The research focuses on a delta wing built around the NACA 0012 airfoil profile, a symmetric section that has been a workhorse of aeronautical testing for nearly a century. What distinguishes the configuration is its sweep angle of fifty degrees, which places it firmly in the non-slender category. Unlike the dramatic, needle-nosed slender deltas of supersonic fighter fame, non-slender delta wings sweep at shallower angles and generate lift through a combination of conventional attached flow and leading-edge vortex systems. That hybrid behavior makes them attractive for small unmanned air vehicles, where compact planforms, structural simplicity, and forgiving stall characteristics are prized, but it also makes their ground-effect behavior genuinely complicated to predict.

The experimental campaign was structured around the full range of angles of attack that a small UAV might encounter between a ground run and a stalled climb-out. Force measurements were taken from zero degrees up to forty-two degrees of angle of attack in three-degree increments, a resolution fine enough to capture the gradual evolution of lift and drag as the wing’s vortex system matured and eventually broke down. To simulate the changing clearance of a vehicle during takeoff and landing, the researchers varied the ratio of the wing’s height above the ground plane to its chord length, testing values of 0.1, 0.2, 0.5, and 1. At the lowest ratio, the wing sits a tenth of a chord above the surface, deep inside the ground cushion; at a ratio of one, it is at the edge of where ground influence is typically considered significant.

Ground effect is not a single phenomenon but a bundle of interacting mechanisms. For a conventional wing, proximity to the surface suppresses the downwash behind the wing and reduces induced drag, which is why racing sailplanes and hovering birds seem to glide effortlessly over water. For a delta wing, the picture is richer. The dominant feature of delta-wing aerodynamics is the pair of primary vortices that roll up along the highly swept leading edges, spinning off the edge and coiling above the wing’s upper surface. These vortices generate additional suction on the upper surface, contributing what aerodynamicists call vortex lift, a mechanism famously formalized by Edward Polhamus in the 1960s through his leading-edge suction analogy. How those vortices behave when the ground is close by is the central question of the study.

Force coefficients alone, however, tell only half the story. To understand why lift and drag changed the way they did, Bay and Kara turned to surface oil flow visualization, a classic experimental technique that reveals the topology of flow on a wing’s surface. A mixture incorporating titanium dioxide pigment is painted onto the wing; as air flows over the surface, shear stresses in the boundary layer drag the oil into streaks, and the resulting patterns record where flow attaches, separates, and reattaches. The researchers conducted these visualization experiments from zero to forty degrees of angle of attack in five-degree steps, building a photographic atlas of the surface flow at each ground clearance.

The oil-flow experiments revealed the key flow phenomena governing the wing’s performance. The team identified the onset and progression of vortex breakdown, the dramatic event in which the coherent leading-edge vortex suddenly expands into a turbulent, disorganized mass, causing the suction peak over the wing to collapse and lift to plateau. They also mapped the reattachment region where the swirling vortex flow impinges back onto the wing surface, the footprint of the inner primary vortex, and the delicate surface signatures of the secondary reattachment line and secondary separation line, features that mark the smaller counter-rotating vortices nested beneath the primary system near the leading edge. Flow traces across the surface connected these features into a coherent topological picture at every angle of attack and ground height tested.

This combination of force measurement and flow visualization is what gives the study its practical value. A designer of a small delta-wing UAV can read the force curves to know how much lift and drag to expect during a ground run at a given clearance, and then consult the flow topology to understand the underlying mechanism, whether it is a strengthened vortex, a delayed breakdown, or a shift in the reattachment line. Because the tested height-to-chord ratios of 0.1 through 1 span the realistic range of wheel heights during takeoff rotation and landing flare, the dataset maps directly onto the flight phases the authors set out to investigate: takeoff, landing, and cruise out of ground influence.

What makes the work particularly compelling for the UAV community is that it did not stop at the wind tunnel. The authors also present the results of real flight tests of an unmanned aerial vehicle incorporating this wing, beginning with a real-time ground takeoff and continuing into flight out of ground effect. Flight test data of this kind is rare in academic ground-effect studies, which often remain confined to wind tunnels and computational models. By anchoring the laboratory measurements to the behavior of an actual aircraft leaving the runway, the study provides a bridge between controlled experimentation and the messy, gusty reality of a small vehicle climbing away from the ground.

The broader context of the research is a growing body of literature on wings in ground effect, a field that stretches from the wing-in-ground-effect vehicles studied extensively by Kirill Rozhdestvensky to recent experimental work on non-slender delta wings by groups including Tumse and colleagues, and Koçak and Yavuz, who examined both static and dynamic ground boundary conditions. Much of the earlier delta-wing ground-effect work used flat-plate or thin airfoil sections; building the wing from a full NACA 0012 profile with realistic thickness adds a layer of fidelity relevant to actual vehicle design. Prior studies have also shown that thickness-to-chord ratio itself alters non-slender delta wing aerodynamics, which makes the choice of a standard airfoil section a meaningful one rather than a mere convenience.

For the emerging fleet of small drones, eVTOL demonstrators, and micro air vehicles that spend much of their operating lives near surfaces, the message of this research is that ground effect is not simply a bonus of extra lift. It reshapes the vortex system that defines delta-wing flight, moves the boundaries of stall and breakdown, and alters the drag budget in ways that depend intimately on height, angle of attack, and planform geometry. By pairing precise force measurements across a dense grid of angles of attack and ground clearances with titanium dioxide surface visualization that exposes the underlying flow structures, and by closing the loop with real flight tests, Bay and Kara have delivered a reference dataset and a physical explanation that should help engineers design delta-wing unmanned aircraft that behave predictably in the most demanding moments of flight: the seconds spent leaving the ground, and the seconds spent returning to it.

Subject of Research: Ground effect aerodynamics of a NACA 0012-based non-slender delta wing for unmanned air vehicles

Article Title: An Experimental Investigation of Aerodynamic Performance of an NACA 0012-Based Non-slender Delta Wing Under Ground Effect

Article References: Bay, A. E., & Kara, T. (2026). An Experimental Investigation of Aerodynamic Performance of an NACA 0012-Based Non-slender Delta Wing Under Ground Effect. International Journal of Aeronautical and Space Sciences. https://doi.org/10.1007/s42405-026-01197-5

Image Credits: AI Generated

DOI: 10.1007/s42405-026-01197-5

Keywords: delta wing, ground effect, NACA 0012, unmanned aerial vehicles, vortex breakdown, aerodynamic performance, surface oil visualization, titanium dioxide, wind tunnel testing, leading-edge vortices, takeoff and landing, flight tests

The research, led by Hao Wu, Kai Pan, and Huatao Chen of Shandong University of Technology, together with Kun Zhao of the Beijing Electro-Mechanical Engineering Institute and Juan L. G. Guirao of the Technical University of Cartagena, addresses a long-standing bottleneck. Accurately simulating water entry requires computational fluid dynamics (CFD) tools that resolve strong nonlinear fluid–structure interaction, free-surface deformation, cavity formation, and turbulence. A single high-fidelity simulation can consume enormous computational resources, making it impractical to sweep across the full space of entry angles and velocities that engineers need to explore when designing a vehicle or planning a mission.

To build their training data, the team simulated the oblique water entry of a delta-wing vehicle using the commercial CFD platform STAR-CCM+. The numerical setup combined the Navier–Stokes equations with the Volume of Fluid method to track the air–water interface, a standard k–ε turbulence model, and a three-degree-of-freedom rigid-body motion model that allowed the vehicle to translate in the vertical plane and pitch about its transverse axis. The researchers examined entry angles from 40 to 60 degrees and entry velocities from 15 to 30 meters per second, a range chosen because prior studies indicate that moderately large oblique angles help minimize instantaneous impact loads while preserving trajectory stability. Mesh independence testing confirmed that the chosen grid resolution reproduced center-of-mass trajectories with a relative error of just over two percent compared with a much finer mesh.

The simulations revealed the tightly coupled physics the model would need to learn. As the vehicle penetrates the surface, free-surface deformation, local pressure peaks, and cavity evolution unfold together in time, directly shaping the tangential force, normal force, and pitching moment acting on the craft. The team found that peak loads rise nearly steadily with entry velocity, and that the normal force becomes especially sensitive to velocity at the steepest 60-degree entry angle. Displacements of the center of mass also grow with velocity, though more gently. These five quantities—two forces, one moment, and two displacement components—formed the prediction targets for the new machine learning framework.

At the heart of the study is a hybrid architecture that merges two strands of modern machine learning: long short-term memory (LSTM) networks and physics-informed neural networks (PINNs). LSTMs are recurrent networks with internal gating structures that allow them to selectively retain and update information over long time horizons, making them well suited to capturing the short-lived but history-dependent transients of water entry. PINNs, first systematically proposed by Raissi and colleagues in 2019, embed physical equations directly into a network’s training loss, forcing predictions to remain consistent with known dynamics. Purely data-driven models, the authors note, can lose physical consistency and robustness when asked to predict conditions not well represented in their training data—a serious limitation for safety-critical tasks such as peak-load estimation.

The innovation lies in how the two components are coupled. The LSTM takes the initial entry conditions and advances the flow of loads in time, outputting the resultant tangential force, normal force, and pitching moment at each step through a linear output layer that avoids imposing artificial bounds on signed, spike-prone quantities. Crucially, the vehicle’s trajectory is not produced by a separate neural output branch. Instead, the LSTM-predicted loads are fed into a discrete Newton–Euler integration layer, which recursively propagates the rigid-body velocities, attitude, and displacements forward in time. This ensures that the predicted forces and the predicted motion remain physically consistent with one another—a property that standalone data-driven models often lack.

Training combines three loss terms: a load-supervision term that matches predicted force and moment histories to the CFD references, a trajectory-supervision term that anchors the integrated displacements to the simulated paths, and a Newton–Euler consistency penalty that enforces the discrete load–motion relation. The physical term is weighted at 0.1, a deliberate compromise so that the physics constraint regularizes the model without smoothing away the sharp transient peaks that matter most in impact engineering. To assess generalization honestly, the team used leave-one-condition-out cross-validation at the level of complete operating sequences: each angle–velocity combination was held out in its entirety during one validation run, so the reported accuracy reflects genuine cross-condition prediction within the tested domain rather than interpolation between scattered time points.

The results show that the hybrid model reproduces the full time histories of loads and trajectories with high fidelity across the 40 to 60 degree range. It captures the rapid rise and multi-peak structure of the normal force and pitching moment under strongly transient conditions, with only minor phase shifts near some secondary peaks. Scatter plots of predicted versus simulated characteristic quantities cluster tightly along the diagonal, and error histograms concentrate in low-error intervals without long tails or systematic bias. In head-to-head comparisons under identical network configurations and training data, the standalone LSTM reproduced broad trends but overshot and shifted phase near peaks, while the standalone PINN fit smoothly but missed peak amplitudes and high-frequency detail. The hybrid LSTM–PINN model achieved lower overall errors and better agreement across MSE, MAE, and R-squared metrics.

The authors are careful to frame the scope of their claims. The demonstrated generalization is in-domain: it covers complete held-out sequences within the investigated ranges of 40 to 60 degrees and 15 to 30 meters per second, not extrapolation to new geometries, steeper angles, or experimental conditions. The Newton–Euler constraint is a consistency relation for rigid-body motion rather than a complete hydrodynamic model; effects such as added mass, hydrodynamic damping, and nonlinear buoyancy are learned implicitly from the CFD-derived resultant loads rather than parameterized explicitly. Even so, the framework offers something engineering practice has lacked: a fast, physically grounded surrogate that can sweep the water-entry parameter space in seconds instead of hours, evaluate peak magnitude and peak timing robustly, and feed directly into attitude optimization and real-time control design. Future work, the team says, will expand the operating-condition database, incorporate experimental measurements, and extend the evaluation to multi-attribute criteria including uncertainty, load-impulse error, and computational efficiency—steps that could bring physics-guided machine learning from the simulation lab into the design loop for the next generation of air-and-sea vehicles.

Subject of Research: Physics-guided deep learning prediction of water-entry impact loads and motion trajectories for cross-medium vehicles

Article Title: Prediction of water entry loads and motion trajectories for a delta wing cross medium vehicle using a physics guided LSTM model

Article References: Wu, H., Pan, K., Zhao, K., Guirao, J. L. G., & Chen, H. (2026). Prediction of water entry loads and motion trajectories for a delta wing cross medium vehicle using a physics guided LSTM model. Discover Artificial Intelligence, 6(1), Article 1129. https://doi.org/10.1007/s44163-026-02085-3

Image Credits: AI Generated

DOI: 10.1007/s44163-026-02085-3

Keywords: cross-medium vehicle, water entry, LSTM, physics-informed neural networks, computational fluid dynamics, fluid–structure interaction, delta wing, hydrodynamic loads, motion trajectory prediction, STAR-CCM+, machine learning, ocean engineering