# Underwater Glider Propulsion Systems VBS Part 1: VBS Sizing and Glider Performance Analysis
## 1 Introduction
### Research Contribution  
The proposed method in this article presents analytical equations that consider the underwater glider as an asymmetrical profile, as well as presenting a particular solution for symmetrical profiles. The particular solution is validated with the results in [27], simultaneously using polynomial coefficients for the hydrodynamic forces and considering the coefficients in the operating velocities of the vehicle as stable. The main advantages of the proposed method respect to [27] are mentioned as follow:  
* The glide angle is an input parameter and main variable. All the output parameters are in function of the desired glide slope of the vehicle, even the flight angles; calculating first the angle of attack and then the pitch angle (controlled by the internal mechanism of the vehicle). * The VBS sizing process is included in the results of the performance analysis in order to obtain one of the main design requirements for the propulsion system. No approach is reported to define the VBS budget volume for underwater gliders, except the previous work presented in 2018 [24]. * The method considers the entire vehicle to have an asymmetrical profile or to have asymmetrical wings when defining the descent (dive) and ascent (climb) state solutions. The analytical equations to evaluate the glider performance analysis are presented to obtain the relation between the VBS and the glider performance in different operation points. In the early design states, the performance analysis is important to size the main mechanisms. The detailed design state could be used to estimate the vehicle performance with updated information, such as detailed CFD analysis of the vehicle with sensors and other components that could modify the hydrodynamics. This paper proposes a practical method to analyze the glider performance, including the VBS sizing process as an output resultant of the analysis process. The main characteristic charts are presented to analyze the effect of the polynomial coefficients in the performance of the vehicle. The discussion about the improvement of resultant velocity with respect to the displaced volume of the VBS, and the effect of the polynomial coefficients is presented. The approach of the proposed method is to consider the VBS sizing as an important design requirement for the propulsion of the vehicle, however, the glider performance analysis could be expanded to obtain the sizing of the other main mechanism (i.e., for the pitch mechanism stroke with the analysis of hydrodynamic torque compensation). The structure of the paper is as follows. The flow chart of the proposed method to analyze the glider performance and the outputs of the method are shown in Section 2; including the VBS sizing. Section 3 describes the main operation states of the underwater gliders and the principle of operation to define the concept of the VBS budget. In Section 4, the performance analysis of underwater gliders is presented, obtaining the analytical equations needed to evaluate the performance of the vehicle; the estimation of flight and the estimated volume of the VBS. In Section 5, the results and discussion are presented, validating the glider performance analysis equations and obtaining the outputs of the method; calculating the VBS budget for the glider Kay Juul 2, and generating the characteristic charts to evaluate its performance. Finally, Section 6 presents the conclusions about the importance of the glider performance analysis in the VBS sizing. This research is divided in two papers: the first one that is presented in this paper has the main contribution to propose the general method to obtain the VBS sizing and the glider performance analysis based on polynomial coefficients; the second one is the modeling, development, and efficiency study of the VBS type piston tank for the academic glider Kay Juul 2. In Table 1, the required variables for the development of this paper are listed.