11 fighter aircraft avionics - part iv

Fighter Aircraft AvionicsPart IV

SOLO HERMELIN

Updated: 04.04.13

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Table of Content

SOLO Fighter Aircraft Avionics

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Introduction

Jet Fighter Generations

Second Generation (1950-1965)Third Generation (1965-1975)

First generation (1945-1955)

Fourth Generation (1970-2010)

4.5 Generation

Fifth Generation (1995 - 2025) Aircraft Avionics

Third Generation Avionics

Fourth Generation Avionics

4.5 Generation AvionicsFifth Generation Avionics

Cockpit Displays

Communication (internal and external)Data Entry and Control

Flight Control

Fighter Aircraft Avionics I

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Table of Content (continue – 1)

SOLO Fighter Aircraft Avionics

Aircraft Propulsion System

Aircraft Flight Performance

Navigation

Earth Atmosphere

Flight Instruments

Power Generation SystemEnvironmental Control System

Aircraft Aerodynamics

Fuel System

Jet Engine

Vertical/Short Take-Off and Landing (VSTOL)

Engine Control System

Flight Management System

Aircraft Flight Control

Aircraft Flight Control Surfaces

Aircraft Flight Control Examples

Fighter

Aircraft

Avionics

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Table of Content (continue – 2)

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Fighter Aircraft Avionics

Equations of Motion of an Air Vehicle in Ellipsoidal Earth Atmosphere

Fighter Aircraft Weapon System

References

Safety Procedures

Tracking Systems

Aircraft Sensors

Airborne Radars

Infrared/Optical Systems

Electronic Warfare

Air-to-Ground Missions

BombsAir-to-Surface Missiles (ASM) or Air-to-Ground Missiles (AGM)

Fighter Aircraft Weapon Examples

Air-to-Air Missiles (AAM)

Fighter Gun

Avionics III













Continue fromFighter Aircraft Avionics

Part III

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AirDataSystem

Multi-Function Display

FlightInstrumentSystem

NavigationSystem

FlightManagementSystem

FlightControlSystem

AutopilotSystem

WeaponSystem

HUD HMD

AVIONICS DATA BUS

Infrared/OpticSensors

RadarSelf-Defense

System

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Fighter/attack aircraft can carry a number of items fastened to racks underneath the aircraft.These items are called ‘‘Stores’’ and include Weapons (Bombs, Rockets, Missiles), Extra FuelTanks, Extra Sensor Pods, or Decoys (e.g., Chaff to fool radar-guided missiles and Flares tofool infra-red guided missiles). The Stores Management System (SMS) manages themechanical and electrical connections to weapons and senses their status under control ofthe Mission Central Computer (MCC); thus all weapons are readied via the SMS.

Weapons carried may include Rockets, Bombs (both Ballistic-dumb and Radar, Infra-red, or TVguided), and Missiles (which are typically ‘‘Fire and Forget’’ Self-guided using TV video, Laser,Imaging Infra-red, or Radar Seekers). Most aircraft also have internal fuselage-mountedGuns.

Weapon release modes include automatic (AUTO) and Continuously Computed Impact Point(CCIP) plus special modes for Guided Weapons. In AUTO mode, the MCC controls weaponrelease based on computed impact point, current target position, and predicted aircraft positionat release. In CCIP mode, the MCC computes a predicted impact point which is displayedon the HUD, and the aircrew controls weapon release with the bomb button on theHOTAS.

Stores

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The Aircraft part of the Weapons System is checked for Operability and Safety on the Ground before the Weapons are Loaded. After the Weapons are Loaded on the Stations and Power (External or Aircraft Internal) and recognized in the Weapon System Inventory (Weapon Type and Station) the Weapons Power Bit check the Weapon Servicibility. This information is displayed to the Avionics.

The Weapons can be loaded on a Fighter Aircraft on the existing External Weapon Stations or if available on Internal Bay Stations (F-22, F-35) .

When the Aircraft is on the Ground the WeaponLaunching Signal are disabled. In addition, usually the Weapons are in a Safe Mode.

The Weapons can be Launched only when theAircraft is on the Air and the Pilot activated the MASTER ARM switch. The Launching sequence can Start after activated the Launch Switch that is usually located on the Flight Control Stick. The Launching sequence is defined to assure the Safety of the Launching Aircraft.

The Weapons System will indicate a Successful or Unsuccessful Launch and will choose the Next Weapon to be Launched according to a predefined sequence.Weapon Management Displays

SOLO Fighter Aircraft Weapon System

The Weapon System advises the Pilot how to Launch the Weapons.In general from the Third Fighter Generation and up the Aircraft Weapon System included a Computer that provided Flight Instruction Displays for the Pilot, to Release Bombs or Launch Missiles (A/A or A/G).

Target Designation

The Aircrew may designate a Target for A/A or A/G Attack in one of two ways: by Radar or by HUD/HMD designate. To designate a target by Radar, the Radar must already be tracking a Target. The Radar Target is identified as the Target by a Member of the Aircrew pushing the designate switch on the HOTAS. To perform a HUD/HMD designation, the Aircrew must first position the HUD/HMD reticle (on the HUD) using the Target Designator Controller (TDC) Switch on the HOTAS (the TDC Switch is similar to a Joystick). Once the HUD Reticle is properly positioned, the aircrew pushes down on the TDC switch to designate a target. The MCC must transform the HUD/HMD Reticle position from HUD coordinates to obtain Range, Azimuth, and Elevation to Target. No matter how the Target was designated, the HUD/HMD Reticle changes shape to indicate that a Target is Designated. A Designated Target may be undesignated by pushing the Undesignate Switch on the HOTAS.


A/G Weapon Selection

Weapon selection includes selecting the type of Weapon, the number to drop, and thedesired spacing on the ground. This is done by the aircrew using the MPD stores display and Keyset switches. Depending on the type of weapon selected, a default delivery mode is defined and displayed. At any time prior to weapon release, the aircrew may push the AUTO/CCIP toggle switch on the Keyset, causing the delivery mode to change from AUTO to CCIP or from CCIP to AUTO. Weapon-ready determination is also assumed to be part of this function.

Mode Selection

The Pilot may choose between Air-to-Air (A/A) and Air-to-Ground (A/G)

Steering in A/G Mode

Compute the Steering Cues for display on the HUD/HMD and MPD based either on WaypointSteering or Target Attack Steering. The MCC can hold a Number of Aircrew-entered Waypoints (Latitude, Longitude, Altitude) which may be used as Steer-to Points and as Target Designation Points. The Aircrew may also associate an Offset (Range, Bearing) from the currently selected Waypoint which is taken into account. Prior to Target Designation, Steering Cues are provided based on the Currently Selected Waypoint (if any). After Target Designation, Steering Cues are provided based on Target Location relative to Aircraft Position

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Air-to-Ground Missions

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MULTI-COMMAND HANDBOOK 11-F16

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Bombs:

-Dumb (Gravity) Bombs - Guided (Smart) Bombs * TV Bombs (Wallay) * Laser Guided Bombs (Paveway) * Gliding Bombs with Data Link and IR/Optical Seeker * Inertial/GPS Bombs (JDAM) * Inertial/GPS/EO (Spice) * Small Diameter Bombs

USAF artist rendering of JDAM kits fitted to Mk 84, BLU-109, Mk 83, and Mk 82 unguided bombs

GBU-39 Small Diameter Bomb

Armement Air-Sol Modulaire (Air-to-Ground Modular Weapon)

(AASM)

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Dumb Bombs Delivery

There is the possibility to program visual cues in the computer of the F-16. Beside waypoints there are 4 types of cues. These are called VIP, VRP, PUP and OA’s. VIP = Visual Initial Point VRP = Visual Reference Point PUP = Pull Up Point OA = Offset Aim

The Bomb Delivery in Type 3 Fighters and up is done by the Weapon Delivery Computer.The Pilot chooses the Bomb Delivery Mode (TOSS, LAT, CCIP,..) in A/G Mode, Designates the Ground Target using the Gun Sight or HUD and after this the WeaponSystem provides Flight Instruction and Automatically Releases the Bombs.

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Dumb Bombs Delivery (continue – 1)

Pop-Up This type of delivery can be useful for all static targets. Think about buildings, bridges, runways and even vehicles. The ordnance that can be used is the whole range from low and high drag dumb bombs, cluster and laser guided bombs.

TOSS (English word for throwing something up in the air)For a low level ingress we should use a LAT delivery. LAT stands for Low Altitude TOSS. During this delivery the bomb will be released upwards. The range will become greater but the accuracy smaller. Therefore the best type of bomb used will be a cluster bomb. This is a very nice way to attack a group of vehicles like a SA-2 or SA-3 site. But also freefall bombs can be used against large targets.

High Altitude Dive Bombing (HADB) This delivery should keep the attacker above a planned altitude and can be used for hitting all types of static target like buildings, bridges and vehicles. Any type of bomb can be used. It is also possible to use missiles like the AGM-65 with this delivery.

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CCIP (Continuous Computed Impact Point)The objective of a CCIP delivery is to fly the Aircraft in a manner to arrive at or close to the Planned Release Parameters (Altitude, Airspeed and Dive Angle) with the CCIP Cue close to the Intended Aiming Point. When the CCIP Cue superimposes the Target, the Pickle Button / Trigger should be actuated to initiate Weapons Release / Firing

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For Dumb Bombs the MCC solves the ballistic trajectory equations of motion.This is done initially to determine Weapon Time of Fall when the Estimated Time-to-Go toRelease (based on Aircraft Ground Speed and Target Ground Range) is less than one minute.Initialization must be repeated if a New Target is Designated. Once initialized, the WeaponTrajectory must be computed at least every 100 ms. Outputs include Time-to-Go to Release,Weapon Time of Fall, Down Range Error, and Cross Range Error. When Time-to-Go to Release falls below ΔT ms. and AUTO delivery mode is selected, Weapon Release is scheduled.Thereafter, whenever Time-to-Go to Release is recomputed, Weapon Release is rescheduled.

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Air-to-Surface Missiles (ASM) or Air-to-Ground Missiles (AGM)

An air-to-surface missile (ASM) or air-to-ground missile (AGM or ATGM) is a missile designed to be launched from military aircraft (bombers, attack aircraft, fighter aircraft or other kinds) and strike ground targets on land, at sea, or both. They are similar to guided glide bombs but to be deemed a missile, they usually contain some kind of propulsion system. The two most common propulsion systems for air-to-surface missiles are Rocket Motors and Jet Engines. These also tend to correspond to the range of the missiles — short and long, respectively. Some Soviet air-to-surface missiles are powered by Ramjets, giving them both long range and high speed.

AGM-65 Maverick

Electro-optical, Laser, or Infra-red Guidance Systems

TAURUS KEPD 350

IBN (Image Based Navigation), INS (Inertial Navigation System), TRN (Terrain Referenced Navigation) and MIL-GPSGuidance System

Storm Shadow

Inertial, GPS and TERPROM. Terminal guidance using imaging infrared

AGM-158 JASSM (Joint Air-to-Surface Standoff Missile)

INS/GPS Guidance

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An air-to-air missile (AAM) is a missile fired from an aircraft for the purpose of destroying another aircraft. AAMs are typically powered by one or more rocket motors, usually solid fuelled but sometimes liquid fuelled. Ramjet engines, as used on the MBDA Meteor (currently in development), are emerging as propulsion that will enable future medium-range missiles to maintain higher average speed across their engagement envelope.

Air-to-air missiles are broadly put in two groups. The first consists of missiles designed to engage opposing aircraft at ranges of less than approximately 20 miles (32 km), these are known as short-range or “within visual range” missiles (SRAAMs or WVRAAMs) and are sometimes called “dogfight” missiles because they emphasize agility rather than range. These usually use infrared guidance, and are hence also called heat-seeking missiles. The second group consists of medium- or long-range missiles (MRAAMs or LRAAMs), which both fall under the category of beyond visual range missiles (BVRAAMs). BVR missiles tend to rely upon some sort of radar guidance, of which there are many forms, modern ones also using inertial guidance and/or "mid-course updates".

Air-to-Air Missiles (AAM)


A detailed description on the subject can be founded in the Power Point“Air Combat” Presentation. Here we give a brief summary of the subject.

Air- to-Air missile launch envelope

Kinematics no-escape-zone

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Air-to-Air Missiles Modes of OperationAir-to-Air Missiles Modes of Operation

Lock-On Before Launch

•High agility

•Tight radius turn

•Excellent minimum ranges

Active Homing Phase

• IMU alignment

• Radar slave- full target data

• HMD Slave- partial target data

• Seeker activation

• Target Lock-On

Pre Launch Phase

01-23

2

• Inertial navigation

• Trajectory shaping for maximum range

Midcourse Guidance Phase

• IMU alignment

• Target data transfer

Lock-On After Launch

3

• Seeker activation• Target Lock-On• Final homing

Homing Phase

1 Pre Launch Phase

AMRAAM

A/A MISSILES

AMRAAM AIM - 120C-5 SpecificationsLength: 12 ft 3.65 mDiameter: 7 in 17.8 cmWing Span: 17.5 in 44.5 cmFin Span: 17.6 in 44.7 cWeight: 356 lb 161.5 kgWarhead: 45 lb 20.5 KgGuidance: Active RadarFuzing: Proximity (RF) and ContactLauncher: Rail and eject

AIM-120CRocket motor PN G672798-1 is an enhanced version with additional 5” (12 cm) of propellant.Estimation: add 10% (12/140) to obtainmp ~ 52 kgWtot ~ 120,000 N s

AMRAAM AIM-120 Movie


http://www.youtube.com/watch?v=CgMMC6PxE2U

AIM-9X AIM-9X Movie

http://www.youtube.com/watch?v=1LxhLMiRklQ&list=PL5BD7102F0086E382

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A-A Missiles Development in RAFAELA-A Missiles Development in RAFAEL

BVRBVR

Short RangeShort Range

PYTHON-4PYTHON-4

PYTHON-3PYTHON-3

SHAFRIR-2SHAFRIR-2

SHAFRIR-1SHAFRIR-1

PYTHON-5PYTHON-5

DERBYDERBY


Rafael Python 5 Promo, Movie

Derby - Beyond Visual Range Air-to-Air Missile, Movie

http://www.youtube.com/watch?v=nWG2PkwKiaQ



http://www.youtube.com/watch?v=bEVqNnId5_s



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Evolution of Air-to-Air Missiles in RAFAELEvolution of Air-to-Air Missiles in RAFAEL

PYTHON-4PYTHON-4

1st GENERATION

SHAFRIR-1SHAFRIR-1

2nd GENERATION

SHAFRIR-2SHAFRIR-2

3rd GENERATION

PYTHON-3PYTHON-3

4th GENERATION

SERVICE: SINCE 1993SERVICE SINCE 1978HITS: OVER 35 A/CDURING 1982 WAR

SERVICE: 1968-1980HITS: OVER 100 A/C

DURING 1973 WAR

SERVICE: 1964-1969

0-(10)

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180

45

30

LEAD/LAGANGLE

0

MAX.ASPECT

ANGLE

TYPICAL 3rd

GENERATIONMISSILE

LAUNCHER

Short Range

DERBYDERBY

ACTIVR BVR

Dual Range

PYTHON-5

5th GENERATION

Full Sphere IR Missile

Full Scale Development

2.9

3. 6

Russian Air-to-Air Missiles

RVV-MD, RVV-BD New Generation Russian Air-to-Air Missiles, Movie

Russian Air Power, Movie

Russian Air Force vs USAF (NATO) Comparison, Movie

SU-30SM Intercept with R-77 Missile, Movie

Ukranian A-A Missile ALAMO, R-27, Movie

Return to Table of ContentReturn to Movies Table

http://www.youtube.com/watch?v=oW8xV_S4zEw

http://www.youtube.com/watch?v=AzGS13zElx4

http://www.youtube.com/watch?v=v7K58XFZaa8

http://www.youtube.com/watch?v=52_bYS4OHTc

http://www.youtube.com/watch?v=V3TlOEeb6Bw

People’s Republic of China (PRC) Air-to-Air Missiles

• PL - 1 - PRC version of the Soviet Kaliningrad K-5 (AA-1 Alkali), retired.

• PL - 2 - PRC version of the Soviet Vympel K-13 (AA-2 Atoll), based on AIM-9 Sidewinder, retired.

• PL - 3 - updated version of the PL-2, did not enter service. PL-2, 3

• PL - 5 - updated version of the PL-2, several versions:

• PL - 5A - Semi-Active Radar homing AAM, resembles AIM-9G. Did not enter service

• PL - 5B - IR version, entered service 1990 to replace PL-2. Limited of boresight.

• PL - 5C - Improved version comparable to AIM-9H or AIM-9L in performance.

• PL - 5E - All-aspect attack version, resembles AIM-9P in appearance.

• PL - 7 - PRC version of the IR-homing French R550 Magic AAM. Did not enter service.• PL - 8 - PRC version of the Israeli RAFAEL Python 3.• PL - 9 - short range IR missile, marked for export. One known improved version PL - 9C.

• PL - 10 - medium-range air-to-air missile. Did not enter service.

PL-5

PL-8

PL-9

PL-7

People’s Republic of China (PRC) Air-to-Air Missiles (continue)

• PL - 11 - Medium Range Air-to-Air Missile (MRAAM), based on the HQ-61C and Italian ASPIDE (AIM-7)technology. Known version include:

PL -11Length: 3.690 mBody diameter: 200 mmWing span: 1 mLaunch weight: 220 kgWarhead: HE-fragmentationFuze: RFGuidance: Semi-Active CW RadarPropulsion: Solid propellantRange: 25 km

• PL - 11 - MRAAM with semi-active radar homing, based on the HQ-61C SAM and ASPIDE seeker technology. Exported as FD-60.

• PL - 11A - Improved PL-11 with increased range, warhead, and moreeffective seeker. The new seeker requires target illuminationonly during the last stage, providing a Lock On After Launchcapability.

• PL - 11B - Also known as PL-11AMR, improved PL-11 with AMR-1,active radar-homing seeker.

• LY - 60 - PL-11, adopted to navy ships for air-defense, sold to Pakistanbut doesn’t appear to be in service with the Chinese Navy.

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F4-Phantom Armament

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F-16

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http://www.freerepublic.com/focus/f-news/2845813/posts

F-15

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Fighter Aircraft Weapon SystemF-15C: M61A1 Vulcan Cannon and AIM-9M Sidewinder, Movie

http://www.youtube.com/watch?v=VZ51tfsnFws

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F-18

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The F/A-18 E/F Super Hornet, with its array of weapons systems, is the world's most advanced high-performance strike fighter. Designed to operate from aircraft carriers and land bases, the versatile Super Hornet can undertake virtually any combat mission.

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F-22 Raptor

http://www.ausairpower.net/APA-Raptor.html


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Internal WeaponBay

http://www.f22-raptor.com/technology/index.html

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Lockheed_Martin_F-35_Lightning_II

Fifth Generation Avionics

F-35 Simulator - AA and AG Modes _ Avionics-1, Movie

Lockheed_Martin_F-35_Lightning_II

Fifth Generation Avionics

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http://www.youtube.com/watch?v=5lPZDc8mzsY

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Su-32/34

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Su-35


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Fighter Gun

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Performance of Aircraft Cannons in terms of their Employment in Air Combat

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Performance of Aircraft Cannons in terms of their Employment in Air CombatSOLO

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Performance of Aircraft Cannons in terms of their Employment in Air Combat

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Safety Procedures

Safety of Personal when the Aircraft is on the Ground and when it is in the Air.Avionics includes Safety Procedures:

Fighter Aircraft on the GroundIn this case the Aircraft Weight is sustained by the Wheels and a Weight-on-WheelsSwitch (WOW) and the Master Arm (MA) Switch are in Safe Mode preventing the Release/Fire Signals to reach the Weapon Storage

Ground Crew will perform the following: * Visual Check of the Unpowered Aircraft * Connect an External Power Generator and will check the Avionics Serviceability * By pressing WOW Safety-Override and MA=ARM will check the Weapon Release System. * Disconnect the External Power Generator and Load the Weapons on Storage * Install the Weapons External Safety Devices, to be removed before Taxiing to Take Off. In general, the Weapons have also internal Safety Devices. * Reconnect External Power Generator, insert the Weapons in the SMS Inventory, (WOW = Safe) and perform Power On BIT of the Weapons to check their Serviceability. * Disconnect the External Power Generator and the Aircraft (already fueled) is ready to be delivered to the Air Crew.

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Safety Procedures

Safety of Personal when the Aircraft is on the Ground and when it is in the Air.Avionics includes Safety Procedures (continue – 1):

Fighter Aircraft on the GroundIn this case the Aircraft Weight is sustained by the Wheels and a Weight-on-WheelsSwitch (WOW) and the Master Arm (MA) Switch are in Safe Mode preventing the Release/Fire Signals to reach the Weapon Storage

Air Crew will perform the following: * Visual Check of the Unpowered Aircraft * Start the Engines that provide Internal Power and will check the Avionics Serviceability (WOW = Safe and MA = Safe) * Insert the Weapons in the SMS Inventory, and perform Power On BIT of the Weapons to check their Serviceability. * Input to Avionics Data necessary for the Mission. * The Avionics will be in NAV Mode. * Before Taxiing to Take Off the Ground Crew will remove all Weapons Safety Devices. * Pilot will Taxi and Take Off. * After Landing the Ground Crew will Reinstall Weapons Safety Devices.

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Safety Procedures

Safety of Personal when the Aircraft is on the Ground and when it is in the Air.Avionics includes Safety Procedures (continue – 2):

Fighter Aircraft in the AirIn this case the Weight-on-Wheels Switch (WOW) is in ARM.MA = Safe preventing Release/Launch of Weapons.To operate the Weapons the pilot must put MA = Arm.The Pilot can switch between the three Operational Modes: - NAV : Navigation Mode - A/A: can Launch A/A Missiles and Fire Gun Projectiles - A/G: can Launch A/G Missile or release Bombs

The Avionics will deliver Safety Warnings due to - An Aircraft Malfunction - A Flight Hazard - Fuel Shortage

In case of a Weapon Release Malfunction the Pilot may:• Jettison the Weapon• Perform Safety Procedures at Landing.

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SOLO AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE

1. Inertial System Frame

2. Earth-Center Fixed Coordinate System (E)

3. Earth Fixed Coordinate System (E0)

4. Local-Level-Local-North (L) for a Spherical Earth Model

5. Body Coordinates (B)

6. Wind Coordinates (W)

7. Forces Acting on the Vehicle

8. Simulation

8.1 Summary of the Equation of Motion of a Variable MassSystem

8.2 Missile Kinematics Model 1 (Spherical Earth)

8.3 Missile Kinematics Model 2 (Spherical Earth)

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Bz

MV

Bx

ByWy

WzBr

Bp

Wp

BqWqWr

Given a missile with a jet engine, we define:

1. Inertial System Frame III zyx ,,

3. Body Coordinates (B) , with the origin at the center of mass. BBB zyx ,,

2. Local-Level-Local-North (L) for a Spherical Earth Model LLL zyx ,,

4. Wind Coordinates (W) , with the origin at the center of mass. WWW zyx ,,

AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERESOLO

I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

Coordinate Systems

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Coordinate Systems

I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

1 .Inertial System (I)

R

- vehicle position vector

Itd

RdV

- vehicle velocity vector, relative to inertia

IItd

Rd

td

Vda

2

2

- vehicle acceleration vector, relative to inertia

AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE

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Coordinate Systems (continue – 2)

2. Earth Center Fixed Coordinate System (E) xE, yE in the equatorial plan with xE pointed to the intersection between the equatorto zero longitude meridian.

The Earth rotates relative to Inertial system I, with the angular velocity

sec/10.292116557.7 5 rad

EIIE zz

11

0

0EC

IE

Rotation Matrix from I to E

100

0cossin

0sincos

3 tt

tt

tC EI


I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

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2 .Earth Fixed Coordinate System (E) (continue – 1)

Vehicle Position ETEI

EIE

I RCRCR

Vehicle Velocity

Vehicle Acceleration

RVRtd

Rd

td

RdV EIE

EI

- vehicle velocity relative to Inertia

Rtd

Rd

td

RdV IE

LE

E

: - vehicle velocity relative to Earth

II

E

I

E

I

Rtd

d

td

VdRV

td

d

td

Vda

RVtd

VdR

td

RdR

td

dV

td

VdEIEEU

U

E

EE

EIU

U

E

IU

0

RVtd

VdRV

td

Vda E

E

EEEU

U

E

22

or

where U is any coordinate system. In our case U = E.


I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

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3 .Earth Fixed Coordinate System (E0)

The origin of the system is fixed on the earth at somegiven point on the Earth surface (topocentric) of Longitude Long0 and latitude Lat0.

xE0 is pointed to the geodesic North, yE0 is pointed to the East parallel to Earthsurface, zE0 is pointed down.

100

0cossin

0sincos

sin0cos

010

cos0sin

2/ 00

00

00

00

30200 LongLong

LongLong

LatLat

LatLat

LongLatC EE

00000

00

00000

sinsincoscoscos

0cossin

cossinsincossin

LatLongLatLongLat

LongLong

LatLongLatLongLat

The Angular Velocity of E relative to I is: EIIEIE zz

110 or

0

0

00000

00

00000

000

sin

0

cos

0

0

sinsincoscoscos

0cossin

cossinsincossin

0

0

Lat

Lat

LatLongLatLongLat

LongLong

LatLongLatLongLat

C EE

EIE


I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

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4 .Local-Level-Local-North (L) The origin of the LLLN coordinate system is located atthe projection of the center of gravity CG of the vehicleon the Earth surface, with zDown axis pointed down, xNorth, yEast plan parallel to the local level, withxNorth pointed to the local North and yEast pointed tothe local East. The vehicle is located at:.

Latitude = Lat, Longitude = Long, Height = H

Rotation Matrix from E to L

100

0cossin

0sincos

sin0cos

010

cos0sin

2/ 32 LongLong

LongLong

LatLat

LatLat

LongLatC LE

LatLongLatLongLat

LongLong

LatLongLatLongLat

sinsincoscoscos

0cossin

cossinsincossin


I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

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4 .Local-Level-Local-North (L) (continue – 1)

Angular Velocity

IEELIL Angular Velocity of L relative to I

Lat

Lat

LatLongLatLongLat

LongLong

LatLongLatLongLat

C LE

Down

East

NorthL

IE

sin

0

cos

0

0

sinsincoscoscos

0cossin

cossinsincossin

0

0

LatLong

Lat

LatLong

Lat

LongLatLongLatLongLat

LongLong

LatLongLatLongLat

Lat

Long

C LE

Down

East

NorthL

EL

sin

cos

0

0

0

0

sinsincoscoscos

0cossin

cossinsincossin

0

0

0

0

LatLong

Lat

LatLong

DownDown

EastEast

NorthNorthL

IECL

ECLL

IL

sin

cos

Therefore


I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

67

SOLO



Vehicle Velocity

Vehicle Velocity relative to I

RVRtd

Rd

td

RdV EIE

EI

HRLatLongLat

LatLongLatLong

LatLatLong

HR

Rtd

RdV EL

L

LE

00

0

0

0cos

cos0sin

sin0

0

0

where is the vehicle velocity relative to Earth.EV

DownE

EastE

NorthE

V

V

V

H

HRLatLong

HRLat

_

_

_

0

0

cos

from which

DownE

EastE

NorthE

Vtd

Hd

LatHR

V

td

Longd

HR

V

td

Latd

_

0

_

0

_

cos


HeightVehicleHRadiusEarthmRHRR 600 10378135.6

I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

68

SOLO



Vehicle Velocity (continue – 1)

We assume that the atmosphere movement (velocity and acceleration) relative to EarthAt the vehicle position (Lat, Long, H) is known. Since the aerodynamic forces on thevehicle are due to vehicle movement relative to atmosphere, let divide the vehiclevelocity in two parts:

WAE VVV

Down

East

NorthL

A

V

V

V

V

- Vehicle Velocity relative to atmosphere

DownW

EastW

NorthW

LW

V

V

V

HLongLatV

_

_

_

,,

- Wind Velocity at vehicle position (known function of time)


I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

69

SOLO




Since:

RVtd

VdR

td

d

td

VdRV

td

d

td

Vda EEL

L

E

II

E

I

E

I

2

WAE VVV

WWIL

L

WAAIL

L

A VVtd

VdRVV

td

Vda

Wa

WWEL

L

WAAEL

L

A VVtd

VdRVV

td

Vd 22

HLongLatVHLongLattd

VdHLongLata WEL

L

WW ,,2,,:,,

WAAEL

L

A aRVVtd

Vd

2

where:

is the wind acceleration at vehicle position.


I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

Table of Content

70

SOLO


5 .Body Coordinates (B)

The origin of the Body coordinate systemis located at the instantaneous center ofgravity CG of the vehicle, with xB pointedto the front of the Air Vehicle, yB pointedtoward the right wing and zB completingthe right-handed Cartesian reference frame.

Bx

Lx

Bz

Ly

LzBy

Rotation Matrix from LLLN to B (Euler Angles):

cccssscsscsc

csccssssccss

ssccc

C BL 321

- azimuth angle

- pitch angle

- roll angle


71

SOLO


5 .Body Coordinates (B) (continue – 1)

Bx

Lx

Bz

Ly

LzBy

Angular Velocity from L to B (Euler Angles):

0

0

0

0

0

0 211

R

Q

PB

LB

0

0

cos0sin

010

sin0cos

cossin0

sincos0

001

0

0

cossin0

sincos0

001

0

0

G

coscossin0

cossincos0

sin01


72

SOLO



Bx

Lx

Bz

Ly

LzBy

Rotation Matrix from LLLN to B (Quaternions):

321

412

143

234

3412

2143

1234

44 3333

BIBLBL

BLBLBL

BLBLBL

BLBLBL

BLBLBLBL

BLBLBIBL

BLBLBLBL

TBLBLBLXBLBLXBL

BL

qqq

qqq

qqq

qqq

qqqq

qqqq

qqqq

qqqIqqIqC

where:

3

2

1

:&4

4

3

2

1

4

3

2

1

BL

BL

BL

BLBL

BLBL

BL

BL

BL

BL

BL

BL

BL

BL

BL

q

q

q

qq

qqor

q

q

q

q

q

q

q

q

q

2sin

2sin

2sin

2cos

2cos

2cos4

BLq

2cos

2sin

2sin

2sin

2cos

2cos1

BLq

2sin

2cos

2sin

2cos

2sin

2cos2

BLq

2sin

2sin

2cos

2cos

2cos

2sin3

BLq


73

SOLO



Bx

Lx

Bz

Ly

LzBy

Rotation Matrix from LLLN to B (Quaternions))continue – 1(

The quaternions are given by the followingdifferential equations:

BL

LIL

BIBBLBLBL

BILBL

BIBBL

BIL

BIBBL

BLBBLBL qqqqqqqqq

2

1

2

1*

2

1

2

1

2

1

2

1

04321

3412

2143

1234

2

1

4

3

2

1

B

B

B

BLBLBLBL

BLBLBLBL

BLBLBLBL

BLBLBLBL

BL

BL

BL

BL

r

q

p

qqqq

qqqq

qqqq

qqqq

q

q

q

q

4

3

2

1

0

0

0

0

2

1

BL

BL

BL

BL

zLzLyLyLxLxL

zLzLxLxLyLyL

yLyLxLxLzLzL

xLxLyLyLzLzL

q

q

q

q

4

3

2

1

0

0

0

0

2

1

BL

BL

BL

BL

zLzLByLyLBxLxLB

zLzLBxLxLByLyLB

yLyLBxLxLBzLzLB

xLxLByLyLBzLzLB

q

q

q

q

rqp

rpq

qpr

pqr

or:


74

SOLO



Bx

Lx

Bz

Ly

LzBy

Vehicle Velocity

Vehicle Velocity relative to Earth is divided in:

WAE VVV

w

v

u

V BA

DownW

EastW

NorthW

BL

zW

yW

xW

BW

V

V

V

C

V

V

V

HLongLatV

B

B

B

_

_

_

,,


WWIB

B

WAAIB

B

A

I

VVtd

VdRVV

td

Vd

td

Vda

W

AELALB

B

A

a

RVVtd

Vd

2


Table of Content

75

SOLO


6 .Wind Coordinates (W)

Bx

Lx

Bz

Ly

LzBy

Wz

V

The origin of the Wind coordinate systemis located at the instantaneous center ofgravity CG of the vehicle, with xW pointedin the direction of the vehicle velocity vectorrelative to air .AV

cos0sin

sinsincossincos

cossinsincoscos

cos0sin

010

sin0cos

100

0cossin

0sincos

23WBC

The Wind coordinate frame is defined by the following two angles:

- angle of attack

- sideslip angle


76

SOLO


6 .Wind Coordinates (W) (continue -1)

Bx

Lx

Bz

Ly

LzBy

Wz

V

Rotation Matrix from L (LLLN) to W is:

- azimuth angle of the trajectory

- pitch angle of the trajectory

Rotation Matrix

32123 BL

WB

WL CCC

The Rotation Matrix from L (LLLN) to W can also be defined by the following Consecutive rotations:

- bank angle of the trajectory

cccssscsscsc

csccssssccss

ssccc

CC WL

WL 321

*1

We defined also the intermediate wind frame W* by:

csscs

cs

ssccc

CWL 032

*


77

SOLO



Bx

Lx

Bz

Ly

LzBy

Wz

V

Angular Velocity of W* relative to LLLN is:

Angular Velocities

cos

sin

0

0

cos0sin

010

sin0cos

0

0

0

0

0

0

2

*

*

**

*

W

W

WW

LW

R

Q

P

Angular Velocity of W relative to LLLN is:

coscossin0

cossincos0

sin01

cos

sin

cossin0

sincos0

001

0

00

0

0

0

0

0 21

W

W

WW

LW

R

Q

P


78

SOLO



Bx

Lx

Bz

Ly

LzBy

Wz

V

We have also:

Angular Velocities (continue – 1)

Down

East

North

WL

WL

LIE

WL

zW

yW

xWW

IE C

Lat

Lat

CC ***

*

*

**

sin

0

cos

Down

East

North

WL

WL

LEL

WL

zW

yW

xWW

EL C

LatLong

Lat

LatLong

CC

***

*

*

**

sin

cos

*

1

sin

0

cosW

IEWL

LIE

WL

zW

yW

xWW

IE

Lat

Lat

CC

*1

sin

cos

WIL

WL

LIL

WL

WIL

LatLong

Lat

LatLong

CC


79

SOLO



Bx

Lx

Bz

Ly

LzBy

Wz

V

The Angular Velocity from I to W is:


DownDown

EastEast

NorthNorth

WL

W

W

WL

ILWL

W

W

WW

ILW

LW

W

W

WW

IW C

R

Q

P

C

R

Q

P

r

q

p

Using the angle of attack α and the sideslip angle β , we can write:

BWBW yz

11

or:

0

0

0

0

3

r

q

p

C

r

q

pWB

W

W

WW

IBW

IWW

BW

but also:

0

0

0

0

3

R

Q

P

C

R

Q

PWB

W

W

WW

LBW

LWW

BW


80

SOLO



Bx

Lx

Bz

Ly

LzBy

Wz

V

We can write:


0

cos

sin

0

0

cos0sin

sinsincossincos

cossinsincoscos

r

q

p

r

q

p

W

W

W

or:

cossin

sinsincossincos

cossinsincoscos

rpr

rqpq

rqpp

W

W

W

This can be rewritten as:

tansincoscos

rpq

q W

Wrrp cossin

cos

sinsincos

tantansincossincossincossincos

W

WW

qrp

qrpqrpp


81

SOLO



Bx

Lx

Bz

Ly

LzBy

Wz

V

We have also:


tansincoscos

RPQ

Q W

WRRP cossin

cos

sinsincos WW

QRPP


82

SOLO



Bx

Lx

Bz

Ly

LzBy

Wz

V

The vehicle velocity was decomposed in:

Vehicle Velocity

WAE VVV

0

0

V

V WA

- vehicle velocity relative to atmosphere

DownW

EastW

NorthW

WL

zW

yW

xW

WW

V

V

V

C

V

V

V

HLongLatV

W

W

W

_

_

_

,,

- wind velocity at velocity position

also

0

0

0

011*

VV

VV WA

WA

DownW

EastW

NorthW

WL

zW

yW

xW

WW

V

V

V

C

V

V

V

HLongLatV

W

W

W

_

_

_

*

*

*

*

* ,,


83

SOLO



Bx

Lx

Bz

Ly

LzBy

Wz

V

The vehicle acceleration in W* coordinates is


WAELALW

W

A

WWIW

W

WAAIW

W

A

I

C

aRVVtd

Vd

VVtd

VdRVV

td

Vd

td

Vda

2*

*

*

*

*

*

from which

*******

*

*

*

2 WW

WA

WWEL

WWA

WLW

W

W

A aVAVtd

Vd

where

RaA

:


84

SOLO



Bx

Lx

Bz

Ly

LzBy

Wz

V

Vehicle Acceleration (continue – 1)

**

*

*

****

****

****

*

*

*

**

**

**

0

0

022

202

220

0

0

0

0

0

0

0

zWW

yWW

xWW

xWxWyWyW

xWxWzWzW

yWyWzWzW

zW

yW

xW

WW

WW

WW

a

a

aV

A

A

AV

PQ

PR

QRV

where

HR

Lat

Lat

C

a

a

a

A

A

A

A WL

zW

yW

xW

zW

yW

xW

W

2*

*

*

*

*

*

*

*

sin

0

cos - Acceleration due to external forces on the

Air Vehicle in W* coordinates

That gives

*****

*****

**

2

2

zWWyWyWzWW

yWWzWzWyWW

xWWxW

aVAVQ

aVAVR

aAV


85

SOLO



Bx

Lx

Bz

Ly

LzBy

Wz

V

Vehicle Acceleration (continue – 2)

Using

cos

sin

*

*

**

*

W

W

WW

LW

R

Q

P

we have

** xWWxW aAV

cos/2 ****

zWzW

yWWyW

V

aA

****

2 yWyWzWWzW

V

aA


Table of Content

86

SOLO

Aerodynamic Forces npp ˆt̂

n̂V

ds

wx1

wy1

wz1

tf ˆ

Pressure force

Friction force

WS

WS

A dstfnppF

11

ntonormalplanonVofprojectiont

dstonormaln

ˆˆ

ˆ

airflowingthebyweatedsurfaceVehicleS

SsurfacetheonmNstressforcefrictionf

Ssurfacetheondifferencepressurepp

W

W

W

)/( 2


7. Forces Acting on the Vehicle

87

SOLO

7. Forces Acting on the Vehicle (continue – 1)

Bx

Lx

Bz

Ly

LzBy

Wz

V

WyT

C

L

D

g

Aerodynamic Forces (continue – 1)

L

C

D

F WA

ForceLiftL

ForceSideC

ForceDragD

L

C

D

CSVL

CSVC

CSVD

2

2

2

2

12

12

1

tCoefficienLiftRMC

tCoefficienSideRMC

tCoefficienDragRMC

eL

eC

eD

,,,

,,,

,,,

ityvisdynamic

lengthsticcharacteril

soundofspeedHa

numberynoldslVR

numberMachaVM

e

cos

)(

Re/

/


88

SOLO


Aerodynamic Forces (continue -2)

W

W

W

SfpL

SfpC

SfpD

dswztCwznCS

C

dswytCwynCS

C

dswxtCwxnCS

C

1ˆ1ˆ1

1ˆ1ˆ1

1ˆ1ˆ1

nCq p ˆt̂

n̂V

ds

wx1

wy1

wz1

tCq fˆ

Pressure force

Friction force

WS SVq 2

2

1

Wf

Wp

SsurfacetheontcoefficienfrictionV

fC

SsurfacetheontcoefficienpressureV

ppC

2/

2/

2

2

ntonormalplanonVofprojectiont

dstonormaln

ˆˆ

ˆ


89

MomentFriction

S

C

Momentessure

S

CCA

WW

dstRRfdsnRRppM 11

Pr

/

Aerodynamic Moments Relative to C can be divided in Pressure Moments andFriction Moments.

FrictionSkinorFrictionViscous

S

essureNormal

S

A

WW

dstfdsnppF 11

Pr

fp

V

ASALM

Aerodynamic Forces can be divided in Pressure Forces and Friction Forces.


npp ˆt̂

n̂V

ds

wx1

wy1

wz1

tf ˆ

Pressure force

Friction force

WS

AERODYNAMIC FORCES AND MOMENTS.

90

SOLO

iopenS

outflowoutopenflowinflowinopenflow dsnppmVmVT

1:

0

/

0

/ THRUST FORCES

iopenS

OoutflowoutopenflowCoutopeninflowinopenflowCiopenCT dsnppRRmVRRmVRRM

1:

0

/

0

/,

THRUST MOMENTS RELATIVE TO C

inopenS

inflowinopenflow dsnppmV

1

00

/

outopenS

outflowoutopenflow dsnppmV

1

0

/

T

outopenR

iopenR

CR

C


Table of Content

CTM ,

91

SOLO


BxLx

Bz

Ly

LzBy

Wz

V

Wy

T

C

L

D

gT

T

Thrust

B

B

B

z

y

x

BWB

W

T

T

T

TCT

cos0sin

sinsincossincos

cossinsincoscos**

*

*

*

cossin0

sincos0

001*

1

W

W

W

W

W

W

z

y

x

W

z

y

x

W

T

T

T

T

T

T

T

T


Bx

Lx

Bz

Ly

LzBy

Wz

V

WyT

C

L

D

g

92

SOLO


Gravitation Acceleration

zgygxg

gg100

0

0

0

010

0

0

0

001

cs

sc

cs

sc

cs

scC EWE

W

gg

cc

cs

sW

2sec/174.322sec/81.90

2

0

00gg ftmg

HR

R


The derivation of Gravitation Acceleration assumes an Ellipsoidal Symmetrical Earth.The Gravitational Potential U (R,ϕ) is given by

,

sin1,2

RUg

PR

aJ

RRU

EE

n n

n

n

μ – The Earth Gravitational Constanta – Mean Equatorial Radius of the EarthR=[xE

2+yE2+zE

2]]/2 is the magnitude of the Geocentric Position Vectorϕ – Geocentric Latitude (sinϕ=zE/R)Jn – Coefficients of Zonal Harmonics of the Earth Potential FunctionPn (sinϕ) – Associated Legendre Polynomials

I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

93

SOLO


Gravitation Acceleration


Retaining only the first three terms of theGravitational Potential U (R,ϕ) we obtain:

R

z

R

z

R

z

R

aJ

R

z

R

aJ

Rg

R

y

R

z

R

z

R

aJ

R

z

R

aJ

Rg

R

x

R

z

R

z

R

aJ

R

z

R

aJ

Rg

EEEEz

EEEEy

EEEEx

E

E

E

342638

515

2

31

342638

515

2

31

342638

515

2

31

2

2

4

44

42

22

22

2

2

4

44

42

22

22

2

2

4

44

42

22

22

I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

sin

cossin

coscos

R

zR

yR

x

E

E

E

2/1222EEE zyxR

94

SOLO

23. Local Level Local North (LLLN) Computations for an Ellipsoidal Earth Model

2

2210

20

20

20

5

21

20

60

sin

sin1

sin321

sin1

sec/10292116557.7

sec/051646.0

sec/780333.9

26.298/.1

10378135.6

Ae

e

p

m

e

HR

RLatggg

LateRR

LateeRR

LateRR

rad

mg

mg

e

mR

LatHR

V

HR

V

HR

V

Ap

EastDown

Am

NorthEast

Ap

EastNorth

tan

Lat

Lat

Down

East

North

sin

0

cos

DownDownDown

EastEast

NorthNorthNorth

East

North

Lat

LatLong

cos

t

t

dtLatLattLat

dtLongLongtLong

0

0

0

0


I

0Ex

0Ey

Iz

Northx

EastyDownz

Bx

ByBz

Iy

Ixt

tLong

Lat

0Ez

Ex

Ey

Ez

AV

SIMULATION EQUATIONS

95

SOLO

Down

East

North

Down

East

North

1 Latcos

1

LatHR

V

HR

V

HR

V

Ap

EastDown

Am

NorthEast

Ap

EastNorth

tan

Long

Lat

Down

East

North

sin

0

cos

Down

East

North

L

V

V

V

V

2

2210

20

20

20

5

21

20

60

sin

sin1

sin321

sin1

sec/10292116557.7

sec/051646.0

sec/780333.9

26.298/.1

10378135.6

Ae

e

p

m

e

HR

RLatggg

LateRR

LateeRR

LateRR

rad

mg

mg

e

mR

s

1

s

1

DownDownDown

EastEast

NorthNorthNorth

pR

mR

AH

Long

0Long

Lat

0Lat

Lat

Long

g

Lat g

LOCAL LEVEL LOCAL NORTHCOMPUTATIONS

Lat

North DownEast

AIR VEHICLE IN ELLIPTICAL EARTH ATMOSPHERESIMULATION EQUATIONS

Table of Content

96

SOLO


Force Equations

Bx

Lx

Bz

Ly

LzBy

Wz

V

WyT

C

L

D

g

Air Vehicle Acceleration

WAELALW

W

A

I

C aRVVtd

Vd

td

Vda

2

WAELALW

W

AA aRVV

td

VdamTF

m

2g

1

Rg

g: where

ccgm

LT

csgm

CT

sgm

DT

A

A

A

zW

yW

xW

sin

sincos

coscos

cg

sg

m

LTm

CTm

DT

A

A

A

zW

yW

xW

0

sin

sincos

coscos

cossin0

sincos0

001

*

*

*


Table of Content

97

SOLO

LBL

BBA

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ma

11

B

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,

Missile Kinematics Model 1 in Vector Notation (Spherical Earth)


98

SOLO

rB

rB

r

rotor

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B

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yBCA

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q

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r

q

p

III

III

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pq

pr

qr

r

q

p

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III

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T

T

T

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M

M

III

III

III

r

q

p

0

0

0

,

,

,

,

,

,

1

rr ,

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r

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r

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a

a

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Down

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a

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a

a

a

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022

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sin

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1

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sinsincossincos

cossinsincoscosW

BC

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1

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Long

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w

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Missile Kinematics Model 1 in Matrix Notation (Spherical Earth)


99

SOLO

LBL

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ma

11

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,

Missile Kinematics Model 2 in Vector Notation (Spherical Earth)


100

SOLO

Missile Kinematics Model 2 in Matrix Notation (Spherical Earth)

rB

rB

r

Crrotor

B

B

B

zzyzxz

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rr ,

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sin

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cos

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References

SOLO

101

PHAK Chapter 1 - 17http://www.gov/library/manuals/aviation/pilot_handbook/media/

George M. Siouris, “Aerospace Avionics Systems, A Modern Synthesis”, Academic Press, Inc., 1993

R.P.G. Collinson, “Introduction to Avionics”, Chapman & Hall, Inc., 1996, 1997, 1998

Ian Moir, Allan Seabridge, “Aircraft Systems, Mechanical, Electrical and AvionicsSubsystem Integration”, John Wiley & Sons, Ltd., 3th Ed., 2008


Ian Moir, Allan Seabridge, “Military Avionics Systems”, John Wiley & Sons, LTD., 2006

References (continue – 1)

SOLO

102


S. Hermelin, “Air Vehicle in Spherical Earth Atmosphere”

S. Hermelin, “Airborne Radar”, Part1, Part2, Example1, Example2

S. Hermelin, “Tracking Systems”

S. Hermelin, “Navigation Systems”

S. Hermelin, “Earth Atmosphere”

S. Hermelin, “Earth Gravitation”

S. Hermelin, “Aircraft Flight Instruments”

S. Hermelin, “Computing Gunsight, HUD and HMS”

S. Hermelin, “Aircraft Flight Performance”

S. Hermelin, “Sensors Systems: Surveillance, Ground Mapping, Target Tracking”

S. Hermelin, “Air-to-Air Combat”

References (continue – 2)

SOLO

103


S. Hermelin, “Spherical Trigonometry”

S. Hermelin, “Modern Aircraft Cutaway”

104

SOLO

TechnionIsraeli Institute of Technology

1964 – 1968 BSc EE1968 – 1971 MSc EE

Israeli Air Force1970 – 1974

RAFAELIsraeli Armament Development Authority

1974 –

Stanford University1983 – 1986 PhD AA

105

SOUND WAVESSOLO

SupersonicV > a

SubsonicV < a

a t a t

V tV t

M

1sin 1

Soundwaves

Machwaves

Disturbances propagate by molecular collision, at the sped of sound a,along a spherical surface centered at the disturbances source position.

The source of disturbances moves with the velocity V.

- when the source moves at subsonic velocity V < a, it will stay inside the family of spherical sound waves.

-when the source moves at supersonic velocity V > a, it will stay outside the family of spherical sound waves. These wave fronts form a disturbance

envelope given by two lines tangent to the family of spherical sound waves. Those lines are called Mach waves, and form an angle μ with the disturbance

source velocity:a

VM

M

&

1sin 1

106

SOUND WAVESSOLO

Sound Wave Definition: p

p

p p

p1

2 1

1

1

2 1

2 1

2 1

p p p

h h h

For weak shocks

up

1

2

11

11

1

11

11

2

12

1

1uuuuuu

)C.M.(

ppuuupuupu

11

111122111

211

)C.L.M.(

21

au 1

1p

1

1T

1e

112 uuu

112 ppp

112

112 TTT

112 eee

SOUND

WAVE

Since the changes within the sound wave are small, the flow gradients are small.Therefore the dissipative effects of friction and thermal conduction are negligibleand since no heat is added the sound wave is isotropic. Since

au 1

s

pa

2valid for all gases

107

SPEED OF SOUND AND MACH NUMBERSOLO

21

au 1

1p

1

1T

1e

112 uuu

112 ppp

112

112 TTT

112 eee

SOUNDWAVE

Speed of Sound is given by

0

ds

pa

RTp

C

C

T

dT

R

C

pT

dT

R

C

d

dp

dR

T

dTCds

p

dpR

T

dTCds

v

p

v

p

dsv

p

00

0

but for an ideal, calorically perfect gas

pRTa

TChPerfectyCaloricall

RTpIdeal

p

The Mach Number is defined asRT

u

a

uM

1

2

1

1

111

a

a

T

T

p

pThe Isentropic Chain:

a

ad

T

Tdd

p

pdsd

1

2

10

108

NORMAL SHOCK WAVESSOLO

Normal Shock Wave ( Adiabatic), Perfect Gas

G Q 0 0,

Mach Number Relations (1)

122

22

1

21

22

222

21

221

22

2

222

1

1

21

1222

2

11

1

22221

211

2211

2

1

2

12

1

2

1

*12

1

2

1

12

1

14..

...

..

uuu

a

u

a

uaa

uaaau

h

au

h

aEC

uuu

p

u

p

pupuMLC

uuMCp

a

Field Equations:

1222

2

11

2

2

1

2

1

2

1

2

1uuu

u

au

u

a

u u a1 22

u

a

u

aM M1 2

1 21 1

Prandtl’s Relation

u

p

T

e

u

p

T

e

11

q

1

1

1

1

1

2

2

2

2

2

1 2

2

1

2

11

2

1

2

1

2

1

21

2

12122

21

12

uu

auuuua

uu

uu

Ludwig Prandtl(1875-1953)

109



G Q 0 0,


M

MM

M

M

M

M

MM

22

22

1

12

12

12

12

12

21

1

2

1 1

2

11

1 21

2 1 2

1 1 1 1 1

12

or

M

M

M

M

MH H

A A

2

12

12

12

121 2

1 21

1

21

2

2

1

11

2

12

11

2

1

1

2

12

1 2

12

2 12 1

2

12

1 2 1

1 2

A A u

u

u

u u

u

aM

M

M

u

p

T

e

u

p

T

e

11

q

1

1

1

1

1

2

2

2

2

2

1 2

110



G Q 0 0,


p

p

up

u

u

u

a

MM

MM

M M

M

2

1

12

1

1

2

1

12

12

1

2

12 1

2

12 1

2 12

12

12

1 1 1 1

1 11 2

11

1 1 2

1

or

(C.L.M.)

p

pM2

1121

2

11

h

h

T

T

p

pM

M

M

a

a

h C T p R Tp2

1

2

1

2

1

1

212 1

2

12

2

1

12

11

1 2

1

s s

R

T

T

p

pM

M

M2 1 2

1

12

1

1

12

1

112

12

1

12

11

1 2

1

ln ln

s s

RM M

M2 1

1 1

2 12 3

2

2 12 41

2 2

3 11

2

11

Shapiro p.125

u

p

T

e

u

p

T

e

11

q

1

1

1

1

1

2

2

2

2

2

1 2

111

STEADY QUASI ONE-DIMENSIONAL FLOWSOLO

STAGNATION CONDITIONS

)C.E.( constuhuh 222

211 2

1

2

1

The stagnation condition 0 is attained by reaching u = 0

2

/

21202020

2

11

12

12

122

12

MTR

u

Tc

u

T

T

c

uTTuhh

TRa

auM

Rc

pp

Tch pp

Using the Isentropic Chain relation, we obtain:

2

10102000

2

11 M

p

p

a

a

h

h

T

T

Steady , Adiabatic + Inviscid = Reversible, , q Q 0 0, ~ ~ 0

G 0 t

0

SOLO

112

Civilian Aircraft AvionicsFlight Cockpit

CIRRUS PERSPECTIVE

Cirrus Perspective Avionics Demo, Youtube Cirrus SR22 Tampa Landing in Heavy Rain

SOLO

113

Flight Displays

CIRRUS PERSPECTIVE

Civilian Aircraft Avionics

SOLO

114

Flight Displays

CIRRUS PERSPECTIVE


SOLO

115

Flight Displays

CIRRUS PERSPECTIVE


SOLO

116

Flight Displays

CIRRUS PERSPECTIVE


SOLO

117

Flight Displays

CIRRUS PERSPECTIVE


SOLO

118

Flight Displays

CIRRUS PERSPECTIVE


SOLO

119

Flight Displays

CIRRUS PERSPECTIVE


SOLO

120

Flight Displays

CIRRUS PERSPECTIVE


11 fighter aircraft avionics - part iv

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Transcript of 11 fighter aircraft avionics - part iv