[american institute of aeronautics and astronautics 37th aerospace sciences meeting and exhibit -...

(c)l999 American Institute of Aeronautics & Astronautics

A994 6677

AIAA 99-0830 FMCAD-Flight Mechanics Computer Aided Design Software GGkmen Mahmutyazxcroglu, Hakan Tiftikqi and $jamil Ktxkmaz Scientific and Technical Council of Turkey Defense Industries Research and Development Institute TUB/TAK-SAGE Pk, 16,0626 1 Mamak, Ankara Turkey

37th Aerospace Sciences Meeting & Exhibit

January 1 l-14, 1999 / Rem, NV

-(c)1999 American Institute of Aeronautics & Astronautics

A&4-99-0830

‘FMCAD - FLIGHT MECHANICS COMPUTER AIDED DESIGN SOFTWARE

$amil Korkmaz, Giikmen Mahmutyaznogu, Hakan Tiftikqi, Taner Giikhan Scientific and Technical Council of Turkey

Defense Industries Research and Development Institute TURITAK-SAGE

Pk. 16,06261 Marnak, Ankara Turkey

ABSTRACT As a consequence of the

developments in computer technology, computer aided design software became an indispensible tool in design. Today it is hard to imagine a design activity without the support of computers. This paper provides information about a new computer software, FMCAD. It is developed. to assist flight mechanists in design by performing solid modeling, aerodynamic calculation and flight simulation, all in one session.

1. INTRODUCTION TijBiTAK-SAGE is a research

institute in defense industry since 1970’s, focused on guided and unguided missiles. During the past years various computer codes have been developed to carry out calculations. Most of these codes are written in Fortran language, which has poor user

’ Cqyight 0 1999 The Amaican In&&e of ~atiics and

Aatlwlatics Inc. Allrights r-ed

interface. Therefore, those software generally can be used only by the developer. In 1995, a project to prepare a professional computer aided design software for flight mechanics was launched. The proposal was submitted to Turkish Ministry of National Defense, Research and Development Directorate in 1996. It was accepted and the project was initiated in 1997. The first task was the selection of computer language. After an investigation of the available programming languages, Delphi was chosen for the sake of readability and its visual programming capabilities. Readability is considered because readable code makes later modifications easier. Also the use of Delphi brings the advantages of Windows based programming like multi-tasking. The basic modules of the FMCAD software are as follows: l Solid Modeling Module,

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American Institiute of Aeronautics and Astronautics


AIAA-99-0830

0 Aerodynamic Module, l Simulation Modules,

n Stability Analysis Module, n Dispersion Analysis Module, . Firing Tables Module, q Propulsion Management Module,

l Warhead Effectiveness Module, In the following part information about some of these modules will be given.

2. SOLID MODELING MODULE One of the preliminary steps in

missile design is to obtain its inertial data and to be able to make modifications in a short time. Solid Modeling Module (Figure 1) was written with these goals in mind. It provides the designer with tools that allow quick and easy entry of main mechanical parts for both standard and user defined geometries.

Figure 1. A view form Solid Modeling Module.

Solid Modeling Module provides applied on the parts that make up the whole mainly three types of functions that can be geometry. These are adding, editing and

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removing. The user can add a part by either choosing it from the standard geometry library, for example from standard warhead types like tangent ogive, or can define a new geometry. Improved accuracy is obtained when the custom parts are defined in a more precise manner but it will also take more time. However, Solid Modeling Module should not be used for very accurate modeling of the missile. Rather it is useful to get some quick estimates of the major parameters during the very initial states of design.

When modification of a part is needed this can be as easily done as adding it. From the related windows the desired editing operations can be carried out. When a part is to be removed, similar procedures described for editing are followed.

Every time the geometry is changed, results are updated and the new geometry is drawn on screen. It can be viewed and rotated in three-dimensional space, which gives a better appreciation of the model.

The figure that appears on the screen can be printed or imported in windows metafile (WMF) or HP graphics language (HGL) formats.

The inertial data comprising mass, center of mass, axial inertia, transverse inertia are updated and shown on screen as soon as a new part is added, edited or removed.

One final function of Solid Modeling Module is preparation of input for Aerodynamic Module, which is included in

the FMCAD package. Specific information is supplied and data that is required by Aerodynamic Module is generated which is to be used in the aerodynamic calculations of the missile.

3. AERODYNAMIC MODULE Obtaining aerodynamic data is a vital

step in performance calculations of a missile. In preliminary design of the missile, one can easily obtain aerodynamic data with Aerodynamic Module.

Aerodynamic Module uses Missile DATCOM to compute aerodynamic coefficients. The Aerodynamic Module does the pre and post processing for the solver. The aerodynamic solver is capable of handling basic missile geometries with cruciform fins and axisymmetric bodies. While arranging the input file, Aerodynamic Module can use an old input file or geometry tie which is prepared by Solid Modeling Module. User can also prepare input file with Aerodynamic Module. This file is used by the aerodynamic calculation so&are to find out the aerodynamic coefficients,

With arrange outputs option necessary tiles for Simulation Module are created. Force and moment coefficient variation with Mach number at zero angle of attack can be seen. Coefficient of normal force, axial force, pitching moment etc. variation with angle of attack and sideslip angle at various math numbers can be plotted. Calculation of jet plume effects is also possible.

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(c)l999 American Institute of Aeronautics &Astronautics

AIAA-99-0830

‘igure 2. A view from the output of the Aerodynamic Module.

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AIAA-99-0830

4. SIMULATION MODULES Flight simulation in FMCAD is used

as a design-by-analysis tool for the design stage of missiles; that is, simulation is performed for a particular con6guration and then corrective actions on design parameters are taken by user to improve flight performance.

Simulation Modules do the following calculations: l Performing time domain flight simulation, l Firing table preparation, l Performing stability analysis, l Petiorming dispersion analysis, 0 Propulsion management computation.

Simulation code is capable of performing 2+1 DOF, 3+1 DOF (+l stands for additional roll motion) and 6 DOF simulations. Ballistic bodies that can simulated by Simulation Modules are limited by Solid Modeling Module and Aerodynamic Module which restricts the geometry of ballistic to axially symmetric bodies with cruciform tins. For Wrap-Around-Fins (WAF), if user has c,,,~ ,c~,, data by some

other means, then this data can be used in aerodynamic module and then in simulation modules to simulate WAF rockets.

Currently Simulation Module has the following mathematical models:

in-launcher dynamics, thrust misalignment, center of gravity and inertia misalignment, atmospheric model for density, temperature, based on mainly US standard 76 Atmosphere axial and side wind profiles, gust model earth rotation model WGS84-reference ellipsoid with related gravity field.

Dispersion Module does the dispersion calculations using the Monte Carlo simulations.

Propulsion Management Module is used for estimation of required propulsion for desired range given the warhead weight, diameter of the missile, desired launcher exit acceleration and specific impulse. This module is needed at the preliminary stages of rocket design.

stability analysis performes gyroscopic stability analysis, computes resonance bands and dynamic roll bounds for artillery weapons and finned rockets.

Each Module has the capability of displaying the outputs.

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AIAA-99-0830

Figure 4 Missile and simulation properties windows

i

i

x{tIl}-z~m} 3857.G ---_-- r-- _--- :,~,~-.~ _---: ----------I;

, : -x :

1 I I , 1 ,’ - ,

I I’ : 1

7 I.. I :

2878.68 .-___-_ :,; ------ --+ -------- ----

I,

__----- -; I’

,, ‘I : :

I : I

8

y. 15 -;---;+- __-_-__L- :- _---__--_ + __-._-____ x . ,, I

I

: 1 I

I ’ A _______ cm---- __-_ I_-- -------,-_-

43

-----+ _ I I

/I : :

‘. I a

1: ’

1; i: .2s ______! ____ - ____-- :--- ---I -J_--------- I

3Y.4 6294.7 1255C 31G7.05 )i 9422.35

y,..-- --m-s

Figure 5 A view from the output of the Simulation Module.

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4.1 Launcher Model In the case of rigid helical rail rocket-

launcher, general equations of motion for a rocket with multiple sabot, rider lock, spin lock is obtained using Newton-Euler formulation. Due to number of contacts, such a system is indeterminate and thus can not be solved explicitly. So specific cases are investigated. For the con&guration of 4 sabots, 4 rider locks, and 2 spin locks, a

t-x

10

8

6

4

2

0

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“semi-explicit” expression could be obtained. By “semi-explicit” it is meant that to find solution all contact configurations are solved and checked for physical realizability. For above mentioned launcher this means 24=16 possible configurations. Below given some plots of results for Multiple Launch Rocket with trapezoidal thrust profile(as an approximation inside launcher).

t-xcbt

Figure 6 Distance travelled and velocity

Figure 7 Contact transition map. Horizontal axis indicates discrete contact states and

vertical axis is an index corresponding to time.

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AIAA-99-0830

petal +i*zeta21 peM+i’zetaq

FizzI

1698.3804

352.957 I~.3604

1898.3604

t-&al&t-zeta2 t-zeta3Bt-zeta4 I I I I I I I 1

Figure 8 Contact forces in sabots and rider locks. Two upper figure are magnitudes of forces

at sabot and rider. Two figure below show individual force magnitudes for sabots and rider

locks.

x IO4 I I I I I

2.5

0 0.05 0.1 0.15 0.2 0.25 0.3

Figure 9 Rider lock normal force

Figure 6 shows time-vs- distance group consisting of two oppositely placed travelled and velocity.Figure 7 shows contact contacts. First two indices correspond to states at rider locks and sabots by discrete rider locks and last two indices correspond logical states 0 and 1. Horizontal axis is to sabot contacts. Discrete values are discrete and gives mutual exclusive contact smoothly rendered to emphasize contact

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transition. Figure 8 shows contact normal forces (6, ,c2) and (c3 ,c4) in body fixed came corresponding to rider and sabot contacts, respectively.

Zn above simulations launcher length and hence simulation time are kept long intentionally to see behaviour in long time. From figures some expected results such as periodic contact switching, increase in frequency of forces, constancy of magnitudes of sabot and rider lock forces can be seen immediately.

Other launcher models can handle rockets with nozzle groove , and rockets without any roll source.

4.2 Atmospheric Model Atmospheric model includes

calculation of l density, temperature for altitudes

ranging from 0 to 80 km, l wind velocity by user defined

protie l gust/discrete gust velocity Thermodynamic properties are

computed from a Gmction fitted to US76 standard atmosphere model where user specifies temperature in ground levelGust model is so-called Dryden gust model. Wind model allows users to define range wind and cross wind profiles. For wind profile data exponential interpolation is used.

4.3 Aerodvnamic model for flipht simulation

Aerodynamic model employs three dimensional aerodynamic data which is tabulated for different angle of attack, sideslip angle and Mach number; or, one dimensional data for only Mach number, depending on the desired DOF of simulation (2/3 or 6).

In calculation of aerodynamic loads following aerodynamic coefficients are considered,

AIAA-99-0830

c ac ma =C,,W,Aa)=:*

c, = c,-”

i

(A4, p, a) if in coast phase

c? (M, p, a) else (in Imost phase)

C, =C,(M,p,a)=:C,(M,-a,p) :

C, = C, W, A a)

Cl =G@f,P,a)

Clp =Cl,W,Pd

C, = C, W, A a) C, = -Cm @4,-a, p)

C ~Wp.p) ac,

= G(Bp,p) W) =: apap

Three indexed coefficients are linearly interpolated in a voxel defined for current Mach number, angle of attack, and side-slip angle (Mach,@). Current voxel is located by locating (Mach,cz$), in corresponding 1 dimensional arrays. Denoting lower index for (Macho, p) by 0 and upper index by 1, for arbitrarily choosen interpretation of 3 indices ( say in order Mach@) voxel vertices are given as

Goo.Gm&J’clooJ Gx~Gl,JG,JG3,

then linear interpolation follows as c = qiqwcooo + H’C& + VW&J + WC,,,)) +

-- ~(V(WC,, +w~ol)+~wc~Io +M’c~,,))

where i = l-u and u,v,w are corresponding (MachaJ3) fractions, viz.

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U= M-M,,

Ml -MO a-a, v=- al -a~

,22- A -A

Most of the time in computation of aerodynamic forces/moments is spent in locating the current (Mach&) in respective 1 dimensional arrays. So various locating algorithms including direct search, binary search are implemented and employed for faster computation.

4.4 Initial Value Problem solvers In simulation module, there are two

solvers for ODE Initial Value Problems (IVP), variable-step RKF45 (Runge-Kutta- Fehlberg45) and the fourth order Rosenbrock stiff method by Kaps-Rentrop algorithm. Stiff-solvers are capable of solving so-called stiff systems for which classical solvers like Runge-Kutta, Adams-Bashforth, Adams-Moulton multistep methods are incapable of solving efficiently or don’t work at all. Since stiff-solvers require Jacobian of system and nonlinearities in missile model like aerodynamics, atmospheric formulation make obtaining Jacobian in symbolic form very complicated, a numerical Jacobian evaluator which selects time difference steps adaptively to attain required accuracy is implemented.

5.FTJTURE WORK FMCAD software provides all the

tools that a designer needs in modeling and simulation of missiles of axi-symmetric geometry. Besides, it prepares firing tables and makes statistical computations for interpretation of simulation results.

Future plans include warhead effectiveness analysis and interior ballistics modules, former of which computes the lethal radius for HE and cargo type warheads&c. and latter computes interior ballistics for artillery weapon gunnery to

AlAA-99-0830

obtain peak thermodynamic conditions such as maximum pressure, temperature, &c and muzzle exit conditions like exit velocity, acceleration. Also present 3d package can be extended to model some 3d primitives and curved profiles to enhance modeling time and accuracy together with better visualization capabilities.

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