EFFECT OF SIDESLIP ANGLE ON THE BALANCE OF AIRCRAFT MOMENTS THROUGH STEADY - STATE SPIN

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1 International Journal of Civil Engineering Technology (IJCIET) Volume 8, Issue 10, October 2017, pp , Article ID: IJCIET_08_10_065 Available online at ISSN Print: ISSN Online: IAEME Publication Scopus Indexed EFFECT OF SIDESLIP ANGLE ON THE BALANCE OF AIRCRAFT MOMENTS THROUGH STEADY STATE SPIN YOUSIF KHUDHAIR ABBAS Lecture, Technology Collage Kirkuk, Kirkuk, Iraq ABSTRACT The present paper studded the lowspeed lateraldirectional aerodynamic derivatives due to the rate of change of sideslip includes a comprehensive bibliography on this related subject matter. The results presented show that the magnitudes of the aerodynamic stability derivatives due to rate of change of sideslip become quite large at high angles of attack for swept delta wing configurations, that such derivatives have large effects on the calculated dynamic stability of these configurations at high angles of attack. The paper also studded the windtunnel test techniques used to measure the derivatives discusses various approaches used to predict them. Both the conventional oscillatingairfoil theory the lagof thesidewash theory are shown to be inadequate for predicting the verticaltail contribution to the accelerationinsideslip derivative however, a flowfieldlag theory, which is discussed, appears to give qualitative agreement with experimental data for a current twinjet fighter configuration. Key words: Steady stat spin. Side slip angle. Rate of change of sideslip angle.. Stability derivatives, Cite this Article: Yousif Khudhair Abbas, Effect of Sideslip Angle on the Balance of Aircraft Moments Through Steady State Spin. International Journal of Civil Engineering Technology, 8(10), 2017, pp INTRODUCTION NOMENCLATURE symbol Definition b Wing span Drag coefficient Lift coefficient Rollingmoment coefficient Pitchingmoment coefficient Yawingmoment coefficient Sideforce coefficient D Drag force Units m N editor@iaeme.com

2 Effect of Sideslip Angle on the Balance of Aircraft Moments Through Steady State Spin L k P r S V λ σ. /. / Subscripts symbol k s exp theo Lift force Moment of inertia about longitudinal body axis Moment of inertia about normal body axis Product of inertia Reduced frequency of oscillction Rolling moment Pitching moment Yawing moment Rolling velocity Yawing velocity Wing area Time required for oscillation to reach halfamplitude velocity Amplitude of lateral oscillation Angle of attack Angle of sideslip Rate of change of sideslip angle Taper ratio Sidewash angle (positive when effective sideslip at the vertical tail is reduced) Phase angles associated with separation effects Frequency of oscillation Increment of due to vertical tail Increment of due to vertical tail Definition quantity measured under oscillatory conditions stabilityaxes data experimental values obtained under static conditions theoretical N Kg Kg Kg mn mn mn sec m/sec M deg deg deg rad Stability Derivatives editor@iaeme.com

3 Yousif Khudhair Abbas 2. DEVELOPMENT OF EQUATIONS FOR AND The equations developed herein for are based on the flowfieldlag theory (ref.3) are developed for the case of a pure sidewise oscillation. However, as will be discussed, they are applicable to the data obtained under conditions of forced oscillation in yaw. For the puresidewiseoscillation technique, discussed in references [2] [4] the yawing velocity yawing acceleration are identically zero the model undergoes continuous changes in sideslip rate of change of sideslip. Therefore, the yawingmoment signal ( ) may be expressed as ( ) ( ) ( ). / ( ) (1) Where, for harmonic oscillation (ref.4), ( ) (2) Introducing the no dimensional frequency parameter yields ( ) (3) Differentiating equation (3) with respect to time introducing the no dimensional from of ( that is )yields (4) Substituting equations (3) (4) into equation (1) yields ( ) ( ). / (5) Multiplying equation (5) by integrating over the period yields ( ) ( ) (6) Similarly, multiplying equation (5) by integrating over the period yields. / ( ) (7) Adding subtracting a theoretical value of (which would be obtained in the absence of flowseparation effects, see ref.[25] to equation (6) yields. /. / ( ). / (8) Since the derivatives are assumed to arise from flowseparation effects, a theoretical yawingmoment coefficient assumes no flow separation may be written as, ( ) ( ) (9) Multiplying equation (9) by integrating over the period yields editor@iaeme.com

4 Effect of Sideslip Angle on the Balance of Aircraft Moments Through Steady State Spin ( ), ( ) (10) Substituting equation (10) into equation (8) yields. /. / * ( ), ( ) + (11) Assuming ( ), ( ) [. /. / ] ( ) (12) Where is the phase angle associated with separation effects, substituting equation (12) into (11) yield, upon carrying out the integration,. /. / [. /. / ] (13) Rearranging equation (13) solving for yields [. /. /. /. / ] (14) Substituting equation (9) into equation (12) substituting the resulting expression for ( ) into equation (7) yield upon carrying out the integration, [. /. / ] (15) Where is given by equation (14) In a similar fashion it can be shown that [. /. / ] (16) Where expression is the phase angle associated with separation effects is given by the [. /. /. /. / ] (17) In the development of these equations, a sideward oscillatory motion was assumed; however, it should be noted that the expression for are function of the inphase derivatives. /. /. Although the inphase data obtained from the forcedoscillationinyaw tests are a combination of derivatives, such as, experience has shown that the magnitudes of the derivatives are usually negligible the total inphase components may be considered as pure derivatives. /. / therefore, the editor@iaeme.com

5 Yousif Khudhair Abbas method in this case for evaluation is also applicable to the data obtained from the forcedoscillationin yaw technique. Additionally, it should be noted that there is no restriction as to the use of the stability or body system of axes. 3. RESULTS AND DISCUSSION The results of reference [1] show that the inclusion or omission of the derivatives in theoretical equations of motion can produce large differences in the calculated dynamic stability characteristics. In particular, reference [1] shows that when data obtained from forcedoscillation tests which represent a combination of derivatives are used as a total value for the pure angularrate derivatives the β derivatives are assumed to equal zero, the results vary significantly from the results obtained when all pure derivatives are used. In addition, reference [16] has shown that the frequency effects of stability derivatives can cause considerable changes in predicted aircraft motion. In order to illustrate these results, calculations are made for a hypothetical deltawing fighter configuration. The mass inertial properties used in the calculations are presented in table 1 the aerodynamic characteristics for the configuration, obtained from references [4, 17], [18], are presented in (figure 14). It should be noted that the static lateraldirectional characteristics of this configuration (fig. 14(b)) are typical of those exhibited by many current fighter configurations. In particular, the configuration exhibits a marked reduction in both directional stability dihedral effect at high angles of attack. Experience has shown that these conditions usually result in a directional divergence, or "nose slice." The yawing rolling derivatives (fig. 14(c)) were obtained by the rolling curvedflow test techniques previously discussed. The derivatives due to rate of change of sideslip (fig. 14(d)) were obtained from windtunnel tests in reference [4], the magnitude of were assumed to be zero for the calculations. The dynamic lateraldirectional stability characteristics were calculated by means of classical threedegreeoffreedom linearized equations for the configuration in trimmed flight at angles of attack of at an assumed altitude of 7620 m. The condition of = 20 represents a case for which the static dynamic data indicate a stable configuration with relatively small values of the β derivatives. At 28, the configuration exhibits static instability (negative value of ),a marked reduction in magnitude of, large values of the derivatives. The results of the calculations are presented in table II in terms of the time to halve amplitude the nondimensional reduced frequency k of the various lateraldirectional modes of motion. Positive values of represent damped (dynamically stable) modes of motion, whereas negative values epresent undamped (dynamically unstable) modes of motion. Case 1 represents the results of calculations in which the true values of the angularrate derivatives were used the derivatives were omitted. Cases 2 to 4 represent the results of calculations in which the angularrate derivatives were used, the experimental values of the derivatives based on data obtained for three different values of k were included. Cases 5 to 7 represent results for which the derivatives were summed with the pure rate derivatives to form combinations similar to those obtained from conventional forcedoscillation tests. For these cases, the resulting sums were used as values for the rate derivatives the terms in the equations were set equal to zero. In table II(a),the results obtained from the calculations for are presented. The results show that including the derivatives (cases 2 to 4)increased the damping of the Dutch roll mode but had essentially no effect on the frequency of the Dutch roll mode or the editor@iaeme.com

6 Effect of Sideslip Angle on the Balance of Aircraft Moments Through Steady State Spin damping of the roll spiral modes. Combining the derivatives (cases 5 to 7) had little additional effect on the Dutch roll roll modes; however, the spiral mode became unstable. The foregoing results, obtained for relatively small values of the derivatives, indicate relatively minor effects caused by neglect or misuse of the derivatives at low angles of attack. For (table II(b)), the data show pronounced differences caused by the relatively large derivatives. Use of the angularrate derivatives omission of the derivatives (case 1) resulted in a stable Dutch roll mode, a virtually neutral stable roll mode, a very unstable spiral mode. However, when the derivatives were included in the calculations (cases 2 to 4) the Dutch roll mode ceased to exist, two additional aperiodic modes were formed. In addition, it is seen that the magnitude of the derivatives used in the calculations has an effect on the computed values of the time to halve amplitude of the spiral aperiodic modes. When the angularrate derivatives were used in combination (cases 5 to 7), the damping of the entire system was redistributed, resulting in highly stable spiral roll modes a highly unstable Dutch roll mode. The foregoing results illustrate that in equations of motion, the conventional use of the rotary forcedoscillation data to represent derivatives due to pure angular rates is erroneous at high angles of attack, where the derivatives are of significant magnitude. In addition to having effects on dynamic stability, it would be expected that the derivatives would also have a large effect on the design of control systems for flight conditions at high angles of attack on related analysis techniques. For example, a recent study (ref. 19) has shown that omission of the derivatives may produce considerable errors in parameteridentification techniques. 4. CONCLUSIONS From the present summary of experimental theoretical results pertaining to the aerodynamic stability derivatives due tothe rate of change of sideslip the following conclusions are made: The derivatives ( ) are large for swept deltawing configurations at high angles of attack. The physical flow phenomenon responsible for the derivatives is associated with the establishment of leadingedge vortex sheets flow separation on the wings at high angles of attack. Additionally, the large values of the derivatives can be attributed to an increment in the aerodynamic moments produced by the separated flow, which lags the motion of the configuration. The derivatives are very dependent on the frequency of oscillation, with the larger values obtained for the lower frequency. In equations of motion, the conventional use of the rotary forcedoscillation data to represent derivatives due to pure angular rates is erroneous at high angles of attack, where the derivatives are of significant magnitude. Both the oscillatingairfoil theory the lagofthe side wash theory are inadequate for predicting the contribution of the vertical tail to. The flowfieldlag theory, devised in NACA RM L55H05 extended herein, is found to yield results which are in reasonable agreement with experimental data for a current twinjet fighter aircraft editor@iaeme.com

7 REFERENCES Yousif Khudhair Abbas [1] Bushgens G.S., Studnev R.V. Aerodynamics of aircraft. Dynamics of longitudinal lateral motion. Moscow, Mashinostroenie, [2] Moroz V.I., Sohi N.P. Method of spin characteristics prediction of amphibian by mean of spin rotation modeling in a horizontal wind tunnel. Proceedings of the IV scientific conference on hydroaviation Hydroaviasalon2002, Gelendjik, pp , [3] Fan, Y., Lutze, F. H., Identification of an Unsteady Aerodynamic Model at High Angles of Attack, AIAA Paper , [4] Stagg, G. A., An Unsteady Aerodynamic Model for Use in the High Angle of Attack Regime, M. Sc. Thesis in Aerospace Ocean Engineering, Virginia Polytechnic Institute State University, Blacksburg, Virginia, Dec., [5] N. Bhagat Shashi Kant, Amit Tiwari, Advanced Tool for Fluid Dynamics CFD its applications in Automotive, Aerodynamics Machine Industry. International Journal of Mechanical Engineering Technology, 7(2), 2016, pp [6] A. Rathan Babu, Shiva Prasad.U, CH. Satya Seep, Suresh Kumar, Aerodynamics Stability of Spacecraft during Earth Entry, International Journal of Mechanical Engineering Technology 8(6), 2017, pp editor@iaeme.com