VOL. 12, NO. 12, DECEMBER 1975 J.

SPACECRAFT 733

Aeroballistics of a Terminally Corrected

Spinning Projectile (TCSP)
Frank J. Reg an*
Naval Surface Weapons Center, White Oak Laboratory, Silver Spring, Md.

and

Jack Smitht
Sanders Associates, Nashua, N. H.
This paper discusses the aerodynamic aspects and ballistic advantages of a method for providing terminal
guidance to the Mk 41 projectile. Guidance and control functions are contained in a single unit, which is adap-
table to the Mk 41 fuze-well. This unit contains all the required power system, sensors, and aerodynamic con-
trols. These controls consist of a set of four canards in a cruciform arrangement. An overview is presented of the
system concept. Indications are given of the increased effectiveness of the guided projectile over the con-
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ventional unguided round.

Nomenclature Subscripts
a = axial
— pitching moment coefficient, My/QSd B
— pitching moment derivative, dCm/do^ c = canard
= damping-in-pitch derivative, dCm/dq M = Magnus
= normal force coefficient, —FZ/QS ss = steady-state or trim conditions
= normal force derivative, dCN/da T — transverse
— Magnus force derivative, d2CN/dpda
Introduction
= fm effectiveness derivative, dC^/dd
— yawing moment coefficient, Mz/QSd
= Magnus moment derivative, 32Cn/dpda
= side force coefficient, F y /QS
I N long-range bombardment, uncertainties in geode-
tics, atmospheric properties, and winds, coupled with
variation in projectile mass and mass distribution, gun wear,
— reference length, body diameter and chamber pressure distribution, all result in an uncertainty
= forces along X, Y,Z axes in projectile impact location. Weapon effectiveness depends
= axial moment, of inertia on a sequential set of corrective commands from, say, a spot-
IT = transverse moment of inertia ter. An empirical method such as this might be acceptable
Ka = axial radius of gyration, (Ia/md2) 1/: against a stationary target of limited defensive capability.
KT = transverse radius of gyration, (IT/md2 ) v- However, against a maneuverable, high-speed offensive
MX)My,Mz = moment about X, Y, Z axes weapon a gun system must function within a response time of
m a few seconds. A corrective algorithm based on the per-
n = maneuvering load factor formance of earlier rounds is obviously inadequate. Rather,
P = spin rate what is required is the existence of a guidance and control
P — reduced spin rate, pd/2 V capability that is an integral part of each projectile.
Q — dynamic pressure A particular example of an operational situation in which
q = pitch rate projectile guidance is essential is in shipboard defense against
Q — reduced pitch rate, qd/2 V the cruise missile. The essence of such an encounter is
S = reference area illustrated in Fig. 1. A ship whose main defensive armament
W = weight against aerial targets is 5-in. deck guns is shown under attack
X — center-of-pressure position by an antiship cruise missile. Under such demanding con-
a. = angle of attack ditions, bias errors associated with this system severely limit
= angle of sideslip the effectiveness of the defense. However, dispersion errors
= atmospheric density may be greatly reduced by adding terminal guidance late in
= complex angle of attack the trajectory.
= fin-cant angle
Superscripts
INTERCEPT
B = body TRAJECTORY CORRECTION
c — canard
T = total
Presented as Paper 74-796 at the AIAA Mechanics and Control of TARGET DETECTED BY
Flight Conference, Anaheim, Calif., August 5-9, 1974; submitted PROJECTILE SENSOR7
August 21, 1974; revision recieved May 9, 1975.
Index categories; LV/M Dynamics and Control; LV/M System and
Component Ground Testing; LV/M Guidance Systems (including
Command and Information Systems).
*Experimental Aerodynamics Division. Member AIAA.
f
Director of Projectile Guidance. Member AIAA. Fig. 1 System concept.
 734 F. J. REGAN AND J. SMITH J. SPACECRAFT

Fig. 2 Mk 41 projectile with terminal guidance.

Fig. 3 Canard control
frame of 2/5 scale wind
tunnel model.
The decision to use terminal guidance was made after other
possible improvements to the gun system effectiveness were
considered. Studies were made of various system components
such as guns, fire control computers, fuzes, and projectile
design. The conclusion reached was that the most significant
improvement that could be made in overall system ef-
fectiveness would be to provide a projectile-borne terminal
guidance capability.

Guidance Package

Guidance implies the need for some means of altering the

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projectile trajectory to reduce miss distance. A general

examination of the problem of projectile guidance might lead
to a number of possibilities. For example, while the technique
of jet interaction might remove the sensitivity that an
aerodynamic control has to projectile speed, the com-
plications of reservoir and conduits rule this technique out.
Even a restriction to aerodynamic controls would leave open
the question of control location. Base location of control fins
would have certain advantages, as will be seen, in increasing
gyroscopic stability. However, rear-mounted fins would be
difficult to use with an existing conventional projectile. The Fig. 4 Forces acting on projectile.
most attractive location for control fins for the terminal
guidance of an otherwise conventional projectile is certainly
in the most forward part of the projectile. Such a location per- makes maximum effective use of g-capability, it was chosen
mits the entire guidance unit—sensors, power systems, as the guidance law.
proximity fuze, S&A booster, and aerodynamic controls—to
be a self-contained package. This package can then become an Aerodynamic Controls
integral part of the projectile through an operation no more
complicated than mounting the fuze. In fact, the guidance The aerodynamic controls have been identified in Fig. 2. A
unit becomes, in a sense, an advanced fuze, containing not clearer view of the canard frame is shown in Fig. 3. Sub-
only the fuze capability for warhead activation but the ad- sequently, a discussion will be given of the various
ditional capacity to provide terminal guidance. aerodynamic and packaging constraints that were imposed on
The Mk 41 projectile with the guidance unit in place is
the canard design. For the present it will be assumed that a
shown in Fig. 2. The canard fins used for controlling projec-
trim-generating capability is available in the canards. Three
tile angle of attack are conspicuous. During passage of the
questions should be addressed regarding these canards. First,
can the canards be used to trim a conventional spinning shell?
projectile through the gun tube, setback locks the canard
Second, what is the effect of the canards upon the projectile
frame to the projectile proper. Once the projectile emerges
gyroscopic and dynamic stability? Third, what is the
from the gun (and setback forces are removed), the canard
maneuverability of the projectile with the canards in place?
frame derotates from the projectile spin rate of about 220 rps
to a spin rate of 5-10 rps in an interval of about 200 msec. One Projectile Trim
pair of opposing canards can be rotated about a common axis
of articulation to generate the required aerodynamic control
In considering projectile trim it is helpful to illustrate the
moments; the other pair of canards is at a small fixed angle of
cant (about 0.1°). The large canard area (and the large essential forces acting on the projectile. Figure 4 is a graphical
resulting roll-damping moment) causes the rapid canard representation of the aerodynamic loads acting on the projec-
frame despin; the fin cant gives the frame a residual rolling tile. These loads may be represented in terms of the total
moment in a direction opposite to that of the shell. During the pitching moment, Cfn, as
guidance phase this slight rotation rate is stopped relative to »,p<p(3 (1)
inertial space and in such an orientation that the axis of ar-
ticulation is normal to the plane defined by the shell axis of This equation indicates that the pitching moment is com-
symmetry vector and a vector from the shell center of gravity prised of four distinct constituents. These contributions are
to the target. This plane is not necessarily coincident with the identified by the four terms on the right as: the static moment
angle-of-attack plane and so loads normal to, as well as in, the due to and proportional to the body angle of attack a; the
target plane are generated. The guidance system continuously static moment due to the canard and proportional to the
changes the orientation of the canard frame to keep most of canard local angle of attack (5 — a ) ; the pitch damping
the aerodynamic loads in the target plane. moment due to both body and canards and proportional to
The generated aerodynamic load results in the development the reduced pitch-rate q\ the Magnus moment due to the body
of a trim angle of attack. The trim angle generates the and proportional to the product of the body reduced spin rate
required body lift to steer the projectile. Because of the con- p and angle of sideslip /3. Since the canard frame rapidly
tinuous decrease in projectile velocity, g's available for despins upon emergence from the gun, it is assumed to make
maneuverability' are limited. Since proportional navigation no Magnus contribution.
 DECEMBER 1975 TERMINALLY CORRECTED SPINNING PROJECTILE AEROBALLISTICS 735

In order to avoid excessive clutter, Fig. 4 is presented

without sideslip /3 indicated. Consistent with Eq. (1), sideslip
is defined as the angle between the axis of symmetry X and the
component of the velocity vector V in the XY plane; the
definition of the angle of attack remains as the angle between
the axis of symmetry X and the component of the velocity vec-
tor Kin theXZ plane. Slightly different definitions of { a,/3 }
might be used, but the restriction of these quantities to small
values would leave Eq. (1) unchanged. Additional com-
plications in Eq. (1) would arise if the canard axis of ar-
ticulation of A A ' is allowed to take an arbitrary rotation with
respect to the Faxis. However, since the goal here is to point
out some of the conditions at trim and not to attempt a
lengthy dynamic analysis, Eq. (1) will be assumed sufficiently
representative of conditions at trim.
Returning now to Eq. (1), trim will be defined as existing
when a = ass , and C£ = 0, 0 = 0, q = 0. With these sim-
plifications Eq. (1) may be written as

+XCCCN.] (2)
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Equation (2) provides the trim angle, cess, per unit fin cant,
6. Before commenting upon Eq. (2), we will give an alternate
derivation. This approach will consider trim conditions using
the classical ballistic equation, which includes body spin and
body mass and mass distribution.
Figure 4 is a simplification of the classical ballistic load for-
mulation. Fox example, there also exists a second complete set
of moments similar to those given in Eq. (1) if the velocity
vector V is not contained in the XZ plane. This second set of
moments would follow from Eq. (1) by replacing m with n , a.
with ]8, and q with r. The canard would not make any con-
tribution to the yawing moment if AA' is normal to the XZ
plane as the second set of canards is at a fixed differential
cant.
The formulation of the ballistic problem in terms of these
moments leads to the classical ballistic equation as formulated Fig. 5 Flight mechanics.
by Murphy 1
Now if the right-hand side of Eq. (6) is normalized by M2 and
(3) expanded in a Taylor series to the second term in PT/M, the
result is
where
= -(AIM) [1-(PT/M)2} (7a)
(4a)

T= [ (CJ£-C£) +K /3 SS = -(AIM) [PT/M] (7b)

~C*Nl + K;2C*N»a (4b) Now, using the definitions of Eq. (4), it is fairly straight-
forward to rewrite Eq. (7) as
A=-Kr2Xc C%1 d (4c)
1
t/_ /^* T __ 7^* j^-2
/? —C / V a — ^ C D — A T - (4d)

P = 2(Ka/KT)2 p (4e)
-P2 (8a)
where the presence of an asterisk indicates an aerodynamic
derivative or coefficient multiplied by the relative density 2XC C^ CNpa
=P (8b)
(psd/2m). Again Eq. (4c) shows that the asymmetry is in only + Xc
one set of canards, pitch, in this case, as the other set is at a
fixed differential cant. In the previous expressions the asterisk has been omitted since
If steady-state conditions are defined to exist when the aerodynamic coefficients appear only in ratios.
In examining Eq. (8) one may reach two interesting con-
clusions. Equation (8a) shows that spin can alter the pitch
(5) angle in trim ass only as a second-order effect. Equation (8b)
indicates that a pitch asymmetry 6, in the presence of spin,
Eq. (3) becomes causes a sideslip angle of trim, 0 SS . However, Eq. (8) may be
simplified when it is recognized that p is .0 (10 - 1 ) and the
= -iA/(M+iPT) (6a) terms in braces, in both equations, are 0(1). Thus Eq. (8a)
may be written as

= -iA(M-iPT)/[M2+P2T2] (6b) (9)

 736 F. J. REGAN AND J. SMITH J. SPACECRAFT

with the trim angle in sideslip /3SS no larger than a tenth of ass The gyroscopic stability parameter l/Sg and the dynamic
and is, for present purposes, negligible. It will now be noted stability parameter Sd can be used to assess the effect of
that Eqs. (2) and (9) are identical. Thus the presence of body canards on projectile stability.
spin, as encountered in any practical projectile, has a There are two conflicting requirements placed upon guided
negligible effect on the trim angle of attack per unit fin cant. projectile canard design; high projectile maneuverability in-
One interesting comment may now be made with regard to dicates large canards, while maintenance of projectile stability
trim. In Fig. 4 it will be noted that angle of attack is defined restricts canard size. A satisfactory design must be a com-
positive with the body vertex above the velocity vector, and promise.
canard angle is defined positive with canard leading edge A necessary, though not sufficient, condition for projectile
downward. Equation (9) shows that the statically unstable stability is that the gyroscopic stability parameter 1 /Sg not ex-
projectile trims body vertex upward for canard leading edge ceed unity. Values of \/Sg between 0.6 and 0.75 are common.
downward—exactly the reverse of a statically stable, non- Equation (12a) shows that the presence of canards has a
spinning, conventional, canard-controlled missile. detrimental effect on the gyroscopic stability of the round,
In developing Eq. (8) the assumption was made that the i.e., increases l/Sg. Taking the derivative of the total pitching
projectile with canards in place is inherently stable—the moment CTm in Eq. (1) gives
canards serve only to vary the trim angle. By letting
£" = £ ' =0, the damped transients are ignored. At this point + Xc 03)
stability must be accepted as a premise subject to later sub-
stantiation by either a numerical integration of the equations Since CcNd, the canard effectiveness derivative, is based on the
of motion or by some kind of data coverage of a projectile reference area S, it may be rewritten based on the area Sc of
firing. Trim stability and performance characteristics of the
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projectile were investigated using a six-degree-of-freedom two canards as

simulation of the configuration. In the simulation, with the
shell subjected to open-loop canard deflections, steady-state (14)
trim angles of attack were obtained corresponding with those
measured in the wind tunnel. The projectile oscillated about to give Eq. (13) as
these values, with a double amplitude of less than 1 ° and with
a fairly low damping ratio. Subsequent simulations of a fully
guided round showed that these small oscillations did not " CL+XBCZ+(S'/S)XcCir (15)
degrade the predicted performance. Unguided firings have
substantiated these conclusions to some extent. These firings Inserting Eq. (15) into Eq. (12a) gives,
have shown that there is only a 2% range degradation with
canards in place, indicating freedom from a large-amplitude
limit cycle. c fSc/S) 8I2xxp (16)
Rather than present the results of these six-degree-of-
freedom simulations, a brief description of projectile motion Quite clearly, the canard area S c- , and its location Xc, can in-
after canard deflection will probably be sufficient. A pictorial crease l/Sg over the base-body value. It will subsequently be
representation of this motion is given in Fig. 5. Assuming that shown from some wind-tunnel results that, while C£ (SC/S)
a positive angle of trim is desired, the canard leading edge is relatively small in comparison with C% (about 1/^-1/8) the
must be deflected downward. The first motion of the projec- extreme forward position of the canard, ?.e., large Xc, causes
tile will be in the direction of the torque, i.e., nose downward. the canard to have a significant effect on decreasing shell
Since this torque vector is orthogonal to the angular momen- stability.
tum vector, the projectile will precess nose left out of the The effect of the canards on the dynamic stability
angle-of-attack plane (plane of the paper). The out-of-plane parameter Sd is less clear. Wind-tunnel testing has indicated
motion develops an angle of sideslip ft the resulting that the presence of the canards increases the Magnus moment
aerodynamic moment, orthogonal to angular moment vector, XMCNpa> and calculations indicate that canards can increase
precesses the nose upwards. This angular motion continues the pitch damping moment Cm . Since these quantities appear
until the projectile has reached a trim angle of attack [as in a ratio, it would appear that the effect of canards on S(i
predicted by Eq. (9)]. might be ignored.

Projectile Stability Projectile Maneuverability

Murphy 1 has shown from the solution to Eq. (2) that the The third consideration in examining the guided projectile
projectile has two modes of motion and that the exponential is the effect of canards on weapon maneuverability. The pur-
damping coefficients of this motion, A, and X 2 , might be ex- pose of the canards is to develop a trim angle which, in turn,
pressed as generates a lift normal to the trajectory. The maneuvering
load factor n may be expressed as
\L2 = (Kr2/2) C*»c{l±[Sd-l]/[l-(l/Sg)]v>} (10)
QS/W (17)
Since motion stability depends upon A being negative, this
requirement is met by the following inequality
If Eq. (9) is inserted into Eq. (12) and Ccm is replaced ac-
l/Sg<Sd(2-Sd) (11) cording to Eq. (14), the maneuverability factor n/d may be
written as
where
(XC-XB) QSC
(12a) W
(18)
and
2[(CTNn-CD)+K;2(XM/2)C»Npn\ It may be seen in Eq. (18) that, as expected, increasing
canard area Sc permits an increase in maneuvering load factor
n. However, it should also be noted that n is a weak function
 DECEMBER 1975 TERMINALLY CORRECTED SPINNING PROJECTILE AEROBALLISTICS 737

CANARD CANT ANGLE (DEC)

1.5

n i.o

0.5
1

^ 0
8 10 12 14
ANGLE OF ATTACK (DEC)
-0.53
Fig. 8 Pitching-moment coefficient vs angle of attack at a Mach
number of 2.28 and a roll angle of 0°.

The launch environment imposes longitudinal accelerations

on the order of 104g and spin accelerations on the order of
Fig. 6 Schlieren photograph of guided projectile at Mach 2.5. 106 rad/sec 2 on the canard assembly. Obviously, the fin con-
figuration should attempt to minimize the normal and chord-
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wise bending moments resulting from this environment.

1.0
A tapered planform with a taper ratio of 0.4 was selected as
o
^ 0.8
the best compromise among the above factors. The airfoil is a
9%, thick double wedge, which was selected from con-
siderations of drag, structural loads, and producibility.
£ 0.6
o Two sets of wind-tunnel tests were carried out: static
o CANARD CANT ANGLE (DEC)
o NONE
measurements to obtain the pitching moment and normal
£ 0.4
o 0 force coefficients, Cm and C v , and Magnus measurements to
i 0.2
10 obtain the Magnus moment and force derivatives,
Cd
o
zr
Cn and CN . From the static tests it is possible to obtain the
0
canard effectiveness derivative, Qv5, and canard center-of-
pressure location^; from the Magnus tests Cn and CN
ANGLE OF ATTACK (DEC)
are measured directly. The damping-in pitch derivative, Cm a,
Fig. 7 Normal-force coefficient vs angle of attack at a Mach number as required in the equation for the dynamic stability
of 2.28 and a roll of 0°. parameter, Eq. (12b), was calculated from the canard ef-
fectiveness and center of pressure, Ccm and Xc as
of Sc since Sc appears in both the numerator and in the
denominator. An interesting speculation can be made, based (19)
on Eq. (18). In the expected operation (Xc— XB) will always
be positive, i.e., canard center of pressure ahead of the body-
alone center of pressure. However, the possibility does exist in This quantity was added to the contribution of the body-
some applications that, with the forward movement of the alone C^ . For body-alone contributions, available Mk-41
body-alone center of pressure with decreasing Mach number, pitch-damping data were used. 2
the term (Xc — XB) changes sign during flight, there would be Figure 6 shows a two-fifths-scale model of the guided
a control reversal. While control reversal does not occur for projectile at a Mach number of 2.5 during the static wind-
the subject guided projectile, the possibility of control rever- tunnel tests. It will be noted that the canards, at this extreme
sal must be considered in the design. upper Mach number, are well within the bow shock.
Because of space limitations the wind-tunnel data reduction
Canard Design and Wind-Tunnel Tests equations will not be given here. In early tests canard effects,
Qv6 and Xc, were obtained by establishing a base line from
Earlier questions were raised concerning projectile trim, the projectile without canards. This base line is then sub-
stability, and maneuverability. Relationships from which tracted from measurements made on the model with canards
these three aspects of projectile performance may be con- in place. In later tests this indirect and less accurate method
sidered have been expressed in Eqs. (9,16, and 18). Since the was replaced by installing a hinge moment balance in a full-
projectile aerodynamic properties expressed in aerodynamic scale (though truncated) model to measure the canard load
derivatives occur in each of these three equations, it is highly and center of pressure directly. However, even in this second
desirable to obtain aerodynamic measurements in a wind tun- set of tests the entire model was mounted on a five-component
nel. balance to provide a check on the hinge moment measure-
The canard configuration selected for testing represented a ments (by the differential procedure described above), as well
compromise among stability, performance, and gun-launch as measuring roll torques on the canard frame.
enviroment requirements. The location of the canards was The normal force coefficient vs angle of attack is presented
more or less fixed by geometrical constraints. The exposed in Fig. 7 for a Mach number of 2.28 and a canard frame roll
span was limited by the inside diameter of the gun. Within angle of 0°. A similar presentation of the pitching moment
these geometric constraints, the product XCCCN was selected coefficient is given in Fig. 8. In both cases it will be noted that
such that the gyroscopic stability criterion woula be satisfied. the increase in canard angle, 5, positively (leading-edge down-
Several aspect-ratio and planform combinations were ward) results in a downward shift in the curves. The presence
examined to select a minimum planform area configuration of the canard increases the normal force and pitching moment
which satisfied the incremental pitching moment. It was also derivatives CN and Cm , as suggested (in the case of the
desirable that the exposed fins be completely within the bow moment) by Eq. (13). Again it is obvious that this effect is
shock over the entire flight regime to preclude nonlinearities greater in the case of the moment than the force derivative.
in the aerodynamic loads. The reason is, of course, that, while CcNf> is only about one-
 738 F. J. REGAN AND J. SMITH J. SPACECRAFT

160 FT

CANARD CANT ANGLE (DEC)

o (V\k 41 NORMAL TRAJECTORY
a NONE CORRECTION DURATION 3 SEC
v* 0.5 A O 6=0 CANARD DEFLECTION 20 DEC
O
oa
3500 4000 4500- 5000 5500 6000
RANGE (YARDS)
1.6 1.8 2.0 2.2 2.4 2.6
Fig. 11 Guided projectile terminal trajectory.
MACH NUMBER

--0.5
o o following mass and inertial properties are used: m — 1.86,
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K~2 = 7.046, Kj2 = 0.6099, and the aerodynamic measure-

UJ
O
o:
O
CO
ments of which Figs. 7, 8, and 9 are typical, it is possible to
rj obtain at the muzzle and at a Mach number of 2.5
z
o
= 0.860 = 0.718 /i/5 = (20)
Fig. 9 Magnus force and moment derivatives vs Mach number.
If the above value of Sd is inserted into Eq. (11), it will be
found that the maximum value of \/Sg for stability is 0.920.
Thus, the guided projectile would have marginal gyroscopic
§
stability in the initial part of its flight. Since the reduced spin
FIN CANT (PEG)
If O 8 =0
rate p in Eq. (12a) tends to increase downrange, projectile
K $ stability will improve downrange.
D 8 =5
The maneuverability factor n/b varies with the square of
the Mach number (since the dynamic pressure Q in Eq. (18)
scc <z 1.0
n D D D
varies with Mach number squared for fixed static flow con-
|i 0.5
o o 0 ditions). At the. muzzle it may be shown that, for a canard
§- 0 >-i—————————————,—————————————,—————————————r-
cant angle of 15°, the projectile should be able to acquire a
< 1.6 1.8 2.0 2.2 2.4 2.6 lateral load of about 2 g. As pointed out, this capability will
0 MACH NUMBER decrease with Mach number squared. Thus, at a Mach num-
ber of 1.75 the lateral maneuvering capability will be about 1
Fig. 10 Canard center of pressure location vs Mach number. g. If it is conservatively assumed that the projectile is capable
of 1 g for 3 sec, there will be the capability to maneuver 160 ft,
16,000 ft downrange. This situation is depicted in Fig. 11.
sixth of C* , the forward position of the canard (i.e., large Thus the projectile can attain about 10 mils of correction,
Xc) makes the canard influential in increasing the pitching which was the original design goal.
moment.
Figure 9 indicates some of the Magnus measurements. The Conclusion
Magnus moment is required for determining the dynamic This preliminary work shows that, from aeroballistic
stability parameter [Eq. (12b)]. It will be noted that the stability considerations a canard-controlled guided projectile
Magnus moment and force are increased in the presence of is feasible. The weapon should be at least marginally stable
canards. over all of its flight. Subsequent unguided firings have sub-
Finally from the hinge moment measurements it is possible stantiated this conclusion. These firings have also shown that
to indicate the center-of-pressure location Xc from the hinge there is only about a 2% range degradation with the canards
axis of the canard. This result is presented in Fig. 10, where it in place. This study has shown that the canards, as designed at
may be seen (for the 5-in. projectile) that, depending on Mach present are capable of effecting at leat a 10-mil correction.
number and fin deflection, the center of pressure is between
1/2 and 1 in. ahead of the hinge axis. References
Weapon Performance 1
Murphy, C.H., "Free-Flight Motion of Symmetric Missiles,"
BRL 1216, July 1963, Ballistic Rearch Labs., Aberdeen Proving
As a result of these wind-tunnel tests, it is possible to Grounds, Md.
2
calculate typical values of the gyroscopic and dynamic Chadwick, W.R., et al., "Dynamic Stability of the 5-in./54
stability factors, \/Sg and Sd [Eqs. (12b), (16b)] and the Rocket-Assisted Projectile," NWL TR-2059, Nov. 1966, Naval Sur-
projectile maneuverability factor, /?/<5[Eq. (18)]. If the face Weapons Center, Dahlgren Laboratory, Dahlgren, Va.
 This article has been cited by:

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Dynamics 39:2, 339-350. [Abstract] [Full Text] [PDF] [PDF Plus]
7. Frank Fresconi, Bernard Guidos, Ilmars Celmins, Wayne Hathaway. Flight Behavior of an Asymmetric Body through
Downloaded by BEIHANG UNIVERSITY on June 23, 2020 | http://arc.aiaa.org | DOI: 10.2514/3.57041

Spark Range Experiments using Roll-Yaw Resonance for Yaw Enhancement . [Citation] [PDF] [PDF Plus]
8. Frank Fresconi, James DeSpirito, Ilmars Celmins. 2015. Flight Performance of a Small Diameter Munition with a
Rotating Wing Actuator. Journal of Spacecraft and Rockets 52:2, 305-319. [Abstract] [Full Text] [PDF] [PDF Plus]
9. M. Pavic, B. Pavkovic, S. Mandic, S. Zivkovic, D. Cuk. 2015. Pulse-frequency modulated guidance laws for a mortar
missile with a pulse jet control mechanism. The Aeronautical Journal 119:1213, 389-405. [Crossref]
10. John W. Robinson, Peter Strömbäck. Velocity To Be Gained Guidance for a Generic 2D Course Correcting Fuze .
[Citation] [PDF] [PDF Plus]
11. Ahmed Elsaadany, Yi Wen-jun. 2014. Accuracy Improvement Capability of Advanced Projectile Based on Course
Correction Fuze Concept. The Scientific World Journal 2014, 1-10. [Crossref]
12. John Robinson, Peter Strömbäck. Perturbation Based Guidance for a Generic 2D Course Correcting Fuze . [Citation]
[PDF] [PDF Plus]
13. Nicolas Hamel, Eric Gagnon. CFD and Parametric study on a 155 mm artillery shell equipped with a roll-decoupled
course correction fuze . [Citation] [PDF] [PDF Plus]
14. Eric Gagnon, Marc Lauzon. Maneuverability Analysis of the Conventional 155 mm Gunnery Projectile . [Citation]
[PDF] [PDF Plus]
15. K.H. Lloyd, D.P. Brown. 1979. Instability of Spinning Projectiles During Terminal Guidance. Journal of Guidance and
Control 2:1, 65-70. [Citation] [PDF]