Trade-off between Lift and Power

In a multi-objective investigation, it is often the case that different goals are in competition when selecting design variables. One tool used to evaluate the trade­offs between objective functions is called the Pareto front [317], which consists of non-dominated points and can be thought of as the set of best possibilities. Non – dominated points are those points for which one could not improve all objective functions simultaneously.

Trizila et al. [301] presented the Pareto front for the competing objectives of maximizing time-averaged lift and minimizing the power requirement in the 2D and 3D hovering flat plate case highlighted in previous sections, as illustrated in Figure 3.28. Points on the Pareto front therefore involve those for which increases in lift are accompanied by increases in power, and vice versa. The resulting Pareto front itself is very comparable between 2D and 3D (see Fig. 3.28). The primary differences are that the peak lift values attained in 2D exceed their 3D counterparts and the density of the design variable combinations near the Pareto front is higher in the 3D case. The paths through the design space are plotted below their respective Pareto fronts in Figure 3.28. Note that the jaggedness of the path is due to the resolution of the tested points and the fine balance in objective functions for design variables in that region. The high-lift region follows the lower bound of the angular amplitude, suggesting that future iterations should decrease the lower bound for higher lift solutions. Overall, the design variable combinations on the optimal front are consistent qualitatively. The high time-averaged lift values are obtained by a combination of advanced rotation and low angular amplitude in the 2D and 3D cases. The general trends remain largely the same.