# Underwater Glider Propulsion Systems VBS Part 1: VBS Sizing and Glider Performance Analysis
## 5 Results and Discussion
### Comparative Performance Charts
Calculating the velocity components with Equations (22) and (23) and considering a displaced volume \(V_{d}=250\) cc, the glider polar chart in Figure 11 is obtained so that it can be compared to the models listed in Table 2.  
Figure 11 shows a comparative chart of the estimated velocities of the hydrodynamic models under the same displaced volume as the glider polar chart. At the same time, with the information in Figure 10, an important variation in the velocities obtained for the same vehicles is observed. For example, at a 35\({}^{\circ}\) glide angle, the Slocum models have a dive velocity increment of 1.77 times in the VCT model [18] with respect to the Conney model [39], and an increment of 1.9 times at 20\({}^{\circ}\). In the case of the vehicle Kay Juul 2, an increment of 1.12 times with respect to the original coefficients [25] is obtained at 35\({}^{\circ}\), and an increment of 1.24 times at 20\({}^{\circ}\), with a correction in the regression range. The parameter described by [PERSON] et al. [15,16] of minimal specific energy consumption \(E_{e}(\alpha_{1,2})\) has a direct relation with the minimal glide angles \(\gamma_{1,2}\), that is the minimal operational flight angle to have the maximal traveled distance per cycle. The operational velocities obtained depend mainly on the drag coefficient at a zero angle of attack \(K_{D0}\). Thus, both parameters have to be considered to improve the performance of the vehicle. To have the maximum horizontal velocity, the value of the glide angle can be obtained by solving Equation (24), considering a symmetrical profile (\(K_{D2}=0\)) and neglecting the factor \(K_{D2}\alpha^{2}\) for small angles of attack. Then, considering the terms inside the root as a constant, the optimal glide angle is obtained as follows:  
\[\frac{\partial u}{\partial\gamma}=0\quad\rightarrow\quad\cos^{2}\gamma=\frac {2}{3}\quad\rightarrow\quad\gamma_{opt}=\cos^{-1}\left[\frac{2}{3}\right]^{1/2 }=35.2644^{\circ}. \tag{24}\]  
[PERSON] et al. [15,16] mentioned that the maximum along-coarse speed (horizontal speed) in still water is always obtained at a 35\({}^{\circ}\) glide angle, regardless of the vehicle shape or other hydrodynamic property. [PERSON] et al. [27] obtained the same result, optimizing their function of the horizontal velocity by considering \(C_{D}(\alpha)\) as a constant for small angles of attack. Figure 11: Glider polar chart of the hydrodynamic models at \(V_{d}=250\) cc. Exceptions are observed in Figure 11 in the [PERSON] [21] and the [PERSON] models [36]. The maximum horizontal velocities are obtained about 40\({}^{\circ}\) and they have the limit glide angles close to 35\({}^{\circ}\). If the higher values of the limit glide angles could be the cause of the exception, it is recommended to verify the results and output charts to validate the estimations of the glider performance. One potential application of the proposed method of asymmetrical profiles is an underwater glider concept with asymmetrical wings. Its conceptual design was presented in 2019 in the 8 th EGO (_Everyone's Gliding Observatories_) meeting [40]; however, the hydrodynamic parameters of the vehicle have not been published, although it could be interesting to evaluate in detail.