A e C l /C d. S j X e. Z i

Transcription

1 DESIGN MODIFICATIONS TO ACHIEVE LOW-BOOM AND LOW-DRAG SUPERSONIC CONCEPTUAL DESIGNS Danil. B. L Advisor: Prof. Jams C. McDanil Univrsity of Virginia, Charlottsvill, VA 94 NASA Mntor: Dr. Wu Li NASA Langly Rsarch Cntr, Hampton, VA 68 A C l /C d M P S j X Z Z i dx da u v α This rsarch was conductd in svral parts. First, a study was conductd which xamind th snsitivity of th quivalnt ara, A, distribution and th sonic boom signatur. Matching of mor than 5% to th thortical A distribution may b ncssary to obtain rasonabl matching to th thortical minimum boom signatur. Nxt, a study was conductd which invstigatd modifications to a targt A distribution. Th rsults indicatd that significant changs can b mad to th A distribution which will rsult in boom signaturs with similar charactristics. Third, a study was conductd which xamind th ffcts of prturbations in th A distribution on th sonic boom signaturs. Th location(x), rang of distribution(dx), and magnitud(da) of th prturbation wr varid. X ffctd th location of th spik in th boom signatur. Incrasing dx of th prturbation is distributd dcrasd th spik. Incrasing da of th prturbation incrasd th spik. Thr was no significant diffrnc btwn positiv or ngativ prturbations. Last, a study was conductd which modifid th wing cambr surfac by lastic movmnts of 8 control points. A dsign xploration tool was usd to optimiz C l /C d to improv arodynamic prformanc. Nomnclatur = Equivalnt ara = Ratio of cofficint of lift to cofficint of drag = Mach numbr = Prssur = Intrnal wing control points = Equivalnt lngth = Wing cambr surfac vrtical location rlativ to airfoil sction lading dg = Wing cornr control points = Rang of quivalnt ara distribution = Chang in quivalnt ara = Normalizd wing span vrtical dir. = Normalizd wing span horizontal dir. = Chang in quantity α Introduction Th dsir for incras air spds has ld to suprsonic flight. Howvr, suprsonic flight rsults in th invitabl sonic boom which is a suddn incras in air-prssur which can caus structural vibrations and undsird nois. Mitigation of th sonic boom signatur has thus bn an important issu, particularly with rspcts to suprsonic commrcial vhicls. Currntly, rgulations rstrict th flight of suprsonic aircraft ovr land du to th ffct of th sonic boom. Thus, for commrcial suprsonic flight to b obtainabl, rsarch must b conductd which is abl mitigat th sonic boom whil maintaining high arodynamic prformanc. Rsarch on boom propagation and lowboom vhicl dsigns has bn conductd for ovr 4 yars. Som founding rsarch on boom propagation was conductd by Whitman, Walkr, and many othrs. -4 An important rsult of thir rsarch is th dvlopmnt of th F-function. Th F-function is a mathmatical formulation which utilizs th aircraft s total quivalnt ara to prdict th aircraft s boom signatur. Th total quivalnt ara is a function of th aircraft s quivalnt ara du to volum and lift, both of which contribut to th aircraft s boom signatur. From works by Sbass and Gorg, 4 Mack and Ndlman 5 and othrs, 6-8 it was shown that modifying th aircraft s dsign, such as swpt wings and pointd, slndr for body and fuslag sctions, aids in th mitigation of th vhicl s boom signatur through vhicl shaping. Rsarch Motivation Dvlopmnt of suprsonic commrcial aircraft dsign, spcifically suprsonic businss jts (SBJ), has rcntly gaind intrst. Howvr, dsigning a SBJ which is abl to mt arodynamic prformanc and sonic boom or nois constraints is difficult. This rsarch is focusd on rsarching and undrstanding th founding works mad by prvious Graduat Rsarch Assistant, Mchanical and Arospac Enginring, Arospac Rsarch Laboratory, PO Box 448, Mmbr AIAA. Profssor, Mchanical and Arospac Enginring #6, PO Box 4746, Snior Mmbr AIAA. NASA Langly Rsarch Cntr Mntor, NASA LaRC, Mail Stop 44, Hampton, VA LE

2 rsarch as wll as introducing novl dsign mthodologis for suprsonic commrcial aircraft dsign. Th objctivs for this rsarch hav bn dfind as such: ) Dvlop a mthodology to analyz vhicl dsign concpts to dtrmin if such a dsign is suitabl for achiving low-boom signaturs ) Dfin ky dsign charactristics which may b idntifid in vhicl dsign concpts which will nhanc th mitigation of boom ovrprssurs. ) Dvlop a dsign mthodology which sks to maintain low boom ovrprssurs during off dsign conditions. Rsarch Mthodology This rsarch will b conductd using prxisting lgacy cods within a modrn dsign nvironmnt. Lgacy cods such as AWAVE, ADRAG, PBOOM, tc. hav bn dvlopd in th past to aid in th dsign of subsonic and suprsonic aircraft. ModlCntr is a novl dsign tool which allows paramtric studis and analysis to b conductd in an intgratd nvironmnt. Othr cods hav bn dvlopd and intgratd in this nvironmnt to aid in th dsign of th SBJ. Currnt Rsarch Invrs suprsonic aircraft dsign is basd on sonic boom thory and sonic boom minimization thory. Sonic boom thory provids a rlationship btwn th gomtry of th aircraft and th sonic boom through th F-Function, dvlopd by Whitham. Sonic boom minimization thory gnrats thortical quivalnt ara distributions which minimiz th ground sonic boom signatur. Invrs suprsonic aircraft dsign typically sks to obtain th thortical quivalnt ara distribution so that a dsirabl minimizd sonic boom signatur can b achivd. Howvr, du to dsign constraints such as minimum fuslag cross-sction ndd for passngr cabin ara, mission constraints, tc, th dsign quivalnt ara distribution may not match th thortical on xactly. Howvr, although th mismatch btwn th quivalnt ara distributions may b small, th mismatch btwn th sonic boom signaturs may b mor dramatic. Thus, it is of intrst to undrstand how changs in th quivalnt ara distribution can b mad such that favorabl sonic boom signatur charactristics can b maintaind or improvd. This situation rprsnts a snsitivity issu btwn th quivalnt ara distribution and th sonic boom signatur. This portion of th rsarch will focus on th snsitivity of th sonic boom signatur to th quivalnt ara distribution is studid hr. First, th thortical quivalnt ara distribution and a dsign quivalnt ara distribution ar combind in various proportions to invstigat how closly th dsign quivalnt ara distribution must match th thortical on to achiv a dsirabl sonic boom signatur. Nxt, thortical quivalnt ara distributions will b combind in svral ways and th corrsponding sonic boom signatur will b obsrvd. Lastly, a schm was dvlopd which prturbs th quivalnt ara distribution. Th ffct of th prturbations on th sonic boom will b xamind. A Snsitivity Study In this study, th thortical and dsign quivalnt ara distributions ar combind in various proportions to xamin th snsitivity of th sonic boom signatur to th quivalnt ara distribution. Th quivalnt ara distributions ar combind such that th thortical quivalnt ara distribution transitions to th dsign quivalnt ara distribution. This ssntially allows th hypothtical situation to b studid whr th dsign quivalnt ara distribution xactly matchs th thortical quivalnt ara distribution up to a spcifid quivalnt lngth, X. In invrs dsign, th goal is to match th dsign quivalnt ara distribution to th thortical quivalnt ara distribution so that th thortical minimizd sonic boom signatur can b achivd. Howvr, as statd bfor, dsign and prformanc constraints may caus a mismatch btwn th dsign and thortical quivalnt ara distributions. Th Dsign quivalnt ara usd in this study rflcts an aircraft that was dsignd by Bill Shilds (Swals Arospac). As can b sn from Figur, thr is not much diffrnc btwn th Dsign and Thortical quivalnt ara distributions. Howvr, th rsulting sonic boom signatur, shown in Figur, indicats that thr is a significant mismatch btwn th Dsign and Thortical sonic boom signaturs. Two cass whr th Dsign and Thortical quivalnt ara distributions ar combind ar shown in Figur to illustrat th snsitivity btwn th sonic boom signatur and th quivalnt ara distribution. For Combind cas, X i =, th quivalnt ara is composd of th Thortical cas up to Xi = and thn transitions to th Dsign quivalnt ara distribution. For th Combind cas, Xi = 9, th quivalnt ara distribution is composd of th thortical on up to = 9 and thn transitions to th Dsign quivalnt ara distribution. Th sonic boom signatur for ach Combind cas can b sn in Figur. Th sonic boom signatur LE

3 for Xi = matchs that of th boom signatur of th Dsign sonic boom signatur. For Xi = 9, it can b sn that thr is rasonabl matching btwn this cas and th Thortical sonic boom signatur. Incrasd matching of th quivalnt ara distributions rsults in incrasd matching of th sonic boom signaturs. Ths rsults may suggst that it may b ncssary to match at last 5% of th dsign quivalnt ara distribution to th thortical quivalnt ara distribution to achiv th dsird minimizd sonic boom signatur. From a dsign aspct, howvr, this is unrasonabl. Howvr, furthr insight may b gaind through obsrvation of th changs in th scond drivativ of th quivalnt ara distribution. Th first and scond drivativs, Figur and Figur 4, rspctivly, of th quivalnt ara distributions wr also xamind. Of particular intrst is th scond drivativ of th quivalnt ara distributions, shown in Figur 4. Th scond drivativ of th Thortical quivalnt ara 6 A Thory Dsign Xi = Xi = Figur Equivalnt ara distributions for Thory, Dsign, and Combind cass (Xi =, Xi = 9). Ovrprssur (psf) Tim (msc) Thory Dsign Xi = Xi = 9 Figur Sonic boom signaturs for quivalnt ara distributions shown in Figur. distribution is zro xcpt at crtain locations. Th locations whr th scond drivativ ar not zro indicat inflctions points in th quivalnt ara distribution. On inflction point of intrst occurs at = 9. Th oscillations in th scond drivativ of th Dsign and Combind cas, Xi =, quivalnt ara distributions occur forward of = 9. This translats to many inflction points in th quivalnt ara distribution. Howvr, th Combind cas, Xi = 9, liminats ths oscillations. Th only dviation in th scond drivativ from th Thortical cas occurs at = 9, whr th quivalnt ara distribution transitions to th Dsign quivalnt ara distribution. Ths rsults suggst that th snsitivity of th sonic boom signatur to th quivalnt ara distribution may b rlatd to scond drivativ oscillations in th quivalnt ara distribution. Ths rsults indicat a corrlation btwn th matching of th dsign and thortical sonic boom signaturs and th oscillations bfor th inflction point of th scond drivativ can b mad. It is suggstd hr that suprsonic aircraft dsigns should minimiz th oscillations in th scond drivativ prior to th inflction point of th thortical quivalnt ara distribution to achiv rasonabl matching of th sonic boom signaturs. A ' A Envlop Analysis A study is conductd hr to invstigat th possibl mthods to gnrat a family of quivalnt ara distributions which ar abl to gnrat sonic Thory Dsign Xi = Xi = 9 Figur First drivativ of quivalnt ara distributions shown in Figur. A'' Thory Dsign Xi = Xi = 9 Figur 4 Scond drivativ of quivalnt ara distributions shown in Figur. LE

4 boom signatur with similar charactristics. As statd bfor, invrs dsign tris to match th dsign quivalnt ara distribution to th thortical on in ordr to achiv a minimizd sonic boom signatur. Although sonic boom signaturs can vary, thy may still shar charactristics such as initial ovrprssur, maximum ovrprssur, and ris tim. Each boom signatur is associatd with a thortical quivalnt ara distribution. Howvr, ach quivalnt ara distribution vary slightly from ach othr. This study will xamin if th quivalnt ara distributions associatd with boom signaturs with similar charactristics can b combind to in various fashions to gnrat boom signaturs with th sam charactristics. Svral thortical sonic boom signatur typs, Ramp, Hybrid, and Flattop, ar shown in Figur 5. Each boom signatur has th sam initial ovrprssur and is gnrally considrd dsirabl sonic boom signaturs. Th corrsponding thortical quivalnt ara distributions ar shown in Figur 6. As can b sn, thr is a small diffrnc btwn th quivalnt ara distributions, but ach on is associatd with a diffrntly shapd sonic boom signatur. During th invrs dsign procss, on of th boom signaturs and quivalnt ara distributions may b chosn as a targt. Howvr, as sn from th prvious study, th boom signatur is snsitiv to changs in scond drivativ of th quivalnt ara distribution. Thus, th qustion is: How can changs in th targt quivalnt ara distribution b mad so that th rsulting boom signatur shars charactristics of th targt boom signatur? For illustrativ purposs, th quivalnt ara distribution and sonic boom signatur of Hybrid4 is chosn hr as th baslin or targt. Th diffrnc in quivalnt ara, A, btwn th othr distributions and th targt is shown in Figur 7. From this figur, th dviation of th quivalnt ara distribution from th targt, Hybrid4, is containd within an nvlop which is largly dfind by th Flattop and Ramp quivalnt ara distributions. In addition, it is notd that thr is a discontinuity in A at approximatly X ~ 9. This discontinuity is th location of th inflction point of th targt quivalnt ara distribution This study will invstigat if this nvlop can b usd to altr th targt quivalnt ara distribution and to gnrat sonic boom signaturs with similar charactristics as that for Hybrid4. Th stimulus for this study is to b abl to achiv modifications in th dsign quivalnt ara distribution so that dsign and mission constraints can b satisfid whil still achiving a dsirabl sonic boom signatur. Th quivalnt ara distributions ar combind in thr ways: ) Linar Avrag, ) Linar Function, and ) Quadratic Function to dtrmin if sonic boom signaturs similar to th targt sonic boom signatur can b achivd. Each mthod will b dscribd and svral tst cass will b shown. Combination of fiv hybrid quivalnt ara distributions will b shown as xampls for ach mthod. Each combination will b labld HiHj whr i and j corrspond to th quivalnt ara of th corrsponding Hybridi and Hybridj boom signatur. For th Linar Avrag mthod, two Hybrid quivalnt ara distributions ar avragd togthr, according to EQ., and th sonic boom signatur is computd using ARAP. Flattop Hybrid.8 Hybrid Hybrid.6 Hybrid4 Hybrid5.4 Hybrid6 Ramp Tim (msc) Figur 5 Ramp, Flattop, and Hybrid boom signaturs 6 Ovrprssur (psf) A Flattop Hybrid Hybrid4 Hybrid6 Hybrid Hybrid Hybrid5 Ramp 5 5 Figur 6 Equivalnt ara distribution for Ramp, Flattop, and Hybrid boom signaturs. A = A-A (Targt) 4 Flattop Hybrid Hybrid Hybrid Hybrid4 Hybrid5 Hybrid6 Ramp Figur 7 Diffrnc in quivalnt ara distribution from Targt. (Targt = Hybrid4) LE 4

5 A ) + [ A( X ) A( X )] = EQ. ( Th diffrnc btwn ach linarly avragd quivalnt ara distribution and th targt quivalnt ara distribution is shown in Figur 8. Th corrsponding sonic boom signatur for ach Hybrid combination is shown in Figur 9. Th rsults indicat modifications to th targt quivalnt ara distribution in this fashion will b abl to gnrat sonic boom signaturs with similar charactristics. For xampl, th linar avrag of th Hybrid and Hybrid quivalnt ara distributions, HH, has an initial ovrprssur qual to th targt boom signatur. Howvr, th maximum ovrprssur of th rsulting sonic boom signatur dcrasd by. psf. Each of th othr combination cass showd boom signaturs with similar charactristics. Th scond drivativ of th quivalnt ara distributions wr also calculatd and ar compard to th targt in Figur. Th rsults show that thr ar small changs in th changs in th scond drivativ compard to th targt. Howvr, th location of th inflction point rmains unchangd. Ths rsults suggst that changs in th quivalnt ara distribution can b mad as long as th scond drivativ rmains smooth and dos not significantly altr th location of th inflction point. For th Linar Function cas, two Hybrid quivalnt ara distributions ar combind using a linar function, P(X ), shown in EQ.. As in th prvious mthod, th quivalnt ara distribution, sonic boom signatur, and th drivativ information ar compard to th targt, Hybrid4. A P( X ) = a + c( X max X ) P ( X ) = {..} X ) = A( X ) P( X ) + A ( X )( P( X )) ( EQ. Th diffrnc btwn th quivalnt ara distributions combind via th linar function and th targt ar shown in Figur. Th corrsponding sonic boom signaturs ar shown in Figur. Ths rsults indicat that combination of two quivalnt ara distributions with dsirabl sonic boom signaturs can b combind using a linar function. As an xampl, th combination of th quivalnt ara distributions for Hybrid and Hybrid, HH, show that significant modifications in th quivalnt ara distribution can rsult in a dsirabl sonic boom signatur. Th rsults indicat that combination of quivalnt ara distributions via this mthod rsults in sonic boom signaturs that ar similar to th targt sonic boom signatur. A = A-A (Targt) Th scond drivativ of th quivalnt ara distributions was also calculatd and is shown in Figur. As in th prvious cas, thr ar not significant changs in th scond drivativ of th quivalnt ara distributions. Th inflction point location rmains largly unchangd. Ths rsults sm to suggst that quivalnt ara distributions, ach with dsirabl sonic boom signaturs, can b combind via a linar function. HH HH5 HH6 HH5 H5H6 Figur 8 Diffrnc of quivalnt ara distribution combind via linar avrag from Targt (Targt = Hybrid4). Ovrprssur (psf).8 H.6 H5 H6.4 H5. H56 Targt Tim (msc) Figur 9 Boom signatur for quivalnt ara distributions combind via linar avrag. (Targt = Hybrid4) A'' H H5 H6 H5 H56 Targt 5 5 Figur Scond drivativ of quivalnt ara distributions combind via linar avrag. (Targt = Hybrid4) LE 5

6 A = A-A (Targt) Figur Scond drivativ of quivalnt ara distributions combind via linar function. (Targt = Hybrid4) Th Quadratic Function cas, two Hybrid quivalnt ara distributions ar combind using a quadratic function, P(X ), shown in EQ.. Th quivalnt ara distribution, sonic boom signatur, and th drivativ information for ach Hybrid combination ar compard to th targt, Hybrid4. Th rsults ar not shown hr but indicat that th rsults ar similar to th prvious mthods. HH HH5 HH6 HH5 H5H6 Figur Diffrnc of quivalnt ara distribution combind via linar function from Targt (Targt = Hybrid4). Ovrprssur (psf).8 H.6 H5 H6.4 H5. H56 Targt Tim (msc) Figur Boom signatur for quivalnt ara distributions combind via linar function. (Targt = Hybrid4) A'' H H5 H6 H5 H56 Targt 5 5 Howvr, it should b notd that non-linar bhavior of th sonic boom signatur is obsrvd. Although this mthod may b usd to gnrat altrnat modifications to th targt quivalnt ara distribution, th boom signatur may not b as dsirabl. A P( X ) = a + cx ( X max X ) P ( X ) = {..} X ) = A( X ) P( X ) + A( X )( P( X )) ( EQ. Th study abov combind quivalnt ara distribution using svral diffrnt mthods: ) Linar Avrag, ) Linar Function, and ) Quadratic Function. Rgardlss of which mthod is usd, thr ar important implications from th rsults. First, this study shows that significant altrations can b mad to th quivalnt ara distribution which rsults in sonic boom signaturs which hav no chang or, in som slct cass, show an improvmnt in th sonic boom ovrprssur. For th most part, ach of th combind quivalnt ara distributions rsultd in boom signaturs with th sam initial ovrprssur. In trms of aircraft dsign, th dsign of th aircraft will not hav to b subjct to matching on particular quivalnt ara distribution. Rcall that sonic boom minimization thory stats that in ordr to achiv a minimizd sonic boom signatur, th thortical quivalnt ara distribution must b matchd. Although this may b tru if on particular sonic boom signatur is dsird, it is not ncssarily tru if th dsirabl boom charactristics, such as initial ovrprssur, maximum ovrprssur, or ris tim, ar th objctiv. Th scond implication of ths rsults is focusd on th mthod of chang in th quivalnt ara distribution. Although ach mthod usd in this study providd diffrnt changs in th quivalnt ara distribution, th scond drivativ of th quivalnt ara distributions ach shar crtain charactristics. Th targt quivalnt ara distribution has an inflction point at approximatly ~9. Th combination of th quivalnt ara distributions prsrvd th location of th inflction point to som dgr. In almost all cass, th location of th inflction point dos not chang. Th location of th inflction point may b critical to th sonic boom signatur. Ths findings may hlp to guid th dsign of th aircraft. According to ths rsults, modifications th aircraft gomtry or lift distribution should b awar of th changs in th scond drivativ of th quivalnt ara distribution, particularly th location of th inflction point. LE 6

7 A Prturbation Study Th snsitivity of th boom signatur to th quivalnt ara distribution is furthr studid hr by introducing prturbations in a thortical quivalnt ara distribution. Th prturbation, shown in Figur 4, is cubic and is distributd ovr a sgmnt of th quivalnt ara distribution. Th schm dvlopd hr adds th prturbation normal to th quivalnt ara distribution to nsur that it rmains smooth. Th mthod dvlopd allows th prturbation to b varid by 4 paramtrs. First, th cntral location of quivalnt lngth, X, can b chosn. This location will obsrv th maximum prturbation. Th rang ovr which th prturbation is distributd, dx, is also allowd to vary. This will allow th prturbation to b localizd or distributd ovr a largr rang of quivalnt lngth. Third, th magnitud of th prturbation, da, is allowd to vary. Lastly, prturbation can incras or dcras th quivalnt ara. Th rsults will show th prturbation in th quivalnt ara distribution, th boom signatur, and th scond drivativ information. Th ffct of ach of ths paramtrs on th sonic boom signatur is studid. Figur 4 Typical prturbation function with first and scond drivativ. Magnitud and rang can b adjustd. First, th cntral location of th prturbation is allowd to vary. Th valus of dx and da wr fixd at and, rspctivly. Th prturbation distributions ar shown in Figur 5. Th rsulting boom signatur and scond drivativ information is shown in Figur 6 and Figur 7, rspctivly. Th location of th prturbation in th A distribution has a dirct ffct on th sonic boom signatur. A prturbation prior to th inflction point in th quivalnt ara distribution will caus a slight spik to occur in th sonic boom signatur. If th prturbation is introducd prior to th inflction point, th maximum ovrprssur will rmain unchangd. If th prturbation is introducd nar th original inflction point such that th inflction point is movd forward, th spik in th sonic boom will hav an ovrprssur which will b gratr than th original maximum ovrprssur. Ths rsults indicat that X ffctivly movs th ffct of th A = A (Hybrid) -A X = X = 4 X = 6 X = 8 X = 5 5 Figur 5 Diffrnc in quivalnt ara distribution from Hybrid for prturbations with varying location. Ovrprssur (psf) Thory X = X = 4 X = 6 X = 8 X = 5 5 Tim (msc) Figur 6 Sonic boom signatur for prturbations with varying location. A'' Thory X = X = 4 X = 6 X = 8 X = 5 5 Figur 7 Scond drivativ of quivalnt ara distributions for prturbations with varying varying location. prturbation on th sonic boom signatur. A corrlation btwn prturbations addd in th quivalnt ara distribution and th location of th LE 7

8 ffct on th sonic boom signatur can b sn. Although th ffct of th prturbations affctd mainly th front of th sonic boom signatur during th ris to a maximum ovrprssur, th movmnt of th prturbation along th quivalnt lngth of th quivalnt ara distribution also movs th ffct on th sonic boom signatur ithr forwards or backwards during this ris in th sonic boom signatur. Nxt, th rang of distribution, dx, is allowd to vary. Th location, X, and th magnitud, da, of th prturbation is hld fixd at valus of 5 and, rspctivly. Th prturbation distributions for dz valus of 5,, and 4 ar shown in Figur 8. Th rsulting boom signatur and scond drivativ information is shown in Figur 9 and Figur, rspctivly. Again, th prturbation is sn to introduc a spik during th ris in th sonic boom signatur, Figur 9. Gnrally, th spik in th sonic boom signatur is mor pronouncd if th prturbation is localizd. As th rang ovr which th prturbation is distributd is incrasd, th spik in th sonic boom signatur will b lss distinguishabl. Th scond drivativ information A = A (Hybrid) -A dx = 5 dx = dx = Figur 8 Diffrnc in quivalnt ara distributions from Hybrid for prturbations with varying rang of distributions. Ovrprssur (psf) Hybrid dx = 5 dx = dx = Tim (msc) Figur 9 Sonic boom signaturs for prturbations with varying rang of distributions. th quivalnt ara distribution, Figur, for ach cas shows that localization of th prturbation gnrats a significant chang in th scond drivativ. This crats a shock wav arlir in th sonic boom signatur. Allowing th prturbation to b distributd ovr a largr quivalnt lngth aids in th mitigation of th spik in th sonic boom signatur. Third, th magnitud, da, of th prturbation was allowd to vary. Th valus of X and dx wr hld constant at 5 and, rspctivly. Th prturbation distributions ar shown in Figur. Th rsulting sonic boom signatur and scond drivativ information ar shown in Figur and Figur, rspctivly. Th spik in th sonic boom signatur, as shown in Figur, incrass as th magnitud of th prturbation incrasd. Th scond drivativ of th quivalnt ara distribution, Figur, indicats that th magnitud of th prturbation affcts th magnitud of oscillations prsnt in th scond drivativ. As statd abov and illustratd furthr in this study, th sonic boom signatur is snsitiv to oscillations in th scond drivativ..4 A'' Hybrid dx = 5 dx = dx = Figur Scond drivativ of quivalnt ara distributions for prturbations with varying rang of distributions. A = A (Hybrid) -A da =. da =. da = 5 5 Figur Diffrnc in quivalnt ara distribution from Hybrid for prturbations with varying magnitud. LE 8

9 Ovrprssur (psf) Hybrid da =. da =. da = 5 5 Tim (msc) Figur Sonic boom signaturs for prturbations with varying magnitud A'' Hybrid da =. da =. da = 5 5 Figur Scond drivativ of quivalnt ara distributions for prturbations with varying magnitud. Th last part of this study xamind diffrnc btwn positiv and ngativ prturbations in th quivalnt ara distribution. Th rsults, not shown hr, indicat an addition or subtraction of ara rsults in a similar ffct on th sonic boom signatur. Th rsults ar somwhat duplicatd for a ngativ prturbation Ths rsults show important insight into how local changs in th quivalnt ara distribution affct th sonic boom signatur. Th majority of th rsults shown indicat that ara can b addd or subtractd from th quivalnt ara distribution which may hav a small or ngligibl chang in th sonic boom signatur. In som particular cass, changs in th quivalnt ara distribution improv th sonic boom signatur. In othrs, th changs typically rsult in an incras in th maximum ovrprssur, but th initial ovrprssur rmains unchangd. Ths rsults ar important in trms of aircraft dsign. Ths rsults indicat that thr may b a larg amount of flxibility in trms of changs to th quivalnt ara distribution. Ths rsults also provid som guidlins, as discussd abov in th rsults, by which changs in th quivalnt ara distribution should b mad to minimiz changs in th sonic boom signatur. Wing Dsign A fasibl concptual suprsonic businss jt (SBJ) must not only b abl to mt sonic boom constraints but also arodynamic constraints. Thus, a study was conductd which modifid th wing cambr surfac of th aircraft by lastic movmnts of 8 dsign or control points. Th modification to th wing cambr surfac includs cambr and twist. Th wing cambr surfac was modifid to optimiz (C l /C d ) whil maintaining a sonic boom initial ovr prssur blow.6 psf. Th mthodology usd is basd on lastic movmnt and partition of unity thory. 9 points on th wing cambr surfac ar dfind as shown in Figur 4. Th wing cambr surfac is normalizd by th wing sction airfoil chord lngth and th wing span lngth. This crats a normalizd wing cambr surfac as shown in Figur 5. Th control points ar dividd into groups: Z i controls th movmnt of th cornrs which ffctivly control th wing twist, and S j controls th movmnt of 5 intrnal points, S Spanwis Dirction Z Chordwis Dirction Figur 4 Wing cambr surfac with control points Z i and S j (i =, j = 5) Z S Z Normalizd Wing Span S4 Z S Z Normalizd Wing Chord Figur 5 Normalizd wing cambr surfac with control points Z i and S j (i =, j = 5) S S S4 S Z Z S5 Z S5 LE 9

10 which modifis th wing cambr. Z is th root wing lading dg and is not movd. Th lastic movmnt of th 8 dsign points is dscribd by EQ. 4 EQ. 6. Equation dscribs th lastic motion of th wing cambr surfac subjct whr g i and f j ar dscribd in EQ. 5 EQ. 6. EQ. 5 and EQ. 6 wr constructd with th intntion of making ach g i and f j qual to on at thir corrsponding locations in th normalizd plan and zro at th othr locations. Th partition of unity thory nsurs that th motion of ach individual location is smoothly distributd throughout th ntir plan. s f 5 = + j j ZNw Zold Zigi ( Z + ) 5 i dzi gi EQ. 4 i= j= i= f j f j= g v, u = u v g ( v, u) = uv g v, u = v u ( ) ( ) ( ) ( ) f ( ) ( v, u = u u ) ( v, u) = 4( u + v )( u + v ) f v u = u, 4 u f v u = v 4, 4 v f ( ) ( 5 v, u = v u ) ( ) ( )( )v ( ) ( )( )u EQ. 5 EQ. 6 A cod was dvlopd and intgratd in th ModlCntr nvironmnt. ModlCntr s Dsign Explorr was usd to dtrmin an optimizd wing cambr surfac to maximiz (C l /C d ). A constraint of P.6 was implmntd. Onc a st of dsigns hav bn xplord via this procss, all dsign cass wr subjct to analysis. First, a st of fasibl dsigns wr dtrmind by implmnting th constraint: (C l /C d ) Dsign (C l /C d ) Orig. From this st of fasibl dsign solutions, two sts of parto optimal solutions wr dtrmind. Th first st of parto optimal solutions, Figur 6, optimizd ovrprssur ( P) vs. (C l /C d ). Th scond st of parto optimal solutions, Figur 7, optimizd max DZ/Z Rang vs. (C l /C d ). DZ is th diffrnc btwn th Z valu of th original and dsign cambr wing surfac at ach location in th spac. Z Rang is th diffrnc btwn th maximum and minimum Z valu in th dsign wing cambr surfac. max DZ/Z Rang is th maximum absolut valu of th ratio of DZ ovr Z Rang for ach dsign wing cambr surfac. This paramtr indicats th amount of chang that has occurrd in th wing cambr surfac. Th intrsction of ths two parto optimal dsign solutions was combind and is shown in Figur. Th total, volum, and lift quivalnt ara distributions for ach of th rsulting dsign solutions Figur 6 Parto optimal dsign solutions comparing P and (C l /C d ). Figur 7 Parto optimal dsign solutions comparing max DZ/Z Rang and (C l /C d ). Figur 8 Total, Volum, and Lift quivalnt ara distributions for ach dsign cas. LE

11 ar shown in Figur 8. Figur 9 and Figur show th boom signatur and chang in total quivalnt ara distribution, rspctivly, associatd with ach dsign cas. Using this mthodology to modify th wing cambr surfac shows that improvmnts can b mad in th arodynamic prformanc of an aircraft Figur 9 Boom signatur for ach dsign cas. with small changs in th wing cambr surfac without significant modifications to th sonic boom signatur. On or svral of ths dsign solutions will thn b slctd. Th slctd gomtry(is) will thn undrgo th boom shaping procss whr th fuslag gomtry will b modifid to improv th sonic boom signatur. This procss has not yt bn compltd but will b so in futur work. Futur Rsarch To furthr invstigat th dvlopmnt of a robust SBJ dsign, an optimization mthod is proposd which will compos of two parts. Th first part, as dscribd abov, will th arodynamic prformanc by altring th wing cambr and twist. This part will also includ optimization of th wing planform dsign givn a st of dsign constraints. Th scond part will optimiz th boom signatur by altring th fuslag shap. If succssful, th mthod could b usd to intgrat arodynamic and boom analysis mthods to gnrat a low-boom and lowdrag suprsonic businss jt. Furthr studis would thn b conductd to invstigat th robustnss of th aircraft oprating undr various flight conditions. Figur A distributions for ach dsign cas. Rfrncs. Whitham, G.B. Th Flow Pattrn of a Suprsonic Projctil. Communications of Pur and Applis Mathmatics. Vol. V. no., August 95, pp Walkdn, F. Th Shock Pattrn of a Wing-Body Combination, Far From th Flight Path. Aronautical Quartrly. Vol. IX. Pt., May 958, pp Jons, L.B. Lowr Bounds For Sonic Bangs. Journal of th Royal Aronautical Socity. Vol. 65. no. 66, Jun 96, pp Sbass, R. and Gorg, A.R. Sonic-Boom Minimization. Journal of th Acoustical Socity of Amrica. Vol. 5. no, pt, Fbruary 97, pp Mack, Robrt J. and Ndlman, Kathy A. Mthodology For Dsigning Aircraft To Low Sonic Boom Constraints. NASA TM Carlson, Harry W., Mach, Robrt J., and Morris, Odll A. A Wind-Tunnl Invstigation Of th Effct Of Body Shap On Sonic-Boom Prssur Distributions. NASA TN D-6. Novmbr McLan, Edward F. Som Nonasymptotic Effcts On th Sonic Boom of Larg Airplans. NASA TN D Jun Dardn, Christin M. Sonic Boom Minimization With Nos-Bluntnss Rlaxation. NASA TP Figur Chang in (C l /C d ) and P as a function of max DZ/Z Rang for ach dsign cas. LE