study on flight mechanics and simulation of f16

STUDY ON FLIGHT MECHANICS AND SIMULATION OF F16

DEPT OF AERONAUTICAL ENGINEERING, NMIT

TABLE OF CONTENTS

1 INTRODUCTION.........................................................................................................2

1.1 F16 Fight Falcon Cockpit....................................................................................2

1.2 Engine...................................................................................................................3

1.3 Navigation and Communication.........................................................................3

1.4 Flight Mechanics..................................................................................................3

1.5 Modelling..............................................................................................................5

1.6 Flight Simulation..................................................................................................5

1.7 Fidelity...................................................................................................................6

1.8 Automatic Control Theory..................................................................................6

2 LITERATURE SURVEY ........................................................................................7

3 OBJECTIVE...............................................................................................................9

4 METHODOLOGY.....................................................................................................9

4.1 12 Equations of Motion.......................................................................................9

4.2 Solving for Equations of Motion.......................................................................11

4.3 Modelling............................................................................................................16

4.4 States....................................................................................................................17

4.5 Controls..............................................................................................................18

4.6 Actuators............................................................................................................20

4.7 Rad2Deg.............................................................................................................23

4.8 Subsystem...........................................................................................................24

5 RESULTS..................................................................................................................26

5.1 Flight Dynamics..................................................................................................26

5.1.1 Condition 1................................................................................................26

5.1.2 Condition 2................................................................................................36

5.2 Linearizing the Nonlinear F16 Plant................................................................44

5.2.1 Condition 1................................................................................................44

5.2.2 Condition 2................................................................................................45

5.2.3 Condition 3................................................................................................46

5.2.4 Condition 4................................................................................................47

5.2.5 Condition 5................................................................................................48

5.2.6 Condition 6................................................................................................49

6 CONCLUSION..........................................................................................................51

7 REFERENCES............................................................................................................52



1. INTRODUCTION

The General Dynamics F-16 Fighting Falcon is a single-engine multirole fighter

aircraft originally developed by General Dynamics for the United States Air Force

Designed as an air superiority day fighter, it evolved into a successful all-

weather multi role aircraft. Over 4,500 aircraft have been built since production

was approved in 1976.

The F-16 is lighter, less expensive alternative to the F-15 Eagle. Unlike the F-15,

which is purely an air superiority fighter, the F-16 is a multi-role aircraft, capable

of attacking air and ground targets. This aircraft is small, but highly

maneuverable. The F-16 has a bubble single-piece canopy for excellent pilot

visibility, which becomes during close combat . In the future it will be replaced by

the new F-35 Lightning II.

The Fighting Falcon has key features including a frameless bubble canopy for

better visibility, side-mounted control stick to ease control while maneuvering, a

seat reclined 30 degrees to reduce the effect of g-forces on the pilot, and the first

use of a relaxed static stability ( the tendency of an aircraft to change

its attitude and angle of bank of its own accord)/fly-by-wire flight control system

which helps to make it a nimble aircraft.

The F-16 was designed to be relatively inexpensive to build and simpler to

maintain than earlier-generation fighters.

The model is extremely a non linear and complicated system. But it is easier to

maintain than like other fighter aircrafts. So it can be used for educational

purposes to learn basic concepts of aircraft simulation and controller design.

1.1 F-16 Fighting Falcon cockpit

Advanced equipment being fitted on the current build of the F-16 includes Honeywell

colour flat-panel liquid crystal multifunction displays, digital terrain system, modular

mission computer, colour video camera to record the pilot's view of the head-up display

(HUD), a colour triple-deck video recorder and an enhanced programmable display

generator.

https://en.wikipedia.org/wiki/Air_superiority

https://en.wikipedia.org/wiki/Day_fighter

https://en.wikipedia.org/wiki/Night_fighter

https://en.wikipedia.org/wiki/Night_fighter

https://en.wikipedia.org/wiki/Bubble_canopy

https://en.wikipedia.org/wiki/Side-stick

https://en.wikipedia.org/wiki/G-force

https://en.wikipedia.org/wiki/Relaxed_stability

https://en.wikipedia.org/wiki/Aircraft_attitude



Under the USAF project Sure Strike, the F-16 is equipped with an improved data modem

(IDM), which automatically provides target data to the HUD using data transmitted by a

ground observer.

The seat-back angle of the aircraft has been increased from 13° to 30° to provide

increased comfort for the pilot.

1.2 Engines

The aircraft is powered by a single engine: the General Electric F110-GE-129 or Pratt and

Whitney F100-PW-229. The fuel supply is equipped with an inert gas anti-fire system.

An in-flight refueling probe is installed in the top of the fuselage.

Lockheed Martin completed developmental flight testing on new conformal fuel tanks

(CFT) for the F-16, which will significantly add to the aircraft's mission radius. First

flight of the F-16 equipped with the new tanks was in March 2003. Greece is the launch

customer for the CFT.

1.3 Navigation and communications

The F-16 was the first operational US aircraft to receive a global positioning system

(GPS). The aircraft has an inertial navigation system and either a Northrop Grumman

(Litton) LN-39, LN-93 ring laser gyroscope or Honeywell H-423.

"The F-16 Fighting Falcon carries the Lockheed Martin LANTIRN infrared navigation

and targeting system."

1.4 Flight Mechanics

Flight mechanics are relevant to fixed wing aircraft (gliders, aeroplanes) and rotary wing

(helicopters) aircraft. Atmospheric flight mechanics is a broad heading that encompasses

three major disciplines; namely, performance, flight dynamics and aero elasticity.

Airplane performance deals with the determination of performance characteristics

such as range, endurance, rate of climb, and takeoff and landing distance as well

as flight path optimization.

Flight dynamics is concerned with the motion of an airplane due to internally or

externally generated disturbance.



The final subject included under the heading of atmospheric flight mechanics is

aeroelasticity. Aero elasticity deals with both static and dynamic aeroelastic

phenomena.

How well an airplane flies and how easily it can be controlled are subjects studied in

aircraft stability and control. By stability we mean the tendency of the airplane to return

to its equilibrium position after it has been disturbed. Stability and control studies are

concerned with motion of centre of gravity relative to the ground and motion of airplane

about the CG. Hence stability and control studies involve the use of 6 DOF equations of

motion. These studies are divided into 2 major categories.

Static stability and control

Dynamic stability and control.

Static stability is a tendency of the aircraft to return to its equilibrium position. In addition

to static stability, the aircraft also must be dynamically stable.

An airplane can be considered to be dynamically stable if after being disturbed from its

equilibrium flight condition the ensuing motion diminishes with time.

The flying qualities of an airplane are related to the stability and control characteristics

and can be defined as those stability and control characteristics important in forming the

pilot’s impression of the airplane. The pilot forms a subjective opinion about the erase or

difficulty of controlling the airplane in steady and maneuvering flight.

These requirements are used by procuring and regulatory agencies to determine

whether an airplane is acceptable for certification.

The purpose of these requirements is to ensure that the airplane has flying

qualities that place no limitation in the vehicle’s flight safety nor restrict the

ability of the airplane to perform its intended mission.



1.5 Modeling

Modeling is one of the most important parts in control engineering. It allows

mathematically representing the desired system and simulating it via appropriate

simulation programs. This way, computer simulations can be run and the controllers can

be tested. The non-linear F16 model has been implemented in Matlab / Simulink

environment.

1.6 Flight Simulation

To determine the flying quality specifications described in a previous section

requires some very elaborate test facilities. Both ground-based and in-flight simulators are

used to evaluate

Pilot opinion on aircraft response characteristics,

Stick force requirements, and

Human factor data such as instrument design, size and location.

Why Simulation?

Simulation is also used to study dynamic systems. There are many methods of modeling

systems which do not involve simulation but which involve the solution of a closed-form

system (such as a system of linear equations). Simulation is often essential in the

following cases:

1) The model is very complex with many variables and interacting components

2) The underlying variables relationships are non linear

3) The model contains random variates

4 )The model output is to be visual as in a 3D computer animation.

The power of simulation is that ---even for easily solvable linear systems--- a uniform

model execution technique can be used to solve a large variety of systems without

resorting to a ``bag of tricks'' where one must choose special-purpose and sometimes

arcane solution methods to avoid simulation. Another important aspect of the simulation

technique is that one builds a simulation model to replicate the actual system. When one

uses the closed-form approach, the model is sometimes twisted to suit the closed-form



nature of the solution method rather than to accurately represent the physical system. A

harmonious compromise is to tackle system modeling with a hybrid approach using both

closed-form methods and simulation. For example, we might begin to model a system

with closed-form analysis and then proceed later with a simulation. This evolutionary

procedure is often very effective.

1.7 Fidelity

Fidelity is the concept that express the degree to which a simulator or simulated

experience imitates the real world. It has been viewed as a critical variable in the design

of both mechanical simulator and computerized simulation experiences.

LOW FIDELITY: The low fidelity model represents a simpler model that doesn’t

include the effects of the leading edge flap. There is decoupling between

longitudinal and lateral directions.

HIGH FIDELITY: The high fidelity model includes the effect of the leading edge

flap and there is a noticeable coupling between the longitudinal and lateral

directions much like in a real aircraft

1.8 Automatic Control Theory

Control theory deals with the analysis and synthesis of logic for the control of a system.

In the broadest sense, a system can be thought of as a collection of components or parts

that work together to perform a particular function.

Autopilot system is to reduce the pilot workload.

Attitude control system to maintain pitch, roll, or heading.

Altitudes hold control system to maintain a desired altitude.

Fig 1: F-16 aircraft



2. LITERATURE REVIEW

Standard text books on Flight Mechanics and Control

Aerodynamic databases for various classes of aircraft

Current literature on control law design, flight simulation evaluation

Aircraft Flight Dynamics is an undergraduate course that presents theory and methods

for describing and predicting the motions of aircraft. The course introduces students to

the performance, stability, and control of a wide range of airborne vehicles. Attention

is given to mathematical models and techniques for analysis, simulation, and

evaluation of flying qualities, with brief discussion of guidance, navigation, and

control issues. Topics include equations of motion, configuration aerodynamics,

analysis of linear systems, and longitudinal/lateral/directional motions.

Nguyen, L.T., et al., Simulator study of stall/post-stall characteristics of a fighter

airplane with relaxed longitudinal static stability, NASA Tech. Pap. 1538, NASA,

Washington, D.C., Dec. 1979. “The mathematical model given here uses the wind-

tunnel data from NASA-Langley wind-tunnel tests on a scale model of an F-16

airplane. The data apply to the speed range up to about Mach=0.6, and were used in a

MASA-piloted simulation to study the maneuvering and stall/post-stall characteristics

of a relaxed static-stability airplane.”

http://www.princeton.edu/~stengel/MAE331.html



3. OBJECTIVE

Analyzing the longitudinal and lateral-directional modes

Carrying out simulation studies at different flight condition for synthetic pilot inputs

viz. elevator, aileron and rudder

Understanding the process of simulation is important to one who has to go beyond

the real world conditions/environments. Here we have selected Matlab as software.

4. METHODOLOGY

• Here we have selected F-16 aircraft for study.

• Flight simulation using nonlinear 6 DOF models of the aircraft.

• Extract the longitudinal, lateral and directional modes.

4.1Equations of motion

Equations of motion are equations that describe the behavior of a physical

system in terms of its motion as a function of time.

The aircraft is treated as a rigid body with six degrees of freedom. This is, of

course, an idealization of actual flight dynamics, but avoids the complexities that a

consideration of elastic forces and the movement of aircraft parts, such as engine

rotors, ailerons, and the like would introduce. Other simplifying assumptions

regarding the dynamics of flight have been made to reduce computational

complexity.

Control of the hypothetical aircraft is accomplished by adjusting values of engine

thrust, aerodynamic lift, and bank angle. This models an aircraft which uses

ailerons, elevators and engines alone to control speed, heading and altitude.

Aircraft yaw in all flight maneuvers is assumed to be constant and zero. Other

ignored are the complexities introduced by considering the effect aircraft shape and

motion have on the external forces which operate on the aircraft. In this model, the

aircraft is capable of both translational and rotational motion.

The equations of motion which are as follows,

The gravitational forces acting on the airplane acts through the center of gravity of

the airplane. Because the body axis system is fixed to the center of gravity, and the

gravitational force will not produce any moments. The gravitational force

components along the X, Y & Z axis are:

(FX) gravity = -mgsinθ

(FY) gravity = mgcosθsinɸ

(FZ) gravity = mgcosθcosɸ

https://en.wikipedia.org/wiki/Equation

https://en.wikipedia.org/wiki/Physical_system

https://en.wikipedia.org/wiki/Physical_system

https://en.wikipedia.org/wiki/Motion_(physics)

https://en.wikipedia.org/wiki/Function_(mathematics)



The force equation for any rigid body

X - mgSθ= m u + qw – rv)

Y + mgCθSɸ= m v + ru – pw)

Z + mgCθCɸ=m + pv – qu)

Where

m =Mass of the airplane

g =Gravitational force

u, v & w =Velocities along X, Y & Z axes respectively

p = Roll rate

q = Pitch rate

r = Yaw rate

The moment equations are

L = Ix ṗ + (Iz – Iy) qr – Ixz(pq + ṙ)

M = Iy q ̇ +(Ix – Iz)pr + Ixz(p2 − r

2 )

N = Iz ṙ+(Iy – Ix)pq + Ixz qr − ṗ)

Where

L= Rolling moment,

M= Pitching moment

N= Yawing Moment

p= Roll rate

q= Pitch rate

r= Yaw rate

Ix =Moment of inertia along X-axis

Iy = Moment of inertia along Y-axis

Iz = Moment of inertia along Z-axis



The relationship between the angular velocities in the body frame (p, q & r) and the

Euler rates ( , & )

Body angular velocities in terms of Euler angles and Euler rates

p = ɸ - Sɸ

q = Cɸ + CɸSθ

r = CθCɸ - Sɸ

Euler rates in terms of Euler angles and body angular velocities

= qCɸ -rSɸ

ɸ = p + qSɸTθ+ rCɸTθ

=(qSɸ + rCɸ)secθ

Where

Sψ= Sinψ

Sθ=Sin

Sɸ=Sin

Cψ= Cosψ

Cθ=Cos

Cɸ=Cos

Tθ= Tanθ



Velocity of aircraft in the fixed frame in terms of Euler angles and body velocity

components

4.2 Solving the equations of motion (Trim or equilibrium)

An airplane is said to be trimmed if the forces and moments acting on the airplane are in

equilibrium. Stability is a property of an equilibrium state. Static stability is the initial

tendency of the vehicle to return to its equilibrium state after a disturbance. In general,

trimming neutralizes the force required to keep control surfaces in a specific position.

Small –Disturbance theory

The equations developed can be linearized using the small-disturbance theory.

In applying the small-disturbance theory, it is assumed that the motion of the aircraft

consists of small deviations about to steady flight condition.

All the variables in the equations of motion are replaced by a reference value plus a

perturbation or disturbance:

u =u0+∆u v=v0+∆v w=w0+∆w

p=p0+∆p q=q0+∆q r=r0+∆r

X=X0+∆X Y=Y0+∆Y Z=Z0+∆Z

M=M0+∆M N=N0+∆N L=L0+∆L

δ= δ0+∆δ

The coefficients in the differential equations are made up of the aerodynamic stability

derivatives, mass, and inertia characteristics of the airplane. The equations can be written

as the set of first order differential equations, called state space or state variable

equations.

=AX + Bη



Where X is the state vector, η is the control vector and the matrices A & B contains the

aircraft’s dimensional derivatives.

The linearized longitudinal rigid body equations of motion are given below:

Longitudinal equation of motion,

(dt

ud) - Xu Δu – (Xw Δw) + gcosθ0) Δθ = XδeΔδe + Xδe ΔδT

-ZU Δu + [ 1-Zu)dt

wd - Zw Δw] -[(uv+Zq)

dt

d - Δθ gsinθ] Δθ = ZδeΔδe+ ZδTΔδT

-Mu Δu - Δw Mw (dt

wd)+ Δw Mw + (

2

2

dt

wd) - Mq(

dt

wd) = MδeΔδe+MδTΔδT

Where Δδ and ΔδT are the aerodynamic and propulsive controls

The force derivatives Zq and Z usually they are neglected because they contribute very

little to the aircraft response.

Tww0wqwwwuwu

0wu

wu

00

ZMMZMM

ZZ

XX

q

v

u

0100

0uMMZMMZMM

0uZZ

g0XX

q

v

u

TT

T

T

Phugoid mode is an aircraft motion where the vehicle pitches up and climbs, and then

pitches down and descends, accompanied by speeding up and slowing down as it goes

"uphill" and "downhill." It has a gradual interchange of potential and kinematic energy

about the equilibrium altitude and airspeed. It is characterized by changing in pitch

altitude, and velocity at a constant angle of attack.

Where the frequency and damping ratios can be expressed as

0

u

npu

gZ

ζp = np

u

2

X

Frequency of oscillation and the damping ratio are inversely proportional to the forward

speed and the lift- to – drag ratio.



Short period mode is usually heavily damped oscillation with a period of only a few

seconds. The motion is a rapid pitching of the aircraft about the center of gravity and

changing the angle of attack.

Where the frequency and damping ratios can be expressed as

ωnsp = [(Mq

0u

z - Mα)]1/2

ζsp = - [(Mq + M

0u

z )] / (2 ωnsp)

Longitudinal derivatives

Xu = (CDu + 2CDo)QS/mu0 Xw = -(CDα- CL0)/ mu0

Zu = -( CLu + 2 CL0) / mu0

Zw = -( CLα + CDo) QS/ mu0 Z =-Czα QS/ mu0

Zα = u0 Z Zα = u0 Z

Zq = -Czq QS /m Zδe = -Cz δeQS/m

Mu =Cmu

Mw = Cmα M = Cmα

Mα = u0 Mw Mα = u0 M

Mq = Cmq Sc )/ Iy Mδe = Cmδe Sc )/ Iy

The lateral directional equations of motion consist of the side force, rolling moment and

yawing moment equation of motion. The lateral equation arranged in state space variable

= AX + Bη

Where X is the state vector, η is the control vector and the matrices A & B contains the

aircraft’s dimensional derivatives.



The linearized lateral rigid body equations of motion are given below

Lateral equations,

dt

vd -Yv Δv -YpΔp +u0Δr -YrΔr - gcosθ0) = Yδr+Δδr

-LΔv +dt

pd - LpΔp - (

X

YZ

I

I

dt

rd) + Lr Δr= Lδa Δδa +Lδr Δδr

-N Δv - (Z

XZ

I

I

dt

pd) +NpΔp +

dt

rd -NrΔr= Nδa Δδa +Nδr Δδr

If the product of inertia Ixz= 0

r

a

rPv

rpv

0r0pv

00

NN

LL

L0

r

p

v

0010

0NNN

0LLL

cosg)Yu(YY

r

p

v

ra

ra

r

The characteristic equation is obtained by expanding

AI = 0

Where I and A are the identity and lateral stability matrices. The characteristic

equation determined from the stability matrix A yields a quadratic equation

Aλ4 + Bλ

3 + Cλ

2 + Dλ + E = 0

Where A, B, C, D and E are the functions of the stability derivatives, mass and inertia

characteristic of the airplane. This equation is called the characteristic polynomial.

Solving it will give four Eigen values λ1 , λ2 , λ3 and λ4 .

In general, we will find the roots of the lateral directional characteristic equation to be

composed of two real roots and a pair of complex roots. The roots will be such that the

airplane response can be characterized by the following motions.

Spiral Mode: The motion is slowly convergent or divergent.

Roll mode: The motion is highly convergent.

Dutch roll mode: The motion is lightly damped oscillatory having low frequency.



Lateral derivatives

Yβ= QSCYβ/m Nβ = QSbCnβ/Iz Lβ=QSbCIβ/Ix

YP = QSbCyp/2mu0 Np = QSb2Cnr/2Izu0

Lp = QSb2CIp/2Ixu0

Yr = QSbCyr/2mu0 Nr = QSb2Cnr/2IZu0

Lr = QSb2CIr/2Ixu0

Yδa = QSCyδa/m Yδr = QSCyδr/m

Nδa = QSbCnδa/Iz Nδr =QSbCnδr/Iz

Lδa = QSbCIδa /Ix Lδr = QSbCIδr/Ix

Longitudinal and lateral stability derivatives

mm

CC

nn

CC

ll

CC

Cmα = Moment of inertia change in pitching moment due to change in angle of attack

Cnβ = Moment of inertia change in yawing moment due to change in side slip rate

Clβ = Moment of inertia change in rolling moment due to change in side slip rate



4.3 Modeling

Modeling is one of the most important parts in control engineering. It allows

mathematically representing the desired system and simulating it via appropriate

synthetic pilot inputs.

The non-linear F16 model has been constructed using Simulink.

The functional Simulink model is shown in fig 2.

Fig 2 : Actual layout of the Simulink model of the F-16 plant

• As can be seen from fig 2, the non-linear plant of the F-16 requires the four

controls, thirteen states, the leading edge flap deflection and a model flag as

inputs.

• The plant will output the twelve state derivatives and six other states of flight.



4.4 States

The non-linear F-16 plant requires thirteen state inputs. The thirteen state inputs are

shown in the Table 1.

State Variables

V

- true velocity, ft/sec

α

- angle of attack, radian

(range–10° ~ 45° )

β

- sideslip angle, radian (range–

30° ~ 30° )

φ

- Euler (roll) angle, rad

θ

- Euler (pitch) angle, rad

ϕ

- Euler (yaw) angle, rad

p

- roll rate, rad/sec

q

- pitch rate, rad/sec

r

- yaw rate, rad/sec

Ndis - north displacement, ft

Edis

- east displacement, ft

h

- altitude, ft

Ppow

- power

Table 1: State variables for non linear F16 aircraft



4.5 Controls

The F-16 Model allows for control over thrust, elevator, aileron and rudder. The

thrust is measured in pounds. Thrust acts positively along the positive body x-axis.

For the other control surfaces a positive deflection gives a decrease in the body

rates. A positive aileron deflection gives a decrease in the roll rate, p, this requires

that the right aileron deflect downward and the left aileron deflect upward. A

positive elevator deflection results in a decrease in pitch rate, q, thus elevator is

deflected downward. And a positive deflection of the decreases the yaw rate, r, and

can be described as a deflection to right. The control variables are shown in the

Table 2. The positive orientations for each control surface are shown in fig 3.

The maximum and minimum values and units for each control input is shown in

Table 3.

Control Variables:

δt

throttle setting, (0.0 – 1.0 )

δe

elevator setting, degree

δa

aileron setting, degree

δr

rudder setting, degree

Table 2: Control variables for F16 aircraft



Table 3: The control input units and maximum values.

Fig 3: simulink model of control input of the cockpit

CONTROL INPUT UNITS used

by nlplant

Min Max

Thrust Lbs Lbs 1000 19000

Elevator Deg Deg -25 25

Aileron Deg Deg -21.5 21.5

Rudder Deg Deg -30 30

Leading edge

flap

Deg Deg 0 25



4.6 Actuators

All of the actuators were modeled as first order lags with a gain (k) and limits on

deflection and rates. The thrust had a unity gain and a rate limit of ±10,000 lbs/s. the

elevator had a gain of 1/0.0495 and rate limits of ±60 deg/s. the aileron had a gain of

1/0.0495 and rate limits of ±80 deg/s. the rudder had a gain of 1/0.0495 and rate limits of

±120 deg/s . finally the leading edge flap had a gain of 1/0.0136 and a rate limit of ±25

deg/s as shown in the table 4.

CONTROL INPUTS GAIN RATE LIMITS

Thrust 1 ±10,000 lbs/s

Elevator 1/0.0495 (20.20) ±60 deg/s

Aileron 1/0.0495 (20.20) ±80 deg/s

Rudder 1/0.0495 (20.20) ±120 deg/s

Leading edge flap 1/0.0136 ±25 deg/s

Table 4: the control unit inputs with rate limits

Fig 4: Thrust model



Fig5: Elevator model

Fig 6: Aileron model



Fig 7: Rudder model

Fig 8: LEF actuator

The above models are the actuators of thrust, elevator, aileron, rudder and leading edge

flap deflections with first order lags of gain (k) and rate limits. These models are

constructed using the table 4.



4.7 Rad2deg

This will be taken from simulink control design, using the block gain as shown in the

fig 9.

Element wise gain (y=k.*u) or matrix gain (y=k*u or y=u*k)

Gain= 180/pi

dr = Radian-to-degree constant = 180/pi = 57.29578

Fig 9: Simulink model Rad2deg



4.8 Subsystem

This subsystem uses the set of scope blocks it is designed to get the result of the whole

model.

The output of the plant are the 12 state derivatives and normalized accelerations in the X,

Y and Z directions (anX, anY and anZ, respectively), Mach number (Ma), free stream

dynamic pressure (q) and static pressure (ps) as shown in the fig 10.

Fig 10: Simulink model of subsystem

Analyzing the longitudinal and lateral directional modes of the F16

For the chosen flight condition representing by altitude (ft) and velocity (ft/sec), the linear

time invariant state-space matrices(A, B, C and D) are obtained for the longitudinal and

lateral directions.

The states for longitudinal modes are altitude, pitch angle, magnitude of the total velocity,

angle of attack and pitch rate. The control inputs are thrust and elevator deflection.



5. RESULTS

5.1 FLIGHT DYNAMICS

LINEARIZING THE NON-LINEAR F-16 PLANT

For the following state-space matrices all angles and rotations are given in

degrees. All measures for distance are given in feet and time is given in seconds.

The longitudinal state-space matrices will in the form:

BuAxX

e

tB

q

h

A

q

h

DuCxY

e

tD

q

h

C

q

h



The lateral directional states are roll angle, yaw angle, magnitude of the total velocity,

side-slip angle, roll rate and yaw rate. The control inputs for this direction are thrust,

aileron deflection and rudder deflection.

The lateral state-space matrices (A, B, C and D) will be of the form:

BuAxX

r

a

t

B

r

p

A

r

p

DuCxY

r

a

t

D

r

p

C

r

p



5.1.1 Condition -1:

The results shown are for steady wings-level flight for an altitude of 15000 ft and a

velocity of 500 ft/s.

HIFI

Longitudinal



From the above values the following conditions are determined

Phugoid condition

Short period condition



Lateral



From the above A, B, C and D matrices following characterized motions are

obtained

Dutch roll

Spiral mode

Roll mode



LOFI

Longitudinal




Phugoid condition




Lateral




obtained

Dutch roll mode

Spiral mode

Roll mode

By observing the above values of LOFI and HIFI models it can be stated that both models

compare well for longitudinal motion and slightly (in decimals) different for lateral

directional motion.



5.1.2 Condition-2:

The results shown are for steady wings-level flight for an altitude of 10000 ft and a

velocity of 500 ft/s.

HIFI

Longitudinal




Phugoid condition




Lateral




obtained

Dutch roll mode

Spiral mode

Roll mode



LOFI

Longitudinal




Phugoid condition




Lateral




obtained

Dutch roll mode

Spiral mode

Roll mode

By observing the above values of LOFI and HIFI models it can be stated that both models

compare well for longitudinal motion and slightly (in decimals) different for lateral

directional motion.

.



5.2 Simulation Responses

Simulation has been carried out for the different flight conditions as below

Demonstration of leveling flights

5.2.1 Condition -1:

The results shown in the fig 11 are level flight for an altitude of 10000 ft and a velocity of

541.3 ft/s. And the responses angle of attack, theta, pitching rate and del elevator are

compared between the HIFI and LOFI models.

Figure 11: For level flight with a 5(rad) elevator doublet, compared between the LOFI

(dash red line) and the HIFI (dashed blue line) models.



5.2.2 Condition -2 :


541.3 ft/s. And the responses angle of attack, theta, pitching rate and del elevator are


Fig12: For Steady wings-level flight with a 5(rad) elevator doublet and the responses are

compared between the LOFI (dash red line) and the HIFI (dashed blue line) models.



5.2.3 Condition -3:


541.3 ft/s. And the responses pitching rate, angle of attack, theta and del elevator are


Fig 13: For Steady wings-level flight with a 5(rad) and the responses are compared

between the LOFI (dash red line) and the HIFI (dashed blue line) models.

5.2.4 Condition -4:



Demonstrating Yawing rate

The results shown in fig 14 are for yawing rate for an altitude of 10000 ft and a velocity

of 541.3 ft/s. The responses Side slip, Yaw rate, Phi, Del elevator, Del aileron and Del

rudder are plotted and compared well in between the HIFI and LOFI models.



Fig 14: For Yaw rate of 5(rad/s) and disturbances of elevator= -2, aileron=1, rudder= -1,

the responses are plotted and they are compared between the LOFI (dash red line) and the

HIFI (dashed blue line) models.



5.2.5 Condition -5:

Demonstrating Pull rate

The results shown in fig 15 are for pull rate for an altitude of 10000 ft and a velocity of

541.3 ft/s. The responses Theta, Angle of attack, Pitch rate and Del elevator are plotted

and compared between the HIFI and LOFI models.

Fig 15: For Pull-up rate of 20(rad/s) and disturbances of elevator= 2.5, aileron=0,

rudder= 0, and the responses are compared between the LOFI (dash red line) and HIFI

(dashed blue line) models.



5.2.6 Condition -6:

Demonstrating Roll rate

The results shown in fig 16 are for roll rate for an altitude of 15000 ft and a velocity of

541.3 ft/s. The responses Angle of attack, Phi and Roll rate and Del aileron are plotted

and compared between the HIFI and LOFI models.



Fig 16: For roll rate of 60(rad/s) and disturbances of elevator=-0, aileron=-5 and

rudder=0, the responses are compared between the LOFI (dash red line) and the HIFI

(dashed blue line) models.



6. CONCLUSIONS

The Lateral-directional motions (roll mode, spiral mode, Dutch roll mode), the

Longitudinal motions (Phugoid condition and Short period conditions) and are

obtained by linearizing the non linear F-16 aircraft model. By observing the

values of LOFI and HIFI models of the flight dynamics, can be state as both the

conditions are same for longitudinal motion and lightly (in decimals) different for

lateral motion.

The model has been simulated at different flight conditions and the results are

plotted for the respective flight conditions. For Level flight, Yawing rate, Pull-up

rate and Roll rate, the respective responses are plotted and compared well between

the LOFI and HIFI models.

By observing the responses of leveling flight, it can be stated as “higher the

altitude, the comparison between the LOFI and HIFI models are not satisfactory.”



7. REFERENCES

Nelson R.C. “Flight stability and automatic control”, McGrew-Hill, 2nd

edition.

Brian L. Stevens, Frank L. Lewis, Aircraft Control and Simulation, John Wiley &

Sons, Inc. 1992

Nguyen, L.T., et al., Simulator study of stall/post-stall characteristics of a fighter

airplane with relaxed longitudinal static stability, NASA Tech. Pap. 1538, NASA,

Washington, D.C., Dec. 1979.

study on flight mechanics and simulation of f16

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