Extended range of a gun launched smart projectile using … · 2019. 8. 1. · M. Costello /...

203

Extended range of a gun launched smartprojectile using controllable canards

Mark CostelloDepartment of Mechanical Engineering, Oregon StateUniversity, Corvallis, OR 97331, USA

This effort investigates the extent to which moveable canardscan extend the range of indirect fire munitions using bothprojectile body and canard lift. Implications on terminal ve-locity and time of flight using this mechanism to extend rangeare examined for various canard configurations. Performancepredictions are conducted using a six-degree-of-freedom sim-ulation model that has previously been validated against rangedata. The projectile dynamic equations are formed in the bodyframe and aerodynamic loads from the body and canards areMach number and angle of attack dependent. The projectilebody aerodynamic moments include unsteady aerodynamicdamping. The focus of the study is directed toward low costcompetent munitions that extend range and as such a simpleflight control system is considered which utilizes only timer,roll rate, and roll attitude inputs.

Symbols: x, y, z: Position vector components of the cen-ter of mass expressed in the inertial reference frame. φ, θ, ψ:Euler roll, pitch, and yaw angles. u, v, w: Translation ve-locity components of the center of mass resolved in the bodyreference frame. p, q, r: Components of the angular velocityvector of the projectile expressed in the body reference frame.X,Y,Z: Total external force components on the projectileexpressed in the body reference frame. L,M,N : Total ex-ternal moments components on the projectile expressed inthe body reference frame. m: projectile mass. [I]: Massmoment of inertia matrix. D: Projectile characteristic length.Ci: Projectile aerodynamic coefficients. qa: Dynamic pres-sure at the projectile mass center. α: Longitudinal aerody-namic angle of attack. β: Lateral aerodynamic angle of at-tack. V : Magnitude of mass center velocity. φCi : ith ca-nard azimuthal angle. γCi : ith canard sweep angle. δCi : ithcanard pitch angle.

1Presented at the 9th Annual Gun Dynamics Symposium, Novem-ber 17–19, 1998, McLean, Virginia.

1. Introduction

Traditionally, field artillery target effects are pro-duced by firing a sufficient number of rounds withknown accuracy at a given target so that, statistically,the target is neutralized. Generally, the goal of im-proving field artillery systems boils down to increasingachievable range and improving terminal accuracy ofthe projectile.

It is obvious that a round with extended range enjoysthe flexibility of being able to engage a greater numberof targets over a larger land area. A less obvious, yetequally important advantage of extended range is thatthe system with greater range requires fewer reposi-tionings on the battlefield and can provide fire supportfor a higher percentage of time. This becomes partic-ularly important in today’s highly mobile battle envi-ronment, where a significant portion of time is spentmoving into position. Since a long-range projectile cancover a large area of land, rounds can be fired at manydifferent targets on the battlefield in a short period oftime. Thus, a long range projectile adds increased flex-ibility to the field artillery commander, allowing him toinfluence a much greater portion of the battlefield, forlonger periods of time.

The intensity of Army operations dictates that thefield artillery optimize target effects with every roundfired. One method of improving target effects is to in-crease the terminal accuracy of each round [1,2]. Cur-rent field artillery doctrine requires large numbers ofrounds to be fired in order to neutralize a particulartarget. Statistically, only a small percentage of theserounds actually produce effects on the target. Increasedaccuracy provides that the ‘extra’ rounds, those nothaving effects on target, are never fired. If more roundsthan necessary are fired, the firing unit accepts an un-necessary risk of being acquired by enemy target ac-quisition assets and subsequently engaged with counterfire. When the firing unit comes under steady counterfire, the unit will reposition and be rendered unavailablefor other missions while in transit. Also, firing morethan the minimum number of rounds needed to elimi-

Shock and Vibration 8 (2001) 203–213ISSN 1070-9622 / $8.00 2001, IOS Press. All rights reserved

204 M. Costello / Extended range of a gun launched smart projectile using controllable canards

nate a target wastes expensive munitions and burdensthe re-supply system. Every extra round expended ona particular target represents an opportunity cost thatcould have been directed at another objective on thebattlefield. More importantly, target effects decreaseexponentially as a function of the number of projectilesfired at a particular target due to the lack of surprise.The first volley fired is by far the most important volleyto achieve maximum target effectiveness. Furthermore,if rounds are inaccurate, targets will reappear on thebattlefield. Potentially, this will require additional ar-tillery engagements and negatively affect the outcomeof the overall battle plan. Thus, increased terminalaccuracy increases target effects by landing more firsthits, reduces vulnerability by firing less shots, and usesless material, which reduces the burden on the supplysystem – all contributing to a more effective and lethalfield artillery unit.

The notion of utilizing canards as an aerodynamiccontrol mechanism is by no means new and has beensuccessfully applied to aircraft and missiles for sometime. A significant aerodynamic database has amassedon aerodynamic modeling of missile configurationswith canards [3]. However, few studies have specifi-cally addressed the use of canards to extend the rangeof a ballistic projectile. Smith, Smith, and Topliffe [4]studied the use of canards on a spin stabilized projectilewith the intended use of accuracy improvement. Therelatively small canards were controlled by a seeker.To reduce the required control moments and actuatorbandwidth, the canards were mounted on a bearingspinning at a different rate than the main body.

The work reported here evaluates the potential ofextending the range of a field artillery projectile us-ing moveable canards. It begins with a description ofthe simulation model used to predict projectile motion.This is followed with the definition of a representa-tive extended range projectile configuration. With thismodel data, a parametric study is conducted which in-cludes different canard geometry and deflection pro-files.

2. Projectile dynamic model

The mathematical model describing projectile mo-tion admits 6 rigid body degrees of freedom comprisedof three body inertial position coordinates as well asthree Euler angle body attitudes. The equations pre-sented below use the ground surface as an inertial ref-erence frame. The body frame is defined in the con-

ventional manner [5] and the dynamic equations arewritten with respect to this coordinate system. The pro-jectile translation and rotation kinematic and dynamicequations are given by Eqs (1) through (4) [5,6].

xyz

=

cθcψ sφsθcψ − cθsψcθsψ sφsθsψ + cθcψ−sθ sφcθ

(1)cφsθcψ + sφsψcφsθsψ − sφcψ

cφcθ

uvw

φ

θ

ψ

=

1 sφtθ cφtθ0 cφ −sφ0 sφ/cθ cφ/cθ

pqr

(2)

uvw

=

X/mY/mZ/m

(3)

−

0 −r qr 0 −p−q p 0

uvw

pqr

= [I]−1

LMN

(4)

−

0 −r qr 0 −p−q p 0

[I]

pqr

where,

[I] =

IR 0 00 IP 00 0 IP

(5)

As shown in Eq. (6), the total applied force is composedof weight (W ), body aerodynamic force (A), and canardaerodynamic force (C ).

XYZ

=

XW

YWZW

+

XA

YAZA

+

XC

YCZC

(6)

The weight portion of the external loads is given byEq. (7),

XW

YWZW

= mg

−sθxφcθcφcθ

(7)

while the aerodynamic force contribution is given byEq. (8).

M. Costello / Extended range of a gun launched smart projectile using controllable canards 205

XA

YAZA

= qaD

(8)

CX0 + CXA2α2 + CXB2β

2

CY B1β + CY B3β3 + CY B5β

5

CZA1α + CZA3α3 + CZA5α

5

The longitudinal and lateral aerodynamic angles of at-tack are computed using Eq. (9).

α = tan−1(w

u

)β = tan−1

( v

u

)(9)

The aerodynamic coefficients in Eq. (10) are functionsof the local Mach number at the projectile mass center.They are computed using linear interpolation from atable of data.

The aerodynamic force due to a single canard ismodeled as a point force acting at the lifting surfaceaerodynamic center. Canard orientation is defined byazimuthal angle (φCi), sweep angle (γCi), and pitchangle (δCi). In this study, canard pitch angle is con-trolled during flight. The ith canard force is describedby Eq. (10),

XCi

YCi

ZCi

= qCiSi[TCi ]

(10)

CLsαi−δi − CDcαi−δi

0−CLcαi−δi − CDsαi−δi

where qCi is the dynamic pressure at the canard com-putation point, Si is the canard reference area, and TCi

is the transformation from the local canard referenceframe to the projectile body frame. The canard lift anddrag coefficients are expanded in terms of canard angleof attack and Mach number.

CL = CL1αi + CL3α3i + CL5α

5i (11)

CD = CD0 + CD2α2i + CIC

2L (12)

The coefficients in Eqs (11) and (12) are Mach numberdependent. Canard angle of attack is computed in thesame manner as the body angle of attack except thelocal relative velocity at the canard computation pointis used.

The right hand side of the rotation kinetic equationscontains the externally applied moments. The externalmoment components are given by Eq. (13) and containcontributions from steady body (SA), unsteady body(UA), and canard (C) aerodynamics.

LAMA

NA

=

LSAMSA

NSA

+

LUAMUA

NUA

+

LCMC

NC

(13)

The steady body aerodynamic moment is computed bya cross product between the distance vector from thecenter of gravity to the center of pressure and the steadybody aerodynamic force vector above. Like the aero-dynamic coefficients, the center of pressure location isdependent on local Mach and is computed by linearinterpolation. The unsteady body aerodynamic mo-ment provides a damping source for projectile angularmotion and is given by Eq. (14).

LUAMUA

NUA

= qaD

2

CDD + pDCLP

2VqDCMQ

2VrDCMQ

2V

(14)

The canard moment is computed through a cross prod-uct operation similar to the steady body aerodynamicmoment. Air density is computed using the center ofgravity position of the projectile in concert with thestandard atmosphere [7].

The mathematical model described above has beenvalidated against spark range data for a generic 25 mmfin stabilized sabot launched projectile [8]. Agreementbetween the model and range data is excellent.

3. Configuration data

Consider a representative extended range field ar-tillery projectile that is fired from a 155 mm cannon.The projectile is 6 ft. long and weighs 120 lb. The pro-jectile is equipped with pop-out rear fins and forwardcanards. The mass center is located 2.75 ft. from thebase.

The body aerodynamic coefficients are shown inFigs 1 through 3 while the canard aerodynamic data isshown in Figs 4 and 5. Various size canards are con-sidered below, however, all canard configurations sharethe same aerodynamic properties shown in Figs 4 and5.

4. Simulation results

Figures 6 through 13 compare the nominal trajectoryand the extended range trajectory for the projectile de-scribed above. Range extension is accomplished with4 equally spaced canards, each with a reference area of0.07 ft2 or a reference area ratio of 0.35. A referencearea ratio of 0.7 represents a practical upper limit onwhat could be installed in a production round. The ini-tial forward body velocity is 750 m/s, the initial roll rate


Fig. 1. Body axial force coefficient (nd).

Fig. 2. Body normal force coefficient (nd).

is 31 rad/s, and the gun elevation is 45 degrees. The finsare slightly canted to provide a slowly rolling projec-tile in steady state. For the range extension trajectory,a proportional plus integral (PI) roll control system isused prior to canard activation. Both canards in the

body pitch plane are activated at the apex of the trajec-tory to an angle of 6 deg. Figure 6 compares range withand without movable canards installed. Under the con-ditions mentioned above, range is more than doubledfrom 17.5 km to 39.9 km. The small discrepancy be-


0 0.5 1 1.5 2 2.5 3 3.5 4-20

-15

-10

-5

0

5

Mach Number (nd)

Clp (Dash Dot)

Cmq/100 (Dashed)

Center of Pressure (Solid) 100*Cldd (Dotted)

Aer

odyn

amic

Par

amet

ers

(nd)

Fig. 3. Body aerodynamic parameters.

Fig. 4. Canard drag force coefficient (nd).

tween the nominal and canard configuration trajectoriesbefore the onset of the canard activation is due to dragof the canards, which are not present on the nominalprojectile. From the altitude time history, it can be seenthat the time of flight of the canard controlled projectile

dramatically increases from 71 to 195 sec. Subsequentto canard pitch activation, a slight steady state yaw ratedevelops that alters the azimuth of the projectile hencecreating a difference in the cross range between thetwo trajectories. As shown in Fig. 8, both the baseline


Fig. 5. Canard lift force coefficient (nd).

0 5 10 15 20 25 30 35 400

1

2

3

4

5

6

7

Range (km)

Alti

tude

(km

)

Fig. 6. Altitude vs. range (Solid = Nominal, Dotted = Extended).

and controlled trajectories have a 45 deg pitch attitudeat launch; however, the baseline trajectory pitch atti-tude monotonically decreases with time, whereas thecontrolled trajectory experiences some transient oscil-lations immediately after the pitch command is exe-

cuted. After transient oscillations settle, pitch attitudeof the controlled trajectory approaches a value of −10deg. The forward velocity time history, given in Fig. 9,shows the nominal trajectory impacts the target with avelocity of 300 m/sec compared to the controlled tra-


0 50 100 150 2000

1

2

3

4

5

6

7

Time (sec)

Alti

tude

(km

)

Fig. 7. Altitude vs. time (Solid = Nominal, Dotted = Extended).

0 50 100 150 200 250 300 350-80

-60

-40

-20

0

20

40

60

Time (sec)

Pitc

h A

ttitu

de (

deg)

Fig. 8. Pitch attitude vs. time (Solid = Nominal, Dotted = Extended).

jectory at a velocity of 166 m/sec. Furthermore, thereduced velocity shown in the controlled trajectory ispresent throughout a large portion of the flight. Theroll rate time history, given in Fig. 10, shows the PIroll control system eliminates roll rate from 31 rad/sec

to 0 within 5 sec whereas the baseline trajectory has asteady state roll rate due to rear fin cant. Roll anglecontrol is vital for this range extension strategy, sincethe pitch attitude commands assume the projectile willmaintain near zero roll angle from the start of pitch


0 50 100 150 200 250 300 350100

200

300

400

500

600

700

800

Time (sec)

For

war

d B

ody

Vel

ocit

y (m

/s)

Fig. 9. Forward body velocity vs. time (Solid = Nominal, Dotted = Extended).

0 50 100 150 200 250 300 350-5

0

5

10

15

20

25

30

35

Time (sec)

Rol

l Rat

e (r

/s)

Fig. 10. Roll rate vs. time (Solid = Nominal, Dotted = Extended).

commands to the terminal point. Figure 11 shows thetotal aerodynamic angle of attack of the projectile forboth the nominal and controlled case. The nominal an-gle of attack is small, less than half a deg. However, thecanards induce maximum angle of attack oscillations

slightly over 7 deg and a steady state glide angle ofattack of 4.1 deg. As canard angle of attack essentiallymimics body angle of attack, the canards can stall dur-ing the transient part of the response. Figures 6 through11 show a dramatic extension of range using body and


0 50 100 150 200 250 300 3500

1

2

3

4

5

6

7

8

Time (sec)

Tot

al A

ngle

of A

ttack

(de

g)

Fig. 11. Total angle of attack vs. time (Solid = Nominal, Dotted = Extended).

0 5 10 15

0.02

0.04

0.06

0.08

0.1

0.12

Command Angle (deg)

Range (km)20

20

2020

25

25

2525

30

30

3030

35

35

35

40

40

40

40 40

20

25

30

35

40

Can

ard

Are

a (f

t^2)

Fig. 12. Range vs. canard area and canard command angle.

canard lift that is achieved by pitching the projectileupward using movable canard lifting surfaces. Whilea dramatic increase in range is achievable, an equallydramatic increase in the time of flight and decrease inthe impact point velocity is realized. Thus, the action

of the moveable canards is to facilitate a transfer of ki-netic energy to potential energy, allowing the projectileto stay aloft longer.

Figures 12 through 14 show range, flight time, andterminal velocity for various canard areas and various


0 5 10 15

0.02

0.04

0.06

0.08

0.1

0.12

Command Angle (deg)

Time of Flight (sec)

100

100

100100

150

150

150150

200

200

200

250

250

80

100

120

140

160

180

200

220

240C

anar

d A

rea

(ft^

2)

Fig. 13. Flight time vs. canard area and canard command angle.

0 5 10 15

0.02

0.04

0.06

0.08

0.1

0.12

Command Angle (deg)

Terminal Velocity (ft/s)

150

150

200

200

200200

250

250

250250

300

120

140

160

180

200

220

240

260

280

300

Can

ard

Are

a (f

t^2)

Fig. 14. Terminal velocity vs. canard area and canard command angle.

canard command angles. For all data points in Figs 12through 14, the canard command was executed at theapex of flight. As would be intuitively expected, in-creasing canard area or the canard command angle in-creases range. However, when canard area is relatively

large, increasing canard command angle tends to re-duce range due to angle of attack vibration, which leadsto higher projectile drag. Also, for a given canard area,flight time is approximately constant for large com-mand angles.


25 30 35 40 4537.5

38

38.5

39

39.5

40

40.5

41

41.5

Command Time (sec)

Ran

ge (

km)

Fig. 15. Range vs. canard command activation time.

Figure 15 shows range versus time of canard activa-tion. For the case shown, the apex of flight was reached31.5 seconds into flight. Figure 15 shows that for max-imum range, the canard command should be executedat the apex of flight. Also, the curve is relatively sym-metric about the maximum range point.

5. Conclusions

Using a six-degree-of-freedom projectile trajectorysimulation model driven by projectile data representa-tive of an indirect fire field artillery round, it is foundthat a small set of four canards can dramatically extendprojectile range. The side effects of increased rangeusing this mechanism are: decreased terminal veloc-ity, increased flight time, increased nose-up terminalpitch attitude, and increased aerodynamic angle of at-tack. Moreover, maximum range is attained when thecanards are activated at the apex of the trajectory.

References

[1] R.W. Pointer and C.E. Dean, Cannon Artillery May One DaySoon Provide Crisis Logistics To Ground Forces, National DE-FENSE LXXX(518) (May 1996).

[2] C.E. Dean and W.P. Wiesman, Combat Resupply by Artillery,Army RD&A PB70-96-1 (January 1996).

[3] USAF Stability and Control DATCOM, AFFDL Wright Patter-son AFB, Ohio, November 1965.

[4] J.A. Smith, K.A. Smith and R. Topliffe, Feasibility Study forApplication of Modular Guidance and Control Units to Exist-ing ICM Projectiles, U.S. Army Armament Research and De-velopment Command, Contractor Report ARLCD-CR-79001,November 1978.

[5] B. Etkin, Dynamics of Atmospheric Flight, John Wiley andSons, New York, 1972.

[6] C. Murphy, Free Flight of Symmetric Missiles, BallisticsResearch Laboratory Report BRL-1216, Aberdeen ProvingGround, Maryland, 1963.

[7] R. Von Mises, Theory of Flight, Dover Publications Inc., NewYork, 1959.

[8] M. Costello and D. Anderson, Effect of Internal Mass Unbal-ance on the Stability and Terminal Accuracy of a Field ArtilleryProjectile, Proceedings of the 1996 AIAA Atmospheric FlightMechanics Conference, San Diego, CA, 1996.

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