The development of low-altitude unmanned aerial vehicles (UAVs) has been proposed for many high-impact civilian-centered applications such as expanding telecommunication networks in remote locations, improved weather monitoring, and terrain surveying. Such missions, which can last anywhere from hours to days, rely on efficient, lightweight, and high-aspect ratio designs to minimize energy consumption. We investigate a method of aerodynamic control that also permits energy harvesting through surface texturing on aircraft wings using multifunctional kirigami composites. These kirigami skins produce 3D surface features when axially strained and have been manufactured using thin-film solar cells. Here, we show that when actuated, these 3D features increase the drag over the wings, which can be used to control yaw. Wind tunnel experiments were conducted to quantify the effects of kirigami actuation on aerodynamic lift, drag, and yaw moment. These results demonstrate excellent yaw-control capabilities and delayed aerodynamic stall, indicating that the actuated kirigami features may delay flow separation. The implied multifunctionality of these kirigami skins is ideal for low-altitude UAVs, which benefit from both lightweight energy sources and actuators.

With modern developments of innovative actuators and aircraft designs, unique methods of aerodynamic control have emerged. One particular application has been tailless aircraft, also known as flying wings. By eliminating the rudder and vertical stabilizer, these aircraft experience less drag and have a reduced radar profile. However, by removing the rudder, engineers must develop new ways to control yaw—the aircraft's rotation about the vertical axis. This is achieved by asymmetrically changing the magnitude or direction of aerodynamic forces on the aircraft. One such method is drag steering, which relies on inducing drag asymmetrically to pivot the nose of the aircraft about the center of gravity. For example, split ailerons have been used to actively control yaw on a flying wing by asymmetrically inducing drag on the aircraft.1–3 More recent advances in multifunctional composites have led to the development of poro-vascular composites that have been used to actively control wing micro-texture, with features up to 0.5 mm in height.4 This mechanism showed potential for yaw control, hypothesized to result from profile drag and lift manipulation, in addition to boundary layer flow control.

Boundary layer flow control, namely, delaying the transition from laminar to turbulent flow, has been a prime subject of interest to engineers due to its potential to reduce drag.5 While many of these advances experimentally demonstrated measurable improvements in performance, those benefits did not materialize outside of controlled experimental environments, due to the variability of real-world operating conditions.6 However, one well-studied method that has shown tremendous success since the 1990s is the use of transverse riblets for turbulent drag reduction.7,8 This surface texturing, which is similar in form to the porovascular composites, has been shown to reduce skin friction and provide a slip condition at the surface.

This surface texturing mechanism has been long observed in biological species as well. An extensively studied example is the Mako shark (Isurus oxyrinchus) whose skin is covered with a series of overlapping denticles.9,10 These denticles have been observed on locations of the shark body where the fluid flow exhibits an adverse pressure gradient, past the location of maximum girth where the fluid is more prone to flow separation. The denticles themselves exhibit a unique geometry that combines streamwise riblets with a flexible scale structure, which can bristle and change the denticle angle.11,12 While both components have been shown to provide drag reduction, the present work is inspired by the flexible scale structure, which is hypothesized to bristle trapping flow that is reversing in direction, thus preventing flow separation.13 This is particularly relevant for long-endurance Unmanned Aerial Vehicles (UAVs) where efficiency is highly desirable and small reductions in drag can substantially extend the length of flight time.

Following this biological inspiration and the work of Thomas et al.,4 the current work considers the preliminary aerodynamic benefits of wing surface texturing using kirigami scale-like substrates. Kirigami is the Japanese art of paper cutting and folding, which requires no adhesive to create complex three-dimensional shapes. Recent advancements in materials science and engineering have seen the development of not only ultra-lightweight thin-film gallium arsenide solar cells but also kirigami-based solar tracking arrays.14 Repeated patterns, shown in Fig. 1, are laser cut into thin-film photovoltaic substrates that exhibit out-of-plane deformations upon application of axial strains as demonstrated in Figs. 1(a), 1(b), and 1(d). These low-cost kirigami substrates are highly customizable and can be rapidly produced unlike many existing surface patterning technologies. In addition to their energy harvesting capabilities, the kirigami skins in the current study may be suitable for active drag steering and possibly delayed flow separation as well. In aircraft, severe flow separation causes aerodynamic stall, which is characterized by a severe drop in lift and increase in drag. Furthermore, due to their lightweight nature, implementing kirigami-based yaw steering in low altitude UAVs has the potential to substantially reduce the aircraft weight by minimizing the working components required for rudder control or, given careful aircraft design, by completely eliminating the vertical stabilizer that is a key contributor to total drag, thereby leading to significant improvements in fuel efficiency.

FIG. 1.

Depiction of the kirigami actuator mechanism. (a) Side view of the undeformed kirigami geometry. (b) Side view of the deformed kirigami geometry in response to axial strain. (c) Aerial view of the parameterization of the kirigami cut pattern. (d) Close-up perspective of deformed kirigami geometry covering an airfoil surface, viewed from the trailing edge.

FIG. 1.

Depiction of the kirigami actuator mechanism. (a) Side view of the undeformed kirigami geometry. (b) Side view of the deformed kirigami geometry in response to axial strain. (c) Aerial view of the parameterization of the kirigami cut pattern. (d) Close-up perspective of deformed kirigami geometry covering an airfoil surface, viewed from the trailing edge.

Close modal

To test these hypotheses, wind tunnel experiments, shown in Fig. 2, were conducted in an open loop wind tunnel with a 0.6 m × 0.6 m closed test section at the University of Michigan. A symmetric wing with a NACA0012 profile, a chord of 0.305 m, and a span of 0.457 m was 3D printed using an Objet Connex 500 multi-material printer that has a print resolution of up to 16 μm. Elliptical end plates, shown in Figs. 2(b) and 2(d), were installed on the wing tips to eliminate three-dimensional flow. The magnitude of the drag coefficients reflect this.

FIG. 2.

Detailed images and schematics of the experimental setup. (a) Flow diagram of the automated experimental data collection procedure. (b) Diagram of the wind tunnel experimental setup detailing equipment and positioning. (c) Illustration of the kirigami actuated at various strains over a symmetric NACA0012 airfoil.15 (d) Photograph of the kirigami fully elongated on a wing mounted in the wind tunnel.

FIG. 2.

Detailed images and schematics of the experimental setup. (a) Flow diagram of the automated experimental data collection procedure. (b) Diagram of the wind tunnel experimental setup detailing equipment and positioning. (c) Illustration of the kirigami actuated at various strains over a symmetric NACA0012 airfoil.15 (d) Photograph of the kirigami fully elongated on a wing mounted in the wind tunnel.

Close modal

The kirigami substrate was made by laser cutting a polymide foil into three sections each with a width of 0.152 m and a length of 0.229 m to cover the wing. For this design, the x and y parameters shown in Fig. 1(c) were 1.9 mm, while the Lc parameter was 19 mm. Note that the unactuated size does not cover the full chord of the airfoil since room must be left to elongate the substrate. This was approximately the largest size capable of being made due to limitations in the fabrication methods. Each of the three kirigami sections were installed along the length of the airfoil to cover the span, as seen in Fig. 2(d). The kirigami was adhered to the surface of the wing at the leading edge using non-intrusive (0.1 mm thick) double-sided tape. This represents a scenario in which the skin is not pre-embedded into the airfoil surface and may be retrofitted into existing wings. The kirigami was manually strained and secured at multiple elongations. Minor contraction in the kirigami was observed, as seen by the slight gaps between kirigami sheets in Fig. 2(d), but the gaps composed only approximately 0.5% of the wing span, and its effects on aerodynamic control can, thus, be assumed to be negligible.

The patterned kirigami shown in Fig. 1 is typically characterized by its feature angle, the angle between the axis of elongation and the deformed kirigami unit cell, which is derived geometrically as

θ=cos1(1ϵA+1),
(1)

where θ is the feature angle and ϵA is the axial strain.15 However, the curvature of the wing induces nonuniform feature angles across the length of the kirigami substrate; thus, for simplicity, kirigami's deformation was characterized by the equivalent axial strain [along kirigami's length, labeled in Fig. 1(c)] using the below equation:

ϵA,eq=ΔlsL,
(2)

where ϵA,eq represents the substrate's equivalent axial strain, L represents the undeformed length of the kirigami, and Δls represents the displacement or change in the length of the substrate along the surface.

The assembled wing was mounted vertically at the quarter chord to a six-axis ATI Delta force balance, which exhibits a force resolution of [1/32, 1/32, 1/16] N in the x, y, and z directions, respectively, and a torque resolution of 1/528 Nm about the x, y, and z axes. The force balance was attached to a Parker 200RT rotary table that can withstand loads up to 200 lbs and exhibits repeatability of up to 12 arc sec. The true wind speed was determined using an Omega PX2650 differential pressure transducer and a J-type thermocouple.

A schematic of the experimental and data collection setup can be seen in Figs. 2(a) and 2(b). The experiments were orchestrated in MATLAB using a dSPACE MicroLabBox and DAQ for data collection. The dSPACE recorded the aerodynamic loads and freestream pressure, while the DAQ recorded the readings from the thermocouple. The aerodynamic curves were generated by conducting alpha sweeps from angles of attack (α) of 0° to 20°. Each test was conducted at a constant wind speed of 10 m/s, which corresponds to a Reynolds number of approximately 2 × 105. The forces, moments, temperature, and pressure were time averaged across 20 s at a sampling frequency of 100 samples per second to obtain the steady state aerodynamic response. With these measurements, the aerodynamic lift (CL), drag (CD), and yaw moment (Cη) coefficients were calculated. It should be noted that the aerodynamic coefficients are non-dimensional parameters that take into consideration the fluid velocity and density as well as the wing size and shape.16 This allows for aerodynamic performance comparisons to be drawn between different aircraft configurations, as will be seen in the subsequent analysis.

As the kirigami is actuated, the lift curve shifts downward, the stall angle (angle of maximum lift) increases by two degrees, and the lift curve slope experiences a minor reduction as seen in Fig. 3(a). This response is very similar to that of aerodynamic trip strips. Trip strips are typically installed at the wing's leading edge and are well known to reduce the lift curve slope prior to the stall angle and reduce the maximum lift coefficient. Although frequently implemented in wind tunnel experiments to more accurately resemble the turbulent boundary layers observed in flight, trip strips can also be implemented to force early boundary layer turbulence, which reduces the likelihood of boundary layer separation.17–20 

FIG. 3.

Aerodynamic response of kirigami actuation. (a) Lift curve as a function of angle of attack. (b) Drag curve as a function of angle of attack. (c) Aerodynamic efficiency as a function of angle of attack. Shaded regions indicate the standard deviation in the measurements.

FIG. 3.

Aerodynamic response of kirigami actuation. (a) Lift curve as a function of angle of attack. (b) Drag curve as a function of angle of attack. (c) Aerodynamic efficiency as a function of angle of attack. Shaded regions indicate the standard deviation in the measurements.

Close modal

The drag coefficient, shown in Fig. 3(b), shows a response consistent with our hypothesis that the kirigami can effectively be used for drag steering and delaying flow separation. Prior to the stall angle, increasing strain on the kirigami sheet increases drag. The inset in Fig. 3(b) shows this trend in more detail near an angle of attack of 0°. This effect is greatest for the first two nonzero strains tested although at higher angles of attack, larger strains show the greatest increase in drag. The shift in the stall angle is also observed in the drag coefficient results, as evidenced by the rightward shift of the point at which CD experiences a rapid increase around an angle of attack of 13°. At high angles of attack, past stall, there does not appear to be any observable trends in the drag response.

The aerodynamic efficiency, shown in Fig. 3(c), can provide additional insight into kirigami's abilities to improve aerodynamic performance. These results show that pre-stall, the efficiency decreases as is predicted by the increase in drag and the decrease in lift coefficients discussed previously. While the porovascular composite actuator studied by Thomas et al.4 did demonstrate an increase in aerodynamic efficiency, the feature height of the kirigami is much larger than that of the porovascular composite. However, above an angle of attack of 14°, actuating the kirigami improves the efficiency. This is due to the fact that the actuated kirigami delays the stall angle, where the airfoil experiences a sharp drop in lift and an increase in drag. The observed improvement exceeds the error bounds of the measurements, lending credence to these findings. While the static kirigami feature alone did not improve cruising flight efficiency for a broad range of angles of attack given the current kirigami geometry, it can be actively deployed to delay stall and improve efficiency in near-stall conditions and maneuvers. More detailed experimental methods of flow characterization are needed to provide a comprehensive assessment of the effects of kirigami surface patterns on boundary layer interactions.

Since yaw control is not strictly a function of drag force, assessing the yaw moment coefficient is essential for understanding the yaw steering capabilities of the kirigami, shown in Fig. 4. As the wind tunnel experiments conducted here used a half-span (left) wing, the raw yaw moment data are processed to remove the clean airfoil's yaw moment and contributions from the mounting rod's length. These results show that, as might be expected, the largest strain tested generated the largest yaw moments as shown in Fig. 4(a). However, by plotting the yaw moment as a function of the kirigami strain, the effectiveness of the actuator can be more thoroughly investigated [Fig. 4(b)]. At an angle of attack of 0°, changes in kirigami strain below 20% do not provide distinguishable yaw moments. Interestingly, this finding mirrors the results observed by Thomas et al.4 However, at an angle of attack of 0° and at maximum strain, the kirigami is able to achieve a yaw moment coefficient of 2.3 × 10–3. This is equivalent in magnitude to traditional split aileron yaw control mechanisms,1,2 and larger than the yaw moments reported for the porovascular composites at this angle.4 As was observed here, Stenfelt et al.21 highlight that unlike traditional aerodynamic control methods that redirect the aerodynamic flow by deflecting the rudder, differential drag methods can have a highly nonlinear response and can have a slope of 0 when unactuated, which slowly increases with actuation. To fully understand why the lower kirigami strains do not produce distinguishable yaw moments, the flow over the wing and at the kirigami cellular unit level would need to be characterized using particle image velocimetry or other detailed flow measurement methods.

FIG. 4.

Control capabilities of the kirigami actuator. (a) Yaw moment coefficient as a function of angle of attack. (b) Yaw moment coefficient as a function of kirigami strain. Shaded regions indicate the error in the data.

FIG. 4.

Control capabilities of the kirigami actuator. (a) Yaw moment coefficient as a function of angle of attack. (b) Yaw moment coefficient as a function of kirigami strain. Shaded regions indicate the error in the data.

Close modal

At larger angles of attack, the data clearly demonstrate that the yaw moment increases with strain across most pre-stall angles of attack. At the maximum tested strain and an angle of attack of 10°, the kirigami achieves a yaw moment coefficient of 6.2 × 10–3, which exceeds the split flap mechanism and mirrors the excellent controllability at high angles observed with the porovascular composites.4 At these larger angles of attack and at kirigami strains above 20%, the yaw response begins to collocate. Post-stall, the yaw control capabilities become unpredictable, likely due to fully separated flow. It should be noted that given kirigami's favorable drag steering capabilities, the rudder may be removed, thereby further increasing the overall efficiency of the aircraft.

While the steering capabilities of the kirigami actuator are the focus of this work, some discussion on kirigami's energy harvesting potential for a small aircraft is merited. Assuming ideal conditions (no haze, unactuated kirigami, 25% solar cell efficiency), the generated power can be written as

P=I*η*A*sin(αs),
(3)

where I represents the solar intensity (nominally 970kW/m2 as per AM1.5G standards), η represents the power conversion efficiency of the solar cell atop the kirigami sheet (around 25%15) αs represents the solar elevation angle that is depicted in Fig. 1(a), and A represents the unactuated kirigami area, which, given the dimensions shown in Fig. 1(c), would be equal to w*l. We can also assess the drag power, which describes the power required in order to overcome drag. This is defined as

Pdrag=FD*V,
(4)

where FD is the drag force and V is the fluid velocity relative to the wing.

Figure 5 demonstrates kirigami's power capabilities. Power generation is greatest when αs equals 90° or, in other words, when the sun is perpendicular to the kirigami substrate [Fig. 5(a)]. These results show that a kirigami substrate of this size would be able to generate up to 27 watts of power. It should be noted that these calculations are performed for a single wing with the dimensions used in our wind tunnel model and that the amount of power generated by the kirigami will be proportional to the wing area. Even given the small wing size tested here, the kirigami is capable of generating enough power for a small-scale UAV, which can require anywhere between 20 and 200 W/kg of power to fly.22 

FIG. 5.

Kirigami actuator power considerations. (a) Power generated by the kirigami composite with respect to the solar altitude angle. (b) Drag power of the wing at a kirigami strain of 30% with respect to the angle of attack. (c) Normalized power represented as the ratio of the generated power to the drag power at an angle of attack of 0°.

FIG. 5.

Kirigami actuator power considerations. (a) Power generated by the kirigami composite with respect to the solar altitude angle. (b) Drag power of the wing at a kirigami strain of 30% with respect to the angle of attack. (c) Normalized power represented as the ratio of the generated power to the drag power at an angle of attack of 0°.

Close modal

The drag power is also considered with respect to the angle of attack [Fig. 5(b)]. In this figure, both the drag power of the entire wing (Pdrag) and the difference in drag power between the unactuated and actuated kirigami (ΔPdrag) are plotted. The sharp dip to negative power in ΔPdrag indicates the improvement in efficiency in the post-stall flight regime. These data can then be used to calculate the ratio of the power generated by the kirigami relative to the drag experienced by the wing, which is shown in Fig. 5(c). For these calculations, Pdrag,0 represents the drag at a kirigami strain of 30% and an angle of attack of 0°. Under these circumstances, the kirigami is able to generate over six times the amount of drag power of the whole wing and almost 30 times the change in drag power due to the actuated kirigami, as is shown in Fig. 5(c). This demonstrates that the kirigami is capable of generating more than enough power to overcome the added drag due to actuation.

This work represents preliminary effort into the application of customizable kirigami substrates for flow control. Experimental results demonstrated that actuating the kirigami such that the three-dimensional features protruded into the flow was an effective means of yaw control. The measured yaw control capabilities at 0° angle of attack mirrored existing state-of-the-art methods and showed superior performance at larger angles of attack. The control effectiveness increased with strain in the pre-stall regime. The kirigami skin was shown to increase the aerodynamic efficiency near stall, which implies that the patterned surface may assist in delaying separation of the boundary layer by tripping the flow. Overall, these results demonstrate that the potential capabilities and customizability of the kirigami substrate allow for multifunctional applications including solar energy harvesting, yaw control, and potentially delayed boundary layer separation. When applied to small-scale UAVs, this could enable lighter and more efficient flight by reducing the battery weight, minimizing or eliminating control surfaces on rudders, and actively improving the glide ratio near stall.

Here, only a single kirigami pattern was tested. While these results are promising, a clear step going forward is to investigate the effects of different pattern sizes and geometries. It is reasonable to assume that a substrate with a larger pattern would be more effective at generating yaw moments, as the height of each protrusion in the kirigami array is dictated by the axial spacing between each cut. In contrast, a finer pattern of similar scale to the riblet studies that have been conducted may provide better drag reduction and aerodynamic efficiency. Due to the customizability of the kirigami substrates, the pattern size and geometry may readily be tailored and placed on specific wing sections to achieve viscous drag reduction and drag steering simultaneously. For example, a macro-scale pattern could be integrated into the outboard section of the wing for drag steering, while a micro-scale pattern can be integrated at the inboard leading edge for drag reduction. This could further open up the possibilities for localized flow tailoring.

See the supplementary material for characterization of the wind tunnel test repeatability and error.

This work was supported in part by the U.S. Air Force Office of Scientific Research under Grant No. FA9550-16-1-0087, titled “Avian-Inspired Multifunctional Morphing Vehicles” monitored by Dr. B. L. Lee, and National Science Foundation Grant No. F031450 “EFRI-ODISSEI: Multi-scale Origami for Novel Photonics and Energy Conversion.”

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Supplementary Material