## 3 Case Study  
A tugboat, though small in size, is a powerful vessel utilized for various towage operations, including search and salvage, firefighting, assisting, transporting, escorting, maneuvering, and berthing other marine vehicles when required within the tugboat's operational scope [49]. Consequently, tugboats can be designed to fulfill one or more of these functions [50].  
Tugs are typically classified according to their operational context, delineated by distinctions among harbor, ocean-going, coastal, and river environments, as well as the nature of their tasks. Additionally, these vessels are further stratified based on the configuration or propulsion systems they employ [51]. Several propulsion system arrangements exist, with the four most prevalent being: conventional propulsion systems, Azimuth Stern Drive (ASD), Tractor tug with Rudder Propellers, and Voth Water Tractor, also known as Voth Schneider Propeller (VSP) tug. A profile view of the different types of tugboats is given in Figure 3[52].  
Presently, the predominant propulsion systems employed in modern ship-assist tugs consist of Z-drive which are equipped with the azimuthing propulsors or VSP configurations, with harbor tugs typically spanning from 20 to 32 m in length and featuring power outputs ranging from 2000 to 4000 kW, albeit subject to variations dictated by port size and the spectrum of ships serviced [51].  
Figure 3: Profile view of different types of tugboats.  
Azimuthing thrusters or azimuthing propulsors, which have been widely utilized for numerous years, are characterized by either non-ducted or ducted propeller configurations, further subdivided into pusher or tractor units, as illustrated in Figure 4.  
In general, the maximum speed and boldard pull of tugboats are critical performance measures that directly affect the effectiveness, safety, and efficiency of port tug operations. Tugboats must possess a high boldard pull to exert adequate force for safely and effectively towing or pushing large ships in various environmental conditions [53]. Tugs are constructed to exceed boldard pull forces through the optimization of their underwater hull form, leveraging hydrodynamic forces to generate higher pull forces [52]. Moreover, a higher maximum speed enables tugboats to reach their destinations more swiftly; handle larger ships efficiently, thus reducing the time and effort needed for maneuvering operations; and respond promptly to changing situations and position themselves effectively.  
The paramount requirements for a tug are the boldard pull and maximum speed, determined during the concept design phase. This determination is contingent upon factors such as the size and type of the ship the tug is designed to assist, the number of tugs in the port, and environmental conditions like currents, tides, and winds prevalent in the tug's operational area. All tugs, particularly harbor tugs, must be designed to be highly maneuverable with exceptional stability.  
The total engine power and hull from parameters of the tugboats with many other parameters such as propeller parameters are limitations for tugboats' maximum speed and boldard pull force [54; 55; 56]. Therefore, the dependent parameters for tugboats, namely boldard pull (BP) and ship speed (V), can be expressed as functions of the primary independent variable parameters related to a tugboat's main dimensions: length (L), width (B), draft (T), block coefficient (C\({}_{\text{B}}\)), and main propulsion power (P). Additionally, other independent variable parameters influencing the boldard pull and ship speed include the vessel's hull form, heel and trim conditions, and the configuration of the propulsion system, encompassing the main engine(s) and power transmission equipment(s). Environmental conditions, such as currents, waves, sea state, wave dimensions, water depth, and towing rope length, also contribute to the variability of boldard pull and ship speed parameters [49].