LESTER L. CRONVICH

MISSILE AERODYNAMICS

This article describes the role of the aerodynamicist as a member of a missile development team, the preliminary design tools available to him, the potential problem areas in designing aerodynam­ ically efficient configurations, and the types and sources of aerodynamic data needed during the en­ gineering development and flight-testing process. The discussions deal primarily with tactical sur­ face-to-air missiles, although the general development philosophy also holds for other types.

SETTING DESIGN REQUIREMENTS configuration can be established from which further The goal of the development team is to develop a development can proceed. tactical missile system either to counter an expected threat to one's own defended area (a defensive sys­ TECHNOLOGY INTERFACES WITH tem) or to destroy or do significant damage to the en­ AERODYNAMICS emy's defended area (an offensive system). For the Launching aerodynamicist, this means designing the external configuration of the airframe so as to provide suffi­ Besides restricting the missile's weight, length, and cient capability (speed, range, and maneuverability) span, the launching system may restrict its permissi­ to accomplish the mission planned for the system. ble motion early in flight. Also, such factors as the The first task of the team is to ascertain the threat motion of the launcher and winds or extraneous flow and, on the basis of feasible battle scenarios, develop fields about it will affect the missile's design. The ex­ a missile system concept to counter it. That concept ternal shape might also be affected by launching will establish broad requirements in most technol­ shoes or other devices that guide the missile out of ogies. The aerodynamicist must carry out his prelimi­ the launcher. Such appendages add drag and weight nary design study while recognizing the limitations and can affect the missile's stability or controllabili­ on his options that are imposed by necessary choices ty. The span limitation for a given launching system in the other technologies or subsystems, as indicated may require lifting and control surfaces to be folded, in Fig. 1 and discussed in the next section. The mis­ which adds to missile weight and drag and introduces sion analysis should lead to design goals for range, a potential dynamic disturbance during deployment. speed, and maneuverability of the missile, to fuzing The aerodynamic design must be done with full and warhead needs, and to an overall guidance phi­ knowledge of these considerations so that detrimen­ losophy. At this stage, first-cut individual choices tal effects can be minimized. can be made by the several related technologies to achieve the mission. Modifications to those choices Propulsion will be made as more-detailed interrelated studies of A missile's shape may depend strongly on its pro­ subsystem performance are made. Thus, a baseline pulsion system. Designers of airbreathing systems

Figure 1 - Factors and systems affecting the design of aerodynamic configurations.

Vo lume 4, N umber 3,1983 175 L. L. Cronvich - Missile Aerodynamics prefer to locate the air inlets in areas free of degrad­ 1.0~------' Mach 3 / N ing aerodynamic interference such as shock waves, fineness ratio = d = 3 vortices, or wakes. At the same time, the inlet itself may degrade the aerodynamic performance. Thus, a S: 0.5 compromise must be made between propulsion per­ cJ formance and aerodynamic performance, or, if pos­ sible, a design should be sought that takes advantage of favorable interactions that improve thrust, lift, stability, and controllability or that reduces drag. Blunted Hemisphere- As fuel is consumed, the center of gravity may Cone Ogive cone cylinder shift, thereby changing the controllability of the mis­ sile. In general, the center-of-gravity shift is more troublesome with solid-fueled propulsion systems than with liquid-fueled propulsion systems, which T have more flexibility in the location of fuel tanks. Offsets of the thrust axis from the center of gravity may also occur for certain propulsion systems (e.g., strap-on booster systems) or may result from design tolerances or from center-of-gravity travel that I moves the center of gravity off the thrust axis. Such I-d-l Figure 2 - The effect of sensor dome bluntness on the offsets can result in overturning moments that re­ wave drag coefficient, Cow' quire additional control capability from the air­ frame. Guidance well forward on the missile, tail controls located well aft, and wing controls located near the midbody. Al­ The choice of guidance system will affect the de­ though several early missiles used wing control mands on missile maneuverability and response, (Talos, Terrier I, J and Sparrow), the missiles requir­ which, in turn, may affect the choice of lifting and ing high maneuverability generally resort to tail con­ control surfaces. Furthermore, the design of domes trol. With canard control (Fig. 3a) or tail control to protect guidance sensors usually calls for com­ (Fig. 3b), maneuverability is achieved by having the promises. For example, a hemispherical dome is usu­ entire airframe at an angle of attack to the airstream ally considered the optimum choice for the sensors, and is controlled by forces from small surfaces at a but it has high drag. A dome with a high fineness large distance from the missile's center of gravity. A ratio (i. e., length/ diameter ratio) has low drag, as wing-controlled missile (Fig. 3c), on the other hand, shown in Fig. 2, but tends to degrade the reception of operates at a much smaller angle of attack and de­ signals by the seeker. A guidance system that uses in­ rives a large portion of its lift from the deflected terferometric homing with spike-like antennas at the wings. Canard controls can be placed near their nose of the missile (as the Talos missile did) can have source of information - the guidance package (which significant effects on the stability and control as well is usually far forward) - but their effectiveness may as on the drag of the configuration. Air-data probes be partially compromised by "interference" needed for setting autopilot gains (as in the Terrier I moments from surfaces situated downstream from missile) or for regulating fuel flow may' have similar them. In some cases the control moment from for­ effects, depending on their placement. ward controls (canard or wing) may be greatly dimin­ ished or even reversed2 through interference Warhead and Fuze moments from the aft surfaces. An illustration of in­ The demands of the warhead and fuzing on the terference effects for the wing-controlled missile of aerodynamic performance occur primarily during the Fig. 3c is shown in Fig. 4. The force normal to the brief interval prior to target engagement when the missile centerline (proportional to the coefficient CN) missile should be placed in a position and an attitude increases nearly linearly with wing incidence when that will maximize the kill by the warhead. The other the body is lined up with the flow (ex = 0), as shown subsystems (guidance, control, propulsion) must in Fig. 4a. When the tails are not present, the force is work in concert with the airframe to provide this given by the colored curve. The down wash on the favorable condition. tails from the deflected wings produces a downward The aerodynamic design is also influenced by the force, causing the resultant force on the configura­ location of the warhead (usually a very dense pack­ tion to drop to the black line. This downward force age) because it affects the missile's center-of-gravity results in a nose-up pitching moment (proportional location and travel. to the coefficient C IIJ that overpowers the nose-down pitching moment from the wings (colored line in Fig. Autopilot and Control 4b) to yield a resultant nose-up pitching moment for Three aerodynamic control systems use all­ the full configuration (black line). The effect of movable control surfaces: canard controls located down wash is the difference between the two curves in

176 Johns Hopkins A PL Technical Digesl L. L. Cronvich - Missile Aerodynamics

2~------~------.------' (a) Sidewinder (a) Body-wing Body-wing-tail Mach 2.5, a = 0, ¢ = 0 <: CJ

(b) Tartar 0

<:::_-.....,..-:'------;@ 0.4

1:: CJ 0 (c) Terrier I test vehicle-model

@ -0.4 0 5 10 15 Wing incidence (iw)

Note: Control surfaces are shaded Figure 4 - The effect of downwash from wing on tail as a function of wing incidence, iw. Figure 3 - Types of aerodynamic control.

each case. Other types of aerodynamic controls are banking (or rolling) to the desired direction and pull­ tip controls and trailing edge controls in which only a ing the maneuver in that direction. This is appropri­ portion of an aerodynamic surface is rotated to pro­ ate for a configuration with a preferred lift direction duce control forces. (e.g., a ramjet missile with an air inlet on one side or With thrust vector control, the flow leaving the ex­ a missile with a single pair of wings). Some compari­ it nozzle is deflected to produce a pitching moment. sons of homing performance have been made3 for Obviously this system is operable only when the en­ selected configurations using skid-to-turn or bank­ gine is delivering thrust. Such systems are well suited to-turn steering policies. to quick reaction when aerodynamic forces are low, In summary, the aerodynamic configuration de­ such as for turning a missile shortly after it leaves its pends strongly on the requirements of the other mis­ launcher or for a rocket missile at an extremely high sile technologies; therefore, achievement of the de­ altitude when aerodynamic forces are small. Control sign goal is usually attained by compromising among by means of side jets, augmented by natural aerody­ them all. namic interference, has been used on some short­ range missiles but may not be adequate for high-per­ PRELIMINARY AERODYNAMIC formance, medium- to long-range tactical missiles. Thus, the type of control system chosen will deter­ DESIGN TOOLS mine the locations of lifting and control or stabilizing In preliminary design, the aerodynamicist may use surfaces and will have a major effect on the missile's the following tools to develop a baseline configura­ stability and control characteristics. tion and to assess the effects of potential configu­ The choice of autopilot to provide proper signals ration changes: to actuate the controls that guide the missile to the target depends on the airframe and controls selected. 1. Existing experimental data bases; For example, with a skid-to-turn autopilot, a missile 2. Theoretical methods; achieves a maneuver in a given direction by pulling 3. Handbooks of theoretical, semi-empirical, and maneuvers in two component directions at right an­ empirical design charts; gles to each other. Such an autopilot is appropriate 4. Computer programs, including computerized for a cruciform configuration, which has equal lift­ handbooks, computerized theoretical methods, ing capability in two mutually perpendicular direc­ computerized data bases, and computational tions. On the other hand, with a bank-to-turn auto­ aerodynamics; pilot, the missile achieves the desired maneuver by 5. Exploratory wind tunnel tests.

Volume 4, Number 3, 1983 177 L. L. Cronvich - Missile Aerodynamics Existing Experimental Data Bases C - -2 al-( VOlUme)- -- (3) 11/ IS' Whenever practical, a designer will base the pre­ base liminary design of a missile on an existing data base for similar configurations and use interpolation or extrapolation as necessary. For example, in an evolv­ where a is the angle of attack in radians, I is the body ing program such as Standard Missile, there is a length (reference length), S base is the base area wealth of data for the preliminary design of ad­ (reference area), and the reference center for C n is vanced versions. With such data, the designer can not the vertex of the nose. The wave or pressure drag: on only get the baseline design started but can also plan the other hand, requires integrations involving sec­ ond derivatives of the axial distribution of the cross­ the necessary wind tunnel test program. 4 In general, it is possible to compile data (forces sectional area. and moments) on the several components of a config­ Eliminating the slenderness restriction but still uration (body, wings, tails, etc.) with reasonable con­ having the restriction of a small perturbation, the fidence for moderate angles of attack and Mach first-order (or linear) theory was applied, which led numbers. More difficult is the assessment of aero­ to theories for axial flow (giving the dragS) and in­ dynamic interactions or interference among those clined flow (giving the lift and the pitching moment 6 components that add to the total aerodynamic be­ at small angles of attack ). The equations had to be havior of the missile. Thus, a data base with full-con­ solved numerically. Similar solutions for ducted bod­ figuration data, complemented with data on its com­ ies of revolution were also obtained, including the ef­ ponents, is very important because the interference fect of the deflected air entering the duct. 7,8 Further effects can be extracted. improvements, using an iteration process, led to the The usual design approach consists of building up second-order theory by Van Dyke,9 which also re­ the aerodynamic characteristics of a full configura­ quired a numerical integration. Since the second­ tion from a knowledge of the characteristics of its order theory could handle axial flow but not cross component parts, augmented by estimates of the mu­ flow, a hybrid theory combining second-order theory tual interference of the parts. The acquisition of in­ for axial flow and first-order theory for cross flow formation on interference phenomena has usually was adopted. Even with pretabulated functions, the lo lagged behind the development of methods for cal­ second-order axial calculations were tedious. With culating the aerodynamic behavior of individual modern computers the solutions became more feas­ components. As Mach number and angle of attack ible and were included in the original Naval Surface increase, the interference effects become much more Weapons Center (Dahlgren) computer code. II A complex and more difficult to predict. A reliable set more exact method for axial flow is the method of of test data on the full configuration is required for characteristics (e.g., Ref. 12), also too tedious for the detailed engineering design of the missile. If the preliminary design calculations. Several of these design requirements point to a configuration con­ methods provide pressure distributions in addition to siderably different from those contained in the exist­ forces and moments. ing data bases, one may turn to other methods dis­ The foregoing perturbation methods are satis­ cussed in the following subsections. factory for the lower supersonic regime. Other meth­ ods were developed for higher speeds. The most fre­ Theoretical Methods - Inviscid Flow quently used are the generalized shock-expansion method 13 and an improvement on it, the second­ Bodies. Most early developments in supersonic order shock-expansion theory, 14 both of which are missile aerodynamics started with the assumption of based essentially on the fact that at high speed, with a inviscid flow that was given a small perturbation by high body fineness ratio, the flow can be considered the movement of the missile. If the body were suffi­ to be locally two-dimensional, so that basic shock­ ciently long and thin, the "slender body" theory wave and expansion-wave theories are applicable. could be used to describe the perturbed flow. A lin­ For even higher speed, the noses of the bodies are earized partial differential equation, the potential usually blunted to alleviate a local thermal condition; equation, described the flow field. That simple solu­ to account for blunt noses, the calculation procedure tion yields estimates of dimensionless coefficients of has been modified to allow the use of the Newtonian lift (C ) and drag due to lift (COL ) that are indepen­ L impact theory over the forward portion of the body dent of Mach number and body shape (within the and an appropriate matching at some location where slenderness restrictions of the theory) and of the stat­ the shock-expansion theory can proceed. 15, 16 For very ic pitching moment (CI/, ) that depends on missile high Mach numbers, the Newtonian impact theory is volume: appropriate. 17 Although much effort has been expended on the theoretical analysis of base flow (with and without CL =2a, (1) I 8 the effects of propulsive jets ), one generally has re­ course to empirically derived design charts for esti­ mating base drag because the theoretical flow models (2) are quite complex.

178 Johns Hopkins APL Technical Digest L. L. Cronvich - Missile Aerodynamics For the transonic flow problem, great effort has been expended in analyzing the flow fields for a var­ iety of conditions (e.g., Ref. 19), but the calculations are very tedious because the perturbation equations are nonlinear and require numerical integration. Sub­ sonic flow has been handled by the slender body theory and linear theories (as was supersonic flow). The solution in the slender body theory, C L = 2, as­ sumes potential flow. The linear theory solutions20 are satisfactory for incompressible flow (Mach = 0) but generally require a compressibility adjustment at 4 higher subsonic Mach numbers. In the design of Mach 2 high-speed, high-performance missiles, the greatest Mach 4 needs are at high angles of attack, and they cannot 3 - be handled by the aforementioned perturbation - methods.

Thin Lifting Surfaces. Most early theoretical ap­ Cj proaches to the problem of inviscid flow about wings u-..J 2 resulted in solutions of the linearized potential flow equation for thin wings at small angles of attack. 21 ,22 Although the solutions for zero-lift wave drag and slopes of lift and pitching moment coefficients have been published for a variety of wing planforms, their applicability to higher angles of attack is somewhat limited. Higher-order approximations are best ob­ o Wing Body on Wing on Total tained by turning to two-dimensional wing theory, alone wing body which is the basis for the so-called shock expansion theory mentioned for bodies. Using two-dimensional ---Interferencev---- theory along stream wise strips does not account for Figure 5 - Wing-body interference - linear theory. the tip losses inside the Mach cone associated with the disturbances from the outermost point of the leading edge. However, as the Mach number in­ On the other hand, when lifting surfaces are in tan­ creases and the Mach cone angle decreases, the af­ dem (such as a canard followed by a wing or a wing fected region becomes smaller, so that the approxi­ followed by a tail), the flow past the forward surface mation may be satisfactory. is deflected (down wash) and also loses energy so that less lift is produced on the aft surface. These effects Interference Effects. When a lifting surface is at­ determine the so-called efficiency of the aft surface. tached to a body, the aerodynamic forces on the Although there are many techniques for calculating combination generally exceed the sum of the forces the downwash, such calculations26 may not be war­ on the isolated elements because the two flow fields ranted if one needs only a rough estimate of tail lift­ interact. ing efficiency for preliminary design. A research program on supersonic wing-body in­ teraction was conducted in the Bumblebee program Combined Angles of Attack and Sideslip. Most at Cornell Aeronautical Laboratory in 1947-1951. 23 ,24 theoretical approaches have been developed for cases It provided theoretical methods for calculating the in which the missile or one of its components is at an velocity potentials corresponding to the flow pertur­ angle of attack to the flow with no sideslip. One can bation of the body on the wing and the wing on the also obtain effects of sideslip with zero angle of at­ body. The methods were validated by detailed pres­ tack. But the problem of combined angles of attack sure measurements. Although the results have pro­ and sideslip, a truly three-dimensional problem, is vided a better understanding of the flow phenomena, not easily handled by these theoretical methods. the designer can obtain satisfactory engineering ap­ Some of the most recent attacks on the problem have proximations with less effort using the method of been made by Nielsen et al. 27 Morikawa. 25 The solutions are meant to be restricted to small angles of attack and moderate supersonic Full Configurations. The characteristics of a full Mach numbers for wing-body configurations with no configuration are calculated theoretically by combin­ afterbody. Nevertheless, the so-called Morikawa fac­ ing the characteristics of the component parts and tors have been used successfully over a wider range of their mutual interferences. The results are limited by parameters. An illustration of the several compo­ whatever restrictions are inherent in the theories for nents contributing to the total lift resulting from the components and their interferences. Consequent­ wing-body interference is given in Fig. 5 for a delta ly, nonsymmetrical configurations are usually very wing mounted on a cylindrical body. difficult to deal with theoretically.

Volume 4, N umber 3, 1983 179 L. L. Cronvich - Missile Aerodynamics Theoretical Methods - Viscous Effects used, i.e., a set of linear partial differential equations The two most important viscous effects are those of potential flow is solved numerically by using "sin­ in the flow direction that produce skin friction drag gularity strengths" on the set of panels to describe and those normal to that direction (cross flow) that the configuration geometrically. The configurations produce additional lift and pitching moment at can be arbitrary in shape. higher angles of attack. To calculate skin friction drag during preliminary design, the aerodynamicist Mark IV Supersonic-Hypersonic Arbitrary Body generally treats the missile configuration as a set of Program - AFFDL (by McDonnell Douglas). 35 .36 simple geometric elements (flat plates, cylinders, etc.) As an engineering approach to preliminary design, on which the turbulent skin friction drag can be cal­ methods are used that can handle configurations not culated by a method such as that of Ref. 28. This skin suited to linear theory without going to the method friction drag is combined with wave and base drags of characteristics or to finite-difference techniques. to give total missile drag. The additional lift and Many analytical techniques are programmed; the pitching moment resulting from viscous cross flow user makes the choice of what is best for his problem. are calculated by a method such as that given in Ref. The configuration is represented geometrically by 29. They are combined with the inviscid lift and sets of quadrilaterals (panels) on which the forces are pitching moment to give the totals for the missile. calculated. The code is applicable from Mach 2 up to very high Mach numbers. Entering the geometry of Handbooks the configuration is a tedious task. Many of the foregoing theoretical methods and Numerical A eroprediction Code - NS WCI some of the wind tunnel and flight data have been as­ 37 38 sembled into handbook form as curves and tables so WO. , The inviscid supersonic flow field about that preliminary design can proceed by a build-up finned configurations is calculated by finite dif­ process without individual calculations having to be ference techniques using mesh spacing that is ad­ made. The most well known of these handbooks are: justed to improve accuracy in regions of expected large flow gradients. It is best suited for selected 1. Handbook of Supersonic Aerodynamics, check calculations because it requires much more NA YORD Report 1488 (published between computer time than, for example, the Approximate 1950 and 1966), Aeroprediction Code. Also, it provides much more 2. Royal Aeronautical Society, Engineering Sci­ detailed information at each condition. Before using ences Data Units (Aeronautical Series, Aero­ any such code, the user should see how well the dynamics Sub-Series) (published between 1943 calculations have agreed with test data on configura­ and the present), tions similar to those being considered for the design. 3. U.S. Air Force Stability and Control DA T­ COM (initially issued in 1956 and updated Exploratory Wind Tunnel Tests periodically). It is always desirable to carry out exploratory wind The DA TCOM has been computerized so that tunnel tests, guided by the calculations discussed in much of the data extraction from families of curves previous sections. Such tests should be aimed at de­ has been speeded up, but preparation of the input to termining the variations from a basic design by mak­ the program is time consuming. Consideration is be- ing configurational changes in the components, by • • 30 109 gIven to the development of a handbook (based spanning the expected Mach number and angle-of­ on DA TCOM) aimed specifically at missile design attack ranges, and by validating the calculations (rather than at general aircraft design as was the ori­ made for the baseline configuration. In addition, ginal DA TCOM) . measurements at nonsymmetric conditions (such as a cruciform configuration maneuvering out of its Computer Programs planes of symmetry) are needed to assess yaw and roll The following four programs now being used are stability not easily calculable by standard methods. representative of those that exist: Measurements of hinge moments of control surfaces Approximate Aeroprediction Code- NSWCI are needed for sizing control servos. It must be re­ 3 1 membered, however, that these moments may be DL. ,32 Available analytical and empirical proce­ dures are used to calculate static and dynamic coef­ changed considerably in the design process by config­ ficents for configurations with axially symmetric uration modifications upstream of the surface. The bodies and stream wise wing and tail tips. The re­ selection of a final hinge line must take into account such modifications. ported region of validity is 0 < M < 8, 0 < Q' < 0 180 , although this region does not hold for all com­ ponents. It is useful for early design studies when PROBLEM AREAS IN CONFIGURATION drag, normal force, and longitudinal static stability DESIGN are the primary concerns. Geometric Limitations PANAIR-NASA (by Boeing Military Airplane Geometric limitations usually result from the CO.). 33,34 In this program, "panel methods" are compatibility requirements of the launching and han-

180 L. L. Cronvich - Missile Aerodynamics dling systems. Restrictions on length place a limit on mal force from the body to the wing and from the available body lift (or normal force). The slope of the wing to the body also tends to lessen the difference normal force coefficient curve, CN ,generally tends attributed to the difference in aspect ratio. An illus­ to increase with body fineness ratio' (Fig. 6) although tration of the total potential normal force from linear this behavior also depends on the Mach number and theory is presented in Fig. 8 (curve W + W 8 + B w). fineness ratio of the nose section. Since normal force The contribution from the wing alone (curve Jf') resulting from viscosity is a function of cross-flow decreases with the reciprocal of the aspect ratio, drag, the normal force coefficient, C N ' also increases whereas the total C N ,induding interference effects, with body fineness ratio because there is an increase peaks near AR = 0.5 for those rectangular wings of body planform area on which the cross flow can evaluated at Mach 2.24. act. The variation of CN with fineness ratio and angle Another limitation is the space available for con­ of attack is shown in Fig. 7 for bodies at Mach 7.69. trol servos of tail-controlled configurations. The ser­ A further observation is that the Newtonian theory vos are usually housed in the annular volume around agrees quite well with experimental data at that Mach the throat of the propulsion nozzle. Optimum design number except at low angles of attack. requires careful attention to the selection of an ap­ Restrictions on the span of stabilizing and control propriate hinge line for control surfaces in order to surfaces result in surfaces of lower aspect ratio, AR, minimize torque requirements over the missile's full that generally produce a smaller slope of the normal operating range. This spatial limitation is generally force curve than those of higher aspect ratio having more severe for a ramjet missile than for a rocket the same planform area, as is shown in Fig. 8 (curve missile because the former requires a larger nozzle Jf'). Because the viscous normal force at angle of at­ throat area to accommodate the greater mass flow tack depends primarily on the planform area, the to­ from the combustion chamber. tal normal force (potential plus viscous) does not show as great a variation with aspect ratio as does the Center-of-Gravity Travel slope of the normal force curve. The carryover nor- The static stability of a missile is a measure of its tendency to return to its equilibrium attitude after be­ ing disturbed. It depends on the relative location of 0.08 Ogive - cylinder the center of gravity (the point at which the resultant of the inertial forces acts) and the center of pressure 2.84 0.06 ~N = (the point at which the resultant of the aerodyamic Q) ~ Mach 4 Cl Q) "tj 8. 0.04 Panel aspect ratio, (j AR = ble <: <...> 0.02 d

OL-____L- __~ ____~ _____L __ ___L ____ ~ o 2 4 6 8 10 12 lid Figure 6 - The effect of fineness ratio on the body normal force coefficient. 3 5 Wing plus interference rN ()c .l (W + W8+ BW) <~ - --Id 4 I N ' - c: 2 t ~f cg _ •• Data x I 'old :.c -8.33 ~ 3 -- Theory ... Q) 6.33 Cl. rJ (j <: 2 4.33 C,.)

0L------2L------4L------~6------8 4 8 28 0' (degrees) 1/AR Figure 7 - The effect of aft body length on the normal Figure 8 - The effect of wing-body interference on the force coefficient. slope of the normal force coefficient at Mach 2.24.

181 L. L. Cronvich - Missile Aerodynamics forces acts). A very stable missile has its center of coefficient. If intercept occurs at high Mach number, pressure well aft of its center of gravity and requires a this center of pressure movement with Mach number, large control authority to maneuver it to another which favors instability, is desirable because the de­ position. For a highly maneuverable missile, it is mand on control moment is lessened. desirable to minimize the margin of stability. Consideration must be given early in the design In the case of missiles propelled by solid rockets, process to the maneuverability requirements at the the change in the center of gravity from ignition of highest altitude because maneuverability depends on the rocket to burnout may be large, so the spread in controllable lift. The latter depends on the configura­ static stability for a given Mach number may also be tion lift coefficient attainable with the available con­ large. In order for the missile to accomplish its mis­ trol authority and the dynamic pressure, q, at which sion (near or after burnout), it must be maneuverable the missile will operate: near the target, at which time the center of gravity is usually in a very forward position. The forward posi­ lift (lb) Maneuverability (in g) = tion favors stability and thus requires a large control weight (lb) - authority. If the missile is designed for very low sta­ S bility at that condition, it may result in unacceptable CLq-, and instability early in flight when the center of gravity is W in an aftward position. Since the center of pressure of q= 'Y PM 2 a configuration varies with Mach number, it is clear 2 , that the designer should consider simultaneously the time histories of center-of-gravity travel and Mach where C L is the lift coefficient, S is the reference area

number in establishing margins of stability. upon which C L is based, W is the missile weight, pis the static pressure at the flight altitude, and 'Y is the Spread in Mach Number and Altitude ratio of the specific heats of air. The center of pressure of a configuration varies For example, at the same speed and for the same with Mach number. Each component contributes to maneuver, the missile needs a lift coefficient at 80,000 ft altitude that is more than 40 times the sea­ this variation. As Mach number increases, CN for the body varies only slightly, and the center of pressure level value. Dynamic pressure is also an important (with a few exceptions) moves aft slightly (Fig. 9). C , parameter in designing the autopilot and in selecting for the tails decreases (nearly inversely with Mach its gain program. number), and the center of pressure varies only slightly. As a result, the center of pressure of such a High Angle-of-Attack Phenomena body-tail configuration moves forward with increas­ High angle-of-attack (0') phenomena arise at both ing Mach number because of the lowered tail force ends of the Mach number regime. During launch, un-

4 I I ¢ = 0° a 3- ~ - 20° <: Body <....> 2- -

1 r--12°------4° 4° ------0 4 Body 5 20° ~~: ~ 4 3 Body-tail Figure 9 - The normal force co­ 12 ° ~ efficient and center of pressure­ G body, body-tail, tail plus carry­ 2 over.

0'---__--'-- __----''--- __---' 3,-----,------,----,

2 All carryover a

12 ~ __....L. __ --I ___ .....J 0'------'------''------' 1 2 3 4 1 2 3 4 Mach nllmber Mach number

182 Johns Hopkins APL Technical Digesl L. L. Cronvich - Missile Aerodynamics der conditions of launcher motion and high winds, during each stage, taking into account the Mach the low subsonic motion of the missile may occur number and altitude regimes covered by it. A key with high angle of attack where the stability char­ problem to be attacked early in the preliminary de­ acteristics are very nonlinear and the control ef­ sign is the separation of the stages so as to avoid any fectiveness is limited because of low dynamic pres­ possible recontact if the relative drag and thrust sure on the surfaces. The dynamic motion required to forces are not sufficient to ensure clean separation. achieve the proper attitude may dictate a need for a In addition, the presence of the separating stage (the supplementary launch-phase control system or may booster) from the continuing stage (the missile) may impose additional requirements on an aerodynamic result in an interference that adversely affects the control system intended for the entire flight phase. missile's stability. It is important that the control sys­ During the high subsonic and transonic phases, if the tem be designed to cope with this change in stability missile is required to operate at high angle of attack and that it be activated without excessive delay. in order to maintain its position in a desired trajec­ tory, it may experience a shedding of unsymmetrical DATA NEEDED FOR DETAILED DESIGN, vortices from its lee side, resulting in side forces and FLIGHT TESTING, TROUBLE SHOOTING moments on a symmetrical airframe in a symmetrical Various methods to provide aerodynamic data for attitude. 39 This phenomenon may present another preliminary design were described earlier. Many of control problem. the problems discussed in the previous section cannot Another high angle of attack phenomenon is that be addressed using the type of data provided by those of coupling between the yaw and roll modes of mo­ methods. Thus, early planning should be made for tion (pitch-yaw-roll coupling). 40 Coupling occurs detailed wind tunnel testing to provide the data when the missile attempts to maneuver in the yaw needed for such critical analyses. direction while pulling a large maneuver in the pitch direction. Increased loading on the windward sur­ Three-Dimensional Data for faces (behind the strong body shock waves) and decreased loading on the lee side (in vortex flows) Six-Degree-of-Freedom Simulation combine to produce instabilities in roll and yaw and A six-degree-of-freedom simulation should be able induced moments resulting from the roll and yaw to describe the missile motion in three translational control deflections that are required to counter those and three rotational modes. The appropriate aerody­ instabilities. The phenomenon is highly dependent on namic forces (axial, normal, lateral) and moments the configuration's shape and attitude in roll. A pro­ (pitching, yawing, rolling) must be provided as func­ per design study of this phenomenon requires a coor­ tions of Mach number, altitude, angle of attack, dinated effort between the autopilot designer and the angle of sideslip, and control deflections in pitch, aerodynamicist in order to achieve maximum con­ yaw, and roll. A well planned wind tunnel testing trollable maneuverability. The data necessary for program must be conducted to acquire these data ef­ such an investigation should be obtained from de­ ficiently and economically. First, one must decide tailed wind tunnel tests that provide a three­ how the data will be used and what format might be dimensional description of the aerodynamic forces best for the simulation. Those factors will have sig­ and moments. nificant influence on the test plan. Wherever pos­ sible, advantage should be taken of known sym­ Launching Environment metries or known regions of small variations in the The housing of a folding mechanism may require expected data in order to reduce the required testing. additional thickness of the inboard cross section, The aerodynamic data will be needed in the engi­ thereby adding to drag. Furthermore, one should in­ neering design phase in order to design the autopilot vestigate the dynamic behavior of the missile during and to check it out over a wide range of potential ma­ deployment of the surfaces, which usually occurs neuvers. The aerodynamicist should assist in plan­ while the missile is under the influence of somewhat ning the flight tests and in analyzing the flight data to random flow fields near the launcher. validate the aerodynamic description of the configu­ The environment of shipboard launchers includes ration. He also should assist in troubleshooting when the ship's angular motions, relative winds, disturbed flight anomalies appear. The money spent in provid­ flow fields about the superstructure, and enveloping ing a proper three-dimensional representation of the gases from the missile's own rocket, each of which aerodynamic characteristics is well spent if it makes taxes the missile's controllability. In the case of possible a more productive and less costly flight test launching from aircraft, the aerodynamic interfer­ program. ence between the flow fields of the aircraft and those of the missile is a major factor to be considered and Pressure Distributions, Panel Loads, has been investigated extensively in recent years. 41 and Moments Pressure distributions may be needed for structural Staging design and for thermal analysis. In some cases, they For a multistage missile, one must be concerned may be obtained with sufficient accuracy for prelim­ with the aerodynamic design of the full configuration inary design from theoretical calculations or from

VO /Ul l1e 4, N umber 3, 1983 183 L. L. Cronvich - Missile Aerodynamics computer codes using finite difference methods to tic effects are usually accounted for by making a calculate the flow fields. For critical conditions that "quasi-static" correction. A structural analysis, may involve complex flow fields and shock waves in­ which depends on a sufficiently accurate distribution teracting with each other or with the boundary layer, of air loads and inertial loads, must provide the de­ or impinging on surfaces, it is usually necessary to in­ scription of the distorted shape. The distorted shape clude some wind tunnel tests with a pressure model essentially describes the changes in angle of attack or and with flow visualization techniques to be able to incidence of the various elements of the configura­ identify critical areas of high temperature or pres­ tion. Forces and moments resulting from the changes sure. Because the volume inside the model is limited, are added to those of the rigid body to give the quasi­ the number of points at which pressure may be mea­ static aerodynamics of the configuration. The pro­ sured is also limited. Thus, it is important to confine cess is iterative but converges rapidly for a properly measurements to areas of expected high pressure gra­ designed airframe. Figure 10 illustrates the effect of dients and to limit them in areas of low pressure elasticity in the Talos missile. gradients. When panel flutter may be a design prob­ lem, pressure distributions are needed for the aero­ Dynamics of Separation elastic studies. At separation of the missile from the booster in a Accurate measurements of control surface hinge two-stage vehicle, at least two goals are sought. The moments are required for sizing the control servos. first is a clean, quick separation. That condition can The design goal is to choose a hinge line that min­ be ensured if the axial forces on the booster greatly imizes the hinge moments over the entire flight re­ exceed the axial forces on the missile at the instant of gime. A surface planform and cross section is desired separation. If the booster cross section is sufficiently with minimum center-of-pressure travel over the full larger than that of the missile and if the booster range of Mach number, angle of attack, and angle of thrust tail-off is steep, a clean, quick separation incidence for the various roll orientations. An impor­ should be expected since such a relationship between tant caution is that any changes in the geometry of axial forces should exist. One factor that might op­ the surface or of the missile ahead of the surface are pose a clean separation is the existence of an angle of likely to affect the hinge moments. For that reason, attack on the missile-booster configuration at separa­ detailed hinge moment measurements are usually tion; that factor could result in individual dynamic postponed until the preliminary design has reached motion of the missile and the booster where each the point where only minor modifications are ex­ could be affected by the other. The angle of attack pected. Theoretical estimates of hinge moments are may result from the use of guidance during the boost­ rather tedious to make and are not very reliable be­ phase of flight or, for an unguided boost phase, from cause the center of pressure of the control forces can­ manufacturing misalignments (particularly in the not be calculated with the needed accuracy as a result booster fins and rocket nozzle) that could cause a sta­ of the complex flow conditions associated with angle ble configuration to seek an equilibrium angle of at­ of attack, roll angle, and control deflections, and of tack to balance the resultant pitching moments. the many interferences from the body, the forward surfaces, or protuberances. It is customary to mea­ 4 sure panel normal loads, hinge moments, and span­ :§ --Rigid wise bending moments simultaneously. If the model Q) (.) c: -- Aeroelastic size permits, the measurements are obtained at the Q) ~ same time that the six components of force and mo­ '(j Sea level ,S ment are measured on the full configuration. 3 A considerable effort was expended in arriving at a E.... c: wing planform for the Talos wing-controlled missile 0 in order to minimize the wing hinge moments. 42 That (.) 0 planform proved to have the desired limited center­ -Q) Sea level Q) ""'" ""- of-pressure travel and has been used for the control g2 ------surfaces of Terrier, Tartar, and the Standard Missile ~ -- family. The hinge line location (in percent of root ~ chord) has been adjusted according to the Mach > ~ number regime to keep the center-of-pressure travel :0 ~ to a minimum and thus to minimize the design hinge Q) ::s> moment. Q) c: ctI Effects of Elasticity on Aerodynamics E 60,000 feet altitude E Under sufficient loading, a missile may change its ~ a shape and thereby cause changes in its aerodynamic 2.0 2.2 2.4 2.6 2.8 characteristics. 42 The body may bend as a freely sup­ Mach number ported beam, the surfaces may "wind-up" about the Figure 10 - The effect of aeroelasticity on maneu- hinge line, and the shaft itself may twist. These elas- verability,

184 Johns Hopkins A PL Technical Digest L. L. Cronvich - Missile A erody nalllics

Figure 11 - Missile booster, first stage. Figure 12 - Missile, second stage.

Instru mented Retracting mechanism missile model

Figure 13 - Missile booster, sep­ aration test model.

\LaunChing lugs Booster headcap (movable)

The second goal is to activate the missile control The many interactions among technologies seeking system as soon as possible after separation. Then, if solutions for the proposed system have a profound the missile is unstable in the presence of the separat­ effect on the philosophy of the wind tunnel testing ing booster, the transient angle of attack can be mini­ needed to arrive at the eventual configuration and to mized, thereby decreasing missile drag and increasing provide an accurate definition of its aerodynamic the chance for a clean separation. Since tail stabiliza­ characteristics for detailed engineering design and tion and control may be adversely affected by the flight testing. Preliminary testing over a broad range flow disturbances caused by the booster head cap, it of parameters should include the so-called "build­ is desirable to obtain wind tunnel test data simulating up" data, which isolate the contributions of the sev­ missile-booster separation conditions for both the eral configurational elements (body, wings, tails, missile alone and the separated booster. launcher shoes, etc.) to the overall forces and mo­ ments measured on the full missile configuration. As changes are necessitated by findings during the pre­ liminary design process, the aerodynamicist can eval­ CONCLUDING REMARKS uate quantitatively the effects that will result from Missile design involves many interacting techno­ those changes, using the body of acquired parametric logies, most of which have significant input to the data. When design has progressed to the point where choice of an aerodynamic configuration. The process only minor external changes are expected, extensive should lead to a compromise solution that seeks an testing can proceed for a three-dimensional descrip­ optimum missile system for the mission. The solu­ tion of the aerodynamics of each configurational tion, however, is likely to be less than optimum for phase of the weapon (first stage (Fig. 11), second each of the technologies contributing to the system. stage (Fig. 12), and separation phase (Fig. 13».

Vu /ulI/e4, N UII/ ber 3, 1983 185 L. L. Cronvich - Missile Aerodynamics

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186 Johns Hopkins A PL Technical Digest