General cargo ships are the most numerous in the merchant fleet. In these vessels, the stowage and securing of non-standardized cargo must be designed prior to being shipped. Furthermore, during sea navigation, the shipmaster must be confident that the secured cargo is safe in any weather conditions. One of the goals of the present research is to provide helpful guides to ship operators about the optimal navigational parameters. Despite different criteria being followed by the shipping industry to calculate the rolling motion accelerations, relevant accidents and losses related to an inadequate securing arrangement still occur. Firstly, this paper analyzes and compares the IMO’s and classification societies’ criteria, obtaining relevant results about the different safety levels along the ship’s dimensions. Secondly, it obtains a novel mathematical model of angular transverse acceleration, considering the sea state conditions and navigational parameters. For this reason, it investigates the combinations of optimization of these parameters. Finally, it proposes novel 3D surface graphs as being easy, useful, and quick to be interpreted by shipmasters when sailing in certain sea state conditions, to know if the limits of the maximum securing arrangement are exceeded and predict the ship’s optimal speed and heading in order to set out.