AN ANALYSIS 0 FU AN

by,

John D. Funk, Jr." and

Corin P. Beck

Aero Analysis Division Naval Air Warfare Center

P.O. Box 5152 Warminster, PA 18974-0591

ABSTRACT Ship-based flight operations include environmental conditions that present challenges when math-

ematically modeling aircraft. An analysis of three methods for incorporating turbulent airflow similar to that near a ship into a blade element rotorcraft dynamic simulation model is presented. The purpose of the analysis is to increase the understanding of the characteristics of rotorcraft dynamic response to tur- bulence using different sampling resolutions. The turbulent airwake of a ship contains regions with severe velocity gradients and widely varying turbulence length scales. The inclusion of turbulence into the mathematical model of a fixed-wing aircraft usually involves the addition of the turbulent wind veloci- ties and gradients at the center of gravity. The motion of the helicopter rotorblades through local velocity variations causes those components to experience turbulent velocities radically different from those experienced by the center of gravity (CG). In this analysis a blade element rotorcraft model has been modified so that the velocities of a simulated flowfield in an inertially based coordinate system may be sampled by individual blade elements, the empenage and the tail rotor. The frequency characteristics of simulated helicopter dynamic responses using two levels of sampling resolution are compared to those produced using CG sampling. These comparisons reveal frequency ranges where strong differences between the responses exist. Within a specific frequency range, magnitude and phase predictions for the distributed sampling schemes depart significantly from those of the CG sampling scheme. Through analysis, the response variations are shown to occur when the input turbulence length scales (spatial wavelengths) are of the same order of magnitude as the main rotor diameter.

LIST OF SYMBOLS p Roll Rate g Pitch Rate r Rotor Radius Station u Forward Body Velocity x Body Axis Coordinate y Body Axis Coordinate z Body Axis Coordinate

C Rotor Rolling Coefficient C MRotor Pitching Coefficient C Rotor Thrust Coefficient CG Center of Gravity

* Member, American Helicopter Society

RP Parial Rotor RT Total Rotor

y Lateral Shaft Angle y Longitudinal Shaft Angle

6Small Perturbation A Difference 0 Euler Pitch Angle

Euler Roll Angle \Y Euler Yaw Angle

Y BRotor Blade Azimuth Angle

This paper is declared a work of the U S . Government and is not subject to copy- right protection in the United States.

1

Dynamic Interface (DI) is the dynamic interac- tion between a ship and a rotorcraft during termi- nal operations. At present, all helicopter/ship combinations must be tested through a range of operating conditions before clearance is given to use that combination. The Dynamic Interface Department at NAWCADPAX is faced with the for- midable task of testing all possible helicopter/ship combinations at all possible operating conditions. The addition of the capabil' to reproduce the DI

assist in the training of DI test pilots, thereby increasing safety and reducing the likelihood of equipment damage. DI simulation capability will also provide information to DI flight test engineers that will allow them to "test smarter', highlighting the critical operating conditions where difficulties were predicted during simulation and optimizing flight test profiles.

During DI testing, an operating condition is pri- marily characterized by wind-over-deck magnitude and the wind azimuthal angle. The result is a polar plot of the recommended launch/recovery envelope for a particular helicopter/ship combina- tion. Other elements encountered in the DI envi- ronment are ship motion, sea state and visual cue limits.

DI simulation requires improvement of vehicle models, modeling of the turbulent atmosphere in the vicinity of the ship, modeling of ship motion and its interaction with both vehicle dynamics and aerodynamics, and the improvement of simulation hardware to facilitate a sonable representation of these conditions. Mc af the DI simulation elements are being addressed by NAWC either directly or through contracts.

environment during manne TT flight simulation will

Turbulence Modeling The vehicle model analyzed here allows the

turbulent atmosphere in the vicinity of the ship to be represented within the rotorcraft math model. For the rotorcraft model to sample the small-scale local air veloctty variations that exist in the turbu- lent air currents around a ship, the model aerody- namic sampling point must be extended from the rotorcraft center of grav to the rotorblades, tail

and aerodynamic interaction of the cyclic encoun- ter of individual rotorblades with the windshear regions in the airwake of the ship to be modeled.

Development of a spatially correlated, three- dimensional turbulence model for rotorcraft appli- cation is ongoing [1,2]. In these turbulence models, the collective influence of arrays of filtered white noise sources is calculated at each spatial location where an aircraft aerodynamic compo- nent exists. The spatial variation of turbulence

surfaces and tail rotor. T % is permits the dynamic

mean velocity, length scale and intensity can be represented using these models. These models are ideally suited to represent the turbulence in a ship airwake and should eventually operate in real-time.

For the successful real-time simulation of DI operations, turbulence will need to be represented efficiently. The minimum resolution required to accurately represent the influence of ship airwake turbulence on the helicopter dynamics for flying qualities applications must be used. Inclusion of ,additional frequencies or spatial resolution will waste computation time. In addition, sampling of the turbulent velocity field must be minimized since it also requires additional computer time. This analysis, though brief, should provide addi- tional information on the resolution requirements for simulation of rotorcraft dynamic response to turbulence.

The analysis presented subjects a rotorcraft math model using three different atmospheric sampling schemes to simulated atmospheric dis- turbance forms so the degree of modeling reso- lution required to simulate flight in turbulence can be better understood. Atmospheric disturbances examined are of a frozen frame form and are fixed to an inertial base, sort of a standing wave form. A turbulence 'frequency sweep' field is used to calculate the frequency response characteristics of all three schemes to a vertical gust and to highlight their differences. A sinusoidal pulse gust input at a specific length scale is used to highlight differences between the models in the time domain.

During simulation of conventional random tur- bulence of the Dryden or Von Karman form [3], output from random number generators is shaped .using digital filters to produce turbulence compo- nent velocities with specific spectral density char- acteristics. The sequences of random gusts are assumed to form a stationary random process, in essence, the spectral density characteristics are invariant with translation. Since the process is stationary it is possible to assume the probable characteristics of the spectral density over a spe- cific aircraft characteristic length. This fact is used to provide spectral density functions for angular disturbance turbulence inputs from which, angular disturbance filters are constructed. These angular disturbance filters induce angular responses that essentially correct the CG sampling simulation models so that the angular rates respond in coor- dination with the stationa turbulence spectra. A

field with a spatially varying spectral denstty dis- turbance field is not stationary. Spectral dens'tty functions become functions of spatial location and the spectral density function at the CG cannot be used to provide the probable angular disturbance characteristics. For this reason angular distur- bance corrections are assumed to be inappropri-

ship airwake, or an inertia 7 ly based disturbance

2

ate for this analysis. There is no way the characteristics of the velocity field can be known without sampling them.

The Rotorcraft Math Model The rotorcraft model in this analysis uses a

blade element rotor model. To date, blade ele- ment models have the highest degree of fidelity for real-time rotorcraft dynamic simulation. Blade element models combine the six rigid-body fuse- lage degrees of freedom with additional rotor degrees of freedom and therefore represent the vehicle dynamics much more precisely than other forms of rotorcraft math models. The blade ele- ment rotor model is required if local veloclty sam- pling is to be utilized.

The GENHEL UH-60 computer program [4,5] was used for the baseline blade element math model. It was developed by Sikors and exten-

ter. The Program has also been validated in hover 61 and forward flight [7]. The model is a total I orce, non-linear, large angle dynamic model that

allows the modeling of any realistic steady or maneuvering flight condition. In the GENHEL model [4] several improvements over a rough strip approximation have been made: Dynamic blade twist corrections have been added. Fuse- lage blockage corrections have been included. Dynamic inflow has been added [8]. These aerodynamic corrections contribute to the result- ing blade element angles of attack and result in a change in force distribution over the main rotor. Calculation of the blade element angles of attack due to prevailing winds, turbulence, and vehicle motion is performed by taking those velocities, as sampled, at the CG location and transforming them through the body axis into the rotating blade axes.

Incorporation of Turbulence into Rotorcraft Simulation

It has been shown analytically [9,10) that CG sampling cannot correctly represent the physics of a rotorcraft encountering atmospheric turbu- lence. When large variations of wind velocity exist in a relatively small region, inaccuracies of CG sampling are compounded with those created by ignoring the rotating frame. To incorporate a ship airwake into rotorcraft simulation, the airwake should be sampled by all represented aerod - tions. In this analysis, this is performed by determining the spatial location of the components in earth-based coordinates, deter- mining the components of the local wind at that location and transforming that velocity into the coordinate system of the component for aerody- namic force calculation.

sively improved at the NASA Ames 2 esearch Cen-

namic components at their respective spatia Y loca-

TH L The rotorcraft dynamic math model utilized in

this analysis is composed of six fuselage degrees of freedom, additional flap and lag degrees of free- dom for each blade and the shaft rotational degree of freedom. To calculate the spatial position and velocity of the blade element at any time, several coordinate transformations must be performed. Velocities referenced to the earth-or ship-based coordinate systems must be resolved into the body, hub, shaft and blade element axes.

The Blade Element Model Aerodynamic Force Calculation,

Rigid Fully Articulated Blades . The aerodynamic components modeled in GENHEL are the rotor blades, the fuselage, the vertical stabilizer, the horizontal stabilizer and the tail rotor. Contributions to the total air velocity on these components are from the wind, motion of the component and the induced velocity from the aerodynamic components. Angles of attack of the components result from their configuration and the sum of the incident velocities.

lage and tail surfaces come from a table lookup using velocity incidence angles. Main rotor downwash effects are included in these calcula- tions. The tail rotor model used is based on Bailey theory [I I ] . This is a linear rotor theory that provides force and moment information resulting from a series of calculations using closed form equations based on the rotor system geometry, mass properties, configuration and operating con- dition. Aerodynamic forces and moments on the main rotor blades are calculated by summing contributions from individual spanwise blade ele- ments. Blade element forces and moments result from a table lookup using angle of attack and Mach number. Corrections to the angle of attack for yawed configurations are also included.

Aerodynamic forces and moments on the fuse-

* Rotor Dynamics The main rotor blade forces and moments act

on the blades, producing flapping and lagging oscillations as well as changes in main rotor torque. The equations used to describe the flap- ping and lagging motion are nonlinear and are derived by taking derivatives of the blade position vector. Variations in the shaft rotational degree of freedom result from the interation of the engine dynamics as well as rotor inertia and torque varia- tions due to aerodynamic blade drag.

To permit real-time operation, the GENHEL program assumes a first-order harmonic solution with time-varying coefficients for the flapping and lagging motion of each blade. This allows the blade motion integration to converge with a larger time step. The equations of motion are integrated numerically.

3

Downwash Calculation An accurate prediction of the veloclty induced

by the main rotor is vital when predicting helicop- ter dynamic response. Comparisons of the calcu- lated UH-60 response using two forms of inflow modeling are given in reference 6. It is best for downwash estimation techniques to have a dynamic character to simulate dynamic responses resulting from rapid changes in cyclic or collective controls, changes in blade angles of attack due to turbulence or rapid rotor configuration changes during maneuvers, Downwash or inflow with this characteristic is termed dynamic inflow.

The Ames GENHEL program has the option to use one of two methods for downwash prediction, the Howlett inflow model [4] or the Pitt and Peters dynamic inflow model [8 ] . For all simulation pur- poses the Pitt and Peters model is recommended and is more theoretically correct when simulating flight in turbulence because it includes an addi- tional airmass degree of freedom that improves the accuracy of the transients in rotor force calculations.

Rotorcraft Coordinate Systems For this analysis helicopter aerodynamic com-

ponent positions must be calculated relative to an inertial reference frame. The component locations are given in non-inertial coordinates and must be resolved into the inertial frame. The primary trans- forms are from the earth to the body coordinates through the Euler angles and from the body into the blade coordinates.

Euler Angles and Body Coordinate Definition The body coordinates are aligned with the air-

craft principal axes, with the body x extending forward through the nose, y out the right side of the fuselage and z extending down from the CG. The Euler angles, ,8 and Y, corresponding to roll, pitch and yaw, are applied to the body axes. These angles provide the information required to transform vectors from the body axes into the inertial reference frame.

Shaft, Hub and Blade Coordinates The hub center is offset from the CG location.

In addition, the axis about which the hub rotates is not aligned with the body z axis but is rotated into the shaft axis through the angles y and y y . The origin of the hub and shaft axes are coincident. The hub axes are parallel to the body axes. The z coordinate of the rotor rotational axis is parallel to the shaft z coordinate, and each blade angle Y.B is measured from the - x coordinate of the shaft axis system. The components of the blade coor- dinate systems line up as y in the spanwise, x parallel to the coning plane and z perpendicular

to the coning plane. A more detailed description of these coordinate systems can be found in Ref- erence 4.

Local Velocity

positions are used to sample local velocities. Wind routines previously implemented within the GENHEL program structure distribute ambient winds, as sampled at the CG, to all helicopter aerod namic components. To reduce the disrup-

ity at an aerodynamic component was computed by sampling the velocity local1 calculating the

then adding the velocity "A' due to the variations.

Methods utilized for the calculation of rotor induced velocities must have the capacity to rep- resent changes in inflow due to changes in the local rotor blade angles of attack. The Pitt and Peters [8] dynamic inflow model used in the GEN- HEL program has this capacity to a limited extent. The inflow model used is in the form of a shape function with time varying coefficients. The shape function is a first-order harmonic distribution in the azimuth angle, Y and a Legendre polynomial in the radial dimension, T-, Since the azimuthal distri- bution is limited to first-order, higher harmonic effects are excluded from the solution. But, since the GENHEL main rotor integration scheme assumes a first-order flapping solution, the higher harmonic effects are also excluded at the rotor dynamics level. Since main rotor pitching, rolling moments and heaving forces have the greatest effect on tangible vehicle responses, these first-order expansions are assumed to be ade- quate for this analysis.

The rotorcraft aerodynamic component inertial

tion o Y original program structure, the local veloc-

veloctty difference due to loca r velocity variations,

Distribution of Turbulence The wind velocity at the CG-is sampled trans-

formed and distributed throughout the aircraft by .the GENHEL program. This produces velocities on the aerodynamic components based on the turbulence as sampled at the CG location. These velocities do not include local wind veloctty varia- tions since they are 'ust the velocity, as seen by

of the aerodynamic components. When the ambi- ent velocities are sampled at the inertial locations of the aerodynamic components by the GENHEL modification routines (turbulence routines) they cannot be added directly to the component veloci- ties since these contain the turbulence contrib- utions as sampled at the CG. The turbulence routines are then used to calculate a " A " that is the turbulence difference between component sampled turbulence and the CG sampled turbu- lence, These " A s"are added to all the aerody- namic component velocities, completing the veloctty distribution process.

the CG, transforme d into the coordinate systems

4

Induced Velocity Considerations and Algorithm Integrity

Ambient velocity variations across the rotor disk cause changes in the disk loading distribu- tion. Through changes in momentum exchange, these loading changes produce variations in the downwash or inflow distribution. Therefore any inflow calculation scheme must, to some extent, be sensitive to changes in the disk loading distri- bution. The inflow model employed by the GEN- HEL program uses a first harmonic distribution of inflow calculated from the disk C , C and C L. More accurate results might be expected if a higher harmonic inflow scheme such as the one described in reference 12 were used, but the addi- tion of this capability is not within the scope of the present work.

The correctness of the enhanced model was checked by simulating translations through known deterministic gust forms. Component velocities were compared with hand calculations. Dynamic responses to the gusts were examined in detail by examining all contributing aerodynamic forces.

RESPONSE TO TURBULENCE WITH AN ALY S I S

The primary objective of the modeling effort is to provide a real time simulation capabili within a ship’s turbulent airwake. Since G sam- pling is less computationally costly, it should be used if it is shown to produce accurate response types. The comparisons presented highlight fre- quency ranges with response differences for the models with different sampling resolutions. Also of interest are the turbulence spatial length scale resolution requirements.

The atmospheric sampling techniques used are CG sampling, partial rotor sampling and total rotor sampling. Using CG sampling, the only air- craft point sensing the turbulence field is the CG location. Total rotor sampling methods calculate the inertial location of all blade elements and sam- ple the turbulence field there. In addition, the CG, empenage and tail rotor points are also sampled with total rotor sampling. Partial rotor sampling uses the blade element closest to .75R, which is segment 4 at .79R and applies that turbulence field value to the entire rotorblade. This has the advantage of rotating frame sampling at one-fifth the computational cost of sampling at all blade elements. CG, empenage and tail rotor sampling are also conducted during partial rotor sampling. Responses calculated with the total rotor sam- pling method are assumed to be the most accu- rate and serve as the baseline for comparison. In this analysis, five blade elements per blade were used and the sampling frequency of 100 Hz was the same as the integration time step.

8 Of flight

The turbulence frequency response is calcu- lated by recording the simulated helicopter response to an atmospheric disturbance field containing a full spectral content in the frequency ranges of interest and processing the input and output spectral density functions. The results of this analysis are then used to predict the frequen- cies of turbulence that strongly or weakly affect the magnitude and phase of the response. Also included in the results is the coherence function. This provides an indication of how much confi- dence can be placed in a linear approximation of the input/output relationship. To use this form of analysis, the aircraft velocity and attitude must remain reasonably close to the initial trim condi- tion (sta within the linear, small perturbation

removed by breaking up the correlation between the turbulence and the control inputs and remov- ing control contributions from the output s ectral densities. Fortunately, the flight condition P input combinations examined here sfayed reasonably close to trim without the use of stabilizing controls. . Frequency Response Analysis Techniques

All frequency response calculations were per- formed using the FRESPID (Frequency RESPonse IDentification) component of the ClFER (Comprehensive Identification from FrEquency Responses) program, which is an integrated soft- ware facili developed at the NASA Ames

z-transform, a fast Fourier transform algorithm which allows very fine frequenc resolution for a

ping Hanning windows to produce low spectral variance through averaging. In this analysis, three different window sizes were used to span the fre- quency ranges of interest. Outputs from FRESPID that were of primary interest were the output/input transfer function magnitude, phase and coher- ence. The recommended system input type to produce responses for analysis with the FRESPID module is a frequency sweep.

Turbulence Frequency Sweep Field

range). t he effects of stabilizing controls must be

Research 2 enter [13]. FRESPID uses the Chirp

specified window size. FRESPI YD uses overlap-

To isolate the response to gusts in one inertial direction, a gust component in the vertical direc- tion was selected (W gust). This is a restriction on .this analysis. In the future, the responses to longitudinal and lateral gust fields should be examined. This turbulence gust field was in the form of a frequency sweep. The form of frequency sweep used in this analysis uses a spatial wave- length that varies as a function of spatial position. The wavelength or turbulence length scale is defined as the peak to peak distance between two adjacent turbulence cycles. The largest turbu- lence length scales considered in this analysis is ap roximately 20 rotor radii. Throughout the tur E ulence field, the primary turbulence wave-

5

length is swept continuously to a length of approx- imately .25 rotor radii. The effect this type of disturbance field has on a helicopter translating through it at a constant speed is that the distur- bance begins at a low frequency and ends at a high frequency, thus exciting a wide variety of vehicle dynamic modes. The combination of the length scale, turbulence frequency sweep velocity field and the nominal flight condition was required to: 1) span the fre uency ranges of interest .1 to 2

est 20R to .25R; 3) represent a DI type flight condi- tion (relatively low ground-track and airspeed). To fill the input spectra at low and high frequencies, a logarithmic frequency sweep was combined with filtered white noise. This technique was sug- gested in 161. A total record time of 100 seconds was required and the nominal field penetration speed was set at 30 FPS. The total field length is 3000 ft. The sweep frequency length scale on the long side is 500 ft. This is swept to 4 feet at the hi h frequenc side. With a gust penetration

are .06 Hz and 7.5 Hz respectively. Figure 1 shows the normalized version of the gust field.

Hz; 2) span the tur a ulence length scales of inter-

ve 7 ocity of 30 FPS, the lower and upper frequency

Nominal Flight Case The airspeed for the nominal flight case was

selected to be approximately 30 knots (50 FPS), and the ground track speed 30 FPS so, a 20 FPS headwind was applied. The spatial position of the turbulence field was shifted 300 feet to permit 10 seconds of undisturbed flight. Total simulated flight time was 100 seconds. The disturbance magnitude was scaled so that reasonable response magnitudes were obtained. Of primary interest was the vertical acceleration, w, the roll rate, p , and the pitch rate, g . The time history of the gust input as sampled at the aircraft CG is shown in Figure 2. The input auto spectrum for this input is shown in Figure 3. The input RMS value IS 7.8. With a .75 radius rotor blade speed of 543 FPS, this corresponds to a rotor perturba- tion angle of attack magnitude of approximately 1 degree. During the run approximate maximum response magnitudes were, 6 w = *6 FPS, 6 p = *lo deg/sec, 6 g = deg/sec. The largest dr i i was in the forward veloctty, u . The time history of this variable, plotted as airspeed, for the CG and total rotor sampling cases is shown in Figure 4. Since the total drift was less than 10 FPS, stabilization controls were not required. The drift of all the other response variables was insig- nificant.

Frequency Response Comparison of Three Sampling Techniques

Comparisons of the calculated fre uency

acceleration, ti, roll rate, p , and pitch rate, q , are shown in Figures 5, 6, and 7 respectively. The

responses for the sampling schemes 9 or vertical

dynamic integration in the rotorcraft model is per- formed at 100 Hz so the analysis cutoff frequency is taken at approximately 10 Hz. The low frequency limit is the minimum frequency for the given data window size. In Figures 5, 6, and 7 a five second window was used corresponding to a minimum frequency of 1.26 rad/sec. With the phase and magnitude information, are values of the coherence function. Tnis pyameter is used to measure the confidence that can be assumed when using the corresponding phase and magni- 4ude information. Generally if frequency range for a response has coherence values less than .6, only a limited amount of confidence can be placed in the response, within that ranae. The responses were processed using two larger window sizes to examine the response characteristics at lower fre- quencies and the magnitude, phase and coher- ence values for all three sampling forms remanded similar. For simplicity, the total rotor model will be referred to as the RT model and the partial rotor model as the RP model.

Several observations can be made from the vertical acceleration response. The values of magnitude, phase and coherence at both the low and high frequency limits of the plots for all three samplin schemes are similar. The trends of the

there are megnitude offsets between the frequen- cies of 2.5 and 3.7 rad/sec. The RT and RP phase is offset between the frequencies of 3.0 and 7.0 rad/sec. The curves are coincident for most of the frequency range. The CG model misses much of the dynamics. The magnitude drop for frequen- cies around 3.2 rad/sec is missed and the fphse shift ocurring at that frequencyls also missed. Values on the coherence curves for the RT and .CG models remain close enough to unity to accept the linear response calculation with confi- dence. The coherence dip that occurs at the 3.2 rad/sec frequency of the RT solution is exaggerated in the RP solution. With the excep- tion of a narrow frequency range the coherence for the RP solution is relatively high.

The roll rate frequency responses for the three schemes are shown in Figure 6. Many of the low and mid frequency response characteristics are missed by the CG sampling scheme, but at fre- quencies above 18 rad/sec the CG magnitude and phase curves are similar to RT and RP curves. The RT and RP phase curves are offset from the CG curve at lower frequencies, but are close at high frequencies. The phase shift in the RP plot at 10 rad/sec occurs at a frequenc with a

difference between the FIT and RP responses is zero. Within two frequenc ranges, RT and RP

6-1 0 rad/sec appears to be from modeling differ- ences. The second range, from 12-1 5 rad/sec occurs when the coherence values are very low and the cause is not clear. Through the entire

RT and B P shemes are very similar, although

low coherence. At most frequencies the p K ase

magnitudes are different. 1: he first range, from

6

frequency range, the coherence of the cg model is relatively high. The coherence curves for the RT and RP models have a dip similar to the dip in the vertical acceleration response, except, it is at a higher frequency. At 9 rad/sec the coherences drop off sharply and remain low up to a frequency of 23 rad/sec only a limited amount of confidence can be placed in the RT and RP magnitude and phase curves in this frequency range. The low and high frequency trends of the responses are similar. When examined at lower frequencies the offsets in the phase magnitude and coherences remained.

The pitch rate frequency response is shown in Figure 7. Throughout the entire frequency range the two distributed sampling schemes have similar magnitude and phase characteristics. There is a cohernece dip at 5.6 rad/sec similar to those in the tirand p plots. Other than a gradual decrease in magnitude over the frequency range, the CG sampling sheme fails to capture most of the dynamic characteristics found in the RT and RP magnitude plots. The CG phase plot also misses the characteristic trends found in the RT and RP plots. At fre uencies less than 3 rad/sec the trends of all R t ree sampling schemes are similar.

One common characteristic of Figures 5, 6 and 7 is that most of the large discrepancies between the responses exist in the frequency range from 1-1 0 rad/sec. To examine this frequency ran e in greater detail a larger window size was used 9 or processing and a second flight case was com- pared to the nominal flight case. The second flight case was simulated with a lower penetration velocity.

Variation of Penetration Velocity The second flight case was selected to have

the same characteristics as the first accept the headwind veloctty was .increased from 20 FPS to 30 FPS this reduced the ground track from 30 to 20 FPS. This had the effect of reducing the tem- poral frequency of turbulence with similar length scales. To understand this better, refer to Figure 8. Shown are plots of the turbulence length scale (spatial wavelength) in feet and encounter fre- quency in rad/sec as a function of time for the two flight cases. From Figure 8 it is apparent that the encounter frequency for the modified 20 FPS penetration velocity case never gets as high as the encounter frequency for the nominal 30 FPS case. The length scale associated with a given frequency can be computed approximately by using Figure 8 and: 1) finding the time at which the specific frequency first occurs (right y axis).; 2) moving up or down on the plot to find the corre- sponding length scale at that time (left y axis). Length scales corresponding to specific similar frequencies for the nominal and modified fli ht cases are different. A check run using the 8 G sampling scheme was performed and the roll rate response comparison is shown in Figure 9. The

frequency responses for the CG sampling case were identical at both penetration velocities. Fig- ures 10 thru 12 compare the responses of these two flight cases using the RT sampling scheme. Since a different window size was used to process the responses, some values may differ from those in Figures 5 through 7.

Figure 10 compares the vertical acceleration responses of modified to the nominal flight case. The character of responses are similar except for a frequency shift. The dip in the magintude curve that occurs at 3.4 rad/sec in the nominal case is shifted to a frequency of 2.3 rad/sec in the modi- fied case. A similar shift is in the phase curve.

Differences in the character of the two roll rate response is evident in Figure 11. It is difficutt to compare the two roll rate response plots because the modified flight case response is shifted so much. A comparison of Figure 11 to Figure 9 reveals that CG sampling does not model this characteristic.

The magnitude curves of the pitch rate responses, shown in Figure 9, show a clear shift. The dip that occurs at 5.8 rad/sec for the nominal case is shifted to 2.8 in the modified case.

Figure 8 is used to correlate the frequencies with the associated turbulence length scales at a specific time. The magnitude dip shown in Figure 10 for the nominal case is at a frequency of 3.4 rad/sec. From Figure 8 the turbulence length scale that corresponds to this dip is 59 feet. The shifted magnitude dip from the modified flight case corresponds to a 62 foot turbulence length scale. The minimum magnitude points in the pitch rate comparison in Fi ure 12 corres ond to length

for the modified case. Since there was some .degree of difficulty with the determination of the shift in the roll rate plots they are not discussed. With this information, three observations can be made

scales of 35 feet 3 or the nomind P case and 49 feet

1. The location of the minimum points on the magnitude curves described appear to be a function of turbulence length scale and not necessarily encounter frequency.

2. The turbulence length scales most likely to exhibit this characteristic are of the approx- imate size as the rotor diameter.

this response characteristic. 3. Single-point CG sampling cannot capture

Response to Discrete Pulse To examine the effects of the large differences

between CG and RT sampling as predicted by frequency domain analysis in the time domain, simulated response time histories for the schemes to a descrete pulse gust are shown in Figure 13. The nominal flight case was used and the input gust is shown in the Figure. The gust is a sinusoi-

7

dal pulse with a base width of 60 feet and a peak amplitude of 20 FPS in the vertical direction. The length scale (width) of this pulse and associated encounter frequency correspond to the low point in the RT magnitude trace in Figure 5. This fre- quency/length scale of 3.4 rad/sec and 60 feet was selected since the frequenc response

between the RT and CG models at that input frequency. The total time of the simulation was 30 seconds, with a time of encounter with the turbu- lence of two seconds. No stablilization controls were used.

As predicted in Figure 5, the magnitude of the CG vertical acceleration response is greater than that of RT and the CG response lags the RT response. The magintude difference seems understandable since in the CG sampling case the entire rotor encounters the gust while the CG is in it and in the RT case the entire rotor only encounteres the gust when it is centered in the gust. In the frequency response analysis, Figure 6 predicts a larger magnitude for the RT roll rate response and again, a phase lag for the CG response. In the roll rate response of Figure 13, the maximum amplitude ot the CG response is approximately half the amplitude of the RT response and it also lags the RT response. Physi- cally it is understandable that the magnitude of the angular rate responses are not as large for CG sampling since none of the assymmetry of the gust over the rotor is included. Figure 7 predicts a large amplitude difference between the CG and RT pitch rate responses, and a near-zero phase difference between them. This compares well with the pitch rate time history in Figure 13. The maxi- mum amplitude of the pitch rate response is about three times as great for the RT sampling scheme as CG scheme and the two responses have a very low phase difference.

CONCLUSIONS This analyses presented comparisons of the

dynamic responses of a rotorcraft model whith three atmospheric sampling schemes. Both the baseline rotorcraft model, the Ames GENHEL model, and the analysis techniques, frequency domain analysis using frequency sweep inputs with the ClFER code for response prediciction were very effective for producing the required results. The results are for flying qualities applica- tions cannot be extended to frequencies above 10 Hz. The following conclusions can be made from the results.

e Turbulence encountered with length scales of approximately the main rotor diameter will create different responses if it is sampled using CG sampling or total rotor sampling. These differences show up in the frequency as well as the time domain.

calculations predict significant di i! erences

Outside of the frequencybength scale range described and shown, the response of this model to vertical gusts should be similar for CG and total rotor sampling. Some offsets remained in the low frequen- cies, but the responses lo high frequency inputs should be similar for both schemes for flying qualities applications.

was captured well using partial rotor sam- pling. There were some frequency/length scale ranges where differences existed, but partial rotor sampling would provide enhanced fidellty at a lower computing cost. A more detalied analysis of partial rotor sampling might improve the scheme and remove some of the descrepancies between the responses.

0 The character of the total rotor response

ACKNOWLEDGEMENTS The author whould like to acknwoledge Mr.

Mark Ballin from the NASA Ames Research Cen- ter, the author of a major portion of the Ames GENHEL UH-60 simulation code for providing the code and assisting during the anal sis. The author would also like to thank Dr. bark Tischler from the Army Aeroflightmechanics Directorate, the author of the ClFER code for providing instruc- tion, and assistance for the analysis.

REFERENCES 1 Riaz, J., Prasad, J. V. R., Schrage, D. P.

and Goankar, G. H.; Atmospheric Turbu- lence Simulations for Rotorcraft Applica- tions ; American Helicopter Society 47th Annual Forum, Phoenix Arizona, 1991

2 Clement, W. F., Gorder, P. J. ; Modeling of Rotorcraft and Ship Dynamic Interface ; Systems Technology, Inc. TR-1288-1 , March 1992

3 Anon ; Military Standard 1797A, Flying Qualities of Piloted Aircraft ; 30 January 1990

4 Howlett, J. J. ; UH-GOA Black Hawk Engi- neering Simulation Program: Volume I - Mathematical Model ; NASA CR-166309, 1981

5 Howlett, J. J. ; UH-GOA Black Hawk En i- neering Simulation Program: Volume 19- Background Report ; NASA CR-166310, 1981

6 Ballin, M. G. and Dalang-Secretan, M. A. ; Validation of the Dynamic Response of a Blade-Element UH-60 Simulation Model in Hovering Flight ; American Helicopter Society 46th Annual Forum, Washington D.C. 1990

8

7 Ballin, M. G. ; Validation of a Real-Time Engineering Simulation of the UH-GOA Heli- copter ; NASA-TM-88360, February 1987

8 Pitt, D. M. and Peters, D. A.. ; Theoretical Prediction of Dynamic lnflow Derivatives ; Vertica, Vol. 5, 1981

9 Costello, M. F. ; A Theory for the Analysis of Rotorcraft Operating in Atmospheric Turbu- lence ; American Helicopter Society 46th Annual Forum, 1990

10 Costello, M. F. ; A Theo for the Anal sis of Rotorcraft Operating in X tmospheric f urbu- lence : Doctoral Thesis, School of Aero- space Engineering, Georgia Institute of Technology, Atlanta GA, 1992

11 Bailey,Jr. F. J. ; A Simplified Theoretical Method of Determining the Characteristics of a Lifting Rotor in forward Flight ; NACA Report 71 6,1941

12 Peters, D. A. and He, C. J. ; A Closed-Form Unsteady Aerodynamic Theory for Lifting Rotors in Hover and Forward Flight ; Ameri- can Helicopter Society 43rd Annual Forum, St. Louis MO, 1987

13 Tischler, M. B. and Cauffman, M. G. ; Com- prehensive Identification from Frequency Responses, ClFER Version 2 Users Manual ; Army Aeroflightmechanics Directorate Ames Research Center, Moffet Field, CA, 1992

9

- 1 . 1 ' ' ' ' ' ' ' ' ' ' ' ' . ' ' * ' ' ' 0 300 600 900 1200 1500 1800 2100 2400 2700 3000

GROUND-TRACK DISTANCE (FT)

Figure 1 Turbulence Frequency Sweep Velocity Field

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0 10 20 30 40 50 60 70 80 90 100 TIME (SEC)

Figure 2 Turbulence Frequency

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Figure 3 Turbulence Frequency Sweep Power Spectral Density

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Figure 4 Longitudinal Airspeed Time History

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Figure 6 Roll Rate Response Comparison

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Figure 7 Pitch Rate Response Comparison

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Figure 8 Time Histories of Turbulence Length Scale and Encounter Frequency

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Figure 10 Vertical Acceleration Response Comparison for Two Penetration Velocities RT Sampling

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Figure 11 Roll Rate Response Comparison for Two Penetration Velocities RT Sampling

Figure 12 Pitch Rate Response Comparison for Two Penetration Velocities RT Sampling

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Figure 13 Time History of Response to Descrete Gust

16