APPENDIX C2: Design of Canard Aircraft This appendix is a part of the book General Aviation Aircraft Design: Applied Methods and Procedures by Snorri Gudmundsson, published by Elsevier, Inc. The book is available through various bookstores and online retailers, such as www.elsevier.com, www.amazon.com, and many others. The purpose of the appendices denoted by C1 through C5 is to provide additional information on the design of selected aircraft configurations, beyond what is possible in the main part of Chapter 4, Aircraft Conceptual Layout. Some of the information is intended for the novice engineer, but other is advanced and well beyond what is possible to present in undergraduate design classes. This way, the appendices can serve as a refresher material for the experienced aircraft designer, while introducing new material to the student. Additionally, many helpful design philosophies are presented in the text. Since this appendix is offered online rather than in the actual book, it is possible to revise it regularly and both add to the information and new types of aircraft. The following appendices are offered: C1 – Design of Conventional Aircraft C2 – Design of Canard Aircraft (this appendix) C3 – Design of Seaplanes C4 – Design of Sailplanes C5 – Design of Unusual Configurations Figure C2-1: A single engine, four-seat Velocity 173 SE just before touch-down. (Photo by Phil Rademacher) GUDMUNDSSON – GENERAL AVIATION AIRCRAFT DESIGN APPENDIX C2 – DESIGN OF CANARD AIRCRAFT 1 ©2013 Elsevier, Inc. This material may not be copied or distributed without permission from the Publisher. C2.1 Design of Canard Configurations It has already been stated that preference explains why some aircraft designers (and manufacturers) choose to develop a particular configuration. In other situations such partiality is absent and the selection of the configuration actually presents an organizational conflict. However, while the selection of a particular tail configuration (e.g. conventional, T-tail, etc.) may pose a challenge, whether to place the horizontal tail in front of or aft of the wing is usually not up for debate. In either case, the location of the horizontal tail is indeed of primary importance and this calls for a deep understanding of the implications of its selection. Most frequently, the configuration options consist of a conventional tail-aft, canard, or a three-surface configuration. Figure C2-2 shows the layout of a typical canard aircraft. The configuration is unique in appearance and offers some good properties. This appendix discusses various issues that must be kept in mind when designing a canard aircraft. The canard configuration was discussed in some detail in Section 11.3.12, Canard Configuration. This section picks up where that discussion left off. Figure C2-2: A small canard configuration. C2.1.1 Pros and Cons of the Canard Configuration The first question to consider regarding the canard configuration has to do with stability and control. A horizontal lifting surface placed forward of the main wing results in a destabilizing pitching moment, which would render the vehicle unstable were it not for the forward placement of the CG. In fact, the CG must be placed far forward of the aerodynamic center of the Mean Geometric Chord in order to produce a stabilizing moment. This renders the aircraft stable, in other words, yields a Cm < 0. The challenge for the designer is to determine the geometry of the canard, which includes an airfoil selection, such that two conditions are satisfied: (1) the Cm is indeed negative and (2) Cmo is greater than zero. The former is controlled using the CG location and the latter using geometry, canard incidence angle, and airfoil selection. While downwash generally reduces the stability of a tail-aft aircraft (as it results in a nose-up pitching moment), it allows the HT to be installed at a much smaller Angle-of-Incidence (AOI) than possible with a canard (assuming symmetrical airfoils – cambered airfoils will be discussed later). Consider a canard featuring a symmetrical airfoil (i.e. Clo = 0). In order to satisfy condition (2) above (i.e. Cmo > 0) this airfoil would require a large AOI (or TED elevator deflection) to allow the aircraft to be trimmed at an AOA that generates positive CL. One of the reasons for this is the limited upwash in front of the main wing. This would hold even at modest Static Margin. This predicament is generally solved by selecting a highly cambered airfoil (which has Clo >> 0) and high AR planform shape (whose CL >> 0). Figure C2-3 highlights the difference in the location of the stick-fixed neutral points of a conventional tail-aft and a canard aircraft. Each configuration has two icons that represent the stick-fixed neutral point and CG location that GUDMUNDSSON – GENERAL AVIATION AIRCRAFT DESIGN APPENDIX C2 – DESIGN OF CANARD AIRCRAFT 2 ©2013 Elsevier, Inc. This material may not be copied or distributed without permission from the Publisher. yields a 0.10 Static Margin. Note that adding a fuselage to would destabilize both configurations and push all points (neutral and, thus, the CG) forward. Figure C2-3: Comparing the stick-fixed neutral points and CG locations required for a Static Margin of 0.10 of a conventional tail aft (left) and canard (right) configurations. The neutral points were determined using potential flow theory. Note the numbers only apply to this specific geometry. Finally, since the CG is in front of the wing, moving it farther forward both shortens the balancing tail arm and increases the wing arm. Since the wing lift force is much greater than that of the canard, the CG cannot move too far forward before an uncontrollable nose-pitch down moment is generated. This limits the practical CG envelope of the configuration. For instance, the twin engine Beech Starship required a swing-wing style canard to increase its nose pitch-up authority when deploying flaps. Another issue is that the chord length of the canard is usually small enough to be subject to Reynolds number effects. One of the consequences can be a diminished pitch authority at low airspeeds, when the small-chord airfoil is subject to early flow separation that reduces its lift curve slope. This can also lead to noticeable longitudinal trim changes when flying in precipitation, as is reflected in a caution, placarded in the Pilot’s Operating Handbook for the Rutan Long-EZ1. The caution states that when entering visible precipitation, the Long-EZ may experience a significant pitch trim change, as experienced in the Long-EZ prototype (N79RA). It goes on to state that owners of Rutan’s earlier canard aircraft, report either nose up or nose down pitch changes. Builders are warned that each aircraft may react differently. It is recommended that airspeed above 90 knots be maintained in rain as this allows the aircraft to be trimmed with hands off the control stick. In spite of these shortcomings, many existing canard aircraft are well designed in the view of this author, including the Rutan LongEz, and the AASI Jetcruzer, the first aircraft to have been certified in the US under 14 CFR Part 23 as “spin-resistant.” C2.1.2 Modeling the Pitching Moment for a Simple Wing-Canard System Figure C2-4 shows a simple Wing-Canard system, intended to derive a few longitudinal static stability methods that are helpful when sizing a canard configuration aircraft. The longitudinal static stability of the configuration can be represented using Equation (11-10), repeated here for convenience: Cm Cmo Cm Cm e e (C2-1) GUDMUNDSSON – GENERAL AVIATION AIRCRAFT DESIGN APPENDIX C2 – DESIGN OF CANARD AIRCRAFT 3 ©2013 Elsevier, Inc. This material may not be copied or distributed without permission from the Publisher. Where: Cmo Coefficient of moment at zero AOA C Change in coefficient of pitching moment due to AOA m Cm Elevator authority; change in coefficient of pitching moment due to elevator deflection e Figure C2-4: Wing-Canard system used to derive Equation (C2-4). Both of the above terms can be determined for this system using the following expressions: Cmo VC CL Cmo Cmo (C2-2) 0C AC W hAC h Cm VC CL Cm CL (C2-3) C AC W CMGC Where: CMGC = Mean Geometric Chord hn = Physical location of the CG at which Cm = 0; i.e. the stick-fixed neutral point hAC = Physical location of the Aerodynamic Center lC = Arm between the aerodynamic center of the canard and CG lCW = Arm between the aerodynamic center of the canard and the wing S = Reference wing area SC = Planform area of the canard SC lC SC lCW h hAC VC = Canard volume S CMGC S CMGC C Longitudinal stability contribution of components other than the wing mo AC C C h h Wing pitching moment due to airfoil camber moW L0 AC CL = Canard lift coefficient at zero AOA 0C Cm = Longitudinal stability contribution of components other than the wing AC CL = Lift curve slope of the canard C CL = Wing lift curve slope W GUDMUNDSSON – GENERAL AVIATION AIRCRAFT DESIGN APPENDIX C2 – DESIGN OF CANARD AIRCRAFT 4 ©2013 Elsevier, Inc. This material may not be copied or distributed without permission from the Publisher. Note that the term refers to the stabilizing effects of components such as the fuselage, nacelles, landing gear, the wing itself, and so on, as a function of the AOA. If the sum of these moments acts to rotate the LE down, then M AC 0 (has a negative sign and is stabilizing). If it acts to rotate LE up, then M AC 0 (has a positive sign and is destabilizing). The sign ultimately depends on the aircraft configuration. Note that the destabilizing effects of fuselages and nacelles can be estimated using the so-called Munk-Multhopp method, which is presented in Appendix C1.6, Additional Tools for Tail Sizing.