###### 1 Introduction  
Wing twist can be used to control the lift distribution on a wing. In general, twist can be categorized as either geometric or aerodynamic. Geometric twist is a spanwise variation in geometric angle of attack. A common form of geometric twist is washout, which is a twisting of the wing to reduce the angle of attack near the wing tips. Aerodynamic twist is a spanwise variation in zero-lift angle of attack. A common form of aerodynamic twist is a flap that extends over only a portion of the wing. In either scenario, wing twist always results in a spanwise variation in the section angle of attack relative to the section zero-lift angle of attack. Twist can be defined as  
\[T(z)\equiv\alpha(z)-\alpha_{LO}(z)-(\alpha-\alpha_{LO})_{\text{root}} \tag{1}\]  
where the components \(\alpha(z)-\alpha_{\text{root}}\) and \(-\alpha_{LO}(z)+\alpha_{LO\text{root}}\) are the contributions from the local geometric and aerodynamic twist, respectively.  
Any form of twist can be applied in a spanwise continuous or discontinuous manner. For example, washout is usually a continuous form of twist, while flaps are a discontinuous form of twist. The original Wright flyer used geometric continuous twist, referred to as wing warping, for roll control [1; 2], but later models switched to discrete flaps for structural reasons. Most aircraft today use discontinuous twist in the form of flaps to control the lift distribution and resultant forces and moments, likely due to structural simplicity. However, with modern morphing technology, it is now possible to accurately control a continuous twist distribution (aerodynamic or geometric) during flight. For example, AFRL [3], NASA [4; 5; 6; 7], and others [8; 9; 10; 11; 12; 13] have developed various methods for varying the camber along a wing during flight, with an emphasis on maintaining continuity of twist along the span.  
The main benefit claimed by those employing continuous twist control rather than discontinuous twist control is a reduction in drag over the flight envelope, and studies have reported varying levels of drag benefits [4; 7; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]. In order to adequately quantify the drag benefits of real-time continuous twist, a consistent and rigorous methodology for drag comparison must be employed. Studies for comparing induced drag, parasitic drag, and total drag of various discrete and continuous designs must be conducted. Here, we provide one sample methodology and evaluate the induced-drag benefits of wings with continuous twist control compared to wings with discrete twist control.  
Wings with mechanisms that control the twist distribution in a spanwise continuous manner are defined here as having a continuous control surface. In contrast, wings with mechanisms that vary the twist at discrete spanwise sections are defined here as having discrete control surfaces. Figure 1 visually indicates the difference between spanwise discrete and continuous control surfaces. Here, we use a numerical potential flow algorithm to evaluate ideal induced-drag solutions over a wide range of wing planforms and control mechanism designs. Comparisons are made between continuous and discrete control surfaces for comparable wing planforms and degrees of freedom within the respective control mechanisms. These results can aid in preliminary design of wings that use active control to minimize induced drag over the flight envelope. While the results presented here are limited to spanwise-symmetric planforms and twist distributions, and therefore spanwise-symmetric lift distributions, the method could be applied to asymmetric scenarios.