# Underwater Glider Propulsion Systems VBS Part 1: VBS Sizing and Glider Performance Analysis
## 5 Results and Discussion
### Comparative Performance Charts  
Figure 8 show the variation of the angle of attack for the models listed in Table 2, calculating the attack angle with Equation (16). The negative glide angles represent the vehicle in descent state and the positive angles in ascent state. As a result of the estimation of hydrodynamic parameters from symmetric profiles, the behaviors of the angles of attack at positive and negative glide angles mirror each other, as observed in Figure 8, except for the model of [PERSON] [36] which is defined with coefficients for the dive (descent) and the climb (ascent) states. It is observed that the curves stop growing at the values of maximum angle of attack and the minimum glide angle obtained in Table 2, representing the limit values of flight angles where the hydrodynamic forces can compensate the buoyancy force in forward movement in steady state, generating a non-operating zone where the equations have no real solution. The angle of attack has an accelerated growth when the glide angle is close to the limit values of operation, so the estimation of the attack angle that corresponds to a flat glide slope becomes relevant for the performance of the vehicle. In Figure 9, the variation of the pitch angle is shown as a function of the glide angle calculated with Equation (17). It can be observed that for almost all the models analyzed, the value of the pitch angle is approximately equal to the value of the glide angle for values greater than 20\({}^{\circ}\), except for the [PERSON] models [36], which has a minimum glide value of about 28\({}^{\circ}\) that causes a considerable deviation around the limit. The Graver model [21] also has a glide angle limit value greater than 20\({}^{\circ}\) but its maximum angle of attack is relatively small, and so no significant deviation is observed for it in Figure 9. This means that it is not necessary to have a small glide angle limit to have a small angle of attack. Figures 8 and 9 also show that when the glider requires a glide angle of 90\({}^{\circ}\) (completely vertical movement), the angle of attack will tend to zero for symmetrical profiles, and, theoretically, the vehicle could perform movements or cycles of virtual mooring [30; 31]. Perhaps the vehicle could be limited to perform only a certain range of this pitch angle with the internal movement of masses that depend on the design of the internal mechanisms of the glider. Figure 8: Attack angle variation chart of the hydrodynamic models. Moreover, the maximum limit of the glide angle should be determined by the ability of the internal mechanism of the vehicle to control the pitch angle, which is out of the scope of the present paper. However, it is important to mention it, so as to improve the present research in the future and to have a more robust method to analyze the performance of underwater gliders. Considering a displaced volume \(V_{d}=250\) cc and a density of water of \(\rho=1026\) kg/m\({}^{3}\), Equation (21) obtains the dive velocity chart that is shown in Figure 10 so that it can be compared to the models listed in Table 2.  
It is observed that from about \(35^{\circ}\) of the glide angle, the velocity that could perform the analyzed models follows an order with respect to the value of the polynomial coefficient \(K_{D0}\). This occurs because the angle of attack and the factor \(K_{D2}\alpha^{2}\) in Equation (21) becomes too small, and the dive velocity is affected mainly by the coefficient \(K_{D0}\). Figure 10: Dive velocity chart of the hydrodynamic models at \(V_{d}=250\) cc. Figure 9: Pitch angle variation chart of the hydrodynamic models. For glide angles below 35\({}^{\circ}\), where the gliders normally operate, the dive velocity does not always follow the same trajectory and the value of the factor \(K_{D2}\alpha^{2}\) could modify the tendency. For this reason, it is important that throughout the entire operation range, all variables are considered without assumptions, especially the angle of attack.