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At least 253 records · Page 14

The dynamic fission instability and the origin of the Moon

A theory for the formation of the Moon which involves the dynamic fission of a rapidly rotating protoplanet, which might then result in the formation of the Earth and the Moon is discussed. The fission hypothesis was originally based on analytic, linearized models of the growth of asymmetry in homogenous bodies. The fully nonlinear evolution of the dynamic instability in inviscid, compressible bodies was calculated by numerical techniques. It was found that the dynamic instability degenerates into the ejection of a ring of matter with a substantial fraction of the mass, leaving behind a central body with most of the mass. The linearized analytical approach and the numerical approach were used to show that dynamic fission probably does not occur in rocky protoplanets. The numerical calculations are performed with a fully three dimensional hydrodynamical code, which allows the nonlinear, time evolution of the instability to be followed. Sequences of uniformly rotating equilibria were constructed and are used as the initial models for the fission calculations. An initially imposed asymmetry consisting of a 10% binary perturbation in the density was found to disappear on the rotational period time scale. No dynamic instability occurred. This result are verified by including the velocity dissipation terms in the linearized analysis of the stability of a Maclaurin spheroid: the dynamic instability disappears when the simulated viscous dissipation terms are included. It is concluded that any rocky body, even with considerable partial melt or a molten core, should be stable to dynamic fission; any rotational instability that occurs can only result in equatorial mass loss.

Boss, A. P.

Predicted effect of dynamic load on pitting fatigue life for low-contact-ratio spur gears

How dynamic load affects the surface pitting fatigue life of external spur gears was predicted by using the NASA computer program TELSGE. Parametric studies were performed over a range of various gear parameters modeling low-contact-ratio involute spur gears. In general, gear life predictions based on dynamic loads differed significantly from those based on static loads, with the predictions being strongly influenced by the maximum dynamic load during contact. Gear mesh operating speed strongly affected predicted dynamic load and life. Meshes operating at a resonant speed or one-half the resonant speed had significantly shorter lives. Dynamic life factors for gear surface pitting fatigue were developed on the basis of the parametric studies. In general, meshes with higher contact ratios had higher dynamic life factors than meshes with lower contact ratios. A design chart was developed for hand calculations of dynamic life factors.

Lewicki, David G.

Dynamic sea surface topography, gravity and improved orbit accuracies from the direct evaluation of SEASAT altimeter data

A method for the simultaneous solution of dynamic ocean topography, gravity and orbits using satellite altimeter data is described. A GEM-T1 based gravitational model called PGS-3337 that incorporates Seasat altimetry, surface gravimetry and satellite tracking data has been determined complete to degree and order 50. The altimeter data is utilized as a dynamic observation of the satellite's height above the sea surface with a degree 10 model of dynamic topography being recovered simultaneously with the orbit parameters, gravity and tidal terms in this model. PGS-3337 has a geoid uncertainty of 60 cm root-mean-square (RMS) globally, with the uncertainty over the altimeter tracked ocean being in the 25 cm range. Doppler determined orbits for Seasat, show large improvements, with the sub-30 cm radial accuracies being achieved. When altimeter data is used in orbit determination, radial orbital accuracies of 20 cm are achieved. The RMS of fit to the altimeter data directly gives 30 cm fits for Seasat when using PGS-3337 and its geoid and dynamic topography model. This performance level is two to three times better than that achieved with earlier Goddard earth models (GEM) using the dynamic topography from long-term oceanographic averages. The recovered dynamic topography reveals the global long wavelength circulation of the oceans with a resolution of 1500 km. The power in the dynamic topography recovery is now found to be closer to that of oceanographic studies than for previous satellite solutions. This is attributed primarily to the improved modeling of the geoid which has occurred. Study of the altimeter residuals reveals regions where tidal models are poor and sea state effects are major limitations.

Marsh, J. G.

Application of numerical optimization techniques to control system design for nonlinear dynamic models of aircraft

Control system design for general nonlinear flight dynamic models is considered through numerical simulation. The design is accomplished through a numerical optimizer coupled with analysis of flight dynamic equations. The general flight dynamic equations are numerically integrated and dynamic characteristics are then identified from the dynamic response. The design variables are determined iteratively by the optimizer to optimize a prescribed objective function which is related to desired dynamic characteristics. Generality of the method allows nonlinear effects to aerodynamics and dynamic coupling to be considered in the design process. To demonstrate the method, nonlinear simulation models for an F-5A and an F-16 configurations are used to design dampers to satisfy specifications on flying qualities and control systems to prevent departure. The results indicate that the present method is simple in formulation and effective in satisfying the design objectives.

Lan, C. Edward

A hybrid procedure for dynamic characterization of ceramics at elevated temperature

A hybrid experimental-numerical procedure to characterize the dynamic fracture response of ceramics and ceramic composites at temperatures in excess of 1400 C is described. This hybrid methodology was developed to characterize dynamic fracture responses and to study the effect of temperature on dynamic fracture responses of ceramics and ceramic matrix composites. The hybrid methodology was used to determine the dynamic stress intensity factors (SIF) associated with a running crack in a three-point bend specimen at elevated temperature. This procedure was utilized to determine the dynamic SIF versus crack velocity relations of alumina, TiB2-particulate/SiC-matrix composite, and SiC-whisker/Al2O3-matrix composite. Minor differences in the dynamic SIF versus crack velocity relations at room and elevated temperature were seen, and significant differences under impact and static loadings were observed in the dynamic SIF versus crack velocity relations.

Yang, K. H.

Comparison of analysis and experiment for dynamics of low-contact-ratio spur gears

Low-contact-ratio spur gears were tested in NASA gear-noise-rig to study gear dynamics including dynamic load, tooth bending stress, vibration, and noise. The experimental results were compared with a NASA gear dynamics code to validate the code as a design tool for predicting transmission vibration and noise. Analytical predictions and experimental data for gear-tooth dynamic loads and tooth-root bending stress were compared at 28 operating conditions. Strain gage data were used to compute the normal load between meshing teeth and the bending stress at the tooth root for direct comparison with the analysis. The computed and measured waveforms for dynamic load and stress were compared for several test conditions. These are very similar in shape, which means the analysis successfully simulates the physical behavior of the test gears. The predicted peak value of the dynamic load agrees with the measurement results within an average error of 4.9 percent except at low-torque, high-speed conditions. Predictions of peak dynamic root stress are generally within 10 to 15 percent of the measured values.

Oswald, Fred B.

Space Station Freedom solar dynamic modules structural modelling and analysis

In support of the Space Station Freedom (SSF) Solar Dynamic Power Module effort, structural design studies were performed to investigate issues related to the design of the power module, its pointing capabilities, and the integration of the module into the SSF infrastructure. Of particular concern from a structural viewpoint are the dynamics of the power module, the impact of the power module on the Space Station dynamics and controls, and the required control effort for obtaining the specified Solar Dynamic Power Module pointing accuracy. Structural analyses were performed to determine the structural dynamics attributes of both the existing and the proposed structural dynamics module designs. The objectives of these analyses were to generate validated Solar Dynamic Power Module NASTRAN finite element models, combine Space Station and power module models into integrated system models, perform finite element modal analyses to assess the effect of the relocations of the power module center of mass, and provide modal data to controls designers for control systems design.

Lawrence, Charles

Dynamic coordination of a self-reconfigurable manipulator system

The authors present the dynamic coordination of a self-reconfigurable manipulator system capable of changing its mechanical structure according to given task requirements. The self-reconfiguration is achieved by reconfiguring the topology of a dual-arm system through serial, parallel, and bracing structures. Particular emphasis is placed on the dynamic coordination of two arms having three different dual-arm topologies. The authors develop the Cartesian space dynamic models of a dual-arm system of three dual-arm topologies and derive the kinematic and dynamic constraints imposed on two arms in cooperation. Dual-arm dynamic manipulabilities are defined to quantify the dynamic performance of three dual-arm topologies in terms of the efficiency of generating Cartesian accelerations. A methodology of selecting serial, parallel, and bracing structures based on dual-arm dynamic manipulabilities is provided.

Kim, Sungbok

Stiffness of magnetic bearings subjected to combined static and dynamic loads

This paper investigates the stiffness of a magnetic bearing that is subjected to the combined action of static and dynamic loads. Since their sum cannot exceed the saturation load, a large static load will imply that the bearing can carry only a small dynamic load. This smaller dynamic load together with the practical vibration amplitude define a practical upper bound to the dynamic stiffness. This paper also presents approximate design formulas and curves for this stiffness capacity as a function of the ratio of dynamic and static loads. In addition, it indicates that vibrations larger than a certain gap fraction can destabilize the magnetic bearing. This gap fraction, called the critical gap fraction, depends on the dynamic and static load ratio. For example, if the dynamic load is half of the static load, the use of more than 25 percent of gap can destabilize the bearing.

Rao, D. K.

The quest for stall-free dynamic lift

During the past decade, numerous major effects have addressed the question of how to control or alleviate dynamic stall effects on helicopter rotors, but little concrete evidence of any significant reduction of the adverse characteristics of the dynamic stall phenomenon has been demonstrated. Nevertheless, it is important to remember that the control of dynamic stall is an achievable goal. Experiments performed at the US Army Aeroflight-dynamics Directorate more than a decade ago demonstrated that dynamic stall is not an unavoidable penalty of high amplitude motion, and that airfoils can indeed operate dynamically at angles far above the static-stall angle without necessarily forming a stall vortex. These experiments, one of them featuring a slat that was designed from static airfoil considerations, showed that unsteadiness can be a very beneficial factor in the development of high-lift devices for helicopter rotors. The experience drawn from these early experiments is now being focused on a program for the alleviation of dynamic-stall effects on helicopter rotors. The purpose of this effort is to demonstrate that rotor stall can be controlled through an improved understanding of the unsteady effects on airfoil stall and to document the role of specific means that lead to stall alleviation in the three dimensional unsteady environment of helicopter rotors in forward flight. The first concept to be addressed in this program will be a slatted airfoil. A two dimensional unsteady Navier-Stokes code has been modified to compute the flow around a two-element airfoil.

Tung, C.

Analysis of shadowing effects on MIR photovoltaic and solar dynamic power systems

The NASA Lewis Research Center is currently working with RSC-Energia, the Russian Space Agency, and Allied Signal in developing a flight demonstration solar dynamic power system. This type of power system is dependent upon solar flux that is reflected and concentrated into a thermal storage system to provide the thermal energy input to a closed-cycle Brayton heat engine. The solar dynamic unit will be flown on the Russian Mir space station in anticipation of use on the International Space Station Alpha. By the time the power system is launched, the Mir will be a spatially complex configuration which will have, in addition to the three-gimbaled solar dynamic unit, eleven solar array wings that are either fixed or track the Sun along one axis and a variety or repositionable habitation and experiment modules. The proximity of arrays to modules creates a situation which makes it highly probable that there will be varying solar flux due to shadowing on the solar dynamic unit and some of the arrays throughout the orbit. Shadowing causes fluctuations in the power output from the arrays and the solar dynamic power system, thus reducing the energy capabilities of the spacecraft. An assessment of the capabilities of the power system under these conditions is an important part in influencing the design and operations of the spacecraft and predicting its energy performance. This paper describes the results obtained from using the Orbiting Spacecraft Shadowing Analysis Station program that was integrated into the Station Power Analysis for Capability Evaluation (SPACE) electrical power system computer program. OSSA allows one to consider the numerous complex factors for analyzing the shadowing effects on the electrical power system including the variety of spacecraft hardware geometric configurations, yearly and daily orbital variations in the vehicle attitude and orbital maneuvers (for communications coverage, payload pointing requirements and rendezvous/docking with other vehicles). The geometric models of the MIR with a solar dynamic power unit that were used in performing shadowing analyses are described. Also presented in this paper are results for individual orbits for several flight attitude cases which include assessments of the shadowing impacts upon the solar dynamic unit and the solar arrays. These cases depict typical MIR flight attitudes likely to have shadowing impact. Because of the time varying nature of the Mir orientation with respect to the Sun and the lack of knowledge of the precise timing of the attitude changes, strategies must be devised to assess and depict the shadowing impacts on power generation throughout the year. To address this, the best, nominal and worst impacts of shadowing considering a wide possible range of parameter changes for typical mission operation period are shown.

Fincannon, James

Static and dynamic strain energy release rates in toughened thermosetting composite laminates

In this work, the static and dynamic fracture properties of several thermosetting resin based composite laminates are presented. Two classes of materials are explored. These are homogeneous, thermosetting resins and toughened, multi-phase, thermosetting resin systems. Multi-phase resin materials have shown enhancement over homogenous materials with respect to damage resistance. The development of new dynamic tests are presented for composite laminates based on Width Tapered Double Cantilevered Beam (WTDCB) for Mode 1 fracture and the End Notched Flexure (ENF) specimen. The WTDCB sample was loaded via a low inertia, pneumatic cylinder to produce rapid cross-head displacements. A high rate, piezo-electric load cell and an accelerometer were mounted on the specimen. A digital oscilloscope was used for data acquisition. Typical static and dynamic load versus displacement plots are presented. The ENF specimen was impacted in three point bending with an instrumented impact tower. Fracture initiation and propagation energies under static and dynamic conditions were determined analytically and experimentally. The test results for Mode 1 fracture are relatively insensitive to strain rate effects for the laminates tested in this study. The test results from Mode 2 fracture indicate that the toughened systems provide superior fracture initiation and higher resistance to propagation under dynamic conditions. While the static fracture properties of the homogeneous systems may be relatively high, the apparent Mode 2 dynamic critical strain energy release rate drops significantly. The results indicate that static Mode 2 fracture testing is inadequate for determining the fracture performance of composite structures subjected to conditions such as low velocity impact. A good correlation between the basic Mode 2 dynamic fracture properties and the performance is a combined material/structural Compression After Impact (CAI) test is found. These results underscore the importance of examining rate-dependent behavior for determining the longevity of structures manufactured from composite materials.

Cairns, Douglas S.

Dynamic analysis of astronaut motions in microgravity: Applications for Extravehicular Activity (EVA)

Simulations of astronaut motions during extravehicular activity (EVA) tasks were performed using computational multibody dynamics methods. The application of computational dynamic simulation to EVA was prompted by the realization that physical microgravity simulators have inherent limitations: viscosity in neutral buoyancy tanks; friction in air bearing floors; short duration for parabolic aircraft; and inertia and friction in suspension mechanisms. These limitations can mask critical dynamic effects that later cause problems during actual EVA's performed in space. Methods of formulating dynamic equations of motion for multibody systems are discussed with emphasis on Kane's method, which forms the basis of the simulations presented herein. Formulation of the equations of motion for a two degree of freedom arm is presented as an explicit example. The four basic steps in creating the computational simulations were: system description, in which the geometry, mass properties, and interconnection of system bodies are input to the computer; equation formulation based on the system description; inverse kinematics, in which the angles, velocities, and accelerations of joints are calculated for prescribed motion of the endpoint (hand) of the arm; and inverse dynamics, in which joint torques are calculated for a prescribed motion. A graphical animation and data plotting program, EVADS (EVA Dynamics Simulation), was developed and used to analyze the results of the simulations that were performed on a Silicon Graphics Indigo2 computer. EVA tasks involving manipulation of the Spartan 204 free flying astronomy payload, as performed during Space Shuttle mission STS-63 (February 1995), served as the subject for two dynamic simulations. An EVA crewmember was modeled as a seven segment system with an eighth segment representing the massive payload attached to the hand. For both simulations, the initial configuration of the lower body (trunk, upper leg, and lower leg) was a neutral microgravity posture. In the first simulation, the payload was manipulated around a circular trajectory of 0.15 m radius in 10 seconds. It was found that the wrist joint theoretically exceeded its ulnal deviation limit by as much as 49. 8 deg and was required to exert torques as high as 26 N-m to accomplish the task, well in excess of the wrist physiological limit of 12 N-m. The largest torque in the first simulation, 52 N-m, occurred in the ankle joint. To avoid these problems, the second simulation placed the arm in a more comfortable initial position and the radius and speed of the circular trajectory were reduced by half. As a result, the joint angles and torques were reduced to values well within their physiological limits. In particular, the maximum wrist torque for the second simulation was only 3 N-m and the maximum ankle torque was only 6 N-m.

Newman, Dava J.

A Parametric Study of Spur Gear Dynamics

A parametric study of a spur gear system was performed through a numerical analysis approach. This study used the gear dynamic program DANST, a computer simulator, to determine the dynamic behavior of a spur gear system. The analytical results have taken the deflection of shafts and bearings into consideration for static analysis, and the influence of these deflections on gear dynamics was investigated. Damping in the gear system usually is an unknown quantity, but it has an important effect in resonance vibration. Typical values as reported in the literature were used in the present analysis. The dynamic response due to different damping factors was evaluated and compared. The effect of the contact ratio on spur gear dynamic load and dynamic stress was investigated through a parameter study. The contact ratio was varied over the range of 1.26 to 2.46 by adjusting the tooth addendum. Gears with contact ratio near 2.0 were found to have the most favorable dynamic performance.

Lin, Hsiang Hsi

Validation of a "Kane's Dynamics" Model for the Active Rack Isolation System

Many microgravity space-science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages, to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. Effective model-based vibration isolation requires (1) an isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller, ARIS provides the ISS response to the first requirement. In November 1999, the authors presented a response to the second ("A 'Kane's Dynamics' model for the Active Rack Isolation System", Hampton and Beech) intended to facilitate an optimal-controls approach to the third. This paper documents the validation of that high-fidelity dynamic model of ARIS. As before, this model contains the full actuator dynamics, however, the umbilical models are not included in this presentation. The validation of this dynamics model was achieved by utilizing two Commercial Off the Shelf (COTS) software tools: Deneb's ENVISION, and Online Dynamics' AUTOLEV. ENVISION is a robotics software package developed for the automotive industry that employs 3-dimensional (3-D) Computer Aided Design (CAD) models to facilitate both forward and inverse kinematics analyses. AUTOLEV is a DOS based interpreter that is designed in general to solve vector based mathematical problems and specifically to solve Dynamics problems using Kane's method.

Beech, Geoffrey S.

Overcoming Dynamic Disturbances in Imaging Systems

We develop and discuss a methodology with the potential to yield a significant reduction in complexity, cost, and risk of space-borne optical systems in the presence of dynamic disturbances. More robust systems almost certainly will be a result as well. Many future space-based and ground-based optical systems will employ optical control systems to enhance imaging performance. The goal of the optical control subsystem is to determine the wavefront aberrations and remove them. Ideally reducing an aberrated image of the object under investigation to a sufficiently clear (usually diffraction-limited) image. Control will likely be distributed over several elements. These elements may include telescope primary segments, telescope secondary, telescope tertiary, deformable mirror(s), fine steering mirror(s), etc. The last two elements, in particular, may have to provide dynamic control. These control subsystems may become elaborate indeed. But robust system performance will require evaluation of the image quality over a substantial range and in a dynamic environment. Candidate systems for improvement in the Earth Sciences Enterprise could include next generation Landsat systems or atmospheric sensors for dynamic imaging of individual, severe storms. The technology developed here could have a substantial impact on the development of new systems in the Space Science Enterprise; such as the Next Generation Space Telescope(NGST) and its follow-on the Next NGST. Large Interferometric Systems of non-zero field, such as Planet Finder and Submillimeter Probe of the Evolution of Cosmic Structure, could benefit. These systems most likely will contain large, flexible optomechanical structures subject to dynamic disturbance. Furthermore, large systems for high resolution imaging of planets or the sun from space may also benefit. Tactical and Strategic Defense systems will need to image very small targets as well and could benefit from the technology developed here. We discuss a novel speckle imaging technique with the potential to separate dynamic aberrations from static aberrations. Post-processing of a set of image data, using an algorithm based on this technique, should work for all but the lowest light levels and highest frequency dynamic environments. This technique may serve to reduce the complexity of the control system and provide for robust, fault-tolerant, reduced risk operation. For a given object, a short exposure image is "frozen" on the focal plane in the presence of the environmental disturbance (turbulence, jitter, etc.). A key factor is that this imaging data exhibits frame-to-frame linear shift invariance. Therefore, although the Point Spread Function is varying from frame to frame, the source is fixed; and each short exposure contains object spectrum data out to the diffraction limit of the imaging system. This novel speckle imaging technique uses the Knox-Thompson method. The magnitude of the complex object spectrum is straightforward to determine by well-established approaches. The phase of the complex object spectrum is decomposed into two parts. One is a single-valued function determined by the divergence of the optical phase gradient. The other is a multi-valued function determined by the circulation of the optical phase gradient-"hidden phase." Finite difference equations are developed for the phase. The novelty of this approach is captured in the inclusion of this "hidden phase." This technique allows the diffraction-limited reconstruction of the object from the ensemble of short exposure frames while simultaneously estimating the phase as a function of time from a set of exposures.

Young, Eric W.

Overcoming Dynamic Disturbances in Imaging Systems

We develop and discuss a methodology with the potential to yield a significant reduction in complexity, cost, and risk of space-borne optical systems in the presence of dynamic disturbances. More robust systems almost certainly will be a result as well. Many future space-based and ground-based optical systems will employ optical control systems to enhance imaging performance. The goal of the optical control subsystem is to determine the wavefront aberrations and remove them. Ideally reducing an aberrated image of the object under investigation to a sufficiently clear (usually diffraction-limited) image. Control will likely be distributed over several elements. These elements may include telescope primary segments, telescope secondary, telescope tertiary, deformable mirror(s), fine steering mirror(s), etc. The last two elements, in particular, may have to provide dynamic control. These control subsystems may become elaborate indeed. But robust system performance will require evaluation of the image quality over a substantial range and in a dynamic environment. Candidate systems for improvement in the Earth Sciences Enterprise could include next generation Landsat systems or atmospheric sensors for dynamic imaging of individual, severe storms. The technology developed here could have a substantial impact on the development of new systems in the Space Science Enterprise; such as the Next Generation Space Telescope(NGST) and its follow-on the Next NGST. Large Interferometric Systems of non-zero field, such as Planet Finder and Submillimeter Probe of the Evolution of Cosmic Structure, could benefit. These systems most likely will contain large, flexible optormechanical structures subject to dynamic disturbance. Furthermore, large systems for high resolution imaging of planets or the sun from space may also benefit. Tactical and Strategic Defense systems will need to image very small targets as well and could benefit from the technology developed here. We discuss a novel speckle imaging technique with the potential to separate dynamic aberrations from static aberrations. Post-processing of a set of image data, using an algorithm based on this technique, should work for all but the lowest light levels and highest frequency dynamic environments. This technique may serve to reduce the complexity of the control system and provide for robust, fault-tolerant, reduced risk operation. For a given object, a short exposure image is "frozen" on the focal plane in the presence of the environmental disturbance (turbulence, jitter, etc.). A key factor is that this imaging data exhibits frame-to-frame linear shift invariance. Therefore, although the Point Spread Function is varying from frame to frame, the source is fixed; and each short exposure contains object spectrum data out to the diffraction limit of the imaging system. This novel speckle imaging technique uses the Knox-Thompson method. The magnitude of the complex object spectrum is straightforward to determine by well-established approaches. The phase of the complex object spectrum is decomposed into two parts. One is a single-valued function determined by the divergence of the optical phase gradient. The other is a multi-valued function determined by, the circulation of the optical phase gradient-"hidden phase." Finite difference equations are developed for the phase. The novelty of this approach is captured in the inclusion of this "hidden phase." This technique allows the diffraction-limited reconstruction of the object from the ensemble of short exposure frames while simultaneously estimating the phase as a function of time from a set of exposures.

Young, Eric W.

Dynamic Stall Characteristics of Drooped Leading Edge Airfoils

Helicopters in high-speed forward flight usually experience large regions of dynamic stall over the retreating side of the rotor disk. The rapid variations in the lift and pitching moments associated with the stall process can result in vibratory loads, and can cause fatigue and failure of pitch links. In some instances, the large time lag between the aerodynamic forces and the blade motion can trigger stall flutter. A number of techniques for the alleviation of dynamic stall have been proposed and studied by researchers. Passive and active control techniques have both been explored. Passive techniques include the use of high solidity rotors that reduce the lift coefficients of individual blades, leading edge slots and leading edge slats. Active control techniques include steady and unsteady blowing, and dynamically deformable leading edge (DDLE) airfoils. Considerable amount of experimental and numerical data has been collected on the effectiveness of these concepts. One concept that has not received as much attention is the drooped-leading edge airfoil idea. It has been observed in wind tunnel studies and flight tests that drooped leading edge airfoils can have a milder dynamic stall, with a significantly milder load hysteresis. Drooped leading edge airfoils may not, however, be suitable at other conditions, e.g. in hover, or in transonic flow. Work needs to be done on the analysis and design of drooped leading edge airfoils for efficient operation in a variety of flight regimes (hover, dynamic stall, and transonic flow). One concept that is worthy of investigation is the dynamically drooping airfoil, where the leading edge shape is changed roughly once-per-rev to mitigate the dynamic stall.

Sankar, Lakshmi N.