ay). The transverse acceleration (ay) includes the components of gravity, pitch, and have parallel to the deck and is represented in Figure 3. Furthermore, as it is evident, the vertical acceleration (az) does not include the static weight component. Figure 1: Basic longitudinal acceleration (ax). However, these basic acceleration data are only valid for ships of 100 m in length, sailing at 15 knots without restrictions, and with a relationship B/GM > 13, B being the ship's moulded breadth and GM the metacentric height. If the ship's speed is different from 15 knots and/or its length is different from 100 m, the three basic accelerations (ax, ay, az) have to be corrected by a correction factor due to length (L) and service speed (Ss). This correction factor can be named C\({}^{\text{on}}\) L&Ss, and the corresponding values are obtained according to Equation (1), which is valid for ships with a length between 50 m and 300 m:  
\[\text{C}^{\text{on}}\text{ L \& S}=\left(\frac{0.345\cdot\text{Ss}}{\sqrt{\text{L}}} \right)+\frac{58.62\cdot\text{L}-1034.5}{\text{L}^{2}} \tag{1}\]  
where L is expressed in meters and Ss in knots. Furthermore, if the relationship between B/GM is lower than 13, the transverse acceleration (ay) has to be corrected by another correction factor, named C\({}^{\text{on}}\) B/GM, which is graphically represented in Figure 4.  
Figure 3: Basic transverse acceleration (ay). Figure 2: Basic vertical acceleration (az). Moreover, the three basic accelerations can also be corrected by a reduction factor (f\({}_{\text{R}}\)) when the significant wave height is lower than 13 m, according to Equation (2):  
\[\text{f}_{\text{R}}=1-\frac{\left(\text{Hs}-13\right)^{2}}{240} \tag{2}\]  
where Hs is the maximum expected 20-year significant wave height (meters) in the navigation area according to ocean wave statistics or the significant wave height according to forecast. Then, finally, the three accelerations are corrected as follows:  
\[\text{ax}_{\text{(C)}}=\text{ax}\cdot\left[\text{f}_{\text{R}}\right]\cdot \left[\text{C}^{\text{on}}\text{ L \& S}\right] \tag{3}\]  
Figure 2.0  
Figure 2.1  
In the case of cargoes stowed on deck (main deck or high deck), they are also affected by the wind pressure (Fw) and the sea sloshing (Fs), both from the longitudinal and transversal points of view.