# Underwater Glider Propulsion Systems VBS Part 1: VBS Sizing and Glider Performance Analysis
## 1 Introduction
### Background  
Considered the natural evolution of float technology, which are oceanographic devices used for the study of ocean circulation and sampling of water columns [2; 3; 4; 5; 6], underwater gliders had an accelerated technological maturation in the 1990s through the program \"autonomous oceanographic sampling networks\" (AOSN) [7]. In 2001, the development results of the vehicles that are known today as legacy gliders were presented. Slocum, Spray, and Seaglider were developed simultaneously by the Webb Research Corporation (WRC), the Scripps Institute of Oceanography, and the Applied PhysicsLaboratory (APL) of the University of Washington, respectively [8; 9; 10; 11; 12]. Today, the commercial vehicles Slocum and Seaglider are the most popular in the ocean engineering community [13; 14]. [PERSON] et al. [15] presented the technical report with the results of the development of legacy gliders of the AOSN program; the base theory of the underwater gliders operation [16]. In the report, they describe some of the concepts used for the development of gliders, one of the most important being the concept of specific energy consumption. This concept evaluates the energy balance of the vehicle in a steady state, showing the characteristic charts of the estimated performance of some glider models with respect to the capacity of their propulsion system, called glider polar charts. The charts were obtained as a result of CFD (computational fluid dynamics) analysis tools and mathematical models from the company Vehicle Control Technology, Inc. (VCT) [17; 18; 19]. The legacy gliders' main feature is the low energy propulsion engine called the Variable Buoyancy System (VBS), which modifies the net buoyancy of the vehicle to descend and ascend in the water at slow velocity (\(\sim 0.25\) m/s). The vehicle glides in the water with steering control systems to change or still the trajectory of the vehicle with the balance of inertial and hydrodynamic forces, generating the characteristic sawtooth movement in the plane [20]. With the development of underwater glider technology, research has been conducted on the dynamics of this type of vehicle to control its main propulsion and steering systems [21; 22; 20], estimating the hydrodynamic forces of lift and drag in steady state with polynomial regressions as a function of the angle of attack (linear and quadratic equations, respectively). The hydrodynamic polynomial estimations simplify the navigation and flight mathematical models of the vehicle, considering the underwater vehicle as an aerodynamic profile to obtain the polynomial coefficients at small angles of attack. To obtain the polynomial regressions, it is required to have real or estimated hydrodynamic forces at a defined velocity in the water for small angles of attack (normally between \(-10^{\circ}\) and \(10^{\circ}\)). [PERSON] et al. [23] presented in 2017 a research paper to validate the use of CFD modeling to estimate the hydrodynamic forces with a variation of the angle of attack between \(-8^{\circ}\) to \(8^{\circ}\) with steps of \(2^{\circ}\). The CFD method was validated by the experimental results of the glider in a towing tank with the same specifications. In the absence of a defined methodology for the development of VBS for underwater gliders, a preview of this article [24] was presented in 2018 with the first results of the theoretical work on the development of a VBS for an academic glider of 200 msw (meters of salt water) depth rating called Kay Juul 2 (from the Mayan \"Row Fish\"). The work presented the glider performance charts and the analytical equations based on polynomial coefficients to estimate the velocity of the vehicle in steady state and the VBS budget for the nominal velocity of operation. The polynomial coefficients were obtained by [PERSON] et al. [25] with CFD modeling based on [22; 23] with angles of attack between \(-15^{\circ}\) and \(15^{\circ}\) with steps of \(5^{\circ}\).