Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

11 fighter aircraft avionics - part iv

5,989 views

Published on

This is from the last presentations from my side. Medical Problems prevent me to continue with new presentations.Please do not contact me.

Published in: Science
  • accessibility Books Library allowing access to top content, including thousands of title from favorite author, plus the ability to read or download a huge selection of books for your pc or smartphone within minutes.........ACCESS WEBSITE Over for All Ebooks ..... (Unlimited) ......................................................................................................................... Download FULL PDF EBOOK here { https://urlzs.com/UABbn } .........................................................................................................................
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here
  • The italian missile aspide was not and is not derived from aim7 sparrow. had an active radar instead that Semi-active, an electronics more resistant to countermeasures, was more agile because the fins of control were mobile and independent while the sparrow moved in pairs,had a PK of over 90%, the rocket motor was far more efficient, had a radius of at least twice and was the fastest. was a true missile medium range with the only drawback that resembled the sparrow.
       Reply 
    Are you sure you want to  Yes  No
    Your message goes here

11 fighter aircraft avionics - part iv

  1. 1. Fighter Aircraft Avionics Part IV SOLO HERMELIN Updated: 04.04.13 1
  2. 2. Table of Content SOLO Fighter Aircraft Avionics 2 Introduction Jet Fighter Generations Second Generation (1950-1965( Third Generation (1965-1975( First generation (1945-1955( Fourth Generation (1970-2010( 4.5Generation Fifth Generation (1995 - 2025( Aircraft Avionics Third Generation Avionics Fourth Generation Avionics 4.5Generation Avionics Fifth Generation Avionics Cockpit Displays Communication (internal and external( Data Entry and Control Flight Control Fighter Aircraft
  3. 3. Table of Content (continue – 1( SOLO Fighter Aircraft Avionics Aircraft Propulsion System Aircraft Flight Performance Navigation Earth Atmosphere Flight Instruments Power Generation System Environmental 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 I I
  4. 4. Table of Content (continue – 2( SOLO 4 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 Bombs Air-to-Surface Missiles (ASM( or Air-to-Ground Missiles (AGM( Fighter Aircraft Weapon Examples Air-to-Air Missiles (AAM( Fighter Gun Avionics III
  5. 5. Continue from Fighter Aircraft Avionics Part III SOLO 5 Fighter Aircraft Avionics
  6. 6. SOLO 6 Fighter Aircraft Weapon System
  7. 7. SOLO 7 Fighter Aircraft Weapon System 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 Fuel Tanks, Extra Sensor Pods, or Decoys (e.g., Chaff to fool radar-guided missiles and Flares to fool infra-red guided missiles(. The Stores Management System (SMS( manages the mechanical and electrical connections to weapons and senses their status under control of the 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 TV guided(, 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-mounted Guns. Weapon release modes include automatic (AUTO( and Continuously Computed Impact Point (CCIP( plus special modes for Guided Weapons. In AUTO mode, the MCC controls weapon release based on computed impact point, current target position, and predicted aircraft position at release. In CCIP mode, the MCC computes a predicted impact point which is displayed on the HUD, and the aircrew controls weapon release with the bomb button on the HOTAS. Stores
  8. 8. SOLO 8 Fighter Aircraft Weapon System 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 Weapon Launching Signal are disabled. In addition, usually the Weapons are in a Safe Mode. The Weapons can be Launched only when the Aircraft 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
  9. 9. 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.
  10. 10. SOLO Fighter Aircraft Weapon System A/G Weapon Selection Weapon selection includes selecting the type of Weapon, the number to drop, and the desired 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 Waypoint Steering 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
  11. 11. SOLO Air-to-Ground Missions 11 Fighter Aircraft Weapon System MULTI-COMMAND HANDBOOK 11-F16
  12. 12. SOLO 12 Fighter Aircraft Weapon System 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(
  13. 13. SOLO 13 Fighter Aircraft Weapon System 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 Weapon System provides Flight Instruction and Automatically Releases the Bombs.
  14. 14. SOLO 14 Fighter Aircraft Weapon System 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.
  15. 15. SOLO 15 Fighter Aircraft Weapon System Dumb Bombs Delivery (continue – 2( 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
  16. 16. SOLO 16 Fighter Aircraft Weapon System Dumb Bombs Delivery (continue – 3( 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 to Release (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 Weapon Trajectory 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.
  17. 17. SOLO 17 Fighter Aircraft Weapon System 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-GPS Guidance System Storm Shadow Inertial, GPS and TERPROM. Terminal guidance using imaging infrared AGM-158 JASSM (Joint Air-to-Surface Standoff Missile( INS/GPS Guidance
  18. 18. 18 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( SOLO Fighter Aircraft Weapon System 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.
  19. 19. Air- to-Air missile launch envelope
  20. 20. Kinematics no-escape-zone Return to Table of Content
  21. 21. 01-21 Air-to-Air Missiles Modes of Operation
  22. 22. 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
  23. 23. 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
  24. 24. AMRAAM A/A MISSILES AMRAAM AIM - 120C-5 Specifications Length: 12 ft 3.65 m Diameter: 7 in 17.8 cm Wing Span: 17.5 in 44.5 cm Fin Span: 17.6 in 44.7 c Weight: 356 lb 161.5 kg Warhead: 45 lb 20.5 Kg Guidance: Active Radar Fuzing: Proximity (RF( and Contact Launcher: Rail and eject AIM-120C Rocket motor PN G672798-1 is an enhanced version with additional 5” (12 cm( of propellant. Estimation: add 10% (12/140( to obtain mp ~ 52 kg Wtot ~ 120,000 N s AMRAAM AIM-120 Movie Return to Table of Content
  25. 25. AIM-9X AIM-9X Movie
  26. 26. 29 A-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 Return to Table of Content Rafael Python 5 Promo, Movie Derby - Beyond Visual Range Air-to-Air Missile, Movie
  27. 27. 30 Evolution 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 1978 HITS: OVER 35 A/C DURING 1982 WAR SERVICE: 1968-1980 HITS: OVER 100 A/C DURING 1973 WAR SERVICE: 1964-1969 0°-(10°) 30° 180° 45° 30° LEAD/LAG ANGLE 0° MAX. ASPECT ANGLE TYPICAL 3rd GENERATION MISSILE LAUNCHER Short Range DERBYDERBY ACTIVR BVR Dual Range PYTHON-5 5th GENERATION Full Sphere IR Missile Full Scale Development
  28. 28. 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
  29. 29. 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
  30. 30. 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 -11 Length: 3.690 m Body diameter: 200 mm Wing span: 1 m Launch weight: 220 kg Warhead: HE-fragmentation Fuze: RF Guidance: Semi-Active CW Radar Propulsion: Solid propellant Range: 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 more effective seeker. The new seeker requires target illumination only during the last stage, providing a Lock On After Launch capability. • 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 Pakistan but doesn’t appear to be in service with the Chinese Navy.
  31. 31. SOLO 34 Fighter Aircraft Weapon System F4-Phantom Armament
  32. 32. SOLO 35 Fighter Aircraft Weapon System F-16
  33. 33. SOLO 36 Fighter Aircraft Weapon System http://www.freerepublic.com/focus/f-news/2845813/posts F-15
  34. 34. SOLO 37 Fighter Aircraft Weapon System F-15C: M61A1 Vulcan Cannon and AIM-9M Sidewinder, Movie
  35. 35. SOLO 38 Fighter Aircraft Weapon System F-18
  36. 36. SOLO 39 Fighter Aircraft Weapon System 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.
  37. 37. SOLO F-22 Raptor http://www.ausairpower.net/APA-Raptor.html Fighter Aircraft Weapon System 40 Internal Weapon Bay
  38. 38. 41 Lockheed_Martin_F-35_Lightning_II Fifth Generation Avionics
  39. 39. F-35 Simulator - AA and AG Modes _ Avionics-1, Movie Lockheed_Martin_F-35_Lightning_II Fifth Generation Avionics 42
  40. 40. 43 Fighter Aircraft Weapon System Su-32/34
  41. 41. 44 Fighter Aircraft Weapon System
  42. 42. 45 Su-35 Fighter Aircraft Weapon System
  43. 43. 46 Fighter Aircraft Weapon System
  44. 44. 47 Fighter Aircraft Weapon System
  45. 45. SOLO 48 Fighter Aircraft Weapon System
  46. 46. SOLO 49 Fighter Aircraft Weapon System
  47. 47. SOLO 50 Fighter Aircraft Weapon System
  48. 48. SOLO 51 Fighter Aircraft Weapon System Fighter Gun
  49. 49. SOLO 52 Fighter Aircraft Weapon System
  50. 50. 53 Performance of Aircraft Cannons in terms of their Employment in Air Combat SOLO
  51. 51. 54 Performance of Aircraft Cannons in terms of their Employment in Air Combat SOLO
  52. 52. 55 Performance of Aircraft Cannons in terms of their Employment in Air Combat SOLO
  53. 53. SOLO 56 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 Ground In this case the Aircraft Weight is sustained by the Wheels and a Weight-on-Wheels Switch (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.
  54. 54. SOLO 57 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 Ground In this case the Aircraft Weight is sustained by the Wheels and a Weight-on-Wheels Switch (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.
  55. 55. SOLO 58 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 Air In 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.
  56. 56. 59 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 Mass System 8.2 Missile Kinematics Model 1 (Spherical Earth) 8.3 Missile Kinematics Model 2 (Spherical Earth)
  57. 57. 60 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 Coordinate Systems Table of Content
  58. 58. 61 SOLO Coordinate Systems 1.Inertial System (I( R  - vehicle position vector I td Rd V   = - vehicle velocity vector, relative to inertia II td Rd td Vd a 2 2   == - vehicle acceleration vector, relative to inertia AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE Table of Content
  59. 59. 62 SOLO 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 equator to zero longitude meridian. The Earth rotates relative to Inertial system I, with the angular velocity sec/10.292116557.7 5 rad− =Ω EIIE zz  11 Ω=Ω=Ω=←ω ( )           Ω =← 0 0 EC IEω  Rotation Matrix from I to E [ ] ( ) ( ) ( ) ( )           ΩΩ− ΩΩ =Ω= 100 0cossin 0sincos 3 tt tt tCE I AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  60. 60. 63 SOLO Coordinate Systems (continue – 3( 2.Earth Fixed Coordinate System (E) (continue – 1) Vehicle Position ( ) ( ) ( ) ( )ETE I EI E I RCRCR  == Vehicle Velocity Vehicle Acceleration RVR td Rd td Rd V EIE EI    ×Ω+=×+== ←ω - vehicle velocity relative to Inertia R td Rd td Rd V IE LE E    ×+== ←ω: - vehicle velocity relative to Earth ( ) ( ) II E I E I R td d td Vd RV td d td Vd a      ×Ω+=×Ω+== ( ) ( )RV td Vd R td Rd R td d V td Vd EIEEU U E EE EIU U E IU              ×Ω×Ω+×             Ω+++=×Ω×Ω+×Ω+× Ω +×+= ← Ω ←←← ω ωωω 0 ( ) ( ) ( )RV td Vd RV td Vd a E E E EEU U E      ×Ω×Ω+×Ω+=×Ω×Ω+×Ω++= ← 22ω or where U is any coordinate system. In our case U = E. AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE Table of Content
  61. 61. 64 SOLO Coordinate Systems (continue – 4( 3.Earth Fixed Coordinate System (E0) The origin of the system is fixed on the earth at some given 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 Earth surface, zE0 is pointed down. [ ] [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) =           −           − − =−−= 100 0cossin 0sincos sin0cos 010 cos0sin 2/ 00 00 00 00 3020 0 LongLong LongLong LatLat LatLat LongLatCE E π ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )          −−− − −− = 00000 00 00000 sinsincoscoscos 0cossin cossinsincossin LatLongLatLongLat LongLong LatLongLatLongLat The Angular Velocity of E relative to I is: EIIEIE zz  110 Ω=Ω== ←← ωω or ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )          Ω− Ω =           Ω          −−− − −− =           Ω =← 0 0 00000 00 00000 00 0 sin 0 cos 0 0 sinsincoscoscos 0cossin cossinsincossin 0 0 Lat Lat LatLongLatLongLat LongLong LatLongLatLongLat CE E E IEω  AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE Table of Content
  62. 62. 65 SOLO Coordinate Systems (continue – 5( 4.Local-Level-Local-North (L) The origin of the LLLN coordinate system is located at the projection of the center of gravity CG of the vehicle on the Earth surface, with zDown axis pointed down, xNorth, yEast plan parallel to the local level, with xNorth pointed to the local North and yEast pointed to the 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 L E π ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )          −−− − −− = LatLongLatLongLat LongLong LatLongLatLongLat sinsincoscoscos 0cossin cossinsincossin AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  63. 63. 66 SOLO Coordinate Systems (continue – 6( 4.Local-Level-Local-North (L) (continue – 1) Angular Velocity IEELIL ←←← += ωωω  Angular Velocity of L relative to I ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )          Ω− Ω =           Ω          − − −− =           Ω =           Ω Ω Ω =← Lat Lat LatLongLatLongLat LongLong LatLongLatLongLat CL E Down East North L IE sin 0 cos 0 0 sinsincoscoscos 0cossin cossinsincossin 0 0 ω  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )               − −=             −+                       −−− − −− =             −+             =           = • • • • • • • ← LatLong Lat LatLong Lat Long LatLongLatLongLat LongLong LatLongLatLongLat Lat Long CL E Down East North L EL sin cos 0 0 0 0 sinsincoscoscos 0cossin cossinsincossin 0 0 0 0 ρ ρ ρ ω  ( ) ( ) ( ) ( ) ( )                         +Ω− −       +Ω =           Ω+ Ω+ Ω+ =+= • • • ←←← LatLong Lat LatLong DownDown EastEast NorthNorth L IEC L ECL L IL sin cos ρ ρ ρ ωωω  Therefore AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  64. 64. 67 SOLO Coordinate Systems (continue – 7( 4.Local-Level-Local-North (L) (continue – 2) Vehicle Velocity Vehicle Velocity relative to I RVR td Rd td Rd V EIE EI    ×Ω+=×+== ←ω ( ) ( ) ( ) ( ) ( ) ( ) ( )          +−               −− − +           +− =×+= •• •• •• ← HR LatLongLat LatLongLatLong LatLatLong HR R td Rd V EL L L E 00 0 0 0cos cos0sin sin0 0 0     ω 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 V td Hd LatHR V td Longd HR V td Latd _ 0 _ 0 _ cos −= + = + = AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE HeightVehicleHRadiusEarthmRHRR =⋅=+= 6 00 10378135.6
  65. 65. 68 SOLO Coordinate Systems (continue – 8( 4.Local-Level-Local-North (L) (continue – 3) Vehicle Velocity (continue – 1( We assume that the atmosphere movement (velocity and acceleration( relative to Earth At the vehicle position (Lat, Long, H( is known. Since the aerodynamic forces on the vehicle are due to vehicle movement relative to atmosphere, let divide the vehicle velocity in two parts: WAE VVV  += ( )           = Down East North L A V V V V  - Vehicle Velocity relative to atmosphere ( ) ( )           = DownW EastW NorthW L W V V V HLongLatV _ _ _ ,,  - Wind Velocity at vehicle position (known function of time( AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  66. 66. 69 SOLO Coordinate Systems (continue – 9( 4.Local-Level-Local-North (L) (continue – 4) Vehicle Acceleration Since: ( ) ( ) ( ) ( )RV td Vd R td d td Vd RV td d td Vd a EEL L E II E I E I        ×Ω×Ω+×Ω++=×Ω+=×Ω+== ← 2ω WAE VVV  += ( ) WWIL L W AAIL L A VV td Vd RVV td Vd a      ×Ω+×++×Ω×Ω+×Ω+×+= ←← ωω ( )         Wa WWEL L W AAEL L A VV td Vd RVV td Vd ×Ω+×++×Ω×Ω+×Ω+×+= ←← 22 ωω ( ) ( ) ( ) ( )HLongLatVHLongLat td Vd HLongLata WEL L W W ,,2,,:,,    ×Ω++= ←ω ( ) WAAEL L A aRVV td Vd   +×Ω×Ω+×Ω+×+= ← 2ω where: is the wind acceleration at vehicle position. AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE Table of Content
  67. 67. 70 SOLO Coordinate Systems (continue – 10( 5.Body Coordinates (B) The origin of the Body coordinate system is located at the instantaneous center of gravity CG of the vehicle, with xB pointed to the front of the Air Vehicle, yB pointed toward the right wing and zB completing the right-handed Cartesian reference frame. Rotation Matrix from LLLN to B (Euler Angles): [ ] [ ] [ ]           −+ +− − == θφψφψθφψφψθφ θφψφψθφψφψθφ θψθψθ ψθφ cccssscsscsc csccssssccss ssccc CB L 321 ψ - azimuth angle θ - pitch angle φ - roll angle AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  68. 68. 71 SOLO Coordinate Systems (continue – 11( 5.Body Coordinates (B) (continue – 1) ψ θ φ Bx Lx Bz Ly Lz By Angular Velocity from L to B (Euler Angles): ( ) [ ] [ ] [ ]           +           +           =           =← ψ θφθφ φ ω    0 0 0 0 0 0 211 R Q P B LB                     −           − +                     − +           = ψθθ θθ φφ φφθ φφ φφ φ    0 0 cos0sin 010 sin0cos cossin0 sincos0 001 0 0 cossin0 sincos0 001 0 0 [ ]           =                     − − = ψ θ φ ψ θ φ θφφ θφφ θ       G coscossin0 cossincos0 sin01 AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  69. 69. 72 SOLO Coordinate Systems (continue – 12( 5.Body Coordinates (B) (continue – 2) ψ θ φ Bx Lx Bz Ly Lz By Rotation Matrix from LLLN to B (Quaternions): ( ) [ ][ ] ( ) [ ][ ] { } { } ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )            −−− − − −           −− −− −− = +×−×−= 321 412 143 234 3412 2143 1234 44 3333 BIBLBL BLBLBL BLBLBL BLBLBL BLBLBLBL BLBLBIBL BLBLBLBL T BLBLBLXBLBLXBL B L qqq qqq qqq qqq qqqq qqqq qqqq qqqIqqIqC  where: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) { } ( ) { } ( ) ( ) ( )          =      =                         =             = 3 2 1 :& 4 4 3 2 1 4 3 2 1 BL BL BL BL BL BL BL BL BL BL BL BL BL BL BL BL q q q q q q qor q q q q q q q q q   ( )                         −                  = 2 sin 2 sin 2 sin 2 cos 2 cos 2 cos4 ϕθψϕθψ BLq ( )                         +                  = 2 cos 2 sin 2 sin 2 sin 2 cos 2 cos1 ϕθψϕθψ BLq ( )                         −                  = 2 sin 2 cos 2 sin 2 cos 2 sin 2 cos2 ϕθψϕθψ BLq ( )                         +                  = 2 sin 2 sin 2 cos 2 cos 2 cos 2 sin3 ϕθψϕθψ BLq AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  70. 70. 73 SOLO Coordinate Systems (continue – 13( 5.Body Coordinates (B) (continue – 3) ψ θ φ Bx Lx Bz Ly Lz By Rotation Matrix from LLLN to B (Quaternions) (continue – 1) The quaternions are given by the following differential equations: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) BL L IL B IBBLBLBL B ILBL B IBBL B IL B IBBL B LBBLBL qqqqqqqqq ⋅−⋅=⋅⋅⋅−⋅=−⋅=⋅= ←←←←←←← ωωωωωωω 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     ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )                          +Ω−+Ω−+Ω− +Ω+Ω+Ω− +Ω+Ω−+Ω +Ω+Ω+Ω− − 4 3 2 1 0 0 0 0 2 1 BL BL BL BL zLzLyLyLxLxL zLzLxLxLyLyL yLyLxLxLzLzL xLxLyLyLzLzL q q q q ρρρ ρρρ ρρρ ρρρ ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )                          +Ω+−+Ω+−+Ω+− +Ω−+Ω−−+Ω+ +Ω−+Ω++Ω−− +Ω−+Ω−−+Ω+ = 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 ρρρ ρρρ ρρρ ρρρ or: AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  71. 71. 74 SOLO Coordinate Systems (continue – 14( 5.Body Coordinates (B) (continue – 4) ψ θ φ Bx Lx Bz Ly Lz By Vehicle Velocity Vehicle Velocity relative to Earth is divided in: WAE VVV  += ( )           = w v u V B A  ( ) ( )           =           = DownW EastW NorthW B L zW yW xW B W V V V C V V V HLongLatV B B B _ _ _ ,,  Vehicle Acceleration ( ) WWIB B W AAIB B A I VV td Vd RVV td Vd td Vd a      ×Ω+×++×Ω×Ω+×Ω+×+== ←← ωω ( ) ( ) W AELALB B A a RVV td Vd    + ×Ω×Ω+×Ω++×+= ←← 2ωω AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE Table of Content
  72. 72. 75 SOLO Coordinate Systems (continue – 15( 6.Wind Coordinates (W) The origin of the Wind coordinate system is located at the instantaneous center of gravity CG of the vehicle, with xW pointed in the direction of the vehicle velocity vector relative to air .AV  [ ] [ ]           − −−=           −          −=−= αα βαββα βαββα αα αα ββ ββ αβ cos0sin sinsincossincos cossinsincoscos cos0sin 010 sin0cos 100 0cossin 0sincos 23 W BC The Wind coordinate frame is defined by the following two angles: α - angle of attack β - sideslip angle AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  73. 73. 76 SOLO Coordinate Systems (continue – 16( 6.Wind Coordinates (W) (continue -1) Rotation Matrix from L (LLLN( to W is: χ - azimuth angle of the trajectory γ - pitch angle of the trajectory Rotation Matrix [ ] [ ] [ ] [ ] [ ] 32123 ψθφαβ −== B L W B W L CCC The Rotation Matrix from L (LLLN( to W can also be defined by the following Consecutive rotations: σ - bank angle of the trajectory [ ] [ ] [ ] [ ]           −+ +− − === γσχσχγσχσχγσ γσχσχγσχσχγσ γχγχγ χγσσ cccssscsscsc csccssssccss ssccc CC W L W L 321 * 1 We defined also the intermediate wind frame W* by: [ ] [ ]           − − == γχγχγ χχ γχγχγ χγ csscs cs ssccc CW L 032 * AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  74. 74. 77 SOLO Coordinate Systems (continue – 17( 6.Wind Coordinates (W) (continue -2) Angular Velocity of W* relative to LLLN is: Angular Velocities ( ) [ ]          − =                     − +           =           +           =           =← γχ γ γχ χγγ γγ γ χ γγω cos sin 0 0 cos0sin 010 sin0cos 0 0 0 0 0 0 2 * * * * *         W W W W LW R Q P Angular Velocity of W relative to LLLN is: ( ) [ ] [ ]                     − − =          −           − +           =                     +           +           =           =← χ γ σ γσσ γσσ γ γχ γ γχ σσ σσ σ χ γγσ σ ω           coscossin0 cossincos0 sin01 cos sin cossin0 sincos0 001 0 00 0 0 0 0 0 21 W W W W LW R Q P AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  75. 75. 78 SOLO Coordinate Systems (continue – 18( 6.Wind Coordinates (W) (continue -3) We have also: Angular Velocities (continue – 1) ( ) ( ) ( ) ( )           Ω Ω Ω =           Ω− Ω ==           Ω Ω Ω = ←← Down East North W L W L L IE W L zW yW xW W IE C Lat Lat CC *** * * * * sin 0 cos ωω  ( ) ( ) ( ) ( )           =               − −==           = • • • ←← Down East North W L W L L EL W L zW yW xW W EL C LatLong Lat LatLong CC ρ ρ ρ ω ρ ρ ρ ω *** * * * * sin cos  ( ) ( ) ( ) ( ) [ ] ( )* 1 sin 0 cos W IE W L L IE W L zW yW xW W IE Lat Lat CC ←←← =           Ω− Ω ==           Ω Ω Ω = ωσωω  ( ) ( ) ( ) ( ) [ ] ( )* 1 sin cos W IL W L L IL W L W IL LatLong Lat LatLong CC ← • • • ←← =                         +Ω− −       +Ω == ωσωω  AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  76. 76. 79 SOLO Coordinate Systems (continue – 19( 6.Wind Coordinates (W) (continue -4) The Angular Velocity from I to W is: Angular Velocities (continue – 2) ( ) ( ) ( ) ( )           Ω+ Ω+ Ω+ +           =+           =+=           = ←←←← DownDown EastEast NorthNorth W L W W W L IL W L W W W W IL W LW W W W W IW C R Q P C R Q P r q p ρ ρ ρ ωωωω  Using the angle of attack α and the sideslip angle β , we can write: BWBW yz    11 αβω −=← or: ( ) ( ) ( ) [ ]           −           =           −           =−= ←←← 0 0 0 0 3 αβ β ωωω    r q p C r q p W B W W W W IB W IW W BW but also: ( ) ( ) ( ) [ ]           −           =           −           =−= ←←← 0 0 0 0 3 αβ β ωωω    R Q P C R Q P W B W W W W LB W LW W BW AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  77. 77. 80 SOLO Coordinate Systems (continue – 20( 6.Wind Coordinates (W) (continue -5) We can write: Angular Velocities (continue – 3)           −           +                     − −−=           0 cos sin 0 0 cos0sin sinsincossincos cossinsincoscos βα βα βαα βαββα βαββα   r q p r q p W W W or: ( ) ( ) βαα βαβαβα βαβαβα    ++−= −−+−= +−+= cossin sinsincossincos cossinsincoscos rpr rqpq rqpp W W W This can be rewritten as: ( ) βαα β α tansincos cos rp q q W +−−= Wrrp +−= ααβ cossin ( ) ( ) ( )( ) ( ) β βαα ββββααβαβαα cos sinsincos tantansincossincossincossincos W WW qrp qrpqrpp ++ = +++=−++=  AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  78. 78. 81 SOLO Coordinate Systems (continue – 21( 6.Wind Coordinates (W) (continue -6) We have also: Angular Velocities (continue – 4) ( ) βαα β α tansincos cos RP Q Q W +−−= WRRP +−= ααβ cossin ( ) β βαα cos sinsincos W W QRP P ++ = AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  79. 79. 82 SOLO Coordinate Systems (continue – 22( 6.Wind Coordinates (W) (continue -7) The vehicle velocity was decomposed in: Vehicle Velocity WAE VVV  += ( )           = 0 0 V V W A  - vehicle velocity relative to atmosphere ( ) ( )           =           = DownW EastW NorthW W L zW yW xW W W V V V C V V V HLongLatV W W W _ _ _ ,,  - wind velocity at velocity position also ( ) [ ] ( ) [ ]           =           −=−= 0 0 0 011 * VV VV W A W A σσ  ( ) ( )           =           = DownW EastW NorthW W L zW yW xW W W V V V C V V V HLongLatV W W W _ _ _ * * * * * ,,  AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  80. 80. 83 SOLO Coordinate Systems (continue – 23( 6.Wind Coordinates (W) (continue -8) The vehicle acceleration in W* coordinates is Vehicle Acceleration ( ) ( ) ( ) WAELALW W A WWIW W W AAIW W A I C aRVV td Vd VV td Vd RVV td Vd td Vd a        +×Ω×Ω+×Ω++×+= ×Ω+×++×Ω×Ω+×Ω+×+== ←← ←← 2* * * * * * ωω ωω from which ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )******* * * * 2 W W W A WW EL WW A W LW W W A aVAV td Vd   −×Ω+−=×+         ←← ωω where ( )RaA  ×Ω×Ω−=: AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  81. 81. 84 SOLO Coordinate Systems (continue – 24( 6.Wind Coordinates (W) (continue -9) Vehicle Acceleration (continue – 1) ( ) ( ) ( ) ( ) ( ) ( )           −                     Ω+Ω+− Ω+−Ω+ Ω+Ω+− −           =                     − − − +           ** * * **** **** **** * * * ** ** ** 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 ρρ ρρ ρρ where ( ) ( ) ( ) ( )HR Lat Lat C a a a A A A A W L zW yW xW zW yW xW W +Ω           −           =           = 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 −Ω++=− −Ω+−= −= ρ ρ  AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  82. 82. 85 SOLO Coordinate Systems (continue – 25( 6.Wind Coordinates (W) (continue -10) Vehicle Acceleration (continue – 2) Using ( )          − =           =← γχ γ γχ ω cos sin * * * * *     W W W W LW R Q P we have ** xWWxW aAV −= ( ) γρχ cos/2 ** **       Ω+− − = zWzW yWWyW V aA  ( )** ** 2 yWyW zWWzW V aA Ω+− − −= ργ AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE Table of Content
  83. 83. 86 SOLO Aerodynamic Forces ( )[ ]∫∫ +−= ∞ WS A dstfnppF  11 ntonormalplanonVofprojectiont dstonormaln ˆˆ ˆ  − − ( ) airflowingthebyweatedsurfaceVehicleS SsurfacetheonmNstressforcefrictionf Ssurfacetheondifferencepressurepp W W W − − −−∞ )/( 2 AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE 7. Forces Acting on the Vehicle
  84. 84. 87 SOLO 7. Forces Acting on the Vehicle (continue – 1) Aerodynamic Forces (continue – 1) ( )           − − − = L C D F W A  ForceLiftL ForceSideC ForceDragD − − − L C D CSVL CSVC CSVD 2 2 2 2 1 2 1 2 1 ρ ρ ρ = = = ( ) ( ) ( ) tCoefficienLiftRMC tCoefficienSideRMC tCoefficienDragRMC eL eC eD − − − βα βα βα ,,, ,,, ,,, ityvisdynamic lengthsticcharacteril soundofspeedHa numberynoldslVR numberMachaVM e cos )( Re/ / − − − −= −= µ µρ AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  85. 85. 88 SOLO 7. Forces Acting on the Vehicle (continue – 2) Aerodynamic Forces (continue -2) ∫∫       ⋅+⋅−= ∫∫       ⋅+⋅−= ∫∫       ⋅+⋅−= ∧∧ ∧∧ ∧∧ W W W S fpL S fpC S fpD dswztCwznC S C dswytCwynC S C dswxtCwxnC S C 1ˆ1ˆ 1 1ˆ1ˆ 1 1ˆ1ˆ 1 Wf Wp Ssurfacetheontcoefficienfriction V f C Ssurfacetheontcoefficienpressure V pp C −= − − = ∞ 2/ 2/ 2 2 ρ ρ ntonormalplanonVofprojectiont dstonormaln ˆˆ ˆ  − − AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  86. 86. 89 ( ) ( ) ( )         MomentFriction S C Momentessure S CCA WW dstRRfdsnRRppM ∫∫∫∫∑ ×−+×−−= ∞ 11 Pr / Aerodynamic Moments Relative to C can be divided in Pressure Moments and Friction Moments. ( )       FrictionSkinor FrictionViscous S essureNormal S A WW dstfdsnppF ∫∫∫∫∑ +−= ∞ 11 Pr Aerodynamic Forces can be divided in Pressure Forces and Friction Forces. AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE AERODYNAMIC FORCES AND MOMENTS.
  87. 87. 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 AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE Table of Content CTM , 
  88. 88. 91 SOLO 7. Forces Acting on the Vehicle (continue – 3) Thrust ( ) ( )                     − −−== B B B z y x BW B W T T T TCT αα βαββα βαββα 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 σσ σσσ  AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  89. 89. 92 SOLO 7. Forces Acting on the Vehicle (continue – 4) Gravitation Acceleration ( ) ( )                         −           −           − == zg yg xg gg 100 0 0 0 010 0 0 0 001 χχ χχ γγ γγ σσ σσ cs sc cs sc cs scC EW E W  ( ) gg          − = γσ γσ γ cc cs s W  2sec/174.322sec/81.9 0 2 0 0 0 gg ftmg HR R == + =           AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE The derivation of Gravitation Acceleration assumes an Ellipsoidal Symmetrical Earth. The Gravitational Potential U (R, ( is given byϕ ( ) ( ) ( ) ( )φ φ µ φ , sin1, 2 RUg P R a J R RU E E n n n n ∇=               −⋅−= ∑ ∞ =  μ – The Earth Gravitational Constant a – Mean Equatorial Radius of the Earth R=[xE 2 +yE 2 +zE 2 ]]/2 is the magnitude of the Geocentric Position Vector – Geocentric Latitude (sin =zϕ ϕ E/R( Jn – Coefficients of Zonal Harmonics of the Earth Potential Function P (sin ( – Associated Legendre Polynomialsϕ
  90. 90. 93 SOLO 7. Forces Acting on the Vehicle (continue – 5) Gravitation Acceleration AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE Retaining only the first three terms of the Gravitational Potential U (R, ( we obtain:ϕ R z R z R z R a J R z R a J R g R y R z R z R a J R z R a J R g R x R z R z R a J R z R a J R g EEEE z EEEE y EEEE x E E E ⋅                 +⋅−⋅      ⋅−        −⋅      ⋅−⋅−= ⋅                 +⋅−⋅      ⋅−        −⋅      ⋅−⋅−= ⋅                 +⋅−⋅      ⋅−        −⋅      ⋅−⋅−= 34263 8 5 15 2 3 1 34263 8 5 15 2 3 1 34263 8 5 15 2 3 1 2 2 4 44 42 22 22 2 2 4 44 42 22 22 2 2 4 44 42 22 22 µ µ µ φ φλ φλ sin cossin coscos = ⋅= ⋅= R z R y R x E E E ( ) 2/1222 EEE zyxR ++=
  91. 91. 94 SOLO 23. Local Level Local North (LLLN) Computations for an Ellipsoidal Earth Model ( ) ( ) ( ) ( ) ( )2 22 10 2 0 2 0 2 0 5 2 1 2 0 6 0 sin sin1 sin321 sin1 sec/10292116557.7 sec/051646.0 sec/780333.9 26.298/.1 10378135.6 Ae e p m e HR RLatgg g LateRR LateeRR LateRR rad mg mg e mR + + = += +−= −= ⋅=Ω = = = ⋅= − Lat HR V HR V HR V Ap East Down Am North East Ap East North tan + −= + −= + = ρ ρ ρ Lat Lat Down East North sin 0 cos Ω−=Ω =Ω Ω=Ω DownDownDown EastEast NorthNorthNorth Ω+= = Ω+= ρφ ρφ ρφ East North Lat Lat Long ρ ρ −= = • • cos ( ) ( ) ∫ ∫ • • += += t t dtLatLattLat dtLongLongtLong 0 0 0 0 AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE SIMULATION EQUATIONS
  92. 92. 95 SOLO AIR VEHICLE IN ELLIPTICAL EARTH ATMOSPHERE SIMULATION EQUATIONS Table of Content
  93. 93. 96 SOLO 7. Forces Acting on the Vehicle (continue – 6) Force Equations Air Vehicle Acceleration ( ) ( ) WAELALW W A I C aRVV td Vd td Vd a    +×Ω×Ω+×Ω++×+== ←← 2ωω ( ) ( ) ( ) WAELALW W A A aRVV td Vd amTF m    +×Ω×Ω+×Ω++×+==++ ←← 2g 1 ωω ( )Rg   ×Ω×Ω−= g:where                   + −− + −− − − =           γσ α γσ βα γ βα ccg m LT csg m CT sg m DT A A A zW yW xW sin sincos coscos          − +                   −− −− −           −=           γ γ α βα βα σσ σσ cg sg m LT m CT m DT A A A zW yW xW 0 sin sincos coscos cossin0 sincos0 001 * * * AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE Table of Content
  94. 94. 97 SOLO ( ) ( ) ( ) ( )LB L BB A B CG gCT m F m a  ++= ∑ 11 ( ) [ ] [ ] ( ) ( ) [ ][ ] ( ) { ( ) ( ) [ ] ( ) }B BrCrrotor B IB B BrCrrotor B IBC B IB B IBCCTCAC B IB II IIMMI ←←← ←←← − ← ⋅×−⋅− ×−−+= ∑ ωωω ωωωω    ,, ,,,, 1 ( ) ( ) ( )B CG TB L L CG aCa  = ( )B IB←ω  ( ) ( ) B L L IL B IBB LB L qqq ←← −= ωω 2 1 2 1 s 1 CT CA M M , ,   ∑ [ ]{ } [ ]{ } TB L IqIqC ρρρρ  +×−×−= 3434 ( )B IB←ω ( )B CGa  ( )L CGa  ( ) ( )B B A T F   ∑ B LC B LC s 1 BLqBLq B LC s 1 ( ) ( ) ( )[ ]( ) ( ) ( ) ( ) ( )L E LL EL LL CG L E VRaV  ×Ω+−×Ω×Ω−= ← 2ω s 1 ( )L EV ( )L EV  ( )L CGa  B LC ( )L MR  ( )L EV  ( ) ( )L M B L B M VCV  = δξωξςξ Mee  +−−= 2 2 δM  s 1 s 1ξ  ξ  ξ  ( )L EV  [ ] [ ] 23 αβ −= W BC α β W BC MV WEM VVV  −= ( )L MV  ( )L WV  ( )B IB←ω  ( ) ( )B Brotor B Brotor ←← ωω  , Missile Kinematics Model 1 in Vector Notation (Spherical Earth) AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  95. 95. 98 SOLO Missile Kinematics Model 1 in Matrix Notation (Spherical Earth) AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  96. 96. 99 SOLO Missile Kinematics Model 2 in Vector Notation (Spherical Earth) AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  97. 97. 100 SOLO Missile Kinematics Model 2 in Matrix Notation (Spherical Earth) AIR VEHICLE IN SPHERICAL EARTH ATMOSPHERE
  98. 98. References SOLO 101 PHAK Chapter 1 - 17 http://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 Avionics Subsystem Integration”, John Wiley & Sons, Ltd., 3th Ed., 2008 Fighter Aircraft Avionics Ian Moir, Allan Seabridge, “Military Avionics Systems”, John Wiley & Sons, LTD., 2006
  99. 99. References (continue – 1) SOLO 102 Fighter Aircraft Avionics 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”
  100. 100. References (continue – 2) SOLO 103 Fighter Aircraft Avionics S. Hermelin, “Spherical Trigonometry” S. Hermelin, “Modern Aircraft Cutaway”
  101. 101. 104 SOLO Technion Israeli Institute of Technology 1964 – 1968 BSc EE 1968 – 1971 MSc EE Israeli Air Force 1970 – 1974 RAFAEL Israeli Armament Development Authority 1974 – Stanford University 1983 – 1986 PhD AA
  102. 102. 105 SOUND WAVES SOLO 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 V M M =      = − & 1 sin 1 µ
  103. 103. 106 SOUND WAVESSOLO Sound Wave Definition: ∆ p p p p p1 2 1 1 1= − << ρ ρ ρ2 1 2 1 2 1 = + = + = + ∆ ∆ ∆ p p p h h h For weak shocks u p 1 2 = ∆ ∆ρ 1 1 11 1 1 1 1 1 2 1 2 1 1 uuuuuu ρ ρ ρ ρρρ ρ ρ ρ ∆ −≅ ∆ + = ∆+ ==(C.M.) ( ) ( ) ppuuupuupu ∆++      ∆ −=+=+ 11 1 11122111 2 11 ρ ρ ρρρ(C.L.M.) Since the changes within the sound wave are small, the flow gradients are small. Therefore the dissipative effects of friction and thermal conduction are negligible and since no heat is added the sound wave is isotropic. Since au =1 s p a       ∂ ∂ = ρ 2 valid for all gases
  104. 104. 107 SPEED OF SOUND AND MACH NUMBERSOLO Speed of Sound is given by 0=       ∂ ∂ = ds p a ρ RT p C C T dT R C p T dT R C d dp d R T dT Cds p dp R T dT Cds v p v p ds v p γ ρ ρ ρ ρ ρ ===      ⇒        =−= =−= =00 0 but for an ideal, calorically perfect gas ρ γγ ρ p RTa TChPerfectyCaloricall RTpIdeal p ==       = = The Mach Number is defined as RT u a u M γ == ∆ 1 2 1 1 111 −−       =      =      = γ γ γ γ γ ρ ρ a a T T p p The Isentropic Chain: a ad T Tdd p pd sd 1 2 1 0 − = − ==→= γ γ γ γ ρ ρ γ
  105. 105. 108 NORMAL SHOCK WAVESSOLO Normal Shock Wave ( Adiabatic), Perfect Gas   G Q= =0 0, Mach Number Relations (1) ( ) ( ) ( )   ( ) 12 2 2 2 1 2 1 2 2 22 2 2 1 22 1 2 2 2 2 22 1 1 2 1 12 22 2 11 1 2 2 221 2 11 2211 2 1 2 1 2 1 2 1 * 12 1 2 1 12 1 1 4.. ... .. uu u a u a uaa uaa au h a u h a EC uu u p u p pupuMLC uuMC p a −=−                  − − + = − − + = → − + =+ − =+ − →−=−→    +=+ = ∗ ∗ = γγ γγ γγ γ γ γγ ρρρρ ρρ ρ γ Field Equations: 122 2 2 1 1 2 2 1 2 1 2 1 2 1 uuu u a u u a −= − + + − − − + ∗∗ γ γ γ γ γ γ γ γ u u a1 2 2 = ∗ u a u a M M1 2 1 21 1∗ ∗ ∗ ∗ = → = Prandtl’s Relation u p ρ T e u p ρ T e τ 11 q 1 1 1 1 1 2 2 2 2 2 1 2 ( ) γ γ γ γ γ γ γ γ γ γ 2 1 2 1 1 2 1 2 1 2 1 21 2 1212 2 21 12 + = − −= + →−=− − + −+ ∗ ∗ uu a uuuua uu uu Ludwig Prandtl (1875-1953)
  106. 106. 109 NORMAL SHOCK WAVESSOLO Normal Shock Wave ( Adiabatic), Perfect Gas   G Q= =0 0, Mach Number Relations (2) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )[ ] ( )( ) ( ) M M M M M M M M M 2 2 2 2 1 1 2 1 2 1 2 1 2 1 2 2 1 1 2 1 1 2 1 1 1 2 1 2 1 2 1 1 1 1 1 1 2 = + − − = + − − = + + − + − − = − + + / + − / / + − / + − − ∗ = ∗ ∗ ∗ γ γ γ γ γ γ γ γ γ γ γ γ γ γ or ( ) M M M M M H H A A 2 1 2 1 2 1 2 1 21 2 1 2 1 1 2 1 2 2 1 1 1 2 1 2 1 1 = + − − − = + + − + + − = = γ γ γ γ γ γ γ ( ) ( ) ρ ρ γ γ 2 1 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 1 2 = = = = = + − + = ∗ ∗ A A u u u u u u a M M M u p ρ T e u p ρ T e τ 11 q 1 1 1 1 1 2 2 2 2 2 1 2
  107. 107. 110 NORMAL SHOCK WAVESSOLO Normal Shock Wave ( Adiabatic), Perfect Gas   G Q= =0 0, Mach Number Relations (3) ( ) ( ) ( ) ( ) ( ) p p u p u u u a M M M M M M M 2 1 1 2 1 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 1 1 1 1 1 2 1 1 1 1 2 1 = + −       = + −       = + − − + +       = + / + − / − − + ρ γ ρ ρ γ γ γ γ γ γ γ or (C.L.M.) ( ) p p M2 1 1 2 1 2 1 1= + + − γ γ ( ) ( ) ( ) h h T T p p M M M a a h C T p RTp 2 1 2 1 2 1 1 2 1 2 1 2 1 2 2 1 1 2 1 1 1 2 1 = = = + + −       − + + = = = ρ ρ ρ γ γ γ γ ( ) ( ) ( ) s s R T T p p M M M 2 1 2 1 1 2 1 1 1 2 1 1 1 2 1 2 1 1 2 1 1 1 2 1 − =                       = + + −       − + +                 − − − − ln ln γ γ γ γ γ γ γ γ γ γ ( ) ( ) ( ) ( ) s s R M M M 2 1 1 1 2 1 2 3 2 2 1 2 41 2 2 3 1 1 2 1 1 − ≈ + − − + − + − << γ γ γ γ K Shapiro p.125 u p ρ T e u p ρ T e τ 11 q 1 1 1 1 1 2 2 2 2 2 1 2
  108. 108. 111 STEADY QUASI ONE-DIMENSIONAL FLOWSOLO STAGNATION CONDITIONS (C.E.) constuhuh =+=+ 2 22 2 11 2 1 2 1 The stagnation condition 0 is attained by reaching u = 0 2 / 21202 020 2 1 1 1 2 1 2 1 22 1 2 M TR u Tc u T T c u TTuhh TRa auM Rc pp Tch p p − += − +=+=→+=→+= = = − = = γ γ γ γγ γ Using the Isentropic Chain relation, we obtain: 2 1 0102000 2 1 1 M p p a a h h T T − +=      =      =      == − − γ ρ ρ γ γ γ Steady , Adiabatic + Inviscid = Reversible, , ( ) q Q= =0 0, ( )~ ~ τ = 0 ( )   G = 0 ∂ ∂ t =      0
  109. 109. SOLO 112 Civilian Aircraft Avionics Flight Cockpit CIRRUS PERSPECTIVE Cirrus Perspective Avionics Demo, Youtube Cirrus SR22 Tampa Landing in Heavy Rain
  110. 110. SOLO 113 Flight Displays CIRRUS PERSPECTIVE Civilian Aircraft Avionics
  111. 111. SOLO 114 Flight Displays CIRRUS PERSPECTIVE Civilian Aircraft Avionics
  112. 112. SOLO 115 Flight Displays CIRRUS PERSPECTIVE Civilian Aircraft Avionics
  113. 113. SOLO 116 Flight Displays CIRRUS PERSPECTIVE Civilian Aircraft Avionics
  114. 114. SOLO 117 Flight Displays CIRRUS PERSPECTIVE Civilian Aircraft Avionics
  115. 115. SOLO 118 Flight Displays CIRRUS PERSPECTIVE Civilian Aircraft Avionics
  116. 116. SOLO 119 Flight Displays CIRRUS PERSPECTIVE Civilian Aircraft Avionics
  117. 117. SOLO 120 Flight Displays CIRRUS PERSPECTIVE Civilian Aircraft Avionics
  118. 118. 121

×