This paper describes a rotorcraft noise prediction system and its development to incorporate time-dependent information including trajectory, attitude, blade loads, and rotor thrust for predicting noise generated during a complex maneuver. The main contribution from the current work is the enhancement of the system to analyze general maneuvering flight in the interest of understanding the noise source generation mechanisms and aiding development of noise abatement procedures. Key enhancements include the incorporation of wall reflection for broadband noise, a quasi-periodic blade loading model, and refined source motion modeling. The noise prediction system was validated through correlations with acoustic flight-test data for five commercial helicopters. The validation process was carried out by comparing the predicted noise levels (SELdBA, OASPL, and A-weighted SPL) with processed flight-test data. Overall, the predicted noise levels matched the trends and levels within 2–4 dB of measured flight-test data. Results are presented for the steady 6° descent and descending turn maneuvers; time histories are studied in detail to illustrate the influence of flight events—steady flight at constant speed, roll angle, or descent rate, and transient flight including roll-in, roll-out, and start and end of deceleration or acceleration—on noise levels and directivity.
Experiments were performed on a two-meter-diameter, four-bladed single rotor and a coaxial counter-rotating (CCR) rotor in hover to extract the mean coefficients of a dynamic inflow model. The frequency response of the rotor-induced velocity to the rotor thrust was measured by introducing stepped-sine collective pitch inputs at frequencies of 0.2–0.7 per revolution, where the rotor rotational frequency was 14 Hz. The induced velocity field was measured using phase-resolved, two-dimensional, three-component particle image velocimetry over a large region of interest (0.84 m×0.77 m) in a radial slice of the rotor flow field, while rotor thrust was measured using a hub-mounted load cell. Limited by the camera frame rate, an undersampling technique was employed to capture one image pair per rotor revolution and reconstruct the time history from phase-resolved measurements. For the isolated single rotor, the thrust amplitude increased with input frequency, reaching 27.4% of steady thrust at 0.7 per revolution, while the induced velocity amplitude decreased to 2.0% of the steady value. The CCR rotor exhibited similar trends, with thrust amplitudes reaching 28.7% and 29.6% of steady thrust for the upper and lower rotors, respectively, at 0.7 per revolution and induced velocity amplitudes decreasing to 3.1% and 2.3% of the steady values. Mean dynamic inflow states were extracted for both configurations; they fit well to a first-order transfer function for the single rotor, whereas the CCR rotor more closely followed a second-order response. Numerical models captured low-frequency dynamics but failed to replicate the high-frequency attenuation and second-order behavior observed in the CCR rotor, underscoring the need for improved modeling approaches to predict coaxial rotor dynamic inflow accurately.
This technical note presents the analytical linearization of the induced velocity components of a free-vortex wake model with applications to rotary wings. The free-vortex wake model features a vortex-lattice near wake and a tip-vortex far wake. Both are formed by vortex line segments. The linearization is obtained through a first-order Taylor expansion of the Biot–Savart law applied to vortex line segments. Analytical linearization results are validated against exact solutions and linearized solutions obtained via finite differencing.
This article describes the theoretical derivation, implementation, and validation of a teetering rotor model for applications in flight dynamics simulations. The rotor formulation is generic and accounts for both positive and negative angular rotor speeds. The module is integrated within a generic multi-rotor/wing flight dynamics code implemented in MATLAB®/Simulink. The model is validated against flight-identified data for an ultralight coaxial helicopter. The impact of the rotor-on-rotor interactional aerodynamics is evaluated in trimmed flight in terms of spectral and frequency response analyses. Model-order reduction methods are investigated to guide the development of linearized models that are tractable for flight control design while still predicting the effect of rotor-on-rotor interactions on the vehicle flight dynamics. Model-following flight control laws based on these reduced-order linearized models are developed and tested on the nonlinear dynamics. Results indicate that incorporating rotor-on-rotor aerodynamic interactions significantly affects trim, dynamic response, and power requirements. These interactions introduce nonzero roll trim attitudes and increased collective and pedal inputs at low speeds due to asymmetric thrust distribution between rotors. The upper rotor generates higher thrust and inflow while the lower rotor operates in its wake, leading to over 60% higher total power consumption. Frequency response analysis shows improved gain and phase alignment with flight-identified data, particularly in roll, yaw, and heave responses above 0.4–0.5 rad/s.
This paper presents X3D version 2.0, a parallel three-dimensional (3D) dynamic solver designed for rotor aeromechanics. Unlike current-generation rotor comprehensive codes, the solver's core structure is built upon the foundational principles of 3D finite element modeling unified with multibody joints. Notably, it distinguishes itself from commercially available finite element codes by incorporating an inherent internal aerodynamics module to facilitate the 3D computational fluid dynamics/computational structural dynamics coupling. The enhancements in version 2.0 are detailed in this paper, encompassing the integration of new parallel solution procedures, the introduction of capabilities such as coaxial rotor analysis, the exploration of novel 3D models, and the addition of new tools essential for generating 3D rotor models from computer-aided design geometry. The implementation of parallel algorithms significantly enhances the speed of this version, while the newly added capabilities make it conducive for exploring advanced rotor configurations.
This study extends previous work on the state-space formulation and analytical linearization of viscous vortex particle methods by incorporating ground effect into rotary-wing simulations. The aerodynamic solver couples a panel method for modeling blade surfaces and near-wake dynamics with a viscous vortex particle method for capturing the far-wake. Ground effect is modeled using the method of images (MOI). The combined formulation is expressed as a system of ordinary differential equations, resulting in a nonlinear time-periodic (NLTP) system in first-order form. Two linearization techniques are applied to this NLTP system: a conventional finite-difference approach and an analytical linearization scheme extended to include ground influence. Harmonic decomposition is then used to convert the linear time-periodic model into a higher-order linear time-invariant system, enabling the development of a reduced-order linear model suitable for real-time analysis and control. The simulation model is implemented in MATLAB® and applied to a utility-scale helicopter rotor blade. Validation is performed against experimental and high-fidelity numerical results for in-ground-effect conditions. The linearized models are shown to closely replicate the nonlinear system dynamics in both the time and frequency domains. A study was conducted to assess the importance of including viscous effects when modeling ground effect, revealing that the inviscid formulation overpredicts rotor thrust near the ground. Furthermore, the analytical linearization offers a substantial computational advantage over finite-difference methods, with an efficiency gain of order O(n2). This simulation model enables accurate and efficient modeling of aerodynamic effects in rotary-wing applications, including ground effect interactions.
This study presents a polynomial chaos expansion (PCE) based uncertainty quantification framework for predicting unsteady loading noise of a hovering rotor subjected to vertical gust disturbances. A sinusoidal gust model, characterized by gust amplitude and gust length, is introduced to represent realistic inflow variability arising from environmental effects or rotor–airframe interactions. Unsteady loading noise is predicted using a frequency-domain acoustic formulation coupled with two aerodynamic models: a quasi-steady blade element momentum theory and an indicial response method to capture aerodynamic memory effects. The PCE approach is employed to efficiently propagate gust-induced uncertainties through the aeroacoustic model and is systematically validated against Monte Carlo simulations, demonstrating excellent agreement while requiring substantially fewer model evaluations. The results show that the largest uncertainty in unsteady loading noise consistently occurs along the rotor axis, with uncertainty levels varying across blade-passing frequency harmonics. Gust length is found to be the dominant contributor to acoustic uncertainty at higher harmonics, whereas gust amplitude more strongly influences mid-harmonic noise levels. Incorporating unsteady aerodynamic effects reduces the mean sound pressure levels at all harmonics but does not significantly alter the overall uncertainty bounds. The proposed framework provides an efficient and physically interpretable tool for assessing rotor noise robustness under realistic inflow disturbances and supports the development of low-noise rotor designs for advanced air mobility applications.
The aeroelastic loads, stability and stresses on the Mars Helicopter rotor were predicted with a special-purpose three-dimensional rotor structural dynamic analysis. This paper documents that analysis and the insights gained from it. The thin and cold Martian atmosphere, with density 1% of Earth and speed of sound 30% lower, produced sufficient lift but unusually challenging dynamics even with one third the gravity of Earth. The aeroelastic stability was positive but low-about 10-50 times lower than Earth. The stresses and strains on the 57#x25; thin carbon fiber blades were unsteady, complex, and three-dimensional, but within material limits. The key conclusion was that the Ingenuity rotor was structurally stable and safe for Martian hover and controlled forward flight, even at the lowest Reynolds number and highest Mach number anticipated on Mars. Fundamental gaps remained in basic knowledge and tools which must be addressed for larger more capable rotorcraft of the future.
Aeroelastic stability prediction is critical to the successful design, development and flight testing of rotorcraft. As configurations reach higher speeds, new challenges in high Mach number unsteady aerodynamic modeling need to be addressed, especially for higher frequency aeroelastic modes with significant coupling. In this paper, Linear Unsteady aerodynamics and Leishman-Beddoes attached flow models are applied and compared to 2D CFD (airfoil) and 3D CFD/CSD (rotor) analysis for operating conditions of interest. The Leishman-Beddoes model demonstrates improved agreement with CFD data. In the 2D assessment, RCAS is used to model a representative airfoil undergoing prescribed pitch and heave oscillations. CFD results are presented to compare each model (Linear Unsteady and Leishman-Beddoes). In the 3D assessment, a full rotor CFD/CSD test case is evaluated for aeroelastic stability and compared to RCAS standalone analysis. The RCAS rotor structural model is coupled with the HELIOS CFD code and a swashplate cyclic pitch input is used to excite a lightly-damped rotor mode. The transient response based on RCASHELIOS is compared to the standalone RCAS internal aerodynamic result for both Linear Unsteady and Leishman- Beddoes unsteady aerodynamics. This study demonstrates that the Leishman-Beddoes model can produce similar stability results to the computationally expensive coupled CFD/CSD approach of RCAS-HELIOS, but at a lower computational cost, even for critical high-speed conditions.
The transition phase of eVTOL aircraft poses a challenge in balancing energy efficiency and stability. This study presents the development and evaluation of an automatic flight control system for eVTOL transition phases, focusing on minimizing energy consumption while ensuring robust performance. The control architecture implements a hybrid response type combining Translational Rate Command below 5 knots and Acceleration Command Speed Hold above 5 knots, with control allocation dynamically adjusted based on airspeed and rotor shaft angle. Stability analysis reveals surge mode instability at high shaft angles due to negative speed stability derivatives, stabilized through carefully tuned feedback control. The system demonstrates Level 1 handling qualities against bandwidth, quickness, and disturbance rejection criteria when evaluated against MIL-DTL-32742 and MIL-STD-1797B standards. Simulation results verify the control system's ability to maintain precise acceleration/deceleration rates and attitude control while ensuring passenger comfort through limited pitch excursions. The control strategy achieves minimum energy transitions by locking rotor shaft angles to optimal schedules while avoiding excessive hub moments. Flight test maneuvers developed specifically for conversion phases confirm the system's capability to execute efficient transitions within defined performance boundaries. This research establishes a framework for certifiable eVTOL flight control systems that balance energy efficiency with robust performance across diverse flight regimes.
This paper presents an experimental and analytical investigation of whirl-flutter stability in tiltrotor aircraft, focusing on the influence of pitch-flap coupling on stability boundaries. Wind-tunnel tests were conducted using the TiltRotor Aeroelastic Stability Testbed (TRAST), a semispan model designed for test-analysis correlation. This study examines variations in pitch-flap coupling and compares measured frequency and damping trends with predictions from RCAS and CAMRAD II. Results indicate that less pitch-flap coupling increases stability, with both analytical models capturing general trends. The analysis accurately predicts the wing inplane mode stability, but larger deviations are observed in the vertical bending mode, suggesting missing physical effects in the modeling approach. Differences in damping trends at higher speeds indicate that improvements in modeling may be necessary to refine stability predictions. These results provide valuable insights into the capabilities and limitations of current whirl-flutter analysis methods and inform future refinements in tiltrotor aeroelastic modeling.
This study introduces three new proposed mission task elements (MTEs), "Big Air," "Giant Slalom," and "Super Combined," aimed at evaluating handling qualities during low-level and high-speed flight profiles. These MTEs are designed to reflect operational task elements critical in military engagements, particularly where rotorcraft capabilities in evading radar detection and maneuvering at high speeds are paramount. Utilizing piloted simulations with four generic rotorcraft configurations under various flight control laws, the MTEs' effectiveness in exposing aircraft characteristics and handling deficiencies is systematically assessed. The evaluation, conducted with a diverse group of pilots, underscores the MTEs' relevance to real-world scenarios and their robustness in handling qualities assessment across different rotorcraft designs. The study reveals that while some configurations exhibit consistent Level 1 handling qualities ratings, others show varied performance, particularly when integrating additional means of velocity control, such as pusher propellers or velocity hold modes. Findings suggest modifications to current evaluation frameworks to better accommodate the dynamic operational requirements of future vertical lift platforms.
This paper presents an overview of the results from the second wind-tunnel test of the TiltRotor Aeroelastic Stability Testbed (TRAST). The objective of this test was to obtain experimental data for understanding the effects of tiltrotor parameters on whirl flutter and analysis-validation data for the prediction of whirl flutter across a range of system configurations. Frequency and damping were measured at multiple rotor speeds for pitch-flap-coupling angles ranging from -0°to -30°. In addition, measurements were made for changes in blade stiffness, air density and wing-pylon connection stiffness. The paper also presents the results from supporting measurements that may aid analysis validation, such as wing-only damping, rotor frequencies and non-spinning modal frequencies.
Over the past four decades, comprehensive rotorcraft analysis has undergone a dramatic evolution. During my 44-year career, including 33 years at Boeing, my goal has been to leverage this evolution and push the limits of existing analysis tools for advanced rotorcraft applications. In pursuit of this goal, I have applied state-of-the-art multidisciplinary analysis tools to a variety of rotorcraft products (e.g., CH-47 Chinook, V-22 Osprey, AH-64 Apache, and RAH-66 Comanche), new concepts (e.g., Boeing Heliwing VTOL uncrewed aircraft system (UAS) tail-sitter, dual-plane tiltrotor, and DARPA DiscRotor), and rotorcraft development programs such as the Joint Multi-Role Technology Demonstration and CH-47F advanced composite rotor blade. I had an opportunity to apply a rotorcraft comprehensive analysis tool to Boeing's high-altitude, very flexible, propeller-driven UAS for the DARPA Vulture program-a breakthrough for design analysis, loads, and whirl flutter stability. Each new application drove new requirements for analysis tools and expanded our horizons for rotorcraft design through the addition of fuselage and flight control modeling, VABS-based rotor blade properties, improved wake theory with viscous vortex particle method, and numerous other modeling and analysis improvements. This paper provides an in-depth review of the rich history of comprehensive analysis code development and applications, organized by decade to highlight the progression over time.
This article presents the implementation of an integrated model for rotorcraft flight dynamics, motion perception, and motion sickness. Merfeld's multidimensional sensory conflict model (MSCM), along with its extension to visual-vestibular interaction, is employed to represent motion perception both with and without visual feedback. A recently developed model is then used to predict motion sickness severity based on the neural signal mismatch generated by the MSCM. These models are coupled with a generic multirotor/wing flight dynamics code, which is adapted to represent a multipurpose helicopter configuration representative of the Bo 105. The bare-airframe flight dynamics is validated against flight-test data in the frequency domain. Closed-loop simulations are used to demonstrate the model's application to coordinated turns, the onset of spatial disorientation during a graveyard spiral, and motion sickness during a slalom maneuver. In addition, the approach is validated against motion sickness flight-test data from the German Aerospace Center (DLR). This modeling strategy supports the prediction of ride quality metrics and enables the integration of flight dynamics with human factors considerations.
This study develops a liquid-cooled battery system design method that accounts for the battery thermal management system and key constraints by synthesizing various analytical models. It includes models for the battery, coolant channels, and heat exchanger, which are integrated into a comprehensive design procedure. The method is applied to the sizing of a notional electric vertical takeoff and landing aircraft and, together with a previously developed air-cooled battery design method, enables a quantitative comparison of air-and liquid-cooled battery systems in terms of payload performance under various operating conditions. The key conclusions are that the proposed liquid-cooled design method yields a battery system with a specific energy of 125 Wh/kg under the baseline mission and aircraft configuration, representing a 40.5% reduction from the cell-level specific energy of 210 Wh/kg, and that, while the aircraft sizing outcomes can vary depending on the battery cooling method and operating conditions, the overall performance difference between the air-and liquid-cooled systems remains small, indicating that both approaches provide comparable results.
This study investigates the integration of a cycloidal tail rotor as a replacement for the conventional tail rotor in helicopter configurations, focusing on its dual functionality as both an antitorque mechanism and an auxiliary propulsion system. Unlike traditional tail rotors, the cycloidal tail rotor can direct thrust in any direction perpendicular to its axis of rotation, enabling enhanced maneuverability, including the ability to hover at arbitrary pitch attitudes, assist in forward flight, and execute rapid acceleration and deceleration. The cycloidal tail rotor was modeled for flight simulation and incorporated into a generic multi-rotor/wing flight dynamics code to simulate two configurations of a utility helicopter similar to an H-60: one with a conventional tail rotor and the other with a cycloidal tail rotor. A design optimization study defined the geometry of the cycloidal tail rotor, followed by trim, performance, and stability analyses. Results showed that the cycloidal tail rotor configuration exhibited similar trim characteristics to the conventional tail rotor, with minor differences in control inputs and power consumption. The cycloidal tail rotor provided additional propulsive force in forward flight, reducing the pitch-forward requirement and offloading the main rotor, leading to slightly higher power consumption in hover but reduced power requirements at high speeds. Additionally, the cycloidal rotor enabled trimming at arbitrary pitch attitudes. Stability and frequency response analyses revealed minimal differences in flight dynamics, suggesting the feasibility of integrating a cycloidal tail rotor without significantly altering stability or handling qualities. Dynamic inversion control laws adopting pseudo-inverse control allocation demonstrated the ability to reallocate control effort between the main rotor and the cycloidal rotor, with the cycloidal tail rotor acting as a pusher propeller. This reduced the main rotor workload and allowed for a less pronounced nose-down/up pitch attitude during aggressive acceleration/deceleration maneuvers.
This paper investigates the amplitude-dependent characteristics of the TiltRotor Aeroelastic Stability Testbed. The recovery rate, MultiProny, and Stockwell transform methods are employed to measure nonlinear effects in the system, overcoming the limitations of conventional methods like logarithmic decrement, moving-block analysis, and Prony series that assume linear (amplitude-independent) behavior. The proposed methods reveal amplitude-dependent trends that conventional methods obfuscate, providing deeper insights into tiltrotor dynamics. A comprehensive study of ground vibration and wind tunnel test data highlights reduced local damping and frequency at larger response amplitudes for various blade materials, rotor speeds, and pitch-flap coupling parameters. This study offers novel analysis capabilities to support design and advances the understanding of tiltrotor nonlinear dynamics.
NASA's fourth New Frontiers Mission is the Titan Dragonfly relocatable lander. This coaxial quadrotor vehicle is scheduled to launch on a rocket in 2028 with the goal of exploring Titan's prebiotic chemistry and habitability. The multirotor design for this unique application has evolved to meet constraints such as Titan's cryogenic atmosphere at 95 K (-288 degrees F), gravity 14% that of Earth's, atmospheric density 4.4 times of Earth's standard sea level, and the inability to test the entire system under these conditions until the first flight on Titan. This paper focuses on rotor design aspects of the Dragonfly lander and introduces a framework for multirotor design optimization considering multiple flight conditions. A new OVERFLOW Machine Learning Airfoil Performance (PALMO) database is first presented. PALMO is then incorporated into a Bayesian optimization framework and applied to a four-rotor system (one side of the Dragonfly lander). Training data are generated on each iteration of the optimization using the CAMRAD-II comprehensive analysis to evaluate rotor designs over the planned mission profile. An optimal design for the four-rotor system was found with approximately 900 rotor designs analyzed in CAMRAD-II, which required 9 million queries of the PALMO surrogate models. This demonstration case evaluated 10,000,000 candidate rotor designs in 5.5 h on 114 CPU cores using uniform inflow, and in 27.8 h using the prescribed wake model.
The aerodynamic interactions of a counterrotating coaxial rotor (CCR) hovering in-ground effect (IGE) were investigated using a mechanically decoupled two-bladed rotor facility. A momentum theory-based theoretical framework was developed to quantify the aerodynamic interactions. Baseline measurements were performed on a single rotor out-of-ground effect (OGE) and IGE, and a coaxial rotor OGE. Then, coaxial rotor IGE measurements were conducted to evaluate the competing rotor-rotor and rotor-ground interactions. The coaxial rotor experienced rotor-ground interactions similar to a single rotor at multiple IGE conditions. At the most extreme IGE condition studied, the rotor-ground interaction reduced the required power of the CCR by roughly 30%. However, changes in the rotor-rotor interactions at this condition significantly altered the performance of the upper and lower rotors, with the lower rotor necessitating 8% more induced power while the upper rotor required 8% less power when compared to the respective performance characteristics of OGE. Flow field measurements indicated that the wake of the upper rotor contracts less in the presence of the ground, which exacerbates the negative performance effect on the lower rotor.
