Chapter 6 Tail Design

Transcription

1 apter 6 Tail Design Moammad Sadraey Daniel Webster ollege Table of ontents apter Tail Design Introduction Aircraft Trim Requirements Longitudinal Trim Directional and Lateral Trim A Review on Stability and ontrol Stability ontrol Handling Qualities Tail configuration Basic Tail onfiguration Aft Tail onfiguration anard or Aft Tail Optimum Tail Arm Horizontal Tail Parameters Horizontal Tail Design Fundamental Governing Equation Fixed, All Moving, or Adjustable Airfoil Section Tail Incidence Aspect Ratio Taper Ratio Sweep Angle Diedral Angle Tail ertical Location Oter Tail Geometries ontrol Provision Final eck apter 6 Tail Design i

2 6.8. ertical Tail Design ertical Tail Design Requirements ertical Tail Parameters Practical Design Steps Tail Design Example Problems References apter 6 Tail Design ii

3 apter 6 Tail Design 6.1. Introduction As introduced in capter, te next appropriate step after wing design would be te tail design. In tis capter, after describing te tail primary functions, and introducing fundamentals tat govern te tail performance, tecniques and procedure to design te orizontal tail and vertical tail will be provided. At te end of te capter a fully solved example tat illustrates te implementation of te design tecnique will be presented. Horizontal tail and vertical tail (i.e. tails) along wit wing are referred to as lifting surfaces. Tis name differentiates tails and wing from control surfaces namely aileron, elevator, and rudder. Due to tis name, several design parameters associated wit tails and wing; suc as airfoil, planform area, and angle of attack; are similar. Tus, several tails parameters are discussed in brief. Te major difference between wing design and tail design originates from te primary function of tail tat is different from wing. Primary function of te wing to generate maximum amount of lift, wile tail is supposed to use a fraction of its ability to generate lift. If at any instance of a fligt mission, tail nears its maximum angle of attack (i.e. tail stall angle); it indicates tat tere was a mistake in te tail design process. In some texts and references, tail is referred to as empennage. Te tail in a conventional aircraft as often two components of orizontal tail and vertical tail and carries two primary functions: 1. Trim (longitudinal and directional). Stability (longitudinal and directional) Since two conventional control surfaces (i.e. elevator and rudder) are indeed parts of te tails to implement control, it is proper to add te following item as te tird function of tails: 3. ontrol (longitudinal and directional) Tese tree functions are described in brief ere; owever, more details are presented in later sections. Te first and primary function of orizontal tail is longitudinal trim; also referred apter 6 Tail Design 74

4 to as equilibrium or balance. But te first and primary function of vertical tail is directional stability. Te reason is tat an aircraft is usually symmetric about xz plane, wile te pitcing moment of te wing about aircraft center of gravity must be balanced via a component. Longitudinal trim in a conventional aircraft is applied troug te orizontal tail. Several pitcing moment, namely, longitudinal moment of te wing s lift about aircraft center of gravity, wing aerodynamic pitcing moment, and sometimes engine trust s longitudinal moment need to be trimmed about y axis. Te summation of tese tree moments about aircraft center of gravity is often negative; ence te orizontal tail often generates a negative lift to counteract te moment. For tis reason, te orizontal tail setting angle is often negative. Since te aircraft center of gravity is moving along x axis; due to fuel burn during fligt duration; te orizontal tail is responsible for longitudinal trim trougout fligt time. To support te longitudinal trimability of te aircraft, conventional aircraft employ elevator as part of its orizontal tail. Since conventional aircraft are almost always manufactured symmetrically about xz plane, te trim is not a major function for vertical tail. However, in few instances, vertical tail as te primary function of directional trim or lateral trim. In a multi-engine aircraft, te vertical tail as great responsibility during one engine inoperative (OEI) situation in order to maintain directional trim. Te vertical tail must generate a yawing moment to balance te aircraft for te yawing moment generated by active engines. Even in single engine prop-driven aircraft, te vertical as to counteract te rolling moment generated by propeller rotation. Tis is to maintain aircraft lateral trim and prevent an unwanted roll. For tis case, te vertical tail as often installed wit few degrees relative to xz plane. Te aircraft trim requirement provides te main design requirements in te tail design process. Te derivation of design requirements based on te trim will be discussed in details in Section 6.. Te second function of te tails is to providing stability. Te orizontal tail is responsible to maintain te longitudinal stability, wile te vertical tail is responsible to maintain te directional stability. Aircraft stability is defined as te tendency of an aircraft to return to te original trim conditions if diverted by a disturbance. Te major disturbance source is te atmosperic penomena suc as gust. Te stability requirement must also be included in te tail design requirements list. Tis topic will be discussed in details in Section 6.3. Te tird major function of te tails is control. Te elevator as part of te orizontal tail is designed to provide longitudinal control, wile te rudder as part of te vertical tail is responsible for providing te directional control. Tails must be powerful enoug to control te aircraft suc tat te aircraft is able to cange te fligt conditions from one trim condition (say cruise) to anoter new trim condition (say take-off and landing). For instance, during take-off, te tail must be able to lift up te fuselage nose in a specified pitc rate. In general, tail is designed based on te trim requirements, but later revised based on stability and control requirements. Te following are te tail parameters wic need to be determined during te design process: 1. Tail configuration. Horizontal tail orizontal location wit respect to fuselage (aft tail or canard) Horizontal tail 3. Planform area (S ) apter 6 Tail Design 75

5 4. Tail arm (l ) 5. Airfoil section 6. Aspect ratio (AR ) 7. Taper ratio ( ) 8. Tip cord ( _tip ) 9. Root cord ( _root ) 10. Mean Aerodynamic ord (MA or ) 11. Span (b ) 1. Sweep angle ( ) 13. Diedral angle ( ) 14. Tail installation 15. Incidence (i ) ertical tail 16. Planform area (S v ) 17. Tail arm (l v ) 18. Airfoil section 19. Aspect ratio (AR v ) 0. Taper ratio ( v ) 1. Tip cord ( t_v ). Root cord ( r_v ) 3. Mean Aerodynamic ord (MA v or v ) 4. Span (b v ) 5. Sweep angle ( v ) 6. Diedral angle ( v ) 7. Incidence (i v ) All 7 tail parameters listed above must be determined in te tail design process. Te majority of parameters are finalized troug tecnical calculations, wile a few parameters are decided via an engineering selection approac. Tere are few oter intermediate parameters suc as downwas angle, sidewas angle, and effective angle of attack wic will be used to calculate some tail parameters. Tese are determined in te design process, but not employed in te manufacturing period. As discussed in apter, te Systems Engineering approac as been adopted as te basic tecnique to design te tail. Te tail design tecnique as been developed by tis approac to satisfy all design requirements wile maintaining low cost in an optimum fasion. Figure 6.1 illustrates te block diagram of te tail design process. As it was explained in apter, te aircraft design is an iterative process; terefore tis procedure (tail design) will be repeated several times until te optimum aircraft configuration as been acieved. Te design of vertical and orizontal tails migt be performed almost in parallel. However, tere is one step in te vertical tail design (i.e. spin recovery) tat te effect of orizontal tail into vertical tail is investigated. Te details on eac step will be introduced in te later sections. Te purpose of tis capter is to provide design considerations, design tecnique, and design examples for te preliminary design of te aircraft tail. apter 6 Tail Design 76

6 Identify and Prioritize te Tail Design Requirements (e.g. Trim, stability, control, producibility, operational requirements, cost, fligt safety) Select tail configuration ertical Tail Select vertical tail volume coefficient Horizontal Tail Select orizontal tail location Determine tail arm Select orizontal tail volume coefficient Determine optimum tail arm Determine planform area Determine airfoil section Determine planform area Determine airfoil section Determine aspect and taper ratios (AR, ), and sweep angle () Determine setting angle Determine sweep and diedral angles Determine aspect and taper ratios alculate setting angle alculate b, MA, r, t alculate b, MA, r, t No eck spin recovery Yes eck tail stall Yes No Analyze longitudinal and directional stability and Optimize Figure 6.1. Te tail design procedure apter 6 Tail Design 77

7 6.. Aircraft Trim Requirements Trim is one of te inevitable requirements of a safe fligt. Wen an aircraft is at trim, te aircraft will not rotate about its center of gravity (cg), and aircraft will eiter keep moving in a desired direction or will move in a desired circular motion. In anoter word, wen te summations of all forces and moments are zero, te aircraft is said to in trim. F 0 M 0 (6.1) (6.) Te aircraft trim must be maintained about tree axes (x, y, and z): 1. lateral axis (x),. longitudinal axis (y), and 3. directional axis (z). Wen te summation of all forces in x direction (suc as drag and trust) is zero; and te summation of all moments including aerodynamic pitcing moment about y axis is zero, te aircraft is said to ave te longitudinal trim. F x 0 M cg 0 (6.3) (6.4) Te orizontal tail is responsible to maintain longitudinal trim and make te summations to be zero, by generating a necessary orizontal tail lift and contributing in te summation of moments about y axis. Horizontal tail can installed beind te fuselage or close to te fuselage nose. Te first one is called conventional tail or aft tail, wile te second one is referred to as te first tail, foreplane or canard. Te equation 6.4 will be used in te orizontal tail design. Wen te summation of all forces in y direction (suc as side force) is zero; and te summation of all moments including aerodynamic yawing moment about z axis is zero, te aircraft is said to ave te directional trim. F y 0 N cg 0 (6.5) (6.6) Te vertical tail is responsible to maintain directional trim and make te summations to be zero, by generating a necessary vertical tail lift and contributing in te summation of moments about y axis. Te equation 6.6 will be used in te vertical tail design. Wen te summation of all forces in z direction (suc as lift and weigt) is zero; and te summation of all moments including aerodynamic rolling moment about x axis is zero, te aircraft is said to ave te lateral trim. F z 0 L cg 0 (6.7) (6.8) Te vertical tail is responsible to maintain directional trim and make te summation of moment to be zero, by generating a necessary vertical tail lift and contributing in te summation of moments about z axis. Te equation 6.8 will also be used in te vertical tail design. More details apter 6 Tail Design 78

8 could be found in most fligt dynamics textbook. As an example, te interested reader is referred to [1], [], and [3]. A major design requirements reference is te Federal Aviation Administration [4]. Te following is reproduced from Section 161 of PAR 3 of Federal Aviation Regulations (FAR) wic concerns about lateral-directional and longitudinal trim of a General Aviation aircraft: (a) General. Eac airplane must meet te trim requirements of tis section after being trimmed and witout furter pressure upon, or movement of, te primary controls or teir corresponding trim controls by te pilot or te automatic pilot. In addition, it must be possible, in oter conditions of loading, configuration, speed and power to ensure tat te pilot will not be unduly fatigued or distracted by te need to apply residual control forces exceeding tose for prolonged application of 3.143(c). Tis applies in normal operation of te airplane and, if applicable, to tose conditions associated wit te failure of one engine for wic performance caracteristics are establised. (b) Lateral and directional trim. Te airplane must maintain lateral and directional trim in level fligt wit te landing gear and wing flaps retracted as follows: (1) For normal, utility, and acrobatic category airplanes, at a speed of 0.9 H,, or MO /M O, wicever is lowest; and () For commuter category airplanes, at all speeds from 1.4 S1 to te lesser of H or MO /M MO. (c) Longitudinal trim. Te airplane must maintain longitudinal trim under eac of te following conditions: (1) A climb, () Level fligt at all speeds, (3) A descent, (4) Approac (d) In addition, eac multiple airplane must maintain longitudinal and directional trim, and te lateral control force must not exceed 5 pounds at te speed used in complying wit 3.67(a), (b)(), or (c)(3), For oter types of aircraft, te reader is encouraged to refer to oter parts of FAR; for instance, for transport aircraft; te reference is Part Longitudinal Trim For te orizontal tail design process, we need to develop a few equations; ence te longitudinal trim will be described in more details. onsider te side view of a conventional aircraft (i.e. wit aft tail) in figure 6. tat is in longitudinal trim. Figure 6.a depicts te aircraft wen te aircraft center of gravity (cg) is beind te wing-fuselage aerodynamic center (ac wf ) 1. In figure 6.b, te aircraft is depicted wen te aircraft center of gravity is forward of te wing-fuselage aerodynamic center. Tere are several moments about y axis (cg) tat must be balanced by te orizontal tail s lift; two of wic are: 1. wing-fuselage aerodynamic pitcing moment,. te moment of lift about aircraft center of gravity. Oter source of moments about cg could be engine trust, wing drag, landing gear drag, and store drag. For te sake of simplicity, tose 1 Te wing-fuselage aerodynamic center is simply te wing aerodynamic center wen te contribution of te fuselage is added. Te fuselage contribution for most conventional aircraft is usually about ±5%. Since te wing aerodynamic center is often located at about quarter mean aerodynamic cord (i.e. 5% ); ence te wing-fuselage aerodynamic center is often located between 0 percent of MA to 30 percent of MA or. Te reader is referred to [1] for more information. apter 6 Tail Design 79

9 moments are not included in tis figure. Te reader is expected to be able to follow te discussion, wen oter moments are present and/or te aircraft as a canard instead of aft tail. L wf D w M o L ac T ac wf cg M owf W a. cg aft of ac wf cg ac wf L wf M owf M o ac T L W D w b. cg forward of ac wf Figure 6.. A conventional aircraft in longitudinal trim Te wing-fuselage lift (L wf ) is te wing lift (L w ) wen te contribution of fuselage lift (L f ) is included. Te fuselage lift is usually assumed to be about 10 percent of te wing lift. Ref. [1] can be consulted for te exact calculation. Wen te cg is aft of te ac wf (as in Fig 6.a), tis moment of te wing-fuselage lift (L wf ) is positive, wile wen te cg is forward of te ac wf (as in Fig 6.a), tis moment of te wing-fuselage lift is negative. Recall from fligt dynamics, tat te clockwise direction is assumed to be positive, and te y-axis is located at te cg and is directed into te page. Anter moment is referred to as te wing-fuselage aerodynamic pitcing moment (i.e. M owf ). Te wing-fuselage aerodynamic pitcing moment (M owf ) is te wing aerodynamic pitcing moment (M ow ) wen te contribution of te fuselage (M f ) is included. Te subscript o denotes tat te aerodynamic moment is measured relative to te wing aerodynamic center. Tis aerodynamic moment is often negative (as sketced in figure 6.); so it is often called a nosedown pitcing moment; due to its desire to pitc down te fuselage nose. Often times, te summation of tese two moments (i.e. te wing-fuselage aerodynamic pitcing moment and te apter 6 Tail Design 80

10 wing-fuselage lift generated moment) is not zero. Hence, te orizontal tail is employed to generate a lift in order to balance tese moments and make te summation to be zero. Tis function maintains te aircraft longitudinal trim. In a similar fasion, a discussion about te directional trim can be addressed. In tis case, despite te symmetricity of te conventional aircraft about xz plane, tere are forces suc as asymmetric engine trust (wen one engine is inoperative in multi-engine aircraft) tat disturb te directional trim of an aircraft. In suc a situation, te vertical tail is required to generate a lift force in te y direction (i.e. side force) to maintain te directional trim about z axis. Te details of tis case are left to te reader. Now, consider te aircraft in figure 6.3 at wic te tail aerodynamic pitcing moment is neglected. Please note tat in tis case, te trust-line is passing troug te aircraft cg, so te engine trust tends to impose no influence on te aircraft longitudinal trim. Altoug te wingfuselage lift is positive in a normal fligt situation, but te moment of te lift about cg migt be positive or negative due to te relationsip between cg and ac wf. Tus, te orizontal tail could be negative or positive. Te application of te trim equation leads to te following : M 0 M M M 0 (6.9) cg owf L wf L Recall, te aircraft weigt generates no moment about aircraft cg. If te engine trust line is not passing troug te aircraft cg, te equation 6.9 must be modified. To make tis equation more convenient to apply, we need to non-dimensionalize it. In order to non-dimensionalize te parameters, it is often customary to measure te distances in te x direction as a factor of mean aerodynamic cord ( or simply ). Moreover, a reference line (or point) must be selected to measure all distances wit respect to it. Here, we select te fuselage nose as te reference line. Hence, te distance between ac wf to te reference line is o times te, (i.e. o ), wile te distance between cg to te reference line is times te, (i.e. ). Bot parameters are sown in figure 6.3. Te distance between orizontal tail aerodynamic center to te wing-fuselage aerodynamic center is denoted as l, wile te distance between orizontal tail aerodynamic center to te aircraft center of gravity is denoted as l t. Now, we can substitute te values of two moments into te equation 6.9: M owf L wf L l 0 o (6.10) To expand te equation, we need to define te variables of wing-fuselage lift (L wf ), orizontal tail lift (L ), and wing-fuselage aerodynamic pitcing moment (M owf ). L 1 wf S Lwf (6.11) L 1 S L (6.1) Te orizontal tail aerodynamic pitcing moment is ignored, due to its small value. apter 6 Tail Design 81

11 M owf 1 S mowf (6.13) were Lwf denotes wing-fuselage lift coefficient, L denotes orizontal tail lift coefficient, mowf denotes wing-fuselage aerodynamic pitcing moment coefficient, S denotes wing planform area, S denotes orizontal tail planform area, denotes te aircraft airspeed, and denotes te air density. x ac wf L wf cg L ac o M wf W l Reference line l Figure 6.3. Te distance between cg, ac t, and ac wf to te reference line By substituting equations 6.11, 6.1, and 6.13 into equation 6.10, we will ave te following: 1 1 S l 0 1 Sm S owf Lwf o Tis equation is ten non-dimensionalized by dividing it to obtained: L 1 S (6.14). Tus, te following is mowf Lwf l S S 0 o L (6.15) Now return to figure 6.3. Te distance between orizontal tail aerodynamic center to te reference line can be written in two ways: l l o (6.16) or l l o (6.17) apter 6 Tail Design 8

12 Substituting equation 6.17 into equation 6.15 yields: mowf Lwf l 0 o o L S S (6.18) Tis can be furter simplified as: mowf Lwf L S S 0 o l S S L (6.19) In contrast, te aircraft total lift is te summation of wing-fuselage lift and te orizontal tail lift: L L wf L (6.0) wic leads to: 1 S L 1 S 1 S Lwf L (6.1) Tis equation is non-dimensionalized as follows: L Lwf L S S (6.) Now, te equation 6. can be substituted into equation mowf L 0 o l S S L (6.3) Te combination ls t S in equation 6.3 of is an important non-dimensional parameter in te orizontal tail design, and is referred to as te Horizontal tail olume oefficient. Te name originates from te fact tat bot numerator and denominator ave te unit of volume (e.g. m 3 ). Te numerator is a function of orizontal tail parameters, wile te denominator is a function of wing parameters. Tus, te parameter is te ratio of orizontal tail geometries to wing geometries. It is sown wit te symbol of H : H ls S (6.4) Tus, te equation 6.3 is furter simplified as followed: H 0 (6.5) mowf L o L Tis non-dimensional longitudinal trim equation provides a critical tool in te design of te orizontal tail. Te importance of tis equation will be explained later, and its application will be described in later sections of te capter. Tis non-dimensional parameter H as a limited apter 6 Tail Design 83

13 range in values and also it is not a function of aircraft size or weigt. From a small aircraft suc as essna 17 (Figure 11.15) to a jumbo jet large aircraft suc as Boeing 747 (Figures 3.7, 3.1, and 9.4) all ave similar tail volume coefficient. Table 6.1 illustrates te tail volume coefficients for several aircraft. Table 6.4 sows typical values for tail volume coefficient for several aircraft types. Te tail volume coefficient is an indication of andling quality in longitudinal stability and H longitudinal control. As increases, te aircraft tends to be more longitudinally stable, and less longitudinally controllable. Te figter aircraft tat are igly maneuverable tend to ave a very low tail volume coefficient, namely about 0.. On te oter and, te jet transport aircraft wic must be igly safe and stable tend to ave a ig tail volume coefficient, namely about 1.1. Tis parameter is a crucial variable in orizontal tail design and must be selected at te early stages of tail plane design. Altoug te primary function of te orizontal tail is te longitudinal stability, but te tail volume coefficient serves as a significant parameter bot in te longitudinal stability and longitudinal trim issues. No Aircraft Type Mass (kg) Wing area (m ) Overall lengt (m) 1 essna 17 Ligt GA (Piston) 1, Piper PA P Ligt transport (Piston) 1, Alenia G Turboprop transport 8, Fokker 100 Jet transport 44, Lake LA-50 Ampibian 1, Boeing Jet transport 36, Airbus Jet transport 57, Pilatus P-1 Turboprop transport 4, Eurofigter 000 Figter 1, F/A-18 Figter 9, Table 6.1. Tail volume coefficients of several aircraft [5] Te wing-fuselage pitcing moment coefficient ( following equation [6]: m owf apter 6 Tail Design 84 mowf H ) in equation 6.5 can be estimated via te AR cos m 0.01 af t (6.6) AR cos were m is te wing airfoil section pitcing moment coefficient, AR is wing aspect ratio, is af wing sweep angle, and t is te wing twist angle (in degrees). Please note tat t is often a negative number. Te value of can be determined using te airfoil graps wic an mowf example is sown in figure 5.1 for NAA airfoil section. For instance, te value of for tis airfoil is m af Te parameter L in equation 6.5 is te aircraft cruise lift coefficient tat is determined by te following equation:

14 W avg L S (6.7) were is te cruising speed and te W avg is te average aircraft weig during te cruising fligt. If te wing as been designed prior to te design of orizontal tail, and te aircraft center of gravity () was decided, te equation 5.5 as only two unknowns; namely L and. However, in practice, te design of te wing and te location of te cg are not independent of te tail design. Hence, tis is an ideal case, and te tail design is indeed an iteration process. Te longitudinal trim equation (i.e. equation 5.6) must be valid in every possible fligt conditions. Tis includes all aircraft allowable load weigts, all feasible fligt speeds, all aircraft designated configurations (e.g. flap and landing gear, up and down), all allowable cg locations, and all possible fligt altitude. Tese various fligt possibilities can be summarized to be between te following two extreme critical conditions: 1. Te first unknown fligt condition at wic te orizontal tail is required to generate te greatest positive pitcing moment about aircraft cg.. Te second unknown fligt condition at wic te orizontal tail is required to generate te greatest negative pitcing moment about aircraft cg. Tese two critical fligt conditions for te orizontal tail are unknown at tis moment, but will be clear later on in te design process. Te cange in te sign of te tail pitcing moment about aircraft cg indicates te necessity of a cange in te tail lift coefficient from positive to negative. Two possible solutions are: 1. Te application of a moving orizontal tail. Te application of a fixed orizontal tail, plus a control surface (i.e., elevator). In te early stage of orizontal tail, te design is performed witout considering te elevator. Te criterion is to design a orizontal tail to satisfy te cruising fligt longitudinal trim requirements. Te reason is tat te aircraft spends te majority of te fligt mission time in te cruising fligt. Due to te effect of wing and fuselage on te orizontal tail (i.e. downwas and sidewas), a new parameter is added to te equation 6.5. Te new parameter is te ratio between te dynamic pressure at te tail to te aircraft dynamic pressure, and is called te tail efficiency ( ) and is defined as follows: H qt q (6.8) were te is te aircraft airspeed, and te is te effective airspeed at te orizontal tail region. Te typical value of te tail efficiency for an aircraft wit a conventional tail is varied from 0.85 to For an aircraft wit a T-tail, te tail efficiency can be considered to be 1, wic means te wing and fuselage ave no effect on te tail dynamic pressure. Te orizontal apter 6 Tail Design 85

15 tail of a T-tail is usually out te region of wing wake and downwas during cruising fligt. Applying te tail efficiency into te equation 6.5 yields a revised version: mowf L 0 o H L (6.9) Tis is te most important equation in te design of orizontal tail and implies te requirements for te longitudinal trim. It will be used in bot conventional aft tail and canard configuration. Te equation is derived in tis section, but its application tecnique will be presented in te Sections 6.6 and 6.8. One of te four parameters in te tail volume coefficient is te distance from wing aerodynamic center to te orizontal tail aerodynamic center (l). Tis distance as statistically a relationsip wit te aircraft overall lengt (L). Te ratio between te distance from te wing aerodynamic center to te orizontal tail aerodynamic center and aircraft overall lengt is illustrated in Table 6. for several aircraft configurations. It may be employed in te early stage of te orizontal tail design as a starting point. Te value will be revised and optimized in te later design steps wen more data are available. No Aircraft configuration/ type l/l 1 An aircraft wose engine is installed at te nose and as an aft tail 0.6 An aircraft wose engine(s) installed above te wing and as an aft tail An aircraft wose engine installed at te aft fuselage and as an aft tail An aircraft wose engine installed under te wing and as an aft tail Glider (wit an aft tail) anard aircraft An aircraft wose engine is inside te fuselage (e.g. figter) and as an aft tail 0.3 Table 6.. Typical values for te l/l for various aircraft configurations 6... Directional and Lateral Trim One of te primary functions for te vertical tail is directional trim. Moreover, te vertical tail tends to ave a considerable contribution in te aircraft lateral trim. In tis section, te role of te vertical tail in te aircraft directional and lateral trim is examined. Two aircraft are illustrated in figure 6.4; one in directional trim, and anoter one in directional trim. In figure te top view of an aircraft is sown were te vertical tail is generating a yawing moment to nullify te yawing moment created by asymmetric trust of te rigt engine. In addition, figure 6.4- te front view of an aircraft is sown were te vertical tail is generating a rolling moment to nullify te rolling moment created by te rotation of te propeller of te engine. In bot cases, te primary production of te vertical tail is an aerodynamic lift in te direction of y-axis. Wen an aircraft is in directional trim, te summation of all moments about z-axis must be zero. N cg 0 (6.6) Wen an aircraft is in lateral trim, te summation of all moments about x-axis must be zero. L cg 0 (6.8) In maintaining te directional and lateral trim, an aerodynamic force along y-axis (lift; L ) needs to be created by te vertical tail. Tus, te directional and lateral trim equations are: apter 6 Tail Design 86

16 N L cg cg 0 T Y L l 0 R T t 0 L L z 0 E (6.30) (6.31) were T R denotes te rigt engine trust, Y T is te distance between trust line and te aircraft cg in te xy plane, l v is te distance between te vertical tail aerodynamic center and te aircraft cg, L E is te yawing moment generated by te prop rotation and z v denotes te distance between vertical tail aerodynamic center and te aircraft cg in te yz plane. Te vertical tail lift is obtained from: L 1 S L v (6.3) y T R ac vt x Y T cg ac v y L z v L Top view l v 1. One Engine Inoperative (directional trim). Single Propeller Engine (lateral trim) Figure 6.4. ertical tail role in te aircraft lateral and directional trim were S is te vertical tail area, and te L is te vertical tail lift coefficient. Four unknowns of S, L, l v and z v are te bases for te design of te vertical tail. Section 6.8 examines application of te tecnique and procedure for te design of te vertical tail to satisfy te directional and lateral trim requirements A Review on Stability and ontrol Stability and control are two requirements of a safe fligt. Bot orizontal tail and vertical tail as a strong role in aircraft stability and control. Altoug orizontal tail and vertical tail are initially designed to satisfy te longitudinal and directional trim requirements, but in te later stages of design, te longitudinal and directional stability and control requirements must also be implemented. Tus, te initial design of orizontal tail and vertical tail will be revised to make sure tat longitudinal and directional stability and control requirements ave been satisfied. In tis section, a brief introduction to aircraft stability and control will be provided. Tis will pave and clarify te pat to te design of orizontal tail and vertical tail. Due to te stability requirements by tail, te orizontal tail is sometimes referred to as orizontal stabilizer and vertical tail to as vertical stabilizer. L E x Front view apter 6 Tail Design 87

17 Stability Te second function of te tail is stability, and te tird function of te tail is control. Due to tis role, te tail is sometimes referred to as te stabilizer or stabilator. Stability is defined as te tendency of an aircraft to oppose a disturbance (e.g. gust) and return to its initial steady state trim condition if disturbed. Stability is often divided into two brances: 1. Static stability. Dynamic stability Static stability is defined as te initial tendency of an aircraft; witout pilot assistance; to develop forces and/or moments wic oppose an instantaneous perturbation of a motion variable from a steady state fligt condition. Dynamic stability is defined as te tendency of an aircraft; witout pilot assistance; to return to initial steady state trim condition after a disturbance disturbs te trim values. Dynamic stability concerns te entire istory of te motion, in particular te rate at wic te motion damps out. As a general rule, an aircraft must ave some form of dynamic stability even toug certain mild disabilities can be tolerated under certain conditions. Wen an aircraft is dynamically stable, it definitely as static stability. However, if an aircraft is statically stable, tere is no guarantee tat it as dynamic stability. Roll Pitc y cg z z Yaw Figure 6.5. Body coordinate system and tree rotational motions of roll, pitc, and yaw An aircraft motion (fligt) as six Degrees-Of-Freedom (6 DOF), due to two types of freedom (one linear and one rotational) about eac tree axis of x, y and z. Terefore, stability is measured about tese tree axes: 1. Lateral stability. Longitudinal stability 3. Directional stability Lateral stability is defined as te stability of any rotational motion about x axis (i.e. roll) and any corresponding linear motion along yz plane (i.e. side motion). Longitudinal stability is defined as te stability of any rotational motion about y axis (i.e. pitc) and any linear motion along xz plane (i.e. forward and aft, and up and down). Directional stability is defined as te apter 6 Tail Design 88

18 stability of any rotational motion about z axis (e.g. yaw) and any corresponding linear motion along xy plane (e.g. sideslip). Figure 6.5 provides aircraft body coordinate system, plus tree rotational motions of roll, pitc, and yaw. Te convention is tat te clockwise rotation about any axis; wen you look from pilot seat; is assumed as te positive rotation. Te requirements for aircraft static and dynamic stability (longitudinal, lateral, and directional) are different. Wen te aircraft derivative m is negative, te aircraft is said to statically longitudinally stable. An aircraft is said to statically laterally stable, wen te aircraft derivative l (known as diedral effect) is negative. Wen te aircraft derivative n is positive, te aircraft is said to statically directionally stable. For an aircraft to be dynamically longitudinally stable, bot sort-period and long-period (pugoid) modes must be damped (damping ratio greater tan zero). Wen all modes and oscillations (including dutc-roll, spiral, and roll) are damped, an aircraft is said to be dynamically laterally-directionally stable. Some dynamic longitudinal, lateral, and directional stability are tabulated in apter 1 (Section 1.3). Among major aircraft components, te orizontal tail as te largest contribution to te aircraft longitudinal stability. Te reason is tat te orizontal tail is able to generate te counter pitcing moment in order to restore te longitudinal trim position. On te oter and, te vertical tail as te largest contribution to te aircraft directional stability. Te vertical tail is able to generate te counter yawing moment in order to restore te directional trim position. Bot orizontal tail and vertical tail as significant contributions to te aircraft lateral stability, since bot are capable of generating counter rolling moment in order to restore te lateral trim position. Since te capter is concerned wit tail design, only longitudinal and directional stability requirements are empasized. Te following is reproduced from Section 173 of PAR 3 of Federal Aviation Regulations [4] wic concerns about static longitudinal stability of a General Aviation aircraft: Under te conditions specified in and wit te airplane trimmed as indicated, te caracteristics of te elevator control forces and te friction witin te control system must be as follows: (a) A pull must be required to obtain and maintain speeds below te specified trim speed and a pus required to obtain and maintain speeds above te specified trim speed. Tis must be sown at any speed tat can be obtained, except tat speeds requiring a control force in excess of 40 pounds or speeds above te maximum allowable speed or below te minimum speed for steady unstalled fligt need not be considered. (b) Te airspeed must return to witin te tolerances specified for applicable categories of airplanes wen te control force is slowly released at any speed witin te speed range specified in paragrap (a) of tis section. Te applicable tolerances are (1) Te airspeed must return to witin plus or minus 10 percent of te original trim airspeed; and () For commuter category airplanes, te airspeed must return to witin plus or minus 7.5 percent of te original trim airspeed for te cruising condition specified in 3.175(b). (c) Te stick force must vary wit speed so tat any substantial speed cange results in a stick force clearly perceptible to te pilot. apter 6 Tail Design 89

19 Te following is reproduced from Section 177 of PAR 3 of Federal Aviation Regulations [4] wic concerns about static directional stability of a General Aviation aircraft: a)te static directional stability, as sown by te tendency to recover from a wings level sideslip wit te rudder free, must be positive for any landing gear and flap position appropriate to te takeoff, climb, cruise, approac, and landing configurations. Tis must be sown wit symmetrical power up to maximum continuous power, and at speeds from 1. S1 up to te maximum allowable speed for te condition being investigated. Te angel of sideslip for tese tests must be appropriate to te type of airplane. At larger angles of sideslip, up to tat at wic full rudder is used or a control force limit in is reaced, wicever occurs first, and at speeds from 1. S1 to O, te rudder pedal force must not reverse. b) Te static lateral stability, as sown by te tendency to raise te low wing in a sideslip, must be positive for all landing gear and flap positions. Tis must be sown wit symmetrical power up to 75 percent of maximum continuous power at speeds above 1. S1 in te take-off configuration(s) and at speeds above 1.3 S1 in oter configurations, up to te maximum allowable speed for te configuration being investigated, in te takeoff, climb, cruise, and approac configurations. For te landing configuration, te power must be tat necessary to maintain a 3 degree angle of descent in coordinated fligt. Te static lateral stability must not be negative at 1. S1 in te takeoff configuration, or at 1.3 S1 in oter configurations. Te angle of sideslip for tese tests must be appropriate to te type of airplane, but in no case may te constant eading sideslip angle be less tan tat obtainable wit a 10 degree bank, or if less, te maximum bank angle obtainable wit full rudder deflection or 150 pound rudder force. Te following is reproduced from Section 181 of PAR 3 of Federal Aviation Regulations [4] wic concerns about dynamic lateral-directional-longitudinal stability of a General Aviation aircraft: (a) Any sort period oscillation not including combined lateral-directional oscillations occurring between te stalling speed and te maximum allowable speed appropriate to te configuration of te airplane must be eavily damped wit te primary controls (1) Free; and () In a fixed position. (b) Any combined lateral-directional oscillations ( Dutc roll ) occurring between te stalling speed and te maximum allowable speed appropriate to te configuration of te airplane must be damped to 1/10 amplitude in 7 cycles wit te primary controls (1) Free; and () In a fixed position. (c) If it is determined tat te function of a stability augmentation system, reference 3.67, is needed to meet te fligt caracteristic requirements of tis part, te primary control requirements of paragraps (a)() and (b)() of tis section are not applicable to te tests needed to verify te acceptability of tat system. apter 6 Tail Design 90

20 (d) During te conditions as specified in 3.175, wen te longitudinal control force required to maintain speeds differing from te trim speed by at least plus and minus 15 percent is suddenly released, te response of te airplane must not exibit any dangerous caracteristics nor be excessive in relation to te magnitude of te control force released. Any long-period oscillation of fligt pat, pugoid oscillation, tat results must not be so unstable as to increase te pilot's workload or oterwise endanger te airplane. Since te longitudinal stability is concerned wit a motion in pitc, te pertinent dynamic caracteristic is te variation of te pitcing moment wit respect to te angle of attack (). Tus, te primary stability derivative tat determines te static longitudinal stability is te m. Moreover, te primary stability derivative tat influences te dynamic longitudinal stability is te m q. Te derivative m is te rate of cange of pitcing moment coefficient ( m ) wit respect to cange in te angle of attack (). Te derivative m q is te rate of cange of pitcing moment coefficient ( m ) wit respect to cange in te pitc rate (q). m m (6.33) m q m q U 1 (6.34) Tese two stability derivatives are most influential in te design of orizontal tail. A statically longitudinally stable aircraft requires to be negative. Te typical value for most aircraft is m about -0.3 to /rad. A dynamically longitudinally stable aircraft requires tat te real parts of te roots of te longitudinal caracteristic equation to be negative. One of te major contributor to tis requirement is ; suc tat a negative value as a strong stabilizing impact. Te typical value of mq mq for most aircraft is about -5 to -30 1/rad. m n Unstable Stable Stable Unstable a. m versus curve b. n versus curve Figure 6.6. Grapical representations of derivatives m.and n apter 6 Tail Design 91

21 It is interesting to note tat te orizontal tail volume coefficient ( ) is te most important parameter affecting bot and. Figure provides grapical representation of stability derivative m mq m. Te detail of te tecnique to determine derivatives H m and available in [6]. Anoter very important parameter tat can be employed to determine te aircraft longitudinal static stability is te aircraft neutral point. Some textbooks refer to tis point as te aircraft aerodynamic center (ac A ). If te aircraft neutral point is beind te aircraft center of gravity, te aircraft is said to ave longitudinal static stability. At tis situation, te static margin (i.e. te non-dimensional distance between te aircraft neutral point to te aircraft cg) is said to be positive. Te details of te tecnique to determine aircraft neutral point and static margin may be found in [1] and [6]. Te directional stability is mainly concerned wit motion in yaw, so te pertinent dynamic caracteristic is te variation of te yawing moment wit respect to te sideslip angle (). Tus, te primary stability derivative tat determines te static directional stability is te n. Moreover, te primary stability derivative tat influences te dynamic directional stability is te n r. Te derivative n is te rate of cange of yawing moment coefficient ( n ) wit respect to cange in te sideslip angle (). Te derivative n r is te rate of cange of yawing moment coefficient ( n ) wit respect to cange in te yaw rate (r). mq are n n (6.35) n r n rb U 1 (6.36) No Requirements Stability derivatives Symbol Typical value (1/rad) 1a Static longitudinal Rate of cange of pitcing moment -0.3 to -1.5 stability coefficient wit respect to angle of attack 1b Static longitudinal Static margin np - cg 0.1 to 0.3 stability Dynamic Rate of cange of pitcing moment -5 to -40 m q longitudinal stability coefficient wit respect to pitc rate 3 Static directional Rate of cange of yawing moment to +0.4 n stability coefficient wit respect to sideslip angle 4 Dynamic directional Rate of cange of yawing moment -0.1 to -1 stability coefficient wit respect to yaw rate Table 6.3. Some static and dynamic longitudinal and directional stability requirements Tese two stability derivatives are most influential in te design of vertical tail. A statically directionally stable aircraft requires to be positive. Te typical value for most n aircraft is about +0.1 to /rad. A dynamically directionally stable aircraft requires tat te real parts of te roots of te lateral-directional caracteristic equation to be negative. One of te m nr apter 6 Tail Design 9

22 major contributor to tis requirement is nr ; suc tat a negative value as a strong stabilizing impact. Te typical value for most aircraft is about -0.1 to -1 1/rad. Tese two derivatives are among te influential parameters in te design of te vertical tail. Table 6.3 summarizes te requirements for static and dynamic longitudinal and directional stability. Figure 6.6- provides grapical representation of te stability derivative. Te tecnique to determine derivatives n and nr is available in [6]. Almost all General Aviation and transport aircraft are longitudinally and directionally stable. Of military aircraft, only advanced figters are exception; wic means figters are te only military aircraft tat may not be longitudinally and/or directionally stable. Te reason lies beind teir toug mission of figting. In order to provide a igly maneuverable figter aircraft, te stability requirements are relaxed, and safety of fligt are left to te pilot plus figter advanced automatic control system. Tus, we primarily design te orizontal and vertical tail to satisfy longitudinal and directional requirements ontrol ontrol is defined as te ability of an aircraft to vary te aircraft condition from trim condition 1 (say cruise) to trim condition (say climb). Due to tree axes in te aircraft coordinate system, tere are tree brances in aircraft control: 1. Lateral control;. Longitudinal control; 3. Directional control. Lateral control is te control of an aircraft about x-axis; longitudinal control is te control of an aircraft about y-axis; and directional control is te control of an aircraft about z-axis. In a conventional aircraft, te lateral control is applied toug aileron; te longitudinal control is applied toug elevator; and te directional control is applied toug rudder. Since te elevator is part of te orizontal tail, and rudder is part of te vertical tail; te tail designer must make sure tat orizontal tail and vertical tail are large enoug to satisfy longitudinal and directional controllability requirements. Based on te Section 145 of PAR 3 of Federal Aviation Regulations [4] wic concerns about longitudinal control of GA aircraft: Wit te airplane as nearly as possible in trim at 1.3 S1, it must be possible, at speeds below te trim speed, to pitc te nose downward so tat te rate of increase in airspeed allows prompt acceleration to te trim speed. Te following is reproduced from Section 147 of PAR 3 of Federal Aviation Regulations [4] wic concerns about directional and lateral control of GA aircraft: (a) For eac multiengine airplane, it must be possible, wile olding te wings level witin five degrees, to make sudden canges in eading safely in bot directions. Tis ability must be sown at 1.4 S1 wit n apter 6 Tail Design 93

23 eading canges up to 15 degrees, except tat te eading cange at wic te rudder force corresponds to te limits specified in need not be exceeded, (b) For eac multiengine airplane, it must be possible to regain full control of te airplane witout exceeding a bank angle of 45 degrees, reacing a dangerous attitude or encountering dangerous caracteristics, in te event of a sudden and complete failure of te critical engine, making allowance for a delay of two seconds in te initiation of recovery action appropriate to te situation, wit te airplane initially in trim. (c) For all airplanes, it must be sown tat te airplane is safely controllable witout te use of te primary lateral control system in any all-engine configuration(s) and at any speed or altitude witin te approved operating envelope. It must also be sown tat te airplane's fligt caracteristics are not impaired below a level needed to permit continued safe fligt and te ability to maintain attitudes suitable for a controlled landing witout exceeding te operational and structural limitations of te airplane. If a single failure of any one connecting or transmitting link in te lateral control system would also cause te loss of additional control system(s), compliance wit te above requirement must be sown wit tose additional systems also assumed to be inoperative. Since te design of control surfaces are covered in details in apter 1, more information about controllability requirements can be found tere. In a case were a orizontal tail design satisfies te longitudinal trim and stability requirements, but is unable to satisfy te longitudinal control requirements, te orizontal tail parameters must be revised. In a similar fasion, if a vertical tail design satisfies te directional trim and stability requirements, but is unable to satisfy te directional control requirements, te vertical tail parameters must be revised Handling Qualities Stability and control are at odds wit eac oter. Te reinforcement of stability in an aircraft design weakens te aircraft controllability, wile te improvement of controllability of an aircraft as negative effect on te aircraft stability. As te stability features of an aircraft is improved, its controllability features is degraded. A igly stable aircraft (suc as passenger aircraft) tends to be less controllable, wile a igly maneuverable aircraft (suc as a figter or a missile) tends to be less stable or even not stable. Te decision about te extent of stability and controllability is very ard and crucial to make for an aircraft designer. Te provision of longitudinal and directional stability are almost straigt forward, compared wit lateral stability tat tends to negatively influence oter desired aspects of an aircraft. In majority of cases, te provision of lateral stability is very ard to acieve suc tat majority of aircraft, even transport aircraft, suffer from te lack of sufficient lateral stability. Te determination of te borderline between stability and control of an aircraft is executed troug a topic referred to as andling qualities. Te degree of stability and te degree of controllability ave been investigated and establised by te standards suc as Federal Aviation Regulations (FAR) standards, or Military Standards (MIL-STD). Te andling qualities (or sometimes called flying qualities) are determined to guarantees te comfort of te pilot and passengers as well as te airwortiness standards. Te andling qualities requirements largely influence several aspects of te orizontal and vertical tail. Te initial selection of tail parameters (suc as tail volume coefficient) must include a satisfactory acievement of andling quality requirements. If your customer as net requested for specific and unique andling qualities, you can trust and follow te publised standards suc as FAR and MIL-STD. More details of andling qualities are presented in apter 1, Section 1.3. Te tecnique outlined in tis apter 6 Tail Design 94

24 capter considers te public aviation standards tat are available to aircraft designers in libraries and official government websites Tail configuration Basic Tail onfiguration Te purpose of tis section is to present design requirements, and design information related to te selection of te tail configuration. Te term tail in tis section means te combination of orizontal and vertical tail. Te first step in te tail design is te selection of te tail configuration. Te coice of te tail configuration is te output of a selection process, not te result of a matematical calculation. Te decision for te selection of te tail configuration must be made based on te reasoning, logic and evaluation of various configurations against design requirements. Te list of design requirements tat must be considered and satisfied in te selection of tail configurations is as follows: 1. Longitudinal trim. Directional trim 3. Lateral trim 4. Longitudinal stability 5. Directional stability 6. Lateral stability 7. Manufacturability and controllability 8. Handling qualities (e.g. passenger comfort) 9. Stealt (only in some specific military aircraft) 10. Operational requirements (e.g. pilot view) 11. Airwortiness (e.g. safety, tail stall, and deep stall) 1. Survivability (e.g. spin recovery) 13. ost 14. ompetitiveness (in te market) 15. Size limits (for example, an aircraft may be required to ave a limited eigt; for instance, for te angar space limits. Tis will influence te vertical tail configuration) Te tecnical details of tese requirements must be establised prior to te selection of te tail configuration. Often times, no single tail configuration can satisfy all design requirements; ence, a compromise must be made. After a few acceptable candidates are prepared, a table based on te systems engineering approac must be provided to determine te final selection; i.e. apter 6 Tail Design 95

25 best coice. Sometimes a design requirement (suc as lateral stability) is completely ignored (i.e. sacrificed), in order to satisfy oter more important design requirements (suc as maneuverability or stealt requirements). In general, te following tail configurations are available tat are capable of satisfying te design requirements in one way or anoter: 1. Aft tail and one aft vertical tail. Aft tail and twin aft vertical tail 3. anard and aft vertical tail 4. anard and twin wing vertical tail 5. Triplane (i.e. aft tail as aft plane, and canard as fore-plane plus wing as te tird plane) 6. Tailless (delta wing wit one vertical tail) 7. No formal tail (also known as flying wing, suc as B- Spirit (Figure 6.8)). Figure 6.7 depicts tese configurations. Based on te statistics, majority of aircraft designers (about 85 percent) are selecting te aft tail configuration. About 10 percent of current aircraft ave canard. And about 5 percent of today s aircraft ave oter configurations tat could be called as unconventional tail configuration. Te general caracteristics of te canard will be described in Section Aft tail and one aft vertical tail. Aft tail and two aft vertical tails 3. anard and aft vertical tail 4. anard and two wing vertical tail 5. Triplane 6. Delta wing wit one vertical tail Figure 6.7. Basic tail configurations Te first configuration (aft tail and one aft vertical tail) as several sub-configurations tat will be examined in Section In te first tree configurations (see figures troug apter 6 Tail Design 96

26 6.7-3), vertical tail is installed at te aft of fuselage, wile in te fourt configuration (see figure 6.7-5); two vertical tails are installed at te wing tips. Te features of te canard configuration will be examined in Section 6.5. Te selection of twin vertical tail (T) largely originates mainly from te fact tat it provides ig directional control, wile does not degrades te roll control. Since two sort-span vertical tails (see figure 6.7-4) tend to ave a lower mass moment of inertia about x axis; compared wit one long-span vertical tail. Figure illustrates te aircraft Piaggio P-180 wit a Triplane configuration. Te primary functions of te tail in aircraft wit no tail configuration are performed via oter component or automatic control system. For instance, in ang gliders, te longitudinal trim of te aircraft is employed by pilot via moving is/er body in order to vary te cg of te aircraft. Furtermore, te longitudinal stability requirements are satisfied troug a particular wing airfoil section tat as a negative camber at te trailing edge (i.e. reflexed trailing edge) as sketced in figure 6.9. Moreover, te pilot is able to continuously control and make a considerable cange to te wing airfoil section via a manual mecanism provided for im/er. Tis tecnique is typically employed in ang gliders. 1. Aero Designs Pulsar (aft tail). Dassault Rafale (canard) 3. B- Spirit (flying wing) (ourtesy of Jenny offey) (ourtesy of Antony Osborne) 4. Lockeed F-117 Nigtawk (-tail) 5. elocity 173 Elite (canard and twin T) 6. Piaggio P- 180 (triplane) (ourtesy of Antony Osborne) (ourtesy of Jenny offey) (ourtesy of Hansueli Krapf) 7. De Havilland DH-110 Sea ixen (unconventional twin T) 8. PZL-Mielec M-8 Bryza (H-tail) (ourtesy of Jenny offey) (ourtesy of Jenny offey) Figure 6.8. Several aircraft wit various tail configurations apter 6 Tail Design 97

27 Majority of GA aircraft ave a conventional aft orizontal tail, and an aft vertical tail configuration. Majority of figter aircraft ave one aft tail and twin vertical tails, due to teir maneuverability requirements. Some European figters (mainly Frenc figters; suc as Dassault Rafale) ave canard configuration (see figure 6.8-). Te primary reason for te Bomber aircraft B- Spirit flying (figure 6.8-3) wing is te stealt requirements. Most ang gliders do not employ a orizontal tail, tey owever, satisfy te longitudinal stability requirements troug a wing reflex trailing edge. In some cases, some aircraft configurations impose some limits on te tail configuration. For instance, wen a prop-driven engine is considered to be installed inside aft fuselage (i.e. puser aircraft as seen in MQ-9 Reaper UA (Figure 6.1), te aft orizontal is not a proper option. Te reason is tat te orizontal tail will be under continuous wake effect of te engine, and its efficiency will be degraded. By te same reasoning, a canard is not a good option, if a prop-driven engine is inside fuselage nose (e.g. Aero Designs Pulsar as sown in figure 6.8-1)). Te main disadvantage for a iger number of tails; suc as tri-plane (figure 6.8-6) or two vertical tails (see figure and 6.8-8); are te iger cost of manufacturing and te complexity of te design. Figure illustrates te PZL-Mielec M-8 Bryza wit an H-tail. Leading edge Trailing edge Figure 6.9. A wing airfoil section wit reflexed trailing edge Te basic rule for te selection of te tail configuration is as follows: In general, te conventional aft tail configuration (Figure 6.7-1) is often able to satisfy all design requirements, unless one or more requirements imply for anoter configuration. Tus, it is recommended to begin wit conventional aft tail configuration and ten to evaluate its features against te design requirements. If one or more requirements are not satisfies, cange to a new configuration nearest wit te current configuration, until all requirements could be satisfied. If te aircraft is in te manufacturing pase and a cange is needed to improve te longitudinal and directional stability, one can utilize a smaller auxiliary orizontal tail (sometimes referred to as stabilon) and ventral stake. Tese tricks are employed in te twin-turboprop regional transport aircraft Beec 1900D Aft Tail onfiguration Aft tail as several configurations tat all are able to satisfy te design configurations. Eac as unique advantages and disadvantages. Te purpose of tis section is to provide a comparison between tese configurations to enable an aircraft designer to make decision and to select te best one. Te aft tail configurations are as follows: 1. onventional,. T-sape, 3. ruciform (+), 4. H-sape, 5. Triple-tail, 6. - tail, 7. Inverted -tail, 8. Improved -tail 9. Y-tail, 10. Twin vertical tail, 11. Boom-mounted, 1. Inverted boom-mounted, 13. Ring-sape, 14. Twin T, 15. alf T, 16. U-tail. Figure 6.10 provides several aft tail configurations. apter 6 Tail Design 98

28 1. onventional Te conventional tail or inverted T-sape configuration (see figure ) is te simplest configuration and te most convenient to perform all tail functions (i.e. trim, stability, and control). Te analysis and evaluation of te performance of a conventional tail is straigt forward. Tis configuration includes one orizontal tail (two left and rigt sections); located on te aft fuselage; and one vertical tail (one section); located on top of te aft fuselage. Bot orizontal and vertical tails are located and mounted to te aft of fuselage. Te orizontal tail is mainly employed to satisfy te longitudinal trim and stability requirements, wile vertical tail is mainly used to satisfy te directional trim and stability requirements. If te designer as low experience, it is recommended to initially select te conventional tail configuration. Almost all fligt dynamics textbook examine te features of a conventional tail, but not every fligt dynamics textbook discuss te caracteristics of oter tail configurations. Te designer must be professional and skillful on te area of te trim analysis, stability analysis, and control analysis, if oter configurations are selected. Tis is one of te reasons tat about 60 percent of current aircraft in service ave conventional tail. Furtermore it as ligt weigt, efficient, and performs at regular fligt conditions. GA aircraft suc essna 17 (Figure 11.15), essna 560 itation, Beec King Air 90B, Learjet 60, Embraer EMB-314 Super Tucano (Figure 10.6), Socata TBM 700, and Pilatus P-9; large transport aircraft suc as Fokker 60, Boeing 747 (Figures 3.7, 3.1, and 9.4), Boring 777 (see figure 6.1-1), Airbus 340 (Figure 8.0), and figter aircraft suc as F-16 Eagle (Figure 3.1), Harrier GR. Mk 7 (Figure 4.19), and Panavia Tornado F. Mk3 (Figure 5.61) all ave conventional tail. Figure 6.8- illustrates te aircraft Aero Designs Pulsar wit a conventional tail configuration. 1. onventional. T-tail 3. ruciform 4. H-tail 5. -tail 6. Y-tail 7. Twin vertical tail 8. Boom mounted Figure Several aft tail configurations apter 6 Tail Design 99

29 . T-tail A T-tail is an aft tail configuration (see figure 6.10-) tat looks like te letter T ; wic implies te vertical tail is located on top of te orizontal tail. Te T-tail configuration is anoter aft tail configuration tat provides a few advantages, wile it as a few disadvantages. Te major advantage of a T-tail configuration is tat it is out of te regions of wing wake, wing downwas, wing vortices, and engine exit flow (i.e. ot and turbulent ig speed gas). Tis allows te orizontal tail to provide a iger efficiency, and a safer structure. Te lower influence from te wing results in a smaller orizontal tail area; and te lower effect from te engine leads in a less tail vibration and buffet. Te less tail vibration increases te life of te tail wit a lower fatigue problem. Furtermore, anoter advantage of te T-tail is te positive influence of orizontal tail on te vertical tail. It is referred to as te end-plate effect and results in a smaller vertical tail area. In contrast, te disadvantages tat associated wit a T-tail are: 1. eavier vertical tail structure,. deep stall. Te bending moment created by te orizontal tail must be transferred to te fuselage troug te vertical tail. Tis structural beavior requires te vertical tail main spar to be stronger; wic cause te vertical tail to get eavier. Aircraft wit T-tail are subject to a dangerous condition known as te deep stall [7]; wic is a stalled condition at an angle of attack far above te original stall angle. T-tail Aircraft often suffer a sever pitcing moment instability at angles well above te initial stall angle of about 13 degrees, witout wing leading edge ig lift device, or about 18 degrees, wit wing leading edge ig lift device. If te pilot allows te aircraft to enter to tis unstable region, it migt rapidly pitc up to a iger angle of about 40 degrees. Te causes of te instability are fuselage vortices, sed from te forward portion of te fuselage at ig angles of attack, and te wing and engine wakes. Tus te orizontal tail contribution on te longitudinal stability is largely reduced. Eventually, at a iger angle of attack, te orizontal tail exits te wing and nacelle wakes and te aircraft become longitudinally stable (see figure 6.11). Wing in stall > s Wing wake > s ertical tail in stall Figure Deep stall in a T-tail configuration aircraft Tis condition may be assumed as a stable condition, but it accompanies an enormous drag along wit a resulting ig rate of descent. At tis moment, te elevator and aileron effectiveness ave been severely reduced because bot wing and orizontal tail are stalled at te very ig angle of attack. Tis is known as a locked-in deep stall, a potentially fatal state. Te apter 6 Tail Design 300

30 design solutions to avoid a deep stall in a T-tail configuration are to: 1. Ensure a stable pitc down at te initial stall,. Extend te orizontal tail span substantially beyond te nacelles, and 3. Employ a mecanism to enable full down elevator angles if a deep stall occurs. In addition, te aircraft must be well protected from te initial stall by devices suc as stick saker, ligts, and stall orn. 1. Boeing 737 (onventional). Sky Arrow 1450L (T-tail) 3. Dassault Falcon 900 (ruciform) (ourtesy of Anne Deus) (ourtesy of Jenny offey) (ourtesy of Jenny offey) 4. Faircild A-10 Tunderbolt (H-tail) 5. Global awk UA (-tail) 6. MQ-9 Reaper UA (Y-tail) (ourtesy of Antony Osborne) 7. F-18 Hornet (twin T) 8. Reims F337F Super Skymaster (Boom mounted) (ourtesy of Antony Osborne) (ourtesy of Jenny offey) 9. Global Flyer (unconventional tail); (ourtesy of NASA) Figure 6.1. Several aircraft wit various aft tail configurations Despite above mentioned disadvantages of T-tail, it becomes more and popular among aircraft designers. About 5 percent of today s aircraft employ T-tail configuration. It is interesting to note tat te GA aircraft Piper erokee as two versions; erokee III (Figure 7.6) wit conventional tail, and erokee I wit T-tail. Te aircraft as a single piston engine apter 6 Tail Design 301

31 at te nose and a low wing configuration. Several GA and transport aircraft suc as Grob Starto, essna 55 itaionjet, Beec Super King Air B00, Beecjet T-1A Jayawk, Learjet 60, Gulfstream I (Figure 11.15), MD-90, Boeing 77, Fokker 100 (Figure 10.6), ARO RJ115, Bombardier BD 701 Global Express, Dassault Falcon 900 (Figure 6.1), Sky Arrow 1450L (see Figure 6.1-3), Embraer EMB-10, Airbus A400M (Figure 8.3), and Boeing (formerly McDonnell Douglas) -17 Globemaster III (Figure 9.9) employ T-tail configuration. 3. ruciform Some tail designers ave combined te advantages of conventional tail and T-tail and came up wit a new configuration known as cruciform (see figure ). Tus, te disadvantages of bot configurations are considerably released. Te cruciform; as te name implies; is a combination of orizontal tail and vertical tail suc tat it looks like a cross or + sign. Tis means tat te orizontal tail is installed at almost te middle of te vertical tail. Te location of te orizontal tail (i.e. its eigt relative to te fuselage) must be carefully determined suc tat te deep stall does not occur and at te same time, te vertical tail does not get too eavy. Several aircraft suc as Turston TA16, Dassault Falcon 000, ATR (Figure 3.8), Dassault Falcon 900B (see figure 6.1-3), Jetstream 41, Hawker 100, Mirage 000D (Figure 9.1) employ te cruciform tail configuration. 4. H-tail Te H-tail (see figure ), as te name implies, looks like te letter H. H-tail comprised of one orizontal tail in between two vertical tails. Te features associated wit an H-tail are as follows: 1. At ig angles of attack, te vertical tail is not influenced by te turbulent flow coming from fuselage.. In a multiengine turboprop aircraft, vertical tails are located beind te prop-was region. Tis causes te vertical tail to ave iger performance in te inoperative engine situation. 3. Te vertical tail end-plate effect improves te aerodynamic performance of te orizontal tail. 4. In military aircraft, te engine very ot exaust gasses could be idden from radars or infrared missiles. Tis tecnique as been employed te close support aircraft Faircild A-10 Tunderbolt (se figure 6.1-4). 5. Te H-tail allows te twin vertical tail span to be sorter. Te aircraft Lockeed constellation ad to employ an H-tail configuration to be able to park inside sort eigt angars. 6. Te lateral control of te aircraft will be improved due to te sorter vertical tail span. 7. Te H-tail allows te fuselage to be sorter, since te tail can be installed on a boom. 8. Te H-tail is sligtly eavier tan conventional; and T-tail configuration. Te reason is tat te orizontal tail must be strong enoug to support bot vertical tails. 9. Te structural design of te H-tail is more tedious tan conventional tail. As can be noticed, an H-tail configuration tends to offer several advantages and disadvantages; ence, te selection of an H-tail must be te result of a compromise process. Several GA and apter 6 Tail Design 30

32 military aircraft suc as Sadler A- Pirana, T-46, Sort Skyvan, and Faircild A-10 Tunderbolt (see figure 6.1-4) utilize H-tail configuration. 5. -tail Wen te major goal of te tail design is to reduce te total tail area, te -tail (see figure ) is a proper candidate. As te name implies, te -tail configuration as two sections, wic forms a sape tat looks like te letter. In anoter word, a -tail is similar to a orizontal tail wit ig anedral angle and witout any vertical tail. Two sections of a -tail act as bot orizontal and vertical tails. Due to te angle of eac section, te lift perpendicular to eac section as two components; one in te y-direction, and one in te z-direction. If no controller is deflected, two components in te y-direction cancel eac oter, wile two lift components in te z-direction are added togeter. Te -tail may perform te longitudinal and directional trim role satisfactorily, but it as deficiencies in maintaining te aircraft longitudinal and directional stability. In addition, te -tail design is more susceptible to Dutc roll tendencies tan a conventional tail, and total reduction in drag is minimal. Te -tail design utilizes two slanted tail surfaces to perform te same functions as te surfaces of a conventional elevator and rudder configuration. Te movable surfaces, wic are usually called ruddervator, are connected troug a special linkage tat allows te control weel to move bot surfaces simultaneously. On te oter and, displacement of te rudder pedals moves te surfaces differentially, tereby providing directional control. Wen bot rudder and elevator controls are moved by te pilot, a control mixing mecanism moves eac surface te appropriate amount. Te control system for te -tail is more complex tan tat required for a conventional tail. Ruddervator induce te undesirable penomenon of te adverse roll-yaw coupling. Te solution could be an inverted -tail configuration tat as oter disadvantages. Few aircraft suc as Beeccraft Bonanza 35, Robin ATL lub, Aviation Farm J5 Marco, igaltitude, long-endurance unmanned aerial reconnaissance veicle Global Hawk (see figure 6.1-5), and Lockeed F-117 Nigtawk (Figure 6.8-4) employ a -tail. Unmanned aircraft General Atomic MQ-1 Predator as an inverted -tail plus a vertical tail under te aft fuselage. 6. Y-tail Te Y-tail (see figure ) is an extension to te -tail, since it as an extra surface located under te aft fuselage. Tis extra surface reduces te tail contribution in te aircraft diedral effect. Te lower section plays te role of vertical tail, wile te two upper sections play te role of te orizontal tail. Terefore, te lower surface as rudder, and te control surface of te upper section plays te role of te elevator. Tus, te complexity of te Y-tail is muc lower tan te -tail. One of te reasons tis tail configuration is used is to keep te tail out of effect of te wing wake at ig angles of attack. Te lower section may limit te performance of te aircraft during take-off and landing, since te tail itting te ground must be avoided. Tis configuration is not popular, and few old aircraft ad tis configuration. Unmanned aircraft General Atomic MQ-9 Reaper (see figure 6.1-6) employ Y-tail configuration. 7. Twin vertical tail A twin vertical tail configuration (see figure ) as a regular orizontal tail, but two separate and often parallel vertical tails. Te twin vertical tail largely improves te directional apter 6 Tail Design 303

33 controllability of an aircraft. Two sort span vertical tails ave smaller mass moment of inertia about te x-axis, compared wit a long span vertical tail. Tus a twin tail as te same directional control power, wile it as a less negative effect of te roll control. In addition, bot rudders are almost out of te fuselage wake region, since tey are not located along fuselage center line. A disadvantage of tis configuration is tat tey ave sligtly eavier weigt compared wit te conventional tail. Several modern figter aircraft suc as F-14 Pantom (Figure 5.46), McDonnell Douglas F-15 Eagle (Figure 4.1), and F/A-18 Hornet (Figure 6.7-4,.11, and 6.1) employ te twin tail configuration. 8. Boom-mounted Sometime some specific design requirements do not allow te aircraft designer to select te conventional tail configuration. For instance, if a prop-driven engine must be installed at te rear of te fuselage, a conventional tail will tend to ave a low efficiency. Te reason is te interference between te propeller flow and te tail. One of te options is to use two booms and install te tail at te end of te booms (see figure ). Tis option in turn, allows using a sorter fuselage, but overall aircraft weigt would be sligtly eavier. Two options are: 1. U-tail,. Inverted U-tail. Te reconnaissance aircraft Reims F337F Super Skymaster (Figure 6.1-8) and Rutan oyager (Figure 4.0) employs a boom mounted U-tail. Te twin turboprop ligt utility aircraft Partenavia PD.90 Tapete Air Truck employs a boom mounted inverted U tail configuration wic allows for an integrated loading ramp/air-stair. 9. Oter configurations Tere is variety of oter unconventional tail configurations wic are usually te forced options to a designer. For instance, sometimes some specific mission requirements suc as loading, operational, structural, and engine requirements removes te conventional or T-tail configuration from te list of possible options. Tus, te designer must come up wit a new configuration to make an aircraft trimmed and stable trougout fligt. Few invented unconventional configurations are as follows: 1. Boom mounted twin vertical tails plus canard (e.g. Rutan oyager),. Boom mounted twin vertical tails plus two separated orizontal tail (e.g. Space Sip One (figure 6.1-9)), 3. Twin T-tail (e.g. Global Flyer (figure 6.1-9)), 4. T-tail plus two fins and an auxiliary fixed orizontal tail (e.g. Beec 1900 D of ontinental Express), 5. Ring tail (e.g. agny 000), and 6. Triple vertical tail anard or Aft Tail One of te critical issues in te design of te orizontal tail is te selection of te location of orizontal tail. Te options are: 1. Aft tail (or sometimes referred to as tail aft), and. Fore plane or anard 3 (sometimes referred to as tail-first). As discussed before, te primary function of te orizontal tail is longitudinal trim, and ten, longitudinal stability. Bot aft tail and canard are capable of satisfactorily fulfilling bot mission requirements. However, tere are several aspects of fligt features tat are influenced differently by eiter of tese two options. It is interesting to note tat te first aircraft in istory (i.e. Wrigt Flyer) ad canard configuration. anard configuration is not as popular as aft tail, but several GA and military and few transport aircraft employ canard. Examples are Rutan arieze (Figure 3.1), Rutan oyager (Figure 4.0), 3 anard is originally a Frenc word wic means duck. Some early aircraft suc as Frenc anard ision ad a tail-first configuration wic was seen by observers to resemble a flying duck. apter 6 Tail Design 304

34 Mirage 000, Dassault Rafale (Figure 6.8), Eurofigter Typoon (Figure 3.7), B-1B Lancer, Saab iggen, Grumman X-9, Piaggio P-180 Avanti (figure 6.8-6), XB-70 alkyrie, and Beeccraft Starsip (Figure 6.18). L wf wing L tail ac wf cg W 1. Positive tail lift L wf cg wing tail L W ac wf. Negative tail lift L wf canard wing L ac wf W cg L wf 3. Negative canard lift L cg wing canard W ac wf 4. Positive canard lift Figure Te lift of te tail (or canard) in four configurations To compreend te fundamental differences between an aft tail and a canard, consider four aircraft configurations as sown in Figure 6.1 wic two aircraft ave aft tail wile te oter two ave canard. In tis figure, te wing nose-down pitcing moment is not sown for apter 6 Tail Design 305

35 simplicity. Te difference between eac two figure is te location of te cg compared wit te wing-fuselage aerodynamic center. Tis simple difference causes a variety of advantages and disadvantages for canard over te conventional aft tail. In all four configurations, te longitudinal trim must old: M M cg cg 0 0 M L l L owf wf o 0 0 M L l L owf F 0 W L z wf F 0 W L z wf L L c wf o (aft tail configuration) (canard configuration) (6.37a) (6.37b) (aft tail configuration) (6.38a) (canard configuration) (6.38b) were L denotes te canard lift. Equations 6.37 and 6.38 indicate tat te aft tail lift or canard lift migt be positive, or negative, depending upon te location of aircraft cg relative to wingfuselage aerodynamic center (see figure 6.13). Equations 6.37b and b are utilized to determine te value and te direction of te canard lift to satisfy trim requirements. It is obvious tat te canard lift is sometimes negative (see figure ). Keeping in mind te above basic difference between aft tail and canard, a comparison between features of canard as compared wit aft tail is presented. Te canard avoids deep stall 100%. Tis gets interesting, wen we note tat about 3 percent of world aircraft cras relates to deep stall. onsider a pilot wo intends to increase te wing angle of attack in order to eiter take-off, or climb, or land, or land. Since canard is located forward of te wing, te canard will stall first (i.e. before wing stalls). Tis causes te canard to drop and exits out of stall before te wing enters to stall. Te canard drop is due to te fact tat wen it stalls, its lift is reduced and causes te aircraft nose to drop. Tis is regarded as one of te major advantages of canard and makes te canard configuration mus safer tat aft tail configuration. Since te canard stalls before te main wing, te wing can never reac its maximum lift capability. Hence, te main wing must be larger tan on te conventional configuration, wic increases its weigt and also zero-lift drag. 1. A canard as a iger efficiency wen compared wit aft tail. Te reason is tat it is located in front of wing, so te wing wake does not influence te canard aerodynamic caracteristics. Wing, owever, is located aft of canard; ence, it is negatively affected by te canard wake. Tus a wing in a canard configuration as a lower aerodynamic efficiency (i.e. lower lift) wen compared wit an aircraft wit aft tail configuration.. It is not appropriate to employ canard wen te engine is puser and located at te fuselage nose. Te reason is tat te aircraft nose will be eavy and te cg adjustment is difficult. Moreover, te structural design of fuselage nose is somewat complicated, since it must old bot engine and canard. 3. An aircraft wit a canard configuration tends to ave a smaller static margin compared wit an aircraft wit a conventional aft tail configuration. In anoter word, te distance between aircraft neutral point and aircraft center of gravity is sorter. Tis makes te apter 6 Tail Design 306

36 canard aircraft longitudinally statically less stable. Tis feature is regarded as a disadvantage for canard configuration. 4. Te center of gravity range in an aircraft wit a canard configuration tends to be wider; ence, it is more flexible in te load transportation area. 5. Due to te forward location of a canard, te aircraft cg moves sligtly forward compared wit an aircraft wit a conventional aft tail configuration. Tis feature requires a sligtly larger vertical tail for directional trim and stability. 6. A canard tends to generate a lower trim drag compared wit an aft tail. In anoter word, a canard aircraft produces less lift-dependent drag to longitudinally trim te aircraft. However, tis feature may leads in a larger wetted area (S wet ). 7. One of te potential design callenges in a canard aircraft is to optimally locate te fuel tank. Te general rule is to place te fuel tank near te aircraft center of gravity as close as possible, in order to avoid a large movement of cg during te fligt operation. Te aircraft cg in a canard configuration, if fuel tank is inside te wing, is often forward of te fuel tank. To improve te cg location, designers would rater to place te fuel tank into te fuselage, wic in turn increases te possibility of aircraft fire. Anoter solution is to considerably increase te wing root cord (i.e. employing strake) and to place te fuel tank in wing root. But tis tecnique increases te wing wetted area and reduces te cruise efficiency. Te canard aircraft Beeccraft Starsip (Figure 6.18) as a wing strake and utilizes tis tecnique. 8. A canard obscures te view of te pilot. Tis is anoter disadvantage of te canard configuration. 9. Often te canard generates a positive lift (see figure ) wile a conventional tail often produces a negative lift (see figure 6.13-). Te reason is tat te aircraft cg in a canard configuration is often forward of te wing-fuselage ac. Te aircraft cg in a conventional tail configuration is typically aft of te wing-fuselage ac. Recall tat te cg move during fligt as te fuel burns. Te cg range, in a modern aircraft wit a conventional tail or a canard is usually determined suc tat te cg is most of te times forward of te wing aerodynamic center. However, in a fewer instances of cruising fligt, te cg is aft of te wing aerodynamic center. Tus, in an aircraft wit a conventional tail, during te cruising fligt, te cg usually moves from te most forward location toward te most aft location. However, in an aircraft wit a canard, during te cruising fligt, te cg often moves from te most aft location toward te most forward location. Tus, a canard often generates part of te aircraft lift, wile a tail most of te times cancels part of te lift generated by te wing. Tis feature tends to reduce te aircraft weigt and increases te aircraft cruising speed. In addition, during a take-off wic te wing nose-down pitcing moment is large, te canard lift is iger. Using te same logic, it can be sown tat te canard lift is iger during supersonic speeds. Recall tat in a supersonic speed, te wing aerodynamic center move aft toward about 50 percent of te mean aerodynamic cord. Tis is one of te reasons tat some European supersonic figters, suc as Mirage 000 (Figure 9.1), ave employed te canard configuration. 10. Item 9 results in te following conclusion: An aircraft wit a canard is sligtly ligter tan an aircraft wit a conventional tail. 11. In general, te canard aerodynamic and stability analysis tecniques are considerably more complicated tan te tecnique to evaluate te aerodynamic feature and stability apter 6 Tail Design 307

37 analysis of te conventional tail configuration aircraft. Literature surveys include a variety of publised materials regarding conventional tail, wile muc less papers and tecnical reports are available for canard analysis. Tus te design of a canard is more time intensive and more complicated tan te conventional tail design. 1. A canard configuration seems to be more stylis and more attractive tan a conventional tail. 13. A canard is more efficient for fulfilling te longitudinal trim requirements, wile a conventional tail tends to be more efficient for fulfilling te longitudinal control requirements. In general, canard designs fall into two main categories: te lifting-canard and te controlcanard. As te name implies, in a lifting-canard te weigt of te aircraft is sared between te main wing and te canard wing. Te upward canard lift tends to increase te overall lift capability of te configuration. Wit a lifting-canard, te main wing must be located furter aft of te cg range tan wit a conventional aft tail, and tis increases te pitcing moment caused by trailing-edge flaps. Te first airplane to fly, te Wrigt Flyer, and X-9 ad a lifting-canard. Figure 6.18 depicts two (Beec Starsip and Saab Gripen (Figures 6.18 and.7)) aircraft wit canard configuration. In is interesting to know tat about 98% of American aircraft are conventional, not canard. In te control-canard, most of te weigt of te aircraft is carried by te main wing and te canard wing serves primarily as te longitudinal control device. A control-canard could be all moving or could ave a large elevator. Te control-canard as often iger aspect ratio and employs a ticker airfoil section tan a lifting-canard. A control-canard mostly operates at zero angle of attack. Figter aircraft wit a canard configuration, suc as Eurofigter Typoon (Figure 3.7), typically ave a control-canard. One benefit obtainable from a control-canard is avoidance of pitc-up. An all-moving canard capable of a significant nose-down deflection will protect against pitc-up. ontrol canards ave poor stealt caracteristics, because tey present large moving surfaces forward of te wing. Te pros and cons of te canard versus a conventional tail configuration are numerous and complex and it is ard to say wic is superior witout considering a specific design requirement. One must use systems engineering tecnique to compromise and to decide te tail configuration. In te preliminary design pase, te suggestion is to begin wit a conventional tail, unless te designer as a solid reasoning to employ a canard configuration Optimum Tail Arm One of te tail parameters tat must be determined during te tail design process is te tail arm (l t ), wic is te distance between tail aerodynamic center to te aircraft center of gravity (see figure 6.3). Tail arm serves as te arm for te tail pitcing moment (i.e. tail lift multiplied by tail arm) about aircraft cg to maintain te longitudinal trim. To determine te tail arm one must establis te criteria based on te design requirements. Two basic tail parameters wic interact most are tail arm and tail area, te latter is responsible for generation of te tail lift. As te tail arm is increased, te tail area must be decreased, wile as te tail arm is reduced, te tail area must be increased. Bot sort arm (as in figters), or long arm (as in most transport aircraft) are capable of satisfying longitudinal trim requirements, given te appropriate necessary tail area. apter 6 Tail Design 308

38 But te question is tat wat tail arm is te optimum one. To answer tis question, one must look at te oter design requirements. Two very significant aircraft general design requirements are aircraft low weigt and low drag. Bot of tese may be combined and translated as te requirement for a low aircraft wetted area. As te orizontal tail arm is increased, te fuselage wetted area is increased, but orizontal tail wetted area is decreased. Also, as te orizontal tail arm is decreased, te fuselage wetted area is decreased, but orizontal tail wetted area is increased. Hence, we are looking to determine te optimum tail arm to minimize drag; wic in turn means to minimize te total wetted area of te aft portion of te aircraft. Te following is a general educational approac to determine te optimum tail arm; ence, one must develop is/er own tecnique and derive more accurate equation based on te suggested approac. Te approac is based on te fact tat te aircraft zero-lift drag is essentially a function of te aircraft wetted area. MA wing ac w Aft fuselage ac tail l L aft-fus Figure Top view of aft portion of te aircraft Terefore, if te total wetted area is minimized, te aircraft zero-lift drag will be minimized. Moreover, te tecnique will influence te fuselage lengt, since te aft portion of te fuselage must structurally support te tail. onsider te top view of aft aircraft (see figure 6.14) tat includes aft portion of te fuselage plus te orizontal tail. Te wetted area of te aft portion of te aircraft is te summation of te wetted area of te aft portion of te fuselage ( ) plus te wetted area of te orizontal tail ( S wet t ). S wetaft fus S wetaft S S (6.39) wetaft fus wet apter 6 Tail Design 309

39 Here we assume tat aft portion of te fuselage is conical. Hence, te wetted area of te aft portion of te fuselage is S wetaft fus 1 D f L fusaft (6.40) were D f is te maximum fuselage diameter and fuselage. At te moment, it is assumed tat L fus is te lengt of te aft portion of te aft L is equal to alf of te fuselage lengt (L f ). On te oter and, te wetted area of te orizontal tail is about twice te tail planform area: fusaft Swet t S (6.41) But, te tail volume coefficient is defined as in equation 6.4, so: H ls S S S l H (6.4) So S S wet l H (6.43) Substituting equation 6.41 and 6.43 into 6.39 yields: S wet 1 S H D f L f (6.44) aft l aft Te relationsip between L fusaft 6.14). We simply assume tey are equal ( and l depends upon te location of te orizontal tail (see figure L fus aft l ). Tis assumption is not accurate for every aircraft configuration, but it is a reasonable assumption based on te data on Table 6.. Tis assumption will be modified later. In order to minimize zero-lift drag of te aft part of te aircraft, we ave to differentiate te wetted area of te aft part of te aircraft wit respect to tail arm (see figure 6.15) and ten set it equal to zero. Te differentiation yields: S wet S wet_min l opt l Figure Te variation of wetted area wit respect to tail arm apter 6 Tail Design 310

40 S wet aft l 1 D f S l H 0 (6.45) Te optimum tail arm is obtained by solving tis equation as follows: l opt 4S D f H (6.46) To compensate for our inaccurate assumption, we add a fudge factor as follows: l opt K c 4S D f H (6.47) were K c is a correction factor and varies between 1 and 1.4 depending on te aircraft configuration. K c = 1 is used wen te aft portion of te fuselage as a conical sape. As te sape of te aft portion of te fuselage goes furter away from a conical sape, te K c factor is increased up to 1.4. As a general rule, for a single-seat single engine prop-driven GA aircraft, te factor K c is assumed to be 1.1, but for a transport aircraft, K c will be 1.4. Note tat in a large transport aircraft, te most of te fuselage sape is cylindrical, and only its very aft portion as a conical sape. Terefore if te orizontal tail is located at l opt, te wetted area of te aft part of te aircraft will be minimized, so te drag of te aft part of te aircraft will be minimized. Wen te orizontal tail arm is less tan tree time te wing MA ( 3 ), te aircraft is said to be sortcoupled. An aircraft wit suc tail configuration possesses te longitudinal trim penalty (e.g. figters). Example 6.1 provides a sample calculation. Example 6.1 onsider a twin-seat GA aircraft wose wing reference area is 10 m and wing mean aerodynamic cord is 1 m. Te longitudinal stability requirements dictate te tail volume coefficient to be 0.6. If te maximum fuselage diameter is 117 cm, determine te optimum tail arm and ten calculate te orizontal tail area. Assume tat te aft portion of te fuselage is conical. Solution: Te aircraft is a GA and as two seats, so te factor K c is assumed to be 1.4. Using equation 6.47, we ave 4S H lopt K c 1.4 lopt D 1.17 f m (6.47) Te orizontal tail area is calculated by employing tail volume coefficient equation as follows: ls S l H H S m (6.4) S apter 6 Tail Design 311

41 6.7. Horizontal Tail Parameters After te tail configuration is determined, te orizontal tail and vertical tail can be designed almost independently. Tis section presents te tecnique to design te orizontal tail and te metod to determine orizontal tail parameters. Since te orizontal tail is a lifting surface and also several caracteristics of wing and tail are similar (as discussed in apter 5), some aspects of te orizontal tail suc as taper ratio, sweep angle, diedral angle and airfoil section, are discussed in brief. Te orizontal tail design is also an iterative process and is strongly functions of several wing parameters and few fuselage parameters. Hence, as soon as te major wing and fuselage parameters are canged, te tail must be redesigned and its parameters need to be updated Horizontal Tail Design Fundamental Governing Equation Horizontal tail design fundamental governing equation must be driven based on te primary function of te orizontal tail (i.e. longitudinal trim). Figure 6. depicts a general case of an aircraft along wit te sources of forces along x and z axes, and moments about y axis wic are influencing te aircraft longitudinal trim. Te longitudinal trim requires tat te summation of all moments about y axis must be zero: M were cg 0 M M M M M M 0 M owf owf Lwf L o Teng denotes nose-down wing-fuselage aerodynamic pitcing moment, pitcing moment generated by te wing-fuselage lift, generated by te orizontal tail lift, pitcing moment, M Teng M o Dw M L M Lwf (6.48) denotes te denotes te pitcing moment denotes nose-down orizontal tail aerodynamic denotes te pitcing moment generated by te engine trust, and denotes te pitcing moment generated by te wing drag. Te sign of te eac pitcing moment depend upon te location of te source force relative to te aircraft center of gravity. Tis equation must old at all fligt conditions, but te orizontal tail is designed for te cruising fligt, since te aircraft spends muc of its fligt time in cruise. For oter fligt conditions, a control surface suc as te elevator will contribute. Based on te aerodynamics fundamentals, two aerodynamic pitcing moments of wing and orizontal tail are always nose down (i.e. negative). Te sign of wing drag moment depends on te wing configuration. For instance, a ig-wing generates a nose up pitcing moment, wile a low-wing generates a nose down pitcing moment. Te sign of engine trust moment depends on te trust line and engine incidence. If te engine as a setting angle oter tan zero, bot orizontal and vertical components will contribute to te longitudinal trim. Te major unknown in tis equation is te orizontal tail lift. Anoter requirements for longitudinal trim is tat te summations of all forces along x and z-axes must be zero. Only te summation of forces along te z axis contributes to te tail design: F z 0 L T sin( i ) L 0 wf T M Dw (6.49) were T is te engine trust and i T is te engine trust setting angle (i.e. te angle between te trust line and te x-axis). Tis angle almost always is not zero. Te reason is te engine trust contribution to te aircraft longitudinal stability. Te typical engine setting angle is about to 4 apter 6 Tail Design 31

42 degrees. Te orizontal tail designer sould expand two equations of 6.48 and 6.49 and solve simultaneously for two unknowns of wing lift and orizontal tail lift. Te latter is employed in te orizontal tail design. Te derivation is left to te reader. It is presumed tat te orizontal tail designer is familiar wit te fligt dynamics principles and is capable of deriving te complete set of longitudinal trim equations based on te aircraft configuration. Since te goal of tis textbook is educational, so a simple version of longitudinal trim equation is employed. If te pitcing moments of engine trust, wing drag, and orizontal tail pitcing moment are ignored (as sown in figure 6.3), te non-dimensional orizontal tail design principle equation is as derived earlier: mowf L 0 o H L (6.9) Te full derivation as been introduced is Section 6.. Tis equation as tree terms, te last of wic is te orizontal tail contribution to te aircraft longitudinal trim. Te cruising fligt is considered for orizontal tail design application. Te equation as only two unknowns (i.e. and L ). Te first unknown (orizontal tail volume coefficient; ) is determined primarily based on te longitudinal stability requirements. Te longitudinal flying qualities requirements govern tis parameter. Te reader is encouraged to consult wit References [1] and [6] for a full guidance. However, apter 1 presents a summary of longitudinal flying qualities requirements. A iger value for results in a longer fuselage, and/or smaller wing and and/or a larger orizontal tail. H H As te value of is increased, te aircraft becomes longitudinally more stable. On te oter and, a more stable aircraft means a less controllable fligt veicle. Hence, a lower value for causes te aircraft to become longitudinally more controllable and less stable. If te orizontal tail design is at te preliminary design pase; and te oter aircraft components ave not yet been designed; a typical value for must be selected. Table 6.4 illustrates te typical values for orizontal and vertical tail volume coefficients. Te values are driven from te current successful aircraft statistics. A number from tis table based on te aircraft mission and configuration is recommended at te early design pase. Wen te oter aircraft components are designed and teir data are available, a more accurate value for H may be determined. H H Te variable o denotes te non-dimensional wing-fuselage aerodynamic center ( position. A typical value for o is about 0. to 0.5 for majority of aircraft configurations. [6] and [1] introduce a precise tecnique to evaluate te value of o. Anoter significant parameter in equation 6.9 is. Te parameter denotes te non-dimensional aircraft center of gravity X cg (cg) position ( ). Te value for must be known prior to te orizontal tail design. H X ac wf H ) apter 6 Tail Design 313

43 No Aircraft Horizontal tail volume coefficient ertical tail volume ( ) coefficient ( ) 1 Glider and motor glider Home-built GA-single prop-driven engine GA-twin prop-driven engine GA wit canard Agricultural Twin turboprop Jet trainer Figter aircraft Figter (wit canard) Bomber/military transport Jet Transport Table 6.4. Typical values for orizontal and vertical tail volume coefficients apter 11 is dedicated to te tecniques and metods to determine te aircraft cg position, provided te details of geometries of all aircraft components. However, if at te early stages of te orizontal tail design, te oter aircraft components suc as fuselage, engine, and landing gear ave not yet been designed, te only option is to pick a value for. Te best value is a mid-value between te most forward and te most aft position of te aircraft cg. Tis minimized te aircraft trim drag wile in cruise. Tis is based on a logical assumption tat te aircraft cg is at it one end of te extreme position (say most forward) at te beginning of te cruise, and moves to anoter end of te extreme position (say most aft) at te end of te cruise. In contrast, in order to reduce te longitudinal control effort during a cruising fligt, te aircraft cg is recommended to be close to te wing-fuselage aerodynamic center. Te aircraft non-dimensional center of gravity limit () is te difference between te most forward and te most aft position of te aircraft cg. Te typical values for te aircraft non-dimensional center of gravity limit are: H 0.1 to 0.3 (6.50) Tis means tat a typical value for te most forward of te aircraft cg is about 10 percent of te wing mean aerodynamic cord. In addition, a typical value for te most aft of te aircraft cg is about 30 percent of te wing mean aerodynamic cord. Terefore, a proper assumption for te value of at te early stage of te orizontal tail design would be about 0.. As soon as a more realistic value for te aircraft cg position () is available, te orizontal tail design must be updated. Te value for te aircraft lift coefficient ( L ) in equation 6.9 is determined based on te cruising velocity, cruise altitude, and te aircraft average weigt (equation 5.10). Finally, by solving te equation 6.9, te only unknown ( L ), is determined. At tis moment, tree orizontal tail parameters are decided (i.e. H, L and l). On te oter and, since te tail volume coefficient is a function of orizontal tail area (S ), te orizontal tail area is readily determined using equation 6.4. By te tecnique tat as just been introduced, tree orizontal tail parameters tat ave been determined are as follows: apter 6 Tail Design 314

44 1. orizontal tail planform area (S ). orizontal tail moment arm (l) 3. orizontal tail cruise lift coefficient ( L ) It is important to remember tat te design is an iterated process, so as soon as any assumption (suc as aircraft cg) is canged; te orizontal tail design must be revised Fixed, All Moving, or Adjustable Due to te fact tat te aircraft as numerous fligt conditions suc as various speeds, cg locations, weigts, and altitudes, te longitudinal trim requirements are satisfied only troug cange in orizontal tail lift. Since te orizontal tail as a fixed planform area and fixed airfoil section, te only way to cange te tail lift is to vary its angle of attack ( ). Tere are tree tail setting configurations (as sketced in figure 6.16) to fulfill a cange te angle of attack: 1. Fixed orizontal tail;. Adjustable tail; 3. All-moving tail. A fixed tail is permanently attaced to te fuselage by some joining tecniques suc as screw and nut or welding. A fixed tail angle of attack cannot be varied unless by pitcing up or down te fuselage nose. On te oter and, te angle of attack of an all-moving tail is easily canged by te pilot using te forward or aft motion of te stick inside te cockpit. a. Fixed b. Adjustable c. All moving Figure Tree orizontal tail setting configurations Tere are several basic differences between tese options. First of all, a fixed tail is muc ligter, ceaper and structurally easier to design compared wit an all-moving tail. Moreover, a fixed tail is safer tan all moving tail, due to te possibility of failure of a moving mecanism. On te oter and, an aircraft wit all-moving tail (suc as in figter aircraft Dassault Rafale as sown in figure 6.8) is more controllable and maneuverable tan an aircraft wit a fixed tail. One difference between tese two tails is tat a fixed tail is equipped wit a longitudinal control surface (i.e. elevator); wile an all-moving tail does not ave any separate deflectable section. In general, te trim drag of a fixed tail is iger tan tat of an all moving tail. An all-moving tail is sometimes referred to as a variable incidence tailplane. apter 6 Tail Design 315

45 1. Adjustable orizontal tail in Faircild -6A Metro III. All moving tail in Panavia Tornado (ourtesy of Luis David Sancez) (ourtesy of Antony Osborne) Figure An adjustable tail and an all moving tail A tail option wic as some advantages of a fixed tail and some advantages of te allmoving tail is referred to as an adjustable tail (suc as in Faircild -6A Metro III as sown in figure ). As te name implies, an adjustable tail allows te pilot to adjust its setting angle for a long time. Te adjustment process usually appens before te fligt; owever, a pilot is allowed to adjust te tail setting angle during te fligt operation. An adjustable tail employs an elevator, but a major between an adjustable tail and all moving tail is in te tail rotation mecanism. An all moving tail is readily and rapidly (in a fraction of a second) rotated about its inge by te pilot. But, te angle of attack adjustment process for an adjustable tail takes time (few or even several seconds). Te range of deflections of an adjustable tail (about +5 to -1 degrees) is considerably less tan tat of an all moving tail (about +15 to -15 degrees). For instance, te tailplane deflection for transport aircraft Boeing 777 is 4 up and 11 down. If te longitudinal maneuverability is not a desired design requirement, it is recommended to employ a fixed tail configuration. But te aircraft is required to be able to perform fast maneuver, te appropriate option is an all moving tail. On te oter and, if te fligt cost is a significant issue in te design requirements list, it is better to employ an adjustable tail. In general, most GA and small transport aircraft (e.g., essna 17 (Figure 11.15), Jetstream 41) ave a fixed tail, most large transport aircraft (e.g., Boeing 767 (Figure 5.4), Airbus 340 (Figure 8.0)) utilize an adjustable tail, and most figter aircraft (e.g., F/A-18 Hornet (Figures.11, 6.1), F-16 Falcon (Figure 3.1), and Harrier GR. Mk 7 (Figure 4.19)) employ an all-moving tail. Table 6.5 sows te setting configuration of orizontal tail for several aircraft. Figure 6.17 demonstrates te adjustable orizontal tail of Faircild -6A Metro III, and all-moving orizontal tail of Panavia Tornado Airfoil Section Horizontal tailplane is a lifting surface (similar to te wing) and requires a special airfoil section. Te basic fundamentals about airfoil section (definition, parameters, selection criteria, and related calculation) as been presented in Section 5.4, ence tey are not repeated ere. In summary, tailplane requires an airfoil section tat is able to generate te required lift wit minimum drag and minimum pitcing moment. Te specific orizontal tail airfoil requirements are described in tis section. apter 6 Tail Design 316

46 No Aircraft m TO Tail type Airfoil (t/) max S /S AR i (deg) (kg) (%) (deg) (deg) Wrigt Flyer 40 Moving ambered plate low essna 177 1,100 Fixed NAA 001/ essna itation I 5,375 Fixed NAA 0010/ Beec Starsip 6,759 Fixed Fokker F-7 19,773 Fixed NAA 63A Boeing ,300 Adjustable 1%-9% Boeing ,30 Adjustable BA Boeing ,390 Adjustable D ,000 Adjustable DSMA Airbus 300B 165,000 Adjustable Lockeed ,305 Fixed Inverted NAA Hercules 1 Lockeed L ,000 Adjustable Lockeed -5A 381,000 Adjustable Eurofigter 000 1,000 Movable F-15 Eagle 36,741 Movable Table 6.5. Horizontal tail caracteristics for several aircraft H a. Beec Starsip b. Saab JAS-39B Gripen (ourtesy of Ken Mist) (ourtesy of Antony Osborne) Figure Two aircraft wit canard configuration apter 6 Tail Design 317

47 Basically, te tailplane airfoil lift curve slope ( L t ) must be as large as possible along wit a considerably wide usable angles of attack. Since te aircraft center of gravity moves during te cruising fligt, te airfoil section must be able to create sometimes a positive (+L ) and sometimes a negative lift (-L ). Tis requirement necessitates te tailplane to beave similar in bot positive and negative angles of attack. For tis reason, a symmetric airfoil section is a suitable candidate for orizontal tail. Figure aracteristics graps of NAA 0009 airfoil section [8] Recall from apter 5 tat te indication of a symmetric airfoil is tat te second digit in a four-digit and te tird digit in a five-digit and 6-series NAA airfoil sections is zero. Tis denotes tat te airfoil design lift coefficient and zero-lift angle of attack are bot zero. NAA airfoil sections suc as 0009, 0010, 001, , , 63-01, , , , 64-01, 64A010, , , 66-01, , and are all symmetric airfoils. Reference [8] is a ric collection for NAA airfoil sections. In several GA aircraft, NAA airfoil sections 0009 or 001 (wit 9% or 1% maximum tickness-to-cord ratio) are employed for orizontal tail. Bot of tis NAA airfoil sections are symmetric. Moreover, it is desired tat te orizontal tail never stalls, and te wing must stall before te tail. Hence, te stall feature of te tail airfoil section (sarp or docile) is not significant. apter 6 Tail Design 318

48 In addition, anoter tail requirement is tat orizontal tail must be clean of compressibility effect. In order te tail to be out of te compressibility effect, te tail lift coefficient is determined to be less tan te wing lift coefficient. To insure tis requirement, te flow Mac number at te tail must be less tan te flow Mac number at te wing. Tis objective will be realized by selecting a orizontal tail airfoil section to be tinner (say about percent of MA) tan te wing airfoil section. For instance, if te wing airfoil section is NAA 3015 (i.e. (t/) max = 0.15 or 15%), te orizontal tail airfoil section can be selected to be NAA 0009 (i.e. (t/) max = 0.9 or 9%). Figure 6.19 sows te caracteristics graps of te NAA 0009 airfoil section. In an aircraft wit an aft tail configuration, wen te center of gravity (most of te time) is beind te wing-fuselage aerodynamic center, te orizontal tail must produce a negative lift to longitudinally trim te aircraft. If te aircraft center of gravity range is suc tat te tail must produce a negative lift coefficient most of te time, an inverted non-symmetric airfoil section may be utilized. Tis is te case for te cargo aircraft Lockeed -130B tail airfoil section Tail Incidence Wen a fixed tail configuration is adopted, te orizontal tail setting angle (i.e., tail incidence); i t ; must be determined. Te tail setting angle (i t ) primary requirement is to nullify te pitcing moment about cg at te cruising fligt. Tis is te longitudinal trim requirement troug wic te tail is generating a lift to counteract all oter aircraft pitcing moments. Tail incidence is determined to satisfy trim design requirement wen no control surface (i.e., elevator) is deflected. Altoug tis fixed setting angle satisfies only one fligt condition, but it must be suc tat a mild cange (troug te application of elevator) is necessary to trim te aircraft on oter fligt situations. Looking at te L - grap of te tail airfoil section (suc as in figure 6.19), it is noticed tat te tail angle of attack is simply a function of te tail lift coefficient. Terefore, as soon as te tail lift coefficient is known, te tail incidence is readily determined by using tis grap as te corresponding angle. As already discussed in section 6., te tail lift coefficient is obtained from te non-dimensional longitudinal trim equation suc as equation 6.9: mowf L 0 o H L (6.9) In summary, te desired tail lift coefficient is calculated troug equation 6.9, and ten te tail incidence will be determined by using te L - grap of te tail airfoil section. L L L L (6.51) Tis is an initial value for te setting angle and will be revised in te later design pases. Te typical value would be about -1 degrees. In case, te tail configuration is adjustable, te igest incidence (usually positive angles) and lowest incidence (usually a negative angle) must be determined. For instance, te large transport aircraft Boeing 77 as an adjustable tail wit +4 degrees for most positive incidence and -1.5 degrees for most negative incidence. Table 6.5 introduces te orizontal tail setting angles for several aircraft. So te orizontal tail angle of attack in tis aircraft is negative most of te time. apter 6 Tail Design 319

49 Anoter factor influencing te value of te tail setting angle is te requirement for longitudinal static stability. Several parameters will affect te aircraft longitudinal static stability, but it can be sown tat te longitudinal diedral will ave a positive impact on te longitudinal static stability. Te term longitudinal diedral is invented by tail designers to transfer te tecnical meaning of te wing diedral angle () form y-z plane to a similar angle in te aircraft x-z plane. As te aircraft lateral stability is benefited from te wing and tail diedral angles, te aircraft longitudinal stability will be improved by a geometry referred to as te aircraft longitudinal diedral angle. Wen te orizontal tail cord line and wing cord line can form a -sape, it is said tat te aircraft as te longitudinal diedral. Tere are a few oter tecnical interpretations for longitudinal diedral as follows: 1. Wen te wing (or foreplane suc as canard) setting angle is positive and te orizontal tail (or aft plane suc as te wing in a canard configuration) angle is negative, te aircraft is said to ave longitudinal diedral. i w > i. Wen te wing (or foreplane) lift coefficient is iger tan tat of te orizontal tail (or foreplane), te aircraft is said to ave longitudinal diedral. Lw > L 3. Wen te wing (or foreplane) zero-lift angle of attack is iger tan tat of te orizontal tail (or aft plane), te aircraft is said to ave longitudinal diedral. ow > o 4. Wen te wing (or foreplane) effective angle of attack is iger tan tat of te orizontal tail (or aft plane), te aircraft is said to ave longitudinal diedral. Longitudinal diedral Longitudinal diedral Figure 6.0. Longitudinal diedral (angle is exaggerated) Tese four above mentioned definitions are very similar, but it seems tat te last one (see figure 6.0) is tecnically more accurate. Hence, in determining te orizontal tail setting angle, make sure tat te aircraft as longitudinal diedral. So tis requirement is as follows: eff w effc efft eff w ( onventional configuration ) ( anard configuration ) (6.5) apter 6 Tail Design 30

50 Te difference between tail setting angle and te effective tail angle of attack needs to be clarified. Due to te presence of te downwas at te orizontal tail location, te tail effective angle of attack is defined as follows: f i (6.53) were f is te fuselage angle of attack and is te downwas at te tail (see figure 6.1). i w downwas f i Horizontal FL Figure 6.1. Horizontal tail effective angle of attack (downwas is exaggerated) Te fuselage angle of attack is defined as te angle between te fuselage center line and te aircraft fligt pat ( ). Te downwas is te effect of te wing trailing vortices on te flow field after passing troug te wing airfoil section. Eac trailing vortex causes a downflow at and beind te wing and an upflow outboard of te wing. Te downwas is constant along te span of a wing wit elliptical lift distribution. Te downwas is a function of wing angle of attack ( w ) and is determined [] as follows: o w (6.54) were o (downwas angle at zero angle of attack) and d/d (downwas slope) are found as: L w o AR L w AR (6.55) (6.56) Te wing lift curve slope ( L w ) is in 1/rad and is in rad. Te parameter Lw is te wing lift coefficient. Te typical value for o is about 1 degree and / is about 0.3 rad/rad. Te ideal value for te orizontal tail setting angle (i ) is zero; owever, it is usually a few degrees close to zero (+ or -). Te exact value for i is obtained in te calculation process as described in tis section. apter 6 Tail Design 31

51 An intermediate orizontal tail parameter tat must be determined is its lift curve slope ( Since te orizontal tail is a lifting surface; similar to te wing; te orizontal tail lift curve slope (3D) is determined [9, 10] as follows: L ). L dl d l l 1 AR (6.57) were l denotes te orizontal tail airfoil section lift curve slope (D) Aspect Ratio Te definition, te benefits and te parameters affecting te aspect ratio was explained in Section 5.6 in apter 5, so tey are not repeated ere. Te tail aspect ratio as influences on te aircraft lateral stability and control, aircraft performance, tail aerodynamic efficiency, and aircraft center of gravity. Most of te tail aspect ratio benefits are very similar to tose of te wing benefits, but in a smaller scale. Te tail designer is encouraged to consult wit section 5.6 for more information. Similar to te wing, tail aspect ratio is defined as te ratio between tail span to te tail mean aerodynamic cord. b AR (6.58) Te tail aspect ratio (AR ) tends to ave a direct effect on te tail lift curve slope. As te tail aspect ratio is increased, te tail lift curve slope is increased. Tere are several similarities between wing and orizontal tail in terms of aspect ratio, but in a smaller scale. Te differences are as follows: 1. Te elliptical lift distribution is not required (but recommended) for te tail.. A lower aspect ratio is desirable for tail, compared wit tat of te wing. Te reason is tat te deflection of te elevator creates a large bending moment at te tail root. Hence, te lower te aspect ratio results in a smaller bending moment. apter 6 Tail Design 3

52 Out of Propwas d P b Prop wake region Out of Propwas Figure 6.. Te tail span and propwas 3. In a single engine prop-driven aircraft, it is recommended to ave an aspect ratio suc tat te tail span (b ) is longer tan te propeller diameter (d P ) (see figure 6.). Tis provision insures tat te tail flow field is fres and clean of wake and out of propwas area. Terefore, te efficiency of te tail ( ) will be increased. Based on te above reasoning, an initial value for te tail aspect ratio may be determined as follows: AR AR w 3 (6.59) A typical value for te orizontal tail aspect ratio is about 3 to 5. Table 6.5 illustrates te orizontal tail aspect ratio for several aircraft. Te final value for tail aspect ratio will be determined based on te aircraft stability and control, cost, and performance analysis evaluations after te oter aircraft components ave been designed Taper Ratio Te definition, te benefits and te parameters affecting te taper ratio was explained in Section 5.7 in apter 5, so tey are not repeated ere. Te tail taper ratio as influences on te aircraft lateral stability and control, aircraft performance, tail aerodynamic efficiency, and aircraft weigt and center of gravity. Most of te tail taper ratio benefits are very similar to tose of te wing benefits, but in a smaller scale. Te tail designer is encouraged to consult wit section 5.7 for more information. Similar to te wing, tail taper ratio ( ) is defined as te ratio between te tail tip cord to te tail root cord. tip root (6.60) apter 6 Tail Design 33

53 Tus te value is between zero and one. Te major difference wit wing taper ratio is tat te elliptical lift distribution is not a requirement (but recommended) for tail. Tus te main motivation beind te value for te tail taper ratio is to lower te tail weigt. For tis reason, te tail taper ratio is typically smaller tan te wing taper ratio. Te tail taper ratio is typically between 0.7 and 1 for GA aircraft and between 0.4 and 0.7 for transport aircraft. For instance, transport aircraft Boeing B-77 and Boeing B-737 (Figure 6.1) as a tail taper ratio of 0.4 and Airbus A-300 as a tail taper ratio of 0.5. Table 6.5 sows te orizontal tail taper ratio for several aircraft. Te final value for tail taper ratio will be determined based on te aircraft stability and control, cost, and performance analysis evaluations after te oter aircraft components ave been designed Sweep Angle Te definition, te benefits and te parameters affecting te sweep angle was explained in Section 5.9 in apter 5, so tey are not repeated ere. Sweep angle is normally measured eiter relative to te leading edge or relative to te quarter cord line. Similar to te wing, tail leading edge sweep angle ( _LE ) is defined as te angle between te tail leading edge and te y-axis in te x-y plane. Te orizontal tail sweep angle as influences on te aircraft longitudinal and lateral stability and control, aircraft performance, tail aerodynamic efficiency, and aircraft center of gravity. Most of te tail sweep angle effects are very similar to tose of te wing effects, but in a smaller scale. Te tail designer is encouraged to consult wit Section 5.9 for more information. Te value of te orizontal tail sweep angle is often te same as wing sweep angle. Table 6.5 sows te orizontal tail sweep angle for several aircraft. As an initial selection in preliminary design pase, select te value of te tail sweep angle to be te same as te wing sweep angle. Te final value for tail sweep angle will be determined based on te aircraft stability and control, cost, and performance analysis evaluations after te oter aircraft components ave been designed Diedral Angle Te definition, te benefits and te parameters affecting te diedral angle was explained in Section 5.11 in apter 5, so tey are not repeated ere. Similar to te wing, tail diedral angle ( ) is defined as te angle between eac tail alf section and te y-axis in te y-z plane. Te orizontal tail diedral angle makes a contribution to te aircraft lateral stability and control, aircraft performance, and te tail aerodynamic efficiency. Most of te tail diedral angle contributions are very similar to tose of te wing effects, but on a smaller scale. Te tail designer is encouraged to consult wit Section 5.11 for more information. Te value of te orizontal tail diedral angle is often te same as wing sweep angle. In some cases, te tail diedral angle is totally different tan te wing diedral angle. Tere are several reasons for tis difference including a need for te aircraft lateral stability adjustment (e.g. few transport aircraft suc as tail diedral of -3 degrees for Boeing 77); a need for lateral control adjustment (e.g. figters suc as McDonnell Douglas F-4 Pantom); and a need for a reduction in aircraft eigt and operational requirements (e.g. unmanned aircraft Predator). Table 6.5 sows te tail diedral angle for several aircraft. In some aircraft instances, te manufacturing limits and considerations force te designer not to employ any diedral for te wing. So te need for lateral stability requires a large diedral for te tail. As an initial selection in preliminary design pase, select te value of te tail diedral angle to be te same as te wing apter 6 Tail Design 34

54 diedral angle. Te final value for tail diedral angle will be determined based on te aircraft stability and control, and performance analysis evaluations after te oter aircraft components ave been designed Tail ertical Location In an aircraft wit aft tail configuration, te eigt of te orizontal tail relative to te wing cord line must be decided. In a conventional aircraft, te orizontal tail as two options for te installation: 1. At te fuselage aft section,. At te vertical tail. Beside te structural considerations and complexities, te orizontal tail efficiency and its contribution to aircraft longitudinal and lateral stability must be analyzed. Unlike wing vertical location, tere are no locations for tail suc as low tail, mid tail or ig tail. However, te low tail implies a conventional tail, te ig tail implies a T-tail and te mid tail implies a cruciform tail. A complete aircraft computational fluid dynamic model allows te designer to find te best location in order to increase te effectiveness of te tail. Tere are few components tat are sources of interference wit te tail effectiveness. Tey include wing, fuselage, and engine. Te wing influences te orizontal tail via downwas, wake and tailing vortices. In general, wing downwas decreases te tail effective angle of attack. Moreover, te wing wake degrades te tail efficiency, reduces te tail efficiency ( t ), and decreases te tail dynamic pressure. Most important considerations about te location of te orizontal tail relative to te wing are te prevention of deep stall. Te orizontal tail location must not be in te wing wake region wen wing stall appens. As te figure 6.3 illustrates, tere are tree major regions for tail installation beind te wing: 1. out of wake region and downwas,. inside wake region but out of wing downwas, 3. out of wake region but affected by downwas. In terms of deep stall avoidance criterion, te region 1 is te best and safest. Te region 3 is safe from deep stall and pitc up, but tail is not efficient. Te region is not safe and not recommended for te orizontal tail installation. Te decision about te vertical eigt of te orizontal tail must be made after a toroug analysis, since a variety of parameters including wing airfoil, tail airfoil, wing-fuselage aerodynamic pitcing moment, and tail arm plus manufacturing considerations are contributing. Te following experimental equations are recommended for te initial approximation of te orizontal tail vertical eigt: l tan i 3 t l tan i 3 t s s w w (6.61) (6.6) apter 6 Tail Design 35

55 . inside wake region but out of wing downwas 1. Out of wake region and downwas i w s wake region 3. Out of wake region but affected by downwas FL Figure 6.3. An aircraft wit tree tail installation locations wen wing stalls were t is te vertical eigt of te orizontal tail relative to te wing aerodynamic center, l is te orizontal tail moment arm, s is te wing stall angle (in degrees), and i w denote te wing incidence (in degrees). Te fuselage interferes wit te tail troug fuselage wake and sidewas. Te reader is referred to aerodynamic text for te details. In a multi-engine jet aircraft, te engine ot and fast speed gas as bot positive and negative effects. Te ig speed gas increase te tail dynamic pressure, wile te ot gas creates a fatigue problem for tail structure. If te tail is made of composite materials, make sure tat te tail is out of engine exaust area. Hence, te orizontal tail location is te output of a compromise process to satisfy all design requirements Oter Tail Geometries Oter orizontal tail geometries include tail span ( b ), tail tip cord ( ), tail root cord ( ), and tail mean aerodynamic cord ( or Figure 6.4 tat sows te top view of an aircraft aft section. Tese unknowns are determined by solving te following four equations simultaneously: tip root MA ). Tese four tail parameters are sketced in b AR tip root (6.63) (6.64) 3 root 1 1 (6.65) S b (6.66) apter 6 Tail Design 36

56 Te first two equations ave been introduced previously in tis section, but te last two equations are reproduced from wing geometry governing equations (see apter 5). Te required data to solve tese equations are te tail planform area, tail aspect ratio, and tail taper ratio. Fuselage _tip MA _root b Figure 6.4. Horizontal tail geometry ontrol Provision One of te secondary functions of te orizontal tail is te aircraft longitudinal control. Te orizontal tail must generate a variety of tail lift forces in various fligt conditions to longitudinally trim te aircraft and create te new trim conditions. For tis purpose, a fixed and an adjustable orizontal tail ave movable sections; wic in a conventional aircraft is called elevator. Terefore, in designing te orizontal tail, one must consider some provisions for future control applications. Te provisions include insuring te sufficient space for elevator s area, span, and cord as well as elevator deflection angle to allow for an effective longitudinal control. Te design of te aircraft control surfaces including te elevator design is examined in apter Final eck Wen all orizontal tail parameters ave been determined, two design requirements must be examined: 1. aircraft longitudinal trim,. aircraft static and dynamic longitudinal stability. In te analysis of te longitudinal trim, te tail lift coefficient needs to be calculated. Te generated orizontal tail lift coefficient sould be equal to te required cruise tail lift coefficient. Tere are several aerodynamic software packages and tools to calculate te orizontal tail lift coefficient. In te early stage of design, it is recommended to employ te lifting line teory as described in apter 5. Wen wole aircraft is designed, modern FD software is utilized to determine aerodynamic feature of te aircraft including orizontal tail. If te longitudinal trim requirements are not satisfied, orizontal tail parameters suc as tail incidence must be adjusted. apter 6 Tail Design 37

57 Te static longitudinal stability is examined troug te sign of te longitudinal stability derivative m or te location of te aircraft neutral point. For an aircraft wit a fixed aft tail, te aircraft static longitudinal stability derivative is determined [6] as: m L wf l d 1 d o L S S (6.67) Wen te derivative m is negative or wen te neutral point is beind te aircraft cg, te aircraft is said to be statically longitudinally stable. Te dynamic longitudinal stability analysis is performed after all aircraft components are designed and te roots () of te longitudinal caracteristic equation are calculated. A general form of te aircraft longitudinal caracteristic equation looks like te following: A B D E (6.68) were coefficients A 1, B 1, 1, D 1, and E 1 are functions of te several stability derivatives suc as m and m q. An aircraft is dynamically longitudinally stable, if te real parts of all roots of longitudinal caracteristic equation are negative. Anoter way to analyze dynamic longitudinal stability is to make sure tat longitudinal modes (i.e. sort period and long period (Pugoid)) are damped. Te reader is encouraged to consult wit [1] to see to see ow to derive te aircraft longitudinal caracteristic equation. Te longitudinal stability derivatives cannot be determined unless all aircraft components including wing and fuselage ave been designed. Tis is wy resort to a simplifying criterion tat could be a base for te orizontal tail preliminary design. Wen te orizontal tail volume coefficient ( ) is in ballpark number (see Table 6.5), we are 90 percent confident tat te longitudinal stability requirements ave been satisfied. Wen oter aircraft components suc as fuselage and wing ave been designed, te orizontal tail design will be revised and optimized in te longitudinal stability analysis process ertical Tail Design ertical Tail Design Requirements H Te tird lifting surface in a conventional aircraft is te vertical tail; wic is sometimes referred to as vertical stabilizer or fin. Te vertical tail tends to ave two primary functions: 1. directional stability,. directional trim. Moreover, te vertical tail is a major contributor in maintaining directional control; wic is te primary function of te rudder. Tese tree design requirements are described briefly in tis section: 1. Te primary function of te vertical tail is to maintain te aircraft directional stability. Te static and dynamic directional stability requirements were discussed in Section 6.3. In summary, te stability derivatives n must be positive (to satisfy te static directional stability requirements), but te stability derivatives n r must be negative (to satisfy te dynamic directional stability requirements). Two major contributors to te value of tese stability derivatives are vertical tail area (S ) and vertical tail moment arm (l ). If vertical tail apter 6 Tail Design 38

58 area is large enoug and vertical tail moment arm is long enoug, te directional stability requirements could be easily satisfied. Te directional stability analysis is performed after all aircraft components are designed and te roots () of te lateral-directional caracteristic equation are calculated. A general form of te aircraft lateral-directional caracteristic equation looks like te following: A B D E (6.69) were coefficients A, B,, D, and E are functions of te several stability derivatives suc as n and n r. An aircraft is dynamically directionally stable, if te real parts of all roots of lateraldirectional caracteristic equation are negative. Anoter way to analyze dynamic directional stability is to make sure tat directional modes (e.g., dutc roll, and spiral) are damped. Te reader is encouraged to consult wit [1] to see ow to derive te aircraft lateraldirectional caracteristic equation. Te directional stability derivatives cannot be determined unless all aircraft components including wing and fuselage ave been designed. Hence, we ave to resort to some oter simplifying criterion tat could be a base for te vertical tail preliminary design. Similar to orizontal tail volume coefficient, a new parameter tat is referred to as vertical tail volume coefficient ( ) is defined. If te value of tis parameter is in ballpark number, we are 90 percent sure tat te directional stability requirements ave been satisfied. Wen oter aircraft components ave been designed, te vertical tail design will be revised and optimized in te directional stability analysis process. Te vertical tail volume coefficient will be introduced in Section Te second function of te vertical tail is to maintain te aircraft directional trim. As discussed in Section 6.3, te summation of all forces along te y-axis and te summation of all moments about z-axis must be zero. F y 0 N cg 0 (6.5) (6.6) An aircraft is normally manufactured symmetrical about x-z plane, so te directional trim is naturally maintained. Altoug tis is an ideal case and is considered in te production of components suc as rigt and left wing sections, but in several cases, tere is a sligt asymmetricity in te aircraft x-y plane. One source for te asymmetricity could be a difference between manufacturing jigs and fixtures of rigt and left sections (wing and tail). Anoter reason for directional asymmetricity lies in te internal components inside fuselage suc as fuel system, electrical wiring, and even load and cargo inside load compartment. However, in a single engine prop-driven aircraft, te aircraft directional trim is disturbed by te rotation of te engine propeller. In a multi-engine prop-driven aircraft, wit odd number of engines, a similar problem exists. Hence, te vertical tail is responsible for maintaining te directional trim by providing an opposing yawing moment about z-axis. One of te critical parameters influencing te directional trim in suc aircraft is te vertical tail incidence angle relative to te x-z plane. apter 6 Tail Design 39

59 Anoter directional trim case is in multi-engine aircraft, were one engine in inoperative. In suc situation, te operative engines create a disturbing yawing moment and te only way to balance tis asymmetric moment is te counteracting yawing moment generated by te vertical tail. A control surface (e.g. rudder) must be deflected to directionally trim te aircraft. Altoug te vertical tail is contributing to te aircraft lateral stability and control, but tis item is not considered as a base for te design of te vertical tail. However, in te analysis of te vertical tail performance, te lateral stability must be studied. Tis is to make sure tat te vertical tail is improving te aircraft lateral stability and not aving a negative impact. Recall tat te aircraft lateral stability is primarily a function of te wing parameters. Te static and dynamic directional trim requirements were discussed in Section Te tird aircraft design requirement in wic te vertical tail is a major contributor is te directional control. Maneuvering operations suc as turning fligt and spin recovery are successfully performed by using a movable section of te vertical tail wic is called rudder. Te design of te rudder is examined in apter 1, but te spin recovery requirements will be discussed in Section ertical Tail Parameters Basically, te vertical tail parameters must be initially determined suc tat te directional stability requirements are satisfied. In te second and tird stage of te vertical tail design process, te directional trim requirements and directional control requirements will be examined. In te design of te vertical tail, te following parameters must be determined: 1. ertical tail location. Planform area (S v ) 3. Tail arm (l vt ) 4. Airfoil section 5. Aspect ratio (AR v ) 6. Taper ratio ( v ) 7. Tip cord ( t_v ) 8. Root cord ( r_v ) 9. Mean Aerodynamic ord (MA v or v ) 10. Span (b v ) 11. Sweep angle ( v ) 1. Diedral angle ( v ) 13. Incidence (i v ) Several of tese vertical tail parameters are illustrated in figure 6.5. Te vertical tail is a lifting surface, wose aerodynamic force of lift is generated in te direction of y-axis. In maintaining te directional stability, control and trim, an aerodynamic force along y-axis needs to be created by te vertical tail (i.e., vertical tail lift; L ). L 1 S L v (6.70) apter 6 Tail Design 330

60 were S is te vertical tail area, and te L is te vertical tail lift coefficient. Te vertical tail lift is generating a yawing moment about z-axis: N cg L l (6.71) Tis moment must be large enoug to maintain directional trim and must ave a positive contribution to te directional stability. As explained in Section 6.8.1, a preliminary evaluation of te directional stability is applied troug a parameter called vertical tail volume coefficient ( ): l S bs (6.7) were l v is te distance between vertical tail aerodynamic center (ac v ) and te wing-fuselage aerodynamic center (see figure 6.5), S is te vertical tail planform area, b is te wing span, and S denotes te wing reference area. Te vertical tail aerodynamic center is located at te quarter cord of te vertical tail mean aerodynamic cord. Te vertical tail volume coefficient is a non-dimensional parameter wic is directly functions of two significant vertical tail parameters: vertical tail area (S ) and vertical tail moment arm (l v ). Two parameters of l v and l vt are very close, suc tat one can be determined from anoter one. Te vertical tail volume coefficient is an indirect representative for te aircraft directional stability. Te typical value for te vertical tail volume coefficient is between 0.0 and 0.1. Table 6.6 illustrates te vertical tail parameters including te vertical tail volume coefficient for several aircraft. Remember tat te vertical tail planform area includes bot te fixed section and te movable section (i.e. rudder). Since te definitions and features of lifting surface basic parameters suc as aspect ratio, taper ratio, and airfoil section ave been presented in apter 5 and also in orizontal tail design section (Section 6.7), tey are introduced briefly ere. 1. ertical tail location In order to maintain te directional stability, te only location for te vertical tail is aft of te aircraft center of gravity. Tree possible candidates are 1. aft of fuselage,. wingtips, and 3. boom(s). If a single aft orizontal tail as been selected, te only place for te vertical tail is on te top of te aft fuselage. Te vertical tail cannot be placed in front of te fuselage (i.e. forward of te aircraft cg), since it makes te aircraft directionally unstable. Oter two options, namely wingtips and boom, are appropriate for some special purposes tat ave been described earlier in Section ertical tail moment arm (l vt ) Te vertical tail moment arm (see figure 6.5) must be long enoug to satisfy te directional stability, control, and trim requirements. In a spinnable aircraft, te vertical tail must also satisfy te spin recovery requirements. Increasing te vertical tail moment arm increases te values of te derivatives n and n r and tus makes te aircraft directionally more stable. Te major contributor to te static directional stability derivative (n ) is te vertical tail [1]: apter 6 Tail Design 331

61 n d n K f L 1 1 d l t S bs (6.73) were L denotes te vertical tail lift curve slope, d d is te vertical tail sidewas gradient, and is te dynamic pressure ratio at vertical tail. Te parameter K f1 represents te contribution of fuselage to aircraft n and depends strongly on te sape of te fuselage and its projected side area. Te fuselage contribution to directional static stability tends to be strongly negative. Te typical value of K f1 for a conventional aircraft is about 0.65 to Te value of for a statically directionally stable aircraft is positive. A iger value for n implies a more n directionally statically stable aircraft. Te parameter l vt in equation 6.65 is in te numerator wic implies te longer moment arm is desirable. In addition, an increase in te vertical tail moment arm improves te directional and lateral control. In te early stage of te vertical tail design; were oter aircraft components ave not been designed; te vertical tail moment arm is selected to be equal to te orizontal tail moment arm (l). Tis assumption means tat te vertical tail is located at te same distance to te wing as te orizontal tail. Te assumption will be modified in te later design stage wen oter aircraft components are designed and te aircraft directional and lateral stability, control and trim are analyzed. Anoter penomenon tat influences te vertical tail moment arm is spin. Wen an aircraft is spinnable, te aircraft is required to be able to recover from spin safely. Spin is a dangerous fligt if te aircraft is not designed to recover safely from it. Some aircraft, owever, are not spinnable by design. Most transport aircraft are not spinnable (i.e., spin resistant), wile most figters and maneuverable aircraft are spinnable. MA tip root ac v b ac wf cg l vt l v Figure 6.5. Te vertical tail parameters apter 6 Tail Design 33

62 A spin is an aggravated stall resulting in autorotation about te spin axis werein te aircraft follows a screw pat. Spins is caracterized by ig angle of attack, low airspeed, ig sideslip angle, and ig rate of descent. In a spin, bot wings are in a stalled condition; owever one wing will be in a deeper stall tan te oter. Tis causes te aircraft to autorotate due to te nonsymmetric lift and drag. Spins can be entered unintentionally or intentionally. In eiter case, a specific and often counterintuitive set of actions are needed to influence recovery. If te aircraft exceeds publised limitations regarding spins, or is loaded improperly, or if te pilot uses incorrect tecnique to recover, te spin may lead to a cras. Te following is reproduced from Section 1 of PAR 3 of Federal Aviation Regulations [4] wic concerns about spinning of GA aircraft: (a) Normal category airplanes. A single-engine, normal category airplane must be able to recover from a one-turn spin or a tree-second spin, wicever takes longer, in not more tan one additional turn after initiation of te first control action for recovery, or demonstrate compliance wit te optional spin resistant requirements of tis section. (b) Utility category airplanes. A utility category airplane must meet te requirements of paragrap (a) of tis section. In addition, te requirements of paragrap (c) of tis section and 3.807(b)(7) must be met if approval for spinning is requested. (c) Acrobatic category airplanes. An acrobatic category airplane must meet te spin requirements of paragrap (a) of tis section and 3.807(b)(6). In addition, te following requirements must be met in eac configuration for wic approval for spinning is requested: (1) Te airplane must recover from any point in a spin up to and including six turns, or any greater number of turns for wic certification is requested, in not more tan one and one-alf additional turns after initiation of te first control action for recovery. However, beyond tree turns, te spin may be discontinued if spiral caracteristics appear. () Te applicable airspeed limits and limit maneuvering load factors must not be exceeded. For flapsextended configurations for wic approval is requested, te flaps must not be retracted during te recovery. (3) It must be impossible to obtain unrecoverable spins wit any use of te fligt or engine power controls eiter at te entry into or during te spin. (4) Tere must be no caracteristics during te spin (suc as excessive rates of rotation or extreme oscillatory motion) tat migt prevent a successful recovery due to disorientation or incapacitation of te pilot. Wen a spin occurs, all tat is mainly required is a sufficient yaw rate wile an aircraft is stalled. Hence te vertical tail must be able to generate te yawing moment to stop autorotation. Tus, te vertical tail plays a vital role in spin recovery. Te vertical tail may ave a long moment arm, but tere is a situation tat could negatively influence te effectiveness of te vertical tail. If te vertical tail is in te orizontal tail wake region, it will lose its effectiveness. Terefore, te vertical tail moment arm needs to be determined suc tat provide a wake free region for te vertical tail. apter 6 Tail Design 333

63 An experimental rule for te vertical tail effectiveness to acieve a recoverable spin is as follows: At least 50 percent of te vertical tail planform area must be out of te orizontal tail wake region to be effective in te case of a spin. Te orizontal tail wake region is considered to lie between two lines. Te first line is drawn at te orizontal tail trailing edge by te orientation of 30 degrees. Te second line is drawn at te orizontal tail leading edge by te orientation of 60 degrees. wake region 60 o 30 o wake region 60 o 30 o 60 o wake region 30 o 1. T is in te wake region. Part of te T is in te wake region 3. T is out of te wake region Figure 6.6. Te vertical tail effectiveness and te wake region of te orizontal tail So, even if te vertical tail moment arm is teoretically calculated to be sufficient, but if te vertical tail is grapically located to be inside te orizontal tail wake region, te moment arm needs to be adjusted. It is clear tat if te moment arm needs to be decreased, te vertical tail area must be increased. However, if te adjustment of te vertical tail arm leads to a larger arm, te vertical tail area could be decreased. Anoter tecnique to move te vertical tail out of te orizontal tail wake region is to employ a dorsal fin. A grapical metod is illustrated in figure 6.6. Figure sows a vertical tail tat is completely inside te wake region. Tis configuration does not satisfy spin recovery requirements. Figure 6.6- demonstrates a vertical tail tat is completely out of te wake region. Tis configuration does satisfy te spin recovery requirements. Figure depicts a vertical tail tat is partly inside te wake region. Altoug te moment arm of te vertical tail (l v ) in figure is sorter tan tat of te two oter vertical tails, but te advantage is tat is wake free. 3. Planform area (S v ) Te parameter S v in equation 6.65 is in te numerator wic implies te larger vertical tail area is desirable. Te vertical tail area must be large enoug to satisfy lateral-directional stability, control, and trim requirements. Increasing te vertical tail area increases te values of te derivatives n and n r and tus makes te aircraft lateral-directionally more stable. In addition, an increase in te vertical tail area improves te directional and lateral control (n R, lr ). If te vertical tail area is too small, te lateral-directional stability requirements will not be satisfied. On te oter and, wen te vertical tail area is too large, te aircraft will be lateral-directionally too stable, but te directional control requirements are not satisfied. Tus, te middle value is very ard to determine. For tis reason, te vertical tail design is utilizing a backward design tecnique. It means tat we select a combination of vertical tail area and vertical tail moment arm in a ballpark area troug a parameter called vertical tail volume coefficient. Anoter criterion for te vertical tail area is tat it must be small suc tat to minimize te manufacturing cost and te aircraft weigt. apter 6 Tail Design 334

64 It is interesting to note tat a typical value for te ratio between vertical tail area and te wing area for a conventional GA aircraft is about 0.1 to Te vertical tail planform area is preliminary determined based on te selection of te vertical tail volume coefficient ( ). Te typical value for te vertical tail volume coefficient for several aircraft type is introduced in Table 6.4. Hence te vertical tail area is determined as: S b S l (6.74) were it is initially assumed tat te parameter l v is equal to te vertical tail moment arm (l vt ). Tis area will be adjusted in te later design stage after oter aircraft components are designed and te aircraft directional and lateral stability, control and trim are analyzed. Te design of te vertical is one of te difficult tasks for aircraft designers, since teoretical and experimental results may not matc concerning te features of te vertical tail. It is often te case for several aircraft tat te vertical tail area is found; in fligt test; insufficient to satisfy lateral-directional stability requirements. If te aircraft is in te manufacturing stage, and te initial vertical tail design may not be canged, one solution to increase te vertical tail area is to employ te dorsal fin. A dorsal fin 4 (see figures and 6.7-) is generally a flat plate (i.e. no airfoil section) installed in front of te original vertical tail wit a greater sweep angle. Te oter benefit of a dorsal fin is to reduce te minimum control speed ( mc ) during take-off operation (as employed in Piper Arapao PA- 40). In addition, it provides a idden antenna feature tat allows te com antennas to be located under te fin for furter drag reduction. Anoter approac to solve te small vertical tail area problem is to employ te ventral fin. A ventral fin 5 (see figure 6.7-3) is simply a flat plate (i.e. no airfoil section) installed under te aft fuselage (almost in te same longitudinal location of te vertical tail). It is also possible and useful to consider te airfoil section for dorsal and ventral fins to improve teir aerodynamic caracteristics. Tese two tecniques improve te lateral-directional stability of an aircraft, wile tey do not touc te original vertical tail geometry. Table 6.6 sows te value for te ratio between vertical tail area and te wing area for several aircraft. Figure 6.7 illustrates te dorsal and ventral fin of Beec 00 Super King Air; te ventral fin of Gates Learjet 35A; and te ventral fin of General Atomics Predator. Te wing and te orizontal tail ave two rigt and left sections. But, unlike te wing and orizontal tail, te vertical tail as normally one section. Tus, te vertical tail span (b v ) is te distance between te vertical tail tip cord and root cord (see figure 6.5). For tis reason, te vertical tail aerodynamic center in a conventional aircraft is normally above te fuselage center line (and most of te time above te aircraft center of gravity). 4 Tis term as been borrowed from fis anatomy. A dorsal fin is a polypyletic fin located on te backs of some fis, wales, and dolpins. 5 Tis term as been borrowed from fis anatomy. apter 6 Tail Design 335

65 4. Airfoil section Te vertical tail airfoil section is responsible for te generation of te vertical tail lift coefficient ( L ). Te airfoil must generate te required lift coefficient wit a minimum drag coefficient. Recall tat a nonsymmetrical airfoil section creates an aerodynamic pitcing moment. One of te basic aircraft design requirement is te symmetricity about te x-z plane. Terefore, to insure te symmetricity of te aircraft about x-z plane, te vertical airfoil section must be symmetric. Moreover, if te engines, wing, orizontal tail and fuselage are designed to be symmetric about x-z plane, te vertical tail is not required to produce any lift to maintain directional trim in a normal fligt condition. Recall from apter 5 tat te indication of a symmetric airfoil is tat te second digit in a 4- digit and te tird digit in a 5-digit and 6-series NAA airfoil sections is zero. Tis denotes tat te airfoil design lift coefficient and zero-lift angle of attack are bot zero. NAA airfoil sections suc as 0009, 0010, 001, , , 63-01, , , , 64-01, 64A010, , , 66-01, , and are all symmetric airfoils. In several GA aircraft, NAA airfoil sections 0009 or 001 (wit 9% or 1% maximum tickness-to-cord ratio) are employed for vertical tail. Bot of tis NAA airfoil sections are symmetric. In addition, anoter tail requirement is tat te vertical tail must be clean of compressibility effect. To satisfy tis requirement, te flow Mac number at te vertical tail must be less tan te flow Mac number at te wing. Tis objective will be realized by selecting a vertical tail airfoil section to be tinner (say about percent of MA) tan te wing airfoil section. For instance, if te wing airfoil section is NAA 3015 (i.e. (t/) max = 0.15 or 15%), te vertical tail airfoil section can be selected to be NAA 0009 (i.e. (t/) max = 0.9 or 9%). Figure 6.18 sows te caracteristics graps of te NAA 0009 airfoil section. Table 6.5 illustrates te airfoil section for vertical tail of several aircraft. Te tird desired feature for te vertical tail airfoil section is te ig value for te lift curve slope ( ), since te static directional stability derivative (n ) is directly a function of L (equation 6.7). Tus, as a general rule, a symmetric airfoil section wit a ig lift curve slope is desirable for te vertical tail. Recall tat te teoretical value for an airfoil section is about 1/rad. Table 6.6 sows airfoil section of te vertical tail for several aircraft. 5. Incidence (i v ) Te vertical tail incidence is defined as te angle between te vertical tail cord line and te aircraft x-z plane (wen look at te aircraft from top view). Te vertical tail is responsible for te generation of te vertical tail lift coefficient ( L ). One of te basic aircraft design objective is te symmetricity about te x-z plane. Hence, if te engines, wing, orizontal tail and fuselage are designed to be symmetric about x-z plane, te vertical tail is not required to produce any lift to maintain directional trim in a normal fligt condition. For tis reason, te vertical tail incidence must be initially zero. L apter 6 Tail Design 336

66 No Aircraft Type m TO (kg) Airfoil (t/) max (%) S /S AR (deg) 1 Wrigt Flyer First aircraft in istory 40 Flat plate low essna 177 GA single prop engine 1,100 NAA 0009/ Hercules Large turboprop cargo 70,305 NAA 64A D-9/10 Large jet transport 41,100 DSMA essna itation I Business jet 5,375 NAA 001/ Fokker F-7 Turboprop transport 19,773 modified NAA Boeing Large jet transport 50, Beecjet 400A Business jet transport 7, D-8-10 Large jet transport 141,000 DSMA-111/ Airbus 300B Large jet transport 165, A Heavy jet cargo 65, Eurofigter 000 Figter 1, F-15 Eagle Figter 36, Table 6.6. ertical tail caracteristics for several aircraft 1. Beec 00 Super King Air (dorsal and ventral fin). Gates Learjet 35A (ventral fin) 3. General Atomics Predator (ventral fin) (ourtesy of Jenny offey) (ourtesy of Antony Osborne) Figure 6.7. Dorsal fin and ventral fin in tree aircraft 6 Te aircraft as a twin vertical tail, so te areas of bot vertical tails are included in te calculation. apter 6 Tail Design 337

67 However, in a prop-driven aircraft wit one single engine (or wit odd number of propdriven engines), te lateral trim is disturbed by te revolution of te propeller and engine saft about x-axis. Te aircraft body is going to roll as a reaction to te rotation of te propeller and its saft (recall te tird law of Newton). Altoug tis rolling moment is not large, but te safety requirements requires te trim to be maintained and aircraft roll be avoided. To nullify tis yawing moment, te vertical tail is required to generate a lift and cancels tis rolling moment. One solution for tis problem is to consider a few degrees of incidence for te vertical tail. Te vertical tail in most single engine prop-driven aircraft ave about 1- degrees of incidence to insure te prevention of aircraft roll in a reaction to propeller revolution. Anoter solution is to select a non-symmetric airfoil for te vertical tail, but tis tecnique as several disadvantages. Te exact value for te vertical tail incidence is determined by calculating te propeller rotation s rolling moment. An experimental approac would be more accurate. 6. Aspect ratio (AR v ) Te vertical tail aspect ratio is defined as te ratio between vertical tail span; b y (see figure 6.5) and te vertical tail mean aerodynamic cord ( ). AR b (6.75) Te general caracteristics of te aspect ratio are introduced in apter 5 (see Section 5.6), so tey are not repeated ere. Te vertical tail aspect ratio as several oter features tan impact various aircraft caracteristics. Tese must be noticed in determining te vertical tail aspect ratio First of all, a ig aspect ratio results in a tall vertical tail tat causes te aircraft overall eigt to be increased. Many aircraft especially large transport aircraft and figter aircraft ave parking limitations in te angar space. Tus, an aircraft is not allowed to ave an overall eigt beyond a pre-specified value.. A ig tail aspect ratio weakens te aircraft lateral control, since te vertical tail mass moment of inertia about x-axis is increased. 3. A vertical tail wit a ig aspect ratio as a longer yawing moment arm compared wit a low aspect ratio vertical tail. Hence, an aircraft wit ig aspect ratio as a iger directional control. 4. As te vertical aspect ratio is increased, te bending moment and bending stress at te vertical tail root are increase wic causes te aft portion of te aircraft to be eavier. 5. A ig aspect ratio vertical tail is prone to fatigue and flutter. 6. A ig aspect ratio vertical tail is longitudinally destabilizing, since te vertical tail drag generates a nose-up pitcing moment. 7. As te aspect ratio of te vertical tail is increased, te aircraft directional stability is improved, due to an increase in te yawing moment arm. 8. As te aspect ratio of te vertical tail is increased, te vertical tail induced drag is increased. 9. If te aircraft as a T-tail configuration, te orizontal tail location and efficiency are functions of vertical tail aspect ratio. Tus, if te deep stall is a major concern, te vertical 7 Reference 10 defines te vertical tail aspect ratio as 1.55(b/). apter 6 Tail Design 338

68 aspect ratio must be large enoug to keep te orizontal tail out of te wing wake wen te wing stalls. 10. A ig aspect ratio vertical tail is aerodynamically more efficient (i.e., as a iger (L/D) max ) tan a vertical tail wit a low aspect ratio. Te reason is te vertical tail tip effect. Te above-mentioned advantages and disadvantages for a ig and low aspect ratio are general guidelines for te vertical tail designer. As a starting point, a value between 1 and is recommended for te vertical tail aspect ratio. Te final value will be determined in te overall aircraft directional stability analysis. Table 6.6 sows te value for aspect ratio of vertical tail for several aircraft. 7. Taper ratio ( v ) As wit oter lifting surfaces (e.g., wing and orizontal tail), te vertical tail taper ratio is defined as te ratio between te vertical tail tip cord; (see figure 6.5) and te vertical tail root cord; root. tip tip root (6.76) General features of te taper ratio are introduced in apter 5 (see Section 5.7), so tey are not repeated ere. Te main purposes of te taper ratio are 1: to reduce te bending stress on te vertical tail root and also : to allow te vertical tail to ave a sweep angle. Te application of taper ratio adds a complexity to te tail manufacturing process and also increases te empennage weigt. As te taper ratio of te vertical tail in increased, te yawing moment arm is reduced wic reduces te directional control of te aircraft. Moreover, an increase in te taper ratio of te vertical tail would reduce te lateral stability of te aircraft. A compromise between tese positive and negative features determines te value for te vertical tail taper ratio. 8. Sweep angle ( v ) Te general features of te sweep angle are introduced in apter 5 (see Section 5.9), so tey are not repeated ere. As te sweep angle of te vertical tail in increased, te yawing moment arm is increased wic improves te directional control of te aircraft. Subsequently, an increase in te vertical tail sweep angle weakens te aircraft directional stability, since te mass moment inertia about z-axis in increased. If te aircraft as a T-tail configuration, an increase in te vertical tail sweep angle increases te orizontal tail moment arm wic improves te aircraft longitudinal stability and control. Anoter reason for te application of te vertical tail sweep angle is to decrease te wave drag in ig subsonic and supersonic fligt regime. For tis reason, it is suggested to initially adopt a sweep angle similar to te sweep angle of te wing. Te final value for te vertical tail sweep angle will be te results of a compromise between tese positive and negative features. Table 6.6 sows te value for te sweep angle of vertical tail for several aircraft. 9. Diedral angle ( v ) apter 6 Tail Design 339

69 Due to te aircraft symmetricity requirement about x-z plane, an aircraft wit one vertical tail is not allowed to ave any diedral angle. However, if te aircraft as a twin vertical tail, (suc as a few figters), te diedral angle as positive contributing to te aircraft lateral control. But it reduces te aerodynamic efficiency of te vertical tails, since two vertical tails will cancel part of teir lift forces. In addition, te vertical tail diedral angle will contribute to detectability features of te aircraft. For instance, McDonnell Douglas F-15 Eagle (Figure 9.14) twin vertical tails canted 15 deg to reduce radar cross section. Te exact value for te diedral angles of a twin vertical tail is determined in te overall aircraft lateral- directional stability analysis process. 10. Tip cord ( t_v ), Root cord ( r_v ), Mean Aerodynamic ord (MA v or v ), and Span (b v ) Te oter vertical tail geometries include vertical tail span ( vertical tail root cord ( root ), and vertical tail mean aerodynamic cord ( b ), vertical tail tip cord ( or MA tip ), ). Tese unknown parameters (see figure 6.5) are determined by solving te following four equations simultaneously: AR b b S (6.77) tip root (6.78) 3 root 1 1 (6.79) S b (6.80) Te first two equations ave been introduced previously in tis section, but te last two equations are reproduced from wing geometry governing equations (see apter 5). Te required data to solve tese equations are te vertical tail planform area, vertical tail aspect ratio, and vertical tail taper ratio Practical Design Steps Te tail design flowcart was presented in section 6.1. Fundamentals of te tail primary functions and design requirements were reviewed in Sections 6. and 6.3. Sections 6.4 troug 6.8 introduced te various tail configurations, orizontal tail parameters, vertical tail parameters and te tecnique to determine eac parameter. Te purpose of tis section is to outline te practical design steps of te tail. Te tail design procedure is as follows: 1. Select tail configuration (Sections 6.4 and 6.7) Horizontal tail. Select orizontal tail location (aft, or forward (canard)); Section 6.5 apter 6 Tail Design 340

70 3. Select te orizontal tail volume coefficient; (Table 6.4) 4. alculate optimum tail moment arm (l opt ) to minimize te aircraft drag and weigt (Section 6.6) 5. alculate orizontal tail planform area; S t (equation 6.4). 6. alculate wing-fuselage aerodynamic pitcing moment coefficient (equation 6.6) 7. alculate cruise lift coefficient ( Lc ); equation alculate orizontal tail desired lift coefficient at cruise from trim equation (6.9) 9. Select orizontal tail airfoil section (Section 6.7) 10. Select orizontal tail sweep angle and diedral (Section 6.7) 11. Select orizontal tail aspect ratio and taper ratio (Section 6.7) 1. Determine orizontal tail lift curve slope; (Equation 6.57) apter 6 Tail Design 341 L 13. alculate orizontal tail angle of attack at cruise; (equation 6.51) 14. Determine downwas angle at te tail equation 15. alculate orizontal tail incidence angle; i t (equation 16. alculate tail span, tail root cord, tail tip cord and tail mean aerodynamic cord (equations 6.63 troug 6.66) 17. alculate orizontal tail generated lift coefficient at cruise (e.g. lifting line teory; apter 5). Treat te orizontal tail as a small wing. 18. If te orizontal tail generated lift coefficient (step 17) is not equal to te orizontal tail required lift coefficient (step 8), adjust tail incidence 19. eck orizontal tail stall 0. alculate te orizontal tail contribution to te static longitudinal stability derivative ( m ). Te value for m derivative must be negative to insure a stabilizing contribution. If te design requirements are not satisfied, redesign te tail. 1. Analyze dynamic longitudinal stability. If te design requirements are not satisfied, redesign te tail.. Optimize orizontal tail H ertical Tail 3. Select vertical tail configuration (e.g. conventional, twin vertical tail, vertical tail at swept wing tip, -tail) (Section ) 4. Select te vertical tail volume coefficient; (Table 6.4) 5. Assume te vertical tail moment arm (l v ) as equal to te orizontal tail moment arm (l) 6. alculate vertical tail planform area; S v (equation 6.74) 7. Select vertical tail airfoil section (Section ) 8. Select vertical tail aspect ratio; AR v (Section ) 9. Select vertical tail taper ratio; (Section ) 30. Determine te vertical tail incidence angle (Section ) 31. Determine te vertical tail sweep angle (Section )

71 3. Determine te vertical tail diedral angle (Section ) 33. alculate vertical tail span (b v ), root cord (v root ), and tip cord (v tip ), and mean aerodynamic cord (MA v ) (equations 6.76 troug 6.79) 34. eck te spin recovery 35. Adjust te location of te vertical tail relative to te orizontal tail by canging l v, to satisfy te spin recovery requirements (Section 6.8.-) 36. Analyze directional trim (Section 6.8.1) 37. Analyze directional stability (Section 6.8.1) 38. Modify to meet te design requirements 39. Optimize te tail Reminder: Tail design is an iterative process. Wen te oter aircraft components (suc as fuselage and wing) are designed, te aircraft dynamic longitudinal-directional stability needs to be analyzed, and based on tat; te tail design may need some adjustments Tail Design Example Example 6. provides a tail design example. Example 6. Problem statement: Design a orizontal tail for a two-seat motor glider aircraft wit te following caracteristics: m TO = 850 kg, D fmax = 1.1 m, c = 95 knot (at 10,000 ft), f = 1 deg (at cruise) Te wing as a reference area 18 m of and te following features: = 0.8 m, AR = 8, = 0.8, i w = 3 deg, twist = -1.1 deg, LE = 8 deg, = 5 deg, airfoil: NAA 301, L = 5.8 1/rad Te aircraft as a ig wing and an aft conventional tail configuration, and te aerodynamic center of te wing-fuselage combination is located at 3% of MA. In cruising fligt condition, te aircraft center of gravity is located at 3 percent of te fuselage lengt. Assume tat te aircraft cg is 7 cm aead of te wing-fuselage aerodynamic center. Ten following tail parameters must be determined: airfoil section, S, _tip, _root, b, i, AR,,,. At te end, draw a top-view of te aircraft tat sows fuselage, wing and orizontal tail (wit dimensions). Solution: Te tail configuration as been already selected and stated, so tere is no need to investigate tis item. Te only parameter tat needs to be decided is te type of setting angle. Since te aircraft is not maneuverable and te cost must be low, a fixed tail is selected. Tus, te design begins wit te selection of te orizontal tail volume coefficient. apter 6 Tail Design 34

72 H = 0.6 (Table 6.4) To determine te optimum tail moment arm (l opt ), we set te goal to minimize te aircraft drag. Hence: l l 4S D H opt K c f 1.1 m (6.47) were te correction factor K c is selected to be 1.. Ten, te tail planform area is determined as: H ls S l H S.77 m (6.4) S Te aircraft cruise lift coefficient is: W avg L L c S (6.7) were te air density at 10,000 ft is kg/m 3. Te wing-fuselage aerodynamic pitcing moment coefficient is: mowf maf AR cos AR cos 8 cos 0.01 t cos were te value for te wing airfoil section pitcing moment coefficient ( extracted from te airfoil graps. Based on te Table 5., te value of airfoil section is maf mowf (6.6) ) is usually for NAA 301 In order to use te trim equation, we need to find and o. Referring on Table 6., for tis type of aircraft, te l opt /L f is So te fuselage lengt is selected to be: L f = l opt /0.65 = 3.795/0.65 = m Te aerodynamic center of te wing-fuselage combination is located at 3% of MA, and te aircraft center of gravity is located at te 3% of te fuselage lengt. Tis cg is 7 cm aead of wing-fuselage aerodynamic center. ombining tese tree data, we ave te following relationsip regarding te wing: X apex MA = 0.3 L f Tus X apex = 0.3 MA L f = m Tis leads us to find te cg location (X cg ) in terms of MA: X cg = 0.3 MA 0.07 = 0.3 (0.8 m) 0.07 = m (from wing leading edge) apter 6 Tail Design 343

73 X cg % MA 0.8 MA So = Te tail efficiency is assumed to be Te orizontal tail required lift coefficient at cruise is calculated by using trim equation. mowf L o H L L L mowf 0.11 L H o (6.9) Te orizontal tail airfoil section must ave several properties tat are described in Section 6.7. Two significant properties are: 1. Symmetric,. Tinner tan wing airfoil. Te wing tickness-to-cord ratio is 1 percent. Tere are several airfoil sections tat can satisfy tese requirements. But we are looking for one wic a low drag coefficient. A symmetric airfoil section wit a low drag coefficient ( do = 0.005) and 3% tinner tan te wing airfoil section is NAA Figure 6.19 provides te caracteristic graps for NAA 0009 airfoil section. From tis figure, oter features of tis airfoil are extracted as follows: li dmin m ( l / d ) max o s lmax l (t/c) max (deg) (deg) (1/rad) % Te initial tail aspect ratio is determined to be: AR AR 3 w (6.59) Te tail taper ratio is initially determined to be equal to te wing taper ratio: = w = 0.8. Te tail sweep angle and te tail diedral angle are tentatively considered to be te same as tose of wing. Te reasons are presented in Section 6.7. = 10 deg, = 5 deg Now we need to determine te tail setting angle (i ) suc tat it produces te tail coefficient of In order to determine tis parameter, we not only need to consider all tail parameters, but also wing downwas. At te beginning, te tail angle of attack is determined based on te tail lift curve slope. In te next step, te lifting line teory is used to calculate te tail generated lift coefficient. If te tail generated lift coefficient is not equal to te tail required lift coefficient, te tail incidence will be adjusted until tese two are equal. In te last, downwas is applied to determine te tail incidence. Te tail lift curve slope is: L l l 1 AR rad (6.57) apter 6 Tail Design 344

74 Te tail angle of attack in cruise is: L L rad 1.0 deg (6.51) To calculate te tail created lift coefficient, te lifting line teory is employed as introduced in apter 5 (Section 5.14). Te following MATLAB m-file is utilized to calculate te tail lift coefficient wit an angle of attack of -1.0 degrees. ================================================================== clc clear N = 9; % (number of segments-1) S =.77; % m^ AR = 18.6; % Aspect ratio lambda = 0.8; % Taper ratio alpa_twist = ; % Twist angle (deg) a_ = -1.0; % tail angle of attack (deg) a_d = 6.1; % lift curve slope (1/rad) alpa_0 = ; % zero-lift angle of attack (deg) b = sqrt(ar*s); % tail span MA = S/b; % Mean Aerodynamic ord root = (1.5*(1+lambda)*MA)/(1+lambda+lambda^); % root cord teta = pi/(*n):pi/(*n):pi/; alpa=a_+alpa_twist:-alpa_twist/(n-1):a_; % segment's angle of attack z = (b/)*cos(teta); c = root * (1 - (1-lambda)*cos(teta)); % Mean Aerodynamics cord at eac segment mu = c * a_d / (4 * b); LHS = mu.* (alpa-alpa_0)/57.3; % Left Hand Side % Solving N equations to find coefficients A(i): for i=1:n for j=1:n B(i,j) = sin((*j-1) * teta(i)) * (1 + (mu(i) * (*j-1)) / sin(teta(i))); end end A=B\transpose(LHS); for i = 1:N sum1(i) = 0; sum(i) = 0; for j = 1 : N sum1(i) = sum1(i) + (*j-1) * A(j)*sin((*j-1)*teta(i)); sum(i) = sum(i) + A(j)*sin((*j-1)*teta(i)); end end L_tail = pi * AR * A(1) ============================================================ Te output of tis m-file is: L_tail = apter 6 Tail Design 345

75 Te tail is expected to generate a L of 0.11, but it generates a L of To increase te tail lift coefficient to te desired value, we need to increase te tail angle of attack. Wit a trial and error and using te same m-file, we find tat te tail angle of attack of 1.9 degrees generates te desired tail lift coefficient. Hence: = 1.9 degrees Now, we need to take into account te downwas. Te o (downwas angle at zero angle of attack) and d/d (downwas slope) are: L w o AR rad deg (6.55) L w AR deg deg (6.56) Tus: o w rad deg (6.54) Terefore, te tail setting angle would be: t f i i f deg (6.53) Te oter orizontal tail parameters are determined by solving te following four equations simultaneously: b AR tip root (6.63) (6.64) S 3 root b 1 1 (6.65) (6.66) Te solution of tese four equations simultaneously yields te following results: b 6.5 m, m, tip m, root m Te last step is to examine te aircraft static longitudinal stability. Te aircraft as a fixed tail, so te aircraft static longitudinal stability derivative is determined as follows: apter 6 Tail Design 346

76 m L wf l d 1 d o L S S (6.67) m rad (6.67) were we assumed tat te wing-fuselage lift curve slope is equal to te wing lift curve slope. Since te derivative m is negative, te aircraft is statically longitudinally stable. Te aircraft longitudinal dynamic stability analysis requires te information about oter aircraft components tat are not provided by te problem statement. So tis analysis is not performed in tis example. Figure 6.8 sows top-view of te aircraft wit details of te tail geometries m ac wf l=3.795 m 3.6 m ac Fuselage center line m Figure 6.8. Top view of te aircraft in Example 6. It is important to note tat tis is te first pase of te orizontal tail design. If te caracteristics of te oter aircraft components are known, te complete analysis for te longitudinal dynamic and static stability may be performed and te tail could be optimized. apter 6 Tail Design 347

77 Problems 1. Using te Reference [5] or oter reliable sources, identify te tail configurations of te following aircraft: Stemme S10 (Germany), Dassault Falcon 000 (France), Embraer EMB 145 (Brazil), anadair L-415, ATR 4, Aeromacci MB-339 (Italy), Eagle X-TS (Malaysia), PZL Mielec M-18 Dromader (Poland), Beriev A-50 (Russia), Sukoi Su-3FN (Russia), Sukoi S- 80, Saab 340B (Sweden), Pilatus P-1 (Switzerland), An-5 (Ukraine), Jetstream 41 (UK), FLS Optica OA7-300 (UK), Bell/Boeing - Osprey, Boeing E-767 AWAS, essna 750 itation X, Learjet 45, Lockeed F-16 Figting Falcon, Lockeed F-117A Nigtawk, McDonnell Douglas MD-95, Nortrop Grumman B- Spirit, Bede BD-10, Hawker 1000, Scweizer SA -38, Sino Swearingen SJ30, isionaire antage. Using te Reference [5] or oter reliable sources, identify an aircraft for eac of te following tail configurations: onventional aft tail, -tail, anard, T-tail, H-tail, Non-conventional, ruciform, Tri-plane, Boom-mounted, twin vertical tail, inverted -tail 3. Using te Reference [5] or oter reliable sources, identify an aircraft wit a conventional aft tail tat te vertical tail is out of wake region of te orizontal tail. 4. An aircraft as a fuselage wit a circular cross section. Derive an equation for te optimum orizontal tail moment arm suc tat te aft portion of te aircraft (including aft fuselage and orizontal tail) as te lowest wetted area. 5. An unmanned aircraft as te following features: S = 55 m, AR = 5, S = 9.6 m, lm Determine te orizontal tail volume coefficient. 6. Te airfoil section of a orizontal tail in a figter aircraft is NAA Te tail aspect ratio is.3. Using te Reference [8], calculate te tail lift curve slope in 1/rad. 7. Te airfoil section of a orizontal tail in a transport aircraft is NAA Te tail aspect ratio is 5.5. Using te Reference [8], calculate te tail lift curve slope in 1/rad. 8. Te airfoil section of a orizontal tail in a GA aircraft is NAA 001. Te tail aspect ratio is 4.8. Using te Reference [8], calculate te tail lift curve slope in 1/rad. 9. Te wing reference area of an agricultural aircraft is 14.5 m and wing mean aerodynamic cord is 1.8 m. Te longitudinal stability requirements dictate te tail volume coefficient to be 0.9. If te maximum fuselage diameter is 1.6 m, determine te optimum tail arm and ten calculate te orizontal tail area. Assume tat te aft portion of te fuselage is conical. 10. onsider a single-seat GA aircraft wose wing reference area is 1 m and wing mean aerodynamic cord is 1.3 m. Te longitudinal stability requirements dictate te tail volume coefficient to be 0.8. If te maximum fuselage diameter is 1.3 m, determine te optimum tail apter 6 Tail Design 348

78 arm and ten calculate te orizontal tail area. Assume tat te aft portion of te fuselage is conical. 11. A 19-seat business aircraft wit a mass 6,400 kg is cruising wit a speed of 40 knot at 6,000 ft. Assume tat te aircraft lift coefficient is equal to te wing lift coefficient. Te aircraft as te following caracteristics: S = 3 m, AR w = 8.7, Wing airfoil: NAA Determine te downwas angle (in degrees) at te orizontal tail. 1. Suppose tat te angle of attack of te fuselage for te aircraft in problem 11 is.3 degrees and te orizontal tail as an incidence of -1.5 degrees. How muc is te orizontal tail angle of attack at tis fligt condition? 13. Te orizontal tail of a transport aircraft as te following features: AR = 5.4, = 0.7, S = 14 m, _LE = 30 degrees Determine span, root cord, tip cord and te mean aerodynamic of te orizontal tail. Ten sketc te top-view of te tail wit dimensions. 14. Te orizontal tail of a figter aircraft as te following features: AR = 3.1, = 0.6, S = 6.4 m, _LE = 40 degrees Determine span, root cord, tip cord and te mean aerodynamic of te orizontal tail. Ten sketc te top-view of te tail wit dimensions. 15. Te vertical tail of a transport aircraft as te following features: AR = 1.6, = 0.4, S = 35 m, _LE = 45 degrees Determine span, root cord, tip cord and te mean aerodynamic of te vertical tail. Ten sketc te side-view of te tail wit dimensions. 16. Te aircraft in problem 11 as oter features as follows: = 0.18, o = 0.3, = 0.97, l = 1 m, S = 8.7 m Determine te aircraft static longitudinal stability derivative (m ) and discuss weter te orizontal tail is longitudinally stabilizing or destabilizing. 17. Design a orizontal tail for a twin jet business aircraft wit te following caracteristics: m TO = 16,000 kg, D fmax = 1.8 m, c = 70 knot (at 30,000 ft), f = 1.5 deg (at cruise) Te wing as a reference area 49 m of and te following features: AR = 8, = 0.6, i w =.4 deg, twist = -1.3 deg, LE = 37 deg, = 3 deg, NAA Te aircraft as a low wing and an aft conventional tail configuration, and te aerodynamic center of te wing-fuselage combination is located at % of MA. In cruising fligt condition, te aircraft center of gravity is located at 4% of te fuselage lengt. Assume tat te aircraft cg is 15 cm aead of te wing-fuselage aerodynamic center. apter 6 Tail Design 349

79 Te following tail parameters must be determined: airfoil section, S, _tip, _root, b, i, AR,,,. At te end, draw a top-view of te aircraft tat sows fuselage, wing and orizontal tail (wit dimensions). 18. A large transport aircraft wit a mass of 63,000 kg is supposed to cruise wit a speed of 510 knots at 4,000 ft. Te maximum fuselage diameter is 3.6 m and fuselage angle of attack at cruise is 3. degrees. Te wing as a reference area 116 m of and te following features: AR = 11.5, = 0.5, i w =.7 deg, twist = -1.6 deg, LE = 30 deg, = 6 deg, NAA Te aircraft as a low wing and a T-tail configuration, and te aerodynamic center of te wing-fuselage combination is located at 0% of MA. In cruising fligt condition, te aircraft center of gravity is located at 49% of te fuselage lengt. Assume tat te aircraft cg is 18 cm aead of te wing-fuselage aerodynamic center. Design a orizontal tail to satisfy longitudinal trail and static longitudinal stability requirements. Ten determine airfoil section, S, _tip, _root, b, i, AR,,,. At te end, draw a top-view of te aircraft tat sows fuselage, wing and orizontal tail (wit dimensions). 19. Figure 6.9 sows te original design for te empennage of a transport aircraft wit a orizontal tail area of 1.3 m. Te wing reference area is 4 m, and wing aspect ratio is acwf ac 6 m Figure 6.9. Side-view of te aircraft in problem 19 Te aircraft is spinnable and te designer found out tat te vertical tail is not effective for spin recovery. Move te orizontal tail orizontally suc tat te vertical tail becomes effective in recovering from spin. Ten determine te orizontal tail area suc tat te orizontal tail volume coefficient remains uncanged. Assume tat te sketc in figure 6.9 is scaled. 0. A figter aircraft as te following features: S = 57 m, AR = 3, S = 10.3 m, S v = 8.4 m, lm, l v = 6. m Determine te orizontal and vertical tails volume coefficients. apter 6 Tail Design 350

80 1. Design a vertical tail for te aircraft in problem 18 to satisfy te static directional stability requirements.. Te airfoil section of te vertical tail for a twin-jet engine aircraft is NAA Oter features of te aircraft is as follows: S = 3 m, AR = 10.3, S = 8.1 m, AR = 1.6, l m, d 0.3 d, = 0.95 Determine te aircraft static directional stability derivative (n ). Ten analyze te static directional stability of te aircraft. 3. Te angle of attack of a orizontal tail for a cargo aircraft is -1.6 degrees. Oter tail features are as follows: S = 1 m, AR = 5.3, = 0.7, airfoil section: NAA 64-08, = 0.96 If te aircraft is flying at an altitude of 15,000 ft wit a speed of 45 knot, determine ow muc lift is generated by te tail. Assume tat te tail as no twist. 4. Te sideslip angle of a vertical tail for a maneuverable aircraft during a turn is 4 degrees. Oter vertical tail features are as follows: S v = 7.5 m, AR = 1.4, = 0.4, airfoil section: NAA 001, = 0.9 If te aircraft is flying at an altitude of 15,000 ft wit a speed of 45 knot, determine ow muc lift (i.e. side force) is generated by te vertical tail. Assume tat te tail as no twist. 5. An aft orizontal tail is supposed to be designed for a single piston engine aircraft. Te aircraft wit a mass of 1,800 kg is cruising wit a speed of 160 knot an altitude of,000 ft. Te aircraft center of gravity is at 19% MA and te wing-fuselage aerodynamic center is located at 4% MA. S = 1 m, AR = 6.4, S =.8 m, lm, mowf 0.06, =1 Determine te orizontal tail lift coefficient tat must be produced in order to maintain te longitudinal trim. 6. Redo te problem 5 wit te assumption tat te aircraft as a canard instead of an aft orizontal tail. apter 6 Tail Design 351

81 References 1. Roskam J., Airplane Fligt Dynamics and Automatic Fligt ontrol, Part I, DAR orp, 007. Nelson R., Fligt Stability and Automatic ontrol, McGraw ill, Etkin B. and Reid L. D., Dynamics of Fligt- Stability and ontrol, tird edition, Jon Wiley, Jackson P., Jane s All te World s Aircraft, Jane s information group, arious years 6. Hoak D. E., Ellison D. E., et al, USAF Stability and ontrol DATOM, Fligt ontrol Division, Air Force Fligt Dynamics Laboratory, Wrigt-Patterson AFB, Oio, Sevell R. S., Fundamentals of Fligt, Prentice Hall, Second edition, Abbott I. H. and on Doneoff A. F., Teory of Wing Sections, Dover, Lan E.. T., Applied Airfoil and Wing Teory, eng ung Book o, Lan E.. T. and Roskam J., Airplane Aerodynamics and Performance, DAR orp, 003 apter 6 Tail Design 35