M ECH AN IKA TEORETYCZNA I STOSOWANA
1/ 2, 25, 1987
PACKET OCHOBHLIX ASPOJIH H AM H ^ECKH X XAPAKTEPHCTHK
CAMOJIETA
IlPEH3eK
Aeuaą uoHHuu uccjiedasame/ itcKuu u ucnumameAwiuu uncmumym, npaia,
1 .
B craT t e KopoTKO on H cwBaeTca MeTOfl p a c ieT a ocHOBHbix aapoflHHaMimecKHx xa-KTepHCTHK caM oneTa, I O K oflH oro Tejia. MeTOfl S t m pa3pa6oTan B JiHHefiHoft oBnacTH
flOKpH TiraecKH x ^H ceji M H no3BOJiHeT nojiy^H Tb flBa pa3a 25 BejiimHH npoH3BOA-KO3(|)(|)HqHeHTOB, H O 3T0T MeTOfl MO>KHO Hcnojib3OBaTb H p,na . KpOMe T o ro , B craTbe flatoTCH pe3yjiExaTbi pacqeTOB H
C 3KCnepHMeHTaJIBHŁIMH flailH blMH .
2 . I I o c T a n o B K a
pa3pa6oTKH 3Toro MeTOfla 6bm o nojry^H Tb HH<J)OpMaijHH 06 OCHOBHWX aapo-xapaKTepncTH Kax caMOJieTa pjin pac^eTa e r o n e r a bix aaraibix H xapaicre-ycroii*iHBOcTH H ynpaBJiHeiwocTH H a n epBbix STanax e r o pa3pa6oTKH . JXna. 3Toro Hy>KHO 6bin o pa3pa6oTaTb TaKofi pacyeTH Bift jwerofl, KOTopbift 6bi ^aBaJi HafleHCHwe p e-3yjIbTaTbI fl(JIH CaMOJICTOB pa3HBIX KOHCpHrypaiJHH B meJIOM 6e3 IipHMeHeHHH KO3(J)C})H-iłueHTOB HHTep(J)epeHHHH u 6e3 BBoaa rrpeflnoJio>KeHHH o H arpy3Kax.
O 6m e e pemeH H e npoSjieM bi o6Tei<aHHH Tejia H BJIH CTCH o^eH b CJIOHCHWM H n o cym ecr-a y He BbinojiHHMbiM n p n noiwomn cym ecTByiom eń Bbrecr-ancjiHTejiŁHOH TCXHHKH AJIH 6ojib-uiHHCTBa cn yqaeB, H MCIOIU H X B TexHHKe 3H aqeH H e. IIooTOMy Swn o Heo6xoflHi«o Bbi6paTb ynpom eH H yio MO^ejib, K an aa yKa3biBaeTCfl, H anpH M ep, B [1], HO KOTOpaH o6ecneqaBaeT flocraTo*myro ToqHOCTb n p n npneMjieMOM 3Ha^eHHH MauiHHHoro BpeMeHH.
M e T o ^ pac^eTa o6Tei<aHHH caiwojieTa 6biji pa3pa6oTaH H JIH H AeanbH oro ra3a H JIHHeHHOH oSjiaCTH 06TeKaHHH. HCXO#H H3 OCHOBHblX $H3HMeCKHX 3aKOH0B H o COCTOHHHH r a 3a nojryiaeTCH o6rqee onH caH H e H BJICH H H — CHcreMa AH c [)
4) e Pe H i :
(H a j n > H E 'I X ypaBHeHHft B ^aCTHHIX npOH3BO#HbIX flJIH CKOpOCTeft, flaBJieH H H , IUIOTHOCTH H 3HTPOIIHH. H ecjwoTpa Ha 6o n biu yio pa3HOBHflHocr& Ha3Ha^eHHH H
KOHcrpyKiiHOHHoro Bbinoji-JieTaromne T&na HjweioT oflHy o6n jyio 'lepTy, T.e. Majiyio BenH^HHy OTH omemra B njiocKocTH nepneH flH KyjiH pH oil K npoflOJiBHoft OCH H AJI H R H n o ee H an
paB-38 3 . IDKO«Aj B . ril>EH3BK
jiem o o . TaKoe oTHomeHHe flencTBH rejiLH O He TOJIBKO pfla n e c ym n x noBepxH ocTeft, HO H H JIH 6ojituiHHCTBa ocrajibH bix uacTeft caMOJiera, T,e, pjm cpio3ejiJi>KeH, MOToronfloji, 6aKOB H T.A- QieflOBaTejiBHO, jieTaiomH e Tejia MOHCHO CHHTaib TOH KH MH TeH n p n npeflnoJioJKeHHH pemeH H H npo6jieMW B JIH H CH H OH oSjiacra MO>KHO n pn MeHHTB MCTOA MajIHX BO3MymeHHH flJM OCHOBHblX JieTHBIX pOKHMOB. YpaBHeHHH flBH -»ceHHH H ^eajibH oro ra3a B KoopflHHaTHOH CH crenie, cBH3aHHoń c TaKHM TCJIOM,
BHA, KaK BblBOAHTCH B [ 2] :
(2.1)
npHHHTbi o6o3HatieHHH: p ... craTjpiecKoe flaBJieH H e, a ... CKopocrb 3ByKa
Uo ... CKopocrB H avan a KoopAHHaTHoft CH creMbi, V ...
(BO3MymeHHofi) CKopocTH ra3a, Q0 • • • nnoiHocih HeBO3MymeHHoro A ... onepaTop J la n ^ a c a . B p ac qerax npeAnoJiaraexcH 6e3OTpbiBH oe o6xei<aHHe Teji.
IIo3TOMy B Ka>KAOH TO«iKe noBepxHOCTH Tejia HopiwajibHan cjiaraeM aa OTHOCHTCJIBHOH CKopocTH paBHa H yjuo.
Vrn = 0 (2.2)
Jlflsi aScojuoTH oii CKopocTH TeHeHHH ra3a fleH CTByeT
V = ~u+ f
r(2,3)
r ^ e U npeflcraBJiH eT nepeHOCHyio cKopocTB H Vr OTHOCHTejiBHyio CKOPOCTB. n epeH ocH an CKopocTB ToiKH Tejia onpeAeJiseTCH cooTHomeHHeM:
U=U
0+Qxf (2.4)
rfle Uo ... 03H anaeT cKopocrb H a ia ^ a CBH3aHOH CHcreMbi KoopAHHaT, Q ... Beicrop yrjiOBoft CKopocTH H r ... n n e ^ o B 3TOH T O ^ K C HopiwajiBHyio CKopocrb Ha noBepxHOCTH MOJKHO noHHMaTb I O K cyMMy mecTH cn araeM bix. B C BH 3H C TeM, I T O AH(J)c[)epeHi^Hai[b-H bie ypaBO AH(J)c[)epeHi^Hai[b-HeO AH(J)c[)epeHi^Hai[b-HO AH(J)c[)epeHi^Hai[b-HO AH(J)c[)epeHi^Hai[b-H (2.1) O AH(J)c[)epeHi^Hai[b-H B^O AH(J)c[)epeHi^Hai[b-H IOTCO AH(J)c[)epeHi^Hai[b-H ^O AH(J)c[)epeHi^Hai[b-HO AH(J)c[)epeHi^Hai[b-HenO AH(J)c[)epeHi^Hai[b-HbiMO AH(J)c[)epeHi^Hai[b-H, TO pem em ae M O »O AH(J)c[)epeHi^Hai[b-H O noJiyiO AH(J)c[)epeHi^Hai[b-H Tb cjiojKeO AH(J)c[)epeHi^Hai[b-HO AH(J)c[)epeHi^Hai[b-HeM
&na OTAejibHbix cjiaraeiwbix.
Vn = ^o + Vnv + V^ + V^ + Vn^ + V^ (2.5)
wajibix BO3MymeHHH n peAn o jiaraer, TTO H3MeHeHHH OTHOCHTejibHO HeKOToporo OCHOBHOrO COCTOaHHH HBJIHIOTCH MajIBIMH. M aJI bie H3MeHeHHH aScOJUOTHOH CKOpOCTH ra3a Bbi3bmaioT He TOJIBKO Majiwe H3MeHeHHH yr a o B aTai<H a , CKOJibJKeHHH fi H JIH yrjio-BQH CKOPOCTH fl, HO H MaJIbie I'eOMeTpHieCKHe H3MeHeHHfl OCHOBHOH (pOpMBI, KOTOpaH
V = 0 AJIH ( a , yS, Q) = 0 n p n Uo # 0. H 3 cooTHomeHHH (2.2) — (2.4) H ypaB-BH euiH eń HopjwajiH K noBepxHOCTH cjieAyeT, ^ T O 3TO n ojiy^aercH n p n c o s( «, x) = = 0. OCHOBHaH ^OP M3
MO»eT 6bITb CJieflOBaTejIBHO C03AaHa CHCTeMOH SeCKOHCIHO TOHKHX nosepxH ocTeH napajuieJiBH bix c npoAcntH OH OCBIO X. Tojim H H bi ceqemifi; T&na B njiocKOCTHx nepneH AH KyjiH pH bix K IUIOCKOCTH STOH CHcreMbi H napaJuieJibH bix c n p o -flOJlBH OH OCbK) H OTKJIOHeHHH OpraHOB ynpaBJieHHH nOTOM CMHTaiOTCa MaJIblMH
BO3My-xapaKTCpHCTHKK caM on era 39
BHeM
OCHOBHOH (J)opMbi. TaK>Ke, KaK H y TOHKoro n po$H JKi, KpaeBoe yoioBH e p a 3-Ha CHMMeTpH^HyiO H aHTHCHMMeTpHtJHyiO yaĆ TB.
H3 aHTHCHMMeTpH^HOH laCTH KpaeBLIX yCJIOBHH — H3MeHeHHH IlOfl #eHCT-KHHeMaTHieCKHX napaAieTpOB — MOHCHO nO^yiH TB BejnmHHBI IipOH3BOflHbIX K03(p<pHUHeHTOB. Cjie^oBaTeJiBHOj 3flect pemaeTCH cjiy^aft, K or^a o6eHX cropoH OCHOBHOH 4>opMbi oflHHaKOBbie. CjieflyiomH e pe3yjn.TaTbi nyTeM npHMeHeHHH TeopeMbi 06 o6paTHOM TeqeHHH. TaKHM o6pa30M MO>KHO, H anpH M ep, nojiy^H TB BejiHHHHbi KOS^K^H I^H CH TOB n pH HyjieBOM yr a e aTaKH HJIH CKOJIB->KeHHH H Koa^^H U H eH Tbi, 3aBHCHmHe OT OTKJiOHeHHH opraH OB ynpaBJieHHH [4]. B cjiy-tiae Hcnoiib3OBaHHH CH M M CTP H ^H OH q a c r a KpaeBoro ycnoBH H — BUHHHHe 4> 0PM
Ł I c a MOJieTa, T.e. pa3H bix flecf)opMai^H H oSen x cropoH OCHOBHOH <JiopMbi — peiueH H e n p o -H3B0flHTCH n o MeTo^y onHcaHHOM B [2]. 3 T O T o i yi a fi B CTaTbe He peinaeTCH . I l p n yqeTe TOJiBKO KHHeMaxn^ecKHx napaM eTpoB cooTH oiueH H e (2.5) nepexo^H T B $o pM y:
v
n= « W+ v
n f j+ v
n a x+ v „
a >+ v
n [ ) i(2.6)
3T 0T MeTOfl nO3BOJIH eT TaKJKe nOJiy^H Tb KO3(j)4)HIj;HeHTbI HHflyKTHBHOrO COnpOTHBJieHHff.
3 . OcHOBHbie
B 3TOH ^aCTH npH BOflH TCH TpH TH n a OCHOBHblX (J)OpM, CKOHCTpyHpOBaHHLIX H a OCHOBe a, yKa3aH H oro B n p eflbiaym eji qacTH . OcHOBHaa (popMa BbiSnpaeTCH TaK, I T O 6 W Bcero ym rrbiBajiocb BJIH H H H C napaM eTpa, <|)yHKi^HeH KOToporo HBJiaeTCH cJia-raeM oe B nepBoft ^ a c r n ypaBHeHHH ( 2.6) . OcHOBHbie (JiopMbi BbinojiH eH bi >KHPHŁIMH JI H H H H M H .
IIpH M ep OCH OBH OH (popMbi fljiH BpameH H fl OTHocHTejiBHO OCH z H nocTynaTejiBH oro n o H anpaBJieH H io OCH y, KOTOpan onpeflenaeTCH napaMeTpaMH Qz H a , Ha (pHT. 1.
40 3 . UlKOflA, B. riPBH3EK
IlpHMepbi ocHOBHfaix 4>opM BpameHHH OTHOCHTejibHO OCH y H nocrynaTejibHoro ne-peivtemeHHH no nanpaBneHHio OCH Z, onpeflejraeMbie napaiweTpaMH Qy H p, noKa3aHbi Ha
(JiHrypax 2 H 3.
CpaBHeHHe o6enx 4)Hryp noKa3WBaeT CBH3B MOK^y flencTBHTejibHOH <J>opMOH caMOJieTa H H3o6pa>KeHHeM peiuaiomnx BHHHHHH ocHOBHbiMH
<E>HT. 2
A9poflHHaMjreecKne xapaKTepHCTHKH caMoneTa 41 H a (J)nrypax 4 H 5 npHBe^eHbi npimepbi BbiSopa OCHOBHOH 4>opMbi # J M npoAOJibHofi: OCH, T . c flJiH p,BWKemin xapaKxepH3OBaHHoro napaivieTpom
B[3].
B
X J , ^ ^ .... 2 \J
/I
SJ
. 4 . 5 4 . PemeHHe B 6e:ipa3MejraoH 4»opiwe TeKCTe BMeCTO fleHCTBHTejIBHLIX (|)H3H<ieCKHX 6e3pa3MepHbie n p n coxpaHeHHH OAHHaKOBbix MOJKHO 3anncaTB- V p x
U
o'
xapaKTepHCTHqecKHit pa3Mep.b'
tb
u
0
b
(4.1)
42 3 . IIlKOflA, B. rlPEii3EK
ypaBHeHHń ABH JKCH H H (2.1) npHHHMaeT cjreflyiom.Hft
r ^ e M npeflCTaBjiHCT I H C JI O M a xa .
I lp H noMoiqH cooTHOixieHHH Mewfly TpaH c4)opMaicieH Jlo pen ija H T ajiajiea B CBH3aHoit cHCTeMe KOopflHHaT noTOM nojiyiaioTCH COOTHOIUCHHH MOKAy HCXOAHBIMH nepeMeHHbiMH B cHCTeiwe (4.2) H HOBBIMH nepeiweHHbiMH x', t', rp,e t' ywe He H B^nercH (J)H3HqecKHM BpeMeHew. 3 T H COOTHOIUCHHH cjie^ yio m n e:
x
=
yx', / = _ + x', y = l/ l- M
2(4.3)
IIocTeneHHbiMH onepaiiHHMH c Hcnojn>3OBaHHeM HopjviaJiBHOH cjiaraeMOH CKOpocrn H3 BToporo ypaBHeHHH (4.2) n o jiyqaerca pe3yjiBTnpyiomafl cncreM a c H OBBIM
H nepeMeH-B cjieAyromeM
(4.4)
3 8 \ . d/»
<9f ^ ' / " 5«
8x'
2 +8y
2 +8z
2npeflH a3H aqeH H bie JIJIK pac^eTa neTH bix xapaicrepH CTH K, MO>KHO Ha npaKTHKe c^wraTb MeaJieHHbiiWH. Y- qHTbiBaa rapM om wecKyro 3aBHCHMocn> OT BpeMeHH, SoJiee noflxoflflimuvi HBJIHCTCH npeflcrraBJieHHe 3aBHCHM0CTH aapoAHHaiviHqecKHX KO3(|)(})H-inieHTOB OT KHHeMaTH^ecKHX napaMCTpOB. IIo3TOMy MOJKHO 3aimcaTB:
q
t— q
0icoskt q\ = — kq
Oiń nkt
q
t, q\
= a, a*, /?, /S\ Q
x, Q'
xtQ
y, Q,, Q
z, Q'
zrp,e k HB^aeTCH npHBefleHHOH qacroTon H qOi aM njnrryAoń. KajKflbrił MO>KHO npeAcTaBHTŁ npH noMomH npoH3BOfl;Hbix. B
Majibix BO3Mym;eHHH, STO MOJKHO c^enaTŁ n p a nomoinH pn fla T e i m o p a . M ero « 3aHHMaeTCH npeHMymecTBeHHO npoH3BOflHbiMH n ep Bo ro nopH flKa, T .K . BO M H ornx npaK-TuiecKHX cjiyqaax MO>KHO orpaHiMHTBCH aHajiH3OM JiHHeftHbix 3aBHCHMocTeii qt H q\ H BeiiHMHHaMH SoJiee BbicoKoro n o p a^ K a n pen e6peraTB. B TeopeTH ^ecKicc aHajiH3ax Ha ocHOBe jiH H enH bix MeTOflOB n p n rapMOHHiecKHx 33BHCHMOCTHX OT BpeMeHH
xapaKTepH cnncn caMOJi&ra 43
(4
-7
>
v -AScoJiioTH biii qjieH c0 MO>KHO onpe^ejiH Tb Ha ocHOBe Teopeivibi 06 oSpamoM TeieHHH [4]. IIoTOM nocneflH H e # Ba ypaBHeHHH H3 cooTHOuieHHft (4.7) Heo6xoMO npeo6pa3OBaTb npH n oM om n H OBBI X KHHeMaTtraecKHX napaiweTpoB Qt,Q\ , KOToptieH BJIH IOTCH <j)yHKm«i-MH x', t', BBefleHHBIMH B ( 4. 3) . nOCTeneHHBIMH npeo6pa3OBaHH«MH H nOflCTaHOBKOH B ( 4.4) , n p e^ n o jiaraH onflTb k - * 0, nojiy^H M HOByro cHcreMy B cjieayiomeM BHfl;e:
m 0 A'pft = 0
3p
Q' 8v%'> 8p
Qi
Q(4.8)
8x' ~ 8n ~ 8x' 8n~
+V"'
nyTeM nojiymiM KpaeBbie ycJioBHH nnn CH creMti (4.8) B BH ^e:
»?' = «!' o?' = M
2x'v*' (4.9)
B C BH 3H c TeM, ^ T O npe# iK>JiaraeTCH peiueH H e pun TOHKoro Tejia n o Mero^y jwanbix B03, KOTopoe MOfleJiHpyercH CHCTCMOH GecKOHe^HO TOHKHX noBepxHOCTeft n a p a n -poffoJiŁHOH OCH (ocHOBHoił 4>opMOH) c pa3pbiBOM flaBJieH H H npH n epexo^e H3 oflHOH CTopoHw H a ^ p yryiO j AJIH peineH H H CHcreMbi (4.8) MO>KHO ncnojib3OBaTb co-OTHOIIieHHH flJIH .HBOHHOrO CJIOH.
5. PeiueHHe MaTeMa- raiecKoft 3a^a^H nnu M C^JICH IIM X KOJieGaiiHii npw
c o o xH o i u e n H i i wm ^BoiiH oro CH OJI
Jlp.fi aapoflHHaMH^ecKHX npoH 3BOflH bix AaBJieHHH pQi>Q
i MOJKHO n pH noM omn c o
-ABoń H oro CJIOH [5] 3anH caTb:
s
rQi.Qt _ nQi.Q\ _„Qi- C\
C
PN ~ P(N)1 P(NO)1 . .
N,N0 o6o3H a^aioT TOMKH C Koop^HHaTaMH (x'} y, z), {x'o,yo> Zo) H C ^ '
I C |
pa3pbiB npOH3BOAHBIX Ha OCHOBHOH (J)OpMe B TO^Ke A^o- HcnOJIB3yH COOTHOIlieHHH ( 5.1) , ( 5.2) H (4.9) MOJKHO noc^eflH we ^Ba ypaBHeHHH H3 (4.8) nocreneH H O npeo6pa3H Tb, n pefln
o-jiaraH vfy®' = 0 SJi« x' - * co
K
x'
(5.3)
m m
44 3 . , B. IIPESSEK
CooTH omeH H e (5.3) HOTOM pem aercH n o MeTO#y flH CKperabix C H JI , KOTopbiń onacan B [2]. IIocTeneH H O MO>KHO nojiy^H Tt cJjopMynbi RSIX BbWHCJieHHH cjie,ayiomH X npoH 3-BORHblX:
m
V"'
(5.4) pa3a 25 BŁ I I H ^H H npoH3BOflHbix HceJi M n a ocHOBe npefl-HBJIHeiCH CynepnOHHpOBaHHblMHq
uq\
= a, a", /?, /
O, 3TOT MexoA no3BOJiHeT oa^^Hifl^eHTOB nun - qTO OCHOBHOe npHMOJIHHeHHOe p H ^ e C K H M H KOJieSaHHflMH.IIporpaM M a JJJIH BbmHCJieHHH cocraB^eH a n a H3biKe O o p i p a H I V AJIH 3 B M E C 1040. TIpH Hcno^i>3OBaHHH CHCTeMbi 100 ypaBHeHHft npoflOJiWHxejibHOCTb p a c i e r a
3HTej(IŁHO 10 MHHyT H flJIH 200 ypaBHeHHH 35 MHHyT.
6. IIpHMepu p aciero ji
H a 4>Hr. 6 yi<a3biBaeTCH npH Mep Bhmucnemm BCH H U H H npoH3BOflHbix H
CHTOB npH HyjreBOM yr a e araKH flJia npoflOJiBHoro fl(BH >KeH H H npH M oyroJibH oro Kpwna
6.
0 5
-- 10 20 a0
1.0 0.8 0.6 0.4 0.2 0 0 . 2 O . i 0 . 6 -- 0.8 M- 0.7 L- 3 9 o o o c "= 5.1263 \ \ PACH ET mf=- 0.21627{ o 3KCnEPKMEHT - 10 10 0.1 0 - 0.1 - 0.2 - 0.3 20 1,0 0,5 0 - 0,5
j
!
M*0.i / / aI
>
I
\
\°
o 0 1 /A°
f 0 • • 1 . 1 o o • • ń • ' m • i .". 1 . —* 0 1 1 I L- 39 • o o o - PACMET 3KCnEPHMEHT • 1 o" . -• -• : -• • 0.1 0,2 0,3 Q, [45]46 3 . B.
H a cbur. 7 noKa3aH pesyjiBTaT BtwHCJieHHH npoH3BOflHbix caMOJieTa J I 39 AJIH n n cjia M «• 0, 7.
H a <J)Hr. 8 noKa3aH npH Mep BBI I H C JI C H BH HH^yKTHBHoro conpOTHBJieHHH JI 39 AJW M = 0, 4.
H a <J)Hr. 9 npH BOflirrca pe3yjibtaT p a c q e r a 3aBHCHMOCTH npoH 3BO^H bix
KosdpdpHiiHeHTOB npoflojibH oro ppamennH. caMOJieTa J I 39 OT mtaia M a xa
, 5 , 0
-JInTepaTypa
1. C M . BEJiouEPKoBCKHftj B. K. CKPHnAy, AspoduHaMWtecKue npousaodHue / lemame/ ibHoeo annapama
u Kpbina npu do3eyKosbix CKOpocmnx, MocKBa 1975.
2. 3 . IIlKOAa, HnmepaiafUH cuctneMU uecyiaux noeepxuocmeu e udeaAhuoju zam. floKTopcKaa paBota, ripara 1979.
3. B. Tlvvu3VK,PacHemOCHOSHUXcGpobuHaMunecKuxxapaKtnepucmuKcaMosiema. O m erAH H H , V- 1457/ 82 4. B. IIPEH 3EKJ Hcnojibweame meopeuu 06 o6parmwm metenuu. O m eT AH H H , V- 1408/ 80
5. H . E . Kownt, BeKinopnoe ucuucMmte u nanajia tneuaopHoio ucHUcneHun, MocKBa 1951.
S t r e s z c z e n i e
OBLICZENIE PODSTAWOWYCH CHARAKTERYSTYK AEROD YN AMICZN YCH SAMOLOTU. W pracy przedstawiono krótko metodę obliczeń podstawowych charakterystyk aerodynamicznych samolotu traktowanego jako jedno ciał o. Metoda został a opracowana dla liniowego zakresu charakterystyk i dokrytycznych liczb Macha. Umoż liwi a wyznaczenie dwa razy po 25 pochodnych charakterystyk aero-dynamicznych. Metoda może być wykorzystana również dla innych obliczeń. W pracy podano wyniki przykł adowych obliczeń i przeprowadzono porównanie z danymi eksperymentalnymi.
S u m m a r y
COMPUTATION OF AN AEROPLANE FU N D AMEN TAL AEROD YN AMIC CHARACTERISTICS A computation method has been presented for an aeroplane aerodynamic characteristics in the case when the aeroplane is treated as a whole body. The method has been worked out for a linear region of characteristics and subcritical Mach numbers. It enables to determine two times 25 derivatives of the aerodynamic characteristics. The method can be used in other computations as well. Example results and the comparison with experimental data have been given.
