AERODYNAMIC MODELING OF AN UNMANNED AERIAL ...

transcript

AERODYNAMIC MODELING OF AN UNMANNED AERIAL VEHICLE USING A

COMPUTATIONAL FLUID DYNAMICS PREDICTION CODE

A thesis presented to

the faculty of

the Russ College of Engineering and Technology of Ohio University

In partial fulfillments

of the requirements for the degree

Master of Science

Isaac D. Rose

March 2009

This thesis titled

COMPUTATIONAL FLUID DYNAMICS PREDICTION CODE

ISAAC D. ROSE

has been approved for

the School of Electrical Engineering and Computer Science

and the Russ College of Engineering and Technology by

_____________________________________________________________

Douglas A. Lawrence

Professor of Electrical Engineering and Computer Science

_____________________________________________________________

Dennis Irwin

Dean, Russ College of Engineering and Technology

Abstract

ROSE, ISAAC D., M.S., March 2009, Electrical Engineering

COMPUTATIONAL FLUID DYNAMICS PREDICTION CODE (192 pp.)

Director of Thesis: Douglas A. Lawrence

The process of creating a six degree-of-freedom model for an aerospace

vehicle requires detailed knowledge of the aerodynamic characteristics. This thesis

presents an implementation of a Computational Fluid Dynamics (CFD) prediction

computer code to generate aerodynamic coefficients for the Brumby Mk. I Unmanned

Aerial Vehicle (UAV). The aerodynamic coefficients include both the force and

moment coefficients. These values are verified by creating a Matlab/Simulink six

degree-of-freedom model.

Approved: ______________________________________________________________

Douglas A. Lawrence

Professor of Electrical Engineering and Computer Science

Acknowledgments

I would like to thank GOD through whom all things are possible. I would like to

thank my wife and son for their understanding and encouragement. The hours spent

working on this thesis were hours spent away from them. I would also like to thank Dr.

Lawrence for the guidance and direction that he has given me over the years. The

research presented in this thesis is a tribute to his resolve in the autonomous control of the

Brumby Unmanned Arial Vehicle. Finally, I would like to thank the faculty of the

department of Electrical Engineering and Computer Science for their help throughout the

years.

Table of Contents

Abstract.................................................................................................................................3

Acknowledgments................................................................................................................4

Glossary of Variables..........................................................................................................14

Chapter 1: Introduction..................................................................................................19

1.1 Overview.............................................................................................................19

1.2 Motivation ..........................................................................................................20

1.3 Modeling Aerodynamic Forces and Moments....................................................21

1.4 Objectives............................................................................................................22

1.5 Thesis Organization.............................................................................................22

1.5.1 Missile DATCOM Input Parameters...........................................................22

1.5.2 Missile DATCOM Model of the Brumby UAV..........................................23

1.5.3 Equations of Motion....................................................................................23

1.5.4 Brumby UAV Model Simulation................................................................23

Chapter 2: Missile DATCOM Modeling Parameters Overview....................................24

2.1 Flight Conditions..................................................................................................26

2.2 Fuselage...............................................................................................................28

2.3 Primary Lifting Surface ......................................................................................29

2.4 Horizontal Stabilizer...........................................................................................33

2.5 Vertical Stabilizer................................................................................................35

2.6 Control Surfaces..................................................................................................36

2.7 Generating Additional Data................................................................................38

2.8 File Format and Content......................................................................................39

2.9 Missile DATCOM Example...............................................................................41

Chapter 3: Missile DATCOM Model of the Brumby Unmanned Aerial Vehicle .........72

3.1 Flight Conditions.................................................................................................72

3.2 Fuselage................................................................................................................75

3.3 Wing Planform....................................................................................................76

3.4 Vertical Stabilizer................................................................................................77

3.5 Control Surfaces .................................................................................................80

Chapter 4: Equations of Motion and Rigid Body Modeling .........................................86

4.1 Equations of Motion for A Rigid Body ..............................................................86

4.2 Aerodynamic Coefficients..................................................................................91

4.3 Six Degree-of-Freedom Aircraft Model............................................................101

Chapter 5: Simulation...................................................................................................103

5.1 Simulink Nonlinear Aircraft Model..................................................................103

5.2 Trimmed Aircraft Flight....................................................................................107

5.3 Linearized Aircraft Model.................................................................................108

5.4 Nonlinear Simulation Results...........................................................................112

5.4 Control Surface Doublet Simulation Results....................................................123

Chapter 6: Conclusions and Future Work....................................................................138

References........................................................................................................................140

Appendix A.1: for005.dat File.........................................................................................141

Appendix A.2 : Truncated for006.dat File.......................................................................145

Appendix A.3 : for003.dat File........................................................................................154

Appendix A.4 : for021.dat File........................................................................................155

Appendix B.1: Equations of Motion s-function...............................................................184

Appendix B.2: forces_moments.m..................................................................................189

Appendix B.3: datcomderive.m.......................................................................................192

List of Tables

Table 2.1: Missile DATCOM Control Cards.....................................................................26

Table 2.2: Missile DATCOM Namelist FLTCON ..........................................................27

Table 2.3: Missile DATCOM Namelist REFQ..................................................................28

Table 2.4: Missile DATCOM Namelist AXIBOD............................................................29

Table 2.5: Missile DATCOM Namelist FINSET..............................................................30

Table 2.6: Missile DATCOM Namelist DEFLCT.............................................................38

Table 2.7: Missile DATCOM File Definitions..................................................................41

Table 3.1: Brumby UAV Flight Conditions (FLTCON) ..................................................73

Table 3.2: Brumby UAV Reference Values (REFQ)........................................................75

Table 3.3: Brumby UAV Body Definition (ASYM).........................................................76

Table 3.4: Brumby UAV Twin Vertical Tail Planform Definition (FINSET2)................79

Table 4.5: Brumby UAV Wing Planform Definition (FINSET1).....................................88

Table 5.1: Brumby UAV Mass Properties.......................................................................104

Table 5.2: S-function Functionality.................................................................................104

Table 5.3: DATCOMTableMex.dll Functionality...........................................................106

Table 5.4: Brumby UAV Control Input Trimmed Values (Case 1)................................107

Table 5.5: Brumby UAV State Variables Initial Condition Values (Case 1)..................108

Table 5.6: Brumby UAV Trimmed Aerodynamic Values (Case 1)................................108

Table 5.7: Brumby UAV Control Input Trimmed Values (Case 2)................................112

Table 5.8: Brumby UAV Control Effector Doublet Values............................................124

List of Figures

Figure 2.1: Missile DATCOM Axes Definition ...............................................................25

Figure 2.2: Missile DATCOM Body Variables.................................................................30

Figure 2.2: Missile DATCOM Finset................................................................................31

Figure 2.3: NACA Airfoil Number Decomposition..........................................................31

Figure 2.4: Missile DATCOM Fin Panel Location Definition..........................................33

Figure 2.5:Twin-Horizontal Stabilzer Fin Panel Location Definition...............................34

Figure 2.6:V-Tail Stabilzer Fin Panel Location Definition...............................................35

Figure 2.7:Twin-Vertical Stabilzer Fin Panel Location Definition...................................36

Figure 2.8: Missile DATCOM Control Surface Definition...............................................38

Figure 2.9: for005.dat File Example..................................................................................43

Figure 2.10: for006.dat File Example (Data Input)...........................................................44

Figure 2.11: for006.dat File Example (Error Checking)....................................................45

Figure 2.12: for006.dat File Example (Case 1 Output, Page 2).........................................46

Figure 2.20: for006.dat File Example (Case 1 Output, Page 10).......................................54

Figure 2.24: for006.dat File Example (Case 2 Output, Page 1 and 2)...............................58

Figure 2.36: for003.dat File Example................................................................................70

Figure 2.37: for021.dat File Example................................................................................71

Figure 3.1: Brumby UAV Fuselage...................................................................................75

Figure 3.2: Brumby UAV Wing Planform........................................................................77

Figure 3.3: Brumby UAV Vertical Planform....................................................................79

Figure 3.4: Brumby UAV Vehicle Description Case for005.dat File................................82

Figure 3.5: Brumby UAV Wing Control Deflection Cases for005.dat File......................83

Figure 3.6: Brumby UAV Twin Vertical Tail Control Deflection Cases for005.dat File. 84

Figure 3.7: Brumby UAV Side-Slip Angle and Altitude Cases for005.dat File................85

Figure 4.1: Aerodynamic Angles.......................................................................................88

Figure 4.2: Lift Coefficient (a) and Drag Coefficient (b)..................................................94

Figure 4.3: Force(a, b, c) and Moment Coefficients(d, e, f)..............................................95

Figure 4.4: Brumby UAV Moment Definition..................................................................98

Figure 4.5: Axial and Normal Forces..............................................................................100

Figure 4.6: Lift and Drag Forces......................................................................................100

Figure 5.1: Simulink Nonlinear Aircraft Model..............................................................103

Figure 5.2: Navigation Position Output (SLF)................................................................113

Figure 5.3: Euler Angles Output (SLF)...........................................................................113

Figure 5.4: Translational Velocities Output (SLF)..........................................................114

Figure 5.5: Angular Velocities Output (SLF)..................................................................114

Figure 5.6: Velocity Magnitude Output (SLF)................................................................115

Figure 5.7: Aerodynamic Angles Output (SLF)..............................................................115

Figure 5.8: Flight-Path Angle Output (SLF)....................................................................116

Figure 5.9: Rate-of-Climb Output (SLF).........................................................................116

Figure 5.10: Navigation Position Ground Track Output (SLF).......................................117

Figure 5.11: Navigation Position 3-Dimensional Output (SLF)......................................117

Figure 5.12: Navigation Position Output (CTROC)........................................................118

Figure 5.13: Euler Angles Output (CTROC)...................................................................118

Figure 5.14: Translational Velocities Output (CTROC)..................................................119

Figure 5.15: Angular Velocities Output (CTROC)..........................................................119

Figure 5.16: Velocity Magnitude Output (CTROC)........................................................120

Figure 5.17: Aerodynamic Angles Output (CTROC)......................................................120

Figure 5.18: Flight-Path Angle Output (CTROC)...........................................................121

Figure 5.19: Rate-of-Climb Output (CTROC).................................................................121

Figure 5.20: Navigation Position Ground Track Output (CTROC)................................122

Figure 5.21: Navigation Position 3-Dimensional Output (CTROC)...............................122

Figure 5.22: Doublet Response Navigation Position Output (SLF)................................125

Figure 5.23: Doublet Response Euler Angles Output(SLF)............................................125

Figure 5.24: Doublet Response Translational Velocities Output(SLF)...........................126

Figure 5.25: Doublet Response Angular Velocities Output (SLF)..................................126

Figure 5.26: Doublet Response Velocity Magnitude Output (SLF)................................127

Figure 5.27: Doublet Response Aerodynamic Angles Output (SLF)..............................127

Figure 5.28: Flight-Path Angle Output (SLF)..................................................................128

Figure 5.29: Rate-of-Climb Output (SLF).......................................................................128

Figure 5.30: Doublet Response Navigation Ground Track Output (SLF).......................129

Figure 5.31: Doublet Response Navigation 3-Dimensional Output (SLF)......................129

Figure 5.32: Control Surface Deflection Input Angles (SLF).........................................130

Figure 5.33: Aerodynamic Control Surface Deflection Input Angles (SLF)...................130

Figure 5.34: Doublet Response Navigation Position Output (CTROC)..........................131

Figure 5.35: Doublet Response Euler Angles Output (CTROC).....................................131

Figure 5.36: Doublet Response Translational Velocities Output (CTROC)...................132

Figure 5.37: Doublet Response Angular Velocities Output (CTROC)...........................132

Figure 5.38: Doublet Response Velocity Magnitude Output (CTROC)..........................133

Figure 5.39: Doublet Response Aerodynamic Angles Output (CTROC)........................133

Figure 5.40: Flight-Path Angle Output (CTROC)...........................................................134

Figure 5.41: Rate-of-Climb Output (CTROC).................................................................134

Figure 5.42: Doublet Response Navigation Ground Track Output (CTROC)................135

Figure 5.43: Doublet Response Navigation 3-Dimensional Output (CTROC)...............135

Figure 5.44: Control Surface Deflection Input Angles (CTROC)...................................136

Figure 5.45: Aerodynamic Control Surface Deflection Input Angles (CTROC)............136

Glossary of Variables

D Drag Force

Y Side Force

L Lift Force

A Axial Force

N Normal Force

C A Axial Force Coefficient

CY Side Force Coefficient

C N Normal Force Coefficient

C L Lift Force Coefficient

C D Drag Force Coefficient

C l Rolling Moment Coefficient (Body axis)

Cm Pitching Moment Coefficient(Body axis)

Cn Yawing Moment Coefficient (Body axis)

Cn Normal Force Coefficient derivative with respect to angle-of-attack

Cm Pitching Moment Coefficient derivative with respect to angle-of-attack

C y Side Force Coefficient derivative with respect to side-slip angle

Cn Yawing Moment Coefficient derivative with respect to side-slip angle (Body

C l Rolling Moment Coefficient derivative with respect to side-slip angle (Body

X cp Center of Pressure in calibers from the moment reference center

l Rolling Moment

m Pitching Moment

n Yawing Moment

l Rolling Moment

m Pitching Moment

n Yawing Moment

l Rolling Moment

m Pitching Moment

n Yawing Moment

C l p Rolling Moment derivative with respect to Roll Rate

Cmq Pitching Moment derivative with respect to Pitch Rate

Cnr Yawing Moment derivative with respect to Yaw Rate

C l r Rolling Moment derivative with respect to Yaw Rate

Cn p Yawing Moment derivative with respect to Roll Rate

C Lr Lift Force derivative with respect to Pitch Rate

CY P Side Force derivative with respect to Roll Rate

CY r Side Force derivative with respect to Yaw Rate

Cq ele Pitching Moment derivative with respect to Elevator Deflection Angle

C L ele Lift Force derivative with respect to Elevator Deflection Angle

C l ail Rolling Moment derivative with respect to Aileron Deflection Angle

Cn ail Yawing Moment derivative with respect to Aileron Deflection Angle

C l rud

Rolling Moment derivative with respect to Rudder Deflection Angle

Cn rud Yawing Moment derivative with respect to Rudder Deflection Angle

∇C Dynamic Derivative

q Dynamic Pressure

b Wing Span

c Mean Aerodynamic Chord

S Wing Span

Mass Density

V T Free Stream Velocity

k Dimensionless Rate Scale Factor

rate Angular Rotation Rate Corresponding to Aerodynamic Force

Coefficient Derivative

Angle-of-Attack

Side-Slip Angle

Flight-Path Angle

U Body-Frame Translational Velocity X-Axis Component

V Body-Frame Translational Velocity Y-Axis Component

W Body-Frame Translational Velocity Z-Axis Component

p Body-Frame Rotational Velocity X-Axis Component

q Body-Frame Rotational Velocity Y-Axis Component

r Body-Frame Rotational Velocity Z-Axis Component

Roll Attitude Euler Angle

Pitch Attitude Euler Angle

Yaw Attitude Euler Angle

N Inertial Navigation Position X-Axis Component

E Inertial Navigation Position Y-Axis Component

D Inertial Navigation Position Z-Axis Component

Cb /n Direction Cosine Matrix of the Body Frame with respect to the Navigation

pne Position Vector of Navigation Frame Derivative taken with respect to the Earth

Fixed Frame

vCM / eb Velocity Vector in the body frame of the Center-of-Mass with respect to the

Fixed Earth

Rotational Rate Vector

Rotational Rate Derivative Vector

b /eb Rotational Rate Vector expressed in the Body Frame of the Body with respect

to the Fixed Earth

vCM / ebb Velocity Vector Body Derivatives in the Body Frame of the Center-of-Mass

with respect to the Fixed Earth

m Mass of Vehicle

F A ,Tb Aerodynamic and Thrust Force Vector expressed in the Body Frame

gn Gravity Vector in the Navigation Frame

b/ eb Cross Product Matrix of Rotational Rates in the Body Frame of the Body with

respect to the Fixed Earth

b / ebb Rotational Rate Vector Body Derivative in the Body Frame of the Body with

respect to the Fixed Earth

M A ,Tb Aerodynamic and Thrust Moment Vector expressed in the Body Frame

J b Mass Moment of Inertia Tensor in the Body Frame

pne Navigation Position Vector expressed in the Earth Fixed Frame

Chapter 1: Introduction

The first step in developing a compensation scheme for a dynamic system is to

create a mathematical model of the dynamic system or plant. For an aerospace vehicle,

developing a mathematical model requires knowledge of the physical characteristics such

as weight, mass properties and aerodynamic parameters. Until the 1970's most

aerodynamic coefficients were obtained from wind tunnel data or through system

identification techniques.[1] Today's computers make it possible to use Computational

Fluid Dynamics (CFD) modeling to generate the aerodynamic coefficients of an

aerospace vehicle.

One method to compute the aerodynamic coefficients of the aircraft is to use the

United States Air Force Data Compendium (DATCOM)[2]. DATCOM was introduced

in the 1970's as a handbook containing tabular aerodynamic coefficients for different

vehicle geometries. The user builds the aerodynamic model from the characteristics of its

components, such as the Aspect Ratio of the wing planform, geometry and location of the

stabilizing and control surfaces, as well as the shape of the fuselage. The DATCOM

handbook was implemented as a computer code, entitled Digital DATCOM, written in

the Fortran language.[3]

Digital DATCOM is a set of computer codes that creates a composite

aerodynamic model based on the user input geometry. The latest version of the United

States Air Force Data Compendium, Missile DATCOM, allows the user to model more

abstract vehicle geometries, as well as expanding the environmental envelope.[4]

1.1 Overview

The Avionics Research Center at Ohio University purchased an unmanned aerial

vehicle for control and navigation research after the recent expansion in the use of

unmanned aerial vehicles for data collection and deployment in hazardous environments.

The unmanned aerial vehicle purchased from the University of Sydney during the 1990's

is a Brumby MK I.[1] The Brumby Unmanned Ariel Vehicle (UAV) provides an ideal

platform for aircraft control and navigation research. The Brumby UAV has a delta wing

planform with twin vertical stabilizers, the contour of the fuselage is that of a cylinder

with a blunted ogive nose. This makes creating a Missile DATCOM model a relatively

straight forward task. The delta wing also contains the Ailevons (aileron and elevator

control on one control surface). The change in deflection angles create changes in the lift,

drag, roll, and pitch coefficients of the main lifting planform. This causes the angle-of-

attack and side-slip angle to be coupled with the deflection angles of the ailevons. This

creates a nonlinear aircraft model, that is an ideal system for a non-linear control research

platform.

1.2 Motivation

There are many methods available to obtain an aerodynamic model of an aerospace

vehicle. Methods such as system identification require data to be taken while the vehicle

is operating over a predefined envelope. This method requires that a physical model be

constructed and operated in the environment for which the aerodynamic model is desired.

This can be costly and very time consuming. It may not be possible to fly the model over

all the desired flight envelopes. Other options such as wind tunnel data also require that a

model be built and tested. Traditionally, full sized aircraft must be scaled down to meet

the size constraints of the wind tunnel. Some unmanned UAV's are small enough to fit

inside the wind tunnel at full scale. Since the model is full sized and full functioning,

forces and moments as well as derivatives for control surface deflection angles may be

measured. All of these methods require that a new model be constructed, and retested for

changes in vehicle geometry.

By using a computational fluid dynamics prediction code it is possible to obtain

aerodynamic coefficients for various vehicle geometries over a wide range of

environmental conditions without the cost or inconvenience associated with wind tunnel

testing. CFD prediction codes can generate aerodynamic coefficients in a shorter time

period and at a lower monetary cost. While computational fluid dynamic prediction codes

may not capture all the nonlinearities of the aerodynamics, the model is still valid and

useful.

1.3 Modeling Aerodynamic Forces and Moments

The processing power of todays computers make it possible to model the

aerodynamic forces and moments using computational fluid dynamics prediction codes.

These codes allow the user to create software models of the aircraft and generate the

forces and moments using only a computer. These mathematical models can then be used

to analyze the dynamic behavior of the aircraft. These models allow the control system

engineer to create compensation schemes that will cause the aircraft to have more

desirable dynamics. For example the aircraft may not respond to inputs fast enough, there

may be an undesirable steady-state error to a control input, or the systems response to

disturbance inputs may need to be analyzed, e.g. wind gusts.

1.4 Objectives

The reader of this thesis will be able to generate aerodynamic force and moment

coefficient data using USAF Missile DATCOM. The reader will be exposed to the basic

definitions and terminology of USAF Missile DATCOM. This data will then be

integrated into a six degree-of-freedom Simulink simulation where the model will be

analyzed for static as well as dynamic stability. The reader should have an understanding

of the basic concepts required for modeling and simulation of an aircraft using

computational fluid dynamic modeling.

1.5 Thesis Organization

The control system engineer must create an accurate model of a mechanical system

before a control system can be designed. Modeling the aerodynamic behavior of an

aircraft typically requires a scale model of the aircraft be built and placed in a wind

tunnel where forces are measured. It may be difficult for researchers in aircraft control

system design to gain access to a wind tunnel or be able to fund the building of a scale

model. Computational fluid dynamics allows the researcher the ability to model the

aircraft without the trouble or expense of creating scale models or obtaining testing time

in a wind tunnel. This thesis will cover the topic of creating an aerodynamic model using

a computational fluid dynamics prediction code.

1.5.1 Missile DATCOM Input Parameters

In order to use the CFD prediction code the user must understand the dimensions and

variables that are needed to create the model using USAF Missile DATCOM. The

physical dimensions of the aircraft are required, such as the lengths of the planforms, the

dimensions of the control surfaces, the location of the center-of-mass to name a few. This

will be illustrated through use of an example in Chapter 2.

1.5.2 Missile DATCOM Model of the Brumby UAV

The Ohio University Avionics Center conducts research using a Brumby UAV

aircraft. This aircraft model is used to perform guidance and navigation research. The

Brumby UAV will be modeled using Missile DATCOM in Chapter 3.

1.5.3 Equations of Motion

The equations of motion for a moving body in 3-dimensions will be presented in

Chapter 4. These equations describe the effect of the forces and moments on the aircraft.

The equations of motion will be used to create a six degree-of-freedom simulation.

1.5.4 Brumby UAV Model Simulation

The Missile DATCOM model of the Brumby UAV will be simulated, analyzed, and

subjected to perturbations from equilibrium in Chapter 5. The model will first be trimmed

for straight wings level flight. Wings level flight is typical of an aircraft that is traversing

between way points. The eigenvalues of the straight wings level flight trim condition will

be evaluated as well as an explanation of the dynamics of the aircraft. The model will

then be trimmed for a coordinated turn with a constant rate of climb. Finally, the Brumby

UAV model will be subjected to input perturbations and the aircraft dynamics will be

observed.

Chapter 2: Missile DATCOM Modeling Parameters

Overview

In this chapter a description of Missile DATCOM terminology and variables will

be presented. Due to the large number of possible geometric configurations, only

terminology and variables needed to create a model of the Brumby Unmanned Aerial

Vehicle (UAV) in Chapter 3 will be discussed. The reader is directed to Reference [4]

for more information on other geometric possibilities or for an expanded list of options

for the discussed variables.

User vehicle geometric configuration and flight condition specifications are input

to Missile DATCOM using a text file. Missile DATCOM parses the input file looking for

predefined “Namelists” that it associates to internal variables. Missile DATCOM requires

only a minimal number of Namelists be used to define the vehicle geometry. Over-

specification of the geometry can generate numerical instability of some calculations in

Missile DATCOM.[4] Missile DATCOM allows the user to set the units that will be

used for the calculations, as well as managing additional output data that can be

calculated through the use of control cards. Control cards are valid only in the case in

which they appear unless the user saves the current case using the SAVE control card.

This allows the user to use different control cards for different cases. A list of control

cards used when creating the model in Chapter 3 is given in Table 2.1. Missile DATCOM

will generate output data based on the commands in the input file that is used. The output

file will contain aerodynamic coefficients, and may also contain dynamic damping

derivative coefficients if the DAMP control card was used.

It is important to understand the coordinate system that will be used in describing

the geometry of the vehicle in question. Let the center of gravity lie inside the vehicle and

let it be at the intersection of the longitudinal plane of symmetry and the lateral plane of

symmetry if it exists. Then Missile DATCOM designates the positive x-axis as being

positive increasing aft from the tip of the nose, the positive y-axis as increasing along the

starboard wing, and the positive z-axis as increasing in a manner that it obeys the right

hand rule. This coordinate system is shown in Figure 2.1. Missile DATCOM allows the

user to place the origin of the coordinate system a specified distance from the tip of the

nose along the x-axis by assigning X0 a non-zero value. If no value is assigned to X0

then Missile DATCOM will use the default value of 0.0 units of distance.

Figure 2.1: Missile DATCOM Axes Definition

2.1 Flight Conditions

Missile DATCOM allows the user to specify the flight conditions in namelist

FLTCON, for which the aerodynamic data will be calculated. The user places the angles-

of-attack values in the ALPHA array, and the Mach values in the MACH array. The size

Table 2.1: Missile DATCOM Control Cards

Control Cards Description Values

DIM Sets the system of length dimension Units (L) M,CM,FT,IN

DERIV Sets the output derivative Units DEG,RAD

INCRMT Calculates correction factors for coefficients on the first run, based on experimental data given in EXPR.

NOGO Allows program to cycle through input cases without computing configuration Aerodynamics

NO LAT Inhibits computation of lateral-directional derivatives, if DAMP is selected

PLOT Creates data file for003.dat, containing aerodynamic data for plotting.

BUILD Prints results of a configuration build-up N/A

CASEID User supplied title output for that case Brumby Flaps

DAMP Computes dynamic damping derivatives. N/A

DELETE name Ignore namelist saved from previous case Namelist value

NAMELIST Prints all Namelist data N/A

NEXT CASE Indicates termination of the case input. N/A

PART Prints partial aerodynamic output. N/A

PRINT AERO name Prints the incremental aerodynamics for name.For more options see reference Page 23.

BODY,FIN1,etc.

PRINT GEOM name Prints the geometric characteristics of component name.For more options see reference Page 23.

BODY,FIN1,etc.

SAVE Saves namelist values from previous case.

TRIM Calculates fin deflection angles for longitudinal trim condition.

NACA Allows use of predefined NACA airfoil types to be used as airfoil geometries

of the MACH array is stored in NMACH and the size of the ALPHA array is stored in

NALHPA. For each vehicle scenario that Missile DATCOM executes, aerodynamic

coefficients will be computed for all combinations of defined Mach and angle-of-attack.

A matrix will be created for each aerodynamic coefficient with NMACH columns and

NALPHA rows. Only one side-slip angle can be run for each case and is stored in the

BETA variable. In order to simplify data input, only a core set of flight condition data

needs to be input by the user. For the model that will be generated in Chapter 3, only

values for Mach and altitude are required. From these values Missile DATCOM will

calculate the internal variable values needed to perform the aerodynamic calculations. A

list of variables from namelist FLTCON that are used are given in Table 2.2.

Missile DATCOM also requires that parameter values be specified by the user for

referencing and scaling purposes. Missile DATCOM will generate aerodynamic

coefficients that have been non-dimensionalized with respect to the reference values. The

reference variables used for the model in Chapter 3 are listed in Table 2.3. Typically, the

Table 2.2: Missile DATCOM Namelist FLTCON

Variable Name Array Size Description Units Default Value

NALPHA - Number of angles of attack - -

ALPHA 20 angle-of-attack Deg -

BETA - side-slip angle Deg 0.0

PHI - Aerodynamic roll angle Deg 0.0

NMACH - Number of Mach values - -

MACH 20 Mach Values - -

ALT 20 Altitude values L 0.0

values used for SREF, LREF, and LATREF on a traditional aircraft are wing planform

area, mean wing chord length, and wing span length respectively.

2.2 Fuselage

Missile DATCOM allows for axially symmetric or elliptical body shapes. These

body shapes can either be input using body diameter and length if the body has a

continuous radius along the body, and trailing nozzle sections, or the body geometry can

be input at different longitudinal stations. These options provide a great deal of

flexibility. The variables used in creating the axial body model in Chapter 3 are listed in

Table 2.4.

Table 2.3: Missile DATCOM Namelist REFQ

Variable Name Description Units Default Value

SREF Reference Area L*L Maximum body cross-sectional area

LREF Longitudinal Reference Length L Maximum body diameter

LATREF Lateral reference length L LREF

XCG Longitudinal position of Center of Gravity (+aft) L 0.0

ZCG Vertical Position of Center of Gravity (+up) L 0.0

2.3 Primary Lifting Surface

Traditional aircraft typically have a geometry that consists of: a body, a wing,

vertical and horizontal stabilizing and control surfaces. Missile DATCOM describes

each planform surface as a finset that is located at a defined position on the body. Missile

DATCOM allows for four finsets, each finset can contain a total of eight panels. Using

this method, the fin geometry must only be defined once. Then the position of each fin on

the body must be specified. Missile DATCOM will not check to see if Finset1 is fore or

aft of Finset2 when it performs an error analysis. Placing Finset2 fore of Finset1 will

cause errors in the interference flow calculations from one fin to the next. Finset1 will be

the foremost finset, which on a traditional aircraft without canards will be the wing

planform. We will start out by describing the planform geometry and then describe the

position of each panel around the body. A basic set of variables are listed in Table 2.5.

Table 2.4: Missile DATCOM Namelist AXIBOD

Variable Name Description Units Default Value

XO Longitudinal coordinate of nose tip. L 0.0

TNOSE Type of nose shape. - OGIVE

LNOSE Nose length L -

DNOSE Nose diameter at base L 1.0

BNOSE Bluntness radius L 0.0

LCENTR Center body length L 0.0

DCENTR Center body diameter at base L DNOSE

It is important to note that when a fin panel PHIF value is greater than 180

degrees, see Figure 2.4, and has a SECTYPE of NACA (National Advisory Committee

for Aeronautics), the airfoil of the fin will also be rotated. This rotation will cause a

positive angle-of-attack to be seen by both the port and starboard panels. The NACA

control card uses the form NACA 1-4-2412, where the first number designates the finset,

in this case FINSET1. The second number designates the NACA series of airfoil, for this

example this is a NACA 4 series. The last number is the NACA airfoil section

designation. For a NACA 4 series the first number is the camber in percent of the chord

Figure 2.2: Missile DATCOM Body Variables

Table 2.5: Missile DATCOM Namelist FINSET

XLE 10 Distance from nose to chord leading edge

CHORD 10 Panel chord at each semi-span station

SSPAN 10 Semi-span locations L -

CFOC 10 Flap chord to Fin chord ratio - 1.0

NPANEL 8 Number of panels in fin set (1-8) - 4.0

PHIF 8 Roll angle of fin about body, Clockwise is positive angle.

Deg Even spacing around body.

GAM 8 Dihedral angle of each fin, Positive angle when PHIF is increased

Deg 0.0

SECTYPE - Type of airfoil section. - HEX

STA 10 Sweep back angle at each span station.

Deg. 0.0

SWEEP 10 Chord station used in measuring sweep:STA=0.0 is leading edgeSTA=1.0 is trailing edge

length, the second is the location of maximum camber aft from the leading edge in tens of

percent of the chord length, and the last two digits are the maximum chord thickness

locate at the point of maximum camber. Figure 2.4 is an example of an airfoil that has 2%

camber, with 12% thickness located at 4% aft of the leading edge.[5]

Figure 2.2: Missile DATCOM Finset

Figure 2.3: NACA Airfoil Number Decomposition

If the wing has a continuous sweep along its leading edge it is possible to only

define XLE for the root chord of the wing. Missile DATCOM only requires that XLE(1)

be defined if the user inputs the sweep back angle for each span station using the SWEEP

namelist. Missile DATCOM will determine that the planform has continuous sweep

between semi-span stations and will calculate the XLE values from one semi-span station

to the next. In order to place the fin panels directly on the body mold line, start the semi-

span at 0.0 and allow each additional element in the SSPAN array to be the distance from

the body mold line to that semi-span station. By setting the first semi-span location at

zero Missile DATCOM will place the panel directly on the body. Care must be taken in

defining SSPAN(1) to be a distance other than the body mold line, SSPAN(1) = 0.0. The

user must ensure that the panel is attached to the body, otherwise there may be a gap

between the body and the root chord of the panel. Missile DATCOM will not check to

see if the panel is attached to the body. Missile DATCOM will not allow cracked panels

or the airfoil shape to change over the panel. In Section 2.6 the method for placing

control surfaces on a planform will be discussed.

2.4 Horizontal Stabilizer

It is possible to define a horizontal stabilizing surface using the same method

described in Section 2.3. For this reason the reader is referred to Section 2.3 for details on

creating horizontal stabilizing planforms. In this section horizontal stabilizers that do not

lie in the same horizontal plane as the wing planform will be defined. It is possible to

create a horizontal stabilizer that is positioned on top of a vertical stabilizer. Because

error analysis used in Missile DATCOM does not check to see if a finset is actually

located on the body, it is possible to create what is known as a T-tail configuration. This

is accomplished by using two panels and setting the two PHIF values to 0.0 degrees.

Then set the SSPAN(1) value to be the distance from the center of the body to the root

chord of the horizontal stabilizer. This value would be 0.0 in most cases so that the root

chord would be located on the x-z plane. However, if the SSPAN(1) value is 0.0 Missile

Figure 2.4: Missile DATCOM Fin Panel Location Definition

DATCOM will place the root chord on the body. This means that the SSPAN(1) value

must be arbitrarily small so that it will reside as near as possible to the x-z plane. The

starboard fin will have a GAM value of 90.0 degrees and the port fin will have a GAM

value of -90.0 degrees. Figure 2.6 contains an illustration of the variables associated with

defining a a twin-vertical stabilizer.

It is also possible to create what is typically known as a V-tail configuration. This

can be accomplished in a manner similar to the method discussed in Section 2.3, with the

exception that the fin planforms are located symmetrically about the x-z plane, and

dihedral angle is zero.

Figure 2.5:Twin-Horizontal Stabilzer Fin Panel Location Definition

2.5 Vertical Stabilizer

It is also possible to create a single vertical stabilizer or twin vertical stabilizers.

In the case of a single vertical stabilizer NPANEL would have a value of 1.0 and both

PHIF and GAM would be 0.0 degrees. This situation would indicate that the fin planform

is aligned with the z-axis and that the dihedral angle is zero. These twin vertical

stabilizers can also be placed off of the body and onto another panel, using a similar

method as described in the previous section. The first element in the SSPAN array is the

distance from the centerline of the body to the location of the root chord of the stabilizer.

To place the stabilizers on another planform the PHIF angles must be the same, e.g. the

PHIF starboard wing is equal to the PHIF angle of the starboard stabilizer. This ensures

that the root chord is placed on the existing panel. The roll angle PHIF would contain

values of 90.0 degrees for the starboard fin and -90.0 degrees for the port fin. The

dihedral values GAM would be used to roll the fins into vertical positions. This would be

accomplished by setting the starboard GAM value to be -90.0 degrees and the port GAM

value to be 90.0 degrees.

Figure 2.6:V-Tail Stabilzer Fin Panel Location Definition

2.6 Control Surfaces

It is often useful and at times necessary to know the contribution of the deflection

angles of the control surfaces to the aerodynamic coefficients. To determine the size of

each control surface on the fin panel, care must be given in defining the fin. First, the

semi-span stations should be defined for all control surface demarcation points along the

planform. It is necessary to define semi-span, chord, and flap chord to fin chord ratio

laterally for each control surface. For a fin planform having a single flap located between

the root and tip chord, it is necessary to define four semi-station points, four chord values

at those station points, and four flap chord to fin chord ratio values. In this particular

example, shown in Figure 2.6, the break between the flap and the chord does not lie on

either the root or the tip chord. Because the length of the flap at the root and tip of the

Figure 2.7:Twin-Vertical Stabilzer Fin Panel Location Definition

wing is zero, both the first and last values of the CFOC array will contain zeros. The

entire stabilizer can be made a movable control surface by setting the values of CFOC to

1.0. This indicates to Missile DATCOM that the flap chord is the total length of the fin

chord, and therefore the entire panel is movable.

In order to set the control surface deflection, Missile DATCOM uses the DEFLCT

namelist that can been seen in Table 2.6. Only the control surfaces that have been defined

should have their deflection values set, any control surface not defined by the user will

have its respective deflection angle set to zero internally by Missile DATCOM. Missile

DATCOM will perform calculations over all eight panels in each of the four finsets. Any

undefined panel is assigned zero length and does not contribute to the aerodynamic

coefficients being calculated. Assuming the panel is placed with the root chord located on

the body and the fin is perpendicular to the x-axis, then the deflection angles are defined

as positive if they induce a negative body axis rolling moment. A negative body axis

rolling moment is defined as counterclockwise when viewed along the x-axis looking

forward toward the nose. This is valid for all flaps regardless of orientation. The

deflection angle for flaps that are not located on the body are defined as if the fins are

located axially around the x-axis.

2.7 Generating Additional Data

Some of the limitations in Missile DATCOM can be overcome by running the

vehicle again in a new case while only changing one value. An example would be to

handle more than one side-slip angle. Even though Missile DATCOM will only consider

one side-slip value per case, by running multiple cases and only changing the side-slip

Figure 2.8: Missile DATCOM Control Surface Definition

Table 2.6: Missile DATCOM Namelist DEFLCT

DELTA1 8 Deflection values for Finset1 Deg. 0.0

value in each case Missile DATCOM will generate data for those side-slip angles. This

becomes especially useful when data for different control surface deflection angles are

desired. By saving the previous vehicle geometry using the SAVE control card, then

overwriting the deflection angle, Missile DATCOM will calculate the aerodynamic

coefficients for the new vehicle configuration.

2.8 File Format and Content

Missile DATCOM uses space delimiting as a method for distinguishing namelists

from control cards. Only a control card should be placed in the first character of a column

in the input file. Namelists should allow one space for the first column and should should

then start and end with a dollar sign ($). Variables in a namelist are separated using

commas and a comma must precede the terminating dollar sign of the namelist. A row

can only contain eighty characters including symbols and blank spaces. Values assigned

to variables must always contain a decimal point, for a value of zero the leading zero is

necessary, while a zero after the decimal point is not. In order for the case to be executed

a NEXT CASE control card must be inserted at the end of each case, including the last

case. Table 2.7 gives a brief explanation of the input and output files created and required

for execution by Missile DATCOM.

The for005.dat file is the input file to Missile DATCOM and contains the control

cards as well as the namelists that are used to describe the vehicle. The for005.dat file for

the Brumby MK. I is listed in Appendix A.1.

The for006.dat file contains two copies of the for005.dat file as well as the output

for the cases to be executed by Missile DATCOM. The first listing is a copy of the

for005.dat file and the second is the for005.dat file containing error checking markups.

The for003.dat file contains the aerodynamic coefficients for the cases executed

by Missile DATCOM. The Columns of the for003.dat file are: Angle-of-Attack

(ALPHA), Normal Force Coefficient (CN), Pitching Moment Coefficient (CM), Axial

Force Coefficient (CA), Side-Force Coefficient (CY), Yawing Moment Coefficient

(CLN), Rolling Moment Coefficient (CLL) , Deflection Angle for zero Pitching Moment

(DELTA), Lift Coefficient (CL), and Drag Force Coefficient (CD). The rows correspond

to the angle-of-attack values ALPHA. Missile DATCOM will generate a matrix of

ALPHA rows and coefficient columns for each MACH value specified, for each case that

is executed.

The for0021.dat file contains all of the necessary aerodynamic coefficients that

would be required to create a nonlinear vehicle simulation using a build up of the

individual components. The for021.dat file contains a row of variables: Mach, altitude,

side-slip angle, the deflection angles for the flaps, the number of rows of data, the total

columns of data, and finally the number of columns of derivatives. The variables are

immediately followed by the angle-of-attack (ALPHA) and the aerodynamic coefficients

which are: normal force coefficient (CN), pitching moment coefficient (CM), axial force

coefficient (CA), side force coefficient (CY), yawing moment coefficient (CLN), rolling

moment coefficient (CLL), normal force due to pitch rate (CNQ), pitching moment due

to pitch rate (CMQ), axial force due to pitch rate (CAQ), side force due to yaw rate

(CYR), yawing moment due to yaw rate (CLNR), rolling moment due to yaw rate

(CLLR), side force due to roll rate (CYP), yawing moment due to roll rate (CLNP),

rolling moment due to roll rate (CLLP). Aerodynamic derivatives are only calculated for

the base model, where the deflection angles for the effectors are set to zero. The base

model is immediately followed by coefficients for each case that is executed by Missile

DATCOM.

2.9 Missile DATCOM Example

In this section an example missile from the Missile DATCOM user manual will

be presented.[4] This particular missile is axially body symmetric with four panels

equally distributed around the body. The dimensions are in inches (DIM IN). The

envelope in consideration is MACH values 0.4, 0.8, 2.0 (MACH= 0.4, 0.8, 2.0) and

angles of attack -8.00, -4.00, 0.00, 4.00, 8.00 (ALPHA=-8.00, -4.00, 0.00, 4.00, 8.00) at

an altitude of zero meters (ALT=0.0) with a side-slip angle of zero degrees (BETA=0.0).

The center of gravity lies 39.0 inches from the origin which is located at the tip of the

nose (XCG=39.0). The body of the missile is 54.0 inches long (LCENTR=54.0) and 12.0

inches in diameter (DCENTR=12.0). The nose of the missile is ogive in shape

(TYPE=OGIVE) and is 12.0 inches long (LNOSE=12.0) and has a base diameter of 12.0

Table 2.7: Missile DATCOM File Definitions

Filename Description

For005.dat User input file.

For006.dat Output file containing results from error checking and calculations.

For003.dat Output file generated by PLOT control card, containing calculated aerodynamic coefficients.

For021.dat Output file to be used with Air Force program DATCOMTableMEX.dll

inches (DNOSE=12.0). The missile has four fins that are evenly distributed around the

body. The Fins have a NACA airfoil shape with a NACA number of 0310

(SECTYP=NACA and NACA-1-4-0310). The leading edge of the fin at the first semi-

span locate is 64.0 inches from the nose (XLE=64.0).The semi-span values of the fins are

0.0 at the root and 9.0 inches at the tip (SSPAN=0.0, 9.0,). The chord length at the root is

14.0 inches and 8.0 inches at the tip (CHORD=14.0, 8.0). The sweep angle of the fins are

0.0 degrees and are measured with respect to the segment trailing edge (SWEEP=0.0 and

STA=1.0). There are four fin panels located at 45.0, 135.0, 225.0, 315.0 degrees around

the body (NPANEL=4.0, PHIF=45.0, 135.0, 225.0, 315.0, GAM=0.00, 0.00, 0.00, 0.00).

The fins have a control flap with a a constant cord to flap ratio of 0.25 that starts at the

second station point and runs to the tip of the chord (CFOC=0.0, 0.25, 0.25, 0.25). Data

must also be generated for a condition where the two fins that are facing horizontal have

a deflection that would cause the missile to pitch nose up (SAVE, NEXT CASE,

CASEID PANEL DEFLECTION, $DEFLCT DELTA1=5.0, 0., 0., -5.0, $, SAVE, NEXT

CASE). This case is presented in Figure 2.8. The for006.dat file is listed in Figures 2.9

through 2.33. Figures 2.34 and 2.35 show listings for the for003.dat and for021.dat files

respectively.

Figure 2.9: for005.dat File Example

CASEID ExampleDAMPPLOTDIM INDERIV RAD $FLTCON NMACH=3.0,ALT=0.,NALPHA=5.0, MACH =0.4,0.8,2.0, ALPHA = -8.00,-4.00,0.00,4.00,8.00, BETA=0.,$ $REFQ XCG=39.0,$ $AXIBOD TNOSE=OGIVE,LNOSE=12.0,DNOSE=12.0,LCENTR=54.0,DCENTR=12.0,$ $FINSET1 SECTYP=NACA, SSPAN=0.0,9.0, CHORD=14.0,8.0, XLE=64.0, SWEEP=0.0, STA=1.0, NPANEL=4., PHIF=45.0,135.0,225.0,315.0, GAM=0.00,0.00,0.00,0.00, CFOC=0.0,0.25,0.25,0.25,$ NACA-1-4-0310SAVENEXT CASECASEID PANEL DEFLECTIONDAMP $DEFLCT DELTA1=5.0,0.,0.,-5.0,$SAVENEXT CASE

Figure 2.10: for006.dat File Example (Data Input)

1 ***** THE USAF AUTOMATED MISSILE DATCOM * REV 01/06 ***** AERODYNAMIC METHODS FOR MISSILE CONFIGURATIONS

CONERR - INPUT ERROR CHECKING

ERROR CODES - N* DENOTES THE NUMBER OF OCCURENCES OF EACH ERROR A - UNKNOWN VARIABLE NAME B - MISSING EQUAL SIGN FOLLOWING VARIABLE NAME C - NON-ARRAY VARIABLE HAS AN ARRAY ELEMENT DESIGNATION - (N) D - NON-ARRAY VARIABLE HAS MULTIPLE VALUES ASSIGNED E - ASSIGNED VALUES EXCEED ARRAY DIMENSION F - SYNTAX ERROR

************************* INPUT DATA CARDS *************************

1 CASEID Example 2 DAMP 3 PLOT 4 DIM IN 5 DERIV RAD 6 $FLTCON NMACH=3.0,ALT=12*0.,NALPHA=5.0, 7 MACH =0.4,0.8,2.0, 8 ALPHA = -8.00,-4.00,0.00,4.00,8.00, 9 BETA=0.,$ 10 $REFQ XCG=39.0,$ 11 $AXIBOD TNOSE=OGIVE,LNOSE=12.0,DNOSE=12.0,LCENTR=54.0,DCENTR=12.0,$ ** SUBSTITUTING NUMERIC FOR NAME OGIVE 12 $FINSET1 SECTYP=NACA, ** SUBSTITUTING NUMERIC FOR NAME NACA 13 SSPAN=0.0,9.0, 14 CHORD=14.0,8.0, 15 XLE=64.0, 16 SWEEP=0.0, 17 STA=1.0, 18 NPANEL=4., 19 PHIF=45.0,135.0,225.0,315.0, 20 GAM=0.00,0.00,0.00,0.00, 21 CFOC=0.0,0.25,0.25,0.25,$ 22 NACA-1-4-0310 23 SAVE 24 NEXT CASE 25 CASEID PANEL DEFLECTION 26 DAMP 27 $DEFLCT DELTA1=5.0,0.,0.,-5.0,$ 28 SAVE 29 NEXT CASE

Figure 2.11: for006.dat File Example (Error Checking)

1 ***** THE USAF AUTOMATED MISSILE DATCOM * REV 01/06 ***** CASE 1 AERODYNAMIC METHODS FOR MISSILE CONFIGURATIONS PAGE 1 CASE INPUTS FOLLOWING ARE THE CARDS INPUT FOR THIS CASE

CASEID Example DAMP PLOT DIM IN DERIV RAD $FLTCON NMACH=3.0,ALT=12*0.,NALPHA=5.0, MACH =0.4,0.8,2.0, ALPHA = -8.00,-4.00,0.00,4.00,8.00, BETA=0.,$ $REFQ XCG=39.0,$ $AXIBOD TNOSE=1.,LNOSE=12.0,DNOSE=12.0,LCENTR=54.0,DCENTR=12.0,$ $FINSET1 SECTYP=1., SSPAN=0.0,9.0, CHORD=14.0,8.0, XLE=64.0, SWEEP=0.0, STA=1.0, NPANEL=4., PHIF=45.0,135.0,225.0,315.0, GAM=0.00,0.00,0.00,0.00, CFOC=0.0,0.25,0.25,0.25,$ NACA-1-4-0310 SAVE NEXT CASE * WARNING * THE REFERENCE AREA IS UNSPECIFIED, DEFAULT VALUE ASSUMED * WARNING * THE REFERENCE LENGTH IS UNSPECIFIED, DEFAULT VALUE ASSUMED THE BOUNDARY LAYER IS ASSUMED TO BE TURBULENT THE INPUT UNITS ARE IN INCHES, THE SCALE FACTOR IS 1.0000

Figure 2.12: for006.dat File Example (Case 1 Output, Page 2)

1 ***** THE USAF AUTOMATED MISSILE DATCOM * REV 01/06 ***** CASE 1 AERODYNAMIC METHODS FOR MISSILE CONFIGURATIONS PAGE 2 Example STATIC AERODYNAMICS FOR BODY-FIN SET 1

******* FLIGHT CONDITIONS AND REFERENCE QUANTITIES ******* MACH NO = 0.40 REYNOLDS NO = 2.827E+06 /FT ALTITUDE = 0.0 FT DYNAMIC PRESSURE = 237.02 LB/FT**2 SIDESLIP = 0.00 DEG ROLL = 0.00 DEG REF AREA = 113.097 IN**2 MOMENT CENTER = 39.000 IN REF LENGTH = 12.00 IN LAT REF LENGTH = 12.00 IN

----- LONGITUDINAL ----- -- LATERAL DIRECTIONAL -- ALPHA CN CM CA CY CLN CLL

-8.00 -1.200 1.360 0.032 0.000 0.000 0.000 -4.00 -0.585 0.682 0.091 0.000 0.000 0.000 0.00 0.000 0.000 0.113 0.000 0.000 0.000 4.00 0.585 -0.682 0.091 0.000 0.000 0.000 8.00 1.200 -1.360 0.032 0.000 0.000 0.000

ALPHA CL CD CL/CD X-C.P.

-8.00 -1.183 0.199 -5.943 -1.134 -4.00 -0.578 0.131 -4.399 -1.165 0.00 0.000 0.113 0.000 -1.165 4.00 0.578 0.131 4.399 -1.165 8.00 1.183 0.199 5.943 -1.134

X-C.P. MEAS. FROM MOMENT CENTER IN REF. LENGTHS, NEG. AFT OF MOMENT CENTER

---------- DERIVATIVES (PER RADIAN) ---------- ALPHA CNA CMA CYB CLNB CLLB -8.00 9.0007 -9.6911 -9.3921 11.8173 0.2469 -4.00 8.5908 -9.7420 -8.7265 10.6220 -0.0021 0.00 8.3861 -9.7675 -8.1787 9.3495 0.0000 4.00 8.5908 -9.7420 -8.7265 10.6220 0.0021 8.00 9.0007 -9.6911 -9.3921 11.8173 -0.2469

PANEL DEFLECTION ANGLES (DEGREES) SET FIN 1 FIN 2 FIN 3 FIN 4 FIN 5 FIN 6 FIN 7 FIN 8 1 0.00 0.00 0.00 0.00

1 ***** THE USAF AUTOMATED MISSILE DATCOM * REV 01/06 ***** CASE 1 AERODYNAMIC METHODS FOR MISSILE CONFIGURATIONS PAGE 4 Example BODY + 1 FIN SET DYNAMIC DERIVATIVES

------------ DYNAMIC DERIVATIVES (PER RADIAN) ----------- ALPHA CNQ CMQ CAQ CNAD CMAD -8.00 42.648 -93.625 3.424 26.852 -13.587 -4.00 40.731 -88.833 0.820 26.852 -13.587 0.00 42.257 -92.660 -2.175 26.852 -13.587 4.00 44.700 -98.776 -4.956 26.852 -13.587 8.00 44.992 -99.495 -7.183 26.852 -13.587

PITCH RATE DERIVATIVES NON-DIMENSIONALIZED BY Q*LREF/2*V

------------ DYNAMIC DERIVATIVES (PER RADIAN) ----------- ALPHA CYR CLNR CLLR CYP CLNP CLLP -8.00 43.645 -96.560 0.057 -0.036 0.090 -13.514 -4.00 42.541 -93.804 0.022 -0.003 0.008 -12.558 0.00 42.082 -92.660 0.000 0.000 0.000 -11.496 4.00 42.541 -93.804 -0.022 0.003 -0.008 -12.558 8.00 43.645 -96.560 -0.057 0.036 -0.090 -13.514

YAW AND ROLL RATE DERIVATIVES NON-DIMENSIONALIZED BY R*LATREF/2*V

-8.00 -1.233 1.421 0.053 0.000 0.000 0.000 -4.00 -0.604 0.721 0.110 0.000 0.000 0.000 0.00 0.000 0.000 0.132 0.000 0.000 0.000 4.00 0.604 -0.721 0.110 0.000 0.000 0.000 8.00 1.233 -1.421 0.053 0.000 0.000 0.000

-8.00 -1.214 0.224 -5.416 -1.152 -4.00 -0.595 0.152 -3.922 -1.192 0.00 0.000 0.132 0.000 -1.192 4.00 0.595 0.152 3.922 -1.192 8.00 1.214 0.224 5.416 -1.152

YAW AND ROLL RATE DERIVATIVES NON-DIMENSIONALIZED BY R*LATREF/2*V*** NOSE TIP ANGLE GREATER THAN MACH ANGLE, HYBRID THEORY INVALID SECOND ORDER SHOCK EXPANSION TO BE USED

*** NOSE TIP ANGLE GREATER THAN MACH ANGLE, HYBRID THEORY INVALID SECOND ORDER SHOCK EXPANSION TO BE USED

-8.00 -1.108 1.049 0.771 0.000 0.000 0.000 -4.00 -0.533 0.569 0.782 0.000 0.000 0.000 0.00 0.000 0.000 0.786 0.000 0.000 0.000 4.00 0.533 -0.569 0.782 0.000 0.000 0.000 8.00 1.108 -1.049 0.771 0.000 0.000 0.000

-8.00 -0.990 0.918 -1.079 -0.946 -4.00 -0.478 0.817 -0.584 -1.067 0.00 0.000 0.786 0.000 -1.067 4.00 0.478 0.817 0.584 -1.067 8.00 0.990 0.918 1.079 -0.946

BODY ALONE LINEAR DATA GENERATED FROM SECOND ORDER SHOCK EXPANSION METHOD

------------ DYNAMIC DERIVATIVES (PER RADIAN) ----------- ALPHA CNQ CMQ CAQ CNAD CMAD -8.00 39.342 -108.127 0.000 28.285 -9.526 -4.00 39.022 -107.260 0.000 28.285 -9.526 0.00 40.288 -110.734 0.000 28.285 -9.526 4.00 40.755 -112.006 0.000 28.285 -9.526 8.00 39.578 -108.773 0.000 28.285 -9.526

Figure 2.24: for006.dat File Example (Case 2 Output, Page 1 and 2)

1 ***** THE USAF AUTOMATED MISSILE DATCOM * REV 01/06 ***** CASE 2 AERODYNAMIC METHODS FOR MISSILE CONFIGURATIONS PAGE 1 CASE INPUTS FOLLOWING ARE THE CARDS INPUT FOR THIS CASE

CASEID PANEL DEFLECTION DAMP $DEFLCT DELTA1=5.0,0.,0.,-5.0,$ SAVE NEXT CASE * WARNING * THE REFERENCE AREA IS UNSPECIFIED, DEFAULT VALUE ASSUMED * WARNING * THE REFERENCE LENGTH IS UNSPECIFIED, DEFAULT VALUE ASSUMED THE BOUNDARY LAYER IS ASSUMED TO BE TURBULENT THE INPUT UNITS ARE IN INCHES, THE SCALE FACTOR IS 1.00001 ***** THE USAF AUTOMATED MISSILE DATCOM * REV 01/06 ***** CASE 2 AERODYNAMIC METHODS FOR MISSILE CONFIGURATIONS PAGE 2 PANEL DEFLECTION STATIC AERODYNAMICS FOR BODY-FIN SET 1

-8.00 -1.200 1.360 0.032 0.000 0.000 0.000 -4.00 -0.585 0.682 0.091 0.000 0.000 0.000 0.00 0.000 0.000 0.113 0.000 0.000 0.000 4.00 0.585 -0.682 0.091 0.000 0.000 0.000 8.00 1.200 -1.360 0.032 0.000 0.000 0.000

-8.00 -1.183 0.199 -5.943 -1.134 -4.00 -0.578 0.131 -4.399 -1.165 0.00 0.000 0.113 0.000 -1.165 4.00 0.578 0.131 4.399 -1.165 8.00 1.183 0.199 5.943 -1.134

1 ***** THE USAF AUTOMATED MISSILE DATCOM * REV 01/06 ***** CASE 2 AERODYNAMIC METHODS FOR MISSILE CONFIGURATIONS PAGE 3 PANEL DEFLECTION STATIC AERODYNAMICS FOR BODY-FIN SET 1

FLAP DEFLECTION ANGLES (DEGREES) SET FIN 1 FIN 2 FIN 3 FIN 4 FIN 5 FIN 6 FIN 7 FIN 8 1 5.00 0.00 0.00 -5.00 EQUIVALENT PANEL DEFLECTION ANGLES (DEGREES) SET FIN 1 FIN 2 FIN 3 FIN 4 FIN 5 FIN 6 FIN 7 FIN 8 1 0.00 0.00 0.00 0.00

1 ***** THE USAF AUTOMATED MISSILE DATCOM * REV 01/06 ***** CASE 2 AERODYNAMIC METHODS FOR MISSILE CONFIGURATIONS PAGE 4 PANEL DEFLECTION BODY + 1 FIN SET DYNAMIC DERIVATIVES