APPENDIX 2: Design of anard Aircraft Tis appendix is a part of te book General Aviation Aircraft Design: Applied Metods and Procedures by norri Gudundsson, publised by Elsevier, Inc. Te book is available troug various bookstores and online retailers, suc as www.elsevier.co, www.aazon.co, and any oters. Te purpose of te appendices denoted by 1 troug 5 is to provide additional inforation on te design of selected aircraft configurations, beyond wat is possible in te ain part of apter 4, Aircraft onceptual ayout. oe of te inforation is intended for te novice engineer, but oter is advanced and well beyond wat is possible to present in undergraduate design classes. Tis way, te appendices can serve as a refreser aterial for te experienced aircraft designer, wile introducing new aterial to te student. Additionally, any elpful design pilosopies are presented in te text. ince tis appendix is offered online rater tan in te actual book, it is possible to revise it regularly and bot add to te inforation and new types of aircraft. Te following appendices are offered: 1 Design of onventional Aircraft 2 Design of anard Aircraft (tis appendix) 3 Design of eaplanes 4 Design of ailplanes 5 Design of Unusual onfigurations Figure 2-1: A single engine, four-seat Velocity 173 E just before touc-down. (Poto by Pil Radeacer) GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 1 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
2.1 Design of anard onfigurations It as already been stated tat preference explains wy soe aircraft designers (and anufacturers) coose to develop a particular configuration. In oter situations suc partiality is absent and te selection of te configuration actually presents an organizational conflict. However, wile te selection of a particular tail configuration (e.g. conventional, T-tail, etc.) ay pose a callenge, weter to place te orizontal tail in front of or aft of te wing is usually not up for debate. In eiter case, te location of te orizontal tail is indeed of priary iportance and tis calls for a deep understanding of te iplications of its selection. Most frequently, te configuration options consist of a conventional tail-aft, canard, or a tree-surface configuration. Figure 2-2 sows te layout of a typical canard aircraft. Te configuration is unique in appearance and offers soe good properties. Tis appendix discusses various issues tat ust be kept in ind wen designing a canard aircraft. Te canard configuration was discussed in soe detail in ection 11.3.12, anard onfiguration. Tis section picks up were tat discussion left off. Figure 2-2: A sall canard configuration. 2.1.1 Pros and ons of te anard onfiguration Te first question to consider regarding te canard configuration as to do wit stability and control. A orizontal lifting surface placed forward of te ain wing results in a destabilizing pitcing oent, wic would render te veicle unstable were it not for te forward placeent of te G. In fact, te G ust be placed far forward of te aerodynaic center of te Mean Geoetric ord in order to produce a stabilizing oent. Tis renders te aircraft stable, in oter words, yields a < 0. Te callenge for te designer is to deterine te geoetry of te canard, wic includes an airfoil selection, suc tat two conditions are satisfied: (1) te is indeed negative and (2) o is greater tan zero. Te forer is controlled using te G location and te latter using geoetry, canard incidence angle, and airfoil selection. ile downwas generally reduces te stability of a tail-aft aircraft (as it results in a nose-up pitcing oent), it allows te HT to be installed at a uc saller Angle-of-Incidence (AOI) tan possible wit a canard (assuing syetrical airfoils cabered airfoils will be discussed later). onsider a canard featuring a syetrical airfoil (i.e. lo = 0). In order to satisfy condition (2) above (i.e. o > 0) tis airfoil would require a large AOI (or TED elevator deflection) to allow te aircraft to be tried at an AOA tat generates positive. One of te reasons for tis is te liited upwas in front of te ain wing. Tis would old even at odest tatic Margin. Tis predicaent is generally solved by selecting a igly cabered airfoil (wic as lo >> 0) and ig AR planfor sape (wose >> 0). Figure 2-3 igligts te difference in te location of te stick-fixed neutral points of a conventional tail-aft and a canard aircraft. Eac configuration as two icons tat represent te stick-fixed neutral point and G location tat GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 2 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
yields a 0.10 tatic Margin. Note tat adding a fuselage to would destabilize bot configurations and pus all points (neutral and, tus, te G) forward. Figure 2-3: oparing te stick-fixed neutral points and G locations required for a tatic Margin of 0.10 of a conventional tail aft (left) and canard (rigt) configurations. Te neutral points were deterined using potential flow teory. Note te nubers only apply to tis specific geoetry. Finally, since te G is in front of te wing, oving it farter forward bot sortens te balancing tail ar and increases te wing ar. ince te wing lift force is uc greater tan tat of te canard, te G cannot ove too far forward before an uncontrollable nose-pitc down oent is generated. Tis liits te practical G envelope of te configuration. For instance, te twin engine Beec tarsip required a swing-wing style canard to increase its nose pitc-up autority wen deploying flaps. Anoter issue is tat te cord lengt of te canard is usually sall enoug to be subject to Reynolds nuber effects. One of te consequences can be a diinised pitc autority at low airspeeds, wen te sall-cord airfoil is subject to early flow separation tat reduces its lift curve slope. Tis can also lead to noticeable longitudinal tri canges wen flying in precipitation, as is reflected in a caution, placarded in te Pilot s Operating Handbook for te Rutan ong-ez 1. Te caution states tat wen entering visible precipitation, te ong-ez ay experience a significant pitc tri cange, as experienced in te ong-ez prototype (N79RA). It goes on to state tat owners of Rutan s earlier canard aircraft, report eiter nose up or nose down pitc canges. Builders are warned tat eac aircraft ay react differently. It is recoended tat airspeed above 90 knots be aintained in rain as tis allows te aircraft to be tried wit ands off te control stick. In spite of tese sortcoings, any existing canard aircraft are well designed in te view of tis autor, including te Rutan ongez, and te AAI Jetcruzer, te first aircraft to ave been certified in te U under 14 FR Part 23 as spin-resistant. 2.1.2 Modeling te Pitcing Moent for a iple ing-anard yste Figure 2-4 sows a siple ing-anard syste, intended to derive a few longitudinal static stability etods tat are elpful wen sizing a canard configuration aircraft. Te longitudinal static stability of te configuration can be represented using Equation (11-10), repeated ere for convenience: o e e (2-1) GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 3 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
ere: o oefficient of oent at zero AOA ange in coefficient of pitcing oent due to AOA e Elevator autority; cange in coefficient of pitcing oent due to elevator deflection Figure 2-4: ing-anard syste used to derive Equation (2-4). Bot of te above ters can be deterined for tis syste using te following expressions: o V 0 (2-2) oa o A V (2-3) A MG ere: MG = Mean Geoetric ord n = Pysical location of te G at wic = 0; i.e. te stick-fixed neutral point A = Pysical location of te Aerodynaic enter l = Ar between te aerodynaic center of te canard and G l = Ar between te aerodynaic center of te canard and te wing = Reference wing area = Planfor area of te canard V = anard volue l MG l ongitudinal stability contribution of coponents oter tan te wing o A MG o 0 A ing pitcing oent due to airfoil caber 0 A = anard lift coefficient at zero AOA = ongitudinal stability contribution of coponents oter tan te wing = ift curve slope of te canard = ing lift curve slope A GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 4 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
Note tat te ter A refers to te stabilizing effects of coponents suc as te fuselage, nacelles, landing gear, te wing itself, and so on, as a function of te AOA. If te su of tese oents acts to rotate te E down, ten M 0 (as a negative sign and is stabilizing). If it acts to rotate E up, ten M 0 (as a positive A sign and is destabilizing). Te sign ultiately depends on te aircraft configuration. Note tat te destabilizing effects of fuselages and nacelles can be estiated using te so-called Munk-Multopp etod, wic is presented in Appendix 1.6, Additional Tools for Tail izing. DERIVATION: It is iperative to keep te orientation of te M A in ind for te following derivation. Also note tat te subscript refers to te canard, but it contrasts HT in te derivation for Equation (11-26). Also, by default, it is assued tat te elevator deflection is neutral, i.e. e = 0. First, deterine te su of oents about te G. For static stability, tis ust equal zero. Taking nose down oents to be negative and treating all distances as aving a positive value (altoug if te G in Figure 2-4 is to te rigt of te E, ten < 0), tis requires: l M 0 M 0 (i) G Note tat te sign for M A ere is +. Terefore, if M A is stabilizing ( 0, were. stands for te absolute value. Te definitions of wing lift is oents, below: M A q MG q q A MG A A A, te lift of te canard is A A M M M ) we will get A A q, and additional. Insert tese into Equation (i) and divide troug by q MG, as sown A q l l MG V q ere V is te canard volue. Note tat it depends on te G location troug l. Tis can also be represented in ters of te fixed distance between te two lifting surfaces, l, as sown in te text above. Next, insert te definitions for and : A MG 0 A 0 A V 0 MG 0 0 A (ii) Note tat unlike te derivation for Equation (11-26), te canard will not be presued to feature a syetrical airfoil. Tis is necessitated by te fact tat canards typically feature igly cabered airfoils to ensure te zeroalpa lift coefficient is not zero; i.e 0. Also note tat since te canard sits in te wing upwas, its AOA is 0 increased sligtly. However, tis effect can be ignored if te canard is relatively far aead of te wing, as is usually te case. Terefore, it is assued tat te AOA of te canard is equal to tat of te wing. In oter words: =. Next, expand Equation (ii): GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 5 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
et A MG A o 0 MG A 0 V V 0 A MG and recall tat A contributions tat do and do not cange wit te AOA: oa A. Insert tese and siplify by gatering A V 0 o A o V A MG ontributi on tat does not cange wit AOA ontributi on tat canges wit AOA Te contribution tat does not cange wit AOA (constant ters) are typically denoted by o, wereas contribution tat canges wit AOA is denoted by. Tis convention is aintained ere as well. QED EXAMPE 2-1: Estiate te o and for te canard configuration in Figure 2-3 and plot for AOAs ranging fro -5 to 20, using te following data. Note te Angle-of-Incidence (AOI) for te wing and canard. MAIN ING ANARD OTHER MG = 2.0 ft b = 20.0 ft = 40 ft² = 1.0 ft b = 6.0 ft = 6.0 ft² (syetrical airfoil) 0.35 0 AOI = 0 = 5.012 per radian 0 0.0 AOI = 0 = 4.247 per radian A = 0.25 MG = 0.5 ft = 0.783 ft (aead of wing E) l = 8.25 A = 6.967 ft 0 0A 0 Assue te wing airfoil is NAA 4415, wic was also te subject of Exaple 11-1, and tat te canard as a syetrical airfoil. Note tat te lift curve slopes were calculated using Equation (9-57). Assue tat te 3- diensional OUTION: 0 is te sae as tat of te airfoil. l 6.0 6.967 40 2.0 Begin by calculating te canard volue: V 0. 5225 MG l for te NAA 4415 fro Table 8-5 is 0.106 per degree or 6.073 per radian. l for a typical syetrical airfoil is 0.100 per degree or 5.730 per radian. Assuing low subsonic airspeed (M 0) and using Equation (9-57) to estiate te 3D lift curve slope of te wing (AR = 10) and canard (AR = 6), yields a 5. 012 and 4.247, respectively. Te 0 A can be estiated using Equation (9-61) and data fro Table 8-5, were te Z = -4 for te NAA 4415 airfoil. Terefore, 4 5.012 0. 350 Ten calculate o 0.5 0.783 A MG 0. 0 Z 180 0.35 0.2245 0 2.0 0 GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 6 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
By plugging and cugging Equations (2-2) and (2-3) we get: o V 0.5225 0 0 0.2245 0.2245 0 o A o A V A MG 0.5 0.783 0.5225 4.247 0 5.012 0.9961 per 2.0 radian Te resulting grap can be seen in Figure 2-5. It sows tat te above prediction places te pitcing oent curve below te orizontal axis for AOAs > 0. Tis eans tat in tis configuration (i.e. featuring a syetrical canard airfoil at an AOI = 0 ), te airplane cannot be tried at an AOA tat generates a positive lift coefficient. To fix tis, an additional positive pitcing oent ust be generated. For instance, if we wanted to tri te aircraft at an AOA of 10, te o ust by sifted up by a agnitude of 0.398, or to o = +0.174. Tis additional oent is typically provided by playing wit te variables of Equation (2-2). Tis is discussed furter in ection 2.1.4, Requireents for te Triability of te anard. Figure 2-5: Te pitcing oent coefficient calculated for te arbitrary value of = 0.783 ft (solid curve). Te dased curve represents ow te solid curve ust be sifted to allow te veicle to be tried at a = 10. Te upward sift can be accoplised by deflecting te elevator TED or using a cabered airfoil (or a cobination tereof). 2.1.3 Te tick-fixed and tick-free Neutral Points of a anard onfiguration iilar to Equation (11-26) of ection 11.2.6, Te tick-fixed and tick-free Neutral Points, te stick-fixed neutral point for a canard configuration can be obtained fro Equation (2-3) wen te slope of te oent curve becoes zero, i.e. = 0: GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 7 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 8 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser. A MG A MG A MG n l (2-4) Note tat Equation (2-4) returns a value tat is easured fro te leading edge of te MG forward toward te canard (as sown in Figure 2-4). ee Exaple 2-2 for ore details. Refer to Figure 2-4 for pysical diensions. DERIVATION: Equation (2-3), repeated below for convenience, is te slope of te pitcing oent curve: A MG A V (2-3) Note tat V is a function of, were te distance between te two lifting surfaces at all ties is constant, l, as sown in Figure 2-4, and is given by: A A l l l l (i) Te neutral point, by definition, occurs wen = 0, i.e.: 0 A MG A MG A l (ii) Tis depends priarily on te location of te G, denoted by. By renaing te G location as n and expanding Equation (ii) and dividing troug by te lift curve slope of te wing leads to: 0 MG n MG A MG n MG A l A (iii) Ten, solve Equation (iii) for n to deterine te stick-fixed neutral point as a fraction of te MG: MG A MG A MG n l A (iv) Apply soe siple algebraic aerobatics to yield: A MG A MG A MG n l QED EXAMPE 2-2: Deterine te stick-fixed neutral point of te canard of Exaple 2-1 (and Figure 2-3), using te sae data presented in tat exaple.
OUTION: By plugging and cugging Equation (2-4) we get: n MG l MG A 8.25 0.5 0.5 6 4.247 400 5.012 2.0 2.0 0.2152 405.012 6 4.247 A A MG Tis places te stick-fixed neutral point soe 0.2152 x 2.0 ft = 0.430 ft aead of te leading edge of te MG. Note tat if n < 0, ten te neutral point is aft of (to te rigt of te E in Figure 2-4). 2.1.4 izing te anard based on Requireents for te Triability One of te ost iportant tasks in canard design is te sizing of te canard itself. Tis involves selecting an airfoil for it and deterining a suitable geoetry (span, cord, and tail ar) and AOI tat allows te airplane can be tried at soe desired airspeed, typically cruising speed, wit te elevator in trail (i.e. e = 0 ). To ake tis possible, we ave to resort to te longitudinal stability teory derived in Equations (2-1), (2-2), and (2-3). Tis is done below. Note tat te sizing etod sould also be used wile considering oter conditions; for instance balked landing at forward G. Ten te tail geoetry tat satisfies all te fligt conditions considered sould be selected. Figure 2-6 sows a standard versus curve, ere representing a canard configuration aircraft. Effectively, it is a cleaner version of Figure 2-5. If te canard airfoil is syetrical and, assuing neutral elevator deflection, te curve tends to be in a location below te orizontal axis, as indicated by te dased curve. Tis was illustrated in Exaple 2-1. In order to tri te configuration at soe desired AOA (denoted by tri ) and given a longitudinal stability derivative,, we want to size te canard so it generates enoug lift to sift te pitcing oent curve to te point o, allowing it to be tried at a positive AOA. Tis, as we recall fro ection 11.2.1, Fundaentals of tatic ongitudinal tability, is necessary so te airplane can be tried at an AOA tat results in a lift force vector tat points in te opposite direction fro te weigt vector. It is a fundaental requireent for static stability. To solve te issue wit te low sitting curve, we ave to look at Equation (2-2), wic wen cobined wit te elevator contribution can be written in te for sown below: o l o e A e 0 0 MG MG e e (2-5) Te proble is coplicated by te fact tat playing around wit te variables ay cange te slope of te pitcing oent curve as well. Tis is given by Equation (2-3), repeated below: Te possible solution approaces are listed below: l A (2-3) A MG MG GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 9 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
0 A (1) ongitudinal stability contribution of coponents oter tan te wing. Tis eans fuselage, nacelles, landing gear, and oters. Tis contribution is not easily estiated unless te designer knows te geoetry well in advance. It ay well place te o lower or iger and, tus, it is necessary to estiate tis contribution before te canard is sized. However, wile te contribution ay elp, it sould not be considered a possible solution. (2) o 0 A ing pitcing oent due to wing airfoil caber. Due to te location of te G forward of te aerodynaic center and te negative sign in front of te ratio in Equation (2-3), tis can only increase o if a reflexed airfoil (i.e. one wose caber is negative) is featured. Tis does not elp wit te sizing of te canard, altoug soe reedy is to be ad by selecting a ain wing airfoil tat does not ave a large positive caber (of course as long as te lift capability of te aircraft is not coproised. Figure 2-6: A pitcing oent for a stable canard wit a syetrical canard airfoil, ounted at a zero AOI, as a function of AOA l (3) V anard volue. Tere are a nuber of options provided ere, altoug tese deand a MG cabered airfoil or an AOI greater tan zero to be used in te canard design (as tis results in a 0 ). Tis 0 way, te designer can increase te canard ar ( l ) or planfor area ( ). Playing around wit te product MG is also possible, albeit arder, as tis will affect te total lift of te aircraft. 0 (4) anard lift coefficient at zero AOA. Tis gives te designer two additional tricks up te sleeve; airfoil caber and AOI. Recall tat tis is te lift coefficient of te canard at zero AOA and tis contribution can be adjusted using a cobination of te zero-aoa lift of te airfoil and te canard s AOI. (5) e e is te contribution of te elevator deflection. Te designer sould use tis paraeter dependent on 12 a particular fligt condition. For instance, for balked landing case tis could be e (TED). en evaluating te canard size for te design ission weigt and G-location, ten te elevator sould be in trail (i.e. e 0 ). Tis contribution is used to accoodate off-design fligt and weigt. Reeber tat no fligt condition sould lead to te pilot running out of elevator deflection. (6) anard lift curve slope. By increasing te lift curve slope of te canard (i.e. increasing its AR), te designer can reduce stability (destabilize te aircraft), i.e. ake sallower. Tis, in turn, requires less o to be establised. For tis reason, te AR becoes an iportant design paraeter. EXAMPE 2-3: Assue te canard of Exaple 2-1 (and Figure 2-3) is to be operated at a cruise condition tat calls for a tri AOA of 5 wit te G located at te previous position ( = 0.783 ft). Evaluate te following: (a) Te canard ar, l, given te airplanes fixed initial planfor area of 6 ft² and, GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 10 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
(b) Te planfor area,, given te airplanes fixed initial canard ar (l ) of 8.25 ft tat will allow for tis, by assuing airfoils tat ave a 0 of 0.1, 0.2, 0.3, and 0.4. Note tat tese factors will cange te as well, so include tis effect as well. OUTION: Tis proble can be tackled by plotting te coplete curves wile olding all but te cited variables constant. (a) First consider ow canging te canard ar will affect te pitcing oent curve, as te initial planfor area of 6 ft² is eld constant. Te resulting trends are sown in Figure 2-7. It sows tat, for canard airfoils tat result in 0 ranging fro 0.1 to 0.4, te required canard ar, l, ranges fro about 9 ft to 14.75 ft. A saple calculation at = 5 for l 2 ft and 0. 4 0 is sown below: o l 0.4 0. 1966 o 0A 0 MG MG A MG l 0.5 0.783 5.15 2. 626 6 2 0 4.52 2.0 40 2.0 o 0.513 62 0 2.0 2.0 40 A MG 180 0. 4258 0.1966 2.6265 (b) Ten, te effect of canging te canard planfor area wile olding te initial canard ar of 8.25 ft constant is sown in Figure 2-8. It sows for te sae canard airfoils tat te required canard planfor area,, ranges fro about 9 ft to 14.75 ft. It indicates tat for te given ar of 8.25 ft, a saple calculation at = 5 for l 2 ft and 0. 4 0 is sown below: 0 in excess of 0.2 is required. A o l 0.513 62 0 2.0 2.0 40 0.4 0. 1966 o 0A 0 MG MG A MG l MG A 0.5 0.783 5.15 2. 626 6 2 0 4.52 2.0 40 2.0 0.1966 2.6265 180 0. o 4258 GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 11 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
Figure 2-7: Te pitcing oent coefficient plotted in ters of te canard ar, constant = 6 ft², and considering four airfoil options. Tis reveals tat te exaple aircraft will need a igly cabered airfoil if te goal is to keep te lengt of te fuselage down. Note tat M = 0.10 and = 5. Figure 2-8: Te pitcing oent coefficient plotted in ters of te canard planfor area, constant l = 8.25 ft, and considering four airfoil options. Tis reveals tat te exaple aircraft will also need a igly cabered airfoil to keep te size of te canard down. Note tat M = 0.10 and = 5. GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 12 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
2.1.5 Acieving tall Proofing in a anard Designing stall-proofing is a callenge and ust be done wit utost care. It can be solved using a cobination of specially selected airfoils, AR, AOI, and even sweep and Taper Ratio. tall proofing requires te stall AOA of te canard to be lower tan tat of te wing. Following are iportant effects to keep in ind: (1) Te canard airfoil sould ave gentle stall caracteristics to avoid too abrupt a nose drop. Tis can be acieved using a igly cabered airfoil. Te preceding discussion sows tat igly cabered airfoils ave a side-benefit in its iger zero AOA lift coefficient, required to allow te veicle to be tried at te ission design airspeed wit zero elevator deflection. (2) Te agnitude of te AR affects te AOA of stall. A large AR reduces te AOA of stall, wile a sall AR does te opposite. Anoter benefit of te ig AR is a steeper lift curve slope tat produces iger lift at a given AOA. Tis allows for a saller canard tan oterwise and an installation at a lower AOI. (3) Hig AR results in a sort cord wit a low Re. Tis ay result in undesirable caracteristics at low speeds, suc as te foration of a lainar separation bubble (or a spanwise vortex) along te surface tat ay yield detriental stall caracteristics. Hig AR canards are also sensitive to surface containation; for a sall corded airfoil, a squised bug is akin to a ountain on a plain. Even precipitation will affect its caracteristics. Bot te VariEze and ongez ave a reputation of nose-drop wen flying in precipitation, as pointed out in ection 2.1.1, Pros and ons of te anard onfiguration. Additionally, using experiental data, Yip 2 deonstrates tat te lift curve of te canard is greatly affected by Reynolds nubers. (4) AOI can be used to furter fine tune te AOA at wic te canard begins to stall. Tis is deonstrated in Reference 2. (5) weepback will odify te lift curve slope in a siilar anner as a reduction in AR. However, it will also tip load te canard and lower its stall AOA. A siilar effect is acieved wit a ig taper. Bot are possible tools to control te stall (and lift) caracteristics, altoug te designer sould keep in ind tat ost of te successful canard aircraft ave straigt constant cord canards. 2.1.6 Rutan VariEze in te ind Tunnel In 1985 NAA released Tecnical Paper 23822, wic presented te results of a wind-tunnel test conducted on a full scale Rutan Varieze. Te airplane was tested in te now leveled 30x60 foot angley Full cale Tunnel (FT) in angley, Virginia (see Figure 2-9). Te paper provides te designer wit a wealt of knowledge on wat actually takes place on a canard as its AOA increases. If you are designing a new canard you would be well adviced to failiarize yourself wit its content. Te paper reveals te secret beind te stall caracteristics of canards. onsider Figure 2-10, wic sows te lift curve for te VariEze. Te left grap sows te lift curve for te coplete airplane and te canard, wile te rigt one sows te lift of te canard only. Bot lift curves are based on te wing area of te aircraft, wic is 53.6 ft². Tis explains wy te lift curve for te canard in te left grap appears so uc lower tan tat of te ain wing. Tis is reedied in te rigt grap, wic effectively zoos in on te lift curve for te canard only. Te left grap of Figure 2-10 sows te ain wing stalls at = 23.5. However, te lift curve for te canard in te rigt grap sows its is sarply reduced at = 13.5. Adering to NAA s definition of stall as te first peak in te lift curve, te canard is tecnically not stalled (even toug it is called so in te reference). Rater it eventually stalls at = 23.5, te sae as te wing! Te cange in slope is ost likely caused by a sudden flow separation along te trailing edge of te igly cabered airfoil, wic operates at a relatively low Reynolds Nuber. It is tis beavior of te GU25-5(11)8 airfoil used for te canard tat as a lot to do wit te gentle stall caracteristics of te airplane. A coparatively abrupt stall of te typical airfoil would likely cause te airplane to drop its nose far ore aggressively. ater odels of te VariEze were equipped wit a cuff or a leading edge extension on te outboard portion of te swept aft ain wings, installed to iprove te airplane s roll stability at stall. GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 13 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
Figure 2-9: An iage fro Reference 2, sowing te Rutan VariEze ounted in te wind tunnel at te FT. Figure 2-10: Te lift curves for te entire aircraft and te canard. Te rigt grap sows te lift curve of te canard in detail. (Reproduced fro Reference 2) Now consider Figure 2-11. Te pitcing oent is plotted as a function of te AOA wit and witout a wing cuff. Te dased vertical lines denotes = 13.5, wic is were te canard s lift curve slope canges suddenly, and = 23.5, were te ain wing stalls. Te cange in te slope of te pitcing oent curve ( ) becoes even ore negative at te forer AOA, due to te reduced growt in te stabilizing force of te canard. Tis elps to force te nose down, preventing te aircraft s ain wing fro stalling. ince te slope of te canard s lift curve is GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 14 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
reduced, rater tan becoing negative for te AOA range fro 13.5 to 23.5, te result is a gentle nose drop, te reason for te airplane s renowned stall recovery caracteristics. Te designer of canards sould be aware of tese effects, and carefully consider airfoils wit aerodynaic properties siilar to tat of te GU25-5(11)8 airfoil used for te VariEze. Te relatively low operational Reynolds Nuber of canard airfoils ust also be considered, as tis will influence te stall caracteristics of te canard. Figure 2-11: Te pitcing oent for te Rutan Varieze wit and witout leading edge droops (cuffs). (Reproduced fro Reference 2) 2.1.7 onfiguration oparison A coon clai aong laypeople olds tat te canard configuration is superior to te tail-aft configuration. Tey point at te Rutan ongez, a truly efficient aircraft, and copare it to oter less efficient airplanes failiar to te, suc as a essna 152 or Piper PA-38 Toaawk. Te astute ask ten, if tis is true, ten wy are tere not ore canard configurations around? For instance, wy aren t ost sailplanes of a canard configuration? Te fact is tat any suc coparison ust be done on a level playing field. Te ongez is not ore efficient tan te 152 or PA-38 because it is a canard, but rater because of te ission of te airplane. Te ongez is not a priary trainer like te oter two, but a touring aircraft. In fact, its take-off and landing caracteristics (ig speed) ake it all but unfit as a priary trainer, not to ention it is unsuitable for gravel runways. Additionally, tere is difference in wing area (ongez as 82 ft², essna 152 as 160 ft² and PA-38 as 125 ft²) and gross weigt (ongez is 1325 lb f, essna 152 and PA-38 are 1670 lb f ), altoug power is siilar (ongez as 115 BHP, essna 152 as 110 BHP and PA-38 as 112 BHP). Te coparison is tus unfair and witout a foundation. Tis section is intended to inspire te designer to conduct realistic apples-to-apples coparison on te candidate configurations. One etod is to copare a basic tail-aft configuration (onfiguration A) to a basic canard configuration (onfiguration B), for instance using potential flow teory. Tis approac is ipleented below. Bot configurations (see Figure 2-12) ave te sae wing and stabilizing surface geoetry (including elevators), te only difference is tat onfiguration A as te HT aft of te wing and B aead of te wing. Bot tail ars are equally long (8.25 ft). For siplicity tere is no provision ade for a fuselage. Bot ave te G at position suc te tatic Margin (M) is 0.1 and bot are assued to weig 400 lb f. Te wing airfoil is NAA 4415 and te stabilizing surface as a syetrical airfoil, wic as sown earlier is probleatic for a canard configuration. GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 15 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
Here, consider te following scenario. If bot configurations are tried at 100 KA at -, te following questions are of interest: (1) at is te difference in AOA and elevator angle to tri ( e ) at a given airspeed? (2) ic configuration generates iger lift-induced drag at tat airspeed? Te answer to tese questions is key in understanding te difference between te two configurations. And tis calls for ore powerful tools tan classical analysis ere potential flow odeling will be used. Tis iproves accuracy as it subjects bot configurations to a reasonably accurate distortion of te flow field and tis is fundaental to teir capabilities. Figure 2-12: Te two V odels. Te conventional configuration is to te left and canard to te rigt. Te code used ere is a coercially available code called URFAE and it uses te Vortex-attice Metod (VM). Te reader can download free VM solvers like Mark Drela s AV and perfor a siilar analysis. However, all talk of potential flow teory sould spur questions of validation: How accurate is it wen copared to experient? To address tis question a detailed odel of te VariEze was prepared, using te geoetry presented in Reference 2. Tis is addressed in Figure 2-13, wic sows a VM odel used to evaluate prediction potential and ow its lift and longitudinal stability predictions copare to tat of te experient. Note tat deviations fro te straigt line predictions of te VM code are due to various viscous effects not being odeled by suc progras. It can be seen tat at least for tis odel, tere is a good agreeent between teory and experient in te linear region. Figure 2-13: oparing lift and pitcing oent of a validation odel to experient. In order to keep te coplexity of te odels to a iniu, bot wings are constant cord and straigt (see Figure 2-12). Te two odels do not feature vertical stabilizers, as te purpose is only to copare teir lifting and GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 16 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
longitudinal stability properties. Additionally, since te purpose of tis appendix is to qualitatively copare properties rater tan deonstrate ow tese were deterined (wic would require considerably larger space) tese are oitted. Instead, te basic geoetry is provided for te interested reader wo ay want to construct own odels for coparison. Differences in ift, Drag, and ongitudinal tability Te properties of te two configurations in Figure 2-12 are sown in Table 2-1 and Figure 2-14 and Figure 2-15. Recall tat bot configurations weig 400 lb f and are tried at 100 KA at -. Te table reveals a nuber of very interesting differences. (1) Te lift-induced drag of te two configurations was predicted using Prandtl-Betz integration on te Trefftz plane. Te results indicate tis drag is less for te canard configuration tan te tail-aft configuration over a range of airspeeds between 40 and 85 KA, but actually greater at iger airspeeds. Te variation ranged fro 14 drag counts at low airspeeds to -10 at ig airspeeds. Naturally, tese are teoretical predictions and tey ay be off. However, tey igligt tat te efficiency of a particular configuration is indeed ission related. (2) Te canard requires lower AOA to generate te sae lift as te tail-aft configuration (-1.09 versus - 0.39 ) at te 100 KA airspeed (see Table 2-1). Tis eans tat te canard is also at a lower AOA and calls for a larger elevator deflection tan oterwise. Figure 2-14: oparing lift-induced drag of te conventional and canard configurations. (3) Note te position of te neutral points sown in Table 2-1. Tese will bot ove forward wit te introduction of a fuselage. (4) Te elevator deflection required to balance te canard configuration is substantially greater tan tat of te tail-aft configuration, or 10.99 versus 1.24. Recall tat te canard is te subject of Exaples 2-1 troug 2-3. Te tail conventional configuration is located in te downwas fro te ain wing, so its angle of attack is iger tan indicated by te incidence angle. onsequently, it requires less elevator deflection to balance te airplane. Te canard, on te oter and, is in a odest upwas. It as to ake up for te deficiency by te extra deflection. Again, tis igligts wy igly cabered airfoils ave to be considered for te canard. Figure 2-15: oparing AOA and elevator deflection required to tri te conventional and canard configurations at te given airspeed. GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 17 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
Table 2-1: Properties of te Two Models Property Description onventional anard ing span 20 ft 20 ft ing cord, root 2 ft 2 ft ing cord, tip 2 ft 2 ft ing Aspect Ratio 10 10 ing airfoil NAA 4415 NAA 4415 Angle of incidence 0 0 HT span 6 ft 6 ft HT cord, root 1 ft 1 ft HT cord, tip 1 ft 1 ft HT Aspect Ratio 6 6 HT airfoil yetrical yetrical Tail ar 8.25 ft -8.25 ft Elevator cord fraction 33% 33% Angle of incidence 0 0 eigt 400 lb f 400 lb f G-location at 10% static argin 1.239 ft -0.783 ft Airspeed (100 KA) 168.8 ft/s 168.8 ft/s Neutral point Absolute 1.239 ft -0.583 ft Neutral point - %MG 61.95% -29.15% AOA to tri at 100 KA at - -0.39-1.09 e to tri at 100 KA at - 1.24 (TED) 10.99 (TED) ift coefficient 0.295 0.295 ift-induced drag coefficient 0.00236 0.00324 Differences in Distribution of ection ift oefficients on ing and tabilizer Figure 2-16 sows te distribution of te lift on te ain wings of eac configuration. Tried at 100 KA, te axiu section lift coefficient on te conventional configuration is 0.331 in te plane of syetry (typical for a constant cord or Hersey bar wing), and 0.333 for te canard. Note te drop in section lift coefficients over te iddle of te ain wing of te canard configuration, caused by te downwas fro te canard. For tis reason, te AOA of te canard configuration is always (sligtly) iger tan if tis effect was absent. Figure 2-16: Distribution of section lift coefficients on te wing. GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 18 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
Te distribution of te section lift coefficients is also of great iportance. Te axiu section lift coefficient on te HT is -0.041 and +0.539 on te canard at te sae condition (tried at 100 KA). Tis sows tat te canard ust be loaded uc ore severely in order to generate a balancing force tan te HT. Table 2-2 sows te difference in lift generated by te wing and te stabilizing surfaces. Note tat te lift coefficient for te HT and canard are based on te reference wing area. Figure 2-17: Distribution of section lift coefficients on te stabilizing surfaces. Table 2-2: ift Generated by te Two Models Property Description onventional anard generated by ain wing 0.3009 0.2228 generated by orizontal tail -0.0055 0.0726 ift coefficient, total 0.2954 0.2954 Te analysis sows tat te ain wing of te conventional configuration ust generate lift in excess of wat is required for level fligt. Tis is caused by te orizontal tail aving to generate balancing lift tat points downward and te ain wing ust carry tis force in addition to te weigt. Te agnitude of tis additional lift increases as te G oves forward. Generally, as a rule-of-tub, te larger te HT load te iger is te AOA required for te configuration and, terefore, te iger te lift-induced drag. Te opposite olds for te canard configuration. Te ain wing of te canard configuration generates less lift tan te conventional configuration and te agnitude of te balancing force generated by te canard is larger tan tat of te HT and it points in te opposite direction and, terefore, contributes indeed to te total lift. Te botto line is tat te designer of efficient airplanes sould attept a careful study of proposed configurations and te ission design conditions in order to justify as particular geoetry and configuration. ile it is possible tat one configuration leads to a ore efficient aircraft tan anoter one, tis is does not constitute a rule-of-tub. GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 19 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.
REFERENE 1 Rutan Aircraft Factory, ong-ez Owner s Manual, 2 nd Ed., October 1981. 2 NAA TP-2382, ind-tunnel Investigation of a Full-cale anard-onfigured General Aviation Airplane, Yip, ong P., 1985. GUDMUNDON GENERA AVIATION AIRRAFT DEIGN APPENDIX 2 DEIGN OF ANARD AIRRAFT 20 2013 Elsevier, Inc. Tis aterial ay not be copied or distributed witout perission fro te Publiser.