М.Г.Гоман, А.В.Храмцовский, В.Л.Суханов, В.А.Сыроватский, К.А.Татарников «Система предотвращения попадания / вывода самолёта из штопора», доклад на 3-й российско-китайской научной конференции по аэродинамике и динамике полёта самолёта, Центральный Аэрогидродинамический институт (ЦАГИ), г.Жуковский, 1993 г., 14 стр. M.Goman, A.Khramtsovsky, V.Soukhanov, V.Syrovatsky and K.Tatarnikov "Aircraft Spin Prevention/Recovery Control System", presented at the Third Russian-Chinese Scientific Conference on Aerodynamics and Flight Dynamics of Aircraft, Central Aerohydrodynamic Institute (TsAGI), Zhukovsky, Moscow region, Russia, November 9-12, 1993, 14 pp.

1. Aircraft Spin Prevention/Recovery
Control System
M. Goman, A. Khramtsovsky, V. Soukhanov,
V. Syrovatsky and K. Tatarnikov
Central Aerohydrodynamic Institute
Zhukovsky-3, Moscow region, Russia
Third Russian–Chinese Scientific
Conference on Aerodynamics and Flight
Dynamics of Aircraft
TsAGI, Zhukovsky, Moscow region, Russia
November 9-12, 1993

2. Aircraft Spin Prevention/Recovery Control System
M. Goman A. Khramtsovsky V. Soukhanov
V. Syrovatsky K. Tatarnikov
Abstract
The problem of spin prevention and spin recovery for the high-performance, high-augmented
airplane is formulated. The methods of the flight dynamics mathematical simulation, sta-
bility and bifurcation analysis at high angles of attack are briefly outlined. Good correlation
between the flight tests data and the results of mathematical modeling of the aircraft dy-
namics at stall and spin regimes made it possible to use the flight simulation as the effective
tool for the design of the algorithms of the automatic spin prevention/recovery system. The
efficiency of various control methods for the spin recovery is analyzed. The efficiency of the
resonance rocking technique for the recovery of the aircraft from deep stall and flat spin
regimes was first demonstrated by the theoretical analysis and mathematical modeling and
later confirmed during the flight tests.
Introduction
The problem of safe and controllable flight of the modern airplane at high angle of attack
is closely joined with the problem of critical aircraft flight regimes such as stall and spin.
For modern aircraft spin remains one of the dangerous regimes. That’s why the search
for the means of spin prevention and recovery continues. One of the possible solutions is
the utilization of the special automatic control system for spin prevention/recovery [1].
The analysis of the aircraft flight accidents shows that the majority of rank-and-file
pilots are unable to cope with spin recovery. Very often they even can’t identify the situation
and don’t use the standard methods recommended for recovery from critical flight regimes.
It is impossible to eliminate totally the possibility of the spin entry by developing al-
gorithms for automatic angle-of-attack limitation. The variety in flight conditions and the
dependence of control system algorithms on a large number of flight parameters result in
either extremely complex limitation system, or reduced maneuverability of the aircraft. Ex-
tensive flight experience shows that various control system limiters, intended for keeping an
aircraft within controlled flight envelope, in definite conditions can not prevent departures
from controlled flight.
The problems which lead to difficulties in maintaining stability and control during
maneuvering flight are common to different types of aircraft configuration. An adverse
behavior of aircraft at high angle of attack is related with the so called Nose slice, Loss of
control power, Wing Rock and other dynamic phenomena. To improve aircraft dynamic
characteristics at low angle of attack a stability augmentation system (SAS) is used, but
for high angle of attack conditions more sophisticated control laws are needed Fig. 1.
From our point of view, optimal solution to the problem lies in using relatively simple
DPS (departure prevention system) together with automatic SRS (spin recovery system).
1

3. The SRS algorithms can be considered as ”back-up” algorithms intended for special flight
situations.
Figure 1: Maneuvering limitation factors. Control subsystems.
The development of mathematical model of aerodynamics for high angle of attack con-
ditions, the investigation of the aircraft behavior at stall and spin regimes are necessary
research elements for control system design and finding the control laws for spin preven-
tion/recovery system. In this paper some attention is given to the methods of mathematical
modeling of aerodynamic coefficients using different wind tunnel data and to the methods
of stability and bifurcation analysis at high angles of attack.
The aircraft dynamics simulation excellently complements the qualitative methods of
analysis for examination the different spin recovery techniques. The adequate mathematical
model permit also to train the test pilots skills and to master new methods of aircraft
handling at the simulator before real flights.
Aerodynamic model for the modeling of the stall and
spin regimes.
The aerodynamic model intended for the modeling of the aircraft dynamics at high angle
of attack and stall/spin regimes, is based on the experimental data obtained from the
following wind tunnel tests:
• static wind tunnel tests,
• forced-oscillation tests,
• rotary balance tests.
The development of the rotation during high angle of attack excursions (at spin, for ex-
ample) can influence significantly the flow pattern. As a result, the aerodynamic coefficients
become nonlinear functions of the reduced rate of rotation. That’s why the aerodynamic
coefficients measured in rotary balance tests are considered as basic ”nondisturbed” part
of the aerodynamic model for high angle of attack conditions.
In the rotary balance wind tunnel experiments the total rotation vector Ω usually is
fairly closely aligned with the velocity vector. From these experiments, the following de-
pendencies of the aerodynamic coefficients on α, β, ω = Ωb
2V and on deflections of control
2

4. surfaces δ are received:
Ci = CiRB
α, β, ω, δ
where i ∈ {l, m, n, X, Y, Z}, δ = (δh, δe, δa)T
, and RB subscript stands for ”rotary bal-
anced”.
There exist a number of methods of designing the ”combined” mathematical model
using the results from various experiments [2], the authors used the approach described
below.
During the disturbed motion, the aircraft parameters deviate from their steady-state
values at spin conditions, and the misalignment between the velocity vector and the total
rotation vector appears. It can be assumed that the disturbed values of the aerodynamic
coefficients are proportional to the kinematic values describing the disturbances. For the
spatial motion with the total rotation vector being fairly closely aligned with the flight
path, the projections of the total rotation vector onto the axes of the wind-body coordinate
system can be considered as such kinematic parameters:
pw = (p cos α + r sin α) cos β + q sin β
qw = − (p cos α + r sin α) sin β + q cos β
rw = r cos α − p sin α
(1)
The projection onto the direction of the velocity vector pw defines the rate of conical
rotation. The values of qw and rw define the rates of change of the angles of attack and
sideslip in the disturbed motion
˙α = qw/ cos β + ˙αT
˙β = −rw + ˙βT
where ˙αT , ˙βT are due to the center-of-gravity translational motion.
Assuming that the disturbances of the pure conical motion are small, the following
representation of the aerodynamic coefficients can be used:
Ci = CiRB
α, β, pwb
2V , δ + Ciqw
qwc
2V + Ci ˙α
˙αc
2V + Cirw
rwb
2V + Ci ˙β
˙βb
2V
= CiRB
α, β, pwb
2V , δ + Ciqw
+ Ci ˙α
/ cos β qwc
2V + Cirw
− Ci ˙β
rwb
2V + Ci ˙α
˙αT c
2V + Ci ˙β
˙βT b
2V
(2)
The aerodynamic derivatives from (2) correspond to the conditions of the conical rota-
tion. They can be measured, for example, by means of the oscillatory coning technique,
such as already in use at ONERA–IMFL [2].
In the present investigations, the data obtained from ”traditional” forced oscillations
tests (measured in the absence of the model rotation) were available, the usage of these
data is certainly not quite consistent with the methodology described. The rotary and
unsteady aerodynamic derivatives were calculated as follows (the influence of ˙αT and ˙βT
was neglected):
Ciqw
+ Ci ˙α
Ciq + Ci ˙α F.O.
Cirw
− Ci ˙β
Cir − Ci ˙β
· cos α0
F.O.
cos α0 − Cip + Ci ˙β
· sin α0
F.O.
sin α0
(3)
where the subscript ”F.O.” denotes the data from forced oscillations tests.
3

5. In the situations when the nonlinear term in (2) can be approximated with a linear
function of the angular rate, the representation (2) becomes equivalent to the common
aerodynamic model usually used for low angles of attack. In this case, the results of static
wind tunnel tests can also be incorporated into the mathematical model, especially at low
angle of attack.
The form of the aerodynamic model (2) for stall/spin conditions is quite natural. For
example, the rotary derivatives Ciqw
and Cirw
don’t affect significantly neither the values
of kinematic parameters at the steady-state spin conditions nor their mean values during
the oscillations with moderate amplitude. These derivatives as well as unsteady derivatives
Ci ˙α
and Ci ˙β
directly affect the placement of the eigenvalues of the linearized equations of
motion in the complex plane. Thus they determine the oscillatory stability of the disturbed
motion.
Our experience shows that the usage of the dependencies CiRB
α, β, ω, δ allows to
get realistic values of the spin kinematic parameters during the modeling. To get the
correct time histories and amplitudes of the oscillations, one can make some adjustments
(if necessary) to rotary and unsteady derivatives Ciqw
, Cirw
, Ci ˙α
, Ci ˙β
.
Cm
Cn
full nose-up
full nose-down
αu αs
α
Cn0 (α)
Cncontr
α
Figure 2: Pitching and yawing aerodynamic moments
Typical pitching and yawing aerodynamic characteristics.
One of the important features in the modern aircraft high angle-of-attack aerodynamics are
the insufficient nose-down pitching control power, and the development of large-magnitude
4

6. nonsymmetrical yawing moments Cn0 . The magnitude of Cn0 can exceed the available
lateral control power. (see fig.2).
The flight tests data analysis shows that the value of Cn0 do not correlate with the value
of sideslip angle, it depends primarily on the value of the angle of attack. For example in
the range of 40o
≤ α ≤ 50o
the Cn0 coefficient has one sign, and in the range of α ≥ 50o
it
has the opposite sign. The direction of the aerodynamic nonsymmetrical moment repeats
rather regularly during the same flight and for a number of successive flights, but may vary
during long period of service.
The deficiency in the nose-down pitching moment within a certain range of the angle
of attack causes deep stall regimes. The unsymmetrical yawing moments may result in the
development of the ”unrecoverable” flat spins.
Methodology of nonlinear aircraft dynamics investiga-
tion.
Modern airplane is a highly nonlinear dynamical system. It is clearly seen during spatial
(6 DOF) maneuvers and the flights at high angle of attack.
Traditional methodology of aircraft motion investigation heavily relies on mathematical
simulation of the aircraft dynamics by means of numerical integration of the full set of
nonlinear equations of motion, and on linear stability analysis using frequency–domain and
algebraic methods. It is not able to predict all the nonlinear phenomena exhibited by the
airplane, for example, in stall, spin or in maneuvers with high roll rates.
New methodology based on recent results in mathematics (Bifurcation theory, Qual-
itative analysis of the nonlinear dynamical systems) is an efficient, but delicate tool for
studying aircraft dynamics in these conditions [3]. And mathematical simulation is a good
complement to it.
New methodology implies calculations of the equilibrium flight conditions and oscilla-
tory motions (for example, an aircraft is in equilibrium during spin if the angle of attack,
sideslip and pitch, roll and yaw rates do not oscillate). The influence of the control in-
puts or flight regime parameters on the aircraft equilibrium can be easily calculated. The
data obtained enable the researcher to predict dangerous phenomena such as stall and spin
entries, and to develop a recovery technique.
Krit package was optimized for such calculations [4]. It is especially useful for studying
the steady–state flight regimes (with or without oscillations, stable or unstable) and their
dependence on certain factors. You may even use a set of mathematical models of the
vehicle during a dialog with the package.
A unique feature of the Krit package is an effective set of procedures for an exact cal-
culation and analysis of the steady–state oscillatory flight regimes using Poincare mapping
technique.
Krit scientific package can be applied to the following problems in aircraft flight dy-
namics:
• Calculation of the equilibrium conditions for the spatial (6 DOF) maneuvers and
high angle of attack regimes (stall, spin, regimes with rapid rotation). Local stability
analysis of these regimes.
• Calculation of the oscillatory flight regimes at high angles of attack ( wing rock,
oscillatory spin). Local stability analysis of these regimes.
• Numerical simulation of the arbitrary spatial aircraft motion.
5

7. • Computation of the critical values of the control inputs and the flight regime param-
eters when an abrupt loss of stability and transfer to the dangerous regimes occur.
• Calculation of the stability regions or stability to finite perturbations.
• Determining control for spin recovery.
Automatic system for the aircraft spin recovery.
The control system of modern maneuverable aircraft may comprise the following subsys-
tems:
• stability and controllability augmentation system for operational flight conditions
(SAS);
• angle-of-attack and g-load limitation system;
• departure and spin prevention system (DPS);
• spin recovery system (SRS);
In this section some aspects of the algorithms for spin recovery are discussed.
The results of these flight tests are used for the improvement of the aircraft aerody-
namic model and for determining of the recovery technique. After that the corresponding
mathematical model for the simulation and the recovery algorithms are developed.
During the investigations on ground-based simulators the parameters of SRS are ad-
justed, and the interaction between SRS and main control system as well as the SRS–pilot
interaction are studied. At the same time pilots assess the serviceability and convenience
of SRS.
”Positional” recovery method.
The experience of flight tests and mathematical simulation revealed the most effective ”po-
sitional” (or ”static”) recovery method for different types of aircraft. It means for example
that the control stick is set to the neutral position (in longitudinal control) hence the ele-
vator deflection is near-zero according to control system algorithms. In lateral channel, the
stick is deflected ”pro spin” (towards the rolling) while pedals are deflected against yawing.
When aircraft rotation is stopped and angle of attack diminishes to operational values, the
stick is pushed forward in order to recover from spin to diving at low angle of attack. SRS
system can easily realize such a technique automatically.
SRS system algorithm incorporates the following modules (see fig.3):
• spin entry identification module;
• the module implementing the ”positional” recovery algorithm;
• the module that switches the signals going to control surfaces’ actuators;
• spin recovery identification module.
The ”positional” recovery algorithm can be realized using yaw rate signal r. The full
aileron, rudder and differential elevator deflection is used taking into account the sign of
the yaw rate r. The elevator is set to ϕmin Cm 0o
÷ 2o
. After stopping the rotation and
6

8. Spin recovery
identification
Spin entry
identification
”positional”
recovery
algorithm
Control
algorithms for
normal flight
Control
surfaces’
actuators
-
-
-
-α
β
nz
Q
r r r r
b b b b
b b b b
-r
-
-
α
r
-
-
-α
r
Q
-
-key
6
δi
δi
Figure 3: Arrangement of spin recovery system
diminishing angle-of-attack from ”spin level” values α 60o
÷ 80o
to ”stall level” values
α 30o
÷ 40o
, the elevator for a short time t 0.5 ÷ 1 s is deflected to a full nose-down
position ϕmax = 15o
. After that spin recovery is checked, and the control system is switched
from SRS to normal flight algorithms.
if |r| < r
if α ≤ 30o
aeroelastic
vibrations
filter
kr
ka
kde
-
-
?b
b
bb
b
-
61
r1r2
aileron
rudder
differential
elevator
α
r
ϕmin Cm
ϕmax
elevator
Figure 4: Implementation of recovery algorithm
Spin entry identification module is rather complex for implementation. The problem
is due to reliability requirements. Turning on SRS by mistake will certainly result in an
accident, especially because SRS algorithm uses full deflections of the control surfaces. It
is possible to use an approach when the spin recovery is performed only if the pilot has
toggled special switch and the spin entry identification module generates the ”aircraft in
spin” signal.
Pitch rocking method.
In the absence of the sufficient nose-down pitching control power and low level of the control
power in roll and yaw at high angle of attack additional problem arises. In these cases the
deep stall and flat spin regimes can be hardly recoverable. In both cases, the ”positional”
deflections of the control surfaces may be insufficient for the aircraft recovery from critical
7

9. regimes, since these regimes keep to exist even when the full controls against the regime
are set.
The resonance pitch rocking technique can be used to recover from these regimes (see
also [5]). For example, the elevator is deflected according to the formula
ϕ = ϕ0 + Aϕ · sign q (4)
The rate saturation of elevator deflection also
should be taken into account during incorporation of the law (4) into real control system.
Since the change of sign of the pitch rate q must correspond to the elevator position in the
middle between extreme deflections of the elevator during rocking, the signal for elevator
reversal should be formed with some time advance.
The level of oscillations is an important qualitative characteristic of the spin regime,
the selection of the recovery technique depends on it. The higher the amplitude of the
oscillations, the easier the recovery from the spin. This fact is supported by the flight tests
data as well as by the mathematical simulation results. Both the intensity and the level
of oscillations depend, in particular, on the form of the function Cn0 (α), Cn0 (α) is the
aerodynamic nonsymmetrical moment.
The magnitude of the aerodynamic nonsymmetrical moment vary from the airplane to
airplane even for the same type of the aircraft. Moreover, it varies for the same plane
during its operating period. No wonder that one can encounter different types of spins.
Correspondingly, the recovery technique and the recovery time may vary. But at the same
time, the above-mentioned qualitative features remain.
Mathematical simulation proved that resonance rocking by means of longitudinal con-
trols is the efficient method of spin recovery. Since rocking algorithms are ”universal” and
independent of any aircraft aerodynamic coefficients, resonance rocking is the most effi-
cient method of flat spin recovery. If high-level nonsymmetrical aerodynamic moments are
developed at high angle of attack, aircraft can’t be recovered from spin using standard ”po-
sitional” methods. In that case the ”static” deflection of longitudinal and lateral controls
doesn’t affect significantly aircraft motion in spin. When applying the resonance rocking,
the aircraft is recovered from flat spin no more than in 8 sec. Thus if the ”positional”
method fails then rocking algorithm is used for spin recovery.
The rocking algorithm can be switched on with some time delay after switching on
”positional” algorithm provided spin recovery identification module doesn’t signals the
recovery.
When the resonance rocking is used for recovery from deep stall or flat spin, the most
complex problem is to determine the moment when the rocking should be switched off.
The elevator deflection according to the algorithm (4) in some conditions doesn’t result
in the transition to low angles of attack, and high-amplitude ±10o
÷ 15o
angle-of-attack
periodic oscillations take place instead. That’s why it is necessary to predict the possibility
of recovery to low angles of attack on-board the airplane. When corresponding conditions
are satisfied, the rocking algorithm is switched off and the elevator is placed into ”maximum
nose-done moment” position. To assess the possibility of the recovery, the angle-of-attack,
angle-of-attack rate ˙α and pitch rate q should be known.
Some speculations and simulation results.
The example of the mathematical modeling of the aircraft dynamics at the flat spin is
shown on fig.5. The deflection of the lateral controls cannot stop the rotation, the rotation
rate remains high (r 1 rad/sec) until t = 65 sec. After that asymmetric thrust of the
engines is used to recover, the level of the yawing moment due to asymmetric thrust is
8

10. rather high because of the large thrust force arm along side axis. The resonance rocking
technique may be also used for recovery from the flat spin.
Figure 5: Simulation of spin recovery
q
S
αu αs α
δ (t)
Figure 6: The domain of asymptotic stability S of the deep stall regime αs
To illustrate the efficiency of the resonance rocking recovery technique, consider short-
period motion of the statically unstable aircraft. At the full nose-down elevator deflection
(see dashed line on fig.2), there exists stable high angle-of-attack trim at αs. The domain
of stability of that deep stall regime is formed by the separating trajectories approaching
unstable singular point in the phase plane (αu, q = 0). The aircraft can be recovered from
deep stall regime only by applying such a control δ (t) that moves the aircraft out of the
region of the asymptotic stability S of the deep stall regime at αs (see fig.6).
The resonance rocking algorithm can be used to select the appropriate deflections of
the control surfaces δ (t). The resonance rocking results to the increase in the amplitude of
the oscillations due to the accumulation of the energy, and can lead to the leaving of the
stability region S.
9

11. Figure 7: The diagram illustrating rocking method
Figure 8: Spin recovery using resonance rocking
For the aircraft spatial motion at flat spin, the idea of rocking can be illustrated using
the ”potential” function with two minimums as an example (see fig.7). It is assumed that
the minimum X2 corresponds to the stable critical regime (spin), and the minimum X1
corresponds to the normal low angle-of-attack flight regime.
The efficiency of the resonance rocking technique as a complementary algorithm to
the positional recovery technique is shown on fig.9. Spin recovery time can be drastically
reduced due to resonance rocking, especially for the aft c.g. position and large values of
the non-symmetrical yawing moment.
The results of the mathematical modeling of the spin recovery using rocking algorithm
are shown on fig.8. First the aircraft enters the flat spin. Then the pilot attempts to
recover using positional deflections of the lateral controls, all these attempts fail. After
that (t 75 sec) the rocking is initiated. The amplitudes of the angle-of-attack and roll
rate oscillations rise, yaw rate decreases and later the angle of attack also decreases.
The results of the mathematical modeling and the results of the experiments at flight
10

12. Figure 9: Efficiency of the resonance rocking technique. Time of the spin recovery.
11

13. simulators are in a good agreement with high angle-of-attack flight tests data provided the
the nonsymmetrical yawing moments are included into the model of the aircraft aerody-
namics.
stall and spin
entry
steady-state
spin
automatic
recovery
from spin
recovery
from diving
H, m
Figure 10: Spin recovery simulation
The example of flight path and the orientation of the aircraft during the modeled spin
entry/spin recovery is shown in fig.10.
12

14. Conclusions
Spin recovery technique for modern aircraft is too complicated for rank-and-file pilots. Only
the best aces having many hours of the flight experience are able to recover from spin.
This problem can be solved very efficiently by means of the special spin prevention/reco-
very control system. The algorithms of such system take into account characteristic features
of the airplane under consideration and use different recovery techniques for different flight
situations.
The control system for the spin recovery has to use ailerons, rudder, elevator deflections
etc. in more optimal manner for high angle of attack conditions. In particular, the method
of pitch rocking is very efficient for recovery from deep stall and steady flat spin regimes.
Extensive simulation of aircraft spin recovery is necessary to select suitable values of
the parameters of prevention/recovery system. The success of the whole project strongly
depend on the development of an adequate mathematical model of aerodynamics and com-
pleteness of the nonlinear dynamics analysis for aircraft spin conditions.
References
[1] Akhrameev V.I., Goman M.G., Khramtsovsky A.V. et al., “Automatic Spin Recovery
System for Modern Fighter”, Technika Vozdushnogo Flota (the journal), no.3, 1991, (in
Russian).
[2] “Rotary-Balance Testing for Aircraft Dynamics”, AGARD-AR-265 Advisory Report,
Advisory Group for Aerospace Research and Development, NATO, published Dec. 1990.
[3] Zagaynov G., Goman M. “Bifurcation Analysis of Critical Flight Regimes”, – Proceed-
ings ICAS–84-4.2.1, pp.217-223.
[4] Goman M., Khramtsovsky A. “KRIT Scientific Package. User Guide.”, TsAGI, 1992.
[5] Medina M., Shahaf M. “Post Stall Characteristics of Highly Augmented Fighter Air-
craft”, Proceedings ICAS–90-5.10.2, pp. 1976-1983.
13