# Underwater Glider Propulsion Systems VBS Part 1: VBS Sizing and Glider Performance Analysis
## 1 Introduction
### Research Contribution
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Description** & **Unit** \\ \hline \(D\) & Drag force—Hydrodynamic reaction in line with glider slope & N \\ \hline \(L\) & Lift force—Hydrodynamic reaction perpendicular at the glider slope & N \\ \hline \(R\) & Resultant hydrodynamic force \(R=\sqrt{D^{2}+L^{2}}\) & N \\ \hline \(\tau_{h}\) & Hydrodynamic reaction moment in the point of analysis & N-m \\ \hline \(\omega\) & Dry weight of the vehicle \(\omega=mg\) & N \\ \hline \(m\) & Mass of the vehicle & kg \\ \hline \(F_{B}\) & Total buoyancy force \(F_{B}=(V_{0}+V_{d})\rho g\) & N \\ \hline \(\rho\) & Density of the fluid (\(p_{s}\)—Surface; \(\rho_{d}\)—depth rating) & kg/m\({}^{3}\) \\ \hline \(V_{0}\) & Total displaced volume of the vehicle in neutral buoyancy & m\({}^{3}\) \\ \hline \(V_{d}\) & Displaced volume of the VBS since the neutral buoyancy reference & m\({}^{3}\) \\ \hline \(V_{D}\) & Total volume capability of the VBS & m\({}^{3}\) \\ \hline \(-V_{S}\) & Volume of the glider outside water in the Surface comms state & m\({}^{3}\) \\ \hline \(B\) & Net buoyancy force \({}^{1}\)\(B=F_{B}-\omega\) & N \\ \hline \(\tau_{g}\) & Inertial moment in the point of analysis by unbalance of masses & N-m \\ \hline \(U\) & Dive velocity of the vehicle at the resultant glider slope & m/s \\ \hline \(u\) & Horizontal velocity component \(u=U\cos\gamma\) & m/s \\ \hline \(w\) & Vertical velocity component \(w=U\sin\gamma\) & m/s \\ \hline \(\alpha\) & Attack angle of the vehicle respect glider slope & rad \\ \hline \(\theta\) & Pitch angle measured with the compass sensor of the vehicle & rad \\ \hline \(\gamma\) & Glide angle of flight \(\gamma=\theta+\alpha\) & rad \\ \hline \(P_{g}\) & Power developed by the gravitational force & W \\ \hline \(P_{e}\) & Power needed to overcome drag & W \\ \hline \(E_{e}\) & Specific Energy Consumption & - \\ \hline \(Re_{L}\) & Reynolds based length \(Re_{L}=U\overline{c}/\
u\) & m/m \\ \hline \(\overline{c}\) & Chord length of the aerodynamic profile & m \\ \hline \(\
u\) & Kinematic viscosity of the fluid & m\({}^{2}\)/s\({}^{2}\) \\ \hline \(A_{C}\) & Characterized area of the aerodynamic profile & m\({}^{2}\) \\ \hline \(C_{D}\) & Dimensionless drag coefficient \(C_{D}(\alpha,Re_{L})\) & - \\ \hline \(C_{L}\) & Dimensionless drag coefficient \(C_{L}(\alpha,Re_{L})\) & - \\ \hline \(K_{D0}\) & Polynomial coefficient for drag force—Independent term & kg/m \\ \hline \(K_{D1}\) & Polynomial coefficient for drag force—First grade term & kg/m/rad \\ \hline \(K_{D2}\) & Polynomial coefficient for drag force—Second grade term & kg/m/rad\({}^{2}\) \\ \hline \(K_{L0}\) & Polynomial coefficient for lift force—Independent term & kg/m \\ \hline \(K_{L1}\) & Polynomial coefficient for lift force—First grade term & kg/m/rad \\ \hline \end{tabular}  
* When the value of Net Buoyancy is negative, it will be positive in direction of \(z\) axis; \(g=9.81\) m/s\({}^{2}\).  
\end{table} 
Table 1: List of variables used to describe the glider operating states in steady state.