The analysis linked cruise propeller performance to advance ratio, while RPM had a stronger association than wing placement with overall hover metrics. In cruise, maximum thrust appeared at lower advance ratios, but propulsive efficiency generally peaked at intermediate settings, reaching 61% at J = 0.7 and a freestream speed of 12 m/s. In hover, the highest reported figure of merit was 0.428. The results come from computer simulations of one configuration, not a flight demonstration.
A computer model of one aircraft setup
The work is a deterministic computational fluid dynamics, or CFD, study, meaning it calculates airflow on a computer rather than measuring it around a flying aircraft. It pairs a Gemfan 51466 propeller with an NACA 4412 wing. The calculations used OpenFOAM-v2412, URANS equations and the k-omega Shear Stress Transport turbulence model. The paper examines the wing-rotor interaction in both cruise and hover.
For cruise, the simulations used freestream speeds of 4, 8 and 12 m/s. The advance ratio J, one of the study's measures for describing propeller operation in forward flight, ranged from 0.2 to 0.8 in steps of 0.1. The wing stayed at the same reported position ratios, Delta Y/R = 0.50 vertically and Delta X/R = 0.50 axially. Because placement was fixed, the study compared operating conditions rather than identifying an optimum cruise wing location.
Cruise exposes a split between thrust and efficiency
The central cruise result was a split between thrust and efficiency. Maximum thrust coefficient occurred at lower advance ratios, J = 0.2 to 0.3, while propulsive efficiency generally peaked near J = 0.6 to 0.7. The highest reported efficiency was 61% at J = 0.7 and 12 m/s. The paper therefore presents no single tested advance ratio as best for every measure: the range associated with the most thrust was not the same as the range associated with peak efficiency. No confidence intervals or formal uncertainty estimates were reported for these values.
The wing generated positive lift across the cruise sweep, but its time-averaged lift coefficient declined as advance ratio rose. Peak propulsive efficiency did not necessarily coincide with maximum wing lift. The model therefore separates the question of how much lift the wing produced from the question of where the propeller operated most efficiently.
The wing changes the downstream flow
Flow structure also differed between the compared cruise cases. At J = 0.3, wake coherence, or how organized the downstream flow remained, was weak and early leapfrogging appeared. At J = 0.7, the simulated wake stayed more coherent farther downstream and formed a narrower, more concentrated jet-like velocity distribution. The authors divided the wing-interaction region into three phases: approaching, interaction and convection. In that sequence, the modeled tip vortex, a swirling flow structure, stretched as it reached the wing's leading edge, then bifurcated into two downstream branches. The branches followed asymmetric trajectories associated in the analysis with vortex-image, blockage and streamwise-momentum effects.
Hover follows a different pattern
Hover produced a different pattern. The freestream was set to 0.0 m/s, and propeller speeds were 8,900, 11,430, 15,740 and 24,200 RPM. Wing positions were varied in the axial and vertical directions at Delta X/R and Delta Y/R values of 0.50, 0.75 and 1.00. Across these cases, wing position had limited influence on overall thrust coefficient, CT, and the study's figure of merit, FM. Higher RPM was associated with higher values for both measures, but the gains were not proportional, and maximum FM was 0.428.
The hover wake changed with rotational speed. At 8,900 RPM, its simulated axial velocity reached approximately 18 m/s. At 24,200 RPM, the high-velocity region was concentrated near the center of the wake and persisted to a reported downstream position of Delta Y/R = 1.25. The comparison came from selected flow contours and carries no statistical uncertainty estimate.
What the simulations leave open
The researchers also checked the numerical setup against CT. Reported relative errors were 4.01% and 3.40% in grid comparisons, and 0.10% and 0.03% in time-step comparisons. In a separate external comparison, a simulation at J = 0.592 and 6,000 RPM, with wing positions from Delta X/R = 0.5 to 2.0, reproduced the reported decreasing Delta CT% trend as Delta X/R increased and was described as in good agreement with experiments reported by Zawodny and colleagues. The comparison used different propeller, airfoil and propeller-radius configurations, so it supports agreement in the direction of the trend rather than an exact numerical match.
That leaves the study with a useful design signal, but a narrow evidence base. It is a URANS model of one small VTOL propeller-wing configuration under selected cruise and hover conditions. Cruise wing placement was fixed rather than systematically varied, and the work does not establish that these modeled relationships would hold in flight or with other propellers, airfoils or geometries. It also does not evaluate hover-to-cruise transition, vertical takeoff or landing dynamics, or full aircraft-level performance.
The document is a preprint identified as arXiv:2608.25150v1 and dated 25 August 2026. Its acknowledgment reports NSERC Discovery grant support, MITACS Globalink Research Internship support and use of Digital Research Alliance of Canada supercomputing clusters.
Paper data and sources
Original title: Wing-Rotor Aerodynamic Interactions in Small UAVs During Hover and Cruise
Authors: Dev Pradeepkumar Nayak, Seungmin Choi, Muhammad Saif Ullah Khalid
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-25
DOI: Not available
Original paper · Full text