# Design Options to Improve the Dynamic Behavior and the Control of Small H-Darrieus VAWTs
## 4 Discussion  
The inspection of Equation (17) enables some observations. First of all, from the physical point of view, the equations appear consistent: the environment index \(E\) shows that higher air density and stronger wind speeds increase the accelerating capability of the turbine, such a result also being achieved if the average gustiness of the site is low. Of course, as the definition of WTI is pseudo-static, the effect of the turbulence intensity cannot be considered in this analysis. As far as the geometric index \(G\) is concerned (Equation (17)), small diameters determine a dramatic reduction in the inertia, with a beneficial effect on the rotor acceleration capability. The same goal is obtained by reducing the blade number, which is responsible for a linear reduction in the rotor inertia (for instance, by a factor of 1/3 if, from the initial 3 blades design choice, one blade is suppressed). Additionally, the adoption of a structurally efficient blade section, implying a substantial reduction of the blade mass required to perform the goal, has the consequence of increasing, by an order of magnitude, the factor \(\Phi_{f}\) (see Figure 6). The functional design parameter index \(F\) shows that an increase in the ratio of the tangent to normal coefficients produces higher torque, thus boosting the acceleration of the rotor. An analogous result is achieved through the reduction of the design tip speed ratio, which implies a higher design solidity and therefore, a higher aerodynamic torque. This outcome aligns with the conclusions of [PERSON] ([PERSON], 1966), stating that, assuming a wind intensity and a given number of blades, the rotor torque is inversely proportional to the tip speed ratio, and thus, a lower tip speed ratio enables a better acceleration capability. Furthermore, lower tip speed ratios produce a decrease in the rotational speed and thus, alleviate the structural stress (which is principally due to centrifugal forces). Finally, the material index \(M\) shows that, if the constraint of blade strength has to be satisfied, the parameter of reference is \(\dfrac{\sigma_{\mathit{adm}}^{2/3}}{\rho_{B}}\). A typical strength-density chart of most materials is given in Figure 8, where also different \(\sigma\) to \(\rho\) relationships are superimposed. Therefore, the selection of high resistance to low-density materials is recommended. Additionally, a proper material property testing campaign is essential to reduce the safety factors. The [PERSON] approach requires all functional groups to be independent for a rigorous analysis. When the groups are separable, as they frequently are, the optimal choice of material becomes independent of the details of the design. This statement has to be discussed in Equation (17) to assess the strength of the assumption of the reciprocal independence of the indexes. The procedure is summarized in the matrix of Table 1. Trivially, the geometrical, functional, and material indices cannot impact the environmental one, so they are mutually independent. The material selection does not impact the functional parameter; under the hypothesis that any geometry can be manufactured with any material or material technology, the dependence of \(G\) on \(M\) can be neglected. The discussion involves the interdependency of the functional and geometrical parameters and should answer the question of whether a maximization of \(G\) (or \(F\)) can be pursued by a contemporary maximization of \(F\) (or \(G\)). To discuss the design dependence of \(G\) and \(F\), let us analyze the function \(G=f(F)\) for a collection of VAWT data retrieved in the open literature and from personal communication of single manufactures, plotted in Figure 9, with the full tabled data listed in Table 1. The data refer to either prototypes and commercial VAWTs operated or produced from the 1970s to today. As shown in Figure 9 left, it is apparent that there is no correlation between the two parameters \(G\) and \(F\).