Experimental and simulation testing of flight spin stability for small caliber cannon projectile

10 Pages·0.287 MB·English

by  Milinović Momčilo, Jerković Damir, Jeremić Olivera, Kovač Mitar.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)No, StartPage-EndPage Paper received: 2011-12-20
DOI:10.5545/sv-jme.2011.277 Paper accepted: 2012-04-03
Experimental and Simulation Testing of Flight Spin Stability
for Small Caliber Cannon Projectile

Momčilo Milinović1,* ‒ Damir Jerković2 ‒ Olivera Jeremić1 – Mitar Kovač2
1 Faculty of Mechanical Engineering, University of Belgrade, Serbia
2 University of Defense, Military academy, Serbia

The basic aim of this paper is to consider correlations of stability flight criteria, derived as the
relations of aerodynamic coefficients and derivatives, on the model of small caliber cannon spin
stabilized projectile. Model of stability criteria calculations are performed by experimentally testing of
aerodynamic data in the wind tunnel, and composed with the semi-empirical data, both applied on the
flight trajectory stability simulation test. Authors’ wind tunnel tests and calculated values of aerodynamic
coefficients, as function of Mach numbers of projectile model are presented in the simulation flight
trajectories stability criteria. The comparative analysis of experimental and calculated aerodynamic
coefficients of projectile model is done, refers to the stability flight criteria. Calculation of projectile
aerodynamic Magnus moment derivatives, with other aerodynamic representatives, is used as the critical
stability factors testing data vs. flight Mach numbers. Influences of this derivative absence and presence
on the model sequence of the flight trajectory are presented for the estimation of angles of attack damping
and stability factors. Simulation tests are presented for the supersonic and subsonic integral flight
velocities and spin damping data. Research is realized due to the considerations of further projectiles
correction possibilities on trajectory, and other new applications, vs. existing of unreliable lateral
moments.
©2012 Journal of Mechanical Engineering. All rights reserved.
Keywords: aerodynamic coefficients spin stabilized small caliber cannon projectile, gyroscopic
stability factor, dynamic stability factor, damping stability coefficients

0 NOMENCLATURE α, angle of attack (pitch)
β, angle of sideslip (yaw)
α, total yaw angle, approx. (α2+β2)1/2
C , pitching moment coefficient, M/QSd. t
M v ξ, complex angle of attack, α+iβ
C , derivative of pitching moment coefficient, ∂C /∂α.
CMα, derivative of pitch damping moment coefficieMnt due to q*, ρ, atmospheric density
Ma V, velocity vector of projectile
∂C /∂q*.
M u, v, w, components of velocity along x, y, z axes
C , derivative of pitch damping moment coefficient due to
Mα H, P, T, M, G, Murphy's coefficients
α ,∂C ∂α.
M E = (ρSd)/(2m), reduction mass expression
CL, lift (normal) force coefficient,‒Fz/QS *, denotes reduction of coefficients and derivatives C*=C E
C , derivative of lift force coefficient, ∂C/∂α ij ij
Lα L
C , yawing moment coefficient, M/QSd
N z
C , derivative of Magnus moment coefficient, ∂2C /∂p*∂α 1 INTRODUCTION
Mpα N
CD, drag (axial) force coefficient, Fx/QS
CD0, zero angle drag coefficient, (CD)α=0 Modern ammunition design, last twenty
d, reference diameter (caliber)
years, extended precision technology applications
I, axial moment of inertia
x
I, transverse moment of inertia of guidance and control on the lower calibers of
y
r , relative axial radius of gyration, reversed to the caliber, tactical ammunition. Analyses to be considered
x
(I/md2)1/2
x for guidance redesigning, is especially
r , relative transverse radius of gyration reversed to the
cayliber, (I/md2)1/2 challenging for the anti-aircraft (AA) cannon
y
F, F, F, forces along x, y, z axes ammunition of smaller dimensions, because of
x y z
Mx, My, Mz, moments about x, y, z axes specific properties of projectiles flight, which
m, mass of projectile
have constraining possibilities of guidance
p, spin rate
p*, reduced spin rate, pd/V technologies applications, [1] to [5]. Unguided
Q, dynamic pressure, ρV2/2 AA projectile is, primarily, used for air targets,
q, pitch rate
shooting with ballistic trajectories, but new
q*, reduced pitch rate, qd/V
S, reference area,πd2/4 considerations may suppose, also, its applications
* Corr. Author's Address: Faculty of mechanical engineering, Kraljice Marije 16, Belgrade, Serbia,
1
[e-mail]
Strojniški vestnik - Journal of Mechanical Engineering Volume(Year)No, StartPage-EndPage
for the ground targets engaged from air and ballistic trajectory. Longitudinal axis very high
ground platforms in, so called, close support spin and lateral disturbance low spin, provides
operations. gyro moment to stabilize projectile pitch.
Ballistic trajectory of AA gun projectile Composed spherical oscillations of body axes and
have significant changes of supersonic transonic direction of velocity vector, is question of
and subsonic velocities during flight, from the stabilization [6] and [7]. These lateral oscillations,
very high initial to the much lower terminal as the result, decrease perturbed amplitudes of
values in the target impact point. Stable free total angle of attack, if spin stabilization is
ballistic flight of projectiles and stability criteria, successful, or increase, if projectile is not realized
determines attitudes of projectile axes toward to enough initial rpm by spin, to form gyro-moment
trajectory, [6] to [8]. It depends of aerodynamic for damping. Complex variable of total angle of
shape, sensitivities on the drag and lift forces, attack ξ, and its lateral angular motion due to
aerodynamic moments their derivatives and spin projectile body, can be described by linearized
rate stabilization efficiency vs. flight Mach differential equation, derived by dimensionless
numbers, but also of less discovered lateral distance, instead of time, as the main argument
Magnus moment and other artificial designed [6], in the form:
moments coupled with them, which changes on ξ′′+(H−iP)ξ′−(M +iPT)ξ=−iPG,
(1)
the flight trajectory.
The importance of experimental where H, P, T, M and G represents so called
aerodynamically accurate estimations coupled Murphy's coefficient, [6] developed from the
with numerical stability criteria simulations is aerodynamic and dynamic solutions of the
required because the spin stabilized symmetric revolution body with gyroscopic low and high
AA cannon type projectile, exposes sensitive spin coupled motion. Since Eq. (1) is complex but
effects on the projectile stability which could linear, its solution is given as:
influencing conclusions about its novel ξ=(K eiΦ10)e(λ1+iΦ1′)s+(K eiΦ20)e(λ2+iΦ2′)s+ξ .
10 20 g (2)
applications and redesigning in the modernization
considering processes. Each values of the angular spin angles as
Comparative analysis of calculated and the frequencies Φ ′, and damping coefficients λ
j j
experimental parameters is well known,
in homogeneous solution, will vary with the
proceeding for preliminary estimation of all kind
relative magnitudes of the H, P, T and M which
of flight bodies, including flight vehicles with
could be expressed as the basic function derived
typical gyro – aerodynamics correlation loads, as
from the projectile designed form its
in the [9] and [10] as rotary wings flight objects.
aerodynamic, flight dynamic, inertial and all over
Spin gyro – aerodynamics correlation loads,
flight performances. In aim to separate conditions
which strongly influenced on stability of flight
of damping abilities of complex angle of attack,
projectiles, are referencing on the second class of
expressed by λ, and gyroscopic frequencies effect
flight bodies, known as the projectiles. j
In this paper, statically wind tunnel tested Φ ′, conditions of projectiles dynamic behavior
j
projectile aerodynamics, and numerical predicted, of inertial axes, enough precise approximation
varied, aerodynamic coefficients and derivatives, have done, [6], [7] and [14], if assumption
is coupled, due to the stability criteria of the between these representative values have taken
projectile spin effect modeling vs. flight Mach
as, Φ′Φ ′ >>λλ.
numbers. Simulated data are used from the AA 1 2 1 2
gun model trajectory designed in, [11] to [13]. This provides using of real solution to be
applied and considered in the form:
2 SPIN STABILIZED CRITERIA AND DATA Φ ′ = 1P± P2−4M, j=1,2,
REQUIREMENTS j 2  (3)

and damping coefficient separated from joint
The key property of spin stabilized
solution as:
projectiles flight could be determined by the
quality of its space spherical motion around the
projectile body gravity center, during flight on the

2 Milinović, M. - Jerković, D. - Jeremić, O. - Kovač, M.
Strojniški vestnik - Journal of Mechanical Engineering Volume(Year)No, StartPage-EndPage
1 P(2T−H) P2(S −1)2
λ =− H , j=1,2.  d <1,
j 2 P2−4M  (4)  P2−4M  (14)
Real values of both λj and Φj′, Eqs. (3) and (4) (5) gyrTohsciso,p Eicq sc.o (n1d3i)t ioannds S(14 >) c1o,u pfilnedal lwy,i thg iEveqs.
g
determines gyroscopic stability criterion in the stability expression inequality as:
form:
1
<S (2−S ).
1 = 4M . Sg d d (15)
S P2
g (5) Eq. (15) describe general criteria of
where, S > 1 as the obvious condition, from the dynamic stability for any axis-symmetric
g
Eq. (5), for the real roots in Eq. (3). Using projectile spin or fin equipped. According to [6]
aerodynamic coefficient [6] and [7] these to [8], the stability criteria Eqs. (6) and (12) are
expressions is determined by: developed in relation to aerodynamic coefficients
I2p2 and derivatives coupled by inertial and dynamic
S = x , properties of the body motion. Eqs. (7), (8), (10)
g 2ρI SdV2C
y Mα (6) and (11) appears as the conditionally for the
aerodynamic behavior of projectile's forces and
where,
moments, as the loadings, expressed by the
P= Ix ⋅ pd , Murphy's coefficients, in the Eq. (1) vs. flight
I V Mach numbers, angle of attack, and so called
y (7)
derivatives, in the changes during flight, [6]. Spin
M =CM*αry−2. (8) stabilized projectiles during the real flight, change
damping coefficients Eq. (4) of characteristic Eq.
The value of S is well known as the
g
(2), λ and λ , and also factors of stability, S ,
gyroscopic stability factor. Coupled requirement 1 2 g
given by Eqs. (5) and (6), and S , given in Eqs.
for stability is that velocity vector angle of attack d
(9) and (12), which is further derived. Calculated
has to be damped. This is satisfied by the
data are used in changes of stability criteria
limξ→0, which requires necessity that λ and
s→∞ 1 estimations, at the expected muzzle distances
λ2 are both negative λj < 0, j = 1, 2. This second after firing from the cannon barrel, [13].
condition evolves to the, so called dynamic For AA cannon projectile of small caliber
criterion of stability Sd as referencing value in this spin stabilized behavior vs. flight Mach
Eq. (4), in the form: number, will be considered further as the result of
2T experimental testing of measured aerodynamic
S = ,
d H (9) coefficients and appropriate semi empirical and
theoretical data in the stability criteria Eqs. (6)
with values,
and (12). The aim is, to discover influence of the
T =C* +C* r−2,
Lα Mpα x (10) longitudinal position of lateral aerodynamic
Magnus force over derivative of Magnus moment
H =CL*α−CD* −(CM*q +CM*α)ry−2, (11) coefficient CMpα, on the spin stabilizing factors,
which changes its values vs. flight Mach number
where using aerodynamic properties [1],
expression is: from high supersonic to the high subsonic values.
Considerations have done using condition
S = 2(CLα+rx−2CMpα) . in Eqs. (6) and (12), by the complex simulation in
d C −C −r−2(C +C ) redesigned basic software showed in the, [8], [11]
Lα D y Mq Mα (12)
and [13].
Condition that damping coefficients λ
j
have to be negative, is respectively to the
3 BASE EXPERIMENTAL EQUIPMENT AND
following inequalities:
TESTING MODEL SET UP
H > 0, (13)
and The base experimental equipment used for
aerodynamic simulation was the three-sonic wind

Experimental and Simulation Testing of Flight Spin Stability for Small Caliber Cannon Projectile 3
Strojniški vestnik - Journal of Mechanical Engineering Volume(Year)No, StartPage-EndPage
tunnel test facility T-38, [15]. Tunnel is a blow Aerodynamic forces and moments of the model
down pressurized type, with a 1.5×1.5 m square were measured by ABLE 1.00 MKXXIIIA
test section, aimed for subsonic and supersonic internal six-component strain gauge balance, [13]
tests, [15]. The tunnel was fully equipped by and [15]. Nominal load range of the balance was
appropriate equipment to simulate flight flow 2800 N for normal, 620 N for side forces, 134 N
conditions. for axial force, 145 Nm for pitching, 26 Nm for
Mach number can be set and regulated to yawing moment and 17 Nm, for static spin
within 0.5% of the required value. Total pressure damping moment; the accuracy was
in the test is within 1.1 bars to 15 bars regulated approximately 0.25% F.S. for each component.
to 0.3% errors of real flight conditions. Run times Instrumentation and data recording, was
are in the range 6 to 60 s, depending on Mach performed after each run, using the standard T38-
number and total pressure. The facility supports, APS software [15], in several stages, i.e.: Data
step-by-step model movement and continuous acquisition system interfacing and signals
movement of model (“sweep mode”) during normalization; Determination of flow parameters
measurements. in the test section of the wind tunnel;
Simulation and experimentally tested Determination of model position (orientation)
model of projectile in the tunnel is shown on the relative to test section and airflow. Determination
Fig. 1, [13]. Characteristic values of mass and of non-dimensional aerodynamic coefficients of
dimensions, approximately, corresponds to the forces and moments for each stage has been
AA cannon 40 mm HE unguided projectile, Table performed by appropriate tunnel tests, different
1. Model is supported in the test section by a tail software modules, [17].
sting mounted on a pitch simulation mechanism
by which desired aerodynamic angle can be Table 2. Test conditions [13]
achieved. Parameter Mark, unit Value
about 5,0 cal. static pressure p [105 Pa] 0.2 to 2.2
s
stagnation pressure p [105 Pa] 2.3 to 6*
0
CP CG atm. temperature T [K] ≈ 280
atm
Mach number Ma 0.2 to 3
Re number Re [106] 0.5 to 2
CP
xCGabout 3,3 cal. angle of attack (pitch) α [ ] ‒10 to 10
Fig. 1. Model of spin stabilized projectile * for all Mach numbers was 2.3·105 Pa, since for Ma = 2.5,
p =4 ·105 Pa and Ma = 3, p⁰ = 6 ·105 Pa.
0 0

Table 1. Model of projectile [13]
4 EXPERIMENTAL RESULTS AND SPIN
Parameter Mark, unit Value
STABILIZED MODELING
Reference diameter (cal) d [mm] 40

Total length l [cal.] ~ 5
4.1 Aerodynamic Coefficients and Derivatives
Nose length l [cal.] ~ 2.5
1
Ogive radius R [cal.] ~ 20
o The characteristic functions of
Boat tail length l [cal.] ~ 0.5
3
aerodynamic coefficients in relation to the flight
Center of mass x [cal.] ~ 3.3
CG
Mach numbers and angles of attack α, measured
Mass of projectile m [kg] ~1.0
Axial inertia moment I [kg m2] ~2.1∙10-4 in the author's testing, [13] in wind tunnel, is
x
Transversal inertia presented on the Figs. 2 to 5, and Fig. 6
I [kg m2] ~2.3∙10-3
moment y represents additional data supposed from [14].
The influenced aerodynamic coefficients tested
Tests on the model were performed in the on the projectile model, are, aerodynamic
Mach number range from 0.2 to 3.0 (14 different coefficient of drag force, Fig. 2, derivative of lift
values of Mach number). Simulated total angles force coefficient presented on the Fig. 3,
of attack α, redefined to the angle of attack in derivative of pitching moment coefficient given
t
vertical plane, α, (pitch angle, as good in the Fig. 4, and all vs. flight Mach number.
approximation to the total yaw angle, pp. 33, [6]), Flight Mach numbers were corresponding to the
were in the interval, –10° to +10°, [12] and [13]. projectile flight velocities on the modeling
Test conditions were given in Table 2. trajectories. Aerodynamic prediction or

4 Milinović, M. - Jerković, D. - Jeremić, O. - Kovač, M.
Strojniški vestnik - Journal of Mechanical Engineering Volume(Year)No, StartPage-EndPage
calculations of coefficients and derivatives are 5 exp.
determined with two semi-empirical methods: ADK1
4
ADK0 for zero angle drag coefficient and ADK1
for others, [13]. Research was developed
3
according to [11] and [16] to [18]. Data of these CαL
predictions for appropriate aerodynamic 2
coefficients are also presented on the same
figures and, compared, with mentioned 1
experimental values. Aerodynamic coefficients
vs. side slip component of total yaw angle β, was 00 0.5 1 1M.5a 2 2.5 3
not tested experimentally and further Fig. 3. Predicted values (ADK1) and
considerations took these effects in integral yaw experimental values (exp.) of derivative of lift
angle, by semi-empirical predictions denoted as force coefficient
ADK1 in mentioned references. Measuring of so 8 exp.
called dynamic derivatives of pitch damp ADK1
coefficient in wind tunnel facilities require 6
complex and expensive testing equipment, and
improvement test model design, which were not CαM4
used in these experiments. Experiments of pitch
derivatives, vs. flight Mach numbers is
2
approximately determined in the tunnel tests
simulations using test model pitch motion, with
00 0.5 1 1.5 2 2.5 3
threshold ability of angular rate, in sweep-mode, Ma
as was 2 degrees per second, [12] and [13]. Fig. 4. Predicted values (ADK1) and experimental
Values of derivatives of aerodynamic coefficient values (exp.) of derivative of pitching moment
C +C , realized in these experiments are coefficient
Mq Mα
presented on the Fig. 5, by dot-points curve -12
exp.sim.
realized in the singular flight test runs, vs. 14 -10 ADK1
values of simulated flight Mach numbers.
Comparison of these values with data calculated Mq -8
C
by ADK1 prediction, is, also, presented on the + .α
same figure. CM -6

-4
0.5
1.05
-20 0.5 1 1.5 2 2.5 3
0.4 Ma
Fig. 5. Predicted values (ADK1) and simulated
0.3
D experimental values (exp.sim.) of dynamic
C

0.2 derivative of pitch damping moment
exp.α=0o
exp. α=+10o
0.1 eAxDpK. α0= α-=100oo 1.5 ccaallcc..udnetd.et.
00 0.5 1 1M.5a 2 2.5 3 ccaallcc..duentd.2et.2
Fig. 2. Predicted values (ADK0) and 1
experimental values (exp.) of drag coefficients α
CMp
0.5
00. 5 1 1.5 2 2.5 3
Ma
Fig. 6. Predicted values (ADK1) of derivative of
Magnus moment coefficient [14]

Experimental and Simulation Testing of Flight Spin Stability for Small Caliber Cannon Projectile 5
Strojniški vestnik - Journal of Mechanical Engineering Volume(Year)No, StartPage-EndPage
The derivative of Magnus moment • absolute values of total angle of attack |α|
t
coefficient, C , which was not able to simulate vs. time, Fig. 7, which corresponds to the
Mpα
by the wind tunnel, was estimated by calculations solution of |ξ| in Eq. (2), with zero initial ξ ,
g
from the approximated model ADK1, [13] • damping behavior λ , of high and law spin
1,2
according to developed estimations in [6], [7] and of complex |ξ| module, vs. stability factors
[14], Fig. 6. Variations are accepted based on data relation Figs. 8a and 8b, all vs. flight Mach
in, [6], [7], [11] and [14]. It was the base number,
challenge in estimation because Magnus force • gyroscopic stability factor S and criteria
g
effects influenced on the stability similarly as the relation, Fig. 9,
any other lateral force and is composed of flight • spin angular velocity damping p, Fig. 10,
Mach number effect and spin peripheral velocity • dynamic stability factor S and criteria ,
d
designed in the stream flow. This aerodynamic
Figs. 11 and 12,
loading coefficient based on the relative small
• total stability criteria Fig. 13.
values of real Magnus forces could make

undetermined problems to the stability of
Two groups of aerodynamic data in flight
projectiles if force lateral position along
projectile stability modeling, are used, calculated
longitudinal axes is not well known, or vary vs.
data, (ADK1), denoted on the Figs. 8 to 13, as the
flight Mach numbers changes. Flight Mach
(calc.) and experimental aerodynamic data used
numbers changes and other model trajectory data
from Figs. 2 to 6, composed in the matrix form
have taken from the motion of projectile on
adapted for the software, and denoted as the
simulated trajectory six degrees of freedom
(exp.) roots simulations. Experimental rooted
software (6DOF) [6], [8], [11] and [13] by flight
data, of α, corresponded to the tunnel measured
t
conditions given in the Table 3, and using ADK0,
values vs. angles of attack α.
ADK1 and presented experimental tests data. The
2.5 calc.
estimated of main derivatives were assumed as
exp.
the challenge for sensitivity tests of so called 2
stability vs. flight Mach number, represented
1.5
v elocities on the any type of trajectory. oα]| | [t 1
Table 3. Flight simulation condition [13]
Parameter Mark, unit Value 0.5
pressure p [105 Pa] 1.013
temperature aTa [K] 288.13 00 0.05 0.1 0.15 t0 [.s2] 0.25 0.3 0.35 0.4
muzzle velocity V [m/s] 985
Fig. 7. Absolute simulated angle of attack on the
x component of muzzle
p [s-1] 6300 initial part of trajectory
angular velocity – spin
Complex yaw simulations taken from
y component of muzzle
q [s-1] 1.0 **
angular velocity calculated data and with total yaw angle αt,
z component of muzzle composed from vertical (pitch) angle of attack α
r [s-1] 7.7 **
angular velocity are simulated to prove damping effect of velocity
Table range angle direction to the projectile body, was preliminary
θ [ ] 5 to 20
(gun elevation) 0 designed by simulation without derivative of
** according to the research of the initial fire disturbing
⁰ Magnus moment coefficient, which means
conditions, [11] and [13]
Magnus force point in the center of mass.

Representative damping quality should be
4.2 Spin Stability Parameters Modeling
exposed on the very beginning of flight within

less than of half second, Fig. 7. These influences
Qualitative evaluation of projectile
are caused by Murphy’s coefficient H were
stability is determined through analysis of
dominant aerodynamic derivatives calculated
simulated data, used by software 6DOF, [11] and
estimations and experimental, shown on the Fig.
[13], expressed in next main representatives:
5, as the summary dynamic derivatives of
coefficient C +C , in the, both, supersonic
Mq Mα

6 Milinović, M. - Jerković, D. - Jeremić, O. - Kovač, M.
Strojniški vestnik - Journal of Mechanical Engineering Volume(Year)No, StartPage-EndPage
and subsonic flight Mach numbers, expressed x 10-4
0.5
deviations of more than 30 percent for calculated
nts 0
iannfdlu enecxipnegr iomne nEtqa.l (1d1a)t,a i.n sTimhiusl atcioanu sdeos nes utrsoinngg oefficie-0.5
sintaatpicp rtoupnrniaetle test ddatear,i vwathiviceh was mpeearfsourrmemede nbtsy. ability c-1-.51 λλ21 ((ccaallcc))
Differences of experimental and calculated data ng st -2 λ1 (exp)
pi λ (exp)
from the initial flight Mach numbers of about 3 to m 2
da-2.5
1.5, are caused in the derivative of pitch damp
moment coefficient CMα, Fig. 4, which strongly -03. 5 1 1.5 Ma 2 2.5 3
influenced on Sg estimations by calculated and -0.5x 10-4
experimental data, Fig. 9. This was significantly
saMeAtnxapapdbpc oirhlsoei etxvnydpau lecmf oruisibrrm evstreheh sneoo twffah al1ni cg. t5ohro on rvio snat thilsatue inae dFmls .if acglTkri.i ghet9hei ,srt c wiiaMrsho, aiesonscrf eih cn c obgnaro ulrctemihunl alb gateyittorehrsodne. mping stability coefficients-1-.51 λλλλ2121 ((((ceecaaxxllppcc)))) ((((CCCCMMMMppppαααα////2222))))
to the values of Fig. 4. da
Other related influences on differences of
the angle, as the Magnus force and their lateral -02. 5 1 1.5 Ma 2 2.5 3
Fig. 8. Damping coefficients vs. Mach number; a)
position along projectile longitudinal axis,
for full value of derivative of Magnus moment
effected on the side-slip component β in the total
coefficient, b) for half value of derivative of
yaw angle α was not considered but was
t
Magnus moment coefficient
performed through influencing estimations in the
stability factors and damping performances in the 7 S (calc)
g
gyro stabilization. The angle damping behavior or6 Sg (exp)
vs. flight Mach numbers, Fig. 7 correlated with act
measurement in flight tunnel tests and calculated bility f5
cindnoea getatfah ftieicv wieFe initgtha .n Cd8M dbpe,oα ,rn eievFx aipgtpri.evo s6essi ,e tiisvno effnl uevegaMnalctuiaevegses n auarosenf dp drm8eaasmo,em pnoietnenndget gyroscopic sta432
coefficients Eq. (4). This data have shown 01. 5 1 1.5 2 2.5 3
disastrous influencing of derivative of Magnus Ma
moment coefficient C , which was tested, using 0.6
Mpα
Fig. 6 values, by 100%, variations, keeping the a
smaemaen so tmheorr ec,o nadni tiuonnksn oinw tnh ep ostsaitbiiolnit yo tfe sMts.a gTnhuiss bility criteri00..45
fvoarlcuee s.a loDnigff epreronjceecst ileb etawxiese nt heenx pethriemire nintatel nsaintdy pic sta0.3
o
calculated data vanished by decreasing this osc
gyr0.2 1/Sg (calc)
derivative vs. Mach number distribution, Fig. 8b. 1/S (exp)
g
This effect is caused by coupling with estimations 0.01. 5 1 1.5 2 2.5 3
of H, Murphy's coefficient, Eq. (10), which Ma
Fig. 9. Gyroscopic stability relation vs. Mach
remains positive values, Eq. (13), but vary,
number; a) gyroscopic stability factor, b)
making influences on the λ , more on the high
1,2 gyroscopic stability criteria
frequency damping coefficient λ then on the λ ,
1 2 Gyroscopic stability factor determined by
low frequency damping coefficient, both
changes of flight Mach number and data of
expressed in the in Eq. (4).
projectile model, are presented in Fig. 9
demonstrates flight gyro-stability factor as
relation of Eq. (6) vs. Mach numbers not violated
by the derivatives.

Experimental and Simulation Testing of Flight Spin Stability for Small Caliber Cannon Projectile 7
Strojniški vestnik - Journal of Mechanical Engineering Volume(Year)No, StartPage-EndPage
The spin velocity, projectile performances dynamic factor bigger than 2 making Eq. (15)
are taken in the both data types of simulations negative, Fig. 12, and violating stability. Double
representative trajectory with equal values vs. less values of C vs. flight Mach numbers
Mpα
Mach number, represented on the Fig. 10, and rearranged stability of dynamic factors, but
corresponding with projectile model data in making neutral stability approximately. Effects
Tables 1 and 3. are related to values of H, by also modest reliable
6500 data, about sum of derivatives C +C , are
6000 Mq Mα
shown influenced on the dynamic stability on the
5500
Fig. 12, with respectable differences between
5000
-1p (s)44500000 seixmpuerlaimteedn tasl tabainldit y caclcriutelartiead Edqa.t a (1v2s.) , Mwaicthh
3500 number. Values are exposed as the coupled with
3000 C influences and mentioned derivatives.
Lα
2500
20000.5 1 1.5 Ma 2 2.5 3 4.5 (1) Sd (calc) (CMpα )
4 (2) Sd (exp)(CMpα )
Fig. 10. Angular spin velocity vs. Mach number (1) (3) Sd (calc) (CMpα /2)
3.5 (4) Sd (exp)(CMpα /2)
mic stability criteria-010...210555 SSdd((22--SSdd)) ((ceaxplc)) ( (CCMMppαα ) ) dynamic stability factor12..55231 (((234)))
dyna -1 0.50. 5 1 1.5 Ma 2 2.5 3
-1.5 Fig. 12. Influences of derivative of Magnus
-02. 5 1 1.5 2 2.5 3 moment coefficient on dynamic stability factor
Ma

2 Sd(2-Sd) (calc) (CMpα /2) Dynamic stability factor S and gyroscopic
1.5 S(2-S) (exp) (C /2) d
d d Mpα stability factor S related by Eq. (15) are
mic stability criteria-00..0155 psatnraedbs ielnitstyiem dte usoltanitn iogth niesn .f FlguiMegn. ac1ien3s vasds. i fMtfheaerc ehnfi cnneausl m vboaeflru ete tshotesf
dyna -1 eexxppeercitmede ntotatla l satanbdi lityc aolcf uplarotejedc tilde aitna thed efnliogthetd.
-1.5
Coupled effects on the Fig. 13 proves that
-02. 5 1 1.5 2 2.5 3 dominant role of estimated positive values C
Ma Mpα
Fig. 11. Dynamic stability relation criteria vs. of about 0.8 to 0.4, in supersonic and subsonic
Mach number; a) for full value of derivative of flight makes negative effect on the projectile
Magnus moment coefficient,b) for half value of flight stability.
derivative of Magnus moment coefficient 2 (1) (3) (5)
1.5
(2) (4) (6)
1
Changes of spin were not tested 0.5
acemlaxsolpocme ureeliaxnmtptie oocnnsotesae dlfl fyoiac.fs iS etnidhgtye nnC iafdMimicpsaαai,cns tti rnodsfutelaursbie vinolacinttei yvst ,he efFoa ifceg ts.Mo ti6rmas, .ga wnteuIandss stability factors--10-..5510 (((231))) 1S1/d/SS(2gg -((Secdxa pl)c )()calc)
-2 (4) Sd(2-Sd ) (exp)
presented, further Figs. 11 and 12, the condition -2.5 (5) Sd(2-Sd ) (calc)(CMpα /2)
goifv deynn ambyi c sEtaqb. ilit(y1 2E) q. w(1it5h) , aMnda gsntaubsi litmy ofamcetonrt -03. 5 1 1.5 Ma 2 (6) Sd2(2.5-Sd ) (exp)(CMpα /2)3
derivative influences were tested. Influencing of Fig. 13. Total stability factors equation influences
derivative of Magnus moment coefficient C , for full and half derivative of Magnus moment
Mpα
which was vary 100% Fig. 6, making stability of coefficient vs. Mach number

8 Milinović, M. - Jerković, D. - Jeremić, O. - Kovač, M.
Strojniški vestnik - Journal of Mechanical Engineering Volume(Year)No, StartPage-EndPage
of aerodynamic coefficients coincides with the
Table 4. Approximately estimations of experimental results of aerodynamic coefficients
aerodynamic parameters influences on the but not satisfies required conclusions about
stability parameters [13] stability without derivatives measurements.
AD Manner of Sensitivity of Comparative calculation model of coefficients
Stability
para- AD parameter stability estimations is tested, to prove possible
meter parameter parameter
undetermined which could appeared as the
λ increase to 20%
2 significant, but missed in the measurement on the
1/S increase to 20%
increasing S(2 ‒g S ) increase to 5% tunnel tests at the approximately steady state
d d
p decrease 3 to 8% conditions. Further researches of ammunition
C
D0 λ2 decrease to 20% correction functions could be possible for
1/S decrease to 20%
decreasing g preliminary consideration by simulated stability
S(2 ‒ S) decrease to 5%
d d methodology of lateral forces required in
p increase 3 to 8%
correction by method of coefficient derivatives
λ increase to 20%
increasing 2 shown in this paper. Damping efficiency of
S(2 ‒ S) increase to 5%
C d d
Lα λ decrease to 20% projectile initial magnitude of angle velocity
decreasing 2
S(2 ‒ S) decrease to 6% vector α (total yaw angle) is about 0.4 seconds
d d t
increasing 1/S increase to 15% after launching, which corresponds to the
C g
Mα decreasing 1/Sg decrease to 15% expected, if lateral force is in the center of mass.
λ1 decrease to 30% Also, sensitivity tests gives satisfied frame values
CMq increasing Sd(2 ‒ Sd) decrea7s%e 2.5 to of gyroscopic stability and dynamic stability
+C influences, for the approximated values of
Mα decreasing λ1 increase to 30% Magnus moments and other similar disturbances
S(2 ‒ S) increase to 8%
d d
λ, λ increase to 30% representatively arranging in its coefficients
increasing 1 2
S(2 ‒ S) increase to 25% derivatives values. Further research have to
C d d
Mpα decreasing λ1, λ2 increase to 30% composed simulations and test, to develop best
S(2 ‒ S) increase to 25%
d d way for ammunition guidance considerations,

based on behavior, of main projectile axes and
This data corresponds with [13] not fully
velocity vector, during flight. Further dynamical
corresponds with [14],and directed on general
testing of aerodynamic derivatives, requires
conclusions in [6], that Magnus moment effect
appropriate tunnel facility, included equipment
could be expected suspicious, if it is taken from
for the well simulation of angular motion, for
data which are not proved by real measurements
ammunition models tests.
which miss in the published data. Paper proves

estimations of instability boundaries and area of
6 AKNOWLEDGMENT
main derivative coupling influenced on the flight.

Lateral force in the center of gravity proves
Results presented in this paper are made
determination of stable flight. Increasing of
within project No III47029 financed by Ministry
lateral moments derivatives caused by variation
of science and technology development Republic
of the force center along projectile axis is not
of Serbia.
suggestible. Sensitivity of stability factors tested

in the [13] and in this paper is presented on the
7 REFERENCES
Table 4.

[1] Regan, F.J. (1975). Aeroballistics of
5 CONCLUSION
terminally corrected spinning projectile
The stability of AA gun projectile model is
(TCSP). Journal of spacecraft. vol. 12, no.
affected by aerodynamic coefficients and
12, p. 733-738.
derivatives, through their steady state testing data.
[2] Morrison, P.H., Amberntson, D.S. (1977).
Test performed by approximately real designed
Guidance and control of a cannon-launched
model of projectile was used, and the obtained
guided projectile. Journal of spacecraft.
measurements are valid but not enough for the
vol. 14, no. 6, p. 328-334.
full reliable estimations of flight stability. The
trait of the change of the based calculated values

Experimental and Simulation Testing of Flight Spin Stability for Small Caliber Cannon Projectile 9
Strojniški vestnik - Journal of Mechanical Engineering Volume(Year)No, StartPage-EndPage
[3] Zarchan, P. (1990). Tactical and strategic [11] Regodić, D. (2003). Exercises in exterior
missile guidance. Progress in Astronautics ballistics. Military academy, Belgrade. (in
and Aeronautics, AIAA, vol. 124, Serbian)

[4] Vogt, R., Glebocki, R. (2000). Impulse [12] Jerkovic, D., Samardzic, M. (2008). The
control of anti-tank mortar missile. RTO AVT aerodynamic characteristics determination of
Symposium on Active Control Technology classic symmetric projectile. The 5th
for Enhanced Performance Operational international symposium about design in
Capabilities of Military Aircraft, Land mechanical engineering, KOD, p. 275-282.
Vehicles and Sea Vehicles, Braunschweig. [13] Jerković, D. (2009). The influence of
[5] Gupta, S.K., Saxena, S., Singhal, A., aerodynamic coefficients on the motion of
Ghosh, A.K. (2008). Trajectory correction axis-symmetrical body. Faculty of technical
flight control system using pulse jet on sciences University of Novi Sad. (in Serbian)
artillery rocket. Defense Science Journal, [14] Regan, F.J., Schermerhorn, V.L. (1971).
vol. 58, no. 1, p. 15-33. Aeroballistic evaluation and computer
[6] McCoy, R.L. (1999). Modern exterior stability analysis of the US Navy 20-mm
ballistics. Schiffer Military History, Atglen. general purpose projectile. NOLTR 71-95.
[7] Carlucci, D.E., Jacobson, S.S. (2008). [15] Elfstrom, G.M., Medved, B. (1986). The
Ballistics – Theory and design of guns and Yugoslav 1.5 m trisonic blowdown wind
ammunition. CRC Press, Boca Raton. tunnel. 14th Aerodynamic Testing Conference.
[8] Regodić, D. (2006). Exterior ballistics. West Palm Beach, AIAA Paper 86-24726, p.
Military academy. Belgrade. (in Serbian) 89-95.
[9] Mitrović, Č., Bengin, A., Cvetković, D., [16] Krasnov, N.F. (1985). Aerodynamics 1 –
Bekrić D. (2010). An optimal main Fundamentals of Theory. Mir Publishers,
helicopter rotor projection model obtained Moscow.
by viscous effect and unsteady lift [17] Krasnov, N.F. (1985). Aerodynamics 2 –
stimulation. Strojniški vestnik – Journal of Methods of Aerodynamic Calculations. Mir
Mechanical Engineering, vol. 56, no. 6, p. Publishers, Moscow.
357-367. [18] Janković, S. (1979). Aerodynamics of
[10] Petrović, Z., Stupar, S., Kostić, I., projectiles, Faculty of mechanical
Simonović, A. (2010). Determination of a engineering, Belgrade (in Serbian)
light helicopter flight performance at the [19] McCoy, R.L. (1985). Aerodynamic and flight
preliminary design stage. Strojniški vestnik – dynamic characteristics of the new family of
Journal of Mechanical Engineering, vol. 5.56 mm NATO ammunition. Memorandum
56, no. 9, p. 535-543. report BRL-MR-3476, US Army Ballistic
Research Laboratory, Aberdeen Proving
Ground, Maryland.

10 Milinović, M. - Jerković, D. - Jeremić, O. - Kovač, M.