Due to its appeal as a renewable, low-carbon energy source, wind energy development has increased rapidly, accounting for 5.6 % of electricity generation in the United States at the end of 2016 . Wind turbines generate electricity by extracting momentum from the atmosphere, thereby creating wakes characterized by a wind-speed deficit and increased turbulence downwind . As the size of turbine rotors increases, turbine wakes also increase, which may pose a greater hazard to nearby flying aircraft . Therefore, improved understanding of turbine wake characteristics is crucial to assess hazards to aircraft posed by wakes.

Numerous studies have investigated the structure, duration, and decay of wind turbine wakes. Most of these studies address wake impacts on surface temperature or surface fluxes . Detailed measurements of winds in turbine wakes have been taken with lidars (e.g., ). Wind tunnel experiments have also been used to further aerodynamic research on wind turbines . Scaling such experiments to utility-scale turbines can be challenging: wind tunnel measurements typically cannot account for complexities in atmospheric profiles, such as inversions and wind veer. Computational fluid dynamics (CFD) simulations of wind turbine wakes provide insights into turbine wakes . Both actuator-disk and actuator-line methods have been used to simulate the rotor and downstream flow to study wake structure.

Extensive wind development occurs in rural locations, where open spaces favorable for wind energy are also home to numerous general aviation airports. Almost 40 % of all wind turbines in the United States exist within 10 km of a small airport and about 5 % exist within 5 km of a small airport (Fig. , based on data from ). Currently, neither the Federal Aviation Administration (FAA) of the United States nor the Civil Aviation Authority (CAA) of the United Kingdom have detailed recommendations on the effects of wind-turbine-induced roll hazards for aircraft .

General aviation pilots are typically most concerned with the rolling moment , and we thus focus our study on this hazard. The rolling moment is the tendency for an aerodynamic force applied at a distance from an aircraft's center of mass to cause the aircraft to undergo angular acceleration about its roll axis, considered a torque in this study . The roll axis is the longitudinal axis, running from the nose to the tail of the aircraft. Other wake hazards of concern to pilots are those generated from the wings of preceding aircraft during take-off as a consequence of lift .

Previous work has argued that turbine wakes present, in particular, a serious roll hazard to general aviation aircraft. Mulinazzi and Zheng (2014) used a helical vortex model to represent a wind turbine wake from which aircraft roll hazards were calculated. The helical vortex model was scaled up from a wind tunnel study using miniature turbines with a rotor diameter of 0.254 m. The 4 m s-1 inflow was meant to trigger transient helical tip vortices . Mulinazzi and Zheng (2014) scaled up these wind tunnel results to the atmosphere by assuming comparable near- and far-wake turbulent flow structures between the tip vortices measured in the wind tunnel and the full wake produced in a real atmosphere by a utility-scale turbine. With calculations derived from this scaling, they suggest wind turbine wakes pose a significant roll hazard to general aviation aircraft at downwind distances as far as 4.57 km (2.84 miles) . These findings have been used in multiple states to limit wind energy development. Reid Bell, airport manager at Pratt Regional Airport in Kansas, confirmed that the Pratt wind-farm project was relocated further away from the airport as a direct result of the study . The study has been used as a warning to aviators in Virginia as well .

Other researchers have also investigated the hazards that wind turbines pose to aircraft by computing the roll hazards from analytic representations of wakes. and found that typical onshore turbines could pose hazards for gliders or ultralight helicopters but perhaps not for general aviation aircraft. computed a wake wind field derived using the Beddoes circulation formula , proven to adequately match lidar field observations made of a wind turbine wake. For a 30 m rotor diameter wind turbine, find that the wake does not pose any roll hazards for aircraft five rotor diameters downstream from the turbine.

Rather than approximating wakes, we seek to explicitly resolve turbine wakes within a dynamic, non-stationary atmosphere. We therefore use large-eddy simulations (LES) to assess wind-generated roll hazards to small aircraft from the wake of a utility-scale wind turbine. Section  provides details on our simulations and methodology for analyzing the model data. Section  presents the results of our analysis, specifically the quantified roll hazards on hypothetical aircraft. We conclude in Sect.  with a discussion of our results and suggestions for future work.

We first analyze the turbine wake impacts on a hypothetical general aviation aircraft by comparing roll hazard calculations of a sample flight track outside of the wake to those within the wake. Rolling moment coefficient (Eq. ) is calculated for an aircraft inside and outside the wake for the neutral (Fig. b) and stable (Fig. d) cases to categorize each moment as a “low”, “medium”, or “high” hazard as used in the and assessments of wake roll hazards. These assessment criteria are based on the maximum rolling moment that the aileron on a typical aircraft can generate to counteract a moment induced by the wake field . A wake-induced rolling moment coefficient |Croll| above 0.28 is considered a high hazard, between 0.1 and 0.28 a medium hazard, and below 0.1 a low hazard. As expected, in both stability conditions, the aircraft inside the wake experiences higher values of rolling moment coefficient, indicating increased turbulence of the turbine wake. However, rolling moment coefficients experienced in both stability cases for the aircraft inside the wake remain within the low hazard threshold of |Croll|<0.1.

While these sample aircraft flight tracks in Fig. b, d show an example for one location in the wake, the LES data set allows us to calculate more instances of roll hazards throughout the entire wake. More conclusive results can be seen by assessing the 540 flight paths down and across the wake spanning all 100 s of data. We summarize occurrences of roll hazard calculations via histograms of neutral (Fig. a, b) and stable (Fig. c, d) cases and down-wake (Fig. a, c) and cross-wake (Fig. b, d) transects as a function of the downwind distance from the turbine.

In all transects and stabilities, over 99.99 % of all calculations exist within the low hazard threshold. Table  lists detailed counts of instances classified as medium hazards (0.1<|Croll|<0.28). The stable cross-wake configuration has the greatest fraction of medium hazards at 188 out of 10 868 000. Across all cases, no moments reach the high hazard threshold. Further, the vast majority of calculated roll hazards are even smaller than the maximum low hazard limit (|Croll|<0.1) and are contained within |Croll|<0.02 (Fig. ). The decreasing frequency of rolling moment coefficients |Croll| greater than 0.02 beyond 8 D suggests that roll hazards decrease with downstream distance at this point (Fig. ). While we hypothesized the stable case would generate more hazardous rolling moment coefficients, we find similar fractions of medium hazards in the stable conditions as in neutral (Fig. ). Even though stable conditions enable the wake to persist longer downwind than in convective conditions, they do not increase turbulence that would pose hazards for general aviation aircraft.

The largest roll hazards, as indicated by Croll, occur most frequently about 5 D downwind from the turbine (Fig. ). The three highest roll hazards in the neutral, down-wake case (Croll=0.128,0.124,0.123) all occur in a sequential line downwind near 6.5 D in the bottom-left quadrant of the rotor disk as looking downwind (black circles in Fig. a). These rolling moment coefficients are all positive, indicating clockwise rotation about the aircraft's longitudinal axis when looking downwind. In the neutral, cross-wake case, the three highest rolling moments (Croll=0.127,0.124,0.124) occur between 3 and 4.5 D in the top-right quadrant of the rotor disk (empty circles in Fig. a). For the stable, down-wake case, the highest two roll hazards (Croll=-0.121, -0.12) occur at 3.5 D downwind, in the top-left quadrant of the rotor (Fig. c). The next highest hazard (Croll=-0.119) occurs 2.5 D downwind, differing from the prior hazards by residing in the bottom-left quadrant of the rotor (Fig. c). The largest hazards across all cases occur in the stable, cross-wake case at Croll=0.14, 0.14, 0.136, with the first two in the bottom-right quadrant of the rotor disk and the third in the top left (empty circles in Fig. c). All of these peak hazards are located in the high-shear zone at the edge of the wake between 3 and 7 D downwind from the turbine (and not closer to the turbine, e.g., 0.5–1 D), which suggests that the rolling moment is more influenced by horizontal shear in the flow than by wake rotation.

As wind energy development increases in the vicinity of general aviation airports, concerns for turbine-wake-induced roll hazards on aircraft grow. Of particular concern is the rolling moment, the aerodynamic force applied at a distance from an aircraft's center of mass that causes the aircraft to undergo angular acceleration about its roll axis. Using LES of stable and neutral flow past a utility-scale wind turbine, we quantify the roll hazards experienced by general aviation aircraft transecting the wake.

We represent a typical general aviation aircraft in the LES data as a 10 m line comprised of eight segments that are 1.25 m in length. At each point along the aircraft, we sample the LES wind vectors to calculate rolling moment and the rolling moment coefficient. We define 540 flight tracks to march through the wake to make the roll hazard calculations. The flight tracks have down-wake and cross-wake orientations and extend through the entire downwind 682 points and 247 points, respectively, yielding 176 880 calculations of a roll hazard for each stability case for each time step of data.

The rolling moment coefficient serves as our primary roll hazard metric, as it normalizes the rolling moment on the aircraft by the aircraft size, shape, and airspeed to produce a standard hazard index. This index has been classified by past studies into thresholds for low, medium, and high roll hazards. When comparing a sample flight path outside of the wake's influence to one within the wake center, we find that an aircraft flying within the wake experiences higher rolling moment coefficient than an aircraft flying in a wake-free environment. However, analyses of all 540 flight paths through the wake reveal that over 99.99 % of hazard calculations remained within the low criterion in both neutrally stratified and stably stratified conditions across 100 s of data. In neutral conditions, the largest of these hazards are classified as medium hazards and exist 6.5 D downwind of the turbine in the bottom-left portion of the rotor disk. The highest hazards in the stable case also remained within the medium threshold and are located in two separate regions of the wake: approximately 4 D downwind in the bottom-right quadrant of the rotor and 6 D downwind in the top-left quadrant of the rotor.

Our calculated roll hazards differ from those in , who used a helical vortex model scaled up from wind tunnel measurements to find significant roll hazards far downwind from a wind turbine. Conversely, our results using an actuator-line representation of a wind turbine in the SOWFA LES model rarely surpass the low roll hazard threshold. Rather, our results agree with those of , whose calculations are computed from the Beddoes circulation formula , as opposed to the wind tunnel extrapolation in . Past successes in turbine wake modeling using LES actuator-line methods can in part validate our results (e.g., ).

This study presents a simple method for quantifying turbine-wake-induced roll hazards on general aviation aircraft and is constrained by the assumptions made to represent an aircraft within LES data of a single turbine wake. While we have shown that individual wakes in neutrally stratified and stably stratified conditions are unlikely to pose hazards to general aviation aircraft, interactions between wakes could also be explored. Future simulations of wind plants that allow for wake interaction (as in ) and larger turbine types could be useful. Our conclusions are drawn from rolling moment calculations, though additional calculations of yawing and pitching moments could also be beneficial. Our results may also be supported by field tests, in which tethersondes or unmanned aircraft vehicles would fly through the wake of a real utility-scale turbine during variable conditions to directly measure roll hazards. Future studies could integrate simulations like these with flight simulators to understand the coupling of the atmospheric behavior to pilot response for an integrated assessment of roll hazard, as in .