М.Г.Гоман, А.В.Храмцовский, Йоуг Патель «Моделирование и анализ режимов штопора самолёта, обусловленных аэродиномической асимметрией», проект доклада на конференции AIAA, 2003 г. M.Goman, A.Khramtsovsky, Y.Patel "Modeling and Analysis of Aircraft Spin Produced by Aerodynamic Asymmetry", draft AIAA paper, 2003

1. Modeling and Analysis of Aircraft Spin Produced
by Aerodynamic Asymmetry
M. Goman A. Khramtsovskyy
De Montfort University, Leicester, UK
Y. Patelz
QinetiQ, Bedford, UK
Abstract
This paper presents modellingand dynamic analysis of aircraft spin, which is typical for modern ma-
neuverable aircraft con gurations having a slender body fuselage, low aspect ratio wings and produced
by asymmetrical aerodynamic loads.
The origin of an aerodynamic asymmetry in the rolling and yawing moments at high incidence ight
is directly connected with the onset of asymmetry in the vortical ow, i.e. due to asymmetry in vortex
breakdown points above the wings or due to asymmetrical shedding of vortices from an aircraft slender
nose. In wind tunnel tests the aerodynamic asymmetry at high angles of attack has been observed for
various aircraft models during many years 1]. However, only recently the signi cance of aerodynamic
asymmetry in aircraft dynamics at high angles of attack has been identi ed in ight tests of the Su-
27 and the X-31 aircraft 2, 3] (see Figs.1). Computational prediction of asymmetrical vortical and
separation ow conditions using Naveir-Stokes equations still encounters many di culties 4], however,
simpli ed modeling approaches reveal the bifurcational nature of ow instability leading to the onset of
aerodynamic asymmetry 5]. All this signi es, that the aerodynamic asymmetry plays important role
and should be included in mathematical modeling and departure/spin dynamics predictions.
Signi cant research has been carried out in the development of adequate mathematical modeling
of high angles of attack aerodynamics in the presence of ow separation and vortex breakdown ?,
6, 7]. Based on this research a simple mathematical model for asymmetric aerodynamic moments is
proposed in the formof di erential equations with account of angle ofattack dependence ofaerodynamic
asymmetry magnitude and the time lag e ects from internal vortical ow dynamics.
The aircraft spin dynamics is analyzed using proposed mathematical model for aerodynamic asym-
metry and application of qualitative and bifurcation analysis methods 10, 11, 12, 13, 14]. The analysis
starts with the simple balance moment equations allowing to identify all possible equilibrium spin
modes for di erent altitudes and control surfaces de ections, to estimate the critical level of aerody-
namic asymmetry leading to onset of equilibrium spin 8, 9] (see Fig.2). These initial estimates are
used later for accurate calculation of equilibrium spin parameters and stability dynamic analysis for all
identi ed spin modes using the 8th-order motion equations. For locally oscillatory unstable spin modes
special analysis is performed for a search of possible steady oscillatory spin modes (Fig.3).
When the aerodynamic asymmetry exceeds some critical level an aircraft can have unrecoverable
at spin modes due to the lack of control authority of traditional aerodynamic control surfaces at high
incidence. The unrecoverable at spin modes with rotation produced by asymmetrical yaw moment
are identical to the deep stall regimes at high angles of attack, which are unrecoverable due to insu -
cient margin of aerodynamic pitch-down control (see Fig.4). Conditions leading to unrecoverable spin
Professor, Faculty of Computing Science and Engineering, e-mail: mgoman@dmu.ac.uk
yVisiting Research Fellow, Faculty of Computing Sciences and Engineering, e-mail: sspchram@online.ru
zPrincipal Scientist, Future Systems Technology Division, e-mail ypatel@qinetiq.com
Copyright c 2003 by British Crown. Published by the American Institute of Aeronautics and Astronautics, Inc.,
with permission.
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2. modes will be analyzed and results demonstrating the e ect of thrust vectoring control and/or anti-spin
parachute will be also presented.
Special attention is given to the pitch-rocking control used for aircraft spin recovery at the presence
of high aerodynamic asymmetry. The principle and algorithms of rocking control are discussed and
illustrated by examples of numerical simulation (see Fig.5). Transition from rocking control to stabi-
lization phase at low angles of attack is speci ed from the analysis of regions of attraction for critical
and normal ight conditions (Fig.7). The computational means developed for spin dynamics analysis
and recovery control design are also discussed (6).
Figure 1: Aerodynamic asymmetry in wind tunnel and ight tests.
References
1] Beyers, M.E. "Interpretation of Experimental High-Alpha Aerodynamics { Implication for Flight
Prediction", Journal of Aircraft, Vol. 32, Number 2, Pages 247-261, 1995.
2] Aerodynamics, stability and controllability of supersonic aircraft. Edited by G.S.Bushgens, "Nau-
ka*Fizmatlit" publ., 1998, Moscow, (Chapter 8, pp.380).
3] Cobleigh, B.R.,Croom,M.A., Tamrat,B.F."ComparisonofX-31 Flight,Wind-Tunnel,andWater-
Tunnel Yawing Moment Asymmetries at High Angles of Attack", Paper HA-AERO-06, High Alpha
Conference IY - Electronic Workshop, NASA Dryden Flight Research Center, July 12-14, 1994,
URL: http://www.dfrf.nasa.gov/Workshop/HighAlphaIV/highalpha.html
4] R.M.Cummings"ComputationalDi cultiesinHigh Angle ofAttackFlowPrediction", Proceedings
of the Third International Conference on "Nonlinear Problems in Aviation & Aerospace", Vol.1,
2001, Florida (Editor: Seenith Sivasundaram).
5] Goman, M.G., Zaharov, S.B., and A.N. Khrabrov "Aerodynamic hysteresis at vortical ow around
a slender body", Reports of Academy of Science (DAN USSR), Vol.282, No.1, 1985.
6] N.Abramov,M.Goman,A.Khrabrovand K.Kolinko"SimpleWingsUnsteady Aerodynamicsat High
Angles of Attack: Experimental and Modeling Results", Paper N 99-4013, AIAA Atmospheric
Flight Mechanics Conference, August 1999, Portland, OR.
7] N.Abramov, M.Goman, D.Greenwell and A.Khrabrov "Two-Step Linear Regression Method for
Identi cation of High Incidence Unsteady Aerodynamic Model", Paper N 2001-4080, AIAA Atmo-
spheric Flight Mechanics Conference, August 2001, Montreal, Canada.
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3. Figure 2: Solutions of approximate spin equations.
Figure 3: Bifurcation diagram: angle of attack steady state solutions for di erent stabilator de ections.
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4. Figure 4: Unrecoverable deep stall and at spin regimes.
Figure 5: Pitch rocking control for spin recovery.
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5. Figure 6: Computational framework for spin dynamics analysis and design of recovery control.
8] Dolzenko, N.N., "Investigation of equilibrium aircraft spin", TsAGI Proceedings No. 8817, 1968
(in russian).
9] Tischler, M.B., andBarlow, J.B., "DeterminationofSpin andRecovery Characteristics of a General
Aviation Design," Journal of Aircraft, Vol.18, No.4, 1981, pp.238-244.
10] Mehra,R.K., "Bifurcation analysis of aircraft high angle of attack ight dynamics", AIAA N 80-
1599, August 1980.
11] Carroll,J.V., and Mehra,R.,K., "Bifurcation Analysis of Nonlinear Aircraft Dynamics," Journal
Guidance, Navigation, and Control, Vol. 5, No. 5, 1982, pp.529-536.
12] Guicheteau, P., "Bifurcation Theory Applied to the Study of Control Losses on Combat Aircraft,"
La Recherche Aerospatiale, Vol. 2, 1982, pp.61-73.
13] M.Goman, G.Zagainov, and A.Khramtsovsky "Application of Bifurcation Methods to Nonlinear
Flight DynamicsProblems,"Progress inAerospace Sciences 33(1977), pp.539-586,Elsevier Science
Ltd.
14] Goman, M.G., and Khramtsovsky, A.V., "KRIT : Scienti c Package for continuation and bifurca-
tion analysis with aircraft dynamics applications," TsAGI, 1993.
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6. 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
0.6
0.8
1
δ
e
=0.0, δ
a
=0.0, δ
r
=0.0
Angle of attack α, rad
pitchrateq,rad/s
Pitch rocking control
trajectory
Region of attraction
of flat spin regime
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5
3
δ
e
=0.0, δ
a
=0.0, δ
r
=0.0
Angle of attack α, rad
yawrater,rad/s
Region of attraction
of flat spin regime
Pitch rocking control
trajectory
Figure 7: Regions of attraction for recon guration of pitch rock recovery control.
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