Chapter 9 Cross-checks on design of tail surfaces ( Lectures 34 to 37)

Transcription

1 hapr-9 hapr 9 ross-hks on dsign of ail surfas ( Lurs 34 o 37 Kywords : ross-hks for dsign of ail surfas; loaion of sik-fr nural poin ; lvaor rquird for rim a Lma nar ground and nos whl lif-off ; dsirabl lvl of nβ ; ruddr onrol in rosswind, on ngin inopraiv ass and spin rovry ; dsirabl valu of of dihdral angl; ailron dsign. Topis 9.1 Inroduion 9.2 ross-hks for longiudinal sai sabiliy and onrol Nural poin ross-hk I Sik-fr nural poin a or byond af mos.g.loaion Longiudinal onrol ross-hk II Adquay of lvaor wih δ 25 o in landing lβ ; hoi onfiguraion wih.g. a h mos forward loaion ross-hk III Adquay of lvaor o dvlop suffiin pihing momn o nabl nos whl lif-off 9.3 ross-hks for dirional sai sabiliy and onrol Dsirabl lvl of nβ Ara of ruddr 9.4 ross-hks for laral sabiliy and onrol Slion of dihdral angl Ailron dsign Rfrns Eriss Dp. of Arospa Engg., Indian Insiu of Thnology, Madras 1

2 hapr-9 hapr 9 ross-hks on dsign of ail surfas - 1 Lur 34 Topis 9.1 Inroduion 9.2 ross-hks for longiudinal sai sabiliy and onrol Nural poin ross-hk I Sik-fr nural poin a or byond af mos.g.loaion Longiudinal onrol 9.1. Inroduion Th final dsign of horizonal and vrial ails rquirs alulaion of h dynami sabiliy and rspons of h airplan in ass lik: (a diffrn fligh ondiions (b diffrn wighs and.g. loaions and ( possibl variaions in onfiguraion. Appndi of Rf.3.1 prsns h produr o alula h sabiliy drivaivs and solving h hararisi quaions for longiudinal and laral sabiliy. This is an labora ask spially for h sudn dsign projs. On h ohr hand, h dsign burau in an airplan faory has ompur pakags o valua h sabiliy drivaivs and o arry ou sabiliy and rspons alulaions for a givn onfiguraion of h airplan. Howvr, h approah in h prsn ours marial is o arriv a a onfiguraion, wihou h us of pakags, whih is rasonably los o h aual airplan. Kping his in viw, h opis dal wih in his hapr ar basd on h following wo obsrvaions. (i For onvnional subsoni airplans, if h airplan has adqua lvl of sai sabiliy, hn i would hav rasonabl dynami sabiliy. Dp. of Arospa Engg., Indian Insiu of Thnology, Madras 2

3 hapr-9 (ii If h aras of h onrol surfas ar adqua o rim h airplan (i.. bring h momns abou h hr airplan as o zro in rain riial ondiions, hn h airplan would hav rasonabl lvl of onrollabiliy. Following his approah and aking guidan from Rf.1.5, hapr 1-9 and Rf.1.24, haprs 6 and 12, h onfiguraion of h airplan arrivd a so far (i.. hrough haprs 2 o 8, is hkd for h following ass. (I Longiudinal sai sabiliy and onrol (a A h rar-mos loaion of.g., h airplan should b a las nurally sabl for sik-fr ondiion. (b A h formos.g. loaion, h lvaor mus b abl o provid onrol (i.. rim, a Lma in landing onfiguraion. ( Thr should b adqua onrol for nos whl lif-off a V = 0.85 V T0 (II Dirional sai sabiliy and onrol (a Th vrial ail should provid dsirabl lvl of dirional sabiliy. (b Ruddr should b powrful nough o provid dirional onrol in (a ross wind ak-off and landing, (b on ngin inopraiv ondiion for muli-ngind airplans, ( advrs yaw during roll and (d spin rovry. (III Adquay of dihdral ff and ailron ara (a Th dihdral angl of wing should b suh as o giv adqua lvl of dihdral ff. (b Th ailron ara should giv dsird ra of roll. Rmarks: i As mniond in sion 6.3 h onfiguraions of h.ail and v.ail hav bn didd. Also h paramrs lik asp raio, apr raio, swp and airfoil sion hav bn naivly didd basd on h daa on similar airplans. In his hapr, h aras of h.ail, v.ail and onrol surfas ar ross-hkd in h ligh of h aforsaid riria. ii I is assumd ha h radr has alrady undrgon a ours in airplan sabiliy and onrol. Rfrn 3.1; Rf.1.18, hapr 16 and Rf.1.24, haprs 6 and 12 may b onsuld o rvis h bakground. Dp. of Arospa Engg., Indian Insiu of Thnology, Madras 3

4 hapr ross-hks for longiudinal sai sabiliy and onrol Th following quaions ar rprodud from Rf.3.1, haprs 2 and 3. Sandard noaions, ar usd. = ( + ( + ( + ( + ( (9.1 mg mg w mg f mg n mg p mg = + α + mδδ (9.2 = ( w+( f+( n+( p+( (9.3 mo = ( mo w+( mo f,n,p+( mo (9.4 I may b nod ha, mg = pihing momn offiin abou.g. of airplan. α= angl of aak of airplan δ = dflion of lvaor mo = Pihing momn offiin a α = 0 = d / mg = d /dδ mδ mg Th suffis w, f, n, p and rfr o h onribuion du o wing, fuslag, nall, powr and h.ail rspivly. Th wing onribuion is : g a mgw = maw + Lw( - L0w Lαw L0w Lαw w 0Lw Lw = Lαw(α +iw - α 0Lw 9. 6 = + α ; = (i -α (9.7 (9.5 g a g mg maw L0w Lαw a = + ( - + α( - w g a w = maw + L0w( - g a ( = ( - w Lαw No : LW = lif offiin of wing (9.8 (9.9 (9.10 Dp. of Arospa Engg., Indian Insiu of Thnology, Madras 4

5 hapr-9 maw = pihing momn offiin of wing Lαw = (dl / w i,α = wing sing(or inidn and angl of zro lif rspivly w olw g, a = loaion of.g. of airplan and arodynami nr of wing rspivly from h lading dg of man arodynami hord of wing = man arodynami hord of wing Th onribuion of h.ail is : = - V η (9.11 mg H L L = Lα α + Lδ δ + Lδ δ (9.12 α = α - ε + i = αw- iw - ε + i (9.13 dε dε ε = ε 0+ α; ε 0 = (iw- α 0Lw dε = i - ε + α(1- + δ + δ L Lα 0 Lδ Lδ (9.14 (9.15 dε mg =mo-vh η Lα[α(1- + δ ] (9.16a mo = -VHη Lα[i -ε 0 + ab δ] (9.16b = / ; ab = / δ α δ α L L L L (9.17 dε ( sik fid = - VH η Lα(1- (9.18 dε hα ( = ' sik fr = -V H η Lα (1- (1- No : V H = h = lhs h / ws w ail volum raio of h.ail η = ρ V / ρ V 2 2 ; V = fr sram vloiy or fligh spd; V = vloiy a h.ail hδ (9.19 Dp. of Arospa Engg., Indian Insiu of Thnology, Madras 5

6 hapr-9 ρ = amosphri dnsiy (rfr subsion of Rf.3.1 for rasons as o why V is no h sam as V α,δ,δ = angl of aak of h.ail, lvaor dflion and ab dflion rspivly. i,ε = ail sing (or inidn and down wash du o wing a ail (rfr subsion of Rf.3.1 = d /, = d /dδ Lα L Th quaniis ε 0, & Lδ L ab ar dfind in quaions abov. Th onribuions of fuslag, nall and powr ar prssd as : = + α (9.20 m f,n,p mo f,n,p f,n,p Subsiuing prssions for various quaniis in Eqs.(9.1, (9.2 and (9.3 and (9.4 yilds : = + α + δ (9.21 mg mδ g a = maw + L0W ( - + ( f,n,p-vh η Lα {i -ε 0+ ab δ } (9.22 mδ = -VHη Lα (9.23 g a ( sik fid = dε Lαw( - +( f,n,p - VH η Lα(1- dε = ( - +( -V η (1-1- No : h = Hing momn offiin g a hα sik-fr Lαw f,n,p H Lα hδ (9.24 (9.25 hα = h/ α, hδ = h / δ ( Nural poin I is known ha h.g. of h airplan movs during h fligh (hapr 8. Furhr, h onribuion of wing o dpnds snsiivly on h loaion of h g a.g. as i is proporional o( -. Whn h.g. movs af, g inrass Dp. of Arospa Engg., Indian Insiu of Thnology, Madras 6

7 hapr-9 and h wing onribuion boms lss and lss ngaiv or mor and mor posiiv. Thr is a.g. loaion a whih ( sik-fid boms zro. This loaion of.g. is alld h sik-fid nural poin. In his as, h airplan is nurally sabl. Th loaion of h nural poin an b obaind by puing = 0. From Eqs.(9.24 and (9.25 i is nod ha h onribuion of ail o ( hangs whn h sik is fid or fr. I may b ralld, from ours on sabiliy analysis, ha in sik-fr as, h lvaor is fr o mov abou is hing. Subsiuing ( sik-fid = 0 in Eq.(9.24, givs h sik fid nural poin. I is dnod by NP. Hn, NP a dε 0= ( - +( -Vη (1- Lαw f,n,p H Lα 1 dε NP a Hn, = - {( f,n,p - VH η Lα(1- } Lαw Similarly, quaing ( ' NP Rmark: sik-fr o zro givs sik-fr nural poin NP as: ( dε = - -V η (1-1- a f,n,p Lα hα H Lαw Lαw hδ Th quaniy in Eq.(9.29 is posiiv. Th quaniis (9.27 (9.28 (9.29 hα and hδ in Eq.(9.29 ar boh gnrally ngaiv. As a onsqun NP / is lowr han NP / or h nural poin sik-fr is ahad of nural poin sik-fid ross-hk I Sik-fr nural poin a or byond af mos.g. loaion From Eq. (9.29 i is nod ha wing, fuslag, nall, powr and h.ail onribu o longiudinal sai sabiliy sik-fr. Howvr, h gomri paramrs of h wing, fuslag, nall and powr hav alrady bn didd from onsidraions ohr han sabiliy. Th gomri paramrs of h.ail, Dp. of Arospa Engg., Indian Insiu of Thnology, Madras 7

8 hapr-9 spially is ara (S is sill undr h onrol of h dsignr. By varying h ara of h.ail h loaion of h nural poin an b onrolld. As mniond in sion 9.1, h ara of h horizonal ail should b suh ha h sik-fr nural is byond h rar mos loaion of.g. or ( g af mos. As a ross-hk, h loaion of h nural poin sik-fr is alulad using Eq(9.29. If i is no byond ( g af mos hn h ara of h h.ail nds o b inrasd. Drminaion of NP for h siy sar urboprop airplan undr dsign, is arrid ou in ampl Longiudinal onrol Th airplan is said o b rimmd a a givn fligh spd and aliud whn h momns ar mad zro by suiabl dflions of onrol surfas. For h longiudinal moion, h rim or mg = 0 is ahivd by suiabl dflion of h lvaor. Th onvnion rgarding h lvaor dflion is ha a downward dflion of h lvaor is akn as posiiv. Th lvaor angl for rim ( δ rim an b obaind from Eq.(9.2 mg = + α+mδ δ For rim, mg = 0. Hn, 0= + α rim+mδ δ rim -1 δ = [ + α ] Or rim rim mδ Rmarks: (i From Eq.(9.23, i is nod ha h quaniy ngaiv. Furhr, for a sabl airplan ou ha, as h airplan boms mor sabl (i.. mδ ouring in Eq.(9.30 is (9.30 is ngaiv. Hn, Eq.(9.30 poins boms mor ngaiv, h lvaor dflion ndd for rim, also boms mor ngaiv. (ii Th maimum ngaiv dflion allowabl for lvaor is 25 o. Dp. of Arospa Engg., Indian Insiu of Thnology, Madras 8

9 hapr-9 (iii From Eq.(9.24, boms mor ngaiv as.g. of h airplan movs forward. In viw of rmark (ii hr is a forward posiion of.g. byond whih h maimum ngaiv valu of lvaor dflion will no b abl o rim h airplan a Lma. (iv Whn h airplan oms in o land, h following hangs ak pla. (A Th airplan has high valu of L. (B Th flaps ar dfld and h valu of ma boms mor ngaiv. ( Th prssion for involvs Lαw, Lα and dε/. Th proimiy of ground : (a inrass Lαw appriably, (b inrass Lα by ngligibl amoun and ( drass dε/. All hs hr faors nd o mak mor ngaiv han whn h airplan is in fr fligh away from ground. Hn, h abiliy of lvaor o rim h airplan in landing onfiguraion wih.g. in h mos forward posiion is a riial as for adquay of h lvaor. Dp. of Arospa Engg., Indian Insiu of Thnology, Madras 9