Fore-aft Direction Research Articles

Fatigue damage mitigation of offshore wind turbines under real wind and wave conditions

Offshore wind turbines (OWTs) subjected to combined wind and wave loadings experience excessive vibrations which will increase fatigue loadings on the structure and reduce the fatigue life. In this paper, a three-dimensional pendulum tuned mass damper (3d-PTMD) is attached to the OWT to mitigate the bi-directional vibrations resulting from wind-wave misalignment so as to increase the fatigue life. An analytical model of the offshore wind turbine coupled with the 3d-PTMD is established using the Euler-Lagrangian equation. To predict long-term metocean condition, a statistical analysis for different properties of wind and wave loading such as, wind-wave misalignment, significant wave height and wind velocity is carried out. The aerodynamic wind loading is calculated using the blade element method and the wave loading is computed using the JONSWAP wave spectrum and Morison equation. Dual linear tuned mass dampers (TMDs) deployed in the side-side and fore-aft directions are used for comparison. The NREL monopile 5 MW baseline wind turbine is used to examine the performance of 3d-PTMD in a realistic metocean condition. The fatigue damage is estimated based on the rain-flow cycle counting method and Miner’s rule. Results indicate that the 3d-PTMD can increase the wind turbine tower fatigue life by more than 50% in comparison with the dual TMDs.

Stability of Mina v2 for Robot-Assisted Balance and Locomotion.

The assessment of the risk of falling during robot-assisted locomotion is critical for gait control and operator safety, but has not yet been addressed through a systematic and quantitative approach. In this study, the balance stability of Mina v2, a recently developed powered lower-limb robotic exoskeleton, is evaluated using an algorithmic framework based on center of mass (COM)- and joint-space dynamics. The equivalent mechanical model of the combined human-exoskeleton system in the sagittal plane is established and used for balance stability analysis. The properties of the Linear Linkage Actuator, which is custom-designed for Mina v2, are analyzed to obtain mathematical models of torque-velocity limits, and are implemented as constraint functions in the optimization formulation. For given feet configurations of the robotic exoskeleton during flat ground walking, the algorithm evaluates the maximum allowable COM velocity perturbations along the fore-aft directions at each COM position of the system. The resulting velocity extrema form the contact-specific balance stability boundaries (BSBs) of the combined system in the COM state space, which represent the thresholds between balanced and unbalanced states for given contact configurations. The BSBs are obtained for the operation of Mina v2 without crutches, thus quantifying Mina v2's capability of maintaining balance through the support of the leg(s). Stability boundaries in single and double leg supports are used to analyze the robot's stability performance during flat ground walking experiments, and provide design and control implications for future development of crutch-less robotic exoskeletons.

Rising STAR: A Highly Reconfigurable Sprawl Tuned Robot

This letter presents Rising STAR (RSTAR) a novel highly reconfigurable robot. RSTAR belongs to the family of the STAR robots with similar sprawling capabilities allowing it to run in a planar configuration, either upright or inverted and change its mechanics from the lateral to the sagittal planes. However, RSTAR is fitted with a new four bar extension mechanism (FBEM) allowing it to extend the distance between its body and legs. This combination of sprawling and extension mechanisms enables RSTAR to overcome extremely challenging obstacles, crawl over flexible and slippery surfaces and even climb vertically in a tube or between two walls. The robot can extend its height and width three-fold and move its center of mass both in the fore-aft and vertical directions. We first describe a kinematic model and the dynamical analysis conducted to improve the design of the robot and evaluate its strength and motor requirements. Based on this analysis, we designed and built a three-dimensional printed prototype and experimentally tested it. The robot can run upside down and climb over obstacles that are even higher than the diameter of its wheeled legs using a turtle-like gait. To increase its mobility, RSTAR can be fitted with wheels or spoked legs or a combination of the two, giving it superiorability to engage different terrains (see video).

On the parameter sensitivity in structural parameter identification using Eigensystem Realization Algorithm for a MW-size wind turbine

Accurate estimation of structural parameters such as the natural frequencies, modal shapes and damping ratios is important for both numerical modelling and structural health monitoring, and ambient vibration analysis is usually used for the estimation. Although the Eigensystem Realization Algorithm (ERA) is widely used, the results are known to depend on the selection of the calculation parameters. In this study, first the sensitivity of the calculation parameters of the NExT-ERA method for the full-scale measurement data of a 2,4MW wind turbine is studied to provide reference for practical application of the method. Small initial model order resulted in unstable estimation of the damping ratios, while higher values gave robust results. The optimum value for the initial model order was 400 to 600, which was much larger than the recommendation in the literature as four times the model order. The optimal values for the correlation length parameter are 3500 to 4000 for the 1st modes, and 100 to 350 for the 2nd modes, which corresponds to the length of the free decay process seen in the cross- correlation function. Higher number of points used for FFT gave lower damping ratios for the 1st mode in both fore-aft and side-side directions. The effect of the number of the FFT points is smaller in 2nd mode, which may be due to difference of the length of data required to capture the characteristics of the system. The structural parameters estimated with NExT-ERA method agreed well with the results of the previously conducted forced vibration test except for the fore-aft 1st mode damping ratio, of which value was especially small compared to other modes.

Comparison of segmental analysis and sacral marker methods for determining the center of mass during level and slope walking

BackgroundA human’s center of mass (COM) is a widely used parameter in both clinical and practical applications. The segmental analysis method for determining the COM is considered the gold standard but is difficult to apply in a real environment. Research questionThe purpose of this study was to confirm the efficacy of an alternative COM determination method—the sacral marker method—by comparing segmental analysis and sacral marker method results in three dimensions during level or slope walking. MethodsTen healthy young subjects (age = 24.0 ± 4.5 yr, height = 174.5 ± 5.9 cm, and weight = 66.9 ± 9.4 kg) participated in the study. Each participant was monitored using a Helen Hayes full-body marker set and asked to walk on level and sloped (7°) terrain. The markers’ trajectories were subsequently recorded. Each participant’s COM was determined using segmental analysis and sacral marker methods via calculation and direct measurement, respectively. ResultsComparative results indicated no significant differences (p > 0.05) between the segmental analysis and sacral marker method results for the COM displacement, velocity, or acceleration in the fore-aft and vertical directions. Conversely, significant differences (p < 0.05) between the two methods were observed for the COM displacement and acceleration in the medial-lateral direction, suggesting kinematic differences. SignificanceBased on this latter finding, caution should be exercised when determining COM kinematics using the sacral marker method.

Correction to 'Walking with wider steps changes foot placement control, increases kinematic variability and does not improve linear stability'.

[This corrects the article DOI: 10.1098/rsos.160627.].

Bi-directional vibration control of offshore wind turbines using a 3D pendulum tuned mass damper

Abstract Offshore wind turbines suffer from excessive bi-directional vibrations due to wind-wave misalignment and vortex induced vibrations. However, most of existing research focus on unidirectional vibration attenuation which is inadequate for real applications. The present paper proposes a three dimensional pendulum tuned mass damper (3d-PTMD) to mitigate the tower and nacelle dynamic response in the fore-aft and side-side directions. An analytical model of the wind turbine coupled with the 3d-PTMD is established wherein the interaction between the blades, the tower and the 3d-PTMD is modeled. Aerodynamic loading is computed using the Blade Element Momentum method where the Prandtls tip loss factor and the Glauert correction are considered. JONSWAP spectrum is adopted to generate wave data. Wave loading is computed using Morisons equation in collaboration with the strip theory. Via a numerical search approach, the design formula of the 3d-PTMD is obtained and examined on a National Renewable Energy Lab (NREL) monopile 5 MW baseline wind turbine model under misaligned wind, wave and seismic loading. Dual linear tuned mass dampers (TMDs) deployed in the fore-aft and side-side directions are utilized for comparison. It is found that the 3d-PTMD with a mass ratio of 2 % can improve the mitigation of the root mean square and peak response by around 10 % when compared with the dual linear TMDs in controlling the bi-directional vibration of the offshore wind turbines under misaligned wind, wave and seismic loading.

Analysis of biases in dynamic margins of stability introduced by the use of simplified center of mass estimates during walking and turning

The ability to control the body’s center of mass (CoM) is critical for preventing falls, which are a major health concern in aging populations. Control of the CoM has been assessed by characterizing dynamic margins of stability (MoS) which capture the dynamic relationship between the CoM and the base of support. Accurate estimation of CoM dynamics is best accomplished using a full-body marker set. However, a number of simplified estimates have been used throughout literature. Here, we determined the biases and sources of bias when computing MoS using four simplified CoM models, and we characterized how these biases varied in straight walking versus turning. CoM kinematics were characterized using a full-body marker set, the lower extremities and trunk, lower extremities only, an average of four pelvic markers, and one pelvic marker alone. Significant bias was demonstrated for most methods and was larger during turning tasks compared to straight walking. In the fore-aft direction, only overestimates in the MoS were observed, and these ranged from 15 to 110% larger than the true MoS value. In the mediolateral direction, both under- and over-estimates were observed and ranged from −175 to 225%. Across tasks, bias was smallest when using the lower extremity plus trunk (−23 to 62%) and pelvis average methods (−71 to 43%). Sources of bias were attributed to misestimates of CoM height, velocity, and position. Together, our findings suggest that the 1) lower extremity and trunk model and 2) pelvis average model should be considered in future studies to minimize bias when simplified models of CoM dynamics are desired.

Dynamic perception of dynamic affordances: walking on a ship at sea.

Motion of the surface of the sea (waves, and swell) causes oscillatory motion of ships at sea. Generally, ships are longer than they are wide. One consequence of this structural difference is that oscillatory ship motion typically will be greater in roll (i.e., the ship rolling from side to side) than in pitch (i.e., the bow and stern rising and falling). For persons on ships at sea, affordances for walking on the open deck should be differentially influenced by ship motion in roll and pitch. Specifically, the minimum width of a walkable path should be greater when walking along the ship's short, or athwart axis than when walking along its long, or fore-aft axis. On a ship at sea, we evaluated the effects of walking in different directions (fore-aft vs. athwart) on actual walking performance. We did this by laying out narrow paths on the deck and asking participants (experienced maritime crewmembers) to walk as far as they could while remaining within the lateral path boundaries. As predicted, participants walked farther along the athwart path than along the fore-aft path. Before actual walking, we evaluated participants' judgments of their walking ability in the fore-aft and athwart directions. These judgments mirrored the observed differences in walking performance, and the accuracy of judgments did not differ between the two directions. We conclude that experienced maritime crewmembers were sensitive to affordances for walking in which the relevant properties of the environment were exclusively dynamic.

Effects of Inertial Power and Inertial Force on Bat Wings.

The inertial power and inertial force of wings are important factors in evaluating the flight performance of native bats. Based on measurement data of wing size and motions of Eptesicus fuscus, we present a new computational bat wing model with divided fragments of skeletons and membrane. The motions of the model were verified by comparing the joint and tip trajectories with native bats. The influences of flap, sweep, elbow, wrist and digits motions, the effects of different bones and membrane of bat wing, the components on vertical, spanwise and fore-aft directions of the inertial power and force were analyzed. Our results indicate that the flap, sweep, and elbow motions contribute the main inertial power and force; the membrane occupies an important proportion of the inertial power and force; inertial power on flap direction was larger, while variations of inertial forces on different directions were not evident. These methods and results offer insights into flight dynamics in other flying animals and may contribute to the design of future robotic bats.

The interrelationship between disease severity, dynamic stability, and falls in cerebellar ataxia

Cerebellar ataxia (CA) results in discoordination of body movements (ataxia), a gait disorder, and falls. All three aspects appear to be obviously interrelated; however, experimental evidence is sparse. This study systematically correlated the clinical rating of the severity of ataxia with dynamic stability measures and the fall frequency in patients with CA. Clinical severity of CA in patients with sporadic (n=34) and hereditary (n=24) forms was assessed with the Scale for the Assessment and Rating of Ataxia (SARA). Gait performance was examined during slow, preferred, and maximally fast walking speeds. Spatiotemporal variability parameters in the fore-aft and medio-lateral directions were analyzed. The fall frequency was assessed using a standardized interview about fall events within the last 6months. Fore-aft gait variability showed significant speed-dependent characteristics with highest magnitudes during slow and fast walking. The SARA score correlated positively with fore-aft gait variability, most prominently during fast walking. The fall frequency was significantly associated to fore-aft gait variability during slow walking. Severity of ataxia, dynamic stability, and the occurrence of falls were interrelated in a speed-dependent manner: (a) Severity of ataxia symptoms was closely related to instability during fast walking. (b) Fall frequency was associated with instability during slow walking. These findings suggest the presence of a speed-dependent, twofold cerebellar locomotor control. Assessment of gait performance during non-preferred, slow and fast walking speeds provides novel insights into the pathophysiology of cerebellar locomotor control and may become a useful approach in the clinical evaluation of patients with CA.

Numerical study of ice-induced loads and responses of a monopile-type offshore wind turbine in parked and operating conditions

Offshore wind is an attractive source of renewable energy. In regions with cold climates, such as Canada, the Baltic Sea, and Bohai Bay, a good understanding of ice loads is essential to design a reliable and cost effective support structure for an offshore wind turbine. This paper presents a study of the dynamic ice–structure interaction of a commonly used monopile-type offshore wind turbine in drifting level ice in both parked and operating conditions. A semi-empirical numerical model for ice–structure interaction was coupled to the aero-hydro-servo-elastic simulation tool HAWC2. A convergence study was performed to determine the proper time step and simulation length to obtain reliable response prediction. The simulated ice load was compared with the formulations in international standards. The coupling between the ice loads and the structural response of the monopile-type wind turbine was investigated and found to be important. The effects of the ice characteristics (e.g., ice thickness and drifting speed) were examined with the turbine being in parked and operating conditions. Compared with current numerical model, standards from International Electrotechnical Commission (IEC) and International Organization for Standardization (ISO) predict lower ice loads. 3-D effect of ice–monopile interaction and failure of local ice sheet are considered. More stochastic dynamic phenomena are captured for ice–structure interaction in our numerical model. The effect of the ice thickness on the response was found to be significant. A negligible drifting speed effect is found on the bending moment response in the fore-aft direction. There is a large increase in the fore-aft response as the inclination angle of the cone increases. Further sensitivity studies and validation against model tests will be performed for the conical waterline of the wind turbine.

Load reduction of a monopile wind turbine tower using optimal tuned mass dampers

ABSTRACTWe investigate to apply tuned mass dampers (TMDs) (one in the fore–aft direction, one in the side–side direction) to suppress the vibration of a monopile wind turbine tower. Using the spectral element method, we derive a finite-dimensional state-space model Σd from an infinite-dimensional model Σ of a monopile wind turbine tower stabilised by a TMD located in the nacelle. Σ and Σd can be used to represent the dynamics of the tower and TMD in either the fore–aft direction or the side–side direction. The wind turbine tower subsystem of Σ is modelled as a non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) system consisting of an Euler–Bernoulli beam equation describing the dynamics of the flexible tower and the Newton–Euler rigid body equations describing the dynamics of the heavy rotor-nacelle assembly (RNA) by neglecting any coupling with blade motions. Σd can be used for fast and accurate simulation for the dynamics of the wind turbine tower as well as for optimal TMD designs. We show that Σd agrees very well with the FAST (fatigue, aerodynamics, structures and turbulence) simulation of the NREL 5-MW wind turbine model. We optimise the parameters of the TMD by minimising the frequency-limited -norm of the transfer function matrix of Σd which has input of force and torque acting on the RNA, and output of tower-top displacement. The performances of the optimal TMDs in the fore–aft and side–side directions are tested through FAST simulations, which achieve substantial fatigue load reductions. This research also demonstrates how to optimally tune TMDs to reduce vibrations of flexible structures described by partial differential equations.

Control algorithm of a floating wind turbine for reduction of tower loads and power fluctuation

A new control algorithm for a MW class spar-type floating offshore wind turbine has been developed to improve its performance and to reduce its mechanical load. The new blade pitch control having two PI control loops applied for different wind speed regions were designed. The bandwidth of the controller at near above-rated wind speed region was made lower to keep the vibration mode of the floating platform from being driven, and the bandwidth of the controller at far above-rated wind speed region was made higher to improve the wind turbine performance. Also, a feedback control loop using the angular acceleration information of the nacelle in the fore-aft direction was designed additionally to reduce the tower vibration. To perform modeling and simulation, a commercial multidynamics simulation program widely used for wind turbine design and certification, DNV-GL Bladed was used. The DNV-GL Bladed simulation results for the proposed new control algorithm showed that the output performance is improved and the tower load is reduced in various wind speeds above the rated wind speed.

Subjective response of standing persons exposed to fore-aft, lateral and vertical whole-body vibration

The aims of this study were to propose multiply scale factors for evaluation of discomfort of standing persons and to investigate whether there exist differences between multiplying factors used for evaluation of discomfort of standing persons and those of seated persons exposed to WBV. Twelve male subjects were exposed to twenty-seven stimuli that comprise three acceleration magnitudes (0.2, 0.4, and 0.8 m/s2 r.m.s.) along fore-aft (x), lateral (y) or vertical (z) direction. The subjects with seated or standing posture on the platform of the vibration test rig rated the subjective discomfort for each stimulus that has frequency contents ranging from 1.0 Hz to 20 Hz with a constant power spectrum density. The order of presentation of the test stimuli was fully randomized and each stimulus was repeated three times. The subjective scale for discomfort was calculated by using the category judgment method. The best combinations of multiplying factors were determined by calculating correlation coefficients of regression curves in-between subjective ratings and vibration magnitudes. In all the directions, body posture significantly influenced on subjective discomfort scales. Particularly in the fore-aft and lateral direction, the upper limit of all the categories for the standing posture resulted in higher vibration acceleration magnitudes than those for the seated posture. In contrast, in the vertical direction, only the upper limit of category “1: Not uncomfortable” for standing posture was observed to be higher than that for seated posture. The best agreement for ISO-weighted vibration acceleration occurred at x factor of 1.8 and y factor of 1.8 in the standing posture and x factor of 2.8 and y factor of 1.8 in the seated posture. The results suggest that seated people respond more sensitively and severely in perception of discomfort to fore-aft and lateral vibration than standing people do while standing people respond more sensitively and severely to vertical vibration than seated people do. Thus the effects of body postures on multiplying factors should be considered in evaluation of discomfort caused by whole-body vibration. Relevance to industryThis study reports differences in subjective response of standing persons to fore-aft, lateral and vertical whole-body vibration. The results obtained in this study propose the fundamental data on the sensitivity to whole-body vibration exposed with standing posture.

How do the substrate reaction forces acting on a gecko's limbs respond to inclines?

Locomotion is an essential character of animals, and excellent moving ability results from the delicate sensing of the substrate reaction forces (SRF) acting on body and modulating the behavior to adapt the motion requirement. The inclined substrates present in habitats pose a number of functional challenges to locomotion. In order to effectively overcome these challenges, climbing geckos execute complex and accurate movements that involve both the front and hind limbs. Few studies have examined gecko's SRF on steeper inclines of greater than 90°. To reveal how the SRFs acting on the front and hind limbs respond to angle incline changes, we obtained detailed measurements of the three-dimensional SRFs acting on the individual limbs of the tokay gecko while it climbed on an inclined angle of 0-180°. The fore-aft forces acting on the front and hind limbs show opposite trends on inverted inclines of greater than 120°, indicating propulsion mechanism changes in response to inclines. When the incline angles change, the forces exerted in the normal and fore-aft directions by gecko's front and hind limbs are reassigned to take full advantage of limbs' different roles in overcoming resistance and in propelling locomotion. This also ensures that weight acts in the angle range between the forces generated by the front and hind limbs. The change in the distribution of SRF with a change in the incline angle is directly linked to the favorable trade-off between locomotive maneuverability and stability.

Biomechanics of gecko locomotion: the patterns of reaction forces on inverted, vertical and horizontal substrates

The excellent locomotion ability of geckos on various rough and/or inclined substrates has attracted scientists’ attention for centuries. However, the moving ability of gecko-mimicking robots on various inclined surfaces still lags far behind that of geckos, mainly because our understanding of how geckos govern their locomotion is still very poor. To reveal the fundamental mechanism of gecko locomotion and also to facilitate the design of gecko-mimicking robots, we have measured the reaction forces (RFs) acting on each individual foot of moving geckos on inverted, vertical and horizontal substrates (i.e. ceiling, wall and floor), have associated the RFs with locomotion behaviors by using high-speed camera, and have presented the relationships of the force components with patterns of reaction forces (PRFs). Geckos generate different PRF on ceiling, wall and floor, that is, the PRF is determined by the angles between the direction of gravity and the substrate on which geckos move. On the ceiling, geckos produce reversed shear forces acting on the front and hind feet, which pull away from the body in both lateral and fore-aft directions. They use a very large supporting angle from 21° to 24° to reduce the forces acting on their legs and feet. On the floor, geckos lift their bodies using a supporting angle from 76° to 78°, which not only decreases the RFs but also improves their locomotion ability. On the wall, geckos generate a reliable self-locking attachment by using a supporting angle of 14.8°, which is only about half of the critical angle of detachment.

The influence of head and body tilt on human fore-aft translation perception.

The tilt-translation ambiguity occurs because acceleration due to translation cannot be differentiated from gravitational acceleration. Head tilt can occur independent of body tilt which further complicates the problem. The tilt-translation ambiguity is examined for fore-aft (surge) translation with head and/or body orientations that are tilted in pitch 10° forward or backward. Eleven human subjects (six female), mean age 40 years participated. Conditions included no tilt (NT), head and body tilt (HBT), head only tilt (HOT), and body only tilt (BOT). The fore-aft stimulus consisted of a 2 s (0.5 Hz) sine wave in acceleration which a maximum peak velocity of 10 cm/s. After each stimulus, the subject reported the direction of motion as forward or backward. Subsequent stimuli were adjusted to determine the point at which subjects were equally likely to report motion in either direction. During the HBT, responses were biased such that upward pitch caused a neutral stimulus to be more likely to be perceived as forward and downward pitch caused the stimulus to be more likely to be perceived as backward. The difference in the point of subjective equality based on the direction of tilt was 3.3 cm/s. During the BOT condition, the bias with respect to the direction of body tilt was in a similar direction with a difference in PSE 1.6 cm/s. During HOT and NT, there was no significant bias on fore-aft perception. These findings demonstrate that body tilt shifts the PSE of fore-aft direction discrimination while head tilt has no influence.

Hurricane-Induced Loads on Offshore Wind Turbines with Considerations for Nacelle Yaw and Blade Pitch Control

During extreme tropical storm systems such as hurricanes, offshore wind turbines are required to have adequate structural integrity in parked condition and with blades pitched to feather. Such turbine states are preferred in order to mitigate loads on the turbine blades; simultaneously, yaw control is required so as to track the changing wind direction in this configuration. During a hurricane, however, it is possible that a turbine's yaw control system might operate abnormally due to damage of the control and protection system or due to loss of the electric grid and/or insufficient backup power. In earlier studies, the authors have shown that feathered blades can lead to higher tower bending moments in the side-to-side (lateral) direction rather than in the fore-aft (longitudinal) direction. In the present study, we carry out an in-depth investigation of the effect of several alternative parked configurations on an offshore turbine's response using numerical simulations with coupled wind-wave fields during a hurricane. We use these output wind-wave fields obtained from the University of Miami Coupled Model (UMCM), a fully coupled atmosphere-wave-ocean model that is used to simulate the storm and associated environmental fields and is able to represent relevant physical processes at the air-sea interface. In this study, we evaluate: (1) the effect of different nacelle yaw angles relative to the wind direction (i.e., different amounts of yaw error or misalignment); (2) the effect of different blade pitch angles; (3) the effect of different turbine parking strategies—e.g., parked and at a standstill or in an idling state; and (4) load maxima at different blade azimuthal configurations while the turbine is in a standstill state. The effects of the different turbine parked configurations on turbine response are evaluated under only wind loads first; later, wave loads are included to reflect possible joint metocean conditions likely to be encountered during a hurricane.

Aerodynamic Damping and Seismic Response of Horizontal Axis Wind Turbine Towers

AbstractAerodynamic damping has an important effect on the seismic response of horizontal axis wind turbines (HAWTs). Some researchers have estimated that aerodynamic damping in operational HAWTs is ∼5% of critical in the fore-aft direction (i.e., perpendicular to the rotor and parallel to the prevailing wind). In most recent studies, dynamic analyses of HAWT towers under seismic loads have neglected aerodynamic damping, and this assumption has significant implications in the predicted seismic response. This paper presents a closed-form solution for the aerodynamic damping of HAWTs responding dynamically in the fore-aft and side-to-side directions. The formulation is intended as a convenient method for structural earthquake engineers to include the effect of aerodynamic damping in the seismic analysis of HAWTs. The formulation is based on blade element momentum theory and is simplified by assuming a rigid rotor subjected to a steady and uniform wind oriented perpendicular to the rotor plane. This paper ex...