## Aerodynamic Forces and Coefficients

3.1 Aerodynamic Forces Relative to the Wind Axis System In this section we will discuss briefly the aerodynamic forces acting on a missile. In particular, and unless otherwise specified, we will assume a skid-to-turn missile because this technique is used in the majority of both surface-to-air and air-to-air missile applications (for more details see Section 3.3.2). However, the reader should be cautioned that both the aerodynamics and rigid-body dynamics are highly nonlinear. For a more...

## 10

Data Preparation Data preparation consists in selecting a fix point area large enough to accommodate the crosstrack and downtrack navigation arrival uncertainties, securing source material that contains contour information, and then digitizing the terrain elevation data into a matrix of cells oriented along the intended flight path. The source material is usually obtained from either topographic charts or from stereo aerial photographs of the terrain. The resulting reference matrix consists of...

## Info

Where aM is the interceptor missile acceleration, aT is the target acceleration, and the APN infinite bandwidth is given by In this case, the interceptor maneuver is equal to the target maneuver for all values N' (aM aT 1.0). The block diagram corresponding to APN is shown in Figure 4.29. In practice, the second derivative of yT would be estimated and added directly as an acceleration command to the missile guidance system. The solution given for (4.78) corresponds to the case where the...

## Pvi R

(note System is also seen as Submunition) Multidisciplinary Expert-Aided Design Multi-Function Control Reference System Multiple Independently targetable Reentry Vehicle Moving Target Indication (or Indicator) Offensive Avionics System Over The Horizon Pilot's Associate Power-By-Wire Precision-Guided Munition Precision Terrain Aided Navigation (used in the TacTom or Tactical Tomahawk missile). Pilot Vehicle Interface

## N

Sj j th measured profile, Rk kth reference profile. Evaluation of the ambiguity expression may be implemented on a computer. Also, computation of the ambiguity between two profiles requires a model of the measured error distribution. The terrain correlation (TC) system is required to update the position of the cruise missile inertial navigation system (see also Section 7.4.7). Crosstrack errors in the inertial navigation system (INS) can cause the missile to cross the map at a slightly skewed...

## 36 English Bias

In order to compensate any aircraft steering error (i.e., a missile aiming error) that exists at launch, an English bias (or lead angle error) signal is provided that will command the missile to turn after launch. The fundamental idea of this command is to provide the means of correcting missile heading error prior to lock-on to the target and thereby minimize the time required after speedgate* lock to solve the guidance problem and effect a satisfactory intercept. At launch, the computer...

## Cdc

-(dVg dt) can thus be controlled by controlling the orientation of aT, which, especially in the latter part of powered flight when aerodynamic forces are trivial, is on average along the longitudinal axis of the missile. It is therefore clear that control over the orientation of the change of Vg, -(dVg dt), can be exercised directly by controlling the orientation of the missile. For control purposes, -(dVg dt) can be aligned with Vg by commanding the missile to rotate so as to drive toward null...

## 2

+ (p 2)(CDSru2 m cos2 y) sin y - (L D) cos y . (6.247) Equation (6.247) must still be reduced in order to obtain a solution. The pair (6.244) and (6.247), representing the equations of motion, can be reduced to a single equation by transforming these equations to a new dimensionless variable. The solution is quite complicated and will not be pursued here further. An Example Here we will assume that the reentry trajectory is described by the translational motion of a rigid body. The equations of...

## Cl

Minuteman Variants Minuteman I (LGM-30A B) Minuteman II (LGM-30F) Minuteman III (LGM-30G) Inertial guidance with post-boost control and stellar inertial. Inertial guidance. Stellar inertial. Advanced inertial reference sphere (AIRS) IMU developed by Rockwell Autonetics Division. The MIRVs are deployed on the ballistic trajectory phase. 15,000mph at the highest point of the trajectory. The Block 4 TLAMs use GPS guidance and have an accuracy of 10-15 meters (32-50 feet) CEP. 6,950 nm The...

## V

Aircraft approaches the target in a horizontal ( 30 ) and vertical ( 100') jink maneuver. Wings level time does not exceed five seconds Fig. 5.11. Typical low-altitude low angle delivery. too slow a speed results in a short hit, and too high a speed results in a long hit. (2) The second error results from the relation between airspeed and angle of attack. As airspeed increases, angle of attack decreases. This, in effect, alters the sight angle. Therefore, a release airspeed greater than planned...

## 3

While the other can move counterclockwise) 3 , 5 . (Note that if the autopilot pitch and yaw axes are each 45 from the planes of adjacent control surfaces, then all four control surfaces are deflected equally by the pitch (or yaw) autopilot.) From the above discussion, we note that the majority of tactical missiles are designed in a cruciform configuration, thus enabling them to maneuver with ease horizontally and vertically. In a cruciform configuration, the two horizontal lifting surfaces are...

## Z

F Fn 0 Pk 0). (Assumptions q 0, V constant, u V, p 0), where x,y,z body (missile fixed axes), X, Y, Z Forces (air), p,q,r angular velocities roll, pitch, yaw), u,v,w velocity components about x, y, z, fin angular deflection (in roll, pitch, and yaw), L, M, N aerodynamic moments (in roll, pitch, and yaw), P thrust (lbs), Pk air stream deviation force (roll displacement), XG distance (i.e., aileron cg), Cx,CY,Cz force coefficients about X, Y, Z, CL, CM, CN aerodynamic...

## [1 R2P1 cos 0xii yij zik

Vcx (VMVP RiR2sin 0) X2 - 1 - (R2 p)(1 - cos 0) xi , Vcy (V VP RiR2sin 0) y2 - 1 - (R2 p)(1 - cos 0) yi , Vcz (V VP RiR2sin 0) Z2 - 1 - (R2 p)(1 - cos 0) zi . For a computer program (also for an airborne computer), the correlated velocity vector can be calculated as follows R1 (x2 + yj2 + z2)1 2 position vector, r2 (x2 + y2 + z )1 2 target vector, C3 (xi X2 + yiy2 + ziz2) (RiR2) cos 0, S3 (1 - C32)1 2 (1 - cos2 0)1 2 sin 0, C1 S3 2S1 sin 0 2 sin (0 2) cos (0 2), Ui 1 M, U2 y R1R2, U3 U2C1...

## P

Conic sections as gravitational trajectories. Figure G-4 illustrates the conic sections as simple gravitational trajectories, and as stated earlier, the dimensionless eccentricity e determines the character of the conic section in question. For more information, see Section 6.2. 1. Battin, R.H. Astronautical Guidance, McGraw-Hill Book Company, New York, 1964. 2. Brouwer, D. and Clemence, G.M. Methods of Celestial Mechanics, Academic Press, Inc., New York, 1961. 3. Danby, J.M.A....

## 30349

CEP 0.9263 (as Ol )2'09 + 0.6745ol. (5.13) (c) Using Table 5.2, select K from the 0.5 probability column for the current ratio of (aS aL) then compute Because most users are interested only in the weapon delivery accuracy about the target, an estimation of sigma may be made by root-sum-square addition of the along-track and crosstrack standard deviations with their respective mean points of impact. Then, the CEP may be computed as indicated in paragraph (5), above. This estimation is fairly...

## Introduction

Rockets have been used as early as a.d. 1232, when the Chinese employed them as unguided missiles to repel the Mongol besiegers of the city of Pein-King (Peiping). Also, in the fifteenth century, Korea developed the sinkijon* (or Sin-Gi-Jeon) rocket. Manufactured from the early fifteenth to mid-sixteenth century, the sinkijon was actively deployed in the northern frontiers, playing a pivotal role in fending off invasions on numerous occasions. Once out of the rocket launcher, the fire-arrows...

## D

CD coefficient of drag CD -- , S reference area for drag and lift, atmospheric density free stream (ambient atmosphere). Furthermore, selecting as the independent variable the expression where uc is the circular orbit velocity, we obtain Introducing now the drag coefficient in (6.242a) results in

## Pt [rt rt t0 dt wt

The first seven parameters of the 3 x M vector p are the initial conditions and initial time. The drag (D) and wind (W) parameters occur in the input tables for CD (Mach number) and W(x, y, h). The t0 parameter allows the error analysis to include a sensitivity for release error time. Letting p(p 1, ,M) denote any member of the set pT above, the sensitivity 3 x M vector may be defined as S(t) (d r dp),- - (d r dp) 1 -j (d r dp). Differentiating (5.31) partially with respect to p and...

## Jv2 2Ao

2p r (roVo cospo) r 2p (roVo cospo) a -1, b 2 roVo cos po, c V2 - (2p ro). (6.99c) Then (6.98) may be written in the form d0 - dx (ax2 + bx + c)1 2 . (6.100) 0 -(1 J a) sin-1 (-2ax - b) b2 - 4ac + k, (6.101) where k is the constant of integration. Substituting the values for a,b,c, and x from (6.99a) and (6.99c), we obtain r in the form r r Vo2 cos2 Po p 1 - (roVo coso) 2 - (2p r0) +(p2 (ro2V2 cos2 Po) 1 2 cos 0 . (6.102) Equation (6.102), like (6.2) and (6.21), is the equation of a conic in...

## J0

We will now summarize the translational and rotational equations of motion of a missile in terms of the body axes Rv - Qw + (Tboost - TSuSt) m - g sin 0 - (CAqS) m. (3.53a) dt Pw- Ru + g cos 0 sin 0 - (CYqS) m. (3.53b) dt Qu - Pv + g cos 0 cos 0 - (CNqS) m. (3.53c) dt (qSlref Ix) CL(Sa) + CL(ap) + CL(ay) + QR (Iy - Iz) Ix . dt (qSlrff Iy) CM + CN((dcg - dcg-ref) lref) + CM(Qlref 2Vm) (qSlref Iz) CN - CY((dcg - dcg-ref ) lref ) + Cn (Rlref 2Vm) Example 1. In Section 2.1, the transformation...

## 68 Missile Flight Model

In this section we will develop the ballistic missile flight model, summarizing the discussion of the previous sections. The development of this flight model will be treated as an example. It should be emphasized that this missile model is by no means complete, and is offered here as a guide for further study. The actual model will depend on the user requirements and missile designer analyst. In essence, the ballistic missile model provides the capability to model multistage missiles with...

## C11 C12 C13

C11 e1 - e2 - e3 + e4, C12 2(e3e4 + e1e2), C13 2(e2e4 - e1e3), Finally, we note that the same 6-DOF equations of motion can be used to model both aircraft and missiles. Example 2. Based on the discussion thus far, let us now consider in this example a 6-DOF aerodynamic model. Furthermore, let us assume an NED coordinate system, in which all units are metric. This model is designed for a generic aircraft. A quaternion fast-processing technique will be employed to simulate aircraft navigation....

## 49 End Game

The guidance techniques discussed in Sections 4.2 and 4.4, that is, command guidance, semiactive homing, and ground-aided semiactive guidance, can be simulated based on threat characteristics. For the end game concept, we will consider a surface-to-air missile (SAM) interceptor. Regardless of the mission, however, all guided missiles, whether tactical or strategic, carry some kind of warhead. In this section, we will discuss briefly the concept of end game. End game consists of two parts (1)...

## 644

F Past and Present Tactical Strategic Missile Systems F.2 Unpowered Precision-Guided Munitions (PGM) In this section we will discuss the role of the precision-guided bomb, or GBU-series. Historically, the unpowered Paveway Bomb Series, known as Paveway I, II and III PGMs, is based on the Mk 80 low-drag general-purpose unguided bomb series that was developed in the 1950s (see also Section 5.6). Specifically, the Paveway family (or series) consists of electronic guidance units and fin kits that...

## 71 Introduction

A cruise missile can be defined as a dispensable, pilotless, self-guided, continuously powered, air-breathing vehicle that flies just like an airplane, supported by aerodynamic surfaces, and designed to deliver a conventional or nuclear device. Specifically, the cruise missile is powered by a small, high-efficiency turbofan engine in the 600-pound thrust class. Cruise missiles exist in three versions (1) land-based or ground-launched cruise missiles (GLCM), (2) sea-based or sea-launched cruise...

## Lv

Forces acting on a ballistic missile during flight through the atmosphere. Fig. 6.29. Forces acting on a ballistic missile during flight through the atmosphere. velocity of the missile with respect to inertial space, R missile position vector with respect to the Earth, Ue angular velocity of the Earth, W wind velocity with respect to the Earth (normally a negligible quantity). Consequently, the missile will fly a gravity turn when (6.207) is satisfied. All the quantities required to...

## 54 The Navigation Weapon Delivery System

The navigation weapon delivery system (NWDS) is the heart of a fighter and or attack aircraft. Attack aircraft are specifically designed for close air support and interdiction missions. They have been designed to incorporate a continuous solution navigation and weapon delivery system for increased bombing accuracy. The NWDS continuously performs the vital computations required for greatly increased delivery accuracy, and for maneuvering freedom throughout the navigation to a target and the...

## 69 Ballistic Missile Intercept 691 Introduction

In recent years, several ballistic missile intercept concepts have been proposed as part of the overall ballistic missile defense (BMD) program. One such program was the midcourse concept. The missile defense technologies pursued presently include (a) the airborne laser (ABL), (b) the space-based laser (SBL), (c) the sea-based kinetic-energy kill concept, and (d) the space-based hit-to-kill experiment. The latter two are being considered to serve as hedges in case the directed-energy (DE)...

## 9

All-Sustain The all-sustain motor has low missile acceleration, resulting in lower aerodynamic drag and longer time of flight, for a given range. Since the motor burns for a long period of time, the motor can be used to overcome gravity in a look-up engagement, and to provide sufficient velocity for maneuvering at high altitude. This motor is suitable for head-on engagements, or in look-up engagements at high altitudes. Boost-Sustain The boost-sustain motor represents an attempt to combine the...

## 53 Weapon Delivery Requirements

The need for precision tactical weapon delivery systems providing day night all-weather, low- and high-altitude capability against targets at ranges to 300 nm can be met by self-contained fail-safe and fault-tolerant guidance aids and advanced kinematic bombing subsystems. To support these, continued development and use of GPS, time-of-arrival (TOA) measurement, distance measuring equipment (DME), down-looking infrared (DLIR), forward-looking infrared (FLIR), moving target indication (MTI)...

## 42 Tactical Guidance Intercept Techniques 421 Homing Guidance

The expression homing guidance is used to describe a missile system that can sense the target by some means, and then guide itself to the target by sending commands to its own control surfaces. Homing is useful in tactical missiles where considerations such as autonomous (or fire-and-forget) operation usually require sensing of target motion to be done from the interceptor missile (or pursuer) itself. Consequently, in such cases the sensor limitations generally restrict the sensed target motion...

## 22 Rigid Body Equations of Motion

In this section we will consider a typical missile and derive the equations of motion according to Newton's laws. In deriving the rigid-body equations of motion, the following assumptions will be made 1. Rigid Body A rigid body is an idealized system of particles. Furthermore, it will be assumed that the body does not undergo any change in size or shape. Translation of the body results in that every line in the body remains parallel to its original position at all times. Consequently, the rigid...

## 55 Factors Influencing Weapon Delivery Accuracy

Before we discuss the various factors that influence weapon delivery accuracy, it is appropriate to briefly state the weapon delivery modes. The common weapon delivery modes are as follows Continuous computation of impact (i.e., target) point (CCIP) that is, compute the point on the ground where the weapon would impact if released at that instant. Continuous computation of release point (CCRP). Computer-generated release signal. Limitation of roll command steering (i.e., number of degrees of...

## Agm88e

Making it most useful for soft targets such as SAMs, SAsM launchers, radar antennas, and radar command vans. Its accuracy is similar to that of the Tomahawk. The HARM was developed as a replacement for the AGM-45 Shrike and AGM-78 standard antiradiation missile ARM . See also Section 3.4.3. An advanced technology demonstration program, called the AARGM, will combine a wide-band passive antiradiation multimode seeker with an active MMW terminal guidance system and precision GPS INS navigation....

## 1 1

Terrain correlation processing. e The system can use either single maps or a voting group of three maps. The voting procedure normally improves the overall correlation probability of an area as compared to a single map, but for some areas, there may only be terrain of sufficient size for a single map. Even so, a single map of sufficient length can be made to have the same equivalent overall correlation probability of the shorter map set of three. With regard to design feature e, some...

## References

Closed-Form Solution of Pure Proportional Navigation, IEEE Transactions on Aerospace and Electronic Systems, Vol. 26, No. 3, May 1990, pp. 526-533. 2. Blakelock, J.H. Automatic Control of Aircraft and Missiles, John Wiley amp Sons, Inc., New York, NY, second edition, 1991. 3. Bryson, A.E. Jr. and Ho, Y.C. Applied Optimal Control, Revised Printing, Hemisphere Publishing Corporation, A Halsted Press Book, Washington, D.C., 1975. 4. Chui, C.K. and Chen G. Kalman Filtering with...

## C21 C22 C23 C31 C32 C33

Where cjk is the direction cosine between the jth axis in the a frame and the kth axis in the b frame. Since each axis system has three unit vectors, there are nine direction cosines. Direction cosines have the advantage of being free of any singularities such as arise in the Euler angle formulation at 90 pitch angle. The main disadvantage of this method is the number of equations that must be solved due to the constraint equations. Note that by constraint equations we mean c11 c22c33 - c23c32,...