As it is introduced in chapter 2, the next appropriate step after wing design would be the tail design. In this chapter, after describing the tail primary functions, and introducing fundamentals that govern the tail performance, techniques and procedure to design the horizontal tail and vertical tail will be provided. At the end of the chapter a fully solved example that illustrates the implementation of the design technique will be presented. Horizontal tail and vertical tail (i.e. tails) along with wing are referred to as lifting surfaces. This name differentiates tails and wing from control surfaces namely aileron, rudder, and rudder. Due to this mane, several design parameters associated with tails and wing; such as airfoil, planform area, and angle of attack; are similar. Thus, several tails parameters are discussed in brief. The major difference between wing design and tail design originates from the primary function of tail that is different from wing. Primary function of the wing to generate maximum amount of lift, while tail are supposed to use a fraction of its ability to generate lift. If at any instance of a flight mission, tail nears its maximum angle of attack (i.e. tail stall angle); it indicates that there was a mistake in the tail design process. In some references, tail is referred to as empennage.
Introduction
Following the wing design discussed in Chapter 2, the next crucial phase is tail design This chapter will outline the primary functions of the tail and the fundamental principles that influence its performance It will also detail the techniques and procedures for designing both the horizontal and vertical tails To conclude, a comprehensive example will be provided to demonstrate the application of these design techniques effectively.
Horizontal and vertical tails, along with wings, are classified as lifting surfaces, distinguishing them from control surfaces like ailerons and rudders This classification leads to similarities in design parameters such as airfoil, planform area, and angle of attack between tails and wings However, the primary difference lies in their functions: wings are designed to generate maximum lift, while tails utilize only a fraction of their lift-generating capability If a tail approaches its maximum angle of attack, known as the tail stall angle, it indicates a flaw in the tail design process Additionally, the tail is sometimes referred to as the empennage.
Tail often in a conventional aircraft has two components of horizontal tail and vertical tail and carries two primary functions:
1 Trim (longitudinal, lateral and directional)
The tails of an aircraft serve a crucial role in control, incorporating conventional surfaces such as the elevator and rudder Therefore, it is essential to recognize a third function of the tails in enhancing overall flight stability and maneuverability.
These three functions are described in brief here; however, more details are presented in later sections The first and primary function of horizontal tail is longitudinal trim; also referred
Chapter 6 Tail Design 2 to as equilibrium or balance But the first and primary function of vertical tail is directional stability The reason is that an aircraft is usually symmetric about xz plane, while the pitching moment of the wing about aircraft center of gravity must be balanced via a component
In conventional aircraft, longitudinal trim is achieved through the horizontal tail, which counters several pitching moments, including the wing's lift moment about the center of gravity, the aerodynamic pitching moment of the wing, and occasionally the longitudinal moment from engine thrust These moments often result in a negative sum, necessitating the horizontal tail to generate negative lift to maintain balance, which is why its setting angle is typically negative As the aircraft's center of gravity shifts along the x-axis due to fuel consumption during flight, the horizontal tail continuously manages longitudinal trim To enhance trim capability, conventional aircraft utilize elevators as integral components of the horizontal tail.
Conventional aircraft are typically designed symmetrically around the xz plane, making vertical tail trim less critical; however, it plays a vital role in certain situations In multi-engine aircraft, the vertical tail is essential for maintaining directional trim during an engine-out scenario, as it must generate a yawing moment to counteract the forces from the operating engines Similarly, in single-engine propeller-driven aircraft, the vertical tail counteracts the rolling moment caused by propeller rotation to maintain lateral trim and prevent unwanted rolls Consequently, vertical tails are often installed at a slight angle relative to the xz plane The trim requirements significantly influence the design process of the tail, which will be explored in detail in Section 6.2.
The tails of an aircraft play a crucial role in providing stability, with the horizontal tail ensuring longitudinal stability and
The third key function of an aircraft's tail is control, which is crucial for maintaining stability during flight The horizontal tail, equipped with an elevator, provides longitudinal control, while the vertical tail, featuring a rudder, ensures directional control Tails must possess sufficient power to enable the aircraft to transition smoothly between different flight conditions, such as from cruising to take-off or landing For example, during take-off, the tail is responsible for elevating the fuselage nose at a specified pitch rate.
The design of a tail is primarily guided by trim requirements, but it is subsequently adjusted to meet stability and control needs Key tail parameters that must be established during the design process include various dimensions and configurations essential for optimal performance.
2 Horizontal tail horizontal location with respect to fuselage (aft tail or canard)
10 Mean Aerodynamic Chord (MACt or C t )
23 Mean Aerodynamic Chord (MACvt or Cvt)
In the tail design process, all 26 tail parameters must be established, with most finalized through technical calculations and a few through engineering selection Additionally, intermediate parameters like downwash angle, sidewash angle, and effective angle of attack are calculated during the design phase but are not utilized during manufacturing.
The "Systems Engineering" approach serves as the foundational technique for tail design, ensuring all requirements are met while keeping costs low Illustrated in Figure 6.1, the tail design process is iterative, necessitating multiple revisions to achieve the optimal aircraft configuration While the vertical and horizontal tail designs can be conducted concurrently, the vertical tail design includes a critical step—spin recovery—where the influence of the horizontal tail is assessed This chapter aims to present design considerations, techniques, and examples for the preliminary design of the aircraft tail.
Figure 6.1 The tail design procedure
(Trim, stability, control, producibility, operational requirements, cost, flight safety)
Determine aspect and taper ratios
Select horizontal tail volume coefficient
Select vertical tail volume coefficient
Determine airfoil section Determine airfoil section
Determine sweep and dihedral angles Determine aspect and taper ratios Determine tail arm
Calculate setting angle Determine setting angle
Check spin recovery Check tail stall
Aircraft Trim Requirements
Trim is essential for safe flight, ensuring that an aircraft maintains its desired direction or circular motion without rotating around its center of gravity (CG) An aircraft is considered to be in trim when the sum of all forces and moments acting on it equals zero.
Maintaining aircraft trim across three axes—lateral (x), longitudinal (y), and directional (z)—is crucial for optimal flight performance Longitudinal trim is achieved when the total forces in the x direction, including drag and thrust, balance to zero, and when the sum of all moments, particularly the aerodynamic pitching moment around the y axis, also equals zero.
The horizontal tail plays a crucial role in maintaining longitudinal trim by generating necessary lift and ensuring that the summation of moments about the y-axis is zero It can be positioned either behind the fuselage, known as a conventional or aft tail, or near the fuselage nose, referred to as a foreplane or canard The design of the horizontal tail utilizes Equation 6.4, which states that when the summation of all forces in the y-direction, including side forces, and the summation of all moments, including the aerodynamic yawing moment about the z-axis, are both zero, the aircraft achieves directional trim.
The vertical tail plays a crucial role in maintaining directional trim by generating necessary lift and ensuring that the summation of moments around the y-axis equals zero In the design of the vertical tail, equation 6.6 is utilized When the total forces in the z-direction, including lift and weight, balance to zero and the aerodynamic rolling moments around the x-axis also sum to zero, the aircraft achieves directional trim.
The vertical tail plays a crucial role in maintaining directional stability by generating vertical lift and ensuring that the moments about the z-axis sum to zero This function is essential for effective vertical tail design, as outlined in Equation 6.8.
Chapter 6 Tail Design 6 could be found in most flight dynamics textbook As an example, the reader is referred to Ref 1,
A key reference for design requirements is the Federal Aviation Administration, specifically Section 161 of PAR 23 of the Federal Aviation Regulations This section addresses the lateral-directional and longitudinal trim of General Aviation aircraft, outlining essential guidelines for ensuring optimal aircraft performance and stability.
Each airplane must comply with specific trim requirements after being properly trimmed, ensuring that the pilot or automatic pilot does not need to exert additional pressure or movement on the primary or trim controls Furthermore, under various loading conditions, configurations, speeds, and power settings, it is essential that pilots are not subjected to excessive residual control forces, which could lead to fatigue or distraction, particularly during normal operations and in scenarios involving engine failure where performance characteristics are defined.
(b) Lateral and directional trim The airplane must maintain lateral and directional trim in level flight with the landing gear and wing flaps retracted as follows:
(1) For normal, utility, and acrobatic category airplanes, at a speed of 0.9 V H , V C , or V MO /M O , whichever is lowest; and
(2) For commuter category airplanes, at all speeds from 1.4 V S1 to the lesser of V H or V MO /M MO
(c) Longitudinal trim The airplane must maintain longitudinal trim under each of the following conditions: (1) A climb, (2) Level flight at all speeds, (3) A descent, (4) Approach
(d) In addition, each multiple airplane must maintain longitudinal and directional trim, and the lateral control force must not exceed 5 pounds at the speed used in complying with §23.67(a), (b)(2), or (c)(3),
For other types of aircraft, the reader is encouraged to refer to other parts of FAR; for instance, for transport aircraft; the reference is Part 25
In the horizontal tail design process, it is essential to establish equations that detail the longitudinal trim of a conventional aircraft As illustrated in Figure 6.2, the aircraft's center of gravity (cg) can be positioned either behind or in front of the wing-fuselage aerodynamic center (ac wf) When the cg is located behind the ac wf, as shown in Figure 6.2a, the balance of moments about the y-axis must be maintained by the lift generated by the horizontal tail Conversely, Figure 6.2b depicts the scenario where the cg is forward of the ac wf Key moments that need to be balanced include the wing-fuselage aerodynamic pitching moment and the moment of lift around the aircraft's center of gravity Additional sources of moments affecting the cg may include engine thrust, wing drag, landing gear drag, and store drag, although these complexities are simplified in this discussion.
The wing-fuselage aerodynamic center is defined as the wing aerodynamic center with the fuselage's contribution included, typically around ±5% of the mean aerodynamic chord (C) for conventional aircraft Since the wing aerodynamic center is generally positioned at approximately 25% of the mean aerodynamic chord, the wing-fuselage aerodynamic center is usually found between 20% and 30% of the mean aerodynamic chord For further details, refer to Reference 1.
Chapter 6 Tail Design 7 moments are not included in this figure The reader is expected to be able to follow the discussion, when other moments are present and/or the aircraft has a canard instead of aft tail a cg aft of ac wf b cg forward of ac wf
Figure 6.2 A conventional aircraft in longitudinal trim
The wing-fuselage lift (L wf) represents the total lift generated by the wing (L w) when accounting for the fuselage lift (L f), which is typically estimated to contribute approximately 10 percent of the wing lift.
When the center of gravity (cg) is located aft of the aerodynamic center of the wing-fuselage (acwf), the moment of the wing-fuselage lift (L wf) is positive, as illustrated in Figure 6.2a Conversely, if the cg is positioned forward of the acwf, the moment becomes negative It's important to remember that in flight dynamics, a clockwise moment is considered positive, with the y-axis situated at the cg and directed into the page.
Other moment is referred to as the wing-fuselage aerodynamic pitching moment (i.e
The wing-fuselage aerodynamic pitching moment (Mowf) represents the total aerodynamic pitching moment of the wing (Mow) when the fuselage's contribution (Mf) is factored in The "o" subscript indicates that this moment is measured relative to the wing's aerodynamic center Typically, this aerodynamic moment is negative, leading to its designation as a nose-down pitching moment, as it tends to push the fuselage nose downward The combined effect of the wing and fuselage moments is crucial for understanding overall aerodynamic behavior.
W acwf cg Mowf ac ht
Chapter 6 Tail Design 8 wing-fuselage lift generated moment) is not zero Hence, the horizontal tail is employed to generate a lift in order to balance these moments and make the summation to be zero This function maintains the aircraft longitudinal trim
Directional trim in aircraft is influenced by factors such as asymmetric engine thrust, particularly in multi-engine aircraft where one engine may be inoperative Despite the conventional aircraft's symmetric design around the xz plane, these forces can disrupt directional trim To counteract this, the vertical tail must produce a side force in the y direction, ensuring stability along the z axis Further details on this topic are provided for the reader's exploration.
A Review on Stability and Control
Stability and control are essential for safe flight, with both horizontal and vertical tails playing crucial roles in these aspects Initially, these tails are designed to meet longitudinal and directional trim requirements; however, later design stages must also address stability and control needs Consequently, the designs of the horizontal and vertical tails are revised to ensure they fulfill these critical requirements This section will offer a brief overview of aircraft stability and control, setting the stage for a clearer understanding of horizontal and vertical tail design.
Front view Top view x y x y ac v ac vt
The tail of an aircraft serves crucial functions, primarily stability and control, earning it the nickname "stabilizer" or "stabilator." Stability refers to the aircraft's ability to resist disturbances, such as gusts, and return to its original steady state This concept of stability is typically categorized into two branches.
Static stability refers to an aircraft's initial tendency to generate forces or moments that counteract any immediate disturbances from a steady flight condition, without pilot intervention In contrast, dynamic stability describes the aircraft's ability to return to its original trim state after being disturbed, focusing on the motion's history and the rate at which it stabilizes Generally, an aircraft must exhibit some level of dynamic stability, although minor deficiencies may be acceptable in specific situations While a dynamically stable aircraft will always possess static stability, the reverse is not necessarily true; an aircraft can be statically stable without ensuring dynamic stability.
Figure 6.5 Body coordinate system and three rotational motions of roll, pitch, and yaw
Aircraft motion, or flight, is characterized by six Degrees of Freedom (6 DOF), which encompass one linear and one rotational movement along each of the three axes: x, y, and z Consequently, stability is assessed in relation to these three axes.
Lateral stability refers to the stability of rotational movements around the x-axis, which involves rolling, as well as the associated linear movements along the yz plane, indicating side motion In contrast, longitudinal stability pertains to the stability of rotational movements around the y-axis, relating to pitching, along with linear movements along the xz plane.
Chapter 6 Tail Design 16 plane (i.e forward and aft, and up and down) Directional stability is defined as the stability of any rotational motion about z axis (e.g yaw) and any corresponding linear motion along xy plane (e.g sideslip) Figure 6.4 provides aircraft body coordinate system, plus three rotational motions of roll, pitch, and yaw The convention is that the clockwise rotation about any axis; when you look from pilot seat; is assumed as the positive rotation
The horizontal tail plays a crucial role in an aircraft's longitudinal stability by generating a counter pitching moment to maintain the longitudinal trim position In contrast, the vertical tail is essential for directional stability, producing a counter yawing moment to restore the directional trim position Both tails also significantly contribute to lateral stability by generating counter rolling moments to achieve lateral trim This chapter focuses on tail design, specifically emphasizing the requirements for longitudinal and directional stability.
The following is reproduced from Section 173 of PAR 23 of Federal Aviation Regulations (Ref
7) which concerns about static longitudinal stability of a General Aviation aircraft:
Under the conditions outlined in §23.175, and with the airplane properly trimmed, the elevator control forces and the friction within the control system must meet specific characteristics.
To achieve and sustain speeds below the specified trim speed, a pull force is necessary, while a push force is needed for speeds above the trim speed This requirement applies to all attainable speeds, with the exception of those that demand a control force exceeding 40 pounds or those that surpass the maximum allowable speed or fall below the minimum speed for steady, unstalled flight.
When gradually releasing the control force, the airspeed should conform to the specified tolerances for the relevant airplane categories within the designated speed range.
(1) The airspeed must return to within plus or minus 10 percent of the original trim airspeed; and
(2) For commuter category airplanes, the airspeed must return to within plus or minus 7.5 percent of the original trim airspeed for the cruising condition specified in §23.175(b)
(c) The stick force must vary with speed so that any substantial speed change results in a stick force clearly perceptible to the pilot
The following is reproduced from Section 177 of PAR 23 of Federal Aviation Regulations (Ref
7) which concerns about static directional stability of a General Aviation aircraft: a)The static directional stability, as shown by the tendency to recover from a wings level sideslip with the rudder free, must be positive for any landing gear and flap position appropriate to the takeoff, climb, cruise, approach, and landing configurations This must be shown with symmetrical power up to maximum continuous power, and at speeds from 1.2 V S1 up to the maximum allowable speed for the condition being investigated The angel of sideslip for these tests must be appropriate to the type of
Chapter 6 Tail Design 17 airplane At larger angles of sideslip, up to that at which full rudder is used or a control force limit in §23.143 is reached, whichever occurs first, and at speeds from 1.2 V S1 to V O , the rudder pedal force must not reverse b) The static lateral stability, as shown by the tendency to raise the low wing in a sideslip, must be positive for all landing gear and flap positions This must be shown with symmetrical power up to 75 percent of maximum continuous power at speeds above 1.2 V S1 in the take off configuration(s) and at speeds above 1.3 V S1 in other configurations, up to the maximum allowable speed for the configuration being investigated, in the takeoff, climb, cruise, and approach configurations For the landing configuration, the power must be that necessary to maintain a 3 degree angle of descent in coordinated flight The static lateral stability must not be negative at 1.2 V S1 in the takeoff configuration, or at 1.3
In testing various configurations of the V S1, it is crucial to ensure that the sideslip angle aligns with the specific type of airplane However, the constant heading sideslip angle should not be less than what can be achieved with a 10-degree bank Alternatively, if this angle is lower, it must not exceed the maximum bank angle attainable with full rudder deflection or a rudder force of 150 pounds.
The following is reproduced from Section 181 of PAR 23 of Federal Aviation Regulations (Ref
7) which concerns about dynamic lateral-directional-longitudinal stability of a General Aviation aircraft:
Short period oscillations, excluding combined lateral-directional movements, that occur between the stalling speed and the maximum allowable speed for a given airplane configuration must be effectively damped using the primary controls.
Any lateral-directional oscillations, known as "Dutch roll," that occur between the stalling speed and the maximum allowable speed for the airplane's configuration must be damped to one-tenth of their amplitude within seven cycles using the primary controls.
Tail configuration
This section outlines the design requirements and essential information for selecting the appropriate tail configuration Here, "tail" refers to the combination of various design elements that contribute to the overall functionality and performance.
Chapter 6 Tail Design 22 horizontal and vertical tail The first step in the tail design is the selection of the tail configuration The choice of the tail configuration is the output of a selection process, not the result of a mathematical calculation The decision for the selection of the tail configuration must be made based on the reasoning, logic and evaluation of various configurations against design requirements
The list of design requirements that must be considered and satisfied in the selection of tail configurations are as follows:
9 Stealth (only in some specific military aircraft)
11 Airworthiness (e.g safety, tail stall, and deep stall)
15 Size limits (for example, an aircraft may be required to have a limited height; for instance, for the hangar space limits This will influence the vertical tail configuration)
Before selecting a tail configuration, it's crucial to establish the technical details of the design requirements Typically, no single tail configuration meets all criteria, necessitating a compromise among various options Once several viable candidates are identified, a systems engineering approach should be employed to create a comparison table that aids in making the final selection In some cases, certain design requirements, like lateral stability, may be overlooked to prioritize more critical factors such as maneuverability or stealth capabilities.
In general, the following tail configurations are available that are capable of satisfying the design requirements in one way or another:
1 Aft tail and one aft vertical tail
2 Aft tail and twin aft vertical tail
3 Canard and aft vertical tail
4 Canard and twin wing vertical tail
5 Triplane (i.e aft tail as aft plane, and canard as fore-plane plus wing as the third plane)
6 Tailless (delta wing with one vertical tail)
7 No formal tail (also known as “flying wing”, such as B-2 Spirit)
According to Figure 6.6, approximately 85 percent of aircraft designers prefer the first tail configuration, while around 10 percent utilize canard designs Only about 5 percent of modern aircraft feature unconventional tail configurations Detailed characteristics of canard designs will be discussed in Section 6.5.
The first configuration of the aircraft features an aft tail with one vertical tail, which includes several sub-configurations detailed in Section 6.4.2 The initial three configurations showcase a vertical tail positioned at the fuselage's rear, while the fourth configuration introduces two vertical tails mounted at the wing tips The advantages of the canard configuration will be discussed in Section 6.5 The choice of twin vertical tails is primarily due to their ability to enhance directional control without compromising roll control Additionally, two short-span vertical tails exhibit a lower mass moment of inertia about the x-axis compared to a single long-span vertical tail An illustration of the Piaggio P- aircraft is provided in Figure 6.7-6.
1 Aft tail and one aft vertical tail 2 Aft tail and two aft vertical tails 3 Canard and aft vertical tail
4 Canard and two wing vertical tail 5 Triplane 6 Delta wing with one vertical tail
In aircraft with no tail configuration, primary functions are managed by other components or automatic control systems For example, in hang gliders, pilots achieve longitudinal trim by shifting their body to adjust the center of gravity Additionally, longitudinal stability is maintained through a specific wing airfoil design featuring a reflexed trailing edge Pilots can also manually alter the wing airfoil section, allowing for continuous control and significant adjustments, a technique commonly used in hang gliding.
Most general aviation (GA) aircraft feature a conventional aft horizontal and vertical tail configuration, while many fighter jets utilize a single aft tail paired with twin vertical tails to enhance maneuverability Some European fighters, particularly those from France, adopt a canard configuration The B-2 Spirit bomber is designed with a flying wing shape primarily to meet stealth requirements In contrast, most hang gliders forgo a horizontal tail, achieving longitudinal stability instead through a reflexed trailing edge on the wing.
1 Cessna 172 (aft tail) 2 Eurofighter (canard) 3 B-2 Spirit (flying wing)
4 F-18 (twin VT) 5 AASI Jetcruzer 500 (canard and twin VT) 6 Piaggio P-180 (triplane)
7 FLS Optica OA7-300 (unconventional twin VT) 8 Space shuttle atop Antonov 225
Figure 6.8 Several aircraft with various tail configurations
Certain aircraft configurations can limit tail design options For example, in pusher aircraft like the AASI Jetcruzer 500, installing a prop-driven engine in the aft fuselage negatively impacts the efficiency of the horizontal tail due to continuous wake interference Similarly, a canard configuration is impractical for aircraft like the Cessna 172, where the prop-driven engine is located at the nose Additionally, designs featuring multiple tails, such as tri-planes or dual vertical tails, face challenges related to higher manufacturing costs and increased design complexity Various aircraft configurations are illustrated in Figure 6.7.
Figure 6.9 A wing airfoil section with reflexed trailing edge
When selecting a tail configuration for aircraft design, it is advisable to start with a conventional aft tail configuration, as it typically meets most design requirements Evaluate its performance against these requirements, and if any are unmet, consider transitioning to a similar configuration that better satisfies them In cases where modifications are necessary during the manufacturing phase to enhance longitudinal and directional stability, incorporating a smaller auxiliary horizontal tail, also known as a stabilon, along with a ventral stake can be effective This approach is exemplified in the twin-turboprop regional transport aircraft, Beech 1900D.
Aft tail configurations in aircraft design offer a variety of options, each with distinct advantages and disadvantages This section aims to compare these configurations, assisting aircraft designers in selecting the most suitable design The aft tail configurations include Conventional, T-shape, Cruciform (+), H-shape, Triple-tail, V-tail, Inverted V-tail, Improved V-tail, Y-tail, Twin vertical tail, Boom-mounted, Inverted boom-mounted, Ring-shape, Twin T, and half T For visual reference, Figure 6.8 illustrates several aft tail configurations.
The conventional tail, characterized by its inverted T-shape configuration, is the simplest and most effective design for performing essential tail functions such as trim, stability, and control Its performance analysis is straightforward, featuring a horizontal tail composed of two sections on either side of the fuselage and a single vertical tail positioned atop the aft fuselage Both tail components are mounted at the rear of the fuselage, ensuring optimal aerodynamic efficiency.
Chapter 6 Tail Design 26 mainly employed to satisfy the longitudinal trim and stability requirements, while vertical tail is mainly used to satisfy the directional trim and stability requirements If the designer has low experience, it is recommended to initially select the conventional tail configuration
While most flight dynamics textbooks focus on conventional tail features, they often overlook alternative tail configurations Designers must possess expertise in trim, stability, and control analysis when considering these alternatives, which is why approximately 60% of aircraft currently in service utilize conventional tails This design is lightweight, efficient, and performs well under typical flight conditions Notable examples include general aviation aircraft like the Cessna 172 and Beech King Air C90B, as well as large transport aircraft such as the Boeing 747 and Airbus A340, and fighter jets like the F-16 Eagle and Harrier GR Mk 7 The Cessna 172, depicted in Figure 6.7-1, exemplifies the conventional tail configuration.
5 V-tail 6 Y-tail 7 Twin vertical tail 8 Boom mounted
Figure 6.10 Several aft tail configurations
A T-tail is an aft tail design resembling the letter "T," where the vertical tail is positioned above the horizontal tail This configuration offers several advantages, notably its placement above the wing's wake, downwash, and vortices, as well as away from the turbulent exhaust of the engines However, it also comes with certain disadvantages.
Chapter 6 Tail Design 27 horizontal tail to provide a higher efficiency, and a safer structure The lower influence from the wing results in a smaller horizontal tail area; and the lower effect from the engine leads in a less tail vibration and buffet The less tail vibration increases the life of the tail with a lower fatigue problem Furthermore, another advantage of the T-tail is the positive influence of horizontal tail on the vertical tail It is referred to as the end-plate effect and results in a smaller vertical tail area
Canard or Aft Tail
The selection of the horizontal tail's location is a critical aspect of aircraft design, with two primary options: the aft tail and the canard configuration While both designs effectively provide longitudinal trim and stability, they influence flight characteristics differently Historically, the first aircraft, the Wright Flyer, utilized a canard configuration, which, despite being less common than the aft tail, is still used in various general aviation, military, and some transport aircraft Notable examples of canard-configured aircraft include the Rutan VariEze, Mirage 2000, Dassault Rafale, and B-1 Lancer, among others.
To understand the key differences between aft tail and canard aircraft configurations, it is essential to examine four specific aircraft designs, two featuring aft tails and two equipped with canards While the wing nose-down pitching moment is omitted for clarity, the primary distinction lies in the location of the center of gravity (cg) relative to the wing-fuselage aerodynamic center This variation leads to several advantages and disadvantages of canard designs compared to traditional aft tail configurations In all four aircraft setups, maintaining longitudinal trim is crucial.
M cg M o wf L ht l t L wf h h o C (aft tail configuration) (6.37a)
M cg M o wf L C l t L wf h h o C (canard configuration) (6.37b)
F z 0 W L wf L ht (aft tail configuration) (6.38a)
4 Canard is originally a French word which means “duck” Some early aircraft such as French Canard Vision had a tail-first configuration which was seen by observers to resemble a flying duck
Chapter 6 Tail Design 32 where LC denotes the canard lift Equations 6.37 and 6.38 indicate that the aft tail lift or canard lift might be positive, or negative, depending upon the location of aircraft cg relative to wing- fuselage aerodynamic center (see figure 6.12) Equations 6.37b and 6.6.38b are utilized to determine the value and the direction of the canard lift to satisfy trim requirements It is obvious that the canard lift is sometimes negative (see figure 6.12-3) Keeping in mind the above basic difference between aft tail and canard, a comparison between features of canard as compared with aft tail is presented
The canard design effectively prevents deep stall incidents, which account for approximately 23 percent of global aircraft crashes When a pilot increases the wing's angle of attack for takeoff, climbing, or landing, the canard, positioned forward of the wing, stalls first This early stalling of the canard leads to a reduction in lift, causing the aircraft's nose to drop and allowing the canard to recover from the stall before the wing does This unique characteristic of the canard configuration enhances safety compared to traditional aft tail designs, making it a significant advantage in aircraft engineering.
Lht wing tail cg acwf
Lht wing tail cg acwf
W wing canard cg ac wf
Figure 6.13 The lift of the tail (or canard) in four configurations
In canard-configured aircraft, the canard stalls prior to the main wing, preventing the main wing from achieving its maximum lift potential This necessitates a larger main wing compared to conventional designs, leading to increased weight and zero-lift drag.
1 Canard has a higher efficiency when compared with aft tail The reason is that it is located in front of wing, so the wing wake does not influence the canard aerodynamic characteristics Wing, however, is located aft of canard; hence, it is negatively affected by the canard wake Thus a wing in a canard configuration has a lower aerodynamic efficiency (i.e lower lift) when compared with an aircraft with aft tail configuration
2 It is not appropriate to employ canard when the engine is pusher and located at the fuselage nose The reason is that the aircraft nose will be heavy and the cg adjustment is difficult Moreover, the structural design of fuselage nose is somewhat complicated, since it must hold both engine and canard
3 An aircraft with a canard configuration tends to have a smaller static margin compared with an aircraft with a conventional aft tail configuration In another word, the distance between aircraft neutral point and aircraft center of gravity is shorter This makes the canard aircraft longitudinally statically less stable This feature is regarded as a disadvantage for canard configuration
4 The center of gravity range in an aircraft with a canard configuration tends to be wider; hence, it is more flexible in the load transportation area
5 Due to the forward location of a canard, the aircraft cg moves slightly aft compared with an aircraft with a conventional aft tail configuration This feature requires a slightly larger vertical tail for directional trim and stability
6 A canard tends to generate a lower “trim drag” compared with an aft tail In another word, a canard aircraft produces less lift-dependent drag to longitudinally trim the aircraft However, this feature may leads in a larger wetted area (Swet)
7 One of the potential design challenges in a canard aircraft is to optimally locate the fuel tank The general rule is to place the fuel tank near the aircraft center of gravity as close as possible, in order to avoid a large movement of cg during the flight operation The aircraft cg in a canard configuration, if fuel tank is inside the wing, is often forward of the fuel tank To improve the cg location, designers would rather to place the fuel tank into the fuselage, which in turn increases the possibility of aircraft fire Another solution is to considerably increase the wing root chord (i.e employing strake) and to place the fuel tank in wing root But this technique increases the wing wetted area and reduces the cruise efficiency The canard aircraft Beechcraft Starship has a wing strake and utilizes this technique
8 A canard obscures the view of the pilot This is another disadvantage of the canard configuration
9 Often times the canard generates a positive lift (see figure 6.12-4) while a conventional tail often produces a negative lift (see figure 6.12-2) The reason is that the aircraft cg in a canard configuration is often forward of the wing-fuselage ac The aircraft cg in a conventional tail configuration is typically aft of the wing-fuselage ac Recall that the cg move during flight as the fuel burns The cg range, in a modern aircraft with a conventional tail or a canard is usually determined such that the cg is most of the times forward of the wing aerodynamic center However, in a fewer instances of cruising flight, the cg is aft of the wing aerodynamic center Thus, in an aircraft with a conventional tail, during the cruising flight, the cg usually moves from the most forward location toward the most aft location However, in an aircraft with a canard, during the cruising flight, the cg often moves from the most aft location toward the most forward location
A canard configuration often contributes to the aircraft's lift, while a tail typically reduces the lift produced by the wings, resulting in decreased weight and increased cruising speed During take-off, when the wing experiences a significant nose-down pitching moment, the lift generated by the canard is enhanced Similarly, at supersonic speeds, the canard lift increases due to the aerodynamic center of the wing shifting aft to approximately 50 percent of the mean aerodynamic chord This aerodynamic advantage is one reason why some European supersonic fighters, like the Mirage 2000, utilize the canard design.
10 Item 10 results in the following conclusion: An aircraft with a canard is slightly lighter than an aircraft with a conventional tail
11 In general, the canard aerodynamic and stability analysis techniques are considerably more complicated than the technique to evaluate the aerodynamic feature and stability analysis of the conventional tail configuration aircraft Literature surveys include a variety of published materials regarding conventional tail, while much less papers and technical reports are available for canard analysis Thus the design of a canard is more time intensive and more complicated than the conventional tail design
12 A canard configuration seems to be more stylish and more attractive than a conventional tail
13 A canard is more efficient for fulfilling the longitudinal trim requirements, while a conventional tail tends to be more efficient for fulfilling the longitudinal control requirements
Canard designs are primarily categorized into two types: lifting-canard and control-canard A lifting-canard shares the aircraft's weight between the main wing and the canard wing, enhancing overall lift capability This design requires the main wing to be positioned further aft of the center of gravity compared to conventional aft tail configurations, which amplifies the pitching moment from trailing-edge flaps Notably, the Wright Flyer and the X-29 featured a lifting-canard design.
Figure 6.17 depicts three aircraft with canard configuration
Optimum Tail Arm
In the tail design process, determining the tail arm (l t), which is the distance from the tail's aerodynamic center to the aircraft's center of gravity, is crucial for maintaining longitudinal trim The tail arm acts as the lever for the tail pitching moment, calculated by multiplying tail lift by the tail arm Establishing the tail arm requires a clear understanding of design criteria, as it interacts closely with tail area, which generates tail lift An increase in tail arm necessitates a decrease in tail area, and vice versa Both short tail arms, typical in fighter jets, and long tail arms, common in transport aircraft, can achieve proper longitudinal trim with the right tail area The challenge lies in identifying the optimal tail arm, which must be evaluated alongside other design requirements.
Figure 6.14 Top view of aft portion of the aircraft
Two crucial design requirements for aircraft are minimizing weight and drag, which can be effectively addressed by reducing the wetted area of the aircraft Increasing the horizontal tail arm leads to a larger fuselage wetted area while simultaneously decreasing the wetted area of the horizontal tail Conversely, a reduction in the horizontal tail arm results in a smaller fuselage wetted area.
Chapter 6 Tail Design 36 area is decreased, but horizontal tail wetted area is increased Hence, we are looking to determine the optimum tail arm to minimize drag; which in turn means to minimize the total wetted area of the aft portion of the aircraft The following is a general educational approach to determine the optimum tail arm; hence, one must develop his/her own technique and derive more accurate equation based on the suggested approach The approach is based on the fact that the aircraft zero-lift drag is essentially a function of the aircraft wetted area
Minimizing the total wetted area of an aircraft is crucial for reducing zero-lift drag Additionally, this approach impacts the fuselage length, as the rear section must provide structural support for the tail.
Consider the top view of aft aircraft (see figure 6.13) that includes aft portion of the fuselage plus the horizontal tail
The wetted area of the aft portion of the aircraft is the summation of the wetted area of the aft portion of the fuselage ( aft fus
S wet ) plus the wetted area of the horizontal tail ( wet ht
S ) fus ht aft aft wet wet wet S S
Here we assume that aft portion of the fuselage is a conic Hence, the wetted area of the aft portion of the fuselage is fus aft aft f fus wet D L
1 (6.40) where D f is the maximum fuselage diameter and fus aft
L is the length of the aft portion of the fuselage At the moment, it is assumed that fus aft
L is equal to half of the fuselage length (Lf) On the other hand, the wetted area of the horizontal tail is about twice the tail planform area: t wet S
But, the tail volume coefficient is defined as in equation 6.24, so: l
Substituting equation 6.41 and 6.43 into 6.39 yields: l
The relationship between fus aft
L and l depends upon the location of the horizontal tail (see figure
In this analysis, we initially assume that the lift forces on the fuselage and the aft section of the aircraft are equal, although this may not hold true for all aircraft configurations This assumption, based on data from Table 6.2, will be refined later To reduce the zero-lift drag of the aircraft's aft section, it is essential to differentiate the wetted area concerning the tail arm, as illustrated in Figure 6.14, and then set the derivative to zero for optimization.
Figure 6.15 The variation of wetted area with respect to tail arm
The optimum tail arm is obtained by solving this equation as follows: f
To compensate for our inaccurate assumption, we add a fudge factor as follows: f
The correction factor Kc, which ranges from 1 to 1.4 depending on the aircraft configuration, is crucial for understanding aerodynamic drag A Kc value of 1 is applicable when the aft fuselage has a conical shape, while deviations from this shape increase Kc up to 1.4 Typically, single-seat, single-engine prop-driven general aviation (GA) aircraft assume Kc to be 1.1, whereas transport aircraft often use Kc as 1.4 In large transport aircraft, the fuselage predominantly features a cylindrical shape, with only the aft section being conical Positioning the horizontal tail at the optimal location (l opt) helps minimize the wetted area of the aft fuselage, thereby reducing drag and enhancing overall aerodynamic efficiency.
For a twin-seat general aviation aircraft with a wing reference area of 10 m² and a mean aerodynamic chord of 1 m, the tail volume coefficient required for longitudinal stability is 0.6 Given a maximum fuselage diameter of 117 cm and assuming the aft fuselage portion is conical, the optimum tail arm can be calculated, which is essential for determining the horizontal tail area.
The aircraft is a GA and has two seats, so the factor K c is assumed to be 1.4 Using equation 6.47, we have m
The horizontal tail area is calculated by employing tail volume coefficient equation as follows: l m
Horizontal Tail Parameters
Once the tail configuration is established, the design of the horizontal and vertical tails can proceed independently This section outlines the techniques for designing the horizontal tail and determining its parameters Given that the horizontal tail functions as a lifting surface and shares similarities with wing characteristics, key aspects such as taper ratio, sweep angle, dihedral angle, and airfoil section are briefly discussed The horizontal tail design is an iterative process heavily influenced by various wing and fuselage parameters; thus, any changes to the major wing or fuselage specifications necessitate a redesign and update of the tail parameters.
6.7.1 Horizontal Tail Design Fundamental Governing Equation
The fundamental governing equation for horizontal tail design is primarily based on its main function of achieving longitudinal trim In Figure 6.2, a general aircraft model illustrates the various forces acting along the x and z axes, as well as the moments about the y axis that affect longitudinal trim For proper longitudinal trim, it is essential that the sum of all moments around the y axis equals zero.
M cg M o wf M L wf M L ht M o ht M T eng M D w (6.48) where o wf
M denotes nose-down wing-fuselage aerodynamic pitching moment,
M denotes the pitching moment generated by the wing-fuselage lift,
M denotes the pitching moment generated by the horizontal tail lift, o ht
M denotes nose-down horizontal tail aerodynamic pitching moment,
M denotes the pitching moment generated by the engine thrust, and
The pitching moment (M) produced by wing drag is influenced by the position of the source force in relation to the aircraft's center of gravity The sign of each pitching moment varies based on this location.
Chapter 6 Tail Design 39 equation must hold at all flight conditions, but the horizontal tail is designed for the cruising flight, since the aircraft spends much of its flight time in cruise For other flight conditions, a control surface such as the elevator will contribute
In aerodynamics, the pitching moments of both the wing and horizontal tail are inherently negative, leading to a nose-down tendency The wing drag moment varies with the wing configuration; for example, a high-wing design results in a nose-up pitching moment, while a low-wing configuration produces a nose-down pitching moment The engine thrust moment is influenced by the thrust line and engine incidence; if the engine is set at an angle, both horizontal and vertical components will affect longitudinal trim A key variable in this scenario is the lift generated by the horizontal tail For effective longitudinal trim, the sum of all forces along the x and z axes must equal zero, with only the forces along the z-axis being significant for tail design.
The engine thrust (T) is influenced by the thrust setting angle (iT), which is typically between 2 to 4 degrees and is crucial for maintaining the aircraft's longitudinal stability To design the horizontal tail effectively, engineers should expand and solve equations 6.48 and 6.49 simultaneously to determine the unknowns of wing lift and horizontal tail lift This information is essential for optimizing horizontal tail design, and readers are encouraged to derive the equations independently.
The horizontal tail designer should have a solid understanding of flight dynamics principles and be able to derive the full set of longitudinal trim equations based on the aircraft's configuration This textbook aims to provide an educational perspective, thus a simplified version of the longitudinal trim equation is used By neglecting the pitching moments from engine thrust, wing drag, and the horizontal tail pitching moment, the non-dimensional horizontal tail design principle equation can be derived as previously shown.
In Section 6.2, the full derivation of the equation, which includes three terms, is presented, with the last term representing the horizontal tail's contribution to the aircraft's longitudinal trim during cruising flight This equation features two unknowns: the horizontal tail volume coefficient (VH) and the lift coefficient of the horizontal tail (CLT) VH is primarily determined by longitudinal stability requirements, which are influenced by the aircraft's flying qualities For comprehensive guidance, readers are encouraged to refer to References 1 and 4, while Chapter 12 provides a summary of longitudinal flying qualities requirements It is important to note that a higher VH value can lead to a longer fuselage, a smaller wing, and/or a larger horizontal tail.
Increasing the value of VH enhances the longitudinal stability of an aircraft, but this stability comes at the cost of reduced controllability Conversely, a lower VH value results in a more controllable yet less stable flight vehicle During the preliminary design phase of the horizontal tail, when other aircraft components remain undetermined, it is essential to select a typical VH value Table 6.4 provides typical values for horizontal and vertical tail ratios, derived from current successful designs.
Chapter 6 Tail Design 40 aircraft statistics A number from this table based on the aircraft mission and configuration is recommended at the early design phase When the other aircraft components are designed and their data are available, a more accurate value for VH may be determined
The variable “h o ” denotes the non-dimensional wing-fuselage aerodynamic center (
In aircraft configurations, the typical value for the non-dimensional parameter "ho" ranges from 0.2 to 0.25 References 1 and 4 provide a detailed method for accurately determining the value of "ho." Additionally, another critical parameter in equation 6.29 is "h," which represents the non-dimensional position of the aircraft's center of gravity (cg).
) The value for “h” must be known prior to the horizontal tail design
No Aircraft Horizontal tail volume coefficient (V H )
3 GA-single prop-driven engine 0.7 0.04
4 GA-twin prop-driven engine 0.8 0.07
Table 6.4 Typical values for horizontal and vertical tail volume coefficients
Chapter 11 is dedicated to the techniques and methods to determine the aircraft cg position, provided the details of geometries of all aircraft components However, if at the early stages of the horizontal tail design, the other aircraft components such as fuselage, engine, and landing gear have not yet been designed, the only option is to pick a value for “h” The best value is a mid value between the most forward and the most aft position of the aircraft cg This minimized the aircraft trim drag while in cruise This is based on a logical assumption that the aircraft cg is at it one end of the extreme position (say most forward) at the beginning of the cruise, and moves to another end of the extreme position (say most aft) at the end of the cruise
To minimize longitudinal control effort during cruising flight, it is advisable for the aircraft's center of gravity (cg) to be positioned near the wing-fuselage aerodynamic center The non-dimensional center of gravity limit (Δh) represents the range between the aircraft's most forward and most aft cg positions Typical values for this non-dimensional center of gravity limit are established to ensure optimal performance.
In aircraft design, the center of gravity (cg) is typically positioned about 10 percent of the wing's mean aerodynamic chord at the forward limit and approximately 30 percent at the aft limit For initial horizontal tail design, a value of 0.2 is often assumed for the cg position (h) Once a more accurate cg position is determined, the horizontal tail design should be revised accordingly The aircraft lift coefficient (C L) is calculated using the cruising velocity, cruise altitude, and average weight, as outlined in equation 5.10 By solving equation 6.29, the unknown lift coefficient for the tail (CLT) can be determined.
Currently, three horizontal tail parameters—V H, C LT, and l—are established Additionally, the horizontal tail area (S t) can be easily calculated using equation 6.24, as the tail volume coefficient depends on it The previously discussed technique allows for the determination of these three horizontal tail parameters effectively.
3 horizontal tail cruise lift coefficient (CLT)
Vertical Tail Design
The vertical tail plays a crucial role in aviation, serving two main purposes: ensuring directional stability and providing directional trim Additionally, it significantly contributes to maintaining directional control, which is primarily managed by the rudder.
1 The primary function of the vertical tail is to maintain the aircraft directional stability The static and dynamic directional stability requirements were discussed in Section 6.3 In summary, the stability derivatives Cn must be positive (to satisfy the static directional stability requirements), but the stability derivatives Cnr must be negative (to satisfy the dynamic directional stability requirements) Two major contributors to the value of these stability derivatives are vertical tail area (SV) and vertical tail moment arm (l V) If vertical tail area is large enough and vertical tail moment arm is long enough, the directional stability requirements could be easily satisfied The directional stability analysis is performed after all aircraft components are designed and the roots () of the lateral-directional characteristic equation are calculated A general form of the aircraft lateral-directional characteristic equation looks like the following:
A (6.69) where coefficients A 2 , B 2 , C 2 , D 2 , and E 2 are functions of the several stability derivatives such as
The directional stability derivatives of an aircraft cannot be accurately determined until all components, including the wing and fuselage, are fully designed To aid in the preliminary design of the vertical tail, a new parameter known as the vertical tail volume coefficient (VV) is introduced If this coefficient falls within an acceptable range, there is a 90 percent likelihood that the directional stability requirements are met Once the other aircraft components are finalized, the vertical tail design will undergo revisions and optimization during the directional stability analysis Further details about the vertical tail volume coefficient will be provided in Section 6.8.2.
2 The second function of the vertical tail is to maintain the aircraft directional trim As discussed in Section 6.3, the summation of all forces along the y-axis and the summation of all moments about z-axis must be zero
Aircraft are typically designed to be symmetrical around the x-z plane to ensure proper directional trim While this ideal symmetry is generally maintained during the manufacturing of components like the right and left wing sections, slight asymmetries can occur in the x-y plane One potential cause of these asymmetries is the variation in manufacturing jigs and fixtures used for the right and left sections, such as the wings and tail.
Chapter 6 Tail Design 56 for directional asymmetricity lies in the internal components inside fuselage such as fuel system, electrical wiring, and even load and cargo inside load compartment
In single-engine prop-driven aircraft, the rotation of the engine propeller disrupts directional trim, while multi-engine prop-driven aircraft with an odd number of engines face a similar challenge To counteract this, the vertical tail generates an opposing yawing moment around the z-axis, essential for maintaining directional trim A key factor affecting this trim is the vertical tail's incidence angle in relation to the x-z plane.
Another directional trim case is in multi-engine aircraft, where one engine in inoperative
In situations where operative engines create a disturbing yawing moment, balancing this asymmetry requires a counteracting yawing moment generated by the vertical tail To achieve directional trim of the aircraft, a control surface, such as the rudder, must be deflected appropriately.
The vertical tail plays a crucial role in enhancing aircraft lateral stability and control, yet it is not the primary basis for its design It is essential to analyze the vertical tail's performance to ensure it positively contributes to lateral stability, as this stability is mainly determined by wing parameters Additionally, the static and dynamic directional trim requirements are outlined in Section 6.2.
3 The third aircraft design requirement in which the vertical tail is a major contributor is the directional control Maneuvering operations such as turning flight and spin recovery are successfully performed by using a movable section of the vertical tail which is called rudder The design of the rudder is examined in Chapter 12, but the spin recovery requirements will be discussed in Section 6.8.3
To ensure directional stability, it is essential to first establish the vertical tail parameters In the subsequent stages of the vertical tail design process, both directional trim and control requirements will be evaluated.
In the design of the vertical tail, the following parameters must be determined:
9 Mean Aerodynamic Chord (MAC v or C v )
The vertical tail, depicted in figure 6.25, serves as a lifting surface that generates aerodynamic lift along the y-axis To ensure directional stability, control, and trim, it is essential for the vertical tail to produce an aerodynamic force, known as vertical tail lift (LV), along this axis.
(6.70) where S V is the vertical tail area, and the C LV is the vertical tail lift coefficient The vertical tail lift is generating a yawing moment about z-axis:
For optimal directional stability, it is essential to achieve a sufficient moment that supports directional trim This is assessed using the vertical tail volume coefficient (V V), as detailed in Section 6.8.1, which plays a crucial role in evaluating the aircraft's directional stability.
The equation V V = l V V (6.72) defines the relationship between the distance (l v) from the vertical tail's aerodynamic center (acvt) to the wing-fuselage aerodynamic center This relationship is influenced by factors such as the vertical tail planform area (SV) and the wing span (b), as illustrated in figure 6.24.
S denotes the wing reference area The vertical tail aerodynamic center is located at the quarter chord of the vertical tail mean aerodynamic chord
The vertical tail volume coefficient is a non-dimensional parameter that depends on two key factors: vertical tail area (SV) and vertical tail moment arm (lv) These parameters are closely related, allowing one to be derived from the other This coefficient serves as an indirect indicator of an aircraft's directional stability, with typical values ranging from 0.02 to 0.12 Additionally, Table 6.6 presents various vertical tail parameters, including the vertical tail volume coefficient for multiple aircraft, highlighting that the vertical tail planform area encompasses both the fixed section and the movable rudder section.
This article briefly revisits the fundamental parameters of lifting surfaces, including aspect ratio, taper ratio, and airfoil section, which were previously detailed in Chapter 5 and the horizontal tail design section (Section 6.7).
Practical Design Steps
The tail design process is detailed in the flowchart presented in section 6.1, while sections 6.2 and 6.3 review the fundamental functions and design requirements of the tail Sections 6.4 to 6.8 explore various tail configurations, along with horizontal and vertical tail parameters, and the methods for determining each parameter This section aims to provide a clear outline of the practical steps involved in tail design.
1 Select tail configuration (Sections 6.4 and 6.7)
2 Select horizontal tail location (aft, or forward (canard)); Section 6.5
3 Select the horizontal tail volume coefficient; V H (Table 6.4)
4 Calculate optimum tail moment arm (l opt) to minimize the aircraft drag and weight (Section 6.6)
5 Calculate horizontal tail planform area; St (equation 6.24)
6 Calculate wing-fuselage aerodynamic pitching moment coefficient (equation 6.26)
7 Calculate cruise lift coefficient (C Lc ); equation 6.27
8 Calculate horizontal tail desired lift coefficient at cruise from trim equation (6.29)
9 Select horizontal tail airfoil section (Section 6.7)
10 Select horizontal tail sweep angle and dihedral (Section 6.7)
11 Select horizontal tail aspect ratio and taper ratio (Section 6.7)
12 Determine horizontal tail lift curve slope;
13 Calculate horizontal tail angle of attack at cruise; (equation 6.51)
14 Determine downwash angle at the tail equation
15 Calculate horizontal tail incidence angle; i t (equation
16 Calculate tail span, tail root chord, tail tip chord and tail mean aerodynamic chord (equations 6.63 through 6.66)
17 Calculate horizontal tail generated lift coefficient at cruise (e.g lifting line theory; Chapter 5) Treat the horizontal tail as a small wing
18 If the horizontal tail generated lift coefficient (item 17) is not equal to the horizontal tail required lift coefficient (item 8), adjust tail incidence
20 Calculate the horizontal tail contribution to the static longitudinal stability derivative (C m ) The value for C m must be negative to insure an stabilizing contribution If the design requirements are not satisfied, redesign the tail
21 Analyze dynamic longitudinal stability If the design requirements are not satisfied, redesign the tail
23 Select vertical tail configuration (e.g conventional, twin vertical tail, vertical tail at swept wing tip, V-tail) (Section 6.8.2-1)
24 Select the vertical tail volume coefficient; VV (Table 6.4)
25 Assume the vertical tail moment arm (l v) as equal to the horizontal tail moment arm (l)
26 Calculate vertical tail planform area; Sv (equation 6.73)
27 Select vertical tail airfoil section (Section 6.8.2-4)
28 Select vertical tail aspect ratio; ARv (Section 6.8.2-6)
29 Select vertical tail taper ratio; V (Section 6.8.2-7)
30 Determine the vertical tail incidence angle (Section 6.8.2-5)
31 Determine the vertical tail sweep angle (Section 6.8.2-8)
32 Determine the vertical tail dihedral angle (Section 6.8.2-9)
33 Calculate vertical tail span (bv), root chord (Cvroot), and tip chord(Cvtip), and mean aerodynamic chord (MACv) (equations 6.76 through 6.79)
35 Adjust the location of the vertical tail relative to the horizontal tail by changing l v, to satisfy the spin recovery requirements (Section 6.8.2-2)
38 Modify to meet the design requirements
Tail design is an iterative process that requires adjustments based on the analysis of the aircraft's dynamic longitudinal-directional stability, which is influenced by the design of other components like the fuselage and wings.
Tail Design Example
Problem statement: Design a horizontal tail for a two-seat motor glider aircraft with the following characteristics: m TO = 850 kg, D fmax = 1.1 m, V c = 95 knot (at 10,000 ft), f = 1 deg (at cruise)
The wing has a reference area 18 m 2 of and the following features:
C = 0.8 m, AR = 28, = 0.8, i w = 3 deg, twsist = -1.1 deg, LE = 10 deg, = 5 deg, airfoil: NACA 23012, C L = 5.8 1/rad
The aircraft features a high wing and a conventional aft tail design, with the aerodynamic center of the wing-fuselage combination positioned at 23% of the Mean Aerodynamic Chord (MAC) During cruising flight, the center of gravity is situated at 32% of the fuselage length, which is 7 cm forward of the wing-fuselage aerodynamic center.
Then following tail parameters must be determined: airfoil section, St,Ct_tip,Ct_root, bt,it,ARt,t,
t,t.At the end, draw a top-view of the aircraft that shows fuselage, wing and horizontal tail (with dimensions)
The tail configuration has been finalized, eliminating the need for further investigation The primary focus now is on determining the setting angle Given the aircraft's lack of maneuverability and the need for cost efficiency, a fixed tail has been chosen Consequently, the design process will commence with the selection of the horizontal tail volume coefficient.
To determine the optimum tail moment arm (l opt), we set the goal to minimize the aircraft drag Hence:
(6.47) where the correction factor Kc is selected to be 1.2 Then, the tail planform area is determined as:
The aircraft cruise lift coefficient is:
L C (6.27) where the air density at 10,000 ft is 0.905 kg/m 3 The wing-fuselage aerodynamic pitching moment coefficient is:
C owf af (6.26) where the value for the wing airfoil section pitching moment coefficient ( m owf
C ) is usually extracted from the airfoil graphs Based on the Table 5.2, the value of m af
To utilize the trim equation effectively, it is essential to determine the values of h and ho According to Table 6.2, the optimal length ratio (l opt /Lf) for this type of aircraft is 0.65, which allows us to calculate the fuselage length accurately.
The aerodynamic center of the wing-fuselage combination is positioned at 23% of the Mean Aerodynamic Chord (MAC), while the aircraft's center of gravity is situated at 32% of the fuselage length, which is 7 cm forward of the aerodynamic center This data establishes a significant relationship concerning the wing's performance and stability.
This leads us to find the cg location (X cg ) in terms of MAC:
Xcg = 0.23 MAC – 0.07 = 0.23 (0.8 m) – 0.07 = 0.114 m (from wing leading edge)
So h = 0.142 The tail efficiency is assumed to be 0.98 The horizontal tail required lift coefficient at cruise is calculated by using trim equation
The horizontal tail airfoil section must possess key properties, including being symmetric and thinner than the wing airfoil, which has a thickness-to-chord ratio of 12 percent Among various airfoil sections that meet these criteria, the NACA 0009 is notable for its low drag coefficient of Cdo = 0.005 and a thickness that is 3% less than that of the wing airfoil section Characteristic graphs for the NACA 0009 airfoil section, as shown in Figure 6.19, reveal additional features that enhance its performance.
The initial tail aspect ratio is determined to be:
The tail taper ratio is initially determined to be equal to the wing taper ratio: t = w = 0.8
The tail sweep angle and the tail dihedral angle are tentatively considered to be the same as those of wing The reasons are presented in Section 6.7
To achieve a tail coefficient of -0.121, it is essential to determine the appropriate tail setting angle (i t), considering both tail parameters and wing downwash Initially, the tail angle of attack is established using the tail lift curve slope Subsequently, the lifting line theory is employed to calculate the tail-generated lift coefficient If this coefficient does not match the required lift coefficient, adjustments to the tail incidence will be made until they align Finally, downwash effects are factored in to finalize the tail incidence The tail lift curve slope is expressed as: rad AR.
The tail angle of attack in cruise is: deg 02 1 018
To determine the tail lift coefficient, the lifting line theory from Chapter 5 (Section 5.14) is applied A MATLAB m-file is used for the calculation, specifically at an angle of attack of -1.02 degrees.
The aircraft features an aspect ratio (AR) of 18.6, with a lambda value of 0.8, indicating its aerodynamic efficiency The taper ratio is set at a minimal alpha_twist of 0.00001, and the twist angle is measured at -1.02 degrees, contributing to the tail's aerodynamic characteristics The lift curve slope is defined as 6.1 (1/rad), while the zero-lift angle of attack is extremely low at 0.000001 degrees Additionally, the tail span (b) is calculated as the square root of the product of the aspect ratio and the wing area (S).
The root chord (Croot) is calculated using the formula Croot = (1.5*(1+lambda)*MAC)/(1+lambda+lambda^2) The angle theta is defined as a series of values from pi/(2*N) to pi/2, while the angle of attack for each segment (alpha) ranges from i_t to i_t + alpha_twist, decreasing by alpha_twist/(N-1) The position z is determined by the equation z = (b/2)*cos(theta) The mean aerodynamic chord (c) for each segment is computed with c = Croot * (1 - (1-lambda)*cos(theta)), and the aerodynamic efficiency (mu) is derived from mu = c * a_2d / (4 * b).
LHS = mu * (alpha-alpha_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((2*j-1) * theta(i)) * (1 + (mu(i) * (2*j-1)) / sin(theta(i))); end end
A=B\transpose(LHS); for i = 1:N sum1(i) = 0; sum2(i) = 0; for j = 1 : N sum1(i) = sum1(i) + (2*j-1) * A(j)*sin((2*j-1)*theta(i)); sum2(i) = sum2(i) + A(j)*sin((2*j-1)*theta(i)); end end
===========================================================The output of this m-file is:
The tail was anticipated to produce a lift coefficient (CLt) of -0.121, but it actually achieved -0.0959 To reach the target CLt, it is necessary to adjust the tail angle of attack Through trial and error using the same m-file, we determined that an angle of attack of -1.29 degrees successfully generates the desired tail lift coefficient.
Now, we need to take into account the downwash The o (downwash angle at zero angle of attack) and d/d (downwash slope) are: deg 558 0 0097
Therefore, the tail setting angle would be: deg 33 1 954 0 1 29
The other horizontal tail parameters are determined by solving the following four equations simultaneously: t t t C
The solution of these four equations simultaneously yields the following results: m C m C m C m b t 6.52 , t 0.349 , t tip 0.309 , t root 0.386
The last step is to examine the aircraft longitudinal stability The aircraft has a fixed tail, so the aircraft longitudinal stability derivative is determined as follows:
Chapter 6 Tail Design 73 where we assumed that the wing-fuselage lift curve slope is equal to the wing lift curve slope Since the derivative Cm is negative, the aircraft is statically longitudinally stable The aircraft longitudinal dynamic stability analysis requires the information about other aircraft components that are not provided by the problem statement So this analysis is not performed in this example Figure 6.28 shows top-view of the aircraft with details of the tail geometries
Figure 6.28 Top view of the aircraft in Example 6.2
The initial phase of designing the horizontal tail is crucial, as it allows for a comprehensive analysis of longitudinal dynamic and static stability once the characteristics of other aircraft components are established This optimization process is essential for enhancing overall aircraft performance, with the tail measuring 3.795 meters in length.
1 Using the Reference 5 or other reliable sources, identify the tail configurations of the following aircraft:
Stemme S10 (Germany), Dassault Falcon 2000 (France), Embraer EMB 145 (Brazil), Canadair CL-415, ATR 42, Aeromacchi MB-339C (Italy), Eagle X-TS (Malaysia), PZL Mielec M-18 Dromader (Poland), Beriev A-50 (Russia), Sukhoi Su-32FN (Russia), Sukhoi S-
The aviation industry features a diverse array of aircraft, including the Saab 340B from Sweden, the Swiss Pilatus PC-12, and the Ukrainian An-225 The UK contributes with models like the Jetstream 41 and FLS Optica OA7-300, while the Bell/Boeing V-22 Osprey and Boeing E-767 AWACS showcase advanced military capabilities Notable private jets include the Cessna 750 Citation X and Learjet 45, alongside fighter jets such as the Lockheed F-16 Fighting Falcon and F-117A Nighthawk The McDonnell Douglas MD-95 and Northrop Grumman B-2 Spirit highlight innovation in design, complemented by unique aircraft like the Bede BD-10 and Hawker 1000 Additionally, the Schweizer SA 2-38, Sino Swearingen SJ30, and Visionaire Vantage represent the ongoing evolution in aviation technology.
2 Using the Reference 5 or other reliable sources, identify an aircraft for each of the following tail configurations:
Conventional aft tail, V-tail, Canard, T-tail, H-tail, Non-conventional, Cruciform, Tri-plane, Boom-mounted, twin vertical tail, inverted V-tail
3 Using the Reference 5 or other reliable sources, identify an aircraft with a conventional aft tail that the vertical tail is out of wake region of the horizontal tail
4 An aircraft has a fuselage with a circular cross section Derive an equation for the optimum horizontal tail moment arm such that the aft portion of the aircraft (including aft fuselage and horizontal tail) has the lowest wetted area
5 An unmanned aircraft has the following features:
S = 55 m 2 , AR= 25, St = 9.6 m 2 , lm Determine the horizontal tail volume coefficient
6 The airfoil section of a horizontal tail in a fighter aircraft is NACA 64-006 The tail aspect ratio is 2.3 Using the Reference 5, calculated that tail lift curve slope in 1/rad
7 The airfoil section of a horizontal tail in a transport aircraft is NACA 641-012 The tail aspect ratio is 5.5 Using the Reference 5, calculated that tail lift curve slope in 1/rad
8 The airfoil section of a horizontal tail in a GA aircraft is NACA 0012 The tail aspect ratio is 4.8 Using the Reference 5, calculated that tail lift curve slope in 1/rad
9 The wing reference area of an agricultural aircraft is 14.5 m 2 and wing mean aerodynamic chord is 1.8 m The longitudinal stability requirements dictate the tail volume coefficient to be 0.9 If the maximum fuselage diameter is 1.6 m, determine the optimum tail arm and then calculate the horizontal tail area Assume that the aft portion of the fuselage is conical