Compared Air Combat Performances g-21 versus F-4
Contents
1. O Extracted Load Factor Smoothed Load Factor Computed load Factor O Extracted Load Factor Smoothed Load Factor Computed load Factor 5 00 4 00 3 00 a i E E 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 1 30 1 00 E H 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 1 30 1 40 1 50 1 60 1 70 1 80 1 90 2 00 2 10 O Extracted Turn Rate Smoothed Turn Rate Computed Turn Rate 12 00 O Extracted Turn Rate Smoothed Turn Rate Computed Turn Rate 8 00 11 00 7 00 10 00 6 00 9 00 gt 8 00 5 00 E 7 00 4 00 4 N 6 00 f 3 00 El 5 00 i Wk 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 1 30 H 2 00 At 20 000ft 1 00 i O Extracted Load Factor Smoothed Load Factor Computed load Factor 5 00 i LT aa LT h _ a CA 0 00 RE A E _ 0 40 0 50 0 60 0 70 0 80 0 90 12. O Extracted Sample Ng Computed Ng Sustained Turn Rate Sustained Turn Rate 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 1 30 1 40 O Extracted Sample Turn rate Computed Turn Rate o 1 50 1 60 Extracted Sample Turn rate 0 60 0 70 0 80 0 90 1 00 1 10 1 20 1 30 1 40 1 50 1 60 1 70 1 80 1 90 2 00 Computed Turn Rate Mach Sample Sample Computed Computed Error Error Ng Turn rate Ng Turn Rate Ng T Mach Sample Sample Computed Computed Error Error Ng pata Ng Tum Rate Ng 1 0 60 150 345 1 50 3 46 0 11 0 20 0 50 1 75 5 11 1 76 5 14 0 46 0 68 0 70 205 474 2 05 4 74 0 05 0 07 0 60 2 35 6 30 2 36 6 33 0 37 0 45 0 80 2 65 5 69 2 65 5 69 0 06 0 07 0 70 3 00 7 19 3 00 7 18 0 14 0 16 0 90 3 10 6 04 3 09 6 02 0 29 0 32 0 80 3 65 7 80 3 66 7 82 0 14 0 15 0 95 3 10 5 73 3 08 5 69 0 52 0 59 0 90 4 20 8 06 4 21 8 08 0 28 0 29 1 00 2 95 5 15 2 94 5 12 0 43 0 49 0 95 4 15 7 54 4 18 7 59 0 60 0 64 1 05 3 02 5 03 3 02 5 03 0 07 0 08 1 00 4 00 6 89 3 99 6 87 0 20 0 21 1 10 3 07 4 89 3 08 4 92 0 45
3. Sustained Load Factor at Oft Here the sustained load factor and turn rate are computed from thrust values deduced form SL acceleration path 7 Sustained Load Factor Extracted values read from figures then smoothed id compared to computed Sustained Load Factor 4 lt A O Extracted Sample Ng Computed Ng Sustained Turn Rate 12 00 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 10 00 O Extracted Sample Ng Computed Ng 8 00 Sustained Turn Rate 16 00 6 00 14 00 m 4 00 12 00 ERE toe TE E 10 00 2 00 8 00 0 00 800 El 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 130 4 00 b O Extracted Sample Turn rate Computed Turn Rate 2 00 0 00 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 Mach Sample Sample Computed Computed Error Error O Extracted Sample Turn rate Computed Turn Rate Ng Turn rate Ng Turn Rate Ng T 0 50 2 60 8 22 2 59 8 19 0 27 0 32 0 60 3 40 9 27 3 41 9 31 0 39 0 43 ae 0 70 410 9 72 4 11
4. 0 50 1051 410 673 412 678 0 58 0 62 1 15 3 10 4 73 3 08 4 70 0 52 0 59 1 10 4 15 6 51 4 15 6 51 0 10 0 11 1 20 3 10 453 3 08 4 51 0 52 0 59 1 15 412 6 18 4 09 6 14 0 62 0 66 1 30 3 10 4 18 3 11 4 20 0 42 0 47 1 20 4 00 5 74 3 96 5 67 1 12 1 19 1 40 310 3 89 3 10 3 88 0 05 0 06 1 30 3 20 4 16 3 14 4 08 1 80 2 00 1 50 3 00 3 50 3 00 3 50 0 11 0 12 1 40 2 00 2 20 2 03 2 24 1 45 1 93 160 230 240 2 38 2 50 3 51 4 31 1 70 1 70 1 50 1 66 1 45 2 19 3 36 1 80 1 30 0 86 1 30 0 85 0 26 0 64 Sustained load factor at 30 000ft Here the thrust values are computed to fit the sampled sustained load factor and turn rate E Mirage III CJ Early version up to 1971 74 The Mirage IlICJ early version keeps all data from Mirage lll C except its AoA limitations that are no more related to ADHEMAR system but set to a value in AoA sector of 42 corresponding to 25 2 true AoA degrees Friday February 15 2013 rev 2 Page 13 Mirage III Flight Model Identification Late version from 1971 74 The late version of Mirage lll CJ is describes airframes retrofitted with ATAR 9C3 engines The late Mirage 111CJ keeps all data from Mirage lll E except its weight airframe fuel and loads that come from Mirage lll C and AoA limitations that are no more related to ADHEMAR system but set to a value in AoA secto
5. 9 75 0 22 0 24 ample Mach Sample STP Computed Computed Error Error 0 80 4 90 10 26 4 91 10 30 0 30 0 32 Ng rate I pee Ng T 0 90 5 70 10 67 5 70 10 67 0 03 0 03 0 50 3 80 12 15 4 01 12 82 5 44 5 46 035 0 S80M 1029 1 383 Rl 0 60 460 12 40 4 81 1296 4 61 4 47 BOO SSO es eet A e ie 0 70 5 30 12 32 5 44 12 62 2 68 2 42 ta 0 A E 0 80 640 13 10 6 38 13 01 0 32 0 67 ee ee O aa O o e E 0 90 7 50 13 69 7 53 13 70 0 39 0 05 pee O O MN Oe Ee 0 95 7 50 12 97 7 45 12 83 0 68 1 04 T20 280 12495 242 1 800 14044 420 100 6 50 10 65 6 39 10 43 1 63 2 01 TOE SA 07 aa 313 an Sustained load factor at 20 000ft Here the thrust values are computed to fit the sampled 1 10 3 50 5 05 4 12 6 00 17 61 18 64 sustained load factor and turn rate Sustained Load factor at 10 000ft Here the thrust values are computed to fit the sampled sustained load factor and turn rate Friday February 15 2013 rev 2 Page 12 Mirage III Flight Model Identification Sustained Load Factor 3 5 Sustained Load Factor 2 5 15 O Extracted Sample Ng Computed Ng 1 Y a 1 50 1 60 0 60 0 70 0 80 0 90 1 00 1 10 1 20 1 30 1 40 1 50 1 60 1 70 1 80 1 90 2 00
6. AoA and over 1 10 set to 16 35 AoA These limitations will be used to compute flight envelope of both Mirage III C and III E used in the French Air Force AdA According to discussion between Israel Air Force pilots and Swiss ones it appears that IAF has experienced higher incidence values than the one recommended by the manufacturer The limit Sector Incidence has been moved from Amber extinction up to 42 corresponding to a true incidence limit moved from 15 19 to 25 2 deg This is very similar with what happen with Mig 21 where index incidence limit recommended as 28 can be moved up to 55 Under these assumptions Mirage Ill CJ incidence limitations to be considered have to be 25 2 deg of true incidence or 42 sector incidence This is also assumed to be the case for IAF Nesher There are other factor that limit the incidence of a Mirage lll first one is the elevon efficiency in low dynamic pressure that prevent a c to reach its maximum incidence at very high flight level the second being related to actuator saturation at high dynamic pressure that prevent the a c to reach high incidence at high indicated speed especially in supersonic and low altitude domain Because these limitations are not easy to model and have few impact on the MO 2 M1 0 x SL FL350 domain that is my main focus they will not be taken into account to compute A C performances C Mirage III E with ATAR 9C Max A B Thrust and Drag coefficie
7. Mirage III Flight Model Identification LICENSE This document has been created by J M LANGERON TOPOLO http topolo free fr All the values used to model the aircraft behavior have been computed by him like all performance charts presented here based on data provided by the people mentioned in the CREDITS section If you want to use these data or part of it please contact the author by personal message to TOPOLO on check six forum http www checksix forums com CREDITS want to thanks particularly and Tom COOPER ACIG org for his huge knowledge on military aerospace in general the history of these aircraft in particular and the fact that he build the working group A Purpose and scope The aim of this document is to identify the Flight Model that is Lift coefficient Drag Coefficient et Thrust laws for some versions of the Mirage lll and for some specific configurations The versions that are considered are the French air force Arm e de l Air aka AdA Mirage IIIC with ATAR 9B engine the AdA Mirage INE with ATAR 9C engine the IAF Israel Mirage IIICJ early version or late retrofitted with ATAR 9C and the IAF Israel Nesher The IAF Mirage IIIC engine retrofit has been performed depending on sources after 1974 ACIG or after 1971 Le Mirage IIICJ au combat The decision to include the late retrofitted version is lead by the fact that this is the version that had to face late Mig 21 M MF or bis
8. Ps E 5 p 2 Cxo Ma k Ma C S V Meaning that for all Mach value we have one equation with 3 values to find Thrust Cxo and k Even if we assume that Cxo and k are common to a large range of Mach number from O to 0 7 we will still have more unknown values 2 than equations In order to get the missing conditions we will analyze the sustained load factor at sea level described in Mirage lllE at page PL A1 11 for a gross weight of 8 175kg 18 046 lbs The sustained load factor extracted from the diagram can be smoothed and sampled through the following figure O Extracted Load Factor Smoothed Load Factor 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 Corresponding to the following values Mach Smoothed Load Factor 0 40 3 19 0 50 4 18 0 60 5 18 0 70 6 10 0 80 6 97 0 90 7 26 1 00 5 90 We can compute sustained turn rate from load factor and get the following figure Friday February 15 2013 rev 2 Page 5 Mirage III Flight Model Identification O Extracted Turn Rate Smoothed Turn Rate Last we have to balance Thrust curve and null lift drag for 16 00 Mach number over 0 8 up to 1 10 15 00 At the end of this iterative process we have frozen 14 00 13 00 The null lift Drag coefficient value along Mach from O 12 00 to 1 10 Cyof Mach 11 00 Zero lift Cx 0 0400
9. when original Mirage lIIC faced Mig 21F or F 13 and this flight model identification is the basis to build a comparison between Mirage lll and Mig 21M MF and bis the only I have reliable performance data The Nesher is assumed to be a locally assembled Mirage 5 with a definition equivalent to the Mirage 5F operated by the French AdA the Mirage 5F have been built as Mirage 5J to be delivered to IAF but due to embargo has been retrofitted to a configuration closer to AdA standard and renamed 5F The engine if the Nesher is also assumed to be an ATAR 9C3 or C5 similar to the one fitted in Mirage INE The configurations to be studied are all representative of close air combat and are the following A Mirage IIIC with ATAR 9B operated by AdA French Air Force by the end of the 60 s with 2 short range A A missiles AIM 9B with pylons and launchers 2 DEFA 30mm guns with their rounds no rocket but the rear fuel tank that take its place and half of the internal fuel A Mirage IIICJ retrofitted with an ATAR 9C when operated by IAF around 1974 2 short range A A missiles AIM 9B because Shafrir Mk 2 data are not known with pylons and launchers 2 DEFA 30mm guns with their rounds no rocket but the rear fuel tank that take its place and half of the internal fuel A Mirage NIE with ATAR 9C operated by AdA French Air Force by the end of the 60 s with 2 short range A A missiles R 550 Magic 1 with pylons and launchers
10. Nesher Mirage 5F Mirage 5 definition is based on late Mirage IIIE SN 546 that implies the two 125 L leading edge tanks are installed The Chassis canon guns is not removable so no front fuselage tank 325 L but the rear fuselage tank 545 L is installed as the SEPR rocket bay can t be The electronic bay behind the pilot seat is replaced in the Mirage 5 by a Top fuselage 465 fuel tank electronic devices are fewer and moved to the nose that does not include the radar any more Fuel density of 0 8kg l is assumed Wings with leading edge 2x670L 1 340 Fuselage main 2x515L 1 030 Top Fuselage 465 Rear Fuselage 545 TOTAL 3 380 L 2 704 kg or 5 969 lbs Load out Weight Same for all Nesher Mirage 5F and Mirage IIIC versions and described in Mirage lIIE at page PL 11 3 Sidewinder AIM 9B 80kg Pylon launcher 30kg TOTAL 2 x 110kg 220kg 486lbs For the AdA Mirage IIIE R 5550 Magic l 89 kg Launcher type 40 39 kg CES3 Pylon Adpator ADP4 36 kg TOTAL 2 x 164kg 328kg 724lbs Gross Weight Mirage III C amp CJ In a configuration with 2xAIM 9 GW can vary depending on internal fuel between 8 785 kg 19 393 lbs at take off 100 of internal fuel and 6 721 kg 14 837 lbs with no fuel So Combat configuration 50 internal fuel gross weight is 7 753 kg 17 115 lbs Mirage III E In a configuration with 2xR 550 GW can vary depending on internal fuel
11. O Psft s sampled Providing for each Mach value the corresponding Ps value at a given gross weight summarized in this table Ps ft s Est Mach sampled Weight 0 30 175 19 961 0 40 238 19 916 0 50 310 19 870 0 60 392 19 800 0 70 500 19 763 0 80 575 19 702 0 90 510 19 593 1 00 320 19 532 1 10 0 19 168 It is now possible for a given mach number to evaluate the corresponding thrust and drag giving the expected Ps value at the related weight From the simplified force equation M mass in kg S reference surface in m Thrust force in N p air volumic mass in kg m 1 M g 5 PleSV f 2 i M i t Thrust pC SV We can express the relation between Drag thrust and Ps in m s V 1 f 3 Ps Mg Thrust 5 0CxSV The drag force cannot be supposed exactly deduced form the minimum drag coefficient null lift drag as a small amount of lift is required even for such a 1G acceleration fly path The lift coefficient will be directly deduced from the gross weight and speed in f 2 lift due to thrust upward orientation with AoA will be neglected so we will use a simplified Drag coefficient formulation f 4 C Ma AoA Cy 9 Ma k Ma C Ma AoA 2 With k where A is the aspect ratio here 1 94 and e the wing efficiency between 0 and 1 So we reach the following equation system to be solved _ 2M g f 6 M g 1 Pe Th Ma
12. 000 968 08 6 653E 05 295 07 90 000 968 08 5 15E 05 295 07 95 000 968 08 4 011E 05 295 07 100 000 968 08 3 138E 05 295 07 Corrected Air Speed CAS CAS Mach tt 0 00 0 50 1 00 1 25 1 50 2 00 3 00 0 0 330 660 825 1000 1325 1975 5 000 0 305 610 760 920 1225 1835 10 000 0 275 555 700 840 1125 1695 15 000 0 250 520 640 775 1025 1525 20 000 0 230 475 585 710 950 1430 25 000 0 205 430 525 640 865 1315 30 000 0 185 390 475 585 790 1200 35 000 0 165 350 435 525 720 1110 40 000 0 145 315 400 475 650 1000 45 000 0 130 280 360 440 590 890 50 000 0 115 250 325 390 535 825 55 000 0 105 220 285 350 475 725 60 000 0 93 195 255 320 425 635 65 000 0 83 174 227 285 386 565 70 000 0 75 157 205 257 342 510 75 000 0 66 139 182 229 304 454 80 000 0 60 126 165 207 274 410 85 000 0 54 114 149 186 248 370 90 000 0 48 101 133 166 221 330 95 000 0 42 89 116 146 194 290 100 000 0 40 83 108 136 181 270 Friday February 15 2013 rev 2 Page 15 Mirage III Flight Model Identification H Bibliography ROYAL AUSTRALIAN AIR FORCE FLIGHT MANUAL MIRAGE IIIO AND IIID AAP 7213 003 1 1 June 1978 from www flight manuals on cd com LTD MANUEL D UTILISATION AVION MIRAGE III E PLANCHES Edition Avril 1965 Computed Performance charts NATOPS_FLIGHT_MANUAL Mirage I11CJ Computed Performance charts NATOPS_FLIGHT_MANUAL Mirage 111CJ Computed Performance charts NATOPS_FLIGHT_MANUAL Mirage I11E Com
13. 10 00 0 0350 9 00 8 00 0 0300 7 00 0 0250 6 00 0 0200 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 0 0150 EEEE 0 ee E E HH 0 0100 22222227 For each Mach number we get the following equations 0 0050 mappa nn nn gt 0 0000 0 00 0 10 0 20 0 30 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 C a The relation between Lift and Drag coefficient 4 7 i p z V Mach number in 0 00 0 85 Th Mach zO Co Mach k C3 S V f 9 C Cro 0 29 C 0 6 Max 0 C 0 4 Mach number in 0 90 1 10 Focus on Mach number 0 6 and 0 7 with Sustained load f 10 Cx Cro 0 27 C 0 6 Max 0 C 0 4 factor and Extra Specific Power give 4 equations and allow computation of the 4 unknown values The Thrust Maximum A B values along Mach number at sea level Cx0 0 02 Seal level Full A B Thrust k 0 29 mo Thrust M 0 6 16 000 lbs Thrust M 0 7 18 500 lbs 20000 15000 Then we include all mach value equations Ps and Ng to determine Thrust values and improve the Drag Coefficient ie law for higher lift Thrust lbs f 8 Cy 0 02 0 29 C 0 6 Max 0 C 0 4 0 00 0 0 0 20 030 040 oso so 0 70 oso 0 90 4 00 10 120 2 TET eT Then in order to
14. 13 32 7 32 13 20 7 26 0 9 0 9 0 95 12 04 6 99 12 07 7 01 0 2 0 2 1 00 9 75 5 98 9 60 5 90 1 5 1 5 At 36 000ft Thrust at 36 000ft and null lift Drag coefficient CxO will be determined using acceleration diagram from MO 9 to 2 0 described in Mirage lIIE at page PL A1 13 for a gross weight of 8 600kg at run start From this diagram we compute Extra specific power Ps in the following table and curves Friday February 15 2013 rev 2 Page 7 Mirage III Flight Model Identification Ps ft s Est FuN AB thrust Mach PE Weight 18000 0 90 160 18 985 a 1 00 150 18 918 1 E 1 10 130 18 830 120 E 1 20 140 18 708 a 1 30 162 18 595 Emp 1 40 185 18 487 H 1 50 207 18 361 E 1 60 229 18 220 dl 1 70 250 18 084 853338358882 5829853395 983 1 80 265 17 944 1 90 215 17 752 And this allows to simulate the acceleration run from MO 9 2 00 120 17 455 and to compare forecasted values with the one from the manual Ps ft s Mach O Extracted oO Sample Computed 300 mdd e 1 90 1 80 75 z 1 70 Dal 50 o 150 200 250 300 0 90 1 00 1 10 1 20 1 30 1 40 1 50 1 60 1 70 1 80 1 90 2 00 DO Psft s extracted Psft s smoothed O Psft s sampled t s M
15. IAF Mirage III C with ATAR 9C Load factor limitations are the same for clean aircraft of for AIM 9 configuration and only depend on gross weight GW lt 9 500kg 20 971lbs Ng in 3 5 6 7 GW gt 9 500kg 20 971lbs Ng in 2 7 5 5 Angle of attack AoA The Angle of Attack value incidence AoA is not displayed to the pilot in an angular value The ADHEMAR device is using three lights green amber and red that switch on an off depending on incidence Values for which these events occur are not expressed in True AoA angular value deg but in Sector AoA also in deg the relation between True AoA 40A7 and Sector AoA AoAs is described in Mirage IIIE at page PL G 14 It s a linear relation AoA AoA 0 deg 0 deg AoA AoA 18 deg 30 deg 5 3 AoA 3 AOAy or AoA 5 A0As Lift coefficient versus AoA Lift coefficient will be computed for Mirage III E and then applied to all other variants From MIRAGE III E at page PL G 13 we have the relation between true incidence Mach number load factor and gross weight We will consider a CoG location at 50 of MAC a gross weight of 9 000kg For each Mach number we read true incidence corresponding to a given load factor that compute C value from load factor by 2 M g e 1 pSV sy Es Where M is the mass gross weight in kg S reference surface in m p air volumic mass in kg m g gravity acceleration 9 81 m s Firs
16. Level flight Acceleration Acceleration at 1 000ft Measures performed with a GW of 8 250 kg 18 212 lbs From acceleration figure Speed along time we compute the Excess Power Extracted Ps smooth it by sampling and compute Thrust value to fit 0A 2 a AL1 000AA2 O PsExtracted ft s Ps Sample Ps Computed ft s 600 m 7 4 4 500 M 400 rt 300 y 200 A 100 HHHH E HH Ht H H HHH 0 30 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 Acceleration Max Thrust AB Acceleration at 36 000ft Measures performed with a GW of 7 705 kg 17 000 Ibs From acceleration figure Speed along time we compute the Excess Power Extracted Ps smooth it by sampling and compute Thrust value to fit O Extracted Ps ft s Computed Ps ft s Sampled Ps ft s 250 100 Then we compute acceleration fly path from the computed thrust and we get the following 36000AA2 36000AA4 RL36 000 AA4 Acceleration Max Thrust AB Sustained Load Factor Measures performed with a GW of 7 600 kg 16 780 Ibs Friday February 15 2013 rev 2 Page 11 Mirage III Flight Model Identification
17. between 10 020 kg 22 119 lbs at take off 100 of internal fuel and 6 721 kg 14 837 Ibs with no fuel So Combat configuration 50 internal fuel gross weight is 8 854 kg 19 545 lbs Nesher Mirage 5F In a configuration with 2xAIM 9 GW can vary depending on internal fuel between 9 834 kg 21 709 Ibs at take off 100 of internal fuel and 7 130 kg 15 740 lbs with no fuel So Combat configuration 50 internal fuel gross weight is 8 482 kg 18 724 lbs Speed and Load Factor limitations They are assumed to be the same for all AdA versions and described in Mirage lIIE at page PL III 1 2 and 3 Friday February 15 2013 rev 2 Page 2 Mirage III Flight Model Identification For clean aircraft speed limitations are defined by IAS lt 750Kts Mach number lt 2 0 For a configuration with R 550 speed limitations are equal to the clean one IAS lt 750Kts Mach number lt 2 0 For a configuration with AIM 9 speed limitations are defined by IAS lt 700Kts Mach number lt 2 0 In RAAF Mirage IIIO Manual AAP 7213 003 1 page AL 31 5 3 the speed limitations for the same 2xAIM9 configuration identified as SW for Sidewinder is declared to be IAS lt 730Kts Mach number lt 2 0 Based on the assumption that limitations to be used by IAF pilots in 1974 should be closer to an 1978 s Export Manual than a AdA 1965 s one will keep the RAAF values for the
18. check the complete model with the values ovo LL MLHA extracted from the Manuals we will compute Extra Specific 05 A aa a a a __ Power and Maximum sustained load factor and turn rate cagan He TT Trt using the non simplified equations so MAA AN p 2 C S V Th Sin A0A M g 0 10 294 2 f 10 Thrust Cos AoA Ps 22 p 2 Cy S V 0 00 0 05 0 10 0 15 0 20 0 25 0 30 0 35 0 40 0 45 V p z C S V Th Sin AoA Ny M g msi f 11 A j Thrust Cos AoA 5 p 2 Cx S V 5 00 4 00 Here are the graphics and tables that compare performances forecasted by the model with the one 200 ia Cz Cx extracted from the manual even if smoothed or sampled Friday February 15 2013 rev 2 Page 6 Mirage III Flight Model Identification Acceleration O Mach document Mach Computed 1 20 1 00 eee 0 80 0 60 0 40 0 20 0 00 0 10 20 30 40 50 60 70 80 time s t s Mach Mach Error document Computed 0 0 31 0 31 0 0 5 0 38 0 39 0 6 10 0 46 0 46 0 7 15 0 54 0 54 1 5 19 0 62 0 61 2 0 24 0 69 0 70 1 5 28 0 77 0 77 0 4 32 0 85 0 84 0 8 37 0 92 0 92 0 0 44 1 00 1 00 0 2 46 1 02 1 01 0 3 54
19. 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 At 20 000ft O Ng Extracted Ng Sampled 3 00 2 00 1 00 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 At 30 000ft t s Mach Mach Error Extracted Computed 30 0 32 0 32 0 0 40 0 46 0 47 2 2 50 0 61 0 62 1 1 60 0 77 0 78 2 0 70 0 92 0 93 1 2 80 1 00 1 00 0 0 90 1 02 1 03 1 1 100 1 02 1 03 1 8 O Ng Extracted Ng Sampled Acceleration from MO 9 with 2 AIM 9 at 36 000ft M EAT 1 30 7 LAA 1 00 EH 4 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 400 150 Ra 3 a den Time s For higher altitude the same variation along Mach number See AA is kept maximum value is defined to fit maximum speed t s mien Manh Erreur External loads Drag Extracted Computed Definition of impact of external loads here 2 AIM 9 or R 550 with their rail and pylons is deduced from Full A B 0 0 90 0 90 0 1 acceleration figures in Mirage lIIIE at page PL A3 1 for 15 0 99 0 97 1 5 1 000ft and PL A3 13 at 36 000ft related to the Sidewider 30 1 05 1 03 1 5 configuration 45 1 10 1 09 1 7 60 1 15 1 13 1 2 The following figures show acceleration values comparison 75 1 20 1 18 1 2 ee il ae and those forecasted 90 1 24 1 23 1 2 e ng the fo ng rule AEE AEE EE vee 105 1 29 1 28 1 2 W
20. 00 1 10 1 20 1 30 1 40 1 50 1 60 1 70 1 80 1 90 2 00 2 10 4 00 1 Z Military Thrust ES E mm Military Thrust is computed to fit the sustained load factor 3 00 x Y _ values described in Mirage IIIE at page PL A1 9 for a gross E weight of 8 175kg 18 046 Ibs di A E mM 1 CIA At Sea Level 5 lg racte Ng Sample Pee m E E 1 00 H 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 1 20 1 30 1 40 1 50 1 60 1 70 5 00 O Extracted Turn Rate Smoothed Turn Rate Computed Turn Rate 2 00 4 00 7 00 3 00 6 00 5 00 2 00 4 00 3100 E 1 00 Wi 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 2 00 y 1 00 A 0 00 0 40 0 50 0 60 0 70 080 0 90 1 00 1 10 1 20 1 30 140 1 50 1 60 1 70 Friday February 15 2013 rev 2 Page 9 Mirage III Flight Model Identification When Mach number is between 0 9 and 1 05 each AlM 9 or R 550 with its pylon and rail add 0 002 to the airplane Cx When Mach number is over 1 05 each AIM 9 or R 550 with its pylon and rail add 0 00125 to the airplane Cx Seal Level acceleration from MO0 32 with 2 AIM 9 Time s E Extracted Computed At 10 000ft O Ng Extracted Ng Sampled 5 00 4 00 co 1 1 3 00 E A 2 00 1 00
21. 1 05 1 05 1 2 76 1 08 1 09 3 5 Extra Specific Power Ps ft s Mach O Psft s extracted Psft s smoothed O Psft s sampled Psft s computed 9 050kg Ps ft s Ps ft s Mach sampled from computed Error Manual 9 050kg 0 30 175 176 0 7 0 40 238 235 1 1 0 50 310 306 1 4 0 60 392 387 1 3 0 70 500 494 1 2 0 80 575 565 1 7 0 90 510 505 1 0 1 00 320 300 6 2 Sustained load factor and turn rate O Extracted Load Factor Smoothed Load Factor Computed Load Factor Smoothed Turn Rate O Extracted Turn Rate Computed Turn Rate 16 00 15 00 14 00 BE 13 00 12 00 11 00 10 00 4 9 00 0 J 7 00 6 00 5 5 00 0 90 1 00 1 10 0 40 0 50 0 60 0 70 0 80 Turn Load mach fate Factor Rate Factor Error Error Forecast oreas Grom Grooms A 0 40 12 33 3 15 12 50 3 19 1 3 1 2 0 45 12 76 3 62 13 00 3 68 1 8 1 7 0 50 13 12 4 09 13 40 4 18 2 1 2 0 0 55 13 51 4 61 13 80 4 70 2 1 2 0 0 60 13 80 511 14 00 5 18 1 4 1 4 0 65 14 22 5 68 14 12 5 65 0 7 0 7 0 70 14 52 6 23 14 20 6 10 2 2 2 2 0 75 14 53 6 67 14 25 6 55 2 0 1 9 0 80 14 49 7 09 14 25 6 97 1 7 1 7 0 85 14 00 7 27 13 90 7 22 0 7 0 7 0 90
22. 2 DEFA 30mm guns with their rounds no rocket but the rear fuel tank that take its place and half of the internal fuel including leading edge fuel tanks that are optional equipment A Nesher Mirage 5F with ATAR 9C operated by IAF in 1973 2 short range A A missiles AIM 9B because Shafrir Mk 2 data are not known with pylons and launchers B Data Collection Dimensional Data Reference Area S 34 79 m 374 5 ft Wing Span 8 22 m Aspect ratio A 7 S 1 94 Weight and Balance Empty Weight Empty mean here without fuel or external loads but all the rest pilot guns and ammo oil and required fluids empty optional fuel tanks Mirage III C and CJ Mirage IIl C empty weight is estimated from PL P32 1 where take off weight with 1 MATRA 530 240kg with its pylon and 2 AIM 9 240Kg with pylons and launchers is said to be 8 915 kg If we supposed this weight being related to a plane with empty gun bay no rounds but with full 2 580 L of fuel 2 064 kg 0 8kg l we have without fuel nor gun rounds but with pilot a weight of 6 371 kg if we remove the pilot 95kg we get an basic weight of 6 276 kg Friday February 15 2013 rev 2 Basic weight without pilot 6 276 kg Equipped Pilot 95 kg DEFA Guns 250rds 130 kg TOTAL 6 501 kg 14 351 lbs Page 1 Mirage III Flight Model Identification Mirage III E From Mirage lllE at page PL 11 3 Basic weight without pilot 6 6
23. 65 kg Equipped Pilot 95 kg Rear fuselage fuel tank 90 kg Leading edge fuel tank 150 kg DEFA Guns Chassis canon w 250rds 360 kg TOTAL 7 360 kg 16 247 Ibs Nesher Mirage 5F From Mirage 5F Manuel d Utilisation at page PL II 3 Basic weight with 95 kg pilot 6 780 kg DEFA Guns rounds 250 130 kg TOTAL 6 910 kg 15 253 Ibs Comment In the maintenance manual of the Mirage 5F the empty weight is said 100kg lighter 6 680 kg with pilot and seat As I ve defined Mirage IIIE weight from its Manuel d Utilisation and not from its Maintenance one GCB l Il do the same for the Mirage 5F Nesher Fuel Weight Mirage III C and CJ With the Chassis canon guns the front fuselage tank 325 L is removed but without the SEPR rocket the rear fuselage tank 460 L can be installed The leading edge tanks do not exists on Mirage III C Fuel density of 0 8kg l is assumed Wings 2x545L 1 090 Fuselage main 2x515L 1 030 Rear Fuselage 460 TOTAL 2 580 L 2 064 kg or 4 556 Ibs Mirage III E With the Chassis canon guns the front fuselage tank 325 L is removed but without the SEPR rocket the rear fuselage tank 545 L can be installed The two 125 L leading edge tanks are installed Fuel density of 0 8kg l is assumed Wings with leading edge 2x670L 1 340 Fuselage main 2x515L 1 030 Rear Fuselage 545 TOTAL 2 915 L 2 332 kg or 5 147 lbs
24. ach Psfts Mach Error extracted smoothed Computed We add from sustained load factor diagram in Mirage IIIE 0 0 90 160 0 90 0 0 at page PL A1 11 for a gross weight of 8 175kg 18 046 15 0 99 152 0 99 0 1 lbs that sustained load factor at MO 8 is around 1 9G and 30 1 06 132 1 06 0 1 last we consider that thrust is constant for mach number 45 1 12 128 1 12 0 4 bellow 0 8 60 1 17 134 1 18 0 5 2 2 a 75 1 23 147 1 24 0 6 The Null lift Drag coefficient variation along the complete 90 1 30 161 1 30 0 5 Mach range is chosen as 105 1 36 176 1 37 0 5 1 44 0 79 Zero lift Cx 120 LB 130 da 0 0400 135 1 50 206 1 51 0 6 150 1 57 220 1 58 0 7 0 0350 165 1 64 236 1 65 0 8 ied 180 1 71 252 1 72 0 7 0 0250 Other altitudes 0 0150 _ _ _ lt gt Here the Thrust curve will be determined using Sustained a0100 HOE EEE EE EEE EEE EEE EEE EEE EEE EEE EEE EE EEE EEE EET load factor bellow at 10 000 20 000 and 30 000ft ds li i 0 0050 HAHAHAHA pitt 0 0000 0 00 0 20 0 40 0 60 0 80 1 00 1 20 1 40 1 60 1 80 2 00 2 20 The Thrust curve Friday February 15 2013 rev 2 Page 8 Mirage III Flight Model Identification At 10 000ft At 30 000ft
25. elo NN 8 Military TAUS Era ra er r E aE Ere EEO RE EE e E aa Ere a OA Ea claus 9 Ext rnal loads Dragasani a a Ea E a AE a a a E aA E a EE ak 10 D Mirage with ATARB ii A VEE EAE EERE EEE EE ae 11 Level flight Ac eler AT O a 11 Acceleration at LO aia 11 Acceleration at 36 OM cid 11 Sustalned Load Factoria iia datada 11 Sustained Load Factor at OME sais winsledas sees sndacesncceseessishtssuatedaccansentosedensade stendaniosanesdesebdnitcadedasdecasndaasettdasdedvichtasvededuadeasbetuatessnsadedilins 12 Sustained Load factor at 10 OOOft ccccccccsesesesesecesesesesesesececesesenecenecececenecesecesecececesecesecececececeeecececeeecereceeeeesececececeeeeeeeeers 12 Sustained load factor at 20 OOOfPt cccccccceseseseseseseseseseseseseceseceseseneceneceseceseceveceeecececeeecesecececeveserenecececececeeeeecececenececeeeeeeecers 12 Sustained load factor at 30 OOOTE cccidccscccecsosscsesvesacedevdenrevdestancvscsvevevsestaredeeseaveuseetaneuseviadersestadedurduaevieesaibeversadbenesdadbaedbenaeddsves 13 AS A a TE E A EA 13 Early version up to t971 74 vereten ie 13 Late version from 1971 74 iia 14 Fe e NN 14 G Appendix and Figures sissi p e a E a E a shes uhaantesuecevsduibeuneedebssdadaunedaceusndsbedviness 15 Standard AtMOSPhET A EEPE EE EES 15 C rrected Air Speed CAS estad 15 H Bibliography oia a io 16 Friday February 15 2013 rev 2 Page 17
26. hen Mach number is under 0 9 each AIM 9 or R 550 with 120 1 34 1 33 1 3 its pylon and rail add 0 001 to the airplane Cx 135 1 39 1 38 0 9 Friday February 15 2013 rev 2 Page 10 Mirage III Flight Model Identification 150 1 44 1 43 0 9 165 1 49 1 48 0 9 180 1 54 1 53 1 2 Then we compute acceleration fly path from the computed thrust and we get the following D Mirage III C with ATAR 9B All aerodynamic data will be kept from Mirage llIE to Mirage lll C we only have to recomputed Thrust data Full A B and Military The thrust values will be determined using performances diagram for clean aircraft from Mirage lll C PL P2 1 Acceleration at sea level GW 8 250kg PL P2 7 Acceleration at 36 000ft PL P2 10 Sustained load factor at MIL Thrust PL P2 12 Sustained load factor at Max A B Thrust The gross weight is only known for the first diagram so we will consider that the weight differences is the same as the one we can compute from M II E between the two acceleration diagram Acceleration at sea level GW 9 145kg Acceleration at 36 000ft GW 8 600Kg 545 kg Concerning the Sustained Load factor diagram we will use the gross weight that allow the best fitting with the thrust values computed from acceleration at sea level So we assume for the Mirage III C Acceleration at 36 000ft performed at a GW 7 705kg Sustained load factor at a GW 7 600 kg
27. nt Seal level 1 000ft We start by Mirage III E at 1 000ft described in Mirage I11E at page PL A1 1 Diagram start from take off at a gross weight of 9 145kg and give speed CAS along time s and fuel spent allowing estimation of the weight along time with an indicated density of 0 77 kg L For each point in time the true speed V in m s and acceleration dV dt in m s can be estimated by linear interpolation and then we can compute the Extra Specific Power Ps in m s according to DP zy Where g gravity acceleration 9 81 m s Data extracted from this figure can be summarized by this table with Ps values converted in f s and weight in Ibs t s CAS Kts Ps ft s ae Weight Ibs 30 200 182 133 19 961 35 250 228 156 19 923 40 300 273 178 19 885 45 350 354 200 19 848 49 400 405 222 19 810 54 450 455 250 19 763 58 500 569 279 19 714 62 550 556 306 19 667 67 600 455 338 19 614 74 650 394 386 19 532 76 660 180 400 19 508 84 680 83 450 19 423 106 700 58 600 19 168 The extracted data are now smoothed and resample in the following figure Friday February 15 2013 rev 2 Page 4 Mirage III Flight Model Identification Ps ft s Mach 700 600 500 400 a 300 200 100 0 0 T 1 T T T T T 0 30 0 40 0 50 0 60 0 70 0 80 0 90 1 00 1 10 O Psft s extracted Psft s smoothed
28. puted Performance charts NATOPS_FLIGHT_MANUAL Mirage 5F Nesher Friday February 15 2013 rev 2 Page 16 Mirage III Flight Model Identification Table of Contents Az PUDO MA SCOP Ce isk acces cc ccrsdncdeccdeaseevertaathevoer ATE EA E EE E T AEE E A T 1 B Data COE O T RRA 1 Dimensional Datak AA a AEE e aE aa ni 1 Welehtand Balan taria ANE LE A A E E A E AEE A AT 1 A NN 1 DM NR 2 LOAG OUE Weight sisene E e rN E S EAEE E a REN a S ai 2 CrOSS WEIR EE E EE A E E E A EE E E E A A A E E E E 2 Speed and Load Factor liMitatloms ioc c cscasvenksencescedvoeantaceccecodaduutarsaecveedsieneveratoavedetanocses sa Pe a EE EEE aE A Laine Eo ETE Nn ASEE oiri 2 Angle of attack ADA ereere eene E EEEE Ee T E E E E E EREE TE Era ESE 3 Lift coefficient VEFSUS AOA crisciessesccscnseseetinseasstanaatdndepsadevnasisdesdenstacesncenielapsadenboseadandanstaenienendiahansedsedaavaiessensadanseosisubensanenian 3 AOA IIMIEATIONS cases scscaicacesentedvaccesstvaionsaetacaddasseassnsedibeicesateeostsstsadevssdesinasosiedusadisntandhiaabeinsadvedanh gt sudicnsobbeasyesdscbensataasadsadinddvstsdad s 4 Ce MirageslllEWwith ATAR 9C issenensis aasan ea aaa Eaa aan aai aaa ia aE E aa Eed aa aaa ENa Eaa ia EaR ieaiai a iaaii BEE 4 Max A B Thrust and Drag COePFICIONt ccccccssecesssecssecssssecssecesseccssecssecessecssseecasecessecasecesseecasecsssaccasecaseecateceateceaseceseeecaeaees 4 AMET E oo A S 4 O 0N AEN EEEE ANENE O NN 7 A ae ei
29. r or 42 corresponding to 25 2 true AoA degrees F Nesher Mirage 5F The Mirage 5F is assumed to have the same aerodynamic definition as the others same hypothesis already made for Mirage llIC vs Mirage I11E Nesher engines are assumed to be ATAR 9C3 and then ATAR 9C5 but there is no known thrust change between the two sub versions to thrust is assumed to be the same as the regular AdA Mirage lllE Nesher Incidence limitations are supposed to be identical to the one of the Mirage IIICJ a value in AoA sector of 42 corresponding to 25 2 true AoA degrees Friday February 15 2013 rev 2 Page 14 Mirage III Flight Model Identification G Appendix and Figures Standard Atmosphere h A z rho z M 1 ft M 1 ft s slug ft m s TAS 0 1116 45 0 0023769 340 29 5 000 1097 09 0 0020481 334 39 10 000 1077 39 0 0017553 328 39 15 000 1057 32 0 0014957 322 27 20 000 1036 86 0 0012665 316 03 25 000 1015 98 0 0010652 309 67 30 000 994 67 0 0008894 303 18 35 000 972 9 0 0007366 296 54 40 000 968 08 0 0005851 295 07 45 000 968 08 0 0004601 295 07 50 000 968 08 0 0003618 295 07 55 000 968 08 0 0002846 295 07 60 000 968 08 0 0002238 295 07 65 000 968 08 0 000176 295 07 70 000 968 08 0 0001384 295 07 75 000 968 08 0 0001089 295 07 80 000 968 08 8 554E 05 295 07 85
30. se a comparative method using the Mig 21 as reference Mig 21 lift at medium mach number around MO 6 when auto flaps device is not activated laws seems to be quite similar to the one of the Mirage III in the low incidence domain null lift close to null incidence linear relation between lift coefficient and incidence sector up to 28 From an index incidence of 33 to 42 the Mig 21 lift coefficient at M 0 6 increase from 0 811 to 0 955 corresponding to 17 5 If we transpose that to the Mirage III we can suppose that increase the sector incidence from 33 to 42 so true incidence from 20 to 25 2 deg corresponding to 26 will also lead to an increase of the lift coefficient of 17 5 AoA limitations The AOA limitations to be followed by the pilot are documented in Mirage lIIE at page PL III 1 2 and 3 For all configurations with 2xAIM 9 or 2xR 550 they are identified as amber light switching off so equivalent to a Sector AoA of 25 deg generally equivalent to a True AoA of 15 deg The True incidence values corresponding to Amber extinction depending on Mach number are described in MIRAGE III E at page PL G 13 Here are the extracted values Mach AoAt AoAs 0 30 15 45 25 75 0 40 15 96 26 59 0 50 16 63 27 72 0 60 17 30 28 84 0 70 18 09 30 15 0 80 18 71 31 18 0 90 19 33 32 21 1 00 18 26 30 43 1 10 16 35 27 25 Limits for Mach number under 0 30 will be set to 15 45
31. t set of computation will be done for Mach number between 0 5 and 1 0 when possible two altitudes will be used With load factor between 1 and 6 we can get Lift values for incidence between 1 00 and 19 00 degrees as all results show clearly a strict linear correlation between incidence and lift coefficient within this range values have been extrapolated up to a true incidence of 20 00 degrees AoAs of 33 33 and down to null lift Results are summarized in the following figure M 05 C2 M 0 6 O C2 M 0 7 Cz M 0 8 Cz M 0 9 C2 M 1 0 Cz M 1 0 Lift Coefficient Cz 5 00 0 00 5 00 10 00 15 00 20 00 True Incidence angle deg The second set of measures is related to the supersonic domain Mach number between 1 05 and 2 0 using M 1 0 as a reference Cz M 1 0 Cz M 1 05 E C2 M 1 1 C2 M 1 2 Co M 13 C2 M 1 5 C2 M 1 9 C2 M 2 0 Lift Coefficient Cz 8 Poe 5 00 0 00 5 00 10 00 15 00 20 00 True Incidence angle deg Then the last question to be answered is what happen for true incidence greater the 20 deg AoAs of 33 Friday February 15 2013 rev 2 Page 3 Mirage III Flight Model Identification do not have any document describing Mirage III behavior in such a domain so will u
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