## 3 Results  
Using the process described above, \(\varepsilon_{T}\) can be calculated for any planform and control mechanism. This process was repeated over the range \(0\leq R_{T}\leq 1\) and \(4\leq R_{A}\leq 20\). Results are shown in Figure 3 for wings with 2-5 actuators per semispan. The reader is reminded that the twist effectiveness \(\varepsilon_{T}\) is a measure of how well the control mechanism can negate the drag increase caused by the planform shape. A twist effectiveness of 1.0 means that the control mechanism is 100% capable and the wing can operate at the lowest induced drag possible for that particular aspect ratio, while a twist effectiveness of 0.0 means that the control mechanism is not capable of reducing the induced drag for that wing geometry. Notice that for both discrete and continuous control surfaces, as the number of actuators per semispan increases, the twist effectiveness improves. Recall that the twist effectiveness was defined as using the best twist distribution possible given the limitations of the control mechanism. Since a control mechanism with more degrees of freedom is better able to match the optimal solution given in Equations (15) and (16), it is expected that the twist effectiveness improves with increasing number of actuators. Also note for any given number of actuators, the continuous control surface generally has better twist effectiveness than the discrete control surface. One exception to this is the two-actuator case in the region of approximately 0.35-0.4 taper ratio, where the discrete control surface has a very slight advantage. This range of taper ratios also appears to be a minimum-value region for the twist effectiveness for the 2-5-actuator cases. This is interesting, especially when considering Figure 2, because the taper ratio that provides the best \(\kappa_{P}\) provides the worst \(\varepsilon_{T}\). One potential explanation for this is that the planform penalty is already very low, so there is less the control mechanism can do to minimize induced drag. It is not uncommon to use a taper ratio near 0.5 for wings that do not use active twist to minimize induced drag. However, in light of Figure 3, if wing twist with only a few actuators is to be used to minimize induced drag, a taper ratio near 0.5 is extremely ineffective. Clearly, both the planform and control-mechanism design should be taken into account when designing a wing that actively uses the control mechanism to minimize drag. From Equation (20), we see that \(\kappa_{P}\) and \(\varepsilon_{T}\) combine to give the optimum induced-drag factor, \(\kappa_{D0}\). Results for \(\kappa_{D0}\) are shown in Figure 4 for different planforms and control mechanisms. Results similar to the continuous cases in Figure 4a have been presented by [PERSON] [26; 27] in the context of a linearly tapered wing with optimal linear washout. Note that the vertical scale between the subplots in Figure 4 decreases significantly with increasing number of actuators. As expected, the more actuators used, the more closely it can produce an elliptic lift distribution. Also note that, as expected, the continuous control surfaces can nearly always outperform the discrete control surfaces for a given number of  
Figure 3: Twist effectiveness for a (**a**) 2-, (**b**) 3-, (**c**) 4-, and (**d**) 5-actuator control mechanism with either discrete or continuous control surfaces, shown as a function of taper ratio for aspect ratios ranging from 4 to 20 in increments of 2.  
actuators, except for the region in the two-actuator case discussed previously. However, the question arises whether the continuous control surfaces provide sufficient benefit over discrete control surfaces to offset the likely increase in manufacturing complexity and weight. It is also insightful to compare the performance of the continuous and discrete control surfaces for a given planform in terms of a percent difference in minimum induced drag between the two designs.