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A COMPREHENSIVE REVIEW of VERTICAL TAIL DESIGN 1 Introduction

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A COMPREHENSIVE REVIEW of VERTICAL TAIL DESIGN 1 Introduction A COMPREHENSIVE REVIEW OF VERTICAL TAIL DESIGN Fabrizio Nicolosi Danilo Ciliberti Pierluigi Della Vecchia Associate Professor Post-Doc Assistant Professor University of Naples University of Naples University of Naples “Federico II” – Dept. of “Federico II” – Dept. of Industrial “Federico II” – Dept. of Industrial Industrial Engineering (DII) Engineering (DII) Engineering (DII) Via Claudio 21, 80125, Via Claudio 21, 80125, Via Claudio 21, 80125, Naples – ITALY Naples – ITALY Naples – ITALY [email protected] [email protected] [email protected] Salvatore Corcione Vincenzo Cusati Post-Doc Consultant University of Naples “Federico II” – University of Naples “Federico II” – Dept. of Industrial Engineering (DII) Dept. of Industrial Engineering (DII) Via Claudio 21, 80125, Via Claudio 21, 80125, Naples – ITALY Naples – ITALY [email protected] [email protected] Abstract. This work deals with a comprehensive review of vertical tail design methods for aircraft directional stability and vertical tail sizing. The focus on aircraft directional stability is due to the significant discrepancies that classical semi-empirical methods, as USAF DATCOM and ESDU, provide for some configurations, since they are based on NACA wind tunnel tests about models not representative of an actual transport airplane. The authors performed RANS CFD simulations to calculate the aerodynamic interference among aircraft parts for hundreds configurations of a generic regional turboprop aircraft, providing useful results that have been collected in a new vertical tail preliminary design method, named VeDSC. Semi-empirical methods have been put in comparison on a regional turboprop aircraft, where the VeDSC method shows a strong agreement with numerical results. A wind tunnel investigation involving more than 180 configurations has validated the numerical approach. The investigation has covered both the linear and the non-linear range of the aerodynamic coefficients, including the mutual aerodynamic interference between the fuselage and the vertical stabilizer. Also, a preliminary investigation about rudder effectiveness, related to aircraft directional control, is presented. In the final part of the paper, critical issues in vertical tail design are reviewed, highlighting the significance of a good estimation of aircraft directional stability and control derivatives. Keywords. Aircraft Design, Vertical tail, Stability and Control, CFD, Wind-Tunnel tests. 1 Introduction The aircraft vertical tail is the aerodynamic surface that must provide sufficient directional equilibrium, stability, and control. Its sizing is determined by critical conditions as minimum control speed with one engine inoperative (for multi-engine airplanes) and landing in strong crosswinds. The airborne minimum control speed VMC is the calibrated airspeed at which, when the critical engine is suddenly made inoperative, it is possible to maintain control of the airplane with that engine still inoperative and maintain straight flight with an angle of bank of not more than 5° [1]. The airborne AviominimumConsult control speed may not exceed 1.13Control times and the Performance reference During stall speed.Asymmetrical Thus, Powered it affects Flight the takeoff field length, which must Onebe ofkept the Lasearning low Oasbj ectivespossible [1] isotherwise the effect of payload weight and could bank anglebe r educedon airplane when the aircraft is operating on shortcontrol runways. after engine The failure. VMC involves Therefore, large the weight rudder of anglesthe airplane dr toand keep the sidea - small angle of sideslip b. See Figure component1 left. This thereof requires during abanking certain in thevertical direction tail parallel area forto the a wingsgiven will rudder be us ed during the weight and bank angle analysis in this paper (Figure 8). Weight vector W effectiveness t, which must be the highestalways pointspossible to the to center keep of control the earth. authority When an airplaneat 25° oris banking more ofwith rudder bank a n- deflection. gle ϕ, a component of the weight vector (W·sin f) acts as side force in the center of A crosswind landing requires a sufficientgravity in a verticaldirection paralleltail area to theto wingsensure. aircraft directional stability in this delicate phase, which involves largeSide force sideslip W·sin anglesf (in body b inaxes full – steady flaps straight conditions flight) canand be possibly used to replace large the rudder angles d to keep the airplane atside the force desired due to flightsideslip path, of the althoughprevious case the (§ rudder 3.3) balancing deflection the side is forceusually due to r rudder deflection when an engine is inoperative (Figure 9). So, by banking, a bal- opposed to the sideslip angle, such thatance the of verticalside forces tail can lift be curve achieved is inwith the zero linear sideslip range, i.e. ( likewith aminimum plain flap drag . Figure 8. Side force produced by at negativebank angle angle (bodyof attack, axes – steadysee F igureRudder 1 right) deflection. remains required though, for counteracting the asymmetrical straight flight). thrust yawing moment. Side force W·sin f generates no rolling or yawing moments because it acts in the center of gravity; its moment arm is zero. Side force W·sin f varies obviously with weight (W) and bank angle (f) and acts in the direction of banking. The effect of weight and bank angle will be discussed in detail in § 5.1. In this zero sideslip or lowest drag case, the rudder side force only has to generate a yawing moment for balancing the asymmetrical thrust moment and does not have to overcome side forces due to sideslip anymore (as shown in Figure 6), so less rudder deflection for the same airspeed is required as compared to straight flight with wings level as discussed in the previous § 3.3. Therefore, the airspeed can be between 8 (small twin) and 25 knots (4-engine airplane) lower until either the rudder and/ or ai- leron limits are again reached, depending on size and engine configuration of the airplane. The airspeed at which this happens is the minimum control speed for straight flight with zero sideslip, i.e. with a small bank angle. The ball of the slip indicator is in this case about half a ball width to the right (into the good engine) be- cause the wings are banked a few degrees, while the side forces are balanced. The engineer designing the vertical tail dimensioned the vertical tail using a small bank angle of maximum 5° away from the inoperative engine as allowed by Regula- tions FAR/ CS 23.149 and 25.149 (ref. [6], [8]). These design considerations are briefly explained in § 4 below. The sideslip for the given tail size is zero only at a certain bank angle, which varies with airspeed. The higher the airspeed, the less Figure 1: Aircraft directional control in rudderaction deflection with one isengine required inoperative to balance (left,the asymmetrical ©Harry Horlings thrust and / W theikimedia smaller the FigureCommons 9. Forces and/ CC moments-BY-SA 3.0)bank and anglerudder (W·sin deflection f) can beto keepto balance a given the ruddersideslip side angle force (right). during straight flight with zero side- slip; small bank angle required. Conclusion. In this zero sideslip case, a rudder generated side force remains re- Another condition not critical forquired safety, for balancing but important the asymmetrical for flight thrust. quality, Banking is a thefew degreesratio between towards the operative engine (live engine low) generates a side force opposite of the rudder gen- directional and lateral static stability eratedderivatives, side force, which therewith should reducing be theless sideslip than andunit hence, for transportthe drag, to aircraft,a minimum, to avoid the annoying dutch roll leavingphenomenon. maximum availableFor general climb performance. aviation and military aircraft this requirement may be different, especiallyFor takeoff for the or gocarrier-around-based after engine airplanes, failure whereor while large an engine lateral is inoperative control ,in it is landing is vital. of vital importance that the remaining climb performance is maximum. This re- Design of the vertical tail is notquir a essimple the drag task, to be due minimal to the, which asymmetrical will be the case flow only behind if the sideslipthe wing is zero- , which in turn will only be the case if a small bank angle, usually between 3° and 5°, fuselage combination and lateral crossis attained-control and (side maintained force away on verticalfrom the inoperativetailplane engithatne. causes For most a rollingsmall twin moment). These aerodynamic issues enginemust airplanes,be addressed this zero in sideslip both the option lin isear the and only non option-line forar maintaining range of controlthe lift curve, and aerodynamic interferenceand achieving must be some accounted climb performance for. Some while indications an engine is comeinoperative from and aircraft the corr e- design books [2]-[8]: the first approachsponding is to opposite look atengine similar is producing aircraft maximum and apply thrust. the The same pilot tailcontrols volume the drag using ailerons and the heading (yawing) using the rudder. Accidents have learned coefficient. This is a non-dimensionalthough, number that pilots defined do not as always the useratio maximum of vertical or adequate tail planformrudder to counter areaact S vthe times the longitudinal distance betweenyawing. wing This and is thevertical subject tail of the aerodynamic
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