Chapter 8 Weights and centre of gravity - 2 Lecture 33 Topics

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1 Chapter 8 eghts and centre of gravty - 2 Lecture 33 Topcs Example 8.1 Example 8.2 Example 8.1 For the sxty seater arplane consdered n examples 3.1, 4.19, 5.1, 6.1, 6.2 and 6.3, obtan the followng. () eghts and c.g. locatons of (a) wng, (b) fuselage, (c) h.tal, (d) v.tal, (e) landng gear, (f) nstalled engne, (g) all else empty (h) fuel () payload. () Locaton of wng such that the c.g. of the entre arplane wth MTO s at quarter chord of m.a.c. () Shft n the c.g. of the arplane for the followng cases. (a) Full payload but no fuel. (b) No payload and no fuel. (c) No payload but full fuel. (d) Full fuel but half of the payload n the front half of passenger cabn. (e) Full fuel but half of the payload n the rear half of passenger cabn. Soluton : From example 3.1 the gross weght of the arplane s 21,280 kgf or 208,757 N I)The weghts and c.g. locatons of varous components are estmated below. (A) ng From examples 5.1 and 6.1 the followng data are obtaned. ng area = m 2 Root chord of wng = m Tp chord of wng = m ng span = m ; semspan = m Constant chord of m upto m from FRL Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 1

2 Fuselage wdth = 2.88 m Mean aerodynamc chord = m Locaton of the leadng edge of m.a.c. from the leadng edge of wng = m Locaton at the a.c. of the wng from the wng root chord = m Referrng to Fg.E5.1 and usng the above data the area of the exposed wng s : (S exposed ) wng = = = m Remark : A smpler way to get the area of exposed wng n ths case, where, the chord s constant n the nboard porton of the wng, s : x = m 2 Usng Table 8.1, the estmated weght of the wng s : x 49 = kgf = 24,462.3 N Or wng = / = % g From Table 8.1, the c.g. of wng s at 40% of m.a.c. Hence, the locaton of the c.g. of wng from the leadng edge of the root chord of the wng s at : x = m (B) Horzontal tal The horzontal tal s mounted on V.tal. Hence, ts exposed area s taken roughly equal to planform area whch equals m 2. Hence, weght of h.tal = x 27 = 300 kgf = 2943 N = 1.41 % of g To arrve at the locaton of the c.g. of the horzontal tal, the followng are noted from example 6.2. Mean aerodynamc chord of h.tal = 1.52 m The dstance between the leadng edge of the root and the leadng edge of m.a.c. s x tan = 0.34 m From Table 8.1, the c.g. of the h.tal s at 40% of ts m.a.c. Consequently, the Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 2

3 dstance between the leadng edge of the root chord of h.tal and the c.g. of h.tal s : x 1.52 = 0.95 m (C) Vertcal tal The contrbuton of dorsal fn to the weght of v.tal s gnored at ths stage of prelmnary desgn. Area of v.tal = m 2 Hence, weght of v.tal = x 27 = kgf = 3422 N = 1.64 % of g To arrve at the locaton of the c.g. of the v.tal, the followng are noted from example 6.2. Mean aerodynamc chord of v.tal = 2.60 m The dstance between leadng edge of the root chord of v.tal and leadng edge of m.a.c. = tan 30 o = m From Table 8.1 the c.g. of v.tal s at 40% of ts m.a.c. Consequently, the dstance between the root chord of v.tal and c.g. of v.tal s : x 2.6 = 2.41 m (D) Engne As mentoned n example 6.3, the weght of each engne s 450 kgf. Hence, from Table 8.1, the nstalled weght of the two engnes s : 2 x 1.3 x 450 = 1170 kgf = N = 5.5 % of g As regards the locaton of c.g. of the engne, Ref.1.24, chapter 11, mentons that for gas turbne engnes the locaton of c.g. from the engne nlet s between 30 to 45% of engne length. In the present case the engne length s 2.13 m. From Fg.6.7a t s assumed that the engne nlet s just behnd the boss of the propeller. From example 6.3 the boss of the propeller s at 1.58 m from the leadng edge of the wng. Takng c.g. of engne to be at 40 % of engne length, the locaton of engne c.g. from the leadng edge of the wng s : x 2.13 = m.e m ahead of the leadng edge of the root chord of the wng. Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 3

4 (E) Landng gear From Table 8.1 the weght of the nose wheel plus the man landng gear s 4.3 % of g.e x = 8977 N Out of ths total weght, the nose wheel and man wheel account for 15 % and 85 % respectvely. Hence, nose wheel weghs 0.15 x 8977 = 1347 N and the man wheels wegh 0.85 x 8977 = 7630 N. As regards the locatons of the c.g. s of nose wheel and man wheels, t s recalled that the nose wheel and man wheels share respectvely 10 % and 90 % of the arplane weght. From example 6.3, the wheel base s chosen as 9.78 m. Hence, the c.g. of the nose wheel s 0.9 x 9.78 = m ahead of the c.g. of the arplane. The c.g. of the man wheels, as a group, s : 0.1 x 9.78 = m behnd the c.g. of the arplane. (F) Fuselage and systems etted area of fuselage s obtaned as follows. Varous dmensons are obtaned from Fg.6.8c (a) Nose porton Length of nose = 0.7 m Dameter at the end of nose = 1.64 m Hence, average dameter = 1.64/2 = 0.82 m Consequently,wetted area or surface area of nose 2 π =1.80m (b) Cockpt porton Length of cockpt = 2.54 m Dameter at the end of cockpt = 2.88 m Hence, wetted area of cockpt porton π 2.54 = m 2 (c) Mdfuselage porton Length of mdfuselage = m Dameter of mdfuselage = 2.88 m Hence, wetted area of mdfuselage = π x 2.88 x = m 2 (d) Tal cone 2 Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 4

5 Average dameter 2.88 / 2 = 1.44 m Length of tal cone = 9 m Hence, wetted area of tal cone 2 π = m Consequently, wetted area of fuselage s : = m 2 Usng value n Table 8.1, the weght of fuselage s : x 24 = kgf = N or % of g Remarks: () An expresson for qucker,but approxmate, estmaton of fuselage wetted area s : f 0.75 l Permeter of the cross secton wth maxmum area In the present case the approxmate estmate would be: 0.75 x π x 2.88 x = m 2 Ths value s 96.3 % of the value obtaned earler. () The weght of the fuselage as percentage or gross weght ( f / g ) appears hgh. However, as noted below Table 8.1, the quantty ( f / g ) ncludes weghts of fuselage, furnshng, consumables etc. Reference 1.19, chapter 8 presents nformaton on weghts of varous tems, as percentage of g, for dfferent types of arplanes. For the turboprop arplane the data ndcates that the weght of fuselage structure, furnshngs and consumables would respectvely be 9 to11 %, 4 to 6 % and 1.5 to 2 % of gross weght. These would add upto 15 to 17 % of gross weght. Further as noted n Remark (), after the subsecton 8.2.2, the weght of fuselage, along wth furnshng etc., and the systems s taken as one unt. Accordngly, fuselage +system empty wng h.tal V.tal engne = landnggear g g g g g g g From example 3.1, ( empty / g ) s Hence, + fuselage g system = ( ) = Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 5

6 Or ( fuselage + systems ) = x = 65,445 N From Table 8.1, the c.g. of the fuselage and systems can be taken to be at 0.45 l f or 0.45 x = m from the nose of the fuselage. (G) Fuel From example 3.1, f =0.143 g Hence, = x 208,757 = 29,852 N f The mass of the fuel s / 9.81 = 3043 kg Takng densty of fuel as 0.8, the volume of fuel s 3804 ltres. From Ref.1.21 ( edton) the arplanes n ths category have ntegral fuel tanks n the wng wth capacty of around 5000 ltres. It may be ponted out that some space for addtonal fuel s ntentonally provded. Ths permts ncreasng the range when needed. However, t should be noted that the desgn gross weght of the arplane cannot be exceeded and consequently, the payload has to be reduced correspondngly.the tem III enttled Range performance n secton presents further detals. As regards the c.g. of fuel, Ref. 1.15, chapter 8 mentons that for fuel stored n the wng, the c.g. of fuel can be taken at the same locaton as the c.g. of the wng. As mentoned earler, the c.g. of the wng s at m behnd the leadng edge of the root chord of the wng. (H) Payload and crew These two tems are generally clubbed together for passenger arplanes. In general avaton arcraft the flght crew can be separately consdered. From example 3.1, the weght of the crew and passangers plus the baggage s 6340 kgf as 62,195 N. The c.g. of these tems s taken n the mddle of the passanger cabn. From Fg.6.8c ths locaton s : = m from the nose of fuselage. 2 II) Determnaton of wng locaton and c.g. of the arplane As mentoned n secton 8.3, the poston the wng s chosen such that the c.g. of the entre arplane wth the gross weght s at 25% of the mean aerodynamc Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 6

7 chord of the wng. Before arrvng at the locaton of wng whch satsfes ths condton, the followng ponts are noted. () The dstance of the leadng edge of the root chord of the wng from the nose of the fuselage s denoted by x lew. () The 25% of the mean aerodynamc chord (m.a.c.) of wng s m behnd x lew (example 5.1). Hence, the chosen locaton of the c.g. of the entre arplane s at (x lew ) m from the nose of fuselage (Table E8.1) () The c.g. of the wng, as calculated n tem A of ths example s at : (x lew ) m The c.g. of the two engnes as mounted on the wngs, and as calculated n tem D of ths example s at : (x lew 0.728) m. The c.g. of the fuel, as mentoned n tem C of ths example s at : (x lew ) m. (v) The tal arm of the horzontal tal.e. the dstance between the a.c. of the wng and the a.c. of h.tal s m. Further the c.g. of the h.tal s at 40% of ts m.a.c. and the m.a.c. beng 1.52 m. Hence, the locaton of the c.g. of the h.tal s at : x lew ( ) x 1.52 = (x lew ) m In a smlar manner, notng that the tal arm of v.tal s m and ts m.a.c. s 2.6 m, the locaton of the c.g. of v.tal s at : x lew ( ) x 2.6 = (x lew ) m (v) The nose wheel and man wheels, as mentoned n tem E of ths example, are respectvely m ahead and m behnd the c.g. Hence, the c.g. of nose wheel s at : x lew = (x lew 7.991) m The c.g. of the man wheels, taken together s at : x lew = (x lew ) m (v) The fuselage plus the systems as a unt have the c.g. at m from the nose of fuselage (tem F of ths example). The full payload plus the crew together have the c.g. at m from the nose of the fuselage (tem H of ths example). Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 7

8 The weghts of varous tems and ther c.g. locatons are presented n Table E 8.1a. Item (N) x (m).x (Nm) ng 24,462 x lew x lew + 28,254 Engnes 11,478 x lew x lew 8,356 Fuel 29,852 x lew x lew + 34,479 H.tal 2,943 x lew ,943 x lew + 42,229 V.tal 3,422 x lew ,422 x lew + 45,140 Nose heel 1,347 x lew ,347 x lew 10,764 Man heels 7,630 x lew ,630 x lew + 13,650 Fuselage + Systems 65, ,220 Payload + Crew 62, ,108 Arplane wth c.g. at 0.25 c 2,08,774 $ x lew x = x lew+1,548,960 $ As per example 3.1, the take-off weght s kgf or N. The value of N shown n the table s obtaned by addng the weghts of ndvdual components. The neglgble dfference between the two values s due to round-off errors. For the sake of consstency, g = N s used n subsequent calculatons. Table E 8.1a Balance table To satsfy the choce, that the c.g. of the entre arplane s at 0.25 c the followng equaton (x lew ) = x lew + 1,548,960, leads to Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 8

9 Or x lew = = m Hence, the c.g. of the arplane s at : = m from nose of the fuselage Snce, the c.g. les at a.c. of wng, the latter s also at m from the nose of the fuselage. Remarks: () In example 6.2, the dstance between the nose of fuselage and the a.c. of wng (l ntacw ) was assumed as m. The value obtaned above s m or 1.09 m behnd earler assumed value. Ths has mplcatons for locatons of the aerodynamc centres of v.tal and h.tal. To retan the same tal arms of v.tal and h.tal (l vt and l nt ) respectvely as m and m, the empennage needs to be shfted aft by 1.09 m as compared to the earler locaton (Fg.E6.2b). Incdently, n the tralng edge of the root chord of the v.tal n Fg.E6.2b s at ( ) or m from the nose of the fuselage. Shftng aft the empennage by 1.09 m would shft the tralng edge of the root chord of the v.tal to = m whch s stll nsde the rear end of fuselage (note: l f = m). However, the tralng edge of the tp chord of v.tal wll project further behnd the rear end of the fuselage. The overall length of the arplane (l overall ) would go up from to = m. Ths would gve l overall / l f = / = Ths value of l overall / l f s almost the same as that for IPTN N and Dash 8 Q300 (Table 6.2). It may be ponted out that rudder has the chord of 0.3 m and as such the rear spar of the v.tal s further ahead of the rear end of the fuselage. Fgure 6.7a shows the features of the attachment between fuselage and v.tal for ATR The cutaway drawng of Dash 8-Q300 can be seen n Ref.1.21( edton) and on the webste of Flght global. () In the balance table (Table E8.1) the dstances of the c.g. of h.tal,v.tal landng gears, engnes and fuel are wth reference to x lew. Hence, the shftng empennage s automatcally taken care-off. However, t must be added that the locatons of wng, h.tal, v.tal and landng gears are stll tentatve. Fnal locatons Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 9

10 are arrved at after varous components are optmsed and more accurate weghs and c.g. locaton are determned. (III) c.g. shft for dfferent loadng condtons To carry out these calculatons, the balance table wth x lew = m s presented as table E8.1b Case (a) Full payload, but no fuel In ths case, the values from Table E8.1b are : = = 178,922 N It may be added that the weght and moment due to trapped fuel s gnored..x = = Nm Hence, c.g. locaton n ths case s at : / = m Hence, c.g. shft as fracton of c Or the c.g. s at c s = ( ) / = % of c Case(b) No payload and no fuel. It may be noted that, whle calculatng c.g. locaton wth = g, the weghts of passangers and crew were clubbed togather. However, for no payload case only the weght of passangers s consdered as payload. In ths case : = = 120,062 N x = (10.71 x 58860) = Nm Hence, c.g. s at = / = m Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 10

11 Item (N) x (m).x (Nm) ng 24, ,688 Engnes 11, ,721 Fuel 29, ,179 H.tal 2, ,043 V.tal 3, ,131 Nose wheel 1, ,797 Man wheel 7, ,130 Fuselage+Sys 65, ,220 Payload + crew 62,195* ,108 x =2,426,017 *eght of 60 passengers = N ; eght of 4 crew members = 3335 N Table E 8.1b eghts and c.g. locatons of varous tems Or c.g. shft as fracton of c s : ( ) / = % Or the c.g. s at c. Case (c) No payload but full fuel In ths case the values from Table E8.1b are : = = N x = (10.71 x 58860) = Nm Hence, c.g. s at : / = m Or c.g. shft as fracton of c : ( ) / = 15.6% Or the c.g. s at c Case (d) Full fuel but wth half of passengers n front half of passenger cabn. Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 11

12 The weght of passengers s N Half of ths would be N To obtan the c.g. of the arplane n ths case, t s consdered that the rear half of the passenger cabn s empty. The c.g. of ths (rear half of passenger cabn) s (Fg.6.8c) at ( ) x 0.75 = m Hence, n ths case, = = 179,344 N x = x = Nm Hence, the c.g. s at : / = m Or c.g. shft as percentage of c = = % Or the c.g. s at c. Case (e) Full fuel but wth half of passengers n rear half of passanger cabn. In ths case = 179,344 N It s consdered that the front half of passenger cabn s empty. The c.g. of the front half of passengers cabn s at : ( ) x 0.25 = m Consequently, x = x = Nm Hence, x cg = / = m Or the c.g. shft s : =33.1 % Or c.g. at c of c Remarks: () The cases (d) and (e) result n large shft of c.g.. They are hypothetcal cases. These are avoded by allotng the wndow seats frst, then asle seat and later the rest. The frst three cases cause c.g. travel between c w and c w or c.g. shft Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 12

13 Δ (c.g.) = c w. Reference 1.12, part II, chapter 10 gves range of c.g. shft for dfferent types of arplanes. For regonal transport arplanes wth turboprop engnes the value of Δ (c.g.) can be between 0.14 to 0.27 of c w. () hen accurate estmates of the weghts of varous components and the locatons of ther c.g. are avalable, a dagram called eght-c.g. excurson dagram (Ref.1.12, part II, chapter 10) s plotted. In ths dagram the c.g. locaton, as fracton of c w, s plotted on the x-axs. The weght of arplane s plotted on the y-axs. The weght of the arplane under dfferent loadng condtons and the correspondng c.g. locaton provde the ponts on the dagram. Such a dagram coverng the full range of weghts and c.g. locatons appears lke a potato and s sometmes referred to(ref.1.19,chapter 8) as Potato curve.ths dagram ndcates the most forward and most aft locatons of c.g. () The arplane s symmetrc about x-z plane and c.g. les n the plane of symmetry. The vertcal locaton of c.g. s calculated after takng nto account the heghts of varous components above the ground.ths locaton s needed for the desgn of landng gear. Example 8.2 A prelmnary three vew drawng was obtaned n example 2.1, for the sxty seater regonal arplane wth turboprop engnes. Revsed estmates of the parameters of wng, fuselage, h.tal, v.tal, engne and landng gear have been obtaned n chapters 3 to 8. Based on these data, obtan a revsed 3-vew drawng of the arplane at ths stage of the prelmnary desgn. Soluton: The followng ponts are noted from the calculatons carred out n chapters 3 to 8. I) ng parameters a) The geometrcal parameters of the wng are presented n Fg.E5.1. b) A hgh wng confguraton s chosen Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 13

14 c) The leadng edge of the root chord of the wng s at m from the nose of fuselage (example 8.1). The wng dhedral s 3 o. II) Fuselage parameters a) The geometrcal parameters of the fuselage are presented n Fg.6.8c and d. The cabn layout s presented n Fg.6.8b. b) The cross secton of the mdfuselage s crcular. The top porton of the rear fuselage, on whch the v.tal s located, s parallel to the fuselage axs. c) Based on data n table 2.1 for IPTN, ATR-72 and Dash-8 the heght of the belly of the fuselage above ground s chosen as 0.7 m. III) The geometrc parameters of the empennage are shown n Fg.E6.2. However, after the calculaton of c.g., the empennage s shfted rearwards by 1.09 m as compared to that shown n Fg.E6.2. A T-tal confguraton s chosen. IV) The two engnes are located n nacelles on each wng half. The spanwse extent of each nacelle ends at 35% of wng sem-span. The maxmum wdth and depth of nacelle are 1.03 m and 1.37 m respectvely (Example 6.3). The propeller dameter s 3.93 m. The boss of the propeller s at 1.58 m ahead of the leadng edge of wng (example 8.1) V) A trcycle landng gear s chosen. The man wheels are retracted n pods attached to fuselage. The tentatve locatons of the nose wheel and the man wheels are respectvely at m and m from the nose of the fuselage. The revsed three vew drawng for the arplane under desgn s shown n Fg.E8.2. Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 14

15 Fg.E8.2 Revsed three-vew drawng Remarks: () At ths stage of the prelmnary desgn, the structural desgn has not been done. Hence, gudelnes from the three-vew drawngs of IPTN, ATR 72 and Dash-8 are taken for the tentatve shapes of (a) wng-fuselage attachment, (b) pods n whch man landng gear s retracted and (c) nacelles and ther attachment. () The heght of the arplane n Fg.2.1 s 7.7 m. However, the heght n Fg.E8.2 s 8.6 m. The reasons for ths ncrease are as follows. The heght of 7.7 m n Fg.2.1 s based on heght of ATR-72 whch s 7.65 m. In ths arplane (ATR-72) and the arplane under desgn, the dstance of the belly of the fuselage above the ground and the maxmum heght of fuselage are nearly Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 15

16 same. However, two dfferences between ATR 72 and the arplane under desgn are ponted out below. (a) The shape of the vertcal tal of ATR-72 s not trapazodal. It s lke a cranked wng.(fg.6.7a) The sweep angle and the chord near the root of v.tal are large as compared to a conventonal trapazodal shape. Ths results n lower heght of vertcal tal for a gven area of v.tal. (b) The upper surface of the fuselage, where v.tal s located s curved. Hence, the root chord of the vertcal tal les along the centre lne of the rear end of fuselage as shown n Fg.6.9b. Thus, the heght of the v.tal above the fuselage s further lowered. If these concepts were used n the arplane under desgn, the overall heght of the arplane would be comparable to that of ATR-72. Presently, the heght s comparable to the overall heght of IPTN whch has a v.tal confguraton smlar to that of arplane under desgn. In an actual desgn, the changes n vertcal tal confguraton and many other aspects would be brought out n later stages of desgn. Dept. of Aerospace Engg., Indan Insttute of Technology, Madras 16