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Aircraft Simulator

Thesis project at Electronics system

Linköping Institute of Technology

by

Hani Iskender

LITH-ISY-EX-ET--05/0299--SE

Linköping 2005

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Aircraft Simulator

Thesis Project at Electronics system

Linköping Institute of Technology

by

Hani Iskender

LITH-ISY-EX-ET--05/0299--SE

Supervisor: Anders Åslund Examiner: Kent Palmkvist

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Språk Language Rapporttyp Report category ISBN Svenska/Swedish

X Engelska/English Licentiatavhandling X Examensarbete ISRN LITH-ISY-EX-ET--05/0299--SE

C-uppsats D-uppsats Serietitel och serienummer

Title of series, numbering ISSN Övrig rapport

____

URL för elektronisk version

http://www.ep.liu.se/exjobb/isy/2005/299/

Titel

Title Simulator för flygfarkost Aircraft Simulator

Författare

Author Hani Iskender

Sammanfattning

Abstract

At Saab Bofors Dynamics there are projects running which purpose are to develop simulators for various weapon systems like RBS 70. In order to manage creating real working simulators Saab Bofors Dynamics has to do more research and this final thesis is a part of this process.

This final thesis has been performed at Saab Bofors Dynamics in the department of modelling and simulation, RTRKM, in Karlskoga. The purpose was to develop a control algorithm which makes it possible for an aircraft to behave real when controlling through a joystick.

The conclusions show that further improvements are needed before the aircraft behaves entirely by the laws of physics. Among other things it is necessary to decrease the number of delimitations that have been done.

Nyckelord

Keyword

force, thrust, drag, lift, simulator, pitch, roll

Institutionen för systemteknik 581 83 LINKÖPING

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Abstract

At Saab Bofors Dynamics there are projects running which purpose are to develop simulators for various weapon systems like RBS 70. In order to manage creating real working simulators Saab Bofors Dynamics has to do more research and this final thesis is a part of this process.

This final thesis has been performed at Saab Bofors Dynamics in the department of modelling and simulation, RTRKM, in

Karlskoga. The purpose was to develop a control algorithm which makes it possible for an aircraft to behave real when controlling through a joystick.

The conclusions show that further improvements are needed before the aircraft behaves entirely by the laws of physics. Among other things it is necessary to decrease the number of delimitations that have been done.

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Table of contents

1 Introduction ...1

1.1 Why this thesis project? ...1

1.2 About Saab Bofors Dynamics ...1

1.3 Report plan ...2 2 Main task ...3 2.1 The task ...3 2.2 Procedure...4 2.2.1 Requirements...4 2.2.2 Limitations ...5 3 Theory ...7

3.1 The four main forces on an aircraft...7

3.1.1 Thrust ...7

3.1.2 Drag...8

3.1.3 Lift...9

3.1.4 Weight ...9

3.2 A simulator...10

3.3 Sketch of the system...10

4 Implementation...13

4.1 From theory to implementation...13

4.2 AircraftDynamics.cpp ...13

4.2.1 The thrust vector...13

4.2.2 The lift vector ...14

4.2.3 The drag vector...15

4.2.4 The weight vector...15

4.2.5 The directedForce vector...15

4.2.6 Yaw–Pitch–Roll angles ...16

5 Results and conclusion ...17

5.1 A well functioning system...17

5.2 Various kinds of problems ...17

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ii 6 Future work ...19 6.1 Things to improve ...19 7 Thanks to… ...21 8 References ...23 8.1 Böcker ...23 8.2 Internetadresser ...23 9 Appendixes...25 9.1 Reset function...25 9.2 Update function ...25 9.3 UpdatePosition function...26 9.4 UpdateOrientation function...28

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List of figures

Figure 2.1 Joystick……….3

Figure 3.1 Four forces on an aircraft [NASA]………..7

Figure 3.2 Wished function – Craft performance………...10

Figure 3.3 Data Control Calculation……….11

Figure 4.1 Affecting of input signals………13

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Explanation of abbreviations

F – Force (N) FT – Thrust force (N) FD – Drag force (N) FL – Lift force (N) FW – Gravitation (N) a – Acceleration (m/s2) m – Mass (kg) v – Velocity (m/s) t – Time (s) s – Stretch (m) S – Span (m) ρ – Density (kg/m3) AD – Frontal Area (m2) Aw – Wing Area (m2) CD – Drag Coefficient CL – Lift Coefficient

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1 Introduction

1.1 Why this thesis project?

Flight simulators are used for both military and civilian training. The flight simulator I am working on is created by my supervisor and his colleague, which they have been working on creating for about three years. The simulator has a full working system, but the aircraft characteristics uses in the simulator are not based on reality.

For me, the main problem to solve in this thesis project is how to make an aircraft act real based on real facts such as thrust, weight and other physical characteristics. The solution has to fulfil all requirements except the limitations I have defined.

The solutions for my problem involve physical calculations for the aircraft aerodynamic and afterward implementation in Microsoft Visual Studio .Net 2003.

As a result, I assume that it is possible to create an aircraft that behaves in the same way as an actual aircraft behaves in real life. My thesis work is performed at Saab Bofors Dynamics in

Karlskoga, between November 2004 and February 2005.

1.2 About Saab Bofors Dynamics

Saab Bofors Dynamics is the dominant supplier of precision

engagement systems for Sweden’s defence and a major force on the international market.

The company is recognized for advanced defence systems that meet the evolving requirements for precision engagement within the current revolution in military affairs.

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Saab Bofors Dynamics state-of-the-art systems are high-performance, reliable and designed to operate in all combat environments. They are the result of the experience, competence, long-term development and manufacturing efforts of the highly skilled scientists, researchers, engineers and production workforce. As one of Saab’s major business areas, Saab Bofors Dynamics both contribute to and benefit from the strength of the group as a whole.

1.3 Report plan

This thesis report consists of three major parts.

1. In the first main part (chapter 2) I look into and examine the main task.

2. The second main part (chapter 3) contains calculating of the formulas and also the sketch for the system function. In this chapter I explain the theoretical part of the task.

3. In the third and last main part (chapter 4) I look into the implementation. In this chapter I explain the practical part of the task.

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2 Main task

2.1 The task

The task is to program a simple aircraft simulator where you have the possibility to choose among various types, such as transport plane, jet plane, or helicopter. Every craft shall have different velocity, dynamics, and characteristics with for example various weapons.

The simulator is created and used on a regular computer with the Windows XP operating system.

The aircraft will be steered by a joystick. And as a suggestion, force feedback will be used to increase the feeling.

Figure 2.1 Joystick

As a base for the simulator, there is a basic application which has many of the functions explained above, but it lacks, for example, various aircrafts and also the possibility to fight.

Roll [f(-1:1)] Pitch [g(-1:1)] Gas [h(0:1)]

Joystick

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4

2.2 Procedure

The following points will show the procedure of the entire thesis work.

• Since this thesis work is limited to ten weeks of work, the task has to be limited. I chose to not directly decide what to do, instead I began to collect information about aircrafts in general and afterward sense what’s being interesting for me to enter deeply into and afterward get the chance to

develop.

• After a couple weeks of studies I had this idea of what to do, so I began to shape the entire process. And during the time of work on my formulas and the understanding of the already existing code, I also continued the searching for furthermore information.

• The next step was to implement the ideas and then starting the testing.

• The last part of the whole thesis project is to document the work as a final thesis report.

2.2.1 Requirements

The following requirements shall be fulfilled by starting from the law of physics.

• The aircraft shall have appropriate values for the acceleration, the velocity, and the position.

• The aircraft shall act correctly when using the joystick. • The aircraft shall have a velocity depending of its

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2.2.2 Limitations

• Air resistance will not depend on the altitude. • Air resistance will not depend on the aircrafts roll

orientation.

• The yaw function is not included.

• The area of the aircraft, AD, is constant when considering

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3 Theory

3.1 The four main forces on an aircraft

There are four main forces affecting the aircraft: thrust, drag, lift, and weight (see figure below). A force is a vector quantity that can be represented either graphically or mathematically, and has both a magnitude and a direction. The relative magnitude and direction of the various forces affect the motion of the aircraft through the air.

Figure 3.1 Four forces on an aircraft

3.1.1 Thrust

Thrust is a force created by a power source which gives an aircraft forward motion. It can either “pull” or “push” an aircraft forward. Thrust is the force which overcomes drag.

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8 3.1.2 Drag

Drag is an aerodynamic force that depends on the shape and size of the aircraft, air conditions, and the flight velocity.

The drag equation states that drag FD is equal to the drag

coefficient CD times the density ρ times half of the velocity V

squared times the reference area AD.

D D D C A F = × × × 2 V2 ρ

There are several complex dependencies between aircraft drag and properties such as shape, inclination, and flow conditions. The drag coefficient is the number used to model all of these complex

dependencies.

The drag coefficient is composed of two main components when considering an aircraft. The first component is a basic constant,

CD0, and the second component is related to the lift of the aircraft.

This additional source of drag is called the induced drag, CDi.

Di D

D C C

C = 0+

The induced drag coefficient CDi is equal to the square of the lift

coefficient CL divided by л times the aspect ratio AR times an

efficiency factor e.

The aspect ratio is the square of the span S divided by the wing area AW.

(

)

(

AR e

)

C C C e AR C C A S AR L D D L Di W × × + = ⇒ × × = = π π 0 2 2 ,

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3.1.3 Lift

Lift is an aerodynamic force that depends on the shape and size of the aircraft, air conditions, and the flight velocity.

The lift equation states that the lift FL is equal to the lift coefficient CL times the density ρ times half of the velocity V squared times

the wing area AW.

W L L C A F = × × × 2 V2 ρ

Lift depends on several complex properties such as shape,

inclination, and some flow conditions. The lift coefficient is the

number used to model all of these complex dependencies. The project has been limited to only take the mass into consideration. This equation is a rearrangement of the lift equation. The lift coefficient CL is equal to the lift FL divided by the density ρ times

half the velocity V squared times the wing area AW.

      × × = W L L A F C 2 V2 ρ 3.1.4 Weight

Weight is the force on the aircraft that is generated by the gravitational attraction of the earth.

The elevator, rudder, or ailerons is the aerodynamic control surfaces that can be used by the pilot to maneuver an aircraft. The center of gravity, the average location of the weight of the aircraft,

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is that point which the aircraft rotates about when the aircraft is maneuvered.

The weight equation states the law of gravity such as the weight force FW is equal to the mass m times the gravitational acceleration g.

g m FW = × .

3.2 A simulator

By sitting in front of the computer “would-be” pilots can practise controlling an aircraft using only a flight simulator.

The user can control the simulator which provides a model of the "world" as well as a model of an aircraft. And this simulator will cause a reaction that makes the world and the aircraft act the same way as the real ones would under real flight conditions, except the advantage that a flight accident won’t cost anything.

3.3 Sketch of the system

Figure 3.2 Wished function – Craft performance

• Calculation of velocity, position and orientation. • Application of results.

• Information sends to craft.

Data Control Calculation Application of function Craft Wished function Craft Performance

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Figure 3.3 Data Control Calculation

There are three inputs: pitch (g), roll (f) and gas (h). There are three outputs: position, orientation and velocity.

• The position has the (x, y, z) coordinates, where o the roll (f) rotates around the z-axle o the pitch (g) rotates around the x-axle

Gas-channel (h) Roll-channel (f) Pitch-channel (g) Pitch Gas Roll Position Velocity Data Control Calculation

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4 Implementation

4.1 From theory to implementation

Figure 4.1 Affecting of input signals

4.2 AircraftDynamics.cpp

When finishing the theoretical part, then it’s time to implement in code. I finally got a formula for each force, so the next step is to make a total force. To be able to do that, a total force is created by adding all the forces.

The important thing now is to try to fulfil the earlier set requirements, see chapter 2.2.1. Each force is equivalent to a quantity vector in the three-dimensional surrounding.

4.2.1 The thrust vector

The thrust vector is always pointed in the –z coordinate for the aircraft. Orientation Position Area Acc FL FD FT Velocity (f) (g) (h)

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Figure 4.2 Thrust

To receive the correct direction in the three-dimensional

surrounding I have to rotate the vector by the Euler rotation, this to get the correct Yaw–Pitch–Roll orientation for the aircraft.

This is how it looks in C-code:

The size of the thrust vector is applied by the joysticks gas control, and shifts between zero and a predetermined maximal value. In this case it is 65 kilo Newton’s.

4.2.2 The lift vector

Also the lift vector is rotated by the Euler rotation. This vector is pointed in the y coordinate for the aircraft.

Since the size of the lift vector is determined by the joystick pitch control and at the same time knowing the knowledge for the maximum capability of g-forces for a human being, I create a function to limit the maximum g-force the pilot is exposed to.

// THRUST m_vecThrust.set(0.f, 0.f, -fThrust); // DIRECTED THRUST nse::alg::Matrix matrix1(4, 4); matrix1.Unit(); matrix1.RotateYPR(m_vecOrientation); matrix1.Translate(m_vecThrust); matrix1.Set(m_vecThrust);

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• When the joystick pitch control value is greater than zero, there can only be maximum nine g-forces.

• When the joystick pitch control value is lower than zero, there can only be maximum four g-forces.

4.2.3 The drag vector

To get the reality feeling when controlling the aircraft, I made the drag vector depended on the velocity vector, looking at both the size and the direction of the vector. But the size is also depended on the drag coefficient, the lift force and the efficiency factor. The direction of the drag vector is opposite of the velocity vector.

4.2.4 The weight vector

The gravity vector is predetermined and does not change. It is always pointed in the –y coordinate.

4.2.5 The directedForce vector

After creating the total force vector called directedForce, I use Newton’s second law

a m F = × .

I use this formula to get the current acceleration, the velocity and afterward the current position of the aircraft. See the following formulas: t v s t a v m F a= ⇒ = × ⇒ = × .

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16 4.2.6 Yaw–Pitch–Roll angles

The next step is to receive the correct yaw and then also pitch angles, by assuming the velocity vector.

Since the aircraft is in three-dimensional surroundings, then it is important to set correct formulas to receive correct angles. It’s all about geometry.

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5 Results and conclusion

5.1 A well functioning system

As a result I got a working system which fulfilled the requirements; as a matter of fact it was more than expected.

5.2 Various kinds of problems

Here are some examples of various (smaller) kinds of problems I ran into during the time of work:

• Difficulty in calculating the drag coefficient CD.

• Difficulty in keeping the aircraft in the air.

5.3 Experiences learned

It is common to make mistakes when a new project is started. But making mistakes does not have to be a bad thing; it is usually a part of the project which gives experience. The important thing to do first is to make a careful plan. A careful plan simplifies the work. After several weeks of intensive studying, I learned basic

knowledge about the airplanes aerodynamic. But still it was difficult to imagine how an aircraft really acts up in the air. As an example of experience during the time of work, I can point out the reaction of the aircraft when making a turn in high speed. At first the idea was to calculate the angles of the curve from the aircraft before the calculation of the current acceleration, the velocity and also the position. But what is missing here is the feeling of the actual behaviour of the aircraft. Therefore I decided

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18

to calculate the angles after the calculation of the acceleration, the velocity and the position.

I made this decision of change fairly late in the time of work; therefore I feel the great experience given to me. Before the change, the system was more or less functioning, but after the change it is safer and more correct.

From the beginning I chose to not include the yaw function, I did that as delimitation. But in the end I included a simple version of the yaw function for easier steering of the aircraft.

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6 Future work

6.1 Things to improve

It is always difficult to create the perfect simulator. The best thing to do is to step by step develop and improve the existing simulator. This was my case. I had an already existing simulator which I improved.

Of course there are many more things to improve, and here are some examples:

• Make the air resistance depended on the altitude. • Add the yaw function for better steering.

• Be able to start from the ground. • Be able to land.

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7

Thanks to…

Anders Åslund, Modelling and Simulation, RTRKM – Saab Bofors

Dynamics for the invaluable help and supervising, and also for the ideas during the time of work.

Kent Palmkvist, “Department of Electrical Engineering –

Linköping Institute of Technology” for the major knowledge which he shared of during this final thesis.

Bashkim Dida, student at the institute of Technology in Linköping

for the valuable point of views about the final report.

Other concerned from the Modelling and Simulation department for the help during the time of work.

Other concerned from Saab Bofors Dynamics and Linköping Institute of Technology.

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8

References

8.1 Böcker

• [Försvarsmakten]

Kent Harrskog, Lennart Berns “FLYGPLAN KORT”, Elander Gummessons, [ISBN 91-973255-8-9], 1999.

8.2 Internetadresser

• [Saab Bofors Dynamics]

http://www.saab.se/dynamics

• [NASA]

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9 Appendixes

9.1 Reset function

9.2 Update function

void AircraftDynamics::reset() { m_vecAcceleration.zero(); m_vecVelocity = nsc::Vector(0.f, 0.f, -100.f); m_vecLocation = m_vecStartPos; m_vecAngularVelocity.zero(); m_vecOrientation.zero(); m_fCdrag = 0.f; m_fClift = 0.f; m_bGoDown = false; m_bExplode = false; m_bLocked = false; m_eDamageStatus = nsc::NoDamage; } void AircraftDynamics::update() { updateControls(); double dT = nse::lgc::Ticker::Instance()->getSnapshotDelta(); m_fThrottle = -(m_joyMap.rglSlider[0] - 1000.f)/2000.f; float fYaw = (float)m_joyMap.lRz/1000.f;

float fPitch = (float)m_joyMap.lY/1000.f; float fRoll = (float)m_joyMap.lX/1000.f;

m_vecPrevLocation = m_vecLocation; if (m_eDamageStatus != nsc::Destroyed) {

updateOrientation(dT, fYaw, fPitch, fRoll);

updatePosition(dT, m_fThrottle, fYaw, fPitch, fRoll); updateButtons(m_joyMap.rgbButtons);

updateForceFeedback(); }

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9.3 UpdatePosition function

void AircraftDynamics::updatePosition(double dT, float fThrottle, float fYaw, float fPitch, float fRoll) {

const float fMASS = 9500.f;

const float fAirDensity = 1.2f; const float fDragArea = 5.f; const float fLiftArea = 46.f;

const float fSpan = 10.6f;

const float fAspectRatio = (pow(fSpan,2.f))/fLiftArea; const float fEfficiencyFactor = 0.3f;

const float fCdrag0 = 0.1964f;

const float fGravityFactor = nse::dat::GRAVITY * fMASS;

const float pi = 3.14159265358979f;

m_fGravityFactor = fGravityFactor; // ENBART FÖR UTSKRIFT m_fClift = (fGravityFactor /* 2.f*/)/(fAirDensity * (m_vecVelocity.magnitude() * m_vecVelocity.magnitude()) * fLiftArea);

m_fCdrag = fCdrag0 + (pow(m_fClift, 2.f)/(pi * fAspectRatio * fEfficiencyFactor));

const float fThrustFactor = 65000.f;

const float fDragFactor = 0.5f * fAirDensity * (m_vecVelocity.magnitude()*m_vecVelocity.magnitude()) * fDragArea * m_fCdrag;

const float fLiftFactor = 0.5f * fAirDensity * (m_vecVelocity.magnitude()*m_vecVelocity.magnitude()) * fLiftArea * m_fClift; // THRUST float fThrust; if (m_bAfterburner) fThrust = (fThrottle*fThrustFactor) * 2.f; else if (m_bExtremeAfterburner) fThrust = (fThrottle*fThrustFactor) * 8.f; else fThrust = (fThrottle*fThrustFactor); m_vecThrust.set(0.f, 0.f, -fThrust); // DIRECTED THRUST nse::alg::Matrix matrix1(4, 4); matrix1.Unit(); matrix1.RotateYPR(m_vecOrientation); //Euler matrix1.Translate(m_vecThrust); matrix1.Set(m_vecThrust); // LIFT nsc::Vector vecLiftForce; if (fPitch > 0.f)

vecLiftForce = nsc::Vector(fYaw * fGravityFactor, ((m_vecVelocity.magnitude()/333.f) * fPitch * fGravityFactor * 8.f), 0.f);

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else

vecLiftForce = nsc::Vector(fYaw * fGravityFactor, (m_vecVelocity.magnitude()/333.f) * fPitch * fGravityFactor * 3.f, 0.f); m_vecLift.set(0.f, fLiftFactor, 0.f); m_vecLift += vecLiftForce; // DIRECTED LIFT nse::alg::Matrix matrix3(4, 4); matrix3.Unit(); matrix3.RotateYPR(m_vecOrientation); //Euler matrix3.Translate(m_vecLift); matrix3.Set(m_vecLift); // DRAG

nsc::Vector vecNyVelocity = m_vecVelocity; vecNyVelocity.normalize();

vecNyVelocity *= -1.f;

m_vecDrag = vecNyVelocity * (fDragFactor + (vecLiftForce.magnitude() * fEfficiencyFactor)); // GRAVITY

nsc::Vector vecGravity(0.f, -fGravityFactor, 0.f); // DIRECTEDFORCE

m_vecDirectedForce = (m_vecThrust) + (m_vecDrag) + (m_vecLift) + (vecGravity);

// REDIRECT ACCELERATION

m_vecAcceleration = m_vecDirectedForce/fMASS; // REDIRECT VELOCITY

m_vecVelocity += m_vecAcceleration * dT; // SET LOCATION (POSITION)

nsc::Vector vecPosDelta = m_vecVelocity * dT; m_vecLocation += vecPosDelta; // Yaw angle if (m_vecVelocity.z >= 0.f) // Nr 2 m_vecOrientation.yaw = (pi + (asin(m_vecVelocity.x/(sqrt(pow(m_vecVelocity.x, 2)+pow(m_vecVelocity.z, 2)))))); else if (m_vecVelocity.z < 0.f) // Nr 1 m_vecOrientation.yaw = -(asin(m_vecVelocity.x/(sqrt(pow(m_vecVelocity.x, 2)+pow(m_vecVelocity.z, 2))))); //Pitch angle m_vecOrientation.pitch = (asin(m_vecVelocity.y/(sqrt(pow(m_vecVelocity.y, 2)+pow(m_vecVelocity.x, 2)+pow(m_vecVelocity.z, 2))))); nse::alg::Limit360(m_vecOrientation.yaw); nse::alg::Limit180(m_vecOrientation.pitch); }

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9.4 UpdateOrientation function

In this last part I update the orientation.

void AircraftDynamics::updateOrientation(double dT, float fYaw, float fPitch, float fRoll)

{

m_vecOrientation.roll -= (fRoll * dT); nse::alg::Limit360(m_vecOrientation.roll); }

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References

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