Subsonic-transonic stall flutter study

TABLE OF CONTENTS Section

Page

1.0 SUMMARY 2.0 INTRODUCTION 3.0 PROGR#¢_ APPROACH 4.0 TEST FACILITY AND EQUIPMENT 4.1 TS22 Fan Rig Description 4.2 Test Stand Description 4.3 Instrumentation and Data Acquisition System 4.3.1 Steady State Aerodynamic Instrumentation 4.3.1.1 Air Flow 4.3.1.2 Temperature 4.3.1.3 Rotor System 4.3.1.4 Air Flow 4.3.2 Structural Instrumentation 4.3.2.1 Optical Mirror System 4.3.2.2 Strain Gage Instrumentation 4.3.3 Unsteady Gage Instrumentation 4.3.3.1 Case Mounted Kulites 9 4.3.3.2 Blade Mounted Kulites 4.3.3.3 Hot Film Anemometers ii 5.0 TEST AND ANALYSIS PROCEDURES II 5.1 Test Procedures Ii 5.1.1 Shakedown Tests 5.1.2 Performance Tests 5.2 Data Reduction Procedures 5.2.1 Data Requirements 5.2.2 Specific Procedures 5.2.2.1 Steady-State Aerodynamic and Blade Deflection Data 5.2.2.2 Unsteady Data Reduction 5.2.2.3 NASTRAN Prediction Procedure 20 5.2.2.4 Blade-Work Interaction Calculation 21 6.0 DISCUSSION OF PROGRAM RESULTS 24 6.1 Overview 24 6.2 Test Matrix 24 6.3 STRUCTURAL DEFORMATIONS 25 6.3.1 Steady-State Deformations 6.3.2 Unsteady Deformations 6.4 PRESSURE DISTRIBUTIONS 27 6.4.1 Steady-State Pressure Distributions 6.4.2 Unsteady Pressure Distributions 6.5 VELOCITY FLUCTUATIONS FROM HOT FILM SENSORS 29 iv

TABLE OF CONTENTS (Cont'd) Section

Page

6.5.1 Upstream ana Downstream Velocity Fluctuations 6.5.2 Blade Surface Unsteady Velocities 6.6 REDUCED VELOCITY VERSUS INCIDENCE ANGLE 7.0 SUMMARY REMARKS 31 7.1 Loading Level 7.2 Local Separation 7.3 Oscillating Shocks 7.4 Reduced Velocity Versus Incidence 7.5 Center of Pressure-Center of Twist 8.0 SUMMARY of RESULTS 9.0 RECOMMENDATIONS 10.0 REFERENCES APPENDIX A - Overall Performance for Test Matrix APPENDIX B - Blade Coordinates APPENDIX C - PART i - Steady Blade Structural Data APPENDIX C - PART 2 - Unsteady Blade Structural Data APPENDIX D - PART 1 - Steady Pressure APPENDIX D - PART 2 - Unsteady Pressure APPENDIX E - Hot Film Data DISTRIBUTION LIST LIST OF ILLUSTRATIONS Number Title I Schematic Diagram of TS22 Rig 2 Distribution of Natural Second Mode Vibration Frequencies of Blades In Assembled Rotor 3 Schematic of X-204 Test Stand Circumferential Schematic View of TS22 Compressor Instrumentation 48 5 Circumferential Location of Blade Instrumentation 49 6 50 Schematic of TS22-X204 Laser Configuration Mirror Installation i_ocations 51 8 Installation Locations for Case-Mounted Kulite Pressure Transducers 52 Installation Locations for Blade-Mounted Kulite Pressure Transducer 53 10 Installation Locations for Blade-Mounted Hot-Film Sensors 54 Typical Laser Mirror Results For Operation at 67 Percent Speed In and Out of Flutter 12 56 Finite Element Diagrams Used for NASTRAN Analysis 13 Identification of Data Points at .70 Percent Speed, Including Transient From Open Discharge Into Surge TS22 Performance Map Showing Test Points In 5_q Relationship to Flutter Boundary 15 Measu:-ed Untwist for TS22 Fan Blade as a Function of Rotor Speed at q5 P..rcent Span lb Measured Untwist for TS22 Fan Blade at 73 Percent Speed Relative to (Intwist at 25.4 Percent Speed 6O 17 Measured Untwist For TS22 Fan Blade as a Function of Flow Rate at 75 Percent Speed LIST OF 1ll, li_lRATlON_ (L,'ont'd_ Title P ,_ _: .'0 'l "l • I _ Ill "4 _tt LIST OF ILLUSTRATIONS (Cont'd) NumbEr Title

Page

Steady-State Pressure Contours at Blade Tip at 73 Percent Speed Inside of Flutter on a High Operating Line Steady-State Pressure Contours at Blade Tip at 75 Percent Speed Outside of Flutter on a Low Operating Line Steady-State Pressure Contours at Blade Tip at 75 Percent Speed Outside of Flutter on a High Operating Line Steady-State Pressure Contours at Blade Tip at 85 Percent Speed Outside of Flutter on a Low Operating Line 78 Steady-State Pressure Contours at Blade Tip at 85 Percent Speed on a High Operating Line Steady-State Pressure Contours at Blade Tip at 85 Percent Speed Near Surge Unstead) Pressure Amplitude Contours for TS22 Rotor in Flutter at 73 Percent Speed Real Component of Unsteady Pressure in Flutter at 73 Percent Speed Imaginary Component of Unsteady Pressure in Flutter at 73 Percent Speed Blade Mounted Kulite Unsteady Pressure Amplitude and Phase Obtained in Flutter at 67 Percent Speed Signal Enhanced Wave Forms of Hot Film Probes at 73 Percent Speed (Noncalibrated Amplitudes) Blade Mounted Hot Film Unsteady Velocity Amplitude and _hase Obtained in Flutter at 67 Percent Speed Observed TS22 Flutter Boundary Correlation of Reduced Velocity as a Function of Incidence 87 viii LIST OF TABLES Title Number I TS22 Fan Stage Design Parameters II TS22 Blade Description Ill Leading Edge Angle Blade Inspection Results IV Trailing Edge Angle Blade Inspection Results 4O V Instrumentation and Readout Equipment Vl High Response Instrumentation Specifications VII TS22 NASA Flutter Test Matrix VIII Unsteady Wall Pressure Amplitudes for Individual Nodal Diameter Patterns Fundamental Modes Only (No Harmonics) IX Computed Damping in Dominant Harmonics at 70 Percent Speed ix

SECTION 1.0 SUMMARY The objective of the Subsonic/Transonic Stall Flutter Program was to obtain detailed measurements of both the steady and unsteady flow field surrounding a rotor and of the mechanical state of the rotor while operating in both steady and flutter modes. The data were obtained to provide a basis for future analy- sis and for development of theories describing the flutter phenomenon.

This objective was met using the Pratt & Whitney Aircraft TS22 research fan stage, which was extensively instrumented with high response rate instrumenta- tion and a laser optical system. The stage was tested over a range of operat- ing conditions both in and out of flutter.

A significant result of the program was a new conceptual understanding of the mode of flutter in the rotor system. Previously, fan flutter had been charac- terized by a single flutter frequency with all blades fluttering with similar amplitudes and equal interblade phase angles. The current program revealed that while all blades flutter at the same frequency, flutter amplitudes are not similar and interblade phase angles are not equal.

The steady pressure contours indicated that flutter may alter the blade pass- age pressure distribution.

The contour maps of unsteady pressure amplitude revealed regions of high amp- litudes near the leading edge, lower amplitudes near the trailing edge, and nodes near the midchord position. This pattern impties that the work input is concentrated near the leading edge. Design changes in this region should, therefore, have potential for preventing flutter.

The data shows that the location of the flutter boundary correlates with blade incidence and loading parameters and is influenced by relative Mach number.

Steady-state blade deformations agreed well with the NASTRAN predictions ex- cept blade uncambering exceeded predictions slightly.

SECTION 2.0 INTRODUCTION Flutter is an aerodynamically self-excited vibration in fan, compressor, and turbine blades. It can cause blades to fail and is of major concern.

The Subsonic/Transonic Stall Flutter Program, an experimental investigation, provided data for use in the formulation of analyses for predicting the onset of stall flutter in high-speed, axial-flow compressors.

The specific objective of the program was to obtain detailed measurementsof both the steady and unsteady flow field surrounding a rotor and the mechanical state of the rotor while the rotor operated in the steady and flutter modes.

This required testing and detailed performance mapping of a stage known to ex- perience subsonic/transonic stall flutter. The Pratt & Whitney Aircraft TS22 stage met this requirement.

A substantial body of data was obtained. The testing and detailed mapping pro- vided overall and blade element aerodynamic performance, information about the instantaneous flow field entering, passing through, and leaving the rotor, and information on the mechanical state of the rotor blades.

Performance and dynamic data were taken for 16 data points. These data have been used to evaluate the flutter boundaries and to determine details of the flow between blades in both the stable and flutter regimes. Blade stress and deflection data have been studied to evaluate analytical blade deflection prediction techniques for steady state operation and to determine mode structure during flutter.

Sections 3.0, 4.0, and 5.0 of this report describe the program approach, the facility and equipment used, and the data acquisition and reduction pro- cedures. The results of the program in terms of new understandings of the flutter phenomenon are presented in Section 6.0, discussed in Section 7.0, and summarized in Section 8.0. Recommendations for future work are given in Sec- tion 9.0, and References are identified in Section 10.0.

The full set of data obtained under the Contract is provided in the appendix.

Rotor overall performance and blade element performance are presented in Ap- pendix A. Rotor blade coordinate data, in Appendix B. The steady-state and dy- namic data, organized by instrument type, are presented in Appendices C, D, and E.

SECTION 3.0

PROGRAMAPPROACH The TS22 test stage selected for this program had aerodynamic and structural characteristics representative of an advanced fan stage and had exhibited stall flutter at intermediate speeds during prior testing.

Performance data were obtained by means of an automatic data acquisition sys- tem coupled with a numerically controlled probe traverse system directly link- ed to a Sigma 8 computer. The instrumentation for measuring steady-state de- flections and flutter characteristics of the rotor blades consisted of strain gages, an optical mirror system, and a speed signal. NASTRAN was used to cal- culate steady-state deflections.

Kulite pressure transducers were used to measure the pressure fluctuations on the case over the blade tips and on the airfoil surfaces. Traversing hot-film probes measured the time fluctuations of the local mass flow entering and leaving the test rotor. Two traversing probes were installed at each location to provide instrumentation backup. Hot-film anemometers located on the blade surfaces were intended to characterize the unsteady flow over the blades as laminar, turbulent, or separated and to determine the instantaneous location of shocks _nd separation.

The tests covered a ranqe of flows at speeds from 55 to 85 percent of design.

Overall p_-formance and detailed blade element data for the rotor were calcul- ated for II 16 data points. Detailed structural and dynamic data were calcu- lated for _ix selected points. Steady-state rotor blade deflections, measured by the optical mirror system data were compared with the deflections calcula- ted using NASTRAN. The unsteady mode shapes, deflection amplitudes, and phase relationships during flutter were determined from the case mounted Kulites, strain gages, and mirror" data.

Stability calculations were made for several mode shapes. Pressure distribu- tions over the blade tips were analyzed to determine shock locations and load- ing changes that occurred as speed and flow were changed. Real and imaginary components of unsteady pressure during flutter were determined as were phase relationships of unsteady pressures. Unsteady velocities ir,to and out of the rotor were determined, and the relative amplitude and phase relationship of unsteady v_locities on the blade surfaces were established. The reduced velo- city parameter and incidence angle based on measured flow and metal angles were determined.

4.0 TEST FACILITY AND EQUIPMENT 4.1 TS22 FAN RIG DESCRIPTION The TS22 fan rig combined moderate tip speed with a high pressure ratio, high flow rate per unit annulus area, and good efficiency. The 3.6 blade aspect ratio was aeroelastically aggressive _ven with a single pa_tspan shroud. The stage, with its 81.8 cm (32.21 in..) rotor tip di&_eter, was large enough to permit good definition of the unsteady flows, blade deflections, and mode shapes during flutter.

The TS22 rig is schematically represented in Figure I. Stage design parameters are listed in Table I, and rotor blade specifications, in Table II. Measured vector diagram data and additional performance data are given in Appendix A.

Blade coordinates are given in Appendix B.

New rotor btades were obtained for this study in order to minimize the poten- tial of fatigue failure, the original TS22 rotor having operated for many hours in the flutter region. The new blades were inspected and found to be within allowable tolerances. Blade leading and trailing edge angles were de- termined. The ,_aximum, minimum, and average edge angles at fourteen span loca- tions are compared with design values in Tabtes Ill and IV.

The second mode bending frequency of the isofated blades was considered to be representative of blade Flutter frequencies. Therefore, the second mode fre- quency with clamped root and unrestrained shrouds was measured for each of the thirty-two rotor blades. The minimum measured frequency was 241 Hz; the maxi- mum, 249 Hz. The blade positions in the rotor (Figure 2) were selected to min- imize differences in frequency between adjacent blades and provide a smooth frequency variation around the rotor.

4.2 TEST STAND DESCRIPTION The tests were conducted in the X-204 test stand at Pratt & Whitney Aircraft's Willgoos Turbine Laboratory in East Hartford, Connecticut. This stand, sho_vn in Figure 3, consisted of a test section with inlet air and exhaust systems, a drive motor, a computerized supervisory controt system with numerous safety devices, a computerized data acquisition system, and a variety of test sup- porting systems.

The airflow entered the rig through a calibrated orifice and a large-diameter plenum chamber. A wire mesh screen and an "egg crate" structure upstream of the plenum provided a uniform inlet pressure profile to the compressor. Air- flow was exh_Jsted into a toroidal cotlector through a back-pressure valve to the exhaust btowers.

The compressor drive was a variable-speed etectric motor connected to the test compressor through a speed-increasing gearbox. Electric power for the drive motor was provided from the laboratory powerhouse by four variable-speed, variable-frequency generators driven by a 6000-hp steam turbine.

4.3 INSTRUMENTATION AND DATA ACQUISITION SYSTEM Instrumentation provided full documentatiun of both steady-state and nonsteady aerodynamics and for rotor structural behavior in and out of flutter. The loc- ation of instrumentation is shown in Figures 4 and 5. Table V lists the in- strumentation and readout systems.

A fully computerized steady-state data acquisition was used during testing.

Data were transmitted to a computer located at the control room and then to an automatic data reduction computer which performed a preliminary data reduction and returned the results to the control room. These preliminary data were used to direct the test program. Positioning and readout of all the traverse probes at the rotor inlet, rotor exit, and stator exit were controlled by the rig automatic traverse system.

The steady-state data acquisition system for the .;tand recorded 232 channels of rig data: 131 pressure channels, 78 temperature channels, and 23 miscel- laneous millivolt channels. This system worked in conjunction with a high-re- sponse-rate system that recorded the data from the Kulite pressure trans- ducers, hot films, and strain gages.

Unsteady data recording systems for the Kulites, hot films and strain gages recorded a common 1:1 speed signal, common time code, and a common strain gage signal. Before start of testing, a common sine wave and a white noise signal were recorded on all system channels in order to determine frequency and phase response.

Data from the blade mirror system were recorded on still photographs, movie film, and video tape.

4.3.1 Steady-State_Aerodynamic Instrumentation Wedge probes measured total pressure, static pressure, and air angle. Combina- tion probes measured total pressure, static pressure, air angle, and total temperature. Wall taps were used for measuring wall static pressures, and to- tal pressure rakes were used for measuring stator exit tota_ pressures.

Pressures for steady-state operation were measured by a system of scanning valves and 24 vressure transducers with various pressure ranges. Pressure readings were distributed among the transducers to maximize measurement accur- acy. Forty close coupled transducers were used to monitor surge. The tempera- tures were measured in millivolts as differentials from a reference tempera- ture and recorded by the automatic data acquisition system.

4.3.1.1 Pressure The pressures sensed by the probes, fixed rakes, and static taps were measured by transducers and recorded in millivoits by the automatic data acquisition system. Pressures from sensors upstream of the rotor trailing edge were mea- sured by means of 10.3 N/cm2 (15 Ibf/in.2) full-scale transducers. Pres- sures from the trailing edge of the rotor and ali downstream locations were measured using 34.6 N/cmL {50 Lbf/in. 2) fuLl-scale transducers. The accur- acy of the pressure measurements was +0.1 percent of full-scale value.

4.3.1.2 Temperature All temperatures were measured with Chromel-Alumel, type-K thermocoupLes con- nected to reference junctions attached to uniform temperature reference blocks located in the test cell. The temperatures of these reference blocks were mon- itored relative to ice-point cells located in the data system room. The re- sulting data were recorded in millivo_ts by the automatic data-acquisition system.

Temperature elements were calibrated for Mach numbers over their full operat- ing range. The thermocoupJe beads were calibrated for each temperature e_e- ment. OveraLl rms temperature accuracy was estimated to be +0.56K (l.OOR).

4.3.1.3 Rotor System Compressor speed was measured using an impulse-type pickup, which counted gear teeth passing in an interval of time. The data were recorded through a fre- quency-to-DC converter. Accuracy was +1 rpm.

4.3.1.4 Ai_f kow Airflow was measured with an orifice calibrated to Internatiorel Standards Organization/DIS 5167 Standards. Total pressure was measured using a 10.3 N/cm 2 (15.0 ibf/in. 2) full-scale transducer. Orifice pressure drop was measured using 3.4 N/cm 2 (5.0 Ibf/in. 2) fuLl-scale differential trans- ducers_ Orifice temperature was measured by the standard temperature measure- ment system. AccuFacy of the airflow measurement was within one percent.

4.3.2 Structural instrumentation Blade deflections were measured by a mirror system consisting of a laser light source, a beam splitter, reflecting mirrors and a screen and were recorded by a video and camera system. Steady state and unsteady Ceflections were recorded using the techniques described in reference I and 4.

One strain gage was placed on each blade to measure unsteady stresses and to detect the onset of flutter. Signals from these gages were transmitted through a slipring and recorded on magnetic tape.

4.3.2.1 Optical Mirror System

It was necessary to accurately measure rotor blade deflections both in and out of flutter. During stable operation these deflections were due to centrifugal and aerod)mamic forces. When in flutter vibrational mode shapes had to be determined. A patented system (reference 4) of optical mirrors and reflected laser light was used to measure rotor blade surface angle changes from which blade deflections were determined.

The optical mirror system consisted of an array of mirrors installed on the blades, a laser light source, and a readout and recording system, shown sche- matically in Figure 6. The laser light was split into a number of beams, each directed to the radial location of one of the mirrors. As the instrumented blade rotated through the beams, the mirrors reflected the beams back to the readout system to separate points that had been selected to avoid pattern in- terference during flutter.

Twenty mirrors were installed on one blade to provide full coverage of the blade in the region above the midspan shroud and along the leading edge below the shroud. Additional mirrors were mounted on other blades. The completp ar- ray of mirrors is shown on Figure 7. Circumferential locations of instrumented blades are shown in Figure 5.

The mirrors were made from silicon wafers 0.244 cm (0.10 in.) square, 0.024 cm (0.0095 in.) thick, sputtered with a iO00-angstrom thick coating of aluminum and over-coated with 2280-angstrom protective coating of silicon dioxide. The mirrors were attached to the blades with epoxy cement. Additional details of the mirror system and mounting techniques are given in reference i.

The laser light and mirror system for measuring the instantaneous blade sur- face positions used a 604.5 cm (238.0 in.) optical path directly upstream of the test stage inlet. This path length was sufficiently large to provide ade- quate light spot defiections for accurate data readout.

Two windows were installed in the inlet section walls of the test facility: one to provide laser light entry; the other to provide a screen for receiving the reflected light beams. The entry port was a 35 cm (12 in.) diameter clear glass window. The exit port was a 50.8 cm x 175 cm (20 in. x 69 in.) semicir- cular piece of frosted 3.81 cm 11.5 in.) thick Lexan, located 604.5 cm (238.0 in.) upstream of the rotor. The output window was centered about the horizon- tal plane.

Inside the plenum chamber, the slipring cable container was braced near the rotor at the 12, 3, 6, and 9 o'clock positions. The light was directed to avoid these blockages. The interior of the inlet was frosted in selected loca- tions to prevent secondary reflections from interfering with the laser beam signal.

Two lasers were used simultaneously: a O.5-watt Hughes provided the reference beam and a 3-watt Spectraphysics provided illumination for the mirrors.

E_und Scientific variable beam splitters were adjusted to ensure an approxi- mately equal intensity of all the light beams. Each splitter was mounted on a five axis adjustment system to facilitate accurate aiming of the light beams.

Glass shims 0.3175 cm (0.125 in.) thick were added to each splitter to block second order images.

The optical data were recorded with a movie camera operating in the streak mode, a Hasselblad still camera, and a television camera. The cameras were placed to receive the maximum scattered light when the beams were on the out- put window. The cameras were located 9.14 m (30 ft) from the screen. An oscil- loscope beneath the output window was photographed simultaneously with the light spots to correlate the time code and rotor speed signals with the mirror deflections. Ali cameras were rigidly mounted to eliminate blurring due to camera vibrations.

The accuracy of the laser optical system was limited by the resolution of the film. The negative film was Kodak 2484, chosen on the basis of the relative spectral sensitivity, grain size, and contrast. Two copy films for the movies were used: Kodak Hi Con 7362 and Kodak black and white fine grain positive 7302. The former provided the best results, producing more contrast and a much finer grain. The optimum processing speed for the negative was 6.1 m/min (20 ft/min). For the copy, a speed of 10.7 m/min (35 ft/min) was used. Both were processed in Kodak D96. The 2484 film had an ASA number of 800, and the print machine speed and print exposure times were selected to produce a print base density of two. These machine speeds and print exposure values were determined with the actual film and the illumination conditions existing at the time. Un- even copy-process illumination was detected with image processing laboratory equipment and corrected during processing. Still pictures were taken on Kodak Tri-X fi Im.

4.3.2.2 Strain Gage Instrumentation To ensure safety and measure the response of all blades in flutter, one Micro-Measurements type WDDY-125AD-350 strain gage was installed on each rotor blade immediately above the shroud at the midchord location since this location was sensitive to the second coupled mode expected in flutter.

The frequency response of the strain gage data was limited by the bandwidth of the data recording system. The accuracy of any given strain gage was statisti- cally determined to be approximately _+5 percent, representing one standard de- viation for typical data.

4.3.3 Unsteady Aerodynamic Instrumentation The instrumentation for measuring unsteady aerodynamic effects included: i) Kulites on the case over the rotor blade tips, 2) an array of Kulite high re- sponse pressure transducers on the rotor blades, 3) traversing hot-film probes at the inlet and exit locations of the rotor, and 4) an array of hot-film ane- mometers on the rotor blades.

b The fan-case Kulites and the hot-film probe outputs were recorded on two Sangamo Ill wide band group I FM tape recorders having a capacity to 40 kHz center frequencies and 40 kHz output filters. In addition to the data signals, 60:1 and 1:1 speed signals were recorded along with 1 kHz IRIG B Format Time Code Signal.

Data from all bl_de-mounted Kulites were recorded on a constant bandwidth fre- quency-division multiplex system, which provided a frequency response of 2 kHz with a resolution of 690 N/m/ (14.4 Ibf/ft Z) and an error no greater than + I dB. Each of the 12 tracks on the system recorded six data signals plus a time code signal. One data channel on each track was used to record a refer- ence strain-gage signal for phase determination. The hot-film anemometer data were also recorded on this multiplex syst_n.

4.3.3.1 Case Mounted Kulltes Ten high response Kulite pressure transducers, Kulite Model XCQL-8B-808 mounted over the blade tips (Figure 8), were used to measure unsteady pres- sures over the blade tips during stable and during flutter type operation.

Specifications for these units are given in Table VI.

4.3.3.2 Blade Mounted Kulites Thirty-two Kulite, high-response pressure transducers were distributed over the pressure and suction surfaces of four blades (Figure 9) instrumented in pairs such that the instrumentation ocations on the suction surface of one blade matched those on the pressure Jrface of the adjacent blade across the flow channel. Kulite Model LQL5-080-:5S transducers were used on the blades.

Transducers specifications are shown in Table VI. The data from these trans- ducers provided detailed mapping of he pressure fluctuations during flutter.

Signals from the rotating Kulite transducers were amplified before passing through the slipring to the recording device. An amplifier package was used which rotated with th_ rotor assembly.

The rotating Kulite pressure transducers were calibrated both before and after mounting on the blade surfaces The accuracy of the calibration facility was 0.1 percent full scale over a range of zero to 345 N/cm2 (500 Ibf/in.2).

4.3.3.3 Hot Film Anemometers Traversing hot-film probes, located Jt the inlet and exit of the rotor, mea- sured fluctuations in inlet and exit flow during stable and flutter operation.

Hot-film anemometers were located _n the rotor blades to characterize the flow over the blade surfaces in and out of flutter and during transition from stable flow to flutter.

Two hot-film probes were located forward of the rotor, and two behind the

rotor. The sensors were oriented with their length tangent to the case and perpendicular to the rig axis.

Thermo-Systems Model 1210-60 cylindrical hot films were chosen for the probes based on their ability to operate in a high velocity gas stream. These sensors were constructed of a 0.0154 _m (0.006 _n.) diameter by 0.203 cm (0.080 in.)

long quartz substrate with a platinum sensor deposited on its surface. Specif- ications for the transducers are presented in Table VI. The hot-film probes were catibrated at ten different flow velocities.

The frequency response of the probes and the associated data acquisition sys- tem was 40 kHz with a resolution of 1.0 percent of the mean flow vetocity. The dynamic accuracy of the probes was I dB for axial Mach numbers below 0.4. The accuracy at higher Mach numbers was less because of a loss in sensor linearity caused by flow compressibility.

Twenty hot-film sensors were instatled on four blades above the shroud at positions corresponding to those of the blade-mounted Kulite pressure trans- ducers, Figure 10. A majority of sensors were instal ted on the suction sur- faces of two blades to provide data of flow separation. A few were also placed on the pressure surface.

The sensors were Micro-Measurements Type EGTSO. The film with its pofyimide backing was mounted on a 0.041 cm (0.016 in.) Kapton film substrate to mini- mize heat transfer to the blades. The grid was oriented in the direction of flow with the leadwires routed off the trailing edge to avoid an _dditionaf turbulence source.

The sensors were calibrated to identify strain induced errors, but their non- linear response and the difficulty in simulating the test situation in the la- boratory made calibration to obtain quantitative data unrealistic. Therefore, their function was limited to qualitative characterization of the flutter.

However, comparing the flutter response from one data point to another gave useful data on suction surface nonsteady flow characteristics. These sensors and associated data acquisition system provided a frequency response to 2 kHz.

I0 J

SECTION 5.0 TEST AND ANALYSIS PROCEDURES 5.1 TEST PROCEDURES The test program was conducted in two phases: an initial shakedown test phase and a performance test phase. The objectives of the shakedown test were to check rig operation, instrumentation, and data recording and reduction sys- tems; to verify the existence of stall flutter; and to compare performance with that of the original TS22 stage. During the performance test phase, over- all aerodynamic perfoY ..... _ obtained over a range of flows at rotor speeds between 54 and 85 percent ,° _' _ign. High response aerodynamic and structural data were obtained at all operating points, and surge points were determined at several speeds bet_ _n 63 and 85 percent of design.

5.1.1 Shakedown Tests During the shakedown test the rig was operated at speeds to 70 percent along a wide-open-discharge throttle line to make sure that the rig was free of vibra- tion and that all steady-state and dynamic instrumentation were operating pro- perly. A transient into flutter was made at 70 percent speed. A full data point was taken with both steady-state and dynamic instrumentation at 70 per- cent speed and wide open discharge. At 63 percent speed a transient into flut- ter was made, and two additional data points were taken: one with wide-open- discharge; the other in flutter. These shakedown tests are listed on Table VII.

The full data points consisted of: A two-minute record of all dynamic instrumentation-strain gages, Hot films, and Ku!ites A two-second high-speed motion picture of optical laser/mirror data for all blade mirrors o Still photographs of mirror data o TV records of all mirror images A two-minute record at each spanwise location of a seven-position radial traverse made ahead of and behind the rotor with hot-film probes Steady-state data including rotor speed, total pressures, total tem- peratures, flows, static pressures, and flow angles for the rotor and stator inlets and discharges.

II The aerodynamic data obtained during the shakedown tests were reduced to vall- date the instrumentation and data reduction systems and to compare performance with the performance observed during previous tests of the TS22 stage. The dynamic data were studied to validate accuracy before the performance phase of the test program.

5.1.2 Performance Tests The performance testing phase of the program involved mapping the extent of the flutter boundary by taking data at operating conditions both in and out of flutter. The initial portion of this phase repeated some of the shakedown testing. Test data was taken over a range of speeds from 54 to 85 percent of design. The test points are listed in Table VII. For this program the flutter boundary was d_fined as the flow at which a vibratory stress of +2068 N/cm 2 (+_3000 Ibf/in. _) was attained.

5.2 DATA REDUCTION PROCEDURES 5.2.1 Data Requirements The following parameters were calculated for all data points: 1. Overall stage performance 2. Blade element performance 3. B]ade untwist and uncamber 4. Flutter frequency 5. Blade stress level 6. Vibratory mode 7. Pressure contours over the blade tips 8. Incidence angle at seven radial stations 9. Reduced velocity for seven radial stations.

In addition more extensive data reduction was performed for six of the data points. This reduction provided: i. Analysis of the mirror data for intrablade amplitudes and phase rela- tions on one blade correlated with strain gage signals and other non- steady signals to define the rotor mode shape and its relationship with the instaneous aerodynamics 2. Intrablade average steady pressure distribution at the watt for two passages Intrablade unsteady pressure distribution at the wall for two passages 4.

Amplitude and phase angles of all fluctuating signals from rotor- mounted sensors--both amplitude and phase angle were determined rela- tive to the signals from the No. 3 blade.

5.2.2 Specific Procedures 5.2.2.1 Steady-State Aerodynamic and Blade Deflection Data All steady-state performance data were automatically recorded in millivolts, converted to engineering units, corrected, and used to calculate overall and blade element parameters.

The measured total pressure and flow angle from the wedge probes were correct- ed using Mach number calibration curves for individual probes. The resulting calibrated Mach number and corrected total pressure were then used in conjunc- tion with standard tables of air properties to calculate static pressure.

Thermocouple signals were converted to temperature measurements using wire calibrations for individual sensors. These temperature measurements were con- verted into total temperature using Mach number calibrations for individual sensors and the pressure-level corrections of Glawe, Simms, and Stickney (ref.

2).

Circumferential distributions of total pressure obtained at the stator exit were mass-flow averaged for each pole rake at each radial location using the corresponding measured distribution of total temperature and a constant cir- cumferential static pressure determined by linearly interpolating static pres- sure data from wall static measurements. Circ,_ferential mass-flow averages of total temperature were also calculated at each radial location, using the cor- respondi._g measured distribution of total pressure and constant circumferen- tial value of static pressure. The three values of total pressure from the pole rakes at each radial location were arithmetically averaged to obtain a single radial distribution of stator-exit total pressure. Total temperatures were averaged similarly. The peak value of total pressure from each circumfer- ential distribution of total pressure was taken as stator inlet pressure. The three radial distributions of stator inlet pressure were also averaged to ob- tain a ._ingle radial distribution. Air angles measured by the two probes at the stator exit were arithmetically averaged for each radial location.

Two separate computer programs wL_re used to transform test measurements into the desired overall and blade-element performance parameters. The first com- puter program converted measurements from miIlivolts to engineering units and corrected, averaged, and prepared the data for input to the second computer program. The second computer program, operating off line, calculated the de- sired overall and blade-element performance parameters by means of a stream- line solution of the axisy_nnetric flow field.

The remaining input to the flow field program ccnsisted of the geometric de-

scription of the rig and aerodynamic data. The geometric description included

the shape of the flowpath wails, axial locations of blade edges, and blade in-

let and exit metal angles and solidity. Blade edges were input as 24 straight-line segments that closely approximated the meridional profile of the manufactured blade edges. Metal angles at the rotor leading edge and trailing edge were input from beam calculations for the blade at design speed.

The output from the second program consisted of corrected speed and inlet flow; the spanwise profile of total pressure ratio at the stator inlet; the spanwise profiles of total pressure ratio, total temperature ratio, and flow angle at the stator exit; and blockage factors for each calculation stati)n.

Total pressures and temperatures were calculated as ratios to the assumed standard day inlet plenum values.

A flow blockage factor was used at each axial Eocation to improve the accuracy of the static pressure velocity calculations. Blockages were applied equally to all stream tubes at each of the axial locations. The axial distribution of blockage factors was selected to give calculated wall static pressures that agreed with measured wall static pressures. A single axial distribution was found to provide reasonable agreement with measurements for all data points.

All static pressures and the flow angles between the rotor and stator wet _ calculated by the flowfield program. The calculation was made assuming a_isym- metric flow and using mass-flow continuity, radial equilibrium, and enerr equations. Streamline curvature and enthalpy and entropy gradient terms ___re inc I uded.

Overall rotor performance was calculated from mass-flow averaqes of tota pressure and temperature at rotor exit and average inlet conditions. Overall stage performance is not presented in this report because it is not required to support data evaluation.

Rotor blade element parameters were calculated for airfoil sections lying on a fixed set of conical surfaces defined by intersections of blade edges and streamlines calculated for a reference point at mid range at 75 percent speed.

Streamlines were selected to include blade-element data at radial locations of transducers for blade surface measurements and mirrors for blade deflection measurements. For the blade element data tabulations presented in Appendix A, the incidence angles were based on measured air angle and the calculated fetal angle at design speed. For the plot of reduced velocity parameter versus inci- dence angle (Figure 43), both air angle and metal angle were measured v_lues.

The blade centrifugal untwist and uncamber resulting from centrifugal and gas bending loads were determined directly from the blade ,_eflection data obtained with the optical mirror system. Images from twenty of the twenty-six blade mounted mirrors were used to determine blade n_ovement.

Steady deflections were determined for speeds from 25 percent to 85 percent of design. Photographs taken at selected speeds in nine percent increments were used to determine steady blade movement. A coordinate system was established based on known details of the screen. The vertical position of each spot on each photograph was measured. Using the idle spot positions as a baseline, the movement of the spots for any speed was scaled. T_is movement on the screen was then converted to angle of twist and change in bending slope.

5.2.2.2 Unsteady Data Reduction The reduction of the high frequency response data from the hot film probes, wall-mounted Kulites, blade mounted hot film sensors, blade mounted Kulites and blade mounted strain gages required sophisticated techniques. Signal en- hancement, signal phasing from rotating instruments, and signal phasing between rotating and stationary in_ truments are di scussed be Iow. These di scus- sions are followed by details of the analysis of each type of data.

5.2.2.2.1 Signal Enhancement The signal enhancement, a time domain technique, extracted or enhanced parti- cular frequency components from a broadband signal. The technique involved averaging numerous time segments of a broadband signal, the start of each seg- ment being triggered by a reference signal. Each successive time segment was summed and averaged in _ storage memory. The result was an enhancement or re- inforcement of those comoonents that were synchronous with the triggering signal and suppression o- components that were not.

5.2.2.2.2 Phasing of Si,_nals fr.om Rotating Instrumentation Phase information betwee ,_ the reference strain-gage signal on the No. 3 blade and all other strain gage and rotating Kulite and hot film signals was pro- duced at the flutter frequency, using cross spectral density techniques, a Nicolet Scientific "Omniferous" Model 401 analyzer being used for this purpose. The analysis range For the task extended to 2 kHz. An 800-element sDectural resolution was selected. To produce each final plot, 128 sweeps From the aralyzer were averaged. The analysis was conducted From zero to 2000 Hz.

The analyzer filter bandwidth yielded a spectral resolution of about 3.75 Hz.

All resulting phase angles were corrected For errors introduced by the signal conditioning and recording systems.

5.2.2.2.3 Phasing of Signals Between Rotating and Stationary, Instrumentation It was necessary to determine the phasing between signals From the rotating blades and the stationary wall instrumentation. Of specific interest was the phasing of the reference signal from the strain gage on the No. 3 blade and the signals from the case-mounted Kulites. A variation or extension of the cross-spectral density technique was used.

The ftutter component of the signals has different frequencies in the rotating and stationary coordinate systems. The Frequencies in the stationary system are either higher or lower than those in the rotating system because they are comoosed of the fundamenta( Flutter frequency plus or minus multiples of rotor rotationaW soeed. This can be seen in the following derivation.

The vibration of the individual blades in a stage in flutter is fully defined by the sum of a finite series of circumferential harmonic waves where the num- ber of component waves equals the number of blades, N, in the stage. The associated unsteady pressure, p, at a particutar axial coordinate, x, varies with tangential coordinate, y, and time, t, is described by the sum of an infinite series of forward and backward rotating harmonic waves having all integer numbers of cycles around the circunn:erence of the stage. This function is expressed in terms of sets of responses to individuai orders, m, of blade vibration where I_< m _< N.

Pm (x,y,t) : _ Pmn (x)ei(_mny+c_t) (i) n=_Qo Where n, the number of full waves per intrabiade passage, is added to the fractional number represented by m waves around the #ull circumference. _ is the flutter frequency cummon to all phenomena in the rotating system. The un- steady periodicity condition defines the wave number @m + 2 xn _mn = (2) 2 _m

where the interblade phase angle, _m - (3)

N and blade spacing, s where r is radius OIRtCJ_,,:' L F OE POOR _: ._ m + Nn hence _3mn = r &

In the stationary system, the coordinates x' and y' are related to their rota-

ting counterparts by

x = x' C:11" : --

(4)

OF HC:C;_ '_-.,-;'i'Y y =y' + £Zrt where £z is the rotor speed. Equation (1) then becomes )ei_mn (y' + ( _ r +¢_/_mn)t) (5) '' ' Pmn (x' Pm (x y , t) = n =-_ This is in the form of waves having wavelength 2 _/_mn, moving at velocity (_r -_ oo/_3 mn). The frequency _sneasured by a stationary probe is the product of the wave number _mn and the wave velocity. Hence oo s = /3ran _r +oo = _m _ Nn ÷oo (6) where £mis a multiple of shaft speed, and £Nn is a positive or negative mul- tiple of blade passing speed. Therefore, the single flutter frequency, c_, in the rotating system becomes a spectrum when detected by a stationary sensor.

The observed frequencies, oot, are spaced at multiples of shaft speed, _ .

The index m identifies the associated harmonic wave component of blade vibra- tion and the index n identifies the added number of waves within a passage be- tween adjacent b lades.

Because flutter was seen at many frequencies by the case-mounted Kulites, phase information could not be produced directly. Instead, an aliasing techni- que was used. By selection of the sampling rate to equal the rotational fre- quency, both the rotating and stationary transducer flutter signals were transformed to a new coordinate system i,_which a single flutter frequency existed for both sets of signals. Phasing of the signals in question could then be performed. The one-per-revolution speed pip was used as the sampling rate command.

Two different procedures were used to produce phase information. One procedure was to allow all the flutter components in the stationary signal to be aliased. The other procedure was to isolate individual spectral components of the flutter with a narrow filter before aliasing. This latter technique ex- tracted a single nodal diameter signal p_us its har_.onics at multiples of tne rotor speed. In all cases, the sampling command was properly conditioned to allow the rotor to be in a selected orientation before a data sample was taken. Corrections to the final phase angle were included for influences of all signal conditioning and the aliasing process.

5.2.2.2.4 Strain Gages

Each of the 32 blades was instrumented with one dynamic strain gage located near the maximum thickness point above shroud at 64 percent span. The stage fldtter response was obtained from the strain-gage signals consisting of amplitude, frequency, and phase. The amplitude and frequency characteristics of the individual blades were obtained from power spectral density (PSD) plots from 0 to 2 kHz. Phases relative to the gage on the No. 3 blade were obtained by using the cross spectral analysis_technique described in Section 5.2.2.2.2.

The strains were of the form Su e i _ where the complex number, S u , repre- senting the strain in the No. 3 blade, defined phase as well as amplitude. The Su numbers, where 1_ u <_ N, may be represented by the finite summation N S u =_ am e" N_] _ (7) m=l where _m is the amplitude of a series of patterns having numbers of lobes, m, where t-<m<--N, rotating with respect to the disk at speed co/m. From the known amplitude and phase of each strain gage, Su , the complex coefficients, a m , of the series in equation (7) may be determined by mathematical inver- sion to give the strength of the m th modal component or spatial harmonic and its phasing with respect to all other components.

The broadband and flutter frequency amplitudes for all strain gages and rota- ting Kulites were plotted versus time to help establish the stability of the data during the two-minute steady-state records. The plots were also used as a cross-check with the power spectral density curves to help identify possible errors in e:_gineering unit conversions.

5.2.2.2.5 Mirrors Blade mode shape was determined by analysis of the laser optics mirror data.

Blade defl__ction amplitudes were determined from the mirror data. For the blades withow_t mirrors, the deflection amplitudes and relative phases were determined thY,)ugh correlation of the strain gage data and the mirror data.

Typical still photographs of the mirror data in and out of flutter are shown in Figure 11. The difference in width of the same spot in the two images is proportional to the torsional amplitude and the difference in height is pro- portional to the axial component of the bending slope.

The 16ram film record of the reflected laser beams was digitized using a Spa- tial Data Systems Scanner. The measurement accuracy was better tF.an +0.00254 cm (0.001 in.). The data were stored on magnetic tape for computer processing.

A fast Fourier transform was used to convert the data from the time domain to the frequency domain. This procedure alIo_ed the calculation of power spectral densities and cross-spectral densities to determine amplitude and phase angles for the different mirrors.

5.2.2.2.6 Case Mounted Kulites The case mounted Kulites were used to obtain nodal diameter patterns present in the rotor system during flutter, contour maps of the pressure distributions over the blade tips during stable operation, contour maps o$ the unsteady pressures during operation with flutter, and contours of the real and imagi- nary components of the unsteady pressure and relative phase during flutter .

The nodal-diameter patterns in the rotor system during flutter operation were determined through Fourier analysis of the signals from the case-mounted Kulite pressure transducers.

The contour maps of pressure distributions over the blade tips were obtained from wall Kulite and wail static tap data. The technique discussed in Section 5.2.2.2.1 was used to enhance the broadband Kulite signals. The one-perrevolu- tion speed signal was the reference signal used in this procedure. Data from 512 rotor revolutions were averaged to produce the final plots. The enhance- ments were timed to allow a selected group of blades to occupy a desired orientation relative to the wall Kulites. These enhancement techniques pro- duced a signal-to-noise improvement factor of about 22.6.

Plots of pressure versus time were digitized to obtain an array of pressures representing the variation from the mean at the specific axial location. A minimum of ten samples per blade gap were digitized. The time location of each pressure sample was translated into a rotating frame, with the leading edge of the No. 2 blade used as the zero reference. The wall mean static pressure for each axial location was added to the local variation to obtain the steady- state pressures. The array of local static jressures was input into a contour plotting package, which linearly interpolates in space to find specified levels of pressure. The lines of constant pressure were normalized as percent- ages of the maximum local steady-state static pre;sure sampled, and contour maps of the constant percentages of pressure were machine plotted.

When the contour maps at the blade tips were plotted, the pressure fields with resoect to the blade leading edges were observed to be. shifted about three degrees tangentially in the direction of rotation, corresponding to a time delay of about 30 microseconds. However, this shift, which was nearly indepen- dent of rotor speed, did not appear in the nonsteady pressure plots obtained from the same data. The shift is therefore believed to have resulted from the data reduction procedure used to obtain the steady-state plots. Considerable time was spent trying to find the source of the shift either in circumferen- tial relation between the time trigger and the blade_ or in unaccounted delays in the electronic equipment. Although the source was not found, the location of the blades was evident from the plots. Each steady pressure plot in the report has been corrected to place the blades in the proper positions. The amount of shift is presented in the Appendix D with the contour maps.

The procedures for obtaining the plots of unsteady pressures over the blade tips, the real and imaginary components of the unsteady pressures, and the phase angles for the unsteady pressures are given in Section 5.2.2.2.3 5.2.2.2.7 B Iade-Mounted Kulites Blade-mounted Kulites provided unsteady pressure amplitude and phase distribu- tion for both the pressure and suction surfaces of the airfoil at two radial positions. Amplitudes were determined from the power spectral density for each signal over a frequency range of 0 to 2 kHz. The power spectral density data were confirmed by backup plots of amplitude against time during the two minute test period.

Cross-spectral density functions were used to determine the phasing of the pressure signals relative to the strain gage signal from No. 3 blade.

5.2.2.2.8 Hot Film Probes The data obtained from the hot-film probes were analyzed using the same en- hancement and reduction techniques used for the case-mounted Kulite data.

Contour maps were not produced, however, because of the very low level of the signals at the flutter frequency.

5.2.2.2.9 Blade-Mounted Hot-Film Sensor Blade-mounted hot-film sensors provided air velocity measurements on the blade suction and pressure surfaces at two radial positions. The flutter response from these sensors consisted of frequency, amplitude, and phase. Amplitude and frequency were obtained from the power spectral density for each signal over a frequency range of 0 to 2 kHz. The measured amplitude had a repeatability of +20 percent, making it possible to relate the data from one point to another.

_he strain gage on the No. 3 blade was used as the reference for determining phase angle. The resulting phase angles were compared with those from the blade-mounted Kulites and strain gages, and the accuracy of the measurements was comparable.

5.2.2.3 NASTRAN Prediction Procedure In structural analysis of rotor blade systems, stresses and deflections are commonly calculated for both the stable and vibrating modes of operation by the NASTRAN finite element approach. To evaluate the effectiveness of this procedure, deflections of the TS22 rotor and blades were calculated and the results compared with measured values obtained during the test program.

NASTRAN calculations were made for both the stable and free-vibration mode for the TS22 rotor system. Calculations were made for speeds of 65, 73, and 75 percent of design. Calculations for vibrating conditions covered tilree through nine nodal diameter patterns. Because NASTRAN's cyclic symmetry analysis was used, only a one-blade wedge of the rotor was modeled. Rotor speed effects were included by adding a centrifugal prestress stiffness matrix to the con- ventional static stiffness matrix.

C_, _ v.,. ....

Finite element mesh diagrams for the blade is shown in Figure 12; the shroud and disk, not shown, were also modeled. Triangular plate elements and beam elements were employed for the NASTRAN calculations. The blade, shroud, and disk models were joined using multi-point constraint __quations. On the basis of previous experience with the TS22 rotor analysis, shroud-to-shroud inter- faces were assumed to be pinned together at a single center node in the cyclic symmetry analysis. The disk used for the TS22 rig was very stiff, and its flexibility did not contribute to the mode shapes.

5.2.2.4 Blade-Work Interaction Calculation The flutter characteristics of the test rotor and the types of data obtained allowed for an evaluation of a theory oF energy transfer that takes place dur- ing flutter. The assumptions associated with this theory are:

I)

Self-excited vibrations occur in a bladed rotor when the energy sup- plied by the air stream exceeds the energy dissipated through the structural damping associated with that mode.

2) The complex rotor vibration mode can be defined as a summation of

simple circumferential harmonic responses (i.e., Fourier decomposi- ti on ).

3)

The net aerodynamic energy of a mode is the algebraic sum of the aerodynamic energy associated with each harmonic response.

4) The susceptibility of a rotor vibration mode to flutter is a function

of the stability of the individual harmonic responses.

An aerodynamic damping exists for each harmonic response. This damping is defined by the log decrement parameter, which is proportional to aerodynamic work divided by kinetic energy of the harmonic Wm 6aero : Em For positive vatues of the aerodynamic damping parameter, the energy flow is from the structure to the flow stream and in the reverse direction for nega- tive values.

The aerodynamic work per cycle done by each of the individual harmonics is computed by integration Wm= aPm d (ojt) db _02_ dhm chord d(c_t) where: pressure jump across the airfoil from the mth harmonic and is of

A Pm

the form _Pm = Pm (X,yp,t) - Pm (X,Ys,t) where: yp and Ys are blade surface coordinates on the pressure and suc- tion surfaces at axial location x = deflection normal to the airfoil surface of the ruth harmonic

hm

(cot) = position angle during the vibration cycle b = chordwise location oo = flutter frequency t = time The pressure at the airfoil tip at any axial location is the summation of the distribution resulting from individual blade harmonic motions.

N P(x,y,t) = _ Pm(x,y,t) m:1 The pressure of each harmonic is defined by a fourier series described in Sec- tion 5.2.2.2.3.

oo Pm(x,y,t ) =_ Pmn(X)e i(oJt + f3mnY) n _ -oo These pressure waves are translated into the stationary system using the rela- tionships given in Section 5.2.2.2.3.

Pm(x, ,y, ,t) = _ Pmn(X,)e i [( c_÷ (m + Nn) _)t ÷ 13mnY'] n: -_ C OF F_,., _ . ;y, The va _es of Pmn at frequencies (OOmn=(m + Nn)_) are obtained by pro- cessing the casing wall Kulite signals through a wave analyzer. The frequency band of the recorded data was 40 kHz which at the maximum rotational test speed of the rotor permitted ten harmonics (i.e., -lO<n<+lO) to be deter- mined.

Since no direct measurement was made of the mode shape at the blade tip, a NASTRAN analysis was used to predict the def{ections.

The predicted mode shapes were scaled and phased in accordance with the mea- sured strain components to define the tip motion, hm, required to calculate the energy transfer in three dominant harmonic compcnents.

The kinetic energy per cycle of the individual harmonics was computed by inte- grati on: pTco2 (fro 2 + gm 2 + hm2) d l db Em = -_" ord Span where: airfoil material density I" = airfoil thickness fm,gm, hm = spatial components of deflection in the mth harmonic spanwise location coordinate b = chordwise location coordinate CO = ftutter frequency The NASTRAN mode shape energy levels were scaled in proportion with the strain component amplitude squared to determine the kinetic energy revel of the indi- vidual harmonic responses.

"3

SECTION 6.0

DISCUSSION OF PROGRAM RESULTS

6.1 OVERVIEW

The large body of time-correlated, high-quality data acquired has broadeneG

our understanding of subsonic/transonic stall flutter. The more significant

results were: i.

Deviations from uniform phase angle from blade-to-blade, previously attributed to insignificant anomalies in the data, are important, being indicative of a complex flutter characteristic.

.

Flutter alters the passage steady pressure pattern only slightly, as shown in the steady-pressure contours.

.

Work input is concentrated near the leading edge, as shown in the unsteady-pressure contours.

4. Local supersonic flow is required in order for this flutter to occur.

Details of these results and a discussion of possible causes of flutter are presented in the followi.._ sections. The bulk of the data obtained in this investigation and blade coordinate data are giv=_n in Appendices A through E: Appendix A - Tabulations of Steady State Performance Data Appendix B - Rotor Blade Coordinates Appendix C - Part I, Steady Blade Structural Data Part II, Unsteady Blade Structural Data Appendix D - Part I, Steady Pressures Part II, Unsteady Pressures Appendix E - Hot Film Data 6.2 TEST MATRIX Tests were run over a range of corrected speeds from 54 to 85 percent of design. A transient was run at each of several speeds from wide-open-throttle to surge, and the points of flutter initiation as well as the surge were determined. Data along the 70 percent speed line are shown in Figure 13.

The data points in Figure 13 were taken during a slow transient in which equilibrium conditions were not fully established. Furthermore, the pressure ratios were obtained from arithmetic averages of a limited number of rake readings. As noted on Figure 13, flutter was first indicated by the hot-film gages at about 67 percent of design flow, and the first indication of flutter on the strain gages appeared at about 63 percent of design flow. Surge occurred at about 56 percent of design flow.

A composite map for all test speeds is shown in Figure 14. These data were obtained at fully stabilized conditions and represent mass-weighted average performance. Flutter occurred at speeds between 63 and 75 percent of design.

The flutter boundary( shown on Figure 14 represents a blade vibratory stress level of +_2068 N/cm L (3000 Ibf/in. Z) as measured on the strain gage just above the shroud. Surge was encountered before flutter at speeds below 63 or above 75 percent of design.

Additional blade-element data and other aerodynamic performance detail are tabulated in Appendix A.

6.3 STRUCTURAL DEFORMATIONS Steady-state structural deformations of the blades were determined from data from the optical mirror system. Unsteady deformations during flutter were determined from the optical mirror system, the strain gages, and by analysis of the high response pressure data.

6.3.1 Steady-State Deformations The mirror system provided what is believed to be the first set of high quality data describing blade deformation at normal fan operating conditions.

The results showed that the deformations under combined centrifugal and gas loads were close to the predicted levels, with slightly higher uncambering.

Results are given in Appendix C, Table C-1.

Local steady-state untwist at from 35 to 85 percent of the design speed are shown in Figure 15 for the 95 percent span location. Above 25 percent speed the amount of untwist varied as the square of the rotational speed, as pre- dicted. Below this speed, the midspan shroud was not seated, and the untwist varied in an unpredictable manner.

The distribution of untwist along the span at 73 percent speed is shown in Figure 16. Approximately equal amounts of untwist occurred above and below the shroud, which was at the 62 percent blade span and constrained untwist to near zero at this location. Untwist was essentially a function of speed only. The effects of gas loading were negligible. As shown in Figure 17, the variation of untwist with flow at 75 percent speed was less than 0.1 degree for a flow change from 70 to 59 kg/sec (155 to 130 Ibm/sec), corresponding to a blade tip D-factor increase of 0.1764.

Measured untwist as a function of chordal position is shown in Figure 18 for

73 percent speed. Uncamberingwas significant at all stations above the

shroud, exceeding 0.3 degrees near the blade tip.

Figure 19 shows both the measureduntwist and the untwist calculated by the

NASTRAN analysis. Generally, good agreement was obtained except close to the

leading and trailing edges, where predicted deformation was greater than

measured. Therefore, the measured uncambering at the tip was slightly higher

than predicted. However, the deformations in this region, where the airfoil

was very thin, were sensitive to the actual airfoil thickness, and slight

variations within specified tolerance might have been sufficient to cause the

observed discrepancies.

Additional steady-state deflection data are given in Appendix C, Part 1.

6.3.2 Unstead_ Deformations

Previous to this program, fan flutte.- had been visualized as a sinusoidal, circularly traveling wave superimposed on the rotor, Forming a single multino- dal pattern, each rotor blade deflecting sinusoidally in sequence as the wave t,_aveled around the rotor (ref. 3).

Such a wave was characterized by concentric ring nodes and traveling nodal diameters or diametral lines of zero deflection. Figure 20 shows such a system with two ring nodes and three nodal diameters. This pattern is referred to as a vibration in the second mode with three nodal diameters. On a rotating stage, the radial lines travel either Forward or backward, and adjacent blades experience a relative tinm delay or phase difference (interblade phase angle) as the wave passes. With such a concept, all blades are assumed to flutter at the same frequency and amplitude, with uniform phase angles between adjacent b lades.

The results of the current program revealed a different picture: all blades fluttered at the same frequency, but not at the same amplitude and interblade phase angles were not equal. Typical amplitudes and phase angles observed dur- ing the program are shown in Figures 21 and 22, respectively. These data were obtained from the strain-gage measurements. Amplitudes in Figure 21 are ex- pressed in terms of measured stress. The patterns shown represent a family of spatial harmonics described by the superposition of a number of rotating nodal diameter patterns, each characterized by a different number of nodal diameters with different but uniform amplitudes and different but uniform phase index- ing, with each pattern rotating at a speed that results in the same flutter Frequency.

The detailed definition of the amplitude and p_ase for each nodal diameter pattern was determined from wall Kulite data. A result of this analysis is presented in Table VIII. As shown in the table the fifth nodal diameter pat- tern had the strongest signal at 67 percent speed. The seventh nodal diameter pattern was strongest at 73 percent speed, and the eighth was slightly strong- er than the others at 75 percent speed.

To further study the complex modeshapes of the rotor and blading, stability

calculations were madeFor the fifth, seventh, and ninth nodal patterns at 70

percent design speed. These patterns represented two strong signals and one

weaker signal. The results of these calculations are given in Table IX in

terms of the logarithmic decrement which is 2_ times the ratio of available

damping to critical damping. Since this number represents the percentage rise or decay of the signal, a negative value of the logarithmic decrement repre- sents an unstable or flutter condition. Complete pressures used in the stability calculations (see equation at bottom of page 21) are listed in Table IX and plotted in Figures D-40, D-41, and D-42 for the upper and lower surfaces of the airfoil. The chordwise position of the pressures is the same as for the wall mounted Kulites from which the data was obtained.

Table IX shows that the fifth harmonic was the principal source of instability at 70 percent speed. The seventh harmonic was marginally unstable; the ninth, marginally stable. The results suggest that Lhe effect of asymmetries, or "mistuning", on the system ip flutter is to couple secondary modes into the instability. This is an important result, clearly demonstrating that any future flutter analysis that is to be correlated against test data for a mis- tuned bladed disk system must be capable of handling several spatial harmonics.

The present analysis is not capable of explaining the mechanism that determin- es what patterns will occur or what their relative indexing will be. However, the mechanism probably relates to the mistuning of the stage, which results from small dimensional differences among these airfoils. These airfoils had bt_n deliberately grouped by frequency when the rotor was assembled, see Fig- ure 2. And it may be significant that the group of airfoils with the highest flutter amplitudes were those that individually had natural vibratory frequen- cies equal to the average frequency for the lade set. It may also be signifi- cant that only forward traveling waves (tra_ sling in the same direction as the rotor) were observed.

Additional stress level and phase angle dat_ From strain gages are given in Appendix C, Part 2, Table C-2 and Figures C-8 through C-I0. Blade deflection data from the mirror syst_ were also reduced to obtain amplitudes of bending and torsional displacements during flutter. These data are tabulated in Tables C-3 and C-4 and plotted in Figures C-11 through C-15 of Appendix C, Part 2.

These additional data corroborate the results presented above.

6.4 PRESSURE DISTRIBUTIONS The study of the steady and unsteady pressure contours obtained with the case-mounted Kulites and unsteady pressures obtained from the blade-mounted Kulites revealed several important features oncerning transonic compressors in general as well as the stall flutter phenomenon.

A review of the pressure contours outside a_d inside the flutter boundary showed the development of the shock structure with increasing rotcF speed and the shifts in position of both the peak pressure point and the shocks with in- creased loading. In general, increasing rotor speed on a given operating line resulted in a strengthening of the expansiun waves and normal shock and a shift rearward of the shock. Moving up a speed line to higher loading and in- cidence shifted the shock forward towards the leading edge. Crossing the flut- ter boundary produced little change althouqh the normal shock appeared to have spread, which is probably indicative of shock oscillation. Details are pre- sented in the following paraqraphs.

Z7

r

|i

6.4.1 Steady-State Pressure Distributions At 63 percent speed outside of flutter, data from the case-mounted Kulites showed that high loading occurred at the leading edge and that the flow was subsonic (Figure 23). Moving up to a high operating line into flutter is shown in Figure 24.

At 67 percent speed on the low operating line, expansion waves occurred behind the leading edge, culminating in a shock at about 15 percent chord (Figure 25). At the flutter boundary at 67 percent speed, the shock appeared to be a gradual compression, which may be indicative of an oscillating shock (Figure 26).

At 70 percent speed outside the flutter boundary, supersonic Mach number expansion at the leading edge was more clearly evident, and the normal shock moved rearward to the 20 percent chord position (Figure 27). At the flutter boundary, the shock moved forward, very close to the leading edge (Figure 28).

Near surge the leading edge expansions appeared to be weaker, but the passage shock appeared stronger (Figure 29).

At 73 percent speed on a low operating !ine (Figure 30), the shock moved further rearward to about the 30 percent chord position. Moving into flutter (Figure 31) the principal loading remained at the leading edge with the data showing considerable smearing of the normal shock. Essentially identical trends occurred at 75 percent speed (Figures 32 and 33).

Significant changes occurred at 85 percent speed. At this speed surge occurred before Flutter. On the low operating line (Figure 34) significant reaccelera- tion occurred behind the shock and the compression process was far from opti- mum, with negative lift occurring on the aft portion of the blade. Moving up the operating line (Figure 35) resulted in a high Mach number with strong leading edge expansion and a strong detached bow shock. Operating near surge (Figure 36) produced little change in this pattern.

Additional plots and tabulations of steady-state pressure distribution data are given in Appendix D, Part I.

6.4.2 Unsteady Pressure Distributions Unsteady pressure data were reduced to contours of unsteady pressure amplitude and contours of the real and imaginary components of the unsteady pressure to provide relative phasing information. Typical plots are presented in Figures 37, 38, and 39. To interpret these plots it should be noted that the real and imaginary components represent the instantaneous unsteady pressures at two time phases separated by 90 degrees. Hence, the square root of the sum of the squares of the real and imaginary amplitudes shown in Figures 38 and 39 is equal to the amplitudes shown in Figure 37, and the relative phase angle of the unsteady pressure is equal to the arctangent of the ratio of the real and imaginary components.

The data showed high unsteady pressures near the leading edge (back to approx-

imately the 25 percent chord position), relatively low values near the trail-

ing edge, and minimumamplitude near midchord. Similar trends were evident in

the blade unsteady surface pressures measured by the blade-mounted Kulite (see

Figure 40). The arrow lengths in this plot represent unsteady amplitudes and

the directions represent phase angle as referenced to the strain-gage signal

from the No. 3 blade. As shown, significant unsteady pressure amplitudes were

confined to the leading edge portion of the airfoils.

These results clearly indicate that the major portion of the action was con- centratea in the first quarter of the airfoil, implying that future flutter research should concentrate on the aerodynamics near the leading edge.

Additional unsteady pressure data and plots are given in Appendix D, Part 2.

6.5 VELOCITY FLUCTUATIONS FROM HOT FILM SENSORS Hot-film probes were located ahead of and behind the rotor to determine the influence of flutter on the inlet and exit fla_s. Hot-film gages were also located on the rotating blades to determine velocity fluctuations occurring on the blade surface during flutter.

6.5.1 Upstream and Downstream Velocity Fluctuations Enhanced wave forms from the hot-film probes ahead of and behind the rotor are shown in Figure 41 for two test points at 75 percent speed: one at wide open discharge, the other in the flutter region. Because these signals were not calibrated for amplitude, the magnitudes of fluctuation are not known. For the open discharge condition, the inlet signal at the blade tip showed a velocity fluctuation of blade passing frequency that was caused by the passage of expansion and shock waves emanating from the blades. There was no defined pattern at the inlet near the shroud and at the blade root where the relative inlet velocity was subsonic. A_'the rotor exit, a well defined blade wake pattern existed for all three radial positions. The inlet probe patterns in flutter, were similar to those for the nonflutter condition. Behind the rotor at the hub, the pattern was also similar to that for wide open throttle. How- ever, at the near shroud and tip exit position, the blade wakes were not as well defined as for the nonflutter condition. The tip pattern had some random fluctuations at other than blade passing frequency, but did not show a signi- ficant fluctuation at flutter frequency.

6.5.2 Blade Surface Unsteady, Velocities Unsteady velocities and phase angles were determined from the hot-film gages mounted on the rotor blades. Data for a flutter condition at 67 percent speed are shown on Figure 42. The arrow length in this plot represents the amplitude of the unsteady velocity relative to the maximum fluctuation observed For that test point. The direction of the arrow indicates the ohase angle referenced to the strain-gage signal from the No. 3 blade. The major fluctuations of velo- city occurred on the forward part of the airfoil, but some significant fluctu- ations also occurred at midchord and near the trailing edge.

The blade-mounted hot-film data were not analyzed from the standpoint of

determining flow separation from evaluation of turbulence levels. Determina-

tion of separation point location within the gage spacing can probably be obtained from the existing data, but the spectral analysis required is beyond the scope of Lhe present analysis.

Adoitional hot-film data are given in Appendix E.

6.6 REDUCED VELOCITY VERSUS INCIDENCE ANGLE Empirical correlations of reduced velocity versus incidence angle have been used extensively as a stall flutter criteria. The range of design types over which any specific correlation will accurately predict flutter boundaries, however, is questionable. Existing correlations were based on measured air angles, but blade metal angles were usually taken as the calculated metal angle at design speed. In this program, actual metal angles were measured.

Figure 43 presents a plot of reduced velocity versus measured incidence angle.

Incidence angles were based on the blade leading-edge mean-line metal angle.

The reduced velocity parameter, V/boo ,is the ratio oF the relative inlet velocity, VI', to the product of the blade half-chord, b, and the rotational flutter frequency, oo, in radians per second.

Figure 43 shows that flutter occurred at high incidence angles only over a limited range of reduced velocity values, with flutter-free operation being obtained at reduced velocities both above and below those at which flutter w_s achieved for a given incidence. A possible explanation is that locally super- sonic flow may be required for flutter and that this was not achieved at low rotor speeds and velocity ratios, even at high incidence. At very high speeds and velocity ratios, the incidence was too low even at surge to support flut- ter.

Conventional values of incidence based on calculated design speed metal angles and reduced velocity parameters for any selected radial position can be ob- tained from interpolation of the blade element data in Appendix A and the blade chord data in Appendix B.

SECTION 7.0 SUMMARY REMARKS Certain phenomena were consistently observed when flutter occurred, and some of these may be necessary for flutter.

7.1 LOADING LEVEL Stall flutter is initiated by an increase in aerodynamic loading level, and reducing the loading level returns the stage to stable operation. The loading level at which flutter occurs, however, is not unique because small modifica- tions to the airfoils--or sometimes simply reassembly of the rotor using a different blade sequence--will move the flutter boundary significantly.

7.2 LOCAL SEPARATION Local separation has been a popular candidate as a cause of flutter. The physical concept by which separation, particularly oscillating separation, might put work into the system to induce flutter is conceptually attractive.

In addition, such a theory would be consistent with the observed relationship between flutter and loading. Although the data analysis procedures used in this program did not clearly reveal regions of separation on the airfoils, a more detailed analysis might reveal that such separation did occur, at least on _nall areas of the airfoils.

7.3 OSCILLATING SHOCKS Oscillating shocks is another intuitively attractive cause of flutter. The pressure step across the shock is on the order of 1.4 N/cm2 (2 Ibf/in. 2) and small oscillation could put work into the system. In addition, stall flutter does not occur, at least in the TS22 stage, at speeds below those where local supersonic flow occurs.

An oscillating shock would also be expected to produce a region of high un- steady pressure on the unsteady pressure amplitude contour plots. Such a region was not observed.

7.4 REDUCED VELOCITY VERSUS INCIDENCE Empirical correlations of reduced velocity versus incidence have been used to predict flutter boundaries for stall flutter. This is essentially an extension of wing flutter theory. This empirical approach, however, has not been com- pletely successful when applied to a variety of design types. The subject pro- gram supplied data for incorporation into existing correlations.

7.5 CENTER OF PRESSURE-CENTER OF TWIST The relative p._itior_ of the aerodynamic center of pressure and the structural ce. ter of twist has been considered significant in flutter. This theory states that flutter will occur if the effective aerodynamic center of pressure moves ahead of the structural center of twist of the airfoil. The case-mounted Kutites in this program gave data on pressure distributions in the blade tip region, which might give a clue to center of pressure location, but data at aft radial positions must be considered in such an analysis.

'q l'T |ON _.0 SIlMMARY OF RFSLIL_TK Althouqh lht' proqr,lm ol_.Ioctlvf" _'._,l,ll_,d pr_nl,'Irllv to the acqu4'_1lion of dal,1.

'_,v_,r,11 h11por_anl conc lu._l_n'_ c.lrl L_, drawn fr_1 tho r_,view of II_' dat._ com- plc'ted un_k'r the cordr,,.ct: l ° tln,.te,ldv work durinq ,.t,'_l I f luttor _ccurr¢,d almo,,t _,ntirelv in the , ° forward ,._,ctic.n of the' ,'_irfoil.

The lllll_|l' .;tructure Jtlrirlq ';tall flutter w,l'., lllOl't, cc._91 leafed tharl prt, viOll_Iy ';tli_l'_o',.¢'_. ,lPl_,ll't'rll Iv l_'_',I_I<,(" lho of f_,_'tk of t11i,,;,tllrlitlt] r¢"_ult frcan l_l,_d¢'-to-hl.lde v.lrl,lt ion'_ thal prov_ou,_Iv w_,r_, a<.';.tlm_,d to b_' i ll';iqll_f i,',111| .

4.

SECTION 9.0 RE COMMEN DAT IONS The development of a design system that will preclude stall flutter requires a better understanding of the physics of the phenomenon. This program provided new data for obtaining that understanding.

The next step should be a more detailed analysis of the available data to determine the behavior of such phenomena as mistuning, localized separation, shock oscillation, and the unsteady pressure change across the blades.

Such a detailed analysis would then suggest additional test programs in which the specific parameters identified as significant could be varied to quantify their effects.

An osciilating shock would also be expected to produce a region of high unsteady pressure on the contour plots. Although such a region was not observed, additional data might be extracted from the recorded data.

SECTION 10.0

REFERENCES

i •

Stargardter, H: "Optical Determination of Rotating Fan Blade Deflections,"

Journal of En_ineerin 9 for Power, April 1977, pp. 204-209.

o

GIawe, G. E.; Simms, F. S.; and Stickney, T. N.: "Radiation and Recovery

Corrections and Time Constants of Several Chromel-Alumel Thermocouple

Probes at High Temperature in High Velocity Gas Streams," NASA TM X-2170, 1971.

t Mikolajczak, A. A.; Arnoldi, R. A.; Snyder, L. E.; and Stargardter, H.:

"Advances in Fan and Compressor Blade Flutter Analysis and Predictions,"

Journal of Aircraft, April 1975, pp. 325-332•

4. Stargardter, H: U.S. Patent 4080823, "Vibration Measurement."

TABLE I

TS22 FAN STAGE DESIGN PARAMETERS

Aerodynamic

Pressure ratio

R ot or

I. 702

1.67

Stage

Adiabatic Efficiency

Rotor

O. 871

O. 838

Stage

Corrected F low

95 56 kg/sec

(210.67 Ibm/sec)

Specific F low

202.78 (kg/sec/m2).

(annulus at rotor inlet) (41.53 Ibm/sec/ft _)

Geometric

O. 8178m

Rotor Tip Diameter

(2.7 ft)

N4mber of Blades

2.6O

F_b Solidity

I. 315

T+p Solidity

Hub/Tip Ratio O. 32

(rotor leading edge)

Partspan Shroud Location

(percent span from hub)

3b

TABLE II

TS22 BLADE DESCRIPTION

11,042 rpm

Corrected Design Speed

Airfoil Series

Multiple Circular Arc

3.6

Aspect Ratio

1.5

Taper Ratio

472.4 m/sec

Tip Speed

(1550 ft/sec)

Root Diameter

26.2 cm

Inlet

(10.3 in.)

Tip Di ameter

81.7 cm

Inlet

(32.2 in.)

79.7 cm

Exit

(31.4 in.)

Bet a l*(a)

Root

54.999 deg

Tip 27.0399 deg

Beta 1" Suction Surface( b )

Root

48.503 deg

25. 398 deg

Tip

Chord Length

Root 7.47 cm

(2.94 in.)

Tip 10.42 cm

(4.10 in.)

Notes:

(a) Beta i* is the leading-edge metal angle, #,*, the angle between the

tangent to the mean camber line and the meridional direction.

(b) Leading-edge metal angle based on suction surface.

(

TABLE Ill

LEADING EDGE ANGLE

BLADE INSPECTION RESULTS

Des ign

Value Minus

Percent (a)

Average Value

Minimum Maximum Average

Span Design

47050' OO04

47o40' 48o12 '

O. 08 47 o 54

0o26

45044'

45o24 . 46o0'

O. 12 46 o 10

42o42 0o12

42o16' 43o12'

O. 22 42o54

0o30

39o28' 39o46 . 39o37

O. 32 40 o 54

37o29 0o29

O. 43 37o 58 37018' 37040'

0o23

3608, 3700, 36o29

O. 52 36052

36o55 0o9'

36050 ' 3700'

O. 55 37o4 '

0o 52'

36c10 , 36028 ' 36o18

O. 58 37010'

3502 ' 0o24 '

O. 62 35026' 3500 ' 3508 '

0o21 '

33030 ' 34o54' 34015'

O. 66 340 36'

31o5 ' 0o55 '

31048 ' 31052'

O. 72 3200 '

30029 ' 0o14 '

28024 ' 28044 '

O. 82 28050 '

.0o05 '

2504 ' 25050 ' 25029 '

O. 92 25o24 '

22058 ' 0o12 '

22056 ' 2304 '

O. 99 23010 '

Note: (a)Percent Span From Hub

DIRECTION

EDGE

LEAO*NG I

ANGLE

(3?, .....

OF prJL;., _." ..L, ,_'='

TABLE IV

TRAILING EDGE ANGLE

BLADE INSPECTION RESULTS

Des ign

Percent (a)

Value Minus

Span Design Mi nimum Maximum Average Average Value

0.08 96o50 ' 95o50 ' 9602 ' 95054 ' OO56

O. 12 87o10 ' 86o14 ' 86042' 860 28' 0o42

O. 22 69o56 ' 69o0 ' 70016 ' 69037 ' 0o29

O. 32 58028 ' 57o58 ' 0o14

58034 ' 58014 '

O. 42 4908 ' 48o42 ' 4900 ' 48040 ' 0o18

O. 52 44034 ' 43o44 ' 44o40 ' 4407,

0o27

O. 55 43042 ' 43o24 ' 43o30 ' 43o28 ' 0o14

0.58 43014 ' 42o22' 42o46' 42037 ' 0o37

O. 62 41o0 ' 4004 '

40028 ' 40015' 0048

O. 66 39042 . 4904 ' 39o52 ' 0o17

39o25 '

0.72 35028 ' 35026'

35038' 35032 ' 004,

0.82 30028 ' 30014' 30048' 300?9' 0o1'

O. 92 24o24 ' 24024' 25o0' 24041' -0o17 '

0.99 21o58' 21038' 21056, 21044' 0o14 '

Note: (a)Percent span from hub

AXIAL l DIRECTION TRAILING EDGE ANGLE

TABLE V

INSTRUMENTATION AND READOUT EQUIPMENT

Non-Steady Instruments Recorded

32 Strain gages

24 Hot films - blade mounted

4 Stationary hot film probes

i0 Wall Kulites

32 Blade mounted Kulites

102 Sensors

Recorders

i 70 channel multiplex

2 9 channels Sangamo

3 11 channels Sangamo

4 12 channels strain gage console

5 4 channels strain gage console

106 channels

Each of the five recorders had strain gage 3 in parallel as a common signal to

permit time correlations between any of the 102 sensors.

TABLE V I

HIGH RESPONSE INSTRUMENTATION SPECIFICATIONS

Kulite - Model XCQL-8V-808

Rated Pressure:

17.24 N/cm 2 (25 Ibf/in. 2)

3.8 x 104 mV/N/m 2 (2.62 mV/Ibf/in. 2)

Sensitivity:

Temperature Compensation

278K to 422K (40OF to 300°F)

Acceleration Sensitivity:

Traverse

0.00004% Full Scale Gage

0.0002% kHz

Perpendicular:

230 kHz

Natural Frequency

+0.75% full scale maximum

Non-Linearity and Hysteresis:

Kulite - Model LQL5-080-25S

Rated Pressure: 17.24 N/cm 2 (25 Ibf/in. 2)

Sensitivity 3.8 x 10 -4 mV/N/m 2 (2.62 mV/Ibf/in. 2)

Temperature Compensation: 278K to 422K (40OF to 300OF)

Acceleration Sensitivity: Transverse:

0.00008% Full Scale Gage per g

Perpendicular:

0.0004% Full Scale Gage per g

125 kHz

Natural Frequency:

Quartz Hot Film

Thermo-systems model 1210-60

0.0154 cm (0.006 in.) quartz rod with platinum sensor deposited 0.203 cm

(0.080 in.) between posts

Temperature coefficient of resistance = 0.0026 ohm/ohm-OK

Frequency Response at 91.44 m/sec (300 ft/sec): 200 kHz

i

TABLE Vl I

TS22 NASA FLUTTER TEST TEST MATRIX Percent Rotor Corrected Pressure Run Speed Point Unsteady Percent Remarks Number Code Number Record Speed Desiqn Flow Ratio Shakedown All Mirrors 72.8 1.228 Wide Open Discharge 001 70 01 20-27 70 ...... 28 70 Closing Discharge Valve, Transient into Flutter 66.9 1.2722 Check Point Wide Open Discharge 001 70 05 43 70 Transient ...... 64T -- 65.8 1.1776 Wide Open Discharge 003 63 01 71 63 53.4 1.2374 Stress Level Fluctuating, Shakedown 003 63 03 76-84 63 Complete Performance All Mirrors 73 74.7 1.2C87 Wide Open Discharge 003 73 01 86-94 Maximum Flutter 73 60.0 1.3 .7 003 73 02 100-10,8 3 Watt Laser 4 Rows Mirrors {Above Shro d_ 128-135 70 59.8 1.3L_ 70% Low Flutter Point 004 70 03 136-143 67 68.5 1.1890 004 67 01 Wide Open Discharge 0O4 75 01 176-183 75 75.3 1.2840 Wide Open Discharge Maximum Flutter 195-202 75 60,3 1.3369 004 75 04 220 70 56.5 1.29/8 005 73 08 All Mirrors 3 Watt Laser Maximum Flutter 239 66 54.5 1.26 007 66 01 242-249 55 52.0 1.1530 007 60 01 Near Surge (Rotating Stall) 27g-286 85 85.8 1.3792 Wide Open Discharge 007 85 02 287 ......

Transient To Surge 288-295 85 75.1 1.4862 007 85 05 Near S4Jrge

TABLE Vlll

UNSTEADY WALL PRESSURE AMPLITUDES FOR INDIVIDUAL

NODAL DIAMETER PATTERNS FUNDAMENTAL MODES ONLY

(NO HARMONICS)

Relative Power Spectral Density

Nodal Percent Chord

Diameters -55.4 -15.1 -3.6 9.4 22.2 34.6 47.5 73.4 99.3 141.4

67 Percent Speed

3 30

4 40 45 24 25 33 34

5 65 58 50 i00 140 220

6 65 60 60 50 7O

7 65 70 75 70 85 80

8 100 140 80 80 85 6O

9 85 100 45 35 28 20

I0 30

73 Percent Speed

3 26 24 25

4 40 36 24 57 41

5 9 25 96 54 78 100 140 170

6 10 32 92 59 86 74 150 125

7 24 84 96 68 165 240 180 340 270 280

8 35 77 130 165 150 140 160 150 120

9 II0 88 75 44 35 38

i0 26 125 80 34 31 24

7 m Percent Speed

3 18 17

4 25 20

5 50 I00 55 39 45 60

6 50 80 78 70 70 100

7 120 70 50 45 45

8 140 Ii0 78 55 75

9 120 85 45 35

I0

.__..__J

TABLEIX

COMPUTED DAMPING IN DOMINANT HARMONICS

AT 70 PERCENT SPEED

Log

Harmonic Decrement

5 -0.012

7 -0.001

9 +0.002

Complex pressures used in damping calculation normalized to 1600 N/m2

(0.232 lbf/in.2).

Percent Upper Upper Lower Lower

Chord Rea_._._L] Imaginary Rea___! Imaginary

-3.4 O. 039 -0.091 O. 022 -0. 022

9.4 0.573 -0.681 0.056 -0.134

22.2 O. 504 -1.000 -0. 254 -0.060

34.6 0.095 -0.12__ -0.069 -0.050

5 Nodal Diameters

47.5 O. 030 -0.24 _': -0.086 -0. 142

73.4 0.138 -O.OE, -0.108 -0.086

99.3 O. 198 -0.02£ -0. 228 -0. 039

-3.4 -0.065 0.01 0 0.043

9.4 -0.250 0.190 0.039 0.026

22.2 -0.177 0.384 -0.091 0,241

7 Nodal Diameters

34.6 -0.091 O. 056 -0.121 O. 052

47.5 -0.095 0.060 -0.129 0.052

73.4 -0. 129 -0. 004 -0. 112 O. 004

99.3 -0.112 -0.052 -0.147 -0.043

-3.4 -0.112 -0.099 0.009 -0.009

9.4 -0.030 -0.259 -0.069 -0.134

22.2 -0. 181 -0. 134 -0. 129 -0. 091

34.6 0.017 -0.03_ -0.043 -0.043

Nodal Diameters

47.5 -0.030 -0. 172 -0.052 -0. 164

i

73.4 -0.043 0.(;56 -0.017 0.060

99.3 0.043 -0.194 0.022 -0.233 J

J 20 MI RRORS LOCATED AT 4 INNER WALL STATIC (_ STATIC PRESSURE 7 RADIAL POSITIONS PRESSURE TAPS 4 IO AND DO WALL STATIC PF_ESSUE PRESSURE TAPS (_ TOTAL PRESSURE. STATIC 20 STRAIN GAGES LOCATED ON PRESSURE AND FLOW ANGLE 10 C:FFERENT BLADES TIME VARIATION IN 16 BLADE MOUNTED LOCAL MASS FLOE FLOW 2WEDGE PROBES TRAVERSED HOT FILMS TO 7 RADIAL POSITIONS (VZ) 1 STRAIN GAGE PER a-L._,_ BY 2 HOT FILMPROBES 2 COMBINATIOM PROBES TRAVERSED TD TRAVERSED TO 7 RADIAL POSITIONS 3_ HIGH RESPONSE PRESSURE 7 RADIAL POSITIONS TRANSDUCERS ON & DIFFEREN1 3 DUAL TOTAL TEMPERATURE AND BLADES LOCATED TO OBTAIN TOTAL PRESSURE PROBESWITH MEASUREMEI_rs AT 7 RADIAL (_2 WEDGE PROBES TRAVERSEO KIEL HEADED SENSORS LOCATED AT 9 POSITIONS TO 7 RADIAL POSITIONS RADIAL POSITIONS. THESE ARE LOCATED APPROXIMATELY 120 ° PROBES TRAVERSED Q2 HOT FILM APART IN A CIRCUMFERENTIALLY (_10 KULITE TO 7 RADIAL POSITIONS ROTATABLE TRAVERSE RING THAT _ENSORS CAN BE POSITIONED TO PROVIDE AT TOTAL AND STATIC PRESSURE.

LEAST 11 TOTAL PRESSURE AND tO STAT IC TOTAL TEMPERA rtJRE. FLOW ANGLE TOTAL TEMPERATURE READoNGS PRESSURE ON ONE COMBINATI(JN PROBE ACROSS A ONE IO STATOR VANE TAPS TRAVERSED TO 7 RAD,A POSITIONS GAP AND TWO DO STATOR VANE GAPS 2 WEDGE PROBES TRAVERSED TO (_)4 OUTER WALL STATIC ? RADIAL POSITIONS PRESSURE TAPS ADDITIONAL INSTRUMENTATION GEARBOx ROTOR ROTAT_VE 2 IMPIJLSE TYPE PICKUPS SPEED (RPMI ;NLET DUCT CALIBRATED ORIF ICE FLOW RATE ROTOR INLET 6 WALL STATIC PRESSURE TOTAL PRESSURE TAPS LOCATED IN THE PLENUM CHAMBER TOTAL TEMPERATURE 6 BASE WIRE CHROMEL ALUMEL THERMOCOUPLES LOCATED IN THE PLENUM CHAMBER

Figure 1 3chematic

Diagram of TS22 Rig

iqmmm"mmm_'_ o_ o_ o_ -.J G; -- c_ I-- 0 -- U. X < -- ._ _ t_ C 0 _0 _w tJ

N °

--J _ O - _ .._

g

C u_ - _ 0_:_ 0_..

_ .r.- I 1 1

l _ 1 l 1 i

¢N C_ C_

Z±W3N ~ _N3003_W

CONTROL ROOM / AIR COLLECTOR /*" ELECTRIC MOTOIq _ ....

OlqlVI! _ TEST $11CTIO N

. °""°_ f---N ;!

---_ _ _'--- ---- -- --t--

EXHAUST TO IXHA_ERS EXHAUST TO ATMOSPHERE OR COMI_I ESSORS INLr;' FROM ATMOSI_411FIE -_-__L_.._

Figure 3 Schematic of X-204 Test Stand

.... _"'_"/, }>,(,h I_

48 (..'i.' l'(.;( )}{ C)UA !,lrY

%

.._-24 VIE.EO ioi-_--

.FROM :- ii /

,REAR

_ \_._,5 "_22 - 12_

# z9 15

NOTE

ALL BLADES HAD ONE

ASMT STRAIN GAGES

Figure 5 Circumferential Location of Blade Instrumentation

4g

/ \

e-" °qF.,- l, ..t..- te- e..

k, ...J O4 X !

¢,t) q..

t_ .i-- 4_ e-" t.J t.O l, t_ t.I- rv"

I

I t.,O

-..I t,,o

I

I

"l., .LL.

I

tj .._1 ...d L_ I.-- V-- m

BLADE MIRROR LOCATION

BLADE

PERCENT CHORD (b)

PERCENT SPAN (a)

NUMBER

86.3 5O

5O

3 86.3

5O

4 66.0

66.0 25

9 95.2 5 25 50 70

86.3 5 25 50 70

76.4 5 25 50

5 25

66.0

25 50

55.0 5

47.0 5

38.0 5

20.0 5

TIP

Note: (a) Percent Span From Hub

Z 86 ------

o.

t_ F-

z 76 "--"--

LU (..)

OC W

a. 66

SHROUD

,-., 55 -----

e_

38 ------

HUB

Figure 7 Mirror Installation Locations

i ! ,__

_I'I ,,..4 I ¢_i _"_I e_l" I',,,.,,. 0'_ e_l- Q,I

I i

0 0 0 0 0 0 0 0 _ 0 Q;

I

C LLJ X !

Q_ -J W C U ..J e.- ,.---_ C CO Q_ U.

o O--

®-I®-®, -®-7 ®-

LOCATION OF KULITE TRANSDUCERS

ON BLADE SURFACE

Blade :Percent Probe Location

(Percent Chord (b)

Suction Surface-

NO. Pressure Surface

Spa n.(a)

2 76.4 5 15 25 40 65 90 5 25

3 76.4 5 25 5 15 25 40 65 90

86.3 5 15 25 40 65 90 5 25

5 86.3 5 25 5 !5 25 40 65 90

86.3 50

Note: (a) Percent Span From Hub

(b) Percent Chord From Leading Edge

RADIUS

76.4 % SPAN

Blade

No.

4 p5_1-525//[ 86.3 % SPAN

Installation Locations For Blade-Mounted Kulite Pressure

Figure 9

Transducers

Location at Hot-Films On Blade Surface

Percent Percent Chord )l-b-T_ Probe Location

B Iade

Surface

Sp an fa) Pressure

No.

76.4 5 4O 5 40

21 76.4 5 15 25 40 65 90

22 36.3 5 40 5 4O

23 86.3 5 15 25 40 65 90

Note:

(a) % Span From Hub

(b) % Chord From Leading Edge /

RADIUS

7B.4 % SPAN

BLADE NO. _URE

201/ ,/'

ORIGINAL PAGE IS

OF POOR QUALITY

21 1 RADIUS

8B.3 % SPA N

//_4/_ cHORD I

23//

Figure 10 Installation Locations For Blade-Mounted Hot-Film Sensors

NO FLUTTER

FL UTTE R

Figure II Typical Laser Mirror Results for Operation at 67 Percent Speed

In and Out of Flutter

_ (jT:,,_"" "' "" OF pOOi'_ ',-.:.- .....

Z

I v Y Figure 12 Finite Element Diagrams Used for NASTRAN Analysis

OTRANSIENT DATA POINTS

RECORD 133

[_]FULL DATA POINTS

1.30

coco #--

CORD 43

1.28

-, __RE

o

_ 1.26

N

W

TRANSIENT DATA POINTS

\

1.24

- I.

RECORD 25 WIDE OPEN \

2. OUT OF FLUTTER _,-'F _F

3. FIRST FLUTTER INDICATION ON HOT FILMS

o,

1.22

-- 4.

FIRST FLUTTER INDICATION ON STRAIN GAGES 2 \

5.

FLUTTER lb

I I [ i

1.20 I I

55 60 65 70 50 75 80

PERCENT DESIGN FLOW

Figure 13 Identification of Data Points at 70 Percent Speed, Including

Transient From Open Discharge Into Surge

r - -

O__ t_3_ _"_ '

• INDICATES NEAR SURGE SURGE LIMIT FLUTTER 8OUNDARY CORRECTED SPEED 75% 73% 60 70 80 5O PERCENT OF CORRECTED DESIGN FLOW

Figure 14 TS22 Performance Map Showiag Test Points In Relationship To

Flutter Boundary

/% 5% CHORD FROM LEADING EDGE 1.5 O 25% 1.4 O 50% 1.3 O 70% 1.2 1.1 //UNTWIST 1.0 ,-- HIGH _ 0.9 -- (4 UJ ,U,J CE (.3 0.8 -- t,u Q (4 0.7 -- z D STATIONARY 0.6 -- 0.5 -- AXIAL DIRECTION 0.4 -- _ STARTING 0.3 REFERENCE SPEED FOR MEASUREMENT 0.2 0.1 -- I I I II1 1 I 1 i I,,,I 10 20 30 40 50 60 70 _ _ 100 ROTOR SPEED, PERCENT OF DESIGN Figure 15 Measured Untwist for TS22 Fan Blade as a Function of Rotor Speed at 95 Percent Span

A

/_ 5% CHORD FROM LEADING EDGE O 25",o CHORD O 50% CHORD E3 70% CHORE) QUESTIONABLE DATA POINT

\

40 50 60 70 80 90 TIP PERCENT SPAN

Measured Untwist for TS22 Fan Blade at 73 Percent Speed

Figure 16

Relative to Untwist at 25.4 Percent Speed

O 5% CHORD

75% CHORD

Z_

I.-" __rr"__ e_ 14 II.]

< Z ...I ,< D

t

70 75 60 65 CORRECTED FLOW

Figure 17 Measured Untwist for T322 Fan Blade as a Function of Flow Rate

at 75 Percent Speed

k, C; p6_i, .

w 1.1 1.0 95.2% FROM HUB __ _.AN 0.9 0.8 0.7 _ 0.6 a " 0.5

g

0.4 _ 55.0% 0.3 0.1 0.2 i

1 1 I 1 I

0 10 20 30 4O 50 70 80 90 1_ L.E.

CHORD, PERCENT

Measured Untwist for TS22 Fan Blade as a Function of Chord at

Figure 18

73 Percent Speed

C ..... '[

1.2 _ DATA m.... ANALYSIS % % RADIUS = 95% SPAN 0.8

0.4 I I I i l I I I I I

20 40 60 80 100 r,r {3 L,U 101, _r _ RADIUS =86% SPAN w" .J L_ Z < g- z 0.4 0 20 40 60 80 100 RADIUS = 77%_PAN 0.2 I I I [ i I I 1 I I 0 20 40 60 80 100 LEADING PERCENT CHORD TRAILING EDGE EDGE

Figure 19 Measured Untwist for TS22 and Predicted by NASTRAN Analysis for

Rotor Speed at 75 Percent Speed

TRAVELING NODAL DIAMETERS

_'2__ ___

Figure 20 Three Nodal Diameter Pattern Second Mode - Previous theory

predicted the presence of only one nodal diameter pattern at

any time

J _J L 4-- m m m m mm <( (-3 n 0 -- x I-- x ow _z (J

I

I U3 LM mr -J k- u3 - i m -- 0 i 4 6 B 10 12 _4 16 18 20 22 24 26 28 30 32 BLADE NUMBER Figure 21 Blade Flutter Amplitude for TS22 Rotor at 67 Percent Speed From Strain-Gage Measurements u_ 36O uJ

O

UJ

O

rr (3 UJ

0 0 0 0

c]

270 O0 o

0 0

z

0 0

.1

(3 180 0

<c (D

0 0

z m

0 0 0 0

n..

_- 90

- 0

o I-- uJ O <c o I _ I I I I I I t i I I I I I I I 1 1 I I 1 ! I I I I I I -I- O,, 1 4 8 12 16 20 24 28 32 BLADE NUMBER

Figure 22 Blade Flutter Phase Angles for TS22 Rotor at 67

Percent Speed From Strain-Gage Measurements

% MAXIMUM PRESSURE CURVE CURVE LRBEL VRLUE 2 0.930000E_02 3 0.8"0000E*02 0.790000E_02 5 0.720000E*02 8 0.850000E*02 ? O.SBOOOOE*02 O 0.SIOOOOE*02 MAXIMUM STATIC PRESSURE 9,63 N/cm2(13._lbf/im 2) ROTATION BLADE 4 BLADE 3 ,.

• T T •

-2_.oo -'2o.oo -'18.oo -',2.oo -e.oo -'_.oo o'.oo _'.oo e.oo

TANGENT IRL (BEG]

Figure 23 Steady-State Pressure Contours at Blade Tip at 63 Percent Speed

Outside of Flutter on a Low Operating Line

% MAXIMUM PRESSURE CURVE CURVE LRBEL VRLLIE 2 0. 95001)0E','02 $ O. 860000E_'02 q O,7900UOE*02 5 0.720000E4"02 8 O. 8500001£ 02 MAXIMUM STA'TIC PRESSURE 10.18 N/cm 2 (14.75 Ibf/in. 2 O O O ROTATION BLADE 4 BLADE 3 /, / / O v r -2tl. 00 -20.00 -18.00 -12.00 -8.00 -_.00 0.00 _.00 8.00 TANt;ENT IRL (DEG)

Figure 24 Steady-State Pressure Contours at Blade Tip at 63 Percent Speed

Inside of Flutter on a High Operating Line

% MAXIMUM PRESSURE CURVE CURVE LRBEL VRLUE 2 0.93OO0OE+02 3 0.880000E+02 ¼ 0.790000E+02 5 0.720000E'02 6 0.650OOOE*02 ? 0.580000E*02 8 0.510000E*02 MAXtMUM STATIC PRESSURE 9.76 N/cm (14,141bf/in. 2) "_ _ ROTATION BLADE 5 BLADE 4 _3 "to.

¢._=P I" ! ! !

-20.00 -iS.00 -'t2.00 -8.00

-28, O0 -2¼° O0 4.00 0.01)

TANGENTI F_L (OEG)

Figure 25 Steady-State Pressure Contours at Blade Tip at 67 Percent Speed

Outside of Fiutter on a Low Operating Line

% MAXIMUM PRESSURE CURVE CURVE L_L VM.U_ l 0. IO_OQOE_ Z 0. S_I(_OOOE H37.

3 O. NOQO_*O_.

0. ?qJ000OC _?.

5 O. 7Z0000_4'0Z 8 0.8S0000(,'OZ MAXIMUM STATIC PRESSURE 10.38 N/cm (1 5.00 Ibf/in, 2 0I ,=mr ROTATION , BLADE 5 BLADE 4 BLADE 3 T_NGENT I Rt_ _, OE G]

Figure 26 Steady-State Pressure Contours at Blade Tip at 67 Percent Speed

Inside of Flutter on a High Operating Line

7O

° _., % MAXIMUM PRESSURE CURVE CURVE LRBEL VRLUE 2 0.930000E*OZ 3 0.880000E÷02 O,?90000E*OZ 5 0.720000E*02 6 0.850000E*02 ? 0.580000E*02 8 0.510000E*0Z MAXIMUM STATIC PRESSURE 9.83 N/cm2(14.251bf/in. 2)

_'L'-

_. ___ _ ROTATION 4

=

"tO.

(.J=P

i

P_

•° ¢3 ¢3 ::=P.

I -'12,00 -8.00 -_.00 0'.00 _.00 8.00 12.00 16.00

TRNGENT IRL [DEG]

Figure 27 Steady-State Pressure Contours at Blade Tip at 70 Percent Speed

Outside of Flutter on a Low Operating Line

7!

% MAXIMUM PRESSURE CURVE LRRE'L VRLUE 2 0. _00go_*02 $ 0. INI0000E'_'02 $ O, _+G_ 8 O. 8S_32 70. 5aooom_.a2 8 O. S_ OQOO["_ 9 O. _O00m[_02 %0 O. $'tOOOOE*02 11 o. _IO0OOOE4.OZ l 2 r,. 2300001[',02 MAXIMUM STATIC PRESSURE 11.87 N/cm 2 117.20 Ibf/in. 2)

/_ ROTAT,O. I K. I_-'X l

F s s BLA _4 4 _ 4

i"

T

-'21l. 01_ -2O.OO - 18. 010' -12.00 -(I. O0 -ll. O0 O. OO ¼.00 8.01) 12.00 TRNGENT IRL (DEG)

Figure 28 Steady-State Pressure Contours at Blade Tip at 70 Percent Speed

Inside of Flutter on a High Operating Line

% MAXIMUM PRESSURE CURVE CLIRYE LRBEL VRLUE 2 0. 930000E+02 3 O. 880000E",'02 l 0. 790000E*02 5 0. 720000E"02 8 O. 850000E*02 7 0. 580000E*02 8 0.510000E','02 MAXIMUM STATIC PRESSURE 10.43 N/cm 2 (15.11 Ibf/in. 2) Q o ROTATION BLADE 4 BLADE 3 -28.00 -2¼.00 -20.0t_ -18.00 -12.00 -8.00 -_.00 0.00 ¼.00 8.00

TflNGENTIRL (DEG}

Figure 29 Steady-State Pressure Contours at Blade Tip at 70 Percent Speed

Near Surge

% MAXIMUM PRESSURE CURVE CURVE LRBE'L VRLUE 2 O. 9300_JOE'*'O'2 3 0. gBOOOOE÷02 ti 0. 790000E÷0"2 5 0.72t_OOE*02 8 O. 850000E_'02 7 O. 51_O00E*Q2 8 0.5t000OE-02 MAXIMUM STATIC PRESSURE 10,25 Ntcm 2 114.85 Ibf/in. _ ROTATION _ e_^.OE _. _LADE 3 _" -2e. oo -}_. ao -20. O0 -'I8. O0 -t2.OO -_.00 -q,. O0 0._0 _.00 8.00 TANGENTIAL (BEG1

Figure 30 Steady-State Pressure Contours at Blade Tip at 73 Percent Speed

Outside of Flutter on a Low Operating Line

?4

r..

• ,,# % MAXIMUM PRESSURE CLIIIYE _I_VE LRa(L VRLUF.

O. 10000OE*O3 2 O. $_OOQOE*O_.

3 o. ee_ooe,.o_ 0, ?gO000E_ 5 O. 720000E*02 II 0. $S0000_ 7 0, SI_00QE-OZ 8 O. S 10000E*O_ MAXIMUM STATIC Pf_ESS;J RE 10,60 N/cm 2 (15.40 Ibf/in, 2) o[ __ ROTATION _ BLADE 5 BLADE 4 BLADE 3 ' ,_ -¼0.0O -.t8.00 -32.00 -28.00 -2_.00 -20.O0 -18.00 -t2.00 -8.00 -_.00 0.OO ;,O0 e. O0 Tt_NGENT IFIL :DEG}

Figure 31 Steady-State Pressure Contours at Blade Tip at 73 Percent Speed

Inside of Flutter on a High Operating Line

?5

C!-. ! -- .. • ,

C."" "

% MAXIMUM PRESSURE CURVE CURItE LAllE"L VALUE $ O._H_ 5 0. "_000Ec'OZ 8 O. $$_¢'02 ? O. _*02 0 O. S 1000W_'02 MAXIMUM STATIC PRESSURE 10.24 N/cm ;Z ( 14.83 lbf/in. 2)

_ _o,,,,ON \/ \" I.._

Figure 32 Steady-State Pressure Contours at Blade Tip at 75 Percent Speed

Outside of Flutter on a Low Operating Line

_ j O: % MAXIMUM PRESSURE _URVIE CURVE LRBEL VgLU( 1 O. 100OO0(-O3 2 0.930000(*02 3 O. !116_O00(*O2 0.790000( *02 S O. 720000('02 8 O. OSOOOOE*OZ "7 O. SlOOOOE*OZ e O.Sl O000E*O2 _tAXIMUM STATIC PRESSURE 11,22 N/crn 2 (16.30 Ibf/in, 2'

=_ o E AOE

-,_0. _0 -3B. 00 -_.00 -E8.O0 -2_. 00 -20.00 -_8,00 -12.30 -8.30 -q,. 0O 0.00 W.00 0.00 TRNGENT ;RL (DEG)

Figure 33 Steady-State Pressure Contours at Blade Tip at 75 Percent Speed

Outside of Flutter on a High Operating Line

7?

% MAXIMUM PRESSURE CURVE CURVE LRBEL VRLUE 2 O. 939000E4'02 $ O. 860000['02 tt O. 790000E+02 S O. 720000E"02 i; O. iiSO00O[*02 7 0. SSO0O0E*O2 O O. StOOOOE÷02 9 O. _OOOOE÷02 10 O. $?0090E+02 MAXIMUM STATIC PRESSU RE 11,65 N/cm 2 (16.88 Ibf/in. 2) ROTATION BLADE 3 _LADE 2

==

-_.00 0.00 _.00 8'.00 t!.O0 te. O0

TRNGENTIRL (OEG}

Figure 34 Steady-State Pressure Contours at Blade Tip at 85 Percent Speed

Outside of Flutter on a Low Operating Line

?8

% MAXIMUM PRESSURE CURVE CURVE' LABEL VALUE 2 0.93000OE*02 3 O. 880000_'.'02 Li O. 790000E','02 50. 720000E'¢"02 8 O. 850000E','02 7 O. 580000E*02 8 O. St O000E÷02 9 O. _liO00OE'*'O2 I 0 0. 3700001_',02 MAXIMUM STATIC PRESSURE 10.46 N/cm 2 (15,16 Ibf/in. 2) ROTATION BLADE 4f',_ _E3_ BLADE 2/_ -2¼.00 -20.00 -I8.OO -12.00 -B. O0 -_.00 0.00 Li. O0 B.O0 12.00 IB.OO TANGENTIAL (DEG)

Figure 35 Steady-State Pressure Contours at Blade Tip at 85 Percent Speed

on a High Operating Line

.

, . '. • % MAXIMUM PRESSURE CURVE CURVE VAI.UE 3 0. _'*'0;!

0,7ii0000E4"0 := II 0. IISO0_I[*02 ? O. StlOO0_*02 I o. s1oo_o2 I O. IIIW_O0_02 MAXIMUM STATIC PRESSURE 1,105 N/cm 2 116.0 Ibf/in. 21 J . BLADE 4 ,. BLADE 3 ., BLADE 2 I 2_ 0O 20 00 1.e O0 1,2 00 e 00 _ 00 0 00 _ 00 8 00 L2 00 III 00 TRNGENTIRL (CEG}

Figure 36 Steady-State Pressure Contours at Blade Tip at 85 Percent Speed

Near Surge

OR[C!_!;_.....

' _ - " L; OF _'" .........

% MAXIMUM PRESSURE CURVE CU_¥E LROEL VRLUE l 0. I00000E*05 Z 0.900990(-02 3 0. I1000001_02 O. 70O000E_,O2 $ O. (IOOOOOE*02 O 0. S000OOE_'O2 7 O. tO0000E*02 8 O. 300000E_'O_ 9 0.2000QOE-02 l0 O. 100000(_02 MAXIMUM STATIC PRESSURE 0.308 N/cm 2 10.4.47 lbf/in. 2) c_ d _, d

._ - . .... \-.__._.%_ _ _-"

-_z.oo i_e.oo -a4.oo -2o.oo -ze.so -zz.oo -e.oo -4.oo O.0O _.00 B.30 _2.00 :8.00 20.00 TANGENTIAL CDEC)

Figure 37 Unsteady Pressure Amplitude Contours For TS22 Rotor in Flutter

at 73 Percent Speed

% MAXIMUM PRESSURE CUR¥_ CURVE L_QEL vIM._JE I 0. t O0O00E*0$ I t -. t 000OOE*0$ ?. O.800000t*OZ tZ - IZOOOOE_O",_ 3 O, lO00001[+OZ I $ - • tqlO0001_*O"_l u+ 0._000001[,'4"_ Ill -. _10000E+'41'3 S O.20000OE_011 IS -. LIO000_,*O_ I 0,0 LI -._O00001_*OqJ -. 2OOOOOt',.Ol _? -. 2200001E'_1'_ II - qOOOOOt,'Ol 11 -.ZqOOOOIt+Cl l -.lO¢O00t,'O"_ tS -+,Zl+1OOOt*O_J t 0 -. lO0000t _ ,ZO -. 28@000E+0'3 MAXIMUM STATIC PRE3SURE 0.150 N/cm 2 (0.21 ? Ibf/in. 2) 2"0_ +,.a :I' .-,,,+

_°

+;- .] f

+'_a. oo -'as. oo -_.oo -}o.oo -te.oo -_z.oo -e.oo -,_. oo o'.oo ,_'. oo s'.oo t}.oo t'=+ oo zo_oo TFINGENT I RL (0EG)

Figure 38 Real Component of Unsteady Pressure in Flutter at 73 Percent

Speed

%MAXIMUM PRESSURE C_qVE cuRvt LRIZI. W_.U( I O. 100000[*03 tP -.tOOOOO[,OZ Z O.II000001[*O;t 10 -.00GQ001[oQZ 3 0. |O0000E*0_ t % -. t300001[-03 q O._OOOQOE*OZ |= -. tZOOOO[_O$ S O. ZOOOOOI_-OZ 13 *. IWGOOOI_*'J3 | O.O Iq -. ISO00,,,31V_O3 ? -.ZOOOOOIr*O;_ IS -, teClOOOE*O] • -._000001[*0_ I I *.200Ocolr*03 MAXIMUM STATIC PRESSURE 0.155 N/cm 2 (0.225 Ibf/in 2) S.; _.. .

!: s.

?.

*|Z.00 *_11.00 oZft.00 -;_0.0O -re,00 -tZ,00 -I,30 -w.00 0,00 _.00 1,00 I='.00 ll.00 Z0.00 TRNGENT IRL 10EG)

Figure 39 Imaginary Component of Unsteady Pressure in Flutter at 73

Percent Speed

e- e_ _J

,g

Cn 1.14 "1" nL ,,.I L _ Q _,l.a

\

W e" m4-_ m_ _r ,_...

1.1_ o u_ _N _J

:lz

_r ul _r ct) _.U eL _ I i OR!C!_;_!.

¢,

OF F_G.'_

_,-...i_i!f

BLADE TIP BLADE TIP BEHIND ROTOR BEHIND ROTOR i' ,y \j ', _ , "v"_ y"y'Y-'c'v__

',:'X_,,; 'J_J _a,,W,'_ ", - "I'JYV

BEFORE ROTOR BEFORE ROTOR ,VV'v_j\.,\\'_J_h/T,%'x>, __. _.% %.\..,Vh, k.'hx_/'_ NEARSHROUD NEAR SHROUQ BEHIND ROTOR BEHIND ROTOR BEFORE ROTOR BEFORE ROTOR BLADE ROOT BLADE ROOT BEHIND ROTOR BEHIND ROTOR

,'Vwv_,VVvw_sm'Yw'vW_,V_,vv_'W'v"_w

. BEFORE ROTOR BEFORE ROTOR

Forms of Hot Film Probes at 73 Percent

Figure 41 Signal Enhanced Wave

Amplitudes)

Speed (Noncalibrated

PRESSURE SURFACE 90 ° SUCTION SURFACE AMPLITUDES ARE RELATIVE TO 180 ° 0 ° MAXIMUM OBSERVED FLUCTUATION 270 ° _. ROTATION PHASE TO SIG 3

,j

J / ./_

Q n- O -r "_ - 5 BLADE 23 BLADE 22 BLADE 21 /BLADE 20

Figure 42 Blade Mounted Hot Film Unsteady Velocity Amplitude and Phase

Obtained in Flutter at 67 Percent Speed

• J STABILITY PLOT BASED ON CONOITIONS AT 77 PERCENT SPAN FROM HUB PERCENT SPEED

O 6o

D 1.9

_7

r-! 63

_7

<> 67 A 70 m 1,8

121 7a

B 7, 75 V 85 1.7 n > B O .J 1.6 '--

A

S LU > ¢3 m

9"

<>

LU rj

Q

¢J 1.5 -- UJ rr UNSTABLE (_ STABLE 1.4 -- m

1.3 I 1 I 1 I 1 [ I I I I I i I I I I

5 6 7 8 9 10 11 12 MEAN INCIDENCE (INCM), DEGREES

Figure 43 Observed TS22 Flutter Boundary Correlation of Reduced Velocity

as a Function of Incidence

APPENDIX A OVERALL PERFORMANCE FOR TEST MATRIX (See Table A-l) PRECEDING P/_P_E BLAN._ NOT FILMED ?

L

T;,BLE A-1 1522 NASA FLUTTER TEST TEST MATRIX Percent Roto_ Run SL)eed Point Unsteady Percent Corrected Pressure _emark$ _umber Cod_._e_e Number REcord Speed _es___._gn Flow Ratio Shakedown All _iirrors 001 73 01 20-Z/ 70 72°8 1.22_ Wide Open Discharge ...... 2B 70 Closing Oischcrge valve, T,-_nsient into F i_tzer 001 ;0 05 13 70 66.9 1.2722 Check Point Wide Open Oischarge ...... 64T ...... Transient 003 6J 31 71 63 65.B 1.1776 Wide Open Discharge 003 63 03 ?b-_4 63 _3.4 1.2374 Stress Level Fluctuating, Sh,ked_ Complete Performance All Mirrors 73 74,7 1.2687 003 73 O1 86-g4 Wide Open Discharge 003 73 O? 100-108 73 60,0 1.3317 Maximum Flutter 3 Watt Laser Rows Mirrors (Above _hroud) 70 03 128-135 70 59.8 1.3004 70% Low Flutter Point 004 67 01 136-143 67 68.5 1.1890 Wide Open Discharge 004 75 O1 176-183 75 75.3 1.2840 Wide Open Discharge 004 75 04 195-201 75 60.3 1.3369 Maximum Flutter 005 73 08 220 70 56,5 1.2978 All Mirrors 3 Watt Laser 007 66 Ol 239 66 54.5 1.26 Maxi_ Flutter 007 60 Ol 242-249 55 52,0 1.1530 Near Surge (Rotating 5tall) OQI 85 02 279-286 05 _5.8 1.3?92 _ide Open Discharge ...... 2B? -- ,....

Transient To Surge 007 85 05 288-295 85 75.1 1.4862 Near Surge O0 OTRANSIENI DATA POINTS RECORD 133 0 FULL DATA POINTS 1.30 _ECORD 2 " 4(_,, 1.28 _ _.IRECORD 43 O 1.26 r_ \ TRANSIENT DATA POINTS c_c • ii J \ 1.24 RECORD 25 - I. WIGE OPEN L_.J r_ 2. OUT OF FLUTTER r_ 3. FIRST FLUTTER T.NDICAIION ON HOT FILMS 1.22 4. FIRST _ FLUTTER INDICATION ON STRAIN GAGES 2 \ • FLUTTER

....... [ l

1.20 [ I J 53 55 60 65 70 75 80 PERCENT DESIGN FLOW F!qure A-! Identification of Data Points at 70 Percent Speed, Including Transient From Open Discharge Into Surge III INDICATES NEAR SU,r.::I(3E St)ROE LIMIT FLUTTER 1.4 b 8(:JUNDAFI_, 7 75_, C..] t:;3% 5,4'_, I.'

j 50 60 "0 £(.)

PERCENT ()F ;ORAE(,TFD t")FSI(;N ;LOW Figure A-2 Compressor Map Showing Test Points In Rel,_tionshiD To Flutter Boundary AERODYNAMIC SUMMARY NOMENCLATURE Air velocity at station into rotor Vl v 2 Air velocity at station out of rotor Air velocity at station into rotor in Vm, l meridional direction VM-2 Air velocity at station out of rotor in Vm,2 meridional direction Air velocity of station into rotor in Vs,l circumferential direction V_-2 Air velocity at station out of rotor in V_,2 circumferential direction Ul Rotor tangential speed into rotor Rotor tangentia speed out of rotor U2 Air velocity re ative to rotor at station v' I into rotor v'2 Air velocity re ative to rotor at station out of rotor Air velocity re ative to rotor at station into rotor in clrcumferential direction Air velocity relative to rotor at station V'8,2 out of rotor in circumferential direction RHOVM- I Product of air density and air velocity in PlV=,I meridional direction at station into rotor Product of air density and air velocity in P2Vm,2 meridional direction, at station out of rotor EPS I-I Angle between tangent to streamline I projected on meridional plane and axial direction at station into rotor EPS I-2 Angle between tangent to streamline projected on meriodional plane and ax_a: direction at station out of rotor , { po/PO Ratio of total pressure leavinc _otor and P2/Pin entering rig B-I Absolute air angle at station into rotor B-2 3z Absolute air ang]e at std+ion out of rotor B'-I Air angle relative to rotor at station into 3'i rotor B '-2 Air angle relative to rotor at station out 3'2 of rotor M-I Absolute Mach No. at rotor entrance M I M-2 Absolute Mach No. at rotor exit M 2 M' -I Relative Mach No. at rotor entrance M' I M' -2 Relative Mach No. at rotor exit M' 2 INCS tss Incidence angle between inlet air direction and line tangent to blade suction surface at leading edge based on calculated metal angle for design speed ICH Incidence angle between inlet air direction and line tanqent to blade mean camber line at leading edge based on calculated metal angle for design sDeed DEV Deviation angle TURN Change in relative air anqle enterinq and leavinq rotor D FAC D Diffusion factor OMEGA-B Total pressure loss coefficient LOSS-P Loss parameter _'cos p' 2 / 2 o Polvtrooic efficiency EFF -P rp P EF F -A Adiabatic efficiency .,_ WC I/Al Corrected flow wl 8_/,S1A 1 TO/TO Ratio of temoerat_Jres le,lvinq rotor ,In_I r2/Tin onterinq riq ¢'N ***.*oleol d. _,,- _NP • leilllllll "_ 0 <_ 0 ellllllell ++;+_++_g; ,- :g O I I I t l I I I I _-_+_:_... . .

II|IIIIIIIP|| c',s,l I .< ,-3 _ll_eelell I <_ _I_ _=_.. .

++ ;_. J *••,• • **., i • , • • • • , , • -%

; i+,++,,o+

• ..,I g4 (}.

L

r, |1 .x * _ * * • * O_ l!

_J _ , _ ,_,, _ ,,_ ,_,, ,11 _ .,,_ _ ,*_ ,I* • ,_ 4" , ;.;, g I d - ,_- J *lb.

,; .: 3 3 .; ,; ./,; .; .; .; .: .; • I • , • • * • • • , • • * , o" • • • , • • • , , • • • £ ,.- • • .- .............. -..,, _ _ - .,, ., • .,, .,., ,_ ..... -.. . ,,,. ;. --. ., I -- * t i i i . I ,_ ' l i i I I i * I s • M ............................. ,, ....................... ., ..... o :., .1 2 , .... " ............................ :_ ........... • _ :; ;. ..........................

I,. ......... ..... _ , ........ ;:;_;,,.., ....... 3" F ..... _ ..... g "; ,.

* , " ', 2 ; T ; ," " : _ _ J " ; £ ," i _ ; _ ; 2 _ ; ; ; : : 2 g ...............

G. UJ _T cJ e.q_ 2_ ,NZ _ uJa: Z • • i • • . • • • :mw- i • • e • • e t we 4" N _JC3 • • • • e * • * _.

3E_'O0_C, O00C, O O0 O0 h,; _ g ff.J I_.

• • • I • • I _ • e I * • U 0.6"_,_ 0 L,_t'_O_P. N,O_r _0 _i--- * e I e • • e e • • e • t _. o tN _.

lg ' ° '' 'TT ........ _"_ ...... >:'7 7"" 5' '?

I I I I I I _ I I g • . . m.u_ b- 0 ,.'_ur, ,.t o_ --.,t u's,o O, _ ,_ T_ _ .0_ ¢_to • o-,_e.

----------''_^_'_ _ T TTT T'l'¥'{ ¥ i' 'i "¢_rq 0 , ae _ _r P I.I e_ ooo_=oooooooo _.

° g qr _OOC_OOCOCO00C u _uJ .t e_ . u.

C q6 {J t_ q7 % I I I I I 1 I t i ra e. t I I I I I I I I I I I _E z ! X t.t.J ..,,.J T _:g " I"- •,.q 00 C3 O000 _00000 _ _ • • * • * * * • _,_ o _ _,"_ ,'_ • * * , • • • *-- .

_.__,_:.,-_o_: ,_ .... _..-,•. _-o._ .,,_.._: I ; • o + o . • , • • . + o +-_,--_o,-_ 7 ..............

t+ -p_ + o 0 .o ...o +. 2 O p,,- . _o _ t g9 _s_ "¸ t_ ,, ,' ' o _2 o0 !

__1 mm t-- .o I00 ': I01 ,<C) 4 | )m e • ,._ _ "4 • t_"4 _ 41' "lt_ 4"11; JO (_ G_ _ .... C _P N ..ddddg; .o-.

Z p,.

_00000_0000 Z _,JiM .. J._ o _J _uJ 0000000_00000 N_j oeoeeeeoeeeel Z__O_O_O_ I_eeooeoellelol II1|111| Q _ IIIIit11111| g / I- Z II.

_Z tl ir _j_eoeeteoeteeel __O_NO _ioeoeoeeoteee E _E LJ --J < .a w.

_0000000000000 __m__ _0000000000000 _ 0 0000000000000 _ _

........ ,. •

_N_ltlIIIIII Itl _t1111111111tl _llltltliltllt I_ O ¢._ o tm z L 1.-I ),.

I ,9[ N Z O a,, _J 4[ .J N 9[ -,,j ]It{ ,-i e

-"II

o', o'+ c_ k- Z N O+ 31- i,_ Isr .f / + 0O er e_ _ ° // i / i/4_ 4.1,,..'+,I * _a_ .0 Z i<{9 ,-I _ .,.4..,I N -M ,%1 _p ? p_ M w_ _J _+-'"++++_++-'-_Y'3 ; .la m 4' J Z Z I I I | i I I I I _ '.l,. I I I I I I I I z m -i ) o.

_ ;'? f 7'7 ? p +p+_._:: i I I I I I I I I I I I _ _, I I I I ,11 • ,, _ ":. ....

11: i=-q I "J --4 . +p ._ .

• • • • . , . • . i+ •

o++++ +

J_ ..)

• • . , * , . * • * , o * 3* LI I' D .... ° '°'+" .... ' _'2._),'';'7'; L g .-,I

o, ,++o++++,+

e _ .* P :" : T ; -.." r • • +_ _1% J e_ j , * . • • , , , * * * , * "_ I,L.

J ++ + ) ) ") a'i-+ p _lJk -,I p _ _ ,.I "4 ,_ I + _ 't +'_ 'J_ 1 J l.,O ,_O.,- pOP, ppl-_..: .:, l _ ............. 1/I t-- ..+ +-+ _ ,,,._ + ,4 +,.+ +.+ _ _ + _ _ J.

) .I ,4 e_ • .+ u .............. _ ............. :,_. _._o .2 P_ L __ L O[3 bb*P* • * * * t e • * • • * , , r.t.1 .... --- ... -,' - - ," _ _g_gdgdg;gddd ,_ ,,,,I _',, _" _ _ _,, _ _ ,_ ,4_ _ t1_ _'_ _ I i I I I * | !

me., eel _ we ,_ m_ _ ,,.e ere •._ m.6 ,ml r_ _ ,.% ..., ,., q[e'_ Z I I I*,- * I,- _,J | vl ...I (3 "* *.J • • • * • * • e • • • • • ,vX _ 0 ,..'1 ¢:_ .'-') 0 0 0 0 0 0 0 0 0 .J 0 * _'t ,._ Q[ o • • • • t • • • • • • _ Z 0'_.

Z 1 ! 1 ! ! I O I I 1 ! I l ,I{ . . ..

_Z u_ i Z _Z _dJ .J :=w, ('_ "" 'o ....... Z ;._ _' ql Z . .. ._; .........

0% _ J 4 • . ';._. :_,_, T_ _ _ .,1 _0 ,_ _ 0 1)_ '_ _" _ 'I_ _ * * * , • , * • , , , • • _7 m I..I _._._._.o._._._._,,,_.-,. • .

all _ % d.-_ I07 0_ O Z • e • e • e e * * e e e • N l 000000000000_ i

0 %

o. _elilee0tieleo r_ *4J _4 u. _,* 14 i _ .4' Ik_ _8 I _fl m a, ¢D ,L, _0--_ IltlIIN Z 0o0o_o0_0000 _ o IC 2_2_g_d;g22_ gd_dgdg_d_g i ,*, _[ i :) ___,,., a_ __ 000000000000 e** z Illltllll I I l | I I i D Z I IIItllllillll IIIll !

0_ 0 Z ,I elleleeeelel |_ ¢_ *.3 4[ .

Z > ). 0 O O K t _Z _ 0 o00000000000 i _ r ee *illlllllli* il_ttll i 0 000000000_00 i o0000 0 00000 '' _ _=o-o # ],,_ x _,J ._ ,,., _ 7a %Zld _ew_ • ,.J .,_. .._ ¢_¢t-@ .t APPENDI X B BLADE COORDINATES MANUFACTURING COORDINATES FOR BLADE SECTIONS NORmaL TO STACKING LINE AIRFOIL SECTION ON PLANE AREA OF SECTION NOHMAL TO RADIAL STACKING LINE N Fibre B-I Airfoil Des.ignations for Manufacturing Coordinates I10 • r, TABLE B-1 METERS INCHES ZC YP YS ZC YP YS 0.0 -0.0003 0.0004 0.0 -0.0117 O.Ol&O 0.0003 -0.0002 0.0005 0.0115 --0.0077 0.0216 0.0021 0.0004 0.0017 0.0827 0.0166 0.0686 0.0042 0.0011 0.0031 0.1654 0,,0448 0._.220 0.0063 0.0018 0(0044 0.2481 0.0711 0.1726 0.0084 0.0024 0.0056 0.3309 0.0957 0.2206 0.0105 0.0030 0.0068 0.4136 0.1187 0.2663 0.0126 0°0036 0.0079 0.4963 0.1402 0.3101 0.01_7 0.0041 0.0089 0.5790 0.1603 0.3508 0.0168 0.0045 0.0099 0.b617 0.1788 0.3879 0.0189 0.0050 0.0107 0.744x_ 0.1955 0.4210 0.02 I0 0.0053 0.0 I14 0.8272 0,,2104. 0.4_02 0.0231 0.0057 0.0121 0.9099 0.2233 0.4754 0.0252 0.0060 0.0126 0.9926 0.2343 0.4060 0.0273 0.0062 0.0131 1.0753 0.2433 0.5144 0.0294 0.0064 0.0134 1.1580 0.2502 0.5282 0.0315 0.0065 0.0137 1.2407 0.2551 0.5382 0.0336 0.0065 0.0138 1.3235 0.2578 0.5443 0.0357 0.0066 0.0139 Io_062 0.2583 0.546& 0.0378 0.0055 0.0138 1.4889 0.2965 0.5445 0.0399 0.0064 0.0137 1.5716 0.2524 0.5384 0.0420 0.0062 0.0134 1.6543 0.2459 0.5279 0.0441 0.0060 0.0130 1.7370 0.2368 0.51Z9 0.04_2 0.00_7 0.0125 1.8197 0.2251 0.4931 0.0_3 0.0054 0.0119 1.9025 0.2107 0.46_3 0.0504 O.OOt+9 O.Olll 1.9852 0.IQ35 0.&380 0.0525 0.0044 0.0102 2.0679 0.1733 0.40Z8 0.0546 0.0038 0.0091 2.1506 0.1500 0.3593 0.0567 0.0031 0.0079 2.2333 0.1235 0.3009 0.0588 0.0024 0.0064 2.3160 0.0936 0.2528 0.0609 0.0015 0.0048 2.39R8 0.0600 0.1873 0.0630 0.0006 0.0028 2._815 0.0227 0.I122 ].0647 -0.0003 O.OOll 2.5477 -0.0106 O. 042g 0.0651 -0.0005 0.0007 2.5642 -0.0189 0.025e RADIUS (METERS) = 0.1307 RADIUS (INCHES) = 5.14.40 CHORD (METERS) = 0.0651 CHORD (INCHES) = 2._64.3 ZCSL (METERS) = 0.034.4 ZCSL (INCHES) = 1.3535 YCSL (METERS) = 0.0080 YCSL (INCHES) = 0.3130 RLE (METERS) =0.000330 RLE (INCHES) = 0.0130 RTE (METERS) =0.000531 RTE fINCHES) = 0.0209 X-AREAiSO.METERS)=O.O00342 X.-_REA (SQ. IN.) --0.5299 GAMM&-CHORO(RAD.)= 0.0890 5.10 GAM_) A-CHOR D ( OEG. )= Ill .., TA B LE B-2 O;" ?C_S.X INCHES METERS ZC YP YS ZC YP YS 0.0 -0.0100 0,0115 0.0 -0.0003 0.0003 0.0086 -0,0050 0.0182 0.0002 -0.000 1 0.0005 0.0856 0.0312 0.0778 0.0022 0.0008 0.0020 0.1711 0,0698 0.|308 0.0043 0.0018 0.0036 0.2567 0.1059 0.1981 0.0065 0.0027 0.0050 0.3423 0.1397 0.2928 0.0087 0,0035 0.0064, 0.4279 0.1710 0,3039 0.0109 0.0043 0,0077 0.5134 0.IQ97 0,3516 0.0130 0.0051 0.0089 0.5990 0.2258 0.3957 0,0152 0.0057 0.0101 0.6846 0.2492 0.4360 0.0174 0.0063 0.0111 0.7701 0.2695 0.4716 0.0196 0.0068 0.0120 0.8557 0.2866 0.5019 0.0217 0.0073 0.0127 0.94]L3 0.3003 0.5273 0.0239 0.0076 0.0134 1.0269 0.3107 0.547R 0,0261 0,0079 0.0139 1.1124 0.3175 0.5634 0.0283 0.008 1 0.0143 1.1980 0.31_8 0.5735 0.0304 0.0081 0.0146 1.2836 0.3195 0.57_0 0.0326 0.0081 0.0147 1.36c_1 0.3170 0.5806 0.0348 0.0081 0.0147 1.6.547 0.3128 0.5787 0.0369 0.0079 0.0147 ]..5403 0,,3065 0.5731 0.0391 0.0078 0.0146 1.625q 0.2981 0.5635 0.041.3 0.0076 0,0143 1.7114 0.2874 O. 5490 0.0435 0.0073 0.0140 ][.7970 0.2744 0,5319 0.0456 0.0070 0.0135 1.8826 O.2_qO 0.5093 0.0478 0.0066 0o0129 1.9681 0.2409 0 .a.8 19 0.0500 0.0061 0.0122 2.0537 0.2202 O.4_ql 0.0522 0.0056 0.0114 2.13o3 0.1966 0,4106 0.0543 0.0050 0.0104 2.2249 0.1701 0,3658 0.0565 0.00_3 0.0093 2.310_ 0,1404 0.3141 0.0587 0.0036 0.0080 2.3960 O.lOTA 0.2544) 0.0609 0.0027 0.0065 2,4,8 16 0.0708 O. _ 866 0.0630 0.0018 0.004.7 2.5671 0.0304. 0.1084, 0.0652 0.0008 0.0028 2.6408 "-0.0077 0.0311 0.0671 --0,0002 O.O00R 2.6527 --0.0139 0.0186 0.0674 -0.0004. 0.0005 ) = 5.7445 RADIUS (INCHES RADIUS (METERS) = 0.1459 ) = 2.6539 CHORD ( INCHES CHORD (METERS) = 0.0674 ZC$L ( INCHES ) = 1._'08'_ ZCSL (METERS) = 0.03F8 YCSL ( INCHES ) = 0.3530 YCSL (METERS) = 0.0090 RLE (INCHES ) = 0.0!01 RLE (METERS) =0.000257 RTE ( INCHES ) = 0.01'51 RTE (METERS) =0.000384 ) = 0.5021 X-AREA (SO. IN, X-AREA(S0.METERS)=O.000324 .)= 8.16 GAMMA-CHORD(DEG GAMMA-CHOQD(RAD.)= 0.142_

C

/ TABLE B-3 METERS INCHES ZC YP YS ZC YP YS 0.0 -0.0002 0.0003 0.0 -0.0097 0.0111 0,.0002 -0.0001 0.0004 0.0083 -0.0057 0.0173 0.0022 0.0008 0.0019 0.086& 0.0312 0.0759 0.0044 0.0018 0.0J35 0.1727 0.0704 Oo ]378 0.0066 0.0027 0.0050 0.2591 0.1076 O. Iq_4 0.0088 0.0036 0.0064 0.3454. 0.1426 0.2518 0.0110 O.OOU5 0.0077 0.4316 0.1755 0.3040 0.5182 0.2060 0.3531 0.0132 0.0052 0.0090 0.0154 0.0059 0.0 I0! 0,6045 0.2336 0.39R3 0.0175 0.0066 0.0112 0.6909 0.2584 0.4398 0.0197 0.0071 0.0121 0.7773 0.2803 0.4768 0.0219 0.0076 0.0129 0.8636 0.2994 0.5090 0.02_1 0.0080 0.0136 0.9500 0.3152 0.S363 0.0263 0.0083 0.014.2 1.0364 0.3278 0.5588 1.1227 0o3371 0.5766 0.0285 0.0086 0.0 1_,45 0.0307 0.0087 0.0150 !.2091 0.3430 0.5895 0.032_ 0.0088 0.0152 1.2954 0.3455 0.5976 0.0351 0.0087 0.0153 1.3818 0.3444 0.6008 0.0373 0.0086 0.0152 1.4682 0.3395 0.5988 0.0395 0.0084. 0.0150 1.5545 0.3307 0.5914.

0.0417 0.0081 0.014.7 1.6409 0.3198 0.5790 O. 04.39 0.0078 0 o014.3 1.7273 0.3069 0.5634 O.O_l 0.0074 0.0138 1.8136 0.2o22 0.5438 0.04.83 0.0070 0.0132 1.9000 0.2750 0.5201 0.0505 0.0065 0.0125 1.9864 0.2551 0.4912 0.0526 0.0059 0.0116 2.0727 0.2326 0.4571 0.054.8 0.0053 0.0106 2.1591 0.2073 0.4!73 0.0570 0.0045 0 .0094 2.2454 0.1791 0.3713 0.0592 0.0038 0.0081 2.3318 0.1477 0.3183 0.0614 0.0029 0.0065 2.4182 0.1130 0.2576 0.0636 0.0019 0.0048 2.5045 0.0748 0.1881 2.5909 0.0329 0.1084 0.0658 0.0008 0.0028 0.0677 --0.0002 0.0007 2.6664. -0.0071 0.0285 O.06RO --0.0003 0.0004 2.6772 --0.0128 0.0171 RADIUS (METERS) : 0.1509 RADIUS (INCHES) = 5.9420 CHORD (METERS) : 0.0680 CHORD (INCHES) = 2.6790 ZCSL (METERS) = 0.0362 ZCSL (INCHES) = 1.4252 YCSL (METERS) = 0.0092 YCSL (INCHES) = 0.3617 RLE (METERS) :0.000249 RLE (INCHES) = 0.0098 RTE (INCHES) = RTE (METERS) :0.000348 0.0137 X-AREA( SO.METER S) =0.000319 X-AREA (SQ. IN.) = 0.493Q GAMM A--CHORD ( RAD. ) = 0.1673 GAMMA-CHORD(DEG.)= 9.5_ TABLE B-4 METERS INCHES ZC YP YS ZC YP YS 0.0 -0.0002 0.0003 0.0 --0.0094 0.0107 0.0002 -000001 0.0004 0.0082 -0.0057 000166 0.0022 0.0008 000019 0.0872 0.0305 0.0736 0,0044 0,0018 0,003_ 0,17t_4 0,0690 001339 000006 0,0027 O,OOw9 0,2616 0,1056 0,19].2 0,0089 0,0036 0.0062 0,3488 0.1403 O, 2455 000111 0.0044 0.0075 0,4360 0,1731 0,2968 0.0133 0.0052 0.0088 0.5232 0.2039 0,3453 000155 000059 000099 006104. 0,2325 003909 000177 0,0066 0,0110 0,6976 0.2590 0.4338 000199 0.0072 0,0120 0.7848 0.2832 0.4728 0,0221 0,0077 0,012 (} 0,8720 0,3048 0,5075 0,024_# 0.0082 0,0137 0.9592 0.3234 0.5375 0,0266 0,0086 0,0143 1,0464 0.3389 0,5630 0.0288 000089 0,0148 Io1336 003507 005835 0.0310 0,0091 0,0152 1,2208 0.3591 0,5987 0.0332 0,0093 0.0155 1,3080 003643 0,6093 0,035# 0,0093 0,0].56 103952 0,3661 0,6152 0,0377 0.0093 000].56 i,A824 0.3643 0,6161 0.0399 0.0091 0.0155 1,5696 0,3589 0,6119 0.0421 0.0089 0.0153 1,6568 0.3496 0,6025 0 00443 0.0085 0.0 ].49 1,7444) 0.3364 0.587& 0.04.65 0.0081 0.0144 1,83].2 0,3188 0,5664 0.0487 0.0075 0.0 ].37 1,9184 0,2968 O,53WO 0.0509 000069 00012q 2,0056 0,2698 0.5043 0.0532 0.0062 0.0118 2.0928 002434 0.z_641 0.0554 0.0055 0.0107 201800 0.2162 0.4220 000576 0.0048 0.0095 2,2672 0.].873 0.3752 000598 0.0039 000082 2.3544 0,].5&5 0,3219 0o0620 0.003(_ 0.0066 2,4416 0.1].83 002601 00064.2 0,0020 000048 2,5288 0°0?86 0.1894 000604 000009 000028 2.6100 000351 0.!084 0.0684 --000002 0.0007 2.6933 -0,0055 0,0264 0.0687 --0,0003 0.0004 2.7032 -O.OllQ 0.0i58 _AO IUS (METERS) = 0.1560 RADIUS (INCHES) = 601_20 CHORD (METERS) = 0.0087 CHORD (INCHES) = 2.7037 ZCSL (METERS) = 0.0367 ZCSL fINCHES) = 1.44.40 YCSL (METERS) = 0.0094 YCSL (INCHES) = 003708 RLE (METERS) =0.0002_, RLE (INCHES) : 0,0096 RTE (METERS) =0.000323 RTE (INCHES) = 0,0127 X-AREA(SQ.METERS)=O.O00313 X--AR EA (SQ. IN.) = 0.4_5 GAMMA-CHORD(RAD.)= 0.1915 GAMMA-CHORD(DEG.)= I0.97 TABLE B-5 METERS INC HE S ZC YP YS ZC YP YS 0.0 -0.0002 0.0003 0.0 -0.0093 0.0104 0.0002 -0.0001 0.0004 0.0082 -0.0057 0.0161 0.0022 0.0008 0.0018 0.0881 0.0296 0.0713 0.0045 0.0017 0.0033 0.1762 0.0671 0.1208 0.0067 0.0026 0.0047 0.2643 0.1030 0.1856 0.0090 0.0035 0.0061 0.352/-, O. 1372 0.2387 0.0112 0,,0043 0.0073 0.44e5 0.16Q8 0.2Ro2 0.0134 0.0051 0.0086 0.5286 0.2006 0.3370 0.0157 0.0058 0.0097 0.6166 0.2295 0.3822 0.0170 0.0065 0.0108 0.7047 0.2564 0.4250 0.0201 0.0071 0.0118 0.7928 0.2814 0.4665 0.0224 0.0077 0.0127 0.880Q 0.3041 0.5001 0.0246 0.0082 0.0135 0.o6o0 0.3240 0.5313 0.0269 0.0087 0.0142 1.0571 0.34.12 0.5580 0.0291 0.0090 0.0147 1.1452 0.3554 0.5803 0.0313 0.0093 0.0152 1.2333 0.3668 0.5982 0.0336 0.0095 0.0155 1.3214 0.3751 0.6118 0.0358 0.0097 0.0158 1.4095 0._803 0.6208 0.0380 0.0097 0.0159 1.4976 0.3822 0.6253 0.0403 0.0097 0.0159 1.5857 0.3807 0.6251 0.0*.25 0.0095 0.0157 1.6737 0.3751 0.6196 0.0448 0.0093 0.0155 1.7618 0.36_7 0.6083 0.0470 0.0089 0.0 150 I._4QO 0.3523 0.5914.

0.0402 0.008_ 0.0144 1.9380 0.3348 0.5684 0.0515 0.0079 0.0137 2.0261 o.3128 0.53o0 0.0537 0.0073 0.0128 2 .I142 0.2861 0.5026 0.0559 0.0065 0.0116 2.2023 0.2542 0.&582 0.0582 0.0055 0 o0103 2.2904 0.2169 0.4,051 0.060_ 0.004_ 0.0087 2.3755 O. 1737 0.3&19 0.0627 0.0031 0.0068 2.4666 O. 1235 0.266?

0.064o 0.0020 0.0048 2.5547 0.080 1 O. 1888 0.0671 0.0009 0.0027 2.6428 0.0355 0.1065 0.0691 --0.0002 0.0006 2.7214 -0.0062 0.0248 0.06o_, --0.0003 0.000_ 2.730o -0.0113 0.0149 RADIUS (METERS) : 0.1612 RJDIUS #INCHES) = 6.3470 CHORD (METERS} : O.Obg4 CHORD (INCHES) = 2.7324 ZCSL #METERS) : 0.0372 ZCSL #INCHES) = i. 46_,3 YCSL #METERS) : 0.0096 vCSL #INCHES) = 0.3783 RLE #METERS) :0.000239 RLE (INCHES) = 0.0094 RTE #METERS) :0.000305 RTE (INCHES) = 0.0120 X-AREA(SO.METERS)=O.O00307 X-aREA (SO. IN.) : 0.4762 _&MM&.--CHORO#RAD.)= 0.21_0 GAMMA--CHOQ 0( DEG. )= 12.32 TABLE B-6 INCHES METERS ZC YP YS ZC YP YS 0.0 -0.0002 0.0102 0.0 -0.0002 0.0003 0.0082 -0.0057 0.0156 0.0002 -0.000 1 0.0004 0.0892 0.0281 0.0686 0.0023 0.0007 0.0017 0.1783 O.Ob41 0.1248 0.0045 0.0016 0,0032 0.2675 0.0987 0.1784 0.0068 0.0025 0.0045 0,,3567 0.1316 0.22°6 0.0091 0.0033 0.0058 0.4&5_ 0.1629 0.2782 0.0113 0.00_I 0.0071 0.5351 0.!927 0.3244 0.0136 0.0040 C .0082 0.6242 0.2208 0.3682 0.0159 0.0056 0.0094 0.713_ 0.2473 0.4,099 0.0181 0.0063 0.0104 0,8026 0.2721 0.44,87 0.0204 0,0069 0.0114 0.8918 0.2949 0.&8_2 0.0227 0.0075 0.0123 0.9809 0.31_1 0.5157 0.0240 0.0080 0.0181 1.0701' 0.3328 0.5428 0.0272 0.0085 0.0138 1.1593 0.3478 0.5656 0.0204 0.0088 0.014_ 1.2485 0.3600 0.5843 0.0317 0.0091 0.0148 1.3376 0,369_ 0.5987 0.0340 0.0094 0.0152 1..4268 0.3759 0.608q 0.0362 0.0095 0.0155 1.5160 0.3793 0.6146 0.0385 0.0096 0.0156 1. 052 0.3796 0.6158 0.0%08 0.0096 0.0156 1. ,944 0.3767 0.612"3 0.0-_30 0.0096 0.0156 1.7835 0.3703 0.6040 0.0453 0.0094 0.0153 1.8727 0.3603 0.5904 0.0476 0.0092 0.0150 1.961Q 0.3465 0.5714 0.0498 0.0088 0.014,5 2.0511 0.3287 0.5464 0.0521 0.0083 0.0139 2.1402 0.3060 0.5149 0.0_. 0.0078 0.0131 2.2294 0.2784 0.4754 0_0566 0.0071 0.0121 2.3186 0.2458 0.4276 0,0589 0.0062 0.0109 2.4078 0.2076 0.3706 _.0612 0.0053 0.0094.

2.4969 0.1633 0.3029 0 _063_ 0.0041 0,0077 2.5861 0.1126 0.2229 0=.0457 0.0029 0.0057 2.6753 0.0545 0.1278 0.0680 0.0014 0.0032 2.7569 -0.0057 0.0244 0.0700 -0.0001 O.O00b 2.7645 --0.0113 0.0148 0.0702 -0.0003 0.0004, 6.5600 RADIUS (INCHES) = RADIUS (METERS) = 0.I&61 2.7666 CHORD (INCHES) = CHORD (METERS) = 0.0703 1.4856 ZCSL (INCHES) = ZCSL (METERS) = 0.0377 0. 3749 YCSL # INCHES) = YCSL (METERS) = 0.0095 0.009_ RLE IINCHES) = RLE (METERS) =0.000236 0.0105 RTE (INCHES) = RTE (METERS) --0.000267 0 ._670 X-AREA (SO. IN.) = X-IREA(SO.METERS)=O.000_01 GAMMA-CHORD(DEG.)= 14.26 GAMMA.-.CHORD(RAO.)= 0.2488 TABLE B-7 METERS INCHES zC Yp YS ZC YP YS 0.0 -0.0002 0.0002 0.0 -0.0089 0.0096 0.0002 -0.000 2 0.0004 0.0085 -0.0061 0.01&,2 0.0024 0.0006 0.0015 0.0926 0.0220 0.0595 0.0047 0.0013 0.0027 0.1852 0.05_9 001077 0.0071 0.0020 0.0039 0.2779 0.0804. 0.1537 0.0004. 0.0027 0.0050 0.3705 0.1076 O. IQ76 0.0118 0 .C034 0 .C06L 0._-6_1 0.1335 0 o 239_- O.Oi_L 0.0040 C .0071 0.5558 0.1580 0.2790 0.0165 0.00_6 0.0080 0.6484. 0.1812 0.3106 0.0188 0.0052 0.0089 0.7_, I0 0.2028 0.3523 0.0212 0.0057 0.0098 0.8336 0.2232 0.3857 0.0235 O.OObl 0.0106 0 °9263 0.2419 0 ._172 0.02'_9 0.0066 0.0113 1.0189 0.2590 0._5_ 0.0282 0.0070 0.0110 1.1115 0.2740 0._700 0.0306 0.0073 0.0125 1.2042 0.2868 0.4907 0.0329 0.0076 0.0129 I.2968 0.2973 0.5077 0.0353 0.0078 0.0132 1.389_ 0.3055 0.5207 0.0376 0.0079 0.0135 1.4.820 0.3113 0.5300 0.0400 0.0080 0.0136 ]..5746 0.3].45 0.5352 0.0423 0.0080 0.0136 I.b673 0.3].51. 0.5364 0.0447 0.0080 0.0135 1.7599 0.3130 0.5334 0.0471 0.0078 0.0134. 1.8525 0.3080 0.5259 0.0_94. 0.0076 0.0131 1 ,9452 0.2999 0.513_ 0.0518 0.0073 0.0126 2.0378 0.2886 0.4Q68 0.0541 0.0070 0.0121 ?.1304. 0.2739 0.47_4 0.0565 0.006,5 0.0113 2.Z230 0.2552 0.4_63 0.0588 0.0059 0.0105 2.3157 0.2323 0.41L8 0.0612 0.0052 0.0094. 2.4083 0.2051 0.3700 0.0635 0.004.4 0.0081 2.5000 0.1732 0.3204.

O.ObSg 0.0035 0.006o 2.5935 O. 1363 0.2616 0.0682 O.O02A 0.0049 2.oU62 0.00_7 O. 1022 0.0706 0.0011 0.0028 2.778_ 0.0451 0.Ii01 0.0727 -0.000 1 0.0005 2.8635 -0.0054 0.0211 0.0729 -0.0003 0,0003 2.8714 -0.0101 0.0!28 RADIUS (METERS} = 0.1775 RADIUS (INCHES) = 6.9882 CHORD (METERS) = 0.0730 CHORD (I%CHES) = 2.8730 ZCSL (METERS) = 0.0391 ZCSL (INCHES) = 1.5387 YCSL (METERS) = 0.0079 YCSL (INCHES) = 0.3116 RLE (METERS) =0.000236 RLE (INCHES) " 0.0093 RTE (METERS) =0.000257 RTE (INCHES) = 0.0101 X-AREA(SO.METERS)=O.OOO28q X--AREA (SO. IN.) = 0.&483 GAMW&-.CHORO(RAD.}= 0,3535 GAMMA-CHORD(DEG.)= 20.25 If' TABLE B-8 INCHES MET_S ZC YP vS ZC YP YS 0.0 -0.0088 0.00o3 0.0 -0.0002 0.0002 0.0090 -(3.0069 0.0126 0.0002 -0.0002 0.0003 O.!OOO O.Oli8 0.0/_63 0.0025 0.0003 0.0012 C.2000 0.0316 0.0819 0.0051 0.0008 O.OOZ!

0,3001 0,0504 0.1160 0.0076 0.0013 0.0029 0._001 0.0683 O. 1484.

0.0102 0.0017 0.003_ 0.5001 0.0852 0.1791 0.0127 0.0022 0.0046 0.6001 0.1010 0.2082 0.0152 0.0026 0.00_3 0o7001 0.1158 0.2356 0.0178 0.0029 O.OObO 0.8002 0.1295 0.2613 0.0203 0.0033 0.0066 0.9002 0.1421 0.2854 0.0229 0.0036 0,,0072 I°0002 0.1536 0.3079 0°0254 0.0030 0.0078 I.I002 0,1641 0,3286 0.0279 0.0042 0.0083 1,2002 0.1733 0,347_ 0.0305 O.O04A 0.0088 io3003 0,1811 0,363Z 0,0330 0,0046 0,0092 1,4003 0,1873 0.3"F59 0.0356 0,0048 0,0095 1.5003 0.1919 0.3854 0.0381 0,0049 0,0098 l°bO03 O. Iq48 0.3916 0.0406 0.00/*9 0.0099 0.0432 0.0050 0.0100 1.7003 O. 1959 0.3q4_ ],.8004 0.195/* 0.3°40 O. 0,,57 0.0050 0.0100 1.9004 0.192 ° 0,3o01 0.0483 0.0049 0.0099 2.0004 O. 1886 0,3826 0,0508 0.0048 0.0097 2,1004 0,1824 0,37_6 0.0534 O. 0046 0,0094 2.2004 0.17/.1 0.3568 0.0559 0.00/.4 0.0091 2.3005 0.1638 0.3380 0.0584 0,0042 O,O08b 2.4005 0.1513 0.3151 0.0610 0.0038 0.0080 2.5005 O. 1364 0.2878 0.0635 0.0035 0,0073 2.6005 0.1192 0.2559 0.0661 0.0030 0.0065 2.7005 0.0995 0.2188 0.068b 0.0025 0.0056 0.0711 0.0020 0.00/*5 2.8005 0.0770 0.1762 2.7006 0.0517 O. 1276 0.0737 0.00 13 0.0032 3.0006 0.0234 0.0721 O. 076Z O.O00b 0.0018 3.002S -0.0055 0.0 l&3 0.0786 --0.0001 0.0004 3.1006 -0.0083 0.0093 0.0788 -0.0002 0.0002 RADIUS (INCHES ) = 7.c)850 ) = 0.2028 RADIUS (METERS CHORD ! INCHES ) = 3.1012 ) = 0.0788 CHCRD (METERS ) = !.6783 ) = 0.0_16 ZCSL ( INCHES ZCSL (METFRS ) = 0.1037 YCSI ( INCHES ) : 0.0049 YCSL (METERS ) = 0.009'_ RL6 ( INCHES ) =0.000239 RLE (METERS RTE ( INCHES ) = 0.0089 RTE (METERS) :0.000226 X--AREA (SO. IN. ) : O. 4234, X-AREA(SW.METERS)=O.O00273 .)= 30.4.6 GAMM4.-CHOKD(RAO.) = 0.53_6 GAMMA-CHORD(DEG ( TABLE B-9 METERS INCHES ZC YP YS ZC YP YS 0.0 -0.3002 0.0002 0.0 --0.0087 0.0090 0.0002 -0.0002 0.0003 0.009! -0.0075 0.0116 0.0027 0.0001 0.0010 0.1057 0.0055 0.038W 0.005_ 0.0005 0.0017 0.2114 O.OIQI 0.0665 0.0091 0.0008 0.002,. 0.]170 0.0318 0.0928 0.3107 0.0011 0.0030 0.4227 0.0_36 0.1178 0.013_ 0.0014 0.0036 0.528_ 0.0546 O.IA14 0.0161 0.0016 0.00,,,2 0.o3&_3 0.0648 0.1635 0.0188 0.0019 0.00_7 0.7397 0.07_2 0.18_I 0.0215 0.0021 0.0052 n.8454 0.0826 0.2033 0.0242 0.0023 0.0056 0.9510 0.0903 0.221_ 0.0268 0.0025 O.OOeO 1.0567 0.0970 0.2374 0.0295 0.0026 0.0064 1.162_ 0.1029 0.2525 0.0322 0.0027 0.0068 1.2681 0.1080 0.2658 0.0340 0.0028 0.0071 1.3737 0.1121 0.2777 0.037b 0.0029 0.0073 I._794 0.1152 0.2876 0.0_03 0.0030 0.0075 1.5851 0.1173 0.2949 O. 0429 O. 0030 O.O07b I.b908 0.1184 0.2g95 0.0456 0.0030 0.0077 1.7964 0.1184 0.3013 0.0_83 0.0030 0.0076} 1.902_ 0.1174 0.3004 0.0510 0.0029 0.0075 2.0078 0._152 0.2967 0.0537 0.0028 0.0074 2.1135 0.1119 0.2902 0.0564 0.0027 0.0071 2.2191 0.1075 0.2808 0.0590 0.0026 O.OOe8 2.32449 0.1018 0.2685 0.0617 O.O02& 0.0064 2._305 0.0950 0.2532 0.06t._ 0.0022 0.00&O 2.5361 0.086Q 0.2348 r_.0671 0.0020 0.00 _r-4 2.b&I8 0.077_ 0.2132 0.0698 0.0017 0.0048 2.7475 O.Oh6@ 0.IB83 0.0725 0.001 _. 0.00_I 2.8552 0.0_49 0.1599 0.0752 0.001 1 0.0032 2.9508 0.041_ 0.IP79 0.077B 0.0007 0.0023 3.0&_5 0.0267 O.OQ20 0.0805 0.0003 0.0013 3.1702 0.010_ 0.0520 r_.0830 -0.0002 0.0003 3.2_80 -0.0060 0.0115 0.0832 -0.0002 0.0002 3.275q -0.0073 0._80 RADIUS (METERS) = 0.2281 RADIUS (INCHES) = 8.QBIQ CHCRO (METERS) = 0.0832 CHORD (INCHES) = 3.2760 ZCSL (M_TERS) = O.O_3b ZCSL (INCH,=S) = 1.7140 YCSL (METERS) = 0.0029 YCSL (INCHFS) = 0.1125 RLE (METERS) =0.00023b RLE fINCHES) = O.OOq3 eTE iMETERS) =0.000208 RIIE (INCHES) = 0.0082 X-AREA X-AREAISQ.METERS)=O.OOO2b3 (SQ. IN,,) -0._074 GAMMA-.-CHORO(RAD.)= 0.b_79 37.69 GAMMA-CHORD(D_G.)=

I

TABLE B-IO INCHES ZC yo YS ZC vo YS 0.0 -0.0002 0.0002 0.0 -0.00_ 0.0090 0.0002 -0.0002 0.0003 0.00_3 -0.00s0 0.019_ 0.002_ 0.0000 O.O00B C.l !0_ 0.3003 0.0320 O.005_ 0.0002 n.0Ol_ 0.2208 0.0088 0.053_ 0.0094 O. 000_- 0.0019 0.3312 0.0168 0.0745 0.0112 0.000(_ 0.002_, 0.4,_ 16 0.02_.2 0.0940 0.01_-0 0.0006 0.002 C, 0.5S20 0.0310 0.!122 0.0108 O.CC09 0.003_ _ 0.e623 0.0_"72 0.1293 C.01o6 0.0011 0.0037 0.7727 0.0_,2_ 0..i_2 0.0224 _1.0012 O.nOc-! 0.88_i 0.0_.7_ O. t5o8 0.0252 0.0013 0.00Z*4 . 0.9935 0.052B O. 173B 0.3280 0.0014 0.00_7 I .IOB'_ 0.0561 0.!856 0.0308 3.0015 0.0050 1.2147 0.05_. 0.1067 0.0536 0.00!6 0.0052 1.32 &,7 0.0620 0.2066 0.0365 0.0016 0.0055 i._351 C.06&l 0.2154 0.0393 o.onl7 0.0057 1.5_-55 0.06 56 0.2220 0.0421 0.0017 0.0058 1 .&559 0.066& 0.2290 0.0449 0.0017 0.0059 I .7_63 0.0667 O. 2__3 | 0.0477 0.00|7 0.0060 1 .e766 0.066_ 0.2 _-'z,8 0.0505 0.00 _7 0.0060 ! .9870 0.065 z. 0.23_-3 0.0533 0.0016 0.0059 2 .097 _, 0.0637 O. 2__ 14 0,0561 n,0015 0.0057 2.207S O.061& 0.2261 0.0589 0.0015 0.0056 2.BI_2 0.0585 0.2185 0.3617 0.0014 0.0053 2._,276 0.0549 0.20@6 0.06_-5 0.0013 0.0050 2._ 3"_0 0.0506 C.I¢_62 0.0673 0.00 12 0.00_6 2.6 _-9_, 0.0&57 0.1814 0.07'01 0.0010 0.00,_2 2.75°8 0.0_-01 0. !6_2 0.072 _) O.OOqO 0.0037 2 ._702 n.n_3q o. 14_-5 0.0757 0.0007 0.0031 2._806 0.0270 0.1222 0.0795 0.3005 0.0025 3.0910 0.Ole5 0.0o74 C.OSI3 9.0003 0.0018 3.2013 0.011_ 0.06o_ 0.08_*I 0.000 I O.OOlO 3.3117 n.002"_ 0.0397 3.0[_ 67 -0.0002 0.0002 3 ._l_.O -0.0060 0.00oi 9.0So9 -r).O0_2 _.0C02 3._.221 -n.On66 O. nOV0 R _ M_ I,JS (METERS) = 0.2?.35 AoIuS (INCHFS) = 9.97_@ CHOuD (METERS) : 0.0_69 C mORO ( INCF, ES) : 3.w222 ZCSL (_FTE_S} : O.OZSl Z CSL (INCHES) : 1.775o YCS, u ( METI=_tS ) : 0,0013 Y CSL (INCF'ES) = 0.05t9 R 4LE (_=TERS) :0.300239 L= (INCHES) = n."0Q_ R Rfc {_ETE_S) =0.000188 [E (T_CwES) : 0.0074 X X-_#F_(L_._=TEWS):O.300253 --AR_A (__0. IN.) : 0._919 GAMMA--CHCUOIqAD.): 0.7633 AMMA-CHCR_(DEG.)= z.?.7"_ B-11 TABLE "]/ METERS INC_4E S ZC YP YS ZC V P YS 3.3 -0.0032 0.3002 0.0 -0.0088 0.0000 0.0002 -O.0¢OZ 0.0003 0.00_3 -0.0083 0.0105 0.00ZQ -0.000 I 0.0007 0 .i tz,O -0.0030 0.0200 ,n.nn_,q O.OOOl n.0012 0.2202 0.0023 0.04_o O.OOH7 O.OOC 2 0.001o 0.3_,28 0.0071 O.qeZo 3.0llo 0.0003 0.0020 0._5 et, 0.0114 0.0782 0.31.-_ 0.0004 0.0024 • 0.57_0 0.0154 O.0o_O 0.0175 0.0005 0.0027 0 .ot_T& 0.01o0 0.1_ 0.0204 0.000t_ 0.0O_0 0 .,q '_ 04._. 0.0222 n.n233 0.0006 0.0033 0._168 O.02_8 0.130o 0.0202 0.0007 0.0030 i .0314 0.0270 O.l_In 0.0281 0.0007 0.0038 1 • I,., oO 0.028? 0.1502 0.0320 0.0008 0.0040 1.2606 O.OPq_ 0.1584 0.03,,o 0.0008 0.002,2 I .2752 0.0307 O.le_ 0.0378 0.0008 0.00_-_ I ._PgQ 0.02 I0 0.1715 0.0408 0.00¢3 0.0045 0.0300 i .60_._ 0.17_& 0.0437 0.00( 3 0.00/_6 I.?Io1 0.0303 0.1803 0.0_06 0.00_ " 0.0046 I .8336 0.0292 0.1_30 0.0_5 0.001 7 0.0047 1 .o482 0.0280 0.1841 0.0524 0.00( "t 0.00 z,7 2.062 o 0.026_ 0.183_ 0.0553 C.OOC ', 0.00_,6 Z .I77_ 0.0250 0.1809 0.0582 0.00¢;0 0.OO_,5 2.2o21 0.0232 0.176_ 0.0_II 0.0005 0.002,3 2.40o7 0.0213 0.17_ 0.06,.0 0.0005 0.0041 2.52]3 0.01_2 0. I_22 0.0670 0.0004 0.003_ 2 ._,35o 0.010o 0.152_ 0.069_ 0.0004 0.003_ 2.7505 0.0145 0.1406 0.0728 0.0003 0.0032 1._o51 C.0120 0.1270 0.0747 0.0002 0 .,0028 2 .o7o7 0.3002 0.III R 0.0786 0.0902 0.0024 3.0o_3 0.00_4 0.0_2 0.0815 0.3001 0.001o 3.20_o 0.003_ 0.0750 0.00,._ 0.0000 0 .OOl,, 3.3235 0.000_ 0.0_40 0.0_73 -0.000 I 0.0008 3.t. BP i -O.OOZ_ 0.031'3 '3.9901 -O.Or31 0.0002 3 . 5,.60 0._077 -O.OOg_ 0.00,'_2 -,0.0_(12 n.O002 3 ._,627 -0.00_! 0.00_3 RADIUS (M6TERS) = 0.27_8 RAO IUS INCNFS ) =13.c752 CHt_P I_ETER£) = 0.0o02 C_CRD INCHES ) ZCSL (_TEqS) = 0.0_6_ ZCSL ITCHES ) = 1._27w YCSL (MFTERS) = 0.0001 YCSL INCHES) = 0.0030 RLE (METERS) =n.oon235 OLE INCHES) = 0.0003 _f6 (M_TERS) =0.000170 R[E INCHES) = 0.0067 X-ARE A ( SO.mE [£R S )=0.000245 X-ARbA (SO. IN.) = 0.37o7 C, AMMA-CHQRD |RAP. ) = 0,81&0 GAMMA-CNORD | DE(,. )= _.7_ L TABLE B-12 METERS INCNFS _C YP YS ZC YP YS 0.0 -0.0002 0.0302 0.0 -'-0.0088 0.0009 C.0002 -0.0002 0.0003 0.00'_3 -O.OOP3 0.0105 0.0029 -0.0001 0.0007 0.1159 -0.002 ° 0.02_0 O.O05Q O.OO01 0.0012 0.2318 C .0025 0.04.F (= 0.347q 0.0073 0.(_23 0.0088 0.0002 0.0016 0.011_ 0.0003 0.0020 0 ._637 0.0115 0.077"7 0.0147 0.0004 0.0023 0.5796 0.0152 0.0917 0.0177 0.000_ 0.0027 0 ._c)_5 0.018_ _ O. I0_7 0.0206 0.0005 0.0030 0.81i5 0.0208 0.]16,, 0.0256 O.OOn_ 0.0032 0 .gZ74 0.0228 0.1270 0.0265 0.0006 0.0035 1.0433 0.0243 0.1364 0.0294 0.0006 0.0037 ! .1592 0.0252 0.]446 0.932_ 0.0007 0.0339 I .2751 0.0256 0.1517 0.0353 0.0006 0.0040 I .3911 0.02_5 0.1576 0.03_3 0.0006 0.00_I 1.5070 0.02_9 0.162 _ 0.0412 O.OOn n._O_2 I .622 ° 0.0238 O. I_,60 0.0442 0.000o 0.0043 1.7388 0.0221 0.1685 0.0471 0.0005 0.00_3 I .8547 0.0200 O. 169q 0.0501 0.0004 0.0043 1.9707 0.0_76 0.1700 0.0530 O.O00& 0.00_3 2 .086(} 0.0153 0._684 0.0559 0.0003 0.0042 Z .-025 0.0130 0.!65_, 0.0589 0.0003 O.00&l Z .318_* 0.0108 0.1607 O.061S 0.0002 0.0039 7..4_43 0.0087 0.154_ 0.0648 0.0002 0.0037 2 .5503 0.0067 O. 1466 0.0677 0.0001 0.0035 2 .6662 0.00/,7 O. ] 372 0.0707 0.0001 0.0032 2.7821 0.0029 0.1262 0.0736 0.0000 0.0029 ._ggo 0.0012 O. I_97 0._766 -0.00_0 0.0025 _.01_0 -0.0004 0.09o_ 0,0795 -0.0000 0.0021 3.12o0 -O.0OIQ 0.08_,0 0.3824 -0.0001 0.0017 5.2_58 --0.0032 0.0668 O.08_& -0.0001 0.0012 .3617 -0.00_T_ O. 0_,80 0.0_3 -0.000! 0.0007 3 ./_776 -0.00S2 0.027H 0.0911 -0.0001 0.0002 3.5871 -0.005 ° 0.0073 0._913 -0.00_2 0.0002 3.5935 -n.OO£O O.O_6I eaOIdS (_ETSRS) = 0.2_72 _AOIUS (INCHES) =]1.3080 CMC<O (METERS) : 0.0913 Cm£_R9 (INCHES) = _.5Q"5 ZCSL (METERS) : 0.0_o8 ZCSL (INCHES) : 1.SAx, 3 YCSL (METERS) : -0.0002 YC_L (INCHES) =--0. OOOh _L5 (METERS} =n._0023_ RL_ (INCHES) : O._r_(_ _.TE IMETERS) :0.0901o5 Q[= (INCH,=S) : 0.0065 X-AR:A(SO.MET_PS):O.OOOZ43 x-AREa (SO. IN.) = 0.?763 GAMMA-C_G_D(_AD.)= 0._204 GAMMA-CHCRQ(D_G.): &7.00 TABLE B-13 METERS INCHES ZC YP YS ZC YP YS 0.0 -0.0002 0.0002 0.0 -0.0088 0.0090 0.0002 -3.0002 0.0003 0.009? -0.0084 0.0105 0.0030 -0.000 ] 0.0007 0.1109 -0.0029 0.0278 0.0059 0.0001 0.0012 0.233_ 0.0025 0.0454 0.008_ 0.0002 n.oolb 0.3507 0.0072 0.0617 C.0119 0.0003 0.0020 0.4676 0.0114 0.0768 0.5845 0.01_9 0.0906 0.0148 0.0004 0.0023 0.7014 0.0178 0.]031 0.0178 0.000_ 0.0026 0.8183 0.0201 0.1145 0.0208 0.0005 O.O02w 0.0238 0.0006 0.0052 0.9392 0.02!9 0.1246 0.0267 0.0006 0.0034 1.0521 0.0230 0.133_ 0.0297 0.0006 0.003o 1.1600 0.0236 0.!411 1.2859 0.0237 0.1477 0.0327 0.0006 0.0038 1.4029 0.0232 0.1530 0.0356 0.0006 0.0039 1.5197 0.0221 0.I_71 0.0386 0.0006 0.0040 0.0416 0.0005 0.0041 1.0367 0.0205 0.1601 0.0445 0.0005 0.0041 1.7586 0.0184 0.1619 0.0475 0.0004 0.0041 1.8705 0.0157 0.1626 0.0505 0.0003 0.0041 1.9874 0.0127 0.1620 0.0534 0.0002 0.0041 Z.I043 0.0097 0.1600 0.0564 0.0002 0.0040 2.2212 0.0071 0.1566 0.0594 O.O001 0.0039 2.3381 0.0046 0.1518 0.0o24 0.000 I 0.0037 2.&550 0.0024 0.1455 0.0653 0.0000 0.0035 2.5719 0.0004 0.1378 2.6888 --0.0014 0.1287 0.0683 -0.0000 0.0033 0.0713 -0.0001 0.0030 2._057 -0.0030 0.1182 0.0742 --0. 000 I 0.0027 2.9226 -0.0042 0.1063 0.0772 -0.0001 0.0024 3.0395 -0.0052 0.0930 0.0802 -0.0002 0.0020 _.1564 -0.0060 0.0783 3.2733 -0.0064 0.0622 0.0831 -0.0002 0.0016 3.3902 -0.0065 0.044_ 0.0861 -0.0002 0.0011 0.0891 -0.0002 0.0007 3.5071 -0.006_ 0.0260 3.6177 -0.0058 0.0070 0.0919 --0.0001 0.0002 0.0921 -0.0001 0.0002 3.62_0 -0.005" 0.C059 RADIUS (METERS ) = 0.293_ RAOIUS (INCHES) :II.5_70 CHORD (METERS ) = O.Oq20 CHORD (INCHES) : 3.6240 ) = 0.0472 ZCSL (INCHrS) = 1.8568 ZCSL (METERS ) = -0.0005 YCSL (INCHES) :-0.0180 YCSL (MITERS ) :0.000239 _L.E (INCHES) = 0.0094 RLE (METERS RTE (INC_-,ES) : 0.006_ RTE (METERS) :o.no0 Io5 X-AREA( SO.MET_RS)=O.O00241 X-AREA (SO. IN.) : 0.3730 CAMMA--CWI]RD(RAD. ): 0.8235 GAMMA-CHORD (DEG.)= 47.19 TABLE B-14 METERS INCHES ZC Y_ YS ZC YP YS 0.0 -0.0002 0.0002 0.0 -0.0089 0.0091 0.0002 -0.0002 0.0003 0.009_ -0.0084 0.0106 0.0030 -0.000 1 0.0007 0.1179 -0. 3030 0.0276 0.2307 0.0025 O.O&51 0.0060 0.000 1 0.00 11 0.353_ 0.0072 0.0612 0.0090 0.0002 0.0016 O .4714 O.OllA 0.07_i 0.0120 0.0003 0.001 a 0.58v3 0.0149 0.0_97 0.0150 0.0004 0.0023 0.0179 O. 1020 0.0190 0.0005 9.0026 0.7072 0.0200 O. 1130 0.0210 0.0005 0.0929 0._250 0.9_Z9 0.0217 O. :228 0.0239 0.0006 0.003_ 1.0608 0.0227 0.1314 0.0260 0.0006 0.0033 1.1786 0.0232 0.1387 0.0299 0.0006 0.0035 I .2965 0.0230 O. |_48 0.0329 0.0006 0.0037 0.9223 O. 1407 0.0359 0.3006 0.0038 1.41_ 0.0210 0.153_.

0.0380 0.0005 0.0039 I .5322 1.6501 0.0191 0.!55 (} 0.0419 0.0005 O.OOAO I. 7670 0.0168 0.15"/2 O.O_Z.9 0.000_ 0.00_0 1.6858 0.0137 O. l_7& 0.0479 0.0003 0.0040 0.0102 0.!563 0.0509 0.0003 0.00_.0 2.0037 0.0068 0.1539 0.0539 0.0002 0.303Q 2.1215 0.00_=7 O. 1502 0.0569 0_0001 0.0038 2.239& 0.0599 O.O000 0.0037 Z .3573 0.0009 O. 1452 0.062 ° -o. 0000 0.0035 2 ._751 -0.001_ O.I_M8 2.5930 --0.0037 0.!312 0.0659 -0.0001 0.0033 2.7108 -0.0055 O. 1222 0.0689 -0.0001 0.0031 2 ._287 -0.0069 O. 1123 3.0718 -0.0002 0.002B 2.946 _, -0.0080 0. 1005 0.0748 -0.0002 0.0026 .06_ -0 .0097 0.087 Q 0.07"78 -0.0002 0.0022 -0. OOQO 0. 07"58 0.0808 -0.0o02 0.001 o 3.1923 -0.0088 n.n_86 0.0838 -C.0002 0.0015 3.3002 -0.0082 0.0422 0.0908 -0.0002 0.0011 3 ._180 3.0898 -3.0002 0.0006 3.535_ -0.0072 0.0246 3.6..75 "0.00=8 0.036_ 0.0(¢26 -'O.OCO I 0.0002 ? .85_q -0.00_7 O.OOS_ 0.0'_2_ -0.C00L 0.0001 R AO f'3S (INCHES) :II.8062 qmOlilS (N_ETERS) : O.2QQ9 CHCRO (INCM_S) : _.653_ C,_O_ 0 (METERS) : 0.09Z8 (INC_S) : I.P674 ZCSL (METERS) : 0.047_ ZCSL YC_L (I'WCHE S) =-0.02&2 YCbL (METEkS) = --0.0005 QL c (INCHES) = 0.00o_ R LF ( METE_ S ) =0.00023q RTE (INCHES) - 0.30_.

_T_ IMETE_S) =O.oonlo?, _--AoF& (S_J. IN. ) = _. _6_& X-a,_ E a lS_J.METER S ):0. 30023_ G. ): 4R._I GAMMA-C_QRO(RAF). ): 0.?_50 _,AMM A-C HUR D ( r)F TABLE B-15 L METERS INCH,=_ S ZC yo YS ZC YP Y[ 0.0 -C.OOSO O.OOOl 0.0 -0.0002 0.0002 0.0002 -O.300Z 9.0003 O.OOQ4 -0.00_5 0.0105 0.3030 -0.000 1 ).0007 0.I I_ -0.0036 0.026M 0.00o0 O.O00C O.OOli G.2375 0.00 I2 0.0_3_ '3,00o1 0,0001 0.0(315 0.3 _o_ 0.005_ 0.0_89 o.O,,, 1 o 0.4753 O.nnOl o.0731 "_.nI21 O.OOn2 0.0022 0.5Q41 0.0122 O.C_bl O.Olfl 0.0003 O,Z|2o 0.01_7 0.0o7o 3.01_I 0.000 z_ 0.002_ 0.8317 0.0166 0,1084 0.0211 O. 000_- 0.002. _ C,02_.i 0.0005 0.0030 0.0505 0.0!80 0.I177 0.0272 0.0009 0.0032 1.06o3 0.0188 0.1258 0.0302 O. 000'5 n .003_, 1.1881 0.01 °0 0.1327 0.0332 0.0005 0.0035 1.3069 0.0187 0.1384 0.3362 0.0005 0.0036 1.4257 O.OlTW 0.I_30 0.0037 1.5_5 0,01_ O,l&6A 0.03o2 0.0004 0.003£ i._634 0.01_7 O.I_B6 0.0_22 0. 000,,,, 0.0038 1.7822 0.0123 0._4o8 0.0_,_3 0.0003 Q .00_8 I.o0 I0 0.00o4 0.!_o8 0.0_,_3 O,O00Z 2.019_ 0.0062 0 .I_88 0.0513 0.0002 0.0038 2.1386 0.0029 0.I_65 0.05_,3 0.000 1 0.0037 0.0573 -0. 0000 0,0036 2.Z574 --0.0002 0.1430 0.060_ -0.0001 0.0039 2.3762 -0.0028 0.13_2 0.003_ --0.000 l 0.003-, 2._0 -0.00_2 0.I_22 0.0032 2.6138 -O.OeTl 0.12_ o 0.0604 -0.0002 2.7327 -0.0087 0.I164 0.069_ -0.0002 0.0030 0.0027 2.8515 --0.00_9 0.1067 0.072_ -0.0003 0.075_ -0.0003 0.0 02",, 2._703 -0.0106 0.0_57 G.078- _ -0.0003 0.00dt 3.0891 -0.010o 0.0836 n.0ql _ -0.00,"3 0 .on 16 5.2070 -0.0108 0.0_03 0.001_ 3.32_7 -0.0102 0.055e 0.0_45 -0.0003 0.0010 3._4_5 -0.00_1 0.0403 0.0875 -0.0002 3.56_3 -0.007_ 0.3235 O.OQO_ -0.0002 0.0006 0.0002 3.6770 -0.00_7 0.0066 O.OQ3_. -0.0001 0.0001 3.6_32 -0.0056 0.0057 (1.0Q3h -O.O00I RAOIUS fINCHES ) :12.0'_'_2 _ AOItlS (wET__RS I = (1.3_o2 ) : 0.0_6 CHORD ( INCHFS I = 3._,831 C_ORO (METERS ZCSL ! INCN;S ) : 1 ._773 ZCSL (.46TERS I : 0.0_77 ) :-0. 0320 YCSL (WETERS ) = "0.0008 YCSL fINCHES ) : 0.00_5 PLE |TNCHFS RL_= (4_TERS ) =0.0002_1 eTF ( INCurS ) : 0.00_0 RT_ 14ETERS) :n,OOn152 X-AR_A (SO. IN, ) : r_• 1654 X-ARFA! SO,METERS):O,OOOZ36 (,AMMA-CHOP[I (DE(, .}= _.9.26 GAMMA-CHORD(RAP,)= O. ,qSg_ TABLE B-16 METERS INCHES ZC ym YS ZC yl:, YS 0.0 -0.008o O.oOOl 0.0 -0.0002 0.0002 0.0002 -0.0002 0.0003 0.0094 -0.0086 0.0104 0.0030 -0.000 1 0.0006 0.1198 -0.00_9 O.02_w 0.0061 -0. 0000 0.0010 0.23_5 -0.0012 O. 0_08 0.0091 0.000 i 0.0014 0.3593 0.0020 0.0540 0.0122 0.0001 0.001Y 0.4790 0.0047 0.0080 0.0152 0.0002 0.0020 0.5988 0.0070 0.0800 0.0183 0.0002 0.0023 0.7185 0.0088 0.0o08 0.8389 0.0101 0.1005 0.0213 0.0003 0.0026 0.9580 0.01 I0 O. 1091 0.02_.3 0.0003 0.0028 !.0778 0.0114 0 • 1167 0.0774 0,0003 0.0030 0.0304 0.0003 0.0031 1.1975 0.0114 0.1232 0.0335 0.0003 0.0033 1.3173 0.0110 O. 1285 0.0365 0.0003 0.0034 _.4__71 0.0102 0.1329 0.0395 0.0002 0.0095 1.5508 0.0090 0.1362 1 °5766 0.0074 O. 138_ 0.0426 0.0002 0.003_ I .7g63 0.0055 O, 13(_o 0.0456 0.0001 0.0036 0.0487 0.0001 0.0036 I .910I 0.0092 0 • 1409 0.0517 0.0000 0.0035 2.035a 0.0006 O. 13(_7 0.0548 -0.000 ! 0.0035 2.1556 -0.0021 0.1381 0.0578 -0.0001 0.0034 2.2753 -0. C)046 0.1352 0.0608 -0.0002 0.0033 Z.3_51 -0.0067 0.1310 0.0699 -0.0002 0.0032 2.5149 -0.0086 0.1250 0.0660 -0.0o03 0.0030 2.0 346 -0.0100 0._I_O 0.0700 -0.0003 0.0028 2.7544 -0.01!2 0.III0 0.0730 -0.0003 0.0026 2.8741 -0.0120 0.1018 2.9939 -0.0124 O. 0(_] 5 0.0760 -0.0003 0.0023 0.07oi -0.0003 0.0020 3.1136 -0.0124 0.0700 0.0821 -0.0003 0.0017 3.233& -0.0121 0.0672 0.0_52 -0.0003 0.0014 3.3531 -0.0113 0.0=33 0.0_82 -0.0003 0.0010 3.4729 -0.00o8 n. 0"_85 0.3913 -0.0002 0.0006 3.5927 -0.007 C) 0.0226 3.7064 --0.0050 0.006 &.

0.0941 -0.000 | 0.0002 3.712_. -0.00 _ O. 00_6 0.0Q43 -0.0001 O.OOO!

_ ADIUS {INCHFS) : 12._0'_0 RADIIJS (METCkS) : 0.3125 C-C)o D IMEYERS) : 0.0943 CHnRD (INC_._S) : 3.7124 ZCSL IMFT@RS) : 0.0479 LCSL (INCH_=S) : I.PF)F7 YCSL IMET=RS) : -0.0013 YCSL ( I _IC__=S ) =-0. Oall RUE (INCHES) : 0.009 _ RLE IMETS_S) :O.O002_-i RTE (INCw.=S) : 0.00'_,_ _[E Im__Tc_ _S) :0.000140 x-AR=AISO.'4FTERS):O.O00233 X-ARFI ISO, IN,) -- O.?_e)Ol_ C, AMMA-CHNRDIQA!_.): 0.8t_25 C_AMMA-CHO_DI[_.¢Q. ): _n.56 L TABLE B-17 i L; INCHES M_TERS ZC YP YS ZC YP YS 0.0 -0.0090 O.OOOl O.n -0.0002 0.0002 0.0002 -0.0002 0.0003 0.0094 -0.0089 0.0100 0.0031 -0.0002 0.0(]05 0.1222 -0.0082 0.0215 0.0652 -0.0002 0.000_ 0.2443 -0.0075 0.0332 0.0093 -0.0002 0.0011 C.3665 -0.0070 0.0442 0.0124 -0.C002 O.O01w 0._887 -0.0067 0.05_3 0._155 -O.On_2 0.0016 0.6108 -0.006_ 0.0636 0.7330 -0.0065 0.0722 0.0186 -O.O00Z 0.0018 0.8551 -0.0066 0.0800 3.0217 -0.0002 0.0020 0.9773 --0.0068 0.0870 O. 02_8 -0.0002 0.0022 1.0995 --0.0071 0_0o33 0.0279 --0.0002 0.0024 0.0310 -0.0002 0.0025 1.2216 --0.0075 0.0988 1.3&38 -0.0080 0.1036 0.0341 -0.0002 0.0026 0.0372 -0.0002 0.0027 1.4660 -0.0085 0.1078 0.0403 -0.0002 0.0028 1.5581 -0.0092 0.1112 1.7103 -0.0098 0.1140 0.3434 -0.0002 0.002¢ 1.8325 -0.0104 0.1161 0.0465 -0.0003 0.0029 I.o546 -O.OIlO 0.1177 0.0_96 -0.0003 0.0030 0.0528 -0.0003 0.0030 Z.0768 -0.0115 0.1187 2.1989 -0.0119 0.I191 0.055q -0.0003 0.0030 0.0590 -0.0003 0.0030 2.3211 -0.0123 0.1184 2.4433 -0.0126 0.1163 0.0621 -0.0003 0.0030 2.5654 -0.0127 0.112 Q 0.0652 --0.0003 0.0029 0.0683 --0.0003 0.0027 2.6876 --0.0128 0.1080 2.8098 -0,0127 0.I018 0.0714 -0.0003 0.0026 0.07_5 -0.0003 0.002_' 2.q319 -0.0124 0.0943 3.0541 -0.0120 0.0854 0.077b -0.0003 0.0022 0.3837 -0. 0003 O.O01g 3.1763 -0.0113 0.0753 0.0@38 -0.0003 0.0016 3.2984 -0.0105 0.0638 0.0869 -0.0002 0.0013 3._206 -0.00g5 0.0510 O.O_no -0.0002 O.O00Q 3.5428 -0.0082 0.0370 0.0931 -0.0002 0.0006 3._649 -0.0068 0.0217 O.Oq61 -O.O00I 0.0002 3.7816 --0.0051 0.0060 3.7871 -0.0051 0.0052 0.0Q62 -0.0001 0.0001 RADIUS fINCHES) :12.o722 RADIUS (METERS) : 0.3205 CHORD (INCHES) = 3.7871 CHORD (METERS) - 0.0q62 (INCHES) = I.@053 ZCSL (METERS) : 0.0484 ZCSL (INCHES) ='-0.0616 YCSL {METERS) : -0.0016 YCSL RLE (INCHES) = O.OOe6 qLE (METERS) =0.0002_ ._, RIE (INCHES) = 0,00_0 RTE (METERS) =0.000127 X-IREA (SQ. IN.) : 0.3475 X-AREA(SQ.METERS)=O.O0022_ GAMMA-CHORO(DEG.)= 5&.lO GAMMA-CHORD(RAO.)= 0.0442 TABLE B-18 INCHES ZC YP YS ZC YP YS 0.0 -0.0002 0.0002 0.0 -0.0003 O.OOOl 0.0002 -0.0002 0.0002 0.0006 -O.OOe5 0.0097 0.0032 -0.0003 0.0004 0.1255 -0.0115 0.0174 0,0064 -0,0003 0.0006 0.2511 -0.0136 0.0252 0.0096 -0.000A 0.0008 0.3766 -0.0155 0.0325 0.5022 -0.01 72 0.0393 0,0128 -0.0004 0.0010 0.6277 -O.OlOO 0.0455 0.0159 -0.0005 0.0012 0,0191 -0.0005 0.00]3 0.7533 -0.0208 0.0512 0.0223 -0.0006 0.0014 0.8788 -0.0225 0.0564 0.0255 -0.0006 0.0016 1.O0_ -0.0241 0.0612 0.0287 -0.0006 0.0017 I.I299 -0.0255 0.0655 0.0319 --0.0007 0.0018 1.2555 -0.0270 0.0693 0.0351 -0.0007 0.0018 I._811 -0.0281 0,0727 1.5066 -0.0288 0.0758 0.0383 -0.0007 0.0019 0.0415 -0.0008 0.0020 1.6322 -0.0296 0.0785 1.7577 -0.0301 0.0808 O. 0440 -0.0008 0.0021 0.0478 -0.0008 0.0021 1.8833 -0.0300 0.0828 0.0510 -0.0008 0.002_ 2.0088 -0.0298 0.08_6 0.0542 -0,0007 0.0022 2.1344. -0.0293 0.0861 0.0574 -0.0007 0.0022 2.2599 -0.0286 0.0873 0,0606 -0.0007 0.0022 2.3655 -0.0274 0.0883 2.5110 -0.0259 0.0882 0.0638 -0.0007 0.0022 0.0670 -0.0006 0.0022 2.6366 -0.0246 0.0869 0.0702 -0.0006 0.0021 2.7621 -0.0232 0.0843 0.0733 -0.0006 0.0020 2.88 7"7 -0.0217 0.080,.

0.0765 -0.0005 0.0019 3.0132 -0.0201 0,,0752 0.0797 -0.0005 0o0017 3.1388 -0.0183 0,0688 0.0829 -0.0004 O.O01b 3.2643 -0.0164 0.0612 5.5899 --0.0 l&3 0.0523 0.0861 --0.000 t- 0.0015 0.0893 --0.0003 0,,0011 3.5_54 --0.0120 0.0423 0.0925 -0.0002 0.0008 3._,4 iO -0.0007 0.0311 3.7665 -0.0074 0.0].83 0.0957 -0.0002 0.0005 0.0987 -0.0001 0.0301 3.8B70 -0,0047 0.0054 0.0989 -0.000 1 0.0001 ,_.8921 -0.0046 O.O04g RADIUS (METERS) : 0.3549 RADIUS (INCHES) =13.9709 CHORD (METERS) : 0.0989 CMORO (INCHES) = 3.8c)21 ZCSL (INCHES) = 1.9327 ZCSL (METERS) = 0.0491 YCSL (METSRS) : -0.0023 YCSL (INCHES) :-0.0908 RLE (METERS) :0.0002_I RLE (INCHES) = 0.0095 RTE (M_TERS) :0.000104 RTE (INCHES) : 0.0041 _,-AREA (SQ. IN.) = 0._213 X-&REA(SO.METERS):O.O00207 GAMMA-CHORD(RAO.) = 1.0226 GAMMA-CHORDIDEG.)= 5_,5o B-19

TABLE

C': i,,.

- TY" METFRS INCHES ZC YP YS ZC YP YS n.O -0.0002 0.0002 0.0 -0.0092 0.0091 0.0002 -0.0002 0.0002 0.0095 -0.r)097 0.00o) 0.0033 -0.0004 0.0003 0.1287 -0.0159 0.0113 0.0065 -0.0006 0.0003 0.2574 --0.022_ 0.0132 0.009_ --0.0007 0.0004 0.3861 -0.0283 0.01_| C.0131 -0.0009 0.0004 0.5 I'_ -0.0340 0.0_.6_ 0.0155 -0.0010 0.0005 0.6435 -0.0393 0.0184 0.0196 -0.0011 0.0005 0.7722 -0.0441 0.01oo 0.0229 -0.0012 0.0005 0.9009 -0.0484 0.0213 0.0262 -0.0013 0.0006 1.0296 --0.0523 0.0227 0.0294 --0.00 14 0.0006 1.1583 -0.0556 0.0241 0.0327 -0.0015 0.0007 1.2870 -(3.0583 0.0256 0.0360 -0.0015 0_0007 1.4157 --0.0604 0.0272 0.0392 --0.00 Ib 0.0007 1.5444 -0.0619 0.0289 0.0425 -0.0016 0.0008 |.6731 -0.0628 0.0308 0.0458 -0.0016 0.0008 1.8018 --0.0628 0.0329 0.0490 -0.0016 0.000@ 1.9305 -0.0621 0.0353 0.0523 -0.0015 0.0010 2.0592 -0.0606 0.0980 0.0556 -0.0015 0.0010 2.187g -0.0582 0.0411 0.0588 -0.00 14 0.0011 2.3164) --0.0549 0.0448 0.062 1 -0.0013 0.0013 2.4453 -0.0504 0.0492 0.0654 -0.001 1 0.0014 2.5740 -0.0453 0.0535 0.0686 --0.0010 0.0014 2.7027 -0.03o9 0.0568 0.0710 -0.0009 0.0015 2.8314 -0.0349 0.0587 0.0752 -0.0008 0.0015 2.w601 --0.0300 0.05@I 0.0795 -0.0006 0.0015 3.0888 -0,,0255 0.0579 0.0817 -0.0005 0.3014 3.2175 -0.02 12 0.0552 0.0850 -0. O00&, 0.0013 3.3462 -0.0173 0.0508 0.0883 "0.0003 0.0011 3.47_9 -0.0137 0.0448 0.0915 _ ,0003 0.0009 3.6036 -0.0106 0.0372 0.09_8 -t .0002 0.0007 3.7323 -0.0r_75 0.027o 0.0981 -0.0001 0.000,, 3.S610 -0.0058 0.0|67 0.1012 -O.O001 0.0001 3.9855 --0.0039 0.0045 0.i013 -0.0001 0.0001 3.9897 -0.0038 0.00@I RADIUS (METERS) : 0.3802 RAOIUF (INCHES) =14.96o9 CHOWD (METERS) : 0.1013 CHORD (INCHES) = 3.0806 ZCSL (METERS) = O. 0_.97 ZCSL (INCHES) - 1.9558 YCSL (METERS) = -0.0032 YCSL (INCHES) --0.1242 RLE (METERS) :0.000239 RLE (INCH_S) = 0.0094 _TE (METERS) -0.000104 RTE (INCH_S) " 0.0041 X-_P EA ( SQ. METERS ) :0.00016b ,<-AREA (_Q. IN.) : 0.28?7 G4MMA-CHORD(Q40.) = 1.1154 GAMMA-CHOQDiDEG.)- 63.01 TABLE B-20 METERS INCHES ZC YP YS ZC YP YS 0.0 -0.0002 0.0002 O.O -0.0092 0.0091 0.0002 -0.000 2 0,0002 0.0094 -0.0098 O.OOQO 0.0033 -0.000 5 0.0002 0.1311 -0.0183 0.0079 0.0067 -0.0007 0.0002 0.2622 -0.0264 0.006_ 0.0 i00 -0. 0000 0.0002 0.3933 -_.03_0 0.0061 0.0133 -0.00 I0 0.0001 0.52_ -_.O@OQ 0.0056 0.0166 -0.0012 0.0001 0.6555 -'0.0471 0.0054 0.0200 -0.0013 O.O001 0.7806 --0.0525 0.0054 0.0233 -0.0015 0.0001 0.9177 -0.0572 0.0058 0.0266 -0.0016 0.0002 1.0488 --0.0611 0.0066 0.0300 --0.0016 0.0002 1.1799 -0.0641 0.0077 0.0333 -0.0017 0.0002 1.3110 --0.0663 0.0093 0.0366 -0.0017 0.0003 1.4421 --0.0677 0.0112 0.0400 -0.0017 0.0003 1.5732 -0.0682 0.0136 0.0_33 --0.0017 0.0004 1.7043 -0.0677 0.01_5 0.0466 --0.0017 0.0005 1o8354 --0.0664 0.0199 0.04.99 --0.0016 0.0006 1.9665 --0.064.1 0.0238 0.0533 -0.0015 0.0007 2.0976 --0.0607 0.0283 0°0566 -0o0014 0.0008 Z.2287 --0.0564 0.0333 0.0599 -0.0013 0.0010 2.3598 --0.0510 0.0393 0.0633 -0.0011 0.0012 2.4909 -0.04.4.1 0.0460 0.0666 -0,0009 0.0013 2.6220 -0.0366 0.0529 0.0699 --0.0007 0.0015 2.7fi31 --0.0291 0.05Q3 0.0733 --0. O00b 0.0016 2.8842 --0.0222 0.0637 0.0766 --0.0004 0.0017 3.0 154 -0.0162 0.0660 0.0799 --0.0003 0.001.7 3.1465 -0,0111 0.066i 0.0832 -0.0002 0.0016 3.2775 -0.0071 0.0639 3.4087 -0.0040 0.0595 0.0866 -0. 000 1 0.0015 0.0899 -0,000 I 0.00_3 3.5398 --0.0020 0.052_ 0.0932 -0.0000 0.0011 3.b700 --0.000 o 0.04._0 0.0 _46 -0. 0000 0.0008 3._020 -0.0008 0.0329 0.0999 --0. 0000 0.0005 3.9331 -0.0018 0.0196 0.1031 -0.0001 0.0001 4.0601 -0.0037 0.00_5 0.1032 -0,0001 0.0001 4.064.2 -0.0037 0.004.0 RAOIUS (METERS) = 0.3977 RADIUS (INCHES) =15.6572 CHORD (METERS) = 0.1032 CMORO fINChES) = 4.0642 ZCSL (METERS) = 0.0505 ZCSL (INCHES) = 1.9877 YCSL (METERS) : -0.0033 YCSL (INCHES) =-0.1304 RLE (METERS) =0.000236 RLE (INCHES) = 0.0093 RTE (METERS) =0.000104 RIb (INCHES) = 0.00_I X-aRE_(SO.METERS)=O.O00173 X--aREa (SO. IN.) = 0.2_75 GAMMA-CHORDiRAD.)= 1.1675 GAMMA--CHORO(DEG.)= 6b.SQ ]30 ..; I'Y

TABLEB-21

METFRS INCHES ZC YP YS ZC YP YS 0.0 -0.0002 C.0002 0.0 -0.0071 O.OOQO 0.0002 -0.0002 0.0002 0.0093 -0.0098 0.0080 0.0033 -0.0005 0.0002 0.1318 -0.0185 0.0071 0.0067 -0.0007 0.0001 0.2635 -0.0272 0.0053 0.0100 -0.0009 O.OCOl 0.3953 -0.0352 0.0039 0.5271 -0.0_24 0.0029 0.0_3_ -0.0011 0.0001 0.658_ -0.0488 0.0022 0.0167 -0.0012 0.0001 0.0201 -0.0014 0.0000 0.7906 -0.0544 0.001 _) 0.0234 -0.0015 0.0001 0.9223 -O.05ql 0.0021 0.0268 -0. O01b 0.0001 1.05_I -0.0630 0.0026 0.0301 -0.0017 0.000 1 1.1859 -0.066! 0.0036 0.0335 -0.0017 0,0001 1.3176 -0.0683 0.0056 1 _44r_ -0.0695 0.0070 0.0368 -0.0018 0.0002 1.5882 -0.0699 0.0094 0.0403 -0.0018 0.0002 1.7129 --0.0693 0.0124 0.0435 -0.0018 0.0003 1.8447 -0.0677 0.0160 0.0A69 -0.0017 0.0004 0.0502 -0.0017 0.0005 1.9764 --0.06_I 0.0201 0.0535 -0.0016 0.000o 2.1082 --0.0615 0.0249 0.056o -0.0014 0.0008 7.2400 -0.0569 0.0303 0.0(,02 -0.0013 0.0009 2.3717 -0.L,513 0.0367 O.O&3o -0.0011 0.0011 2._03fi -0.0439 0.0_37 0.0669 --0.0009 0.0013 2.6353 -0.0360 0.0509 2.7670 "-0.0281 0.0281 0.0703 -0.0007 0.0015 2.8988 -0.0207 0.06_1 0.0736 --0.0005 0.00_6 0.0770 --0.0004 0.0017 3.0306 -0.0].45 0.0658 0.0803 --0.0002 0.0017 3.1623 -0.0093 0.0662 0.0837 --0.0001 0.0016 3.2941 -0.0051 0.0644 0.0870 --0.0001 0.0015 3.4258 -0.0021 0.0602 0.0904 -0.0000 0.001_ _.5576 -0.000 1 0.053_ 0.0937 0.0000 0.0011 3.68o_ 0.0008 0.0_50 3.8211 0.0005 0.0338 0.0071 O. 0000 0 .0000 0.1004 -0.0000 0.0005 3.9529 -0.0009 0.0203 _.0807 -0.0036 O. 00_5 0.1036 -0.0001 0.0001 L,.0847 -0.0037 0.00_0 0.1038 -0.0001 0.0001 RADIUS ( INCHES ) =15._554 RADIUS (METERS) = 0.4027 ) = 4.0847 CHOkO (METERS) = 0.I038 CHORD ( INCHFS ZCSL (METERS) = 0.0507 ZCSL ( INCHES ) = 1.0973 YCSL ( INCHES ) =-0.132Q YCSL (ME_EKS) = -0.0034 RLE ( INCHES ) = 0.0093 RLE (METERS) =0.000236 RTE ( INCHES ) = 0.004].

RTE (METERS) =0.000104 X-AREA ( S(J. ME TER S )=0.000 le, q X-JRFA (SQ. IN. ) = 0.2620 GAMMA-CHORD (RAO.) = I. lBO'_ G_MMA-CNORD(DEG .)= 67.64 B-22 TABLE MET:RS INCHES ZC YP YS ZC YP YS 0.0 -0.0002 0.0002 0.0 -0.0091 0.008o 0.0002 -0.0002 0.0002 0.0092 -0.0008 O.OOg8 0,0034 -0.0005 0.0002 0.1324 -0.0190 0.0062 0.0067 -0.0007 O.0001 0.2648 -0.0281 0.0038 0.3 qTl -0.0364 0._018 O.OlOl -0.0009 0.0000 0.5195 -0.043o 0.0003 0.0135 -0.00] 1 0.0000 0.6619 -0.0505 -0.0008 0.0168-0.0013 -0.0000 0.0202 -0.0014 -0.0000 0.7943 --0.0562 --0.0015 0.0235 -0.001o -0.0000 0.9267 --0.0611 --0.0016 0.0269 -0.0017 -0.0000 1.059. --0.0651 --0.0013 0.0303 -0.0017 -0.0000 1.1915 --0.0682 --0.0005 ]= .3238 --0.0703 0.0008 0.0336 -0.0018 0.0000 1.4.562 --0.0716 0.0027 0.0370 -0.0018 0.0001 ]=.5886 --0.0718 0.0052 0.0404 -0.0018 0.000]= 0.04.37 -0.0018 0.0002 ], .72 I0 -0.0711 0.0083 0.0471 -0.00;8 0.0003 1.8534 --0.06)94 0.C 120 0.0504. -0.0017 0.0004 1.9858 "0.0666 O. :163 0.0538 -0.0016 0.0005 2.1181 --0.0628 O. _13 0.0572 -0.0015 0.0007 2.2505 -0.057O O. _260 0.0605 -0.0013 0.0009 2.3829 -0.0520 0.5336 0.0639 -0.0011 0.0010 2.5153 -0.04._ O. _410 0.0673 -0. 0009 0.0012 2 .6477 -0.0361 O. _8_ 2.7801 -0.0279 0.0562 0.0706 -0.0007 0.0014 2.91.24 -0.0201 0.0618 0.0740 -0.0005 0.0018 0.0773 -0.0003 0.0017 3.044.8 -0.0135 0.0651 0.0807 -0.0002 0.0017 3.]=772 -0. 008 I. 0.0659 0.0841 -0.0001 0.0010 3.3096 -0.0038 0,0644 3._420 -0.0007 0.0005 0.0874 --0.0000 0.0015 3.57_ 0.00 12 0.0542 0.0908 0.0000 0.00l_ 3.7067 0.001 (_ 0.0455 0.0_42 0.0000 0.00L2 0.0975 0.0000 0.0009 3.8391 0.0013 0.0343 0.1009 -0.0000 0.0005 3.9715 -0. 0004 0.0206 3.I0_I -0.300 1 O.O00! 4.090_ -0.0037 0._046 O. I042 --0.0001 0.0001 _.I03Q -0.0038 0.0041 RADIUS (MFTERS) : 0.&078 RJDIUS lYNCHES ) : 16.0534 CHORD (INCHES ) = 4.103_ CHORD (METERS) = 0.1042 ZCSL (INCHES ) : 2.0064 ZCSL (METERS) : 0.0510 ) :-0.13'_6 YCSL (METERS) : --9.0034 YCSL (INCHES RLE IMETERS) =0.000236 RLE (INCHES ) = 0.0093 RYE (METERS) :0.00010_ RYE (INCHES ) = 0.0041.

X-AREA(S_.METERS)=O.OOOIbb X--AREA (SO. IN. ) = 0.2568 GAMMA-CMOR 0 (OEG . )= 68.34 GAM_A-CmORO(RAO.)= 1.1o2_

APPENDIX ',:

PART 1

3T_AUY uLAU£ .... T, ,

TABLE C-I

k_ _ i" .....

3LADE LuCA_ U,,TWIST 1;I UE3REES

(>IIRROR ,;E_SURE;;E;ITS)

Percent

Chord

PercenE

_;easured

Span

Percent Design Speed

From Lead-

14easured

54 73 82 85

From Hub ing Edge

0.57 1.03

.F.._

O.54 0._2 ". 15 i _e

LD

0.42 0.71 (3.33 1.01

5O

3.33 ].J2 O. 73 0.88

0.47 O.SO 1.04 !.13

So o=

") 0.72 0 _O 0._8

0.39 0.64 0.81 c

5O

iO , 3 8 0 . 5 2 0.79 0.37

7O

0.35 3.57 0.71 0.78

0.26 0.45 0.62 0._?

5O

0 O 0 0.3 _

oo

3.09 9.1i 0.12 0.21

0.32 0.51 0.66 0.72

0.i9 0.29 0.36 0.39

0.04 0.09 0.11 0.11

5O

25 0.40 0.33

33 5 0.5*

25 0 0 -O.05 -0.L3

2O

GS 25

25 0._,3 0.71 0.33 0.90

50 0.25 O.51 0.52 O._J_

25 3.3S 3.30 9.3_ :3.J9

_b

*_uestlonaDle Ja,L,_.

1 I

¢iqure C-I "easu, ed Untwist for ,S,__ Fan 3]ade ,Is ,_ Function of [_hord at

_.3 Po','ent Speed

t-_ _ .,.'• "T: _

5% CHORD FROM LEAE)ING EDGE Z_

1.0 D O 25% CHORD B

0 _ CHORD

70% CHORD 09- 0.8- QUESTIONABLE 07- DATA POI NT

\

0.6- ,H L_J rr 0.5-- uJ C3 C/3 0.4-- 0.3- 02-- 0•I-

0 - 1 I 1 I I

4O 50 60 7O 80 90 O0 TIP PERCENT SPAN

Figure C-2 Measured Untwist for TS22 Fan Blade at 73 Percent Speed

Relative to Untwist at 25.4 Percent Speed

/% 5%RHORD FROM LEADING EDGE 1,5 O 25% 14 --

0 5o_

1.3 -- E] 70% 1.2 -- 11 -- //_U N'T%'VIST 10 -- ROTOR 0.9 -- HIGH LU LIJ

II

rr L_ 0.8- -- I.U ,m y,, 07 -- t-- z / STATIONARY 0.6 -- 0.5 -- AXIAL DIRECTION 0.4 -- STARTING REFERENCE SPEED _ cOR MEASUREMENT 01 --

1 1 I, I 1 1 1 I 1 I ,,, I

10 20 30 40 50 (_O 70 ,_O ,_] 1 DO

ROTOR SPEED. PERCENT OF OESI_,;N

Figure C-3 _leasured Untwist for T522 Fan 3lade ,Is a Function Of Rotor

Speed at 95 Percent SDan

13_

O 5% CHORD

].4 m A

75% CHORD w nr L3 w < m © ],3 c_ co < L_ z "r D L3 12-- L_ D < I ] 6O 65 70 75 CORRECTED FLOW

Figure C-4

Measured Untwist for TS22 Fan Blade as a Function of Chord at

73 Percent Speed

-"_DATA ------ANALYSIS 0 8 RADIUS = 95% SPAN

04 L 1 l I 1 1 _ L

1 1

-'t 77-

_t

o4 1 i

,) , 1 i 1 1 1

1 1 1

1 1

.',_ ,10 GO 4O 1 O0 Tq,klL_Nt_ E D_,'_ E

Fi,lure C-5 Me._sured Untwist For %22 Fan ._lade ]nd Predicted by NASTRAN

Analysis for Rotor Sp_?ed ._t 65 Percent Speed

13o

Ci £O_,'"""_

DATA 1.2 ANALYSIS _ RADIUS = 95% SPAN 1.0 0.8 0.6

04 1 I I [ I I I 1 I 1

o 2o 40 6o 8o 1Do

,ll UJ m ,0 RADIUS = 86% SPAN nr L_ LU 0.8 ,.u" LO Z 0.6 oo

0.4 I i I I I I I I I I

z

o 20 4o 60 8o 1oo

1.0 n RADIUS = 7"/% SPAN 08-- Q6

1 I

04, I O0 2O 4O 6O 80 TRAILING EDGE LEADING EDGE PERCENT CHORD

Figure C-6 Measured Untwist for TS22 Fan Blade and Predicted by NASTRAN

Analysis for Rotor Speed at 73 Percent Speed

'I

1.2 DATA _ ,,,,,-- ANALYSIS _ _ RADIUS = 95% SPAN 0._

o.4 I I 1 I I I I t _ J

o 20 4o 6o go loo

Iii .-.r _9 u,.l _ RADIUS = 86% SPAN 0.8 z 0.6 z

I I I

0.4 t I i I I I I 80 100 o 20 40 60 RADIUS = 77% SPAN O4

0.2 I I I I I i t i i

0 20 40 60 _0 , oo LEADING PERCENT CHORD TRAILING EDGE EDGE

_easured Untwist For TS?2 Fan Blade and Predicted by NASTRAN

F ,gure C-7

Analysis for Rotor Speed at 75 Percent Speed

l

_PPENDIX C

PAKT 2

UNSTEADY BLADE STrUCTURaL D_TA

,. ;.,. ".."_ :'. ,i",; ,,_ ._.'.';, ,.._ ;._'_. _"',-;_ r;L?! ILL!, ,.-'L _

14,]

TABLE C-2 $13_Ai_ GAGE ;$1PLIT'JOE AND PHASES 72 75 SoeeO (Perce,t) 619 638 Frequency (Hz) Phase Phase Phase Relative Relatwe Relative to 3 lade Stress to 31ede Stress to Bl_de Stress Number 3 Nu_N}er 3 Blade 2 2 Number 3 Pos,tion N/_ _ g7 123 2.275 3,300 1,723 2,5_0 120 I 2.275 3.300 70 2.215 3,3G0 2 2.482 3.500 ? .620 3.800 0 1.723 2.5C0 G 0 2,068 3,000 3 2.068 3.000 2BO 2.895 '4.200 283 1,585 2.300 290 4 2.0_B 3.O0O 248 2.482 3.6_ 1.585 2.300 251 5 2,068 3,000 gO g9 1.034 1.500 827 1.200 104 6 965 1,4O0 117 1,103 1,600 148 l 1,:03 1,600 128 1.378 2.000 g4 102 1.310 1.900 396 1,300 120 8 1,241 _,BO_ 9 1,034 1, F:w_ 164 1.241 1.800 1,103 1,600 182 42 965 1,400 32 689 1,000 49 i0 689 i,000 482 700 55 4Z 5Sl 800 31 11 68g 1.000 22 344 500 32 344 500 50 12 344 500 413 600 47 1.3 413 600 136 _44 ._ 347 255 551 800 280 551 800 295 14 551 800 264 551 800 272 551 BOO 270 1S 413 600 16 482 lO0 258 68g i ,000 256 482 700 267 271 482 700 291 17 551 800 27_ 827 1.200 413 6C0 254 18 551 . 800 i, 034 1,500 240 2_ 827 1,200 204 482 700 200 IS 482 700 ZO - 126 896 l, 300 138 827 1.200 153 82 %5 1.400 130 21 827 1,200 94 1,516 2,200 Z'Z 827 1.200 69 1,241 1.800 327 1.200 88 23 413 600 318 551 B00 316 896 1,300 25 264 620 900 235 24 551 800 P96 1,300 343 25 551 800 113 344 500 101 827 1,200 244 .

i I0; 413 _.00 27 551 800 188 - 128 31B 344 ' 500 270 344 500 328 28 Z/S 400 29 551 800 301 551 800 287 a82 700 2gg 30 _13 600 267 287 827 L,200 %5 1.400 278 31 321 1.172 1.700 1.172 1./00 334 L31 200 194 g65 l.aO0 203 202 965 1,400 41 m 31 l i i i m 2- < eo © - x 2m:_

z

Z _3 m

7- I

rr _3 m m- , D ] O_" O 2 6 a 10 12 14 16 18 20 22 24 26 28 30 32 BLADE NUMBER

Figure C-8 Blade Flutter Amplitude for TS22 Rotor at 67 Percent Speed

From Strain-Gage Measurements

mmmm mm m mmm mm mmmm

i ,1t/.) _ 0 0 0 w 000 0

I

o,.

_u 0 0 j] .2" 0 0 0 u_ O O O :t0 _-- 0 0 / O O0 1 I .L_.L_.i t I 1 1.__1 i i l [_ I I I l I I ,1 _ 1 2 ; b 20 24 .'1:1 32 tlt ADF _tJMB! _9 ri'.lUrO '" q Perip.hor,_l _li,;i:ributiv, n ot [_I _, , ,- . at,_ 'itr,lin-Li,}qe .Xnqles in Flutter fit ":'1.9 HZ. t:_7 Poi't'_H_t %p+_ecl t i I -+t_ "r"

L

,!

•'i" ,_

OZ

,._ _,_ _ Z _ f,',f-

_o

__ ,7" _.

4 0

<3 0

< 0

<

<3

<3

<3 0

L,"}

0-

I t l l I l 1 l i 1 1 J I I J I [ I 1 • I

o o o o

;4J !

q L,.} rr,..

<3

,,r. _ o

< 0 - o0

<1 O

0 <3 -

Z £.- _

o

0 _'_

O-

l • L t a I J l L l .t 1 J L L ! I 1 i ! 1 , o o

0 -Z

...7

<3 0

0 _

0<3

I 0 <3 .,

0 _ -

0 .'-, HIDN]_IIS 7t/N,r)f3 7_/NOIINOdOI:Jd

14"

TABLE C-3 BLADE AMPLITUDE IN FLUTTER (Measured From Mirrors From Still Photographs) 75 Percent Speed 57 Percent Speed 73 Percent Speed Peak-to-Peak Peak-to-Peak Peak-to-Peak Peak- Axial Peak- Axial Peak- Axial to-Peak Component to-Peak Component to-Peak Component Torsion Bending Slope Torsion Bending Slope Torsion .Bending Slope Blade Percent Percent (Degrees) (Degrees) Number (Degrees) (Degrees) IDeqrees) _Degrees) _S.pan Chord o 95 5 0.33 0.23 0.12 0.46 0.23 0.28 25 0.20 0.35 0.18 0.59 0.17 0,26 50 0.21 0.40 0.20 0.53 0.18 0.26 70 0.18 0.50 5 0.22 0.25 0.20 0.50 0.25 0.30 25 0.15 0.21 0.I0 0.28 0.17 0.17 50 0.17" 0.30 0,15 0.45 0.20 0.17 70 0.13 0.30 0.17 0.43 0.17 0.ii 76 5 0.17 0.18 C.12 0.43 0.18 0.2 50 0.17 0.21 0.08 0.25 0.18 0.2 0.07 0.03 66 5 0.05 0.08 0.15 25 0.02 0.05 0.06 0.05 0.05 0.05 0.I0 0.03 0.i0 47 25 0.10 0.17 38 5 0.05 0.08 2O 5 0.24 0.40 3 86 50 0.44 0.48 0.54 0.69 0.14 C.23 4 86 50 O. 50" O. 53 O. 53 O. 55 0.24 0.40 2 76 50 0.58 0.55 0.43 0.63 0.10 0.17 5 %6 25 0.21 0.17 0.17 0.23 Relative to strain gages 4 and 9 'r 'v" _" -r © O _ 0 _e _e _e _e

O<]0[3

_z _ _ p /......

el) o o o c- t_

-.,_ )

c-" "l_ O. r.," Z

_o

m _ 0 m • _,- _ t_

1 4 c)

TABLE C-4 BLADE AMPLI_DE AND PHASE DEFLECTIONS DETERMINED FROM MIRRORS (Reduced from High Speed M_vies) Bending - Torsion Location Benc,n_ Torsional Phase Percent Percent Phase Phase Angle B Iade Number Span Chord (Degrees) (Degrees) (Degrees) 65% Speed 95 25 41.1 26.6 45.2 95 50 -12.1 0.50 14.2 95 70 -72.6 -28.9 -8.9 86 25 31.9 36.3 25.1 86 50 0 0 31.8 86 50 -72.7 65.9 -i06.8 86 50 19.3 -59.9 113.8 77 5 63.6 69.6 23.5 77 50 -0.3 9.4 24.1 77 50 49.4 -18.4 103.2 65 25 -95.3 -86.2 25.5 7_ Spee_ 9 95 25 -20.5 1.0 -86 9 95 50 -6.1 20.9 -91.9 9 95 70 8.8 28.7 -84.8 9 86 25 -22.3 2.i -89.0 9 86 50 0 -64.9 4 86 50 -125.8 -99 -97.8 9 86 70 14.4 34.6 -85 9 77 5 -24.5 -23 -66.6 2 77 50 6.5 35 -93.4 5 65 25 2.6 -19.2 -76.2 75% Speed 95 25 -5.9 15.3 -45.7 95 50 0.4 23.1 -41.I 95 70 2.0 14.5 -30.9 86 5 a.2 44.2 -67.0 86 25 0.7 22.9 -48.7 86 50 0 3 -15.0 86 50 -2.6 -117.0 99.9 86 50 -6.6 -i03.7 81.9 86 70 -1.7 18.6 -443.4 77 5 5.9 56.9 -i01.!

77 50 -5.5 28.2 -52.0 77 50 -14.8 54.0 -83.3 65 25 134.5 -i15.2 -16.8

_o

O,_OV1

Z c-- er"

111 111 11 11 111 lllll II

w C_ m 4..a_ u e_ c- ._a

1 1 1 I 1 1 1 I 1 I 1 1 I 1 1 1 1 1 1 1

i.. l...

% I Q..2 ,D

I 1 1 1 1 1 1 1 1 1 1 ' i l 1 1 l I l 1

_n _" O k.

rr" Z Z Z Z

._i__ _

" i

<lOOm

I i i , * , I , , r_

%

c- o k.

o tll i _ k.

o

.. ti a_

m'" _

r_ k.

o c- o I I i i | | i _ 0 '_, e0 Z ._ L Z - k. k.

oo v 2: <m

ii=

- ._

_J k- r_

8° I

40-- RADIUS = 95% SPAN FROM HUB 20-

t f I l J I 1 l

-20 -- < 60 ,:C , = I' z "r" _ 20 z < -20 ,11 <

• l 1 l 1 1 I I [ l 1

•r -40 r- ,=, 6O 4,O RADIUS = 76% SPAN 0 .......

20 1 1 I i I { I 1 ', l

0 20 40 60 80 I O0 -_[)l"iG _Di_E T_AILING EDGE PERCENT CHORD

Figure C-14 Vibratory Phase of Torsional Deflection _t 75 Percent Speed

o..

i

I I I ! I I I I I

{D

%

c- "tD ...,n c- D GJ r,m

rr %

x

o..

_o

O r_

<I["IO

_3 q.- O r_ {3.} _. 4-_ _D o tn ¢- co *- O __ _D_ O O _J Q_3 £,q I L.D

o

(D

!

£- f_ LA_ $3 :]Hg..,3r'd '31_3d-O1 31"_'3d '3dO7S 9NIC]N38 7VIX'v"

APPE,_DI X D

PART !

STEADY PRESSURE

,_OTE" On the following tables, "Tangential" data

represents the angular displacement on the rotor.

Pressure data represents static pressure.

Or r'd_,:.: ;_ _../

TABLE D-1

STEADY STATE STATIC PRESSURE FOR CONTOUR PLOTS

55% SPEED RECORD 247

Inlet Total Pressure = 90,400 N/m 2 (1888 Ibf/ft2)

Axial Location

Static Pressure to Inlet

Total Pressure Ratio

(Percent Chord)

-55.4 0.962

-15.1 O. 962

3.6 0.971

9.4 O. 964

22.2 i. 004

34.6 1.029

47.5 i. 041

73.4 1.053

99.3 1. 063

141.4 I .065

,d: Q or" i • _ _ o e 6 e e e e _ • o t_

?,?_'_??????'?_T'_'TTI"I"_'I"'_',, 1"i" ' '

I,,- -- I I I I I I I I I I I I i I I I I I I I I I I I I I I I I I I ! 4( o C _A O, II Z-- I I I I I I I I I I I I I I I I I I i I I I I I i I I I I I I I--- ,,J I-- Y .J • " uJ 4( r_ ,4P I _" f_ II © ,.J _J _,_ 3_ Z _ I 1 I I I 1 I I I I I I I I I l i I t I I I I I I | I I I i I k.,- _g II _P .2 &.

_,_

g

a.

)"2_ D_ (_ W ; 2 2 ' 'd '2a_2 " '2 ..............................

o.

I: IZ it 2, 4" m _ ?)c_.

_'- . . . . ', . .

"n _. _ I I I I I 1 1 1 I I ; t I I I I I I I I I I I I I I I I t I I #- O. tD <O _D .4-1 O 1.1.1 0 I.--_ (%J I &IJ U.I ,,n .J _j -J O.

< "Z I" e. ;X a_ =[ :E )c • u: ._._. ..... . ................ , .......... ...........

tl _')l_'_t , r ' I , r r . _, ".1.,._ ¢.1 ? P C. _* .... ' -- _. , _ _ .. ,, I I I 1 I I I I I [ 1 ---- t I I I I I I I I I I I I I I I I I I I I 1 I I I I I I I I I o ,it % MAXIMUM PRESSURE CURVE CURVE LABEL VALUE 2 _.93000QE+02 3 _.SBOO_OE*O2 O.?90OOQE+O2 5 0o720013'0E*02 MAXIMUM ST ATIC PR ESSU RE g8.8 KPa i14.31 PSI) c_P _i ROTATION ) BIJ_DE 5 BLADE 4

I_ i "/" / "/ --.'/ 1

-t" _ /." -/'"

_.U 2x/>_. • ) //Yc:> > / ._._, / .s._

;? rc,- 'Is,r- <,.,. %:¢1

' k t \!

-36.00 -32.00 -28.00 -2¼.00 -20.30 -I8.00 -I2.00 -8.00 -4.00 0.130

TFINGENT IRL _OEG_

15o

TABLE D-3

STEADY STATE STATIC PRESSURE FOR CONTOUR PLOTS

63% SPEED RECORD 71

Inlet otal Pressure = 83,410 N/m 2 (1742 Ibf/ft2

Static Pressure to In!et

Axia Location

Total Pressure Ratio

IPercent Chord)

-55.4 0.935

-15. i O. 941

- 3.6 0.9.58

9.4 O. 949

22.2 1.002

34.6 1.018

47.5 1.020

73.4 1.019

99.3 I. 031

14! 4 1.038

f,_ _,e _,._,._ _',- ,_ _ _J £_ _ _'_ _, _ _,,,_ -_,-, _-- ,.-"_ _*_, _ _ ,--,.._ _,,"_,=_ I I I I I J I I I l I I I I | I J I .._-- I I I I_I I I I I I I I I I I t I I I I I I I I I i I ,-, 0', v') G.

,0 ..J e _Y r_ C3 A ,=,, :£ w- v_ ,.J Z • e e • o • • e e * • • • • • e • • _ • • e e e • • • • • • e • , • • • • e • v • • e • • • e • I I I I I I I I I I I I I I I l I I I I I I I I Im "_ * ID_J I I . _Z _'_ . . , - • . .

.=J _ _ __ _,P_ _ _-_ __ _ I I I I t I I I I I I I I CZ3 Z--IIIIIIIIIIIIIIIlllllllllllillll

,,<

I--

o , o , • • _ o • * , e • o • e • , • e • * o e , e • e Z -- I I I I I I I I I I I I I I I I I I / I I i I I I I I N e , a , • , • • • • • • • • • , v • , e • • _ e , , e e , * , , o • • * • • • e e e • • • • , , l,_q.

I!

_J e," C) m .

.......... . . . . . .h ._ ._ . ...... . _

Illlllllllllllllllllll )- ?- t+_. + I.i,_ • v e • • o <i 5" ii e,-., .,.I ev- M I-- .,j..

Z

• . _ _ '"

Z o,.

• < C _A ,,,-,i l,/'i Z_ ,.-i Z_ .3 ey" 4( ol _ ii O _ no 8 i.i.i ,.,.,,.i ,,,..i I,.-- ,.,,.l ,.,.l

;'. 7

_ il ..J .is _ I" + ,._ t",, (_i r.+ , P_ -I v; +, ,_ +L; _+_ ", k-.

t+aj ,r • M • e i o o + i • i o il cl_ 4( e+_,_ _ _.._ • • • • i . o i i l o • _I[ --"

t_2

T ,i, C,"_ t, II _1,.

_ ¢_ .. ,% ._ _ _ r-_ r-., ,_ _ _ _ _ _ .4 ... _ .._ _ _ ._ I I I I I I I I t I I I 1 I I I Z_ I I I I_ I I I I t I I I i I I I I I I 1 I I $,,.

e • _ • • j • t e _ • t • e e e • • Q t • , • • , • _ Q e o • • t • t o e _ • • i • • • • • • _< w'l O.

wl

,4

A ,.q

_J

e¢ 0 " Z_ I I I I 1 I I I I I I 1 1 I I I I I I I I .,.1 Im T_ .J "_ ,m II .,.I 0 b-- O" _;m _, • • _ • e , _ _ • • o • • o • e w • e_ e • e • • • o • | t e _ • • w • • _ • • • e e • • ,i • • LL: _. _. ¢% _ e,_ "_ ¢': ,,_ ¢N _. _,. ¢_ c_ c,. .-* ,-*.,-_ ,..* _ ,m _ ,._ *.._ _ ,-. _ _ _ _ _ _ _ _ _ I I I l I I I I I I I I I I I I II II :_ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I C., --..,I ,,,J e¢_ g e,_ < ; o I--

,J1 ....... " '' '_' ';_ "''''' '_; 'g ..... ,4_; ' 'g ".,_

.,.I" u,.J II .y "Z; ,..i,., ,.J z_: ................... . . , _ ''" ....................

,_ _ ,x_ ,_ _. _, *. -i _, . , _ ._ _ 4 - I I I I I I I I I I I I I I i I t I I -- 1 I I I I I t _ I l I I I I I I I I I I _m II ,,., :.. j .':- ,.: ...... _ - :,,.. ,-. . .: ,', _. . ,, ,, _. ,, -'. . '-._.q ": ,, _. ,,._, ..,," ,': ,'; ,': _. ,'. _,. . . . . ..... . . ,';.," _.

_ I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Q • • • t o o e • • e Zw 5" _t, • _./_ o • 0 o • e • e • N G..

,o

g_

7_ 4.

p.,.

c- O ¢...J 4r v I _m k- ,..J _t

2 ........ _" 8'

"z" k-- C_ _ I.

r- ., , _-,

% MAXIMUM PRESSURE

CURVE CURVE

LRBEL VRL_E

2 0.930000E'02

3 0._'_O00E'0d

0.?$000QE-02

5 0.7_0000E_(3"2

8 0.6$a_00E*_2

? O.580000E*92

8 0.510000E_02

MAXIMUM STATIC _E$SURE

96.3 KPa(1396 PSI)

Steady St_Jte Pressure Contour It Blade TiD; No Flutter, Low

Figure D-2

Operating Line, 63 Percent Speed, 65.8 Percent Flow, Pressure

Ratio 1.177b

TABLE D-5

STEADY STATE STATIC PRESSURE FOR CONTOUR PLOTS

63% SPEED RECORD 82

Inlet Total Pressure = 88,770 N/m 2 (1854 Ibf/ft 2)

Axial Location Static Pressure to Inlet

Total Pressure Ratio

(Percent Chord)

-55.4 0.965

-15.1 0.960

- 3.6 0.963

9.4 0.977

22.2 1.033

34.6 1.067

47.5 1.089

73.4 1.118

99.3 1.136

141.4 1.127

_J _f i!

p.,.

ql

........ _. _._._._-_._._._-_.. _I

I I I I I I I I | I I I I I | I I [ 1 I I I I I I I I I z u._ -.I Q. _.1 e_ II Z--IIIIIIIIIIIIIIIIIIIIIIIIIIIIIII _ _ _ _*_ _ _ _* _ _ _ _ _ _ _ _ _j _ `_ _ q[: _`_ _ _ _ _¢_ _r _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ,_ _ "*. f"_ _ .,,._ ,CJ _T _, _ I 7_ ,'_ S.PO,,.

I II .,, 9[ e_

_ .......................... ,:. :_; .... • ..... .., .._g •

_ I I I ) I 1 I I I I I I I I I I F 1 I I i * I I I I 1- _llllllltlllllllllllllllt & ,'N _-,- _.=_, _ _-: _, _ _.-I _.

,( Q. r_ y.

r_ ).: A _ ...,, 2' IN.

e • • e e • • • • • • N 0_ X v,') I!

r"" _-.e O_ _Z Z 6/I I"'- ,_C ',40 _- e 9.- _.

x .4 A >- I,'-- ,,_ O _ .Oee.oeoe.e ',,.O I,"- !

Z_ ( W -..._ ..J CO -,_0. _ee' ._ , , ._.; ';_ . .

X _ es

1_8

t.

_1" I,l.,l '91 "J" ,',,"

_J

Z_ I,,,- I!

f_ _.-,j A C_m_ __""''" _'__" _ .... ""-:" _'T?I'_7_11'_I_'777;'7 _ ....

Z --IIit11111111111111 111111111 Im u._ I.-.0..

'_C:] c- II O !

C_ u_ _-- I I I I I I I I I I I I I I I I I I I I I I I I I I I I ..I ,-,,m _u

,t

,2 x }_ I,,"I II I,'- • 'i_ e _i._ ; _" _'_ • _ _ r_ - _ _

........... .'. I"', 77 ," i 111 f?:' f? _'_

_ | I I I I I I I I I I I I I I I I I I I I I I I I v_ Z 4" _J _eeeeeo eeoe ..4" ii J--e Z _ o • O • • I o • • • b?

Z_ t,--.

u5 _eeeooo eeoc :_ ii _t _ _J .J a_ ,,_ _oeovee . o I.- .J i _ I v'_C, "r I..IJ I,- .,J ,.,.1 _eoeeee ee e x )...

5r li ...., ..

1"0

_£ MAXIMUM PRESSURE

CURVE CURVE

LABEL VRLUE

2 O.93g0O0E_82

3 O.880000_02

O.?BOOuOE_02

5 0.720000_-02

8 O.8_O000E 02

_XI_U_,ST_F:C PRESSURE

101.8 KPa(14.75 PSI)

_ _e _v_ _L State .2resst, re t.')nt _,_rs _f.. m1 ad_ Tip', In ,_ILJt t_r,,

Flow, Or_ss,_e R._tio 1.2_7_

TABLE O-7

STEADY STATE STATIC PRESSURE FOR CONTOUR PLOTS

66% SPEED RECORD 239

Inlet Total Pressure = 89,440 N/m 2 (1867 Ibf/ft2)

Static Pressure to Inlet

Axial Location

Total Pressure Ratio

(Percent Chord)

-55.4 0.963

-15.1 0.960

- 3.6 0.962

9.4 O. 981

22.2 I. 041

34.6 1.079

47.5 I. i00

73.4 1.130

99.3 1.149

141.4 1,139

!

< il.

2, tl Q O

i

lid Z "4" tl lit , il

g

4_ i tl il i ,< _l I I i I i i I i I I I 11 I I I 1 i I 11 I I i i I I t 11 i i-- 'S, _< I II .J I I.,I.1 li' i I'P Z i-" I,,- 2" ,..,* _ i 0,...

|ollil|eiiloileloitilillotililiiei|ieleeell liie x tl 0 ..l m C_ I II Z i i I _ 17 Z_ X I'i II.

II N "i" p"" I I"_i _l_l _i" i,#i w,i II Z_ p,., w.i __t 5"=: Oe_,- II I,.... m !

ill I.,_ _ ,,=i Z_ ..J I,,.,.

.,.,,,.I ,_ .=.1 _U._ I _ Iv,_ II.

s.J_" _,JZ_,.D i el e Z Z_ X IJ lg II '.i.I I,,_ _l:l _ C,,.

_Z

1"4

r_ _" LU _.-,, J Q.

tl ., ,. . ?,-?, i--

5_

Q.

li _.=_ _:_'_,, .... . • , , ., ' ., Z-- I I I I I I 1 I I I I I I I l I I I I t I i I I I ! I t I I I I M.,.

A t- O r,- _[ CO I

_TTT.TT?TTT?71,????????,??T77777T777 , 0 , , ' , ' ' '

e,a _C .-3 C_ v_Z X X ,,4 ,,r t-',_ • o o Z

_ MAXIMLJM P_ESSLJRE

:,,.RVI[ :,.+_tVE +_. _2_JI30_E _3Z

'_AX;,",,4_JM STATIC P_ESSURE

103.8 KPa t 15.'00 PSI)

ROTATION

BLADE 5 BL_OE 4

t ,J / i • ,= j_

/s; _ \

L

+=

CTT ....... ........ '_

TABLE D-9

STEADY STATE STATIC PRESSURE FOR CONTOUR PLOTS

RECORD 141

67% SPEED

Inlet Total Pressure : $2,500 N/m 2 (1723 Ibf/ft 2)

Static Pressure to Inlet

Axial Location

Total Pressure Ratio

(Percent Chord)

-55.4 0.931

-15.1 0.938

- 3.6 O. 957

9.4 0.952

22.2 0.994

34.6 1.020

47.5 I. 022

73.4 1.017

99.3 I. 030

141.4 1.036

r uJ _r_ C* II --J e * * * , • , • L'} E Z_ I i I I i i I I i I i i I I I i I I ; I I ; I i I I | ; I I I I I I I i I I i p..

]E , l * i v * * v • * , , , @,x _f I v_ I1 ' -_ I 1 I I Z-- 1 I I I I I I I i I I I I I I I I I 1 t I I I l I I I I I ' ' * ' ' ' I , I v1 U t_ v_ ,4 II I p.. i '_ C) m.

t/1 M I!

| I I I I I I I I I 1 I I I | I I ! I I I I I I | I ! I I I I -_t', ..J ..J 3t_ v_ I !

il .d _Y _r _E .... '? ' 7"; /5'7"," 7 7,'7 ....

-, , , ; ?? ? ? 777,7,777,'T'777,7'' * ' ' ' ' ' ' ' ' ' '

_r 4" II c_ ..J e¢ .-{ C;

.=,-_._:': ..... ; =. , . .-: ................... %"

I- ................................... i ,,_, . -- I I I I I I I I I I I t I I I I I I I I I I I I I I I I I I I I I I 1 I F- ()Lt_'/'t..,.

0_,'/,'_'Y 1

." ,.;.

-, t / 17,_,

l-q

• , _" . _. :.,J

"% t_ il r- • o o • _-" _ "" I I I I I I I I ¢..

G.

¢m _J _l; II _ _-_ ?,'777;" , I,,,,, J _ _ _ 0"_ f".. I"_ _ ,_ ,._ ,_ ,_ ,._ ,_ ,_ e- )- ¢..) _( ,0 _J e 0 _ t_ I Z_ I,-- • _v,_ • • • • _ e g v • • • 2 -- h U_veetleete_ I I I Q.

4" _J ,+M ,.,,I" "_ o,_ I • • v i • • • v i • ,4 ,.q+ ,..4_ t+ e • o i) • • i • v e e Z ee_ e_

.; =

• -, "r"

,7T _

t_ Z p- a."

I-- e. B _,q • • e • • • I • o • e O r_ X "0 le e[ ,0 _.-I _ i,--, _,'_a _ 2P _eee_ee ev_ee I _IiIII ..J ..J e_ ep=.+ _eeO+ee mvmmm "Jr ..d ,..+.,<-..+ ++ ...... ,.,. ,-.., ,,,,,., _E k.,.

_L U9 = 3" q_ rx +...l _° _ • • 41 • • + _ • * • e LJ _ I k..,-.

Ill ,.I et ," .-.* e-+ r" ,J' ,1" ,0 f_ _r- C-- -+

%MAXIMUM PRESSURE

CURVE CURVE

LRBEL VBLUE

2 0.930000E*02

3 0.860000E_02

5 0.720000E*02

8 0.8500g0E*O2

7 0.580000E*02

@ 0.510000E'02

MAXIM WM STATIC PRESSURE

976KPaC14 74 PSi)

_ ROT,&TION t

_, _ _ _o_jJ _ _o__

-a@.O0 -2_.00 -20.00 -IS,gO -12.00 -8.00 q. O0 O.OO

TRNGENT I_L CCEG_'

f" 4- , . ,.mp

Ste,e_,, State Press,ire _on..ourS _t %l._,'ie Tip, . _t of

_,:rcent Flnw, Pr_ssur_ 2atio !.]_'r]

- 1

wl r_ 4{ 3I::_ U ¢_.._ e t • _ o e o • _ v • I'_ _.3Zv _' '?. --.--e_'_ _ ¢_, _. m *% _ ,i _ ,i "_ I I I I I I I I I I I I I I,,,' Q_, tl / ,1,- la lee Z'-,, I I i I I I I I I I I I I I I I I I I I I I I I I _ I I I I I I I l,,- X _ _ _¢_ _'_,_ L_ p- _" ¢_, ,0 "_ _ 4" _ ph_ _., 0,:, _ I'.-,_t" P _ _ r?. _M _ _'h.,_ -_,_O ..T _1" _l_l {'_ _,,,, ,_r -O_r_ _ _n P- _ _ _ _ _ _j .'3 >.

v .J 4( P,- r',. (_ Z_" I I I I I t I I I i I I I 1 I I i I I I I I I ! I I I I I .J P ..M

<

EUJ m_ I _"_ _r X :;_" I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I ,,{ im I _r_ I!

Z-- I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I l I I J I I I w ,_," i" ,:' ();;\! rF'; Q. (%J II r_ Z4,.g • • • • • e • • w e * Z_ I"" I!

M_ _eoeo e o*eee L_JJ ,..J 0,. ,,,..j 2_ I,.J..J ,_C ,G I-,0. _eooo • e_ooe X I.-. ,,.I I :0- II k., .J )'-- r'. O "T i O-'- m N Z ,.J _=

<

.J.J uJ ...i e_ I _,j e,,- II Ou._ r_ Z

u.J .... _ .;_ "_ '

I 5- Z IN .< x )..

.,F

...... . _

x I II _D "I" Z_ li_I ! loll!

I1",_ |Jl *tj '[ 2.

1o em j ¢'_ 0,-0_., , _?????_,, _???,77TTTI'T'_TTT_'__ ,TT' ' ' * ' ' _ ' ' ' ' i , I,- eL _r 7' II l-q o.i a¢ II _???T????_??_'?T?TTTTTTTTTTTT77T' _'' ,,, , , , , , , ill l,_ l J)

_m

I.- ..J l,olP n,., ar_ 0 It i#_ 0',

"T

m l,- IF_.._'_I'_I_I_I_II_II',II'_I%I'_I_.I_,¢_I_I,...,,-'___ I I I I I I I I I I I I I I o-, II _'" I I ; I I I I I I I I I I I I I I I I l I I I I I I I I I l.IJ ..J ..t 3al eml_ l.ll_ "m I.

_ I I I I I I t I I I I I I I I I I I I I I I I l I I I I I I I :I_ ,ii II .,.t I# Z -- I I I I I I I I I I I I t I I I I I I I I I I I I I I I I I I I I | IIi Z ,,J i| _e_Oeoeeeelel _r n.

0"

d

Lu Ua ._ e- LM _J lit', ,I[0 l.-.J t_ P..4 5-,.,- il r_._l -7 iJU • I.

_J _u .J I...

P,e It := ve._ ,.,i ..1 _E_u t_ u.J N_ ii ou_ U_L_ * • e , • • • • _ • • • _ _..._ _ I ! I I x x _._ZL._ * * v • * • • • o • * • 7_ I-- uJ¢l_ T_ v_7

OE POOR L.'/_L!TY

% MAXIMUM PRESSURE

CURVE CURVE

LRBEL VRLUE

2 0.930000E*02

0.860000E_02

K 9.7900001_÷02

S 0._Z000OE*02

0.350000E_02

7 0.580000E÷02

8 0.5tOOOOE_02

M_XIMUM STATIC PRESSURE

97_ KPa (14.19 PSI)

e-i

O=P

-28.00 -2q.00 -20.00 -L6.00 -t2.00 -8 00 -q,00 _.00 _.00

TRNGENT IAL tOEGl

F i gure D-6 Steady State Pressure Contours at Blaoe Tip; Transient

Into Flutter, 70 Percent Speed, 74.5 Percent Flow,

Pressure Ratio 1.2120, Incidence to Mean Camberline 5.6

Degrees

_-_F , ,: _ , _ ....

<{ 0 N f_ u.l ,_" II Z-,,. I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I,,- U.I .,I eL U ¢} Ua"( <0 I".1 p.

>" _1[ I¢'t i I"N UJ I-- _w II

<

p-

ul ,_ ,=,1 ,,J_.

mu_ _W !"

J_J _Z _. _. ,_. _. _._._. _._. _ _._.

OF POOR

e( G.

H_ # • • • # • • • • • • • • 0e _._ c3 z_ < l- G. _r,v 04_.

r- o j..

_.,_ _-:_.-. _._.-:_. _._,_ _._._ . .

r-, _J I_C,, e-.

II _. • I"_- • _' _t_ ..r ¢": .f' ._ ,-_ f'.- e...J .4" ¢0 W_ _.J:P_.D • • v • • • • • • • • • i Z_ k_

<

X _ amo_ _,,J Z_ _ • • • e • • • _ • • • I_ ,.._ ;_ I I _" 8e_.

C" .._ et_ • C') ,,.e _ 04' _,,)_ p-- _" 4.) ,-.e e_ f_ .1' _ .01 _ _t_ f_' C

IQO

_q _r fv II Z_ im i I I i i i I " _ _ 3' '? ? ? ? ? 3' ? ? ? ? ? ? ? ? ? " " " - ,,, ,-,-',-?',",-,_,"_-,',"_--,_________.'_______._'' *' N- w I 01 lm,_, L.

______,___%____

¢NI I_ _--IIIIIIIIIIIIIIIIIII1,1111111111111111 I&l '_ .,,J O.

,iT It., 0_ ,,( ill .l_ 1.1_1 Q,.

f It _ I I I I I I I I I I I 1 I I I I I I I I I I I I I I I I I I I I I I I ;n 114_.

k CI ,ll I,,-

° ...... " 4¢

_1111111111111111111111111111tll mr II,

01_1( "'_' 15 191

MJ ,4,1 D_ L

C_

II O,.I _o_,_ I...

X_ D_ a.

• :, it "_ W'D A, JZ,5,_ • e • e • • o • • • • • 0 _ Z',- -,,,j

_ -,., _T_,-:_.-:_,t._ "

I:= )" II IJ ,eto_ lJpe (_ e,,e ,e, II__,._ _ I Z_ e_ w D_ O_oe_eeoogOooo _ L_ II _l..J _3,v C_ e-o ,,,._ "_' I_- o I'_ _._ _1 _ P",., _'%J ,,_ _. p,.. ('_ ..3 p,....,t1" o.J ZA._ • • • o • • • 6 • • • • oe_,.._,-t i 1 I I I ,el 1- 5" D_ _X__@__ II I_et O i,,e _m q,.l_(_ • • • e • • • • • • • • I.- ,.J _.u O.c[_ v_Z

% MAXIMUM PRESSURE

climtl CUIIVll

LlielL Vii.ill

S O,Im_Wl_lil

t O, "tlI_WI_II

s o. ?lmoooE*w!

tl o. IlSOOOOl*wI

T O. 1400GOE*W!

o o. siooml*_ll

g

_; _,_.. ,O,ATION I

_!.1 J ' " " "'"- \ "

,-, t. L-.__.i ,..,_. \ .. .

-ll,oo -ll,oo " -_il,o_ -ll,oo -li,oo o,oo i;oo -_o. oo - iI. oo

TRNGEN'F IRL (DE(;)

F ir_tlre _i_7

Steady State Pressure Contours at Blade Tip; Transient

Into Flutter, 70 Percent Speed, 7?.5 Percent Flow,

Presst:re Ratio _.3230, Incidence to Mean Camberline 6.35

Deelrees

ICi._

;';L t'''''_" _

C I_ .:_; • ' -,

OF POOR QUALIT_

_L ¼ 0_ = _N_'_ _'_f=N_ ___._=_ I I I I I I I I I I I I I Z ",,.'

I i I I--I I I i I I I I I I I I I I I I I I I I I I I I I I I

L ==

__N__'__--_ I I i I I I I I I i i I I I I I I I i ? t i I I I I I I I I I I I I _ I I I I I I I I I I I i/I _,,- .,Jr' 0¢ tic Ill {t.

_al_ O ,,.,I [._ I,m C_ =.= ,,=.