# Underwater Glider Propulsion Systems VBS Part 1: VBS Sizing and Glider Performance Analysis
## 3 General Operation States of Underwater Gliders
### VBS Budget  
The propulsion system VBS for underwater gliders must have enough volume capability to generate the required speeds in the descent and ascent states, and the required volume to operate in the surface comms state. Therefore, once the main operating states of the vehicle have been described, the operating points of the VBS have to be identified to determine its sizing.  
In Figure 6, a general diagram is shown with the different points of volume displacement \(V_{d}\) that the VBS system needs to generate the different operating states. These points are measured with respect to the state of neutral buoyancy or inflection state with the reference volume \(V_{d}=0\), generating upward movements for \(V_{d}>0\) and downward movements for \(V_{d}<0\).  
Figure 5: Schematic diagram of the surface comms state of an underwater glider.  
Figure 6: Basic VBS states for glider operation.  
Figure 6 shows two states of descent, two of ascent, the state of neutral buoyancy with the volume reference value \(V_{d}=0\), and the surface comms state with a reference volume \(V_{d0}\) calculated with Equation (3). As mentioned in Section 3.1, the estimation of the displaced volume \(V_{d}\) for the descent and ascent states, at nominal and max velocity, depends on the analysis of the glider performance of the glider that is described in Section 4.  
Obtaining the \(V_{d}\) values of each of the descent and ascent states, the sizing of the VBS system can be estimated by means of Equation (4) or (5) depending on the application case:  
\[V_{D}=V_{d2}-V_{d1}\ \ \ \ \ if\ \ \ \ \ V_{d2}>V_{d0}, \tag{4}\]  
\[V_{D}=V_{d0}-V_{d1}\ \ \ \ \ if\ \ \ \ \ V_{d0}>V_{d2}. \tag{5}\]  
Therefore, Equations (4) and (5) consider the size limits of the VBS with the minimum volume capacities to reach the nominal velocities in descent and ascent. However, if the calculation is carried to its limit capacity to perform maximum velocities, the dimensioning of the VBS can be estimated with Equations (6) and (7):  
\[V_{D}=V_{d4}-V_{d3}\ \ \ \ \ if\ \ \ \ V_{d4}>V_{d0}, \tag{6}\]  
\[V_{D}=V_{d0}-V_{d3}\ \ \ \ \ if\ \ \ \ V_{d0}>V_{d4}. \tag{7}\]  
It is not recommended to perform the sizing of the VBS with the limit values of Equations (4) and (5) because in practice it is necessary to have an additional VBS volume budget to overcome low and moderate currents. It is recommended to perform the calculation of the VBS capacities using Equations (6) and (7) in order to have a budget that is more adequate to the vehicle's operating capacities. For example, in the case of the commercial vehicle Seaglider, it has a budget for its VBS system that allows to overcome average currents of up to 40 cm/s with a maximum volume displacement of \(V_{d3}=350\) cc with respect to its neutral buoyancy point, moving with vertical speeds of approximately 20 cm/s [33; 34].  
The calculation of the volumes found in Equations (4) and (5) can be considered as a point of reference to estimate a base volume \(V_{D}\) for considering an operating environment without sea currents or to estimate the energy consumed in a specific mode of operation for deeper analysis.  
Section 5 presents the study of the hydrodynamic performance of underwater gliders, which shows that the basic flight parameters of the vehicle and the limit volumes used to size the VBS system can be estimated through analytical relationships and analyzed with glider polar charts.