Category AIRCRAF DESIGN

Figure 12.3 depicts the conditions for aircraft longitudinal static stability. In the pitch plane, by definition, the angle of attack, a, is positive when an aircraft nose is above the direction of free-stream velocity. A nose-up pitching moment is considered a positive. Static-stability criteria require that the pitching-moment curve exhibit a negative slope, so that an increase in the angle of attack, a, causes a restoring neg­ative (i. e., nose-down) pitching moment. At equilibrium, the pitching moment is equal to zero (Cm = 0) when it is in trimmed condition (atrim). The higher the static margin (see Figure 12.11), the greater is the slope of the curve (i. e., the greater is the restoring moment). Using the spring analogy, the stiffness is higher for the response.

The other requirement for static stability is that at a zero angle of attack, there should be a positive nose-up moment, providing an opportunity for equilibrium at a positive angle of attack (+atrim), typical in any normal flight segment.

It is pertinent here to briefly review the terms static and dynamic stability. Stability analyses examine what happens to an aircraft when it is subjected to forces and moments applied by a pilot and/or induced by external atmospheric disturbances. There are two types of stability, as follows:

1. Static Stability. This is concerned with the instantaneous tendency of an aircraft when disturbed during equilibrium flight. The aircraft is statically stable if it has restoring moments when disturbed; that is, it shows a tendency to return to the original equilibrium state. However, this does not cover what happens in the due course of time. The recovery motion can overshoot into oscillation, which may not return to the original equilibrium flight.

2. Dynamic Stability. This is the time history of an aircraft response after it has been disturbed, which is a more complete picture of aircraft behavior. A stati­cally stable aircraft may not be dynamically stable, as explained in subsequent discussions. However, it is clear that a statically unstable aircraft also is dynam­ically unstable. Establishing static stability before dynamic stability is for proce­dural convenience.

The aircraft motion in 3D space is represented in the three planes of the Cartesian coordinate system (see Section 3.4). Aircraft have six degrees of freedom of motion in 3D space. They are decomposed into the three planes; each exhibits its own sta­bility characteristics, as listed herein. The sign conventions associated with the pitch, yaw, and roll stabilities need to be learned (they follow the right-handed rule). The brief discussion of the topic herein is only for what is necessary in this chapter. The early stages of stability analyses are confined to small perturbations – that is, small changes in all flight parameters.

1. Longitudinal Stability in the Pitch Plane. The pitch plane is the XZ plane of aircraft symmetry. The linear velocities are u along the X-axis and w along the Z-axis. Angular velocity about the Y-axis is q, known as pitching (+ve nose up). Pilot-induced activation of the elevator changes the aircraft pitch. In the plane of symmetry, the aircraft motion is uncoupled; that is, motion is limited only to the pitch plane.

2. Directional Stability in the Yaw Plane. The yaw plane is the XY plane and is not in the aircraft plane of symmetry. Directional stability is also known as weather­cock stability because of the parallel to a weathercock. The linear velocities are u along the X-axis and v along the Y-axis. Angular velocity about the Z-axis is r, known as yawing (+ve nose to the left). Yaw can be initiated by the rudder; however, pure yaw by the rudder alone is not possible because yaw is not in the plane of symmetry. Aircraft motion is coupled with motion in the other plane, the YZ plane.

3. Lateral Stability in the Roll Plane. The roll plane is the YZ plane and also is not in the aircraft plane of symmetry. The linear velocities are v along the Y-axis and w along the Z-axis. Angular velocity about the X-axis is p, known as rolling (+ve when right wing drops). Rolling can be initiated by the aileron but a pure roll by the aileron alone is not possible because roll is associated with yaw. To have a pure rolling motion in the plane, the pilot must activate both the yaw and roll controls.

It is convenient now to explain the static and dynamic stability in the pitch plane using diagrams. The pitching motion of an aircraft is in the plane of symmetry and is uncoupled; that is, motion is limited only to the pitch plane. The static and dynamic behavior in the other two planes has similar characteristics, but it is difficult to depict the coupled motion of yaw and roll. These are discussed separately in Sections 12.3.2 and 12.3.4.

Pitch-plane stability may be compared to a spring-mass system, as shown in Figure 12.1a. The oscillating characteristics are represented by the spring-mass sys­tem, with the resistance to the rate of oscillation as the damping force (i. e., propor­tional to pitch rate, q) and the spring compression proportional to pitch angle в. Figure 12.1b shows the various possibilities of the vibration modes. Stiffness is represented by the stability margin, which is the distance between the CG and the neutral point (NP). The higher the force required for deforming, the more is the stiffness. Damping results from the rate of change and is a measure of resis­tance (i. e., how fast the oscillation fades out); the higher the H-tail area, the more is the damping effect. An aircraft only requires adequate stability; making it more stable than what is required poses other difficulties in the overall design.

Figure 12.2 depicts the stability characteristics of an aircraft in the pitch plane, which provide the time history of aircraft motion after it is disturbed from an initial

equi librium

state

Figure 12.1. Aircraft stability compared to a spring-mass system equilibrium. It shows that aircraft motion is in an equilibrium level flight – here, motion is invariant with time. Readers may examine what occurs when forces and moments are applied.

A statically and dynamically stable aircraft tends to return to its original state even when it oscillates about the original state. An aircraft becomes statically and dynamically unstable if the pitching motion diverges outward – it neither oscillates nor returns to the original state. The third diagram of Figure 12.2 provides an exam­ple of neutral static stability – in this case, the aircraft does not have a restoring

moment. It remains where it was after the disturbance and requires an applied pilot effort to force it to return to the original state. The tendency of an aircraft to return to the original state is a good indication of what could happen in time: Static sta­bility makes it possible but does not guarantee that an aircraft will return to the equilibrium state.

As an example of dynamic stability, Figure 12.2 also shows the time history for when an aircraft returns to its original state after a few oscillations. The time taken to return to its original state is a measure of the aircraft’s damping characteristics – the higher the damping, the faster the oscillations fade out. A statically stable air­craft showing a tendency to return to its original state can be dynamically unstable if the oscillation amplitude continues to increase, as shown in the last diagram of Figure 12.2. When the oscillations remain invariant to time, the aircraft is statically stable but dynamically neutral – it requires an application of force to return to the original state.

12.1 Overview

Chapter 11 completed the aircraft configuration in the conceptual study phase of an aircraft project by finalizing the external dimensions through the formal-sizing and engine-matching procedures. The design now awaits substantiation of aircraft per­formance to ensure that the requirements are met (see Chapter 13). Substantiation of aircraft performance alone is not sufficient if the aircraft-stability characteristics do not provide satisfactory handling qualities and safety, which are flying qualities that have been codified by NASA. Many good designs required considerable tailor­ing of the control surfaces, which sometimes affected changes to and/or reposition­ing of the wing and incorporated additional surfaces (e. g., dorsal fin and ventral fins).

Preliminary stability analyses, using semi-empirical methods (e. g., DATCOM and RAE data sheets [now ESDU]), are conducted during the conceptual study as soon as the three-view aircraft configuration is available. The analyses include the CG location (see Chapter 8) and preliminary stability results from geomet­ric parameters (e. g., surface areas, wing dihedral, sweep, and twist), which are determined from past experience and statistics. Aircraft dynamic-stability analy­sis requires accurate stability derivatives obtained from extensive wind-tunnel and flight testing. These are cost-intensive exercises and require more budget appropri­ation after the project go-ahead is obtained in the next phase (i. e., Project Defini­tion, Phase 2). Manufacturing philosophy is firmed up during Phase 2 after aircraft geometry is finalized, when the jig and tool designs can begin. Phase 2 activities are beyond the scope of this book.

New-generation aircraft incorporate artificial stability such as the use of FBW technology, which is control-configured vehicles (CCV). This is a good example of a systems approach (see Figure 2.1) to aircraft design. Phase 1 activities of commer­cial transport aircraft design with FBW can begin with available statistics of similar designs and then proceed to developing the aircraft-control laws. Advanced combat aircraft design requires the control laws to establish the initial FBW architecture at an early stage, which is not addressed in this book. For this reason, the author sug­gests that coursework on complex designs be postponed until the basics are learned. This book is limited to conventional aircraft design, a generalized procedure that also can be applied to CCV designs.

Aeroelasticity affects control but, in general, during the conceptual phase of the study, the aircraft is seen as a rigid body. The next phase takes into account the aeroelastic effects using an integral approach to fine-tune the control-surfaces design.

This chapter is not a definitive study of aircraft stability and control (see [1] through [4] for more details on the subject), but it qualitatively examines and pro­vides an understanding of the geometrical arrangement of aircraft components that affect aircraft stability. The reason for discussing stability here is to provide expe­rience through the use of statistics in shaping aircraft as early as possible so that, if necessary, fewer changes are required in subsequent design phases. This chapter presents a rationale for a designer’s experience and provides an opportunity to examine whether the final aircraft configuration reflects all other considerations at this stage of the design process. There are no changes in the worked-out examples.

Only the equations governing static stability are given to explain design fea­tures. A classic example of how stability affects aircraft configuration is the depar­ture of what the Wright brothers accomplished with the “tail” in the front (see Section 1.2) by later designers to put the tail where it should be, at the back. The Wright brothers used a warping wing for lateral control; later designers introduced ailerons. A tail-in-front canard later returned to aircraft design with far better appli­cation than what the Wright brothers had contemplated.

12.1.1 What Is to Be Learned?

This chapter covers the following topics:

Introduction to stability considerations affecting aircraft design

Basic information on static and dynamic stability

Elementary theory examining uncoupled pitch and coupled

directional and lateral stability to determine empennage size

Current statistical trends in empennage-sizing parameters

Inherent aircraft motions as characteristics of design

Aircraft spinning

Design considerations for stability

Military aircraft stability: nonlinear effects

Active control technology

12.1.2 Coursework Content

Readers may examine the final configuration to review its merits. There is little coursework in this chapter. (The aircraft configuration is unlikely to change unless performance falls short of the requirements; see Chapter 13.)

12.2 Introduction

Inherent aircraft stability is a result of the CG location, the wing and empennage siz­ing and shaping, the fuselage and nacelle sizing and shaping, and their relative loca­tions. Because the initial control-surface positioning and sizing are accomplished
empirically from statistical data, the important aspect of whether the aircraft has safe-handling characteristics is not examined. This chapter highlights some of the lessons learned on how to arrange aircraft components relative to one another.

The pitching motion of an aircraft is in the plane of aircraft symmetry (about the Y-axis, elevator-actuated) and is uncoupled with any other type of motion. Direc­tional (about the Z-axis, rudder-actuated) and lateral (about the X-axis, aileron- actuated) motions are not in the plane of symmetry. Activating any of the controls (e. g., rudder or ailerons) causes a coupled aircraft motion in both the directional and lateral planes.

Finally, at the end of a project, flight tests reveal whether the aircraft satisfies the flying qualities and safety considerations. Almost all projects require some type of minor tailoring and/or rigging of control surfaces to improve the flying qualities as a consequence of flight tests – in hindsight, possibly making it better than what was initially envisaged. For civil aircraft designs, this is a routine procedure and is neither expensive nor a major hurdle to program milestones. Military aircraft design projects are preceded by technology demonstrators, which results in obtaining vital information for the final design that may incorporate configuration changes from the lessons learned. The design still must undergo fine-tuning as a result of flight tests. This is a relatively more expensive and time-consuming process, but it saves funds by minimizing errors during the design of military aircraft, which often incorporates cutting-edge advanced technologies that are yet to be operationally proven.

Designers should be aware of the preferred flying qualities so that the aircraft is configured intelligently to minimize changes in the final stages; this is the main objective of this chapter.

Previous military aircraft designs laid the foundation for future designs. Even a rad­ically new design extracts information and, if possible, salvageable component com­monalities from older designs. Figure 11.7 is a conceptual example showing how far newer designs can benefit from older designs through their systematic exploitation. The figure summarizes designs from the AJT to the light air superiority aircraft. It could be debated about how effective the last two designs could be (without the stealth consideration); however, at this stage, it only reflects a scheme.

The designs of the AJT and CAS are sized in detail. The advanced CAS (ACAS) is an AB version of the CAS with a new wing for high-subsonic flight. Mis­sions for these aircraft are more suited to the counterinsurgency-type role, where the 1960s and 1970s designs are still creating havoc. The 6,900-lb thrust can reach
10,000 lb with AB that should enable the ACAS to carry a high weapon load («5,000 lb) (this design has not been properly checked).

The ultimate extension can be toward the air superiority role (two possibilities are shown in Figure 11.7). In this case, it is unlikely that the baseline engine can be further extended; therefore, re-engine work with a more powerful turbofan (i. e., an AB producing around 18,000 lb) and a totally new wing (i. e., SW « 22 m2) are required. A clean aircraft weight would reach approximately 5,700 kg, pushing the supersonic speed to approximately Mach 1.8, but with a very tight turning capability at subsonic speed. However, such a design may be controversial because its viability in combat would be questioned. A new combat aircraft design should have a stealth factor, which is not discussed herein due to having few backup data. However, there may be substantial commonalities in the forward fuselage and the systems design.

This extended section of the book on military aircraft sizing analysis can be found on the Web at www. cambridge. org/Kundu and includes the following:

Figure 11.5. Aircraft sizing – military aircraft

11.7.1 Single-Seat Variant in the Family of Aircraft Design

Figure 11.6. Variant designs in the family of military aircraft

11.5 Sensitivity Study

The sizing exercise offers an opportunity to conduct a sensitivity study of the phys­ical geometries so that designers and users have better insight in making finer choices. An example of an AJT wing-geometry sensitivity study is in Table 11.7 showing what happens with small changes in the wing reference area, SW; aspect

Table 11.7. AJT sensitivity study

Perturbed Geometr)

ASir — ± 1.0 m

A Mach = ±0.004

AF = ±4.35 mph (3.78 kts)

Baseline two-seat trainer aircraft design.

Next variant: single-seat, uprated engine, lighter material, higher weapon load, advanced avionics on same LRUs.

Next variant: newwing, reheat engine basic FBW, highly manueverable.

Next variant: new cranked delta wing, new advanced engine, latest avionics. Fully FBWfor air-superiority role.

Same as above but with alternative design having canard wing and structural changes.

ratio, AR; aerofoil t/c ratio, t/c; and wing quarter-chord sweep, Л14. (A Bizjet air­craft sensitivity study is not provided in this book.)

A more refined analysis could be made with a detailed sensitivity study on var­ious design parameters, such as other geometrical details, materials, and structural layout, to address cost-versus-performance issues in order to arrive at a satisfying design. This may require local optimization with full awareness that global opti­mization is not sacrificed. Although a broad-based MDO is the ultimate goal, deal­ing with a large number of parameters in a sophisticated algorithm may not be easy. It is still researched intensively within academic circles, but the industry tends to use MDO conservatively, if required in a parametric search, by addressing one vari­able at a time. The industry cannot afford to take risks with an unproven algorithm simply because it bears promise. The industry takes a more holistic approach to minimize costs without sacrificing safety, but it may compromise performance if it pays off.

Figure 11.4 shows the final configuration of the family of variants; the baseline air­craft is in the middle (see Figure 6.1 for the plug sizes).

Section 6.10 proposes one smaller (i. e., four to six passengers) and one larger (i. e., fourteen to sixteen passengers) variant from the baseline design that carries ten to twelve passengers by subtracting and adding fuselage plugs from the front and aft
of the wing box. The baseline and variant details are worked out in Chapter 6 as the preliminary configuration, followed by the undercarriage design in Chapter 7. Aircraft mass is calculated in Chapter 8. After obtaining the aircraft drag, this chap­ter finalizes the size of the baseline along with the two variants.

The final sized aircraft came very close to the preliminary baseline aircraft con­figuration suggested in Section 6.10. Therefore, iterations to fine-tune the aircraft mass, drag, and so forth have been avoided. It is unlikely for a coursework exercise to be that fortunate. It is highly recommended that any exercise should make at least one iteration in order to get a sense of the task. Setting up a spreadsheet is part of the learning process; all equations in this book are provided to set up the required spreadsheet.

The family concept of aircraft design is discussed in previous chapters and high­lighted again at the beginning of this chapter. Maintaining large component com­monality (genes) in a family is a definite way to reduce design and manufactur­ing costs – in other words, “design one and get two or more almost free.” This

Short van ant

(4 to 6 passengers)

……………… JtL………………….. J 41.71 ft (1271 m)

Baseline aircraft

(8 to 10 passengers)

Ш

49.54 ft (15.1 m)

Long vanant

(12 to 14 passengers)

‘ d

58.2 ft (17.74 m)

Figure 11.4 Variant designs in the family of civil aircraft encompasses a much larger market area and, hence, increased sales to generate resources for the manufacturer and nation. The amortization is distributed over larger numbers, thereby reducing aircraft costs.

Today, all manufacturers produce a family of derivative variants. The Airbus 320 series has 4 variants and more than 3,000 have been sold. The Boeing 737 fam­ily has 6 variants, offered for nearly 4 decades, and nearly 6,000 have been sold. It is obvious that in three decades, aircraft manufacturers have continuously updated later designs with newer technologies. The latest version of the Boeing 737-900 has vastly improved technology compared to the late 1960s 737-100 model. The latest design has a different wing; the resources generated by large sales volumes encour­age investing in upgrades – in this case, a significant investment was made in a new wing, advanced cockpit/systems, and better avionics, which has resulted in continu­ing strong sales in a fiercely competitive market.

The variant concept is market and role driven, keeping pace with technology advancements. Of course, derivatives in the family are not the optimum size (more so in civil aircraft design), but they are a satisfactory size that meets the demands. The unit-cost reduction, as a result of component commonalities, must compromise with the nonoptimum situation of a slight increase in fuel burn. Readers are referred to Figure 16.6, which highlights the aircraft unit-cost contribution to DOC as more than three to four times the cost of fuel, depending on payload-range capability.

The worked-out examples in the next section offer an idea of three variants in the family of aircraft.

From the market requirements, Vapp = 120 knots = 120 x 1.68781 = 202.5 ft/s (61.72 m/s). Landing CLmax = 2.1 at a 40-deg flap setting (from testing and CFD analysis). For sizing purposes, the engine is set to the idle rating, producing zero thrust using Equation 11.22.

In the FPS system, W/Sw = 0.311 x 0.002378 x 2.1 x (202.5)2 = 63.8 lb/ft2. In the SI system, W/Sw = 0.311 x 1.225 x 2.1 x (61.72)2 = 3,052 N/m2. Because the thrust is zero (i. e., idle rating) at landing, the W/Sw remains constant.

Performance. Chapter 13 verifies whether the design meets the aircraft perfor­mance specifications.

11.3 Coursework Exercises: Military Aircraft Design (AJT)

This extended section of the book on coursework exercises – military aircraft design (AJT) is found on the Web at www. cambridge. org/Kundu and includes the following subsections.

11.5.1 Takeoff – Military Aircraft

Table 11.4. AJT takeoff sizing

11.5.2 Initial Climb – Military Aircraft

Table 11.5. AJT climb sizing

11.5.3 Cruise – Military Aircraft

Table 11.6. AJT cruise sizing

11.5.4 Landing – Military Aircraft

11.4 Sizing Analysis: Civil Aircraft (Bizjet)

The four sizing relationships (Sections 11.3.1 through 11.3.4) for wing-loading, W/Sw, and thrust-loading, TSlS_inStalled/W, meet (1) takeoff, (2) approach speed

Figure 11.3. Aircraft sizing: civil aircraft

for landing, (3) initial cruise speed, and (4) initial climb rate. These are plotted in Figure 11.3.

The circled point in Figure 11.3 is the most suitable for satisfying all four requirements simultaneously. To ensure performance, there is a tendency to use a slightly higher thrust-loading TSLS_INSTALLED/W; in this case, the choice becomes Tsls-installed/W = 0.32 at a wing-loading of W/SW = 63.75 lb/ft2 (2,885 N/m2).

Now is the time for the iterations for the preliminary configuration generated in Chapter 6 from statistics, in which only the fuselage was deterministic. At 20,720 lb (9,400 kg) MTOM, the wing planform area is 325 ft2, close to the original area of 323 ft2; hence, no iteration is required. Otherwise, it is necessary to revisit the empennage sizing and revise the weight estimates. The TSLSINSTALLED per engine then becomes 0.32 x 20,720/2 = 3,315 lbs. At a 7% installation loss at takeoff, this gives uninstalled TSLS = 3,315/0.93 = 3,560 lb/engine (TSLS/W = 3,560 x 2/20,720 = 0.344). This is very close to the TFE731-20 class of engine; therefore, the engine size and weight remain the same. For this reason, iteration is avoided; otherwise, it must be carried out to fine-tune the mass estimation.

The entire sizing exercise could have been conducted well in advance, even before a configuration was settled – if the chief designer’s past experience could “guesstimate” a close drag polar and mass. Statistical data of past designs are useful in guesstimating aircraft close to an existing design. Mass fractions as provided in Section 8.8 offer a rapid mass estimation method. Generating a drag polar requires some experience with extraction from statistical data.

In the industry, more considerations are addressed at this stage – for example, what type of variant design in the basic size can satisfy at least one larger and one smaller capacity (i. e., payload) size. Each design may have to be further varied for more refined variant designs.

From the market requirements, an initial climb starts at an 800-ft altitude at a speed Veas = 250 knots (Mach 0.38) = 250 x 1.68781 = 422 ft/s (128.6 m/s) and the required rate of climb, RC = 2,600 ft/min (792.5 m/min) = 43.33 ft/s (13.2 m/s). From the TFE731 class engine data, TSLS/T ratio = 1.5 (factor k2 from Section 10.11.3, Figure 10.46). The undercarriage and high-lift devices are in a retracted position. Lift coefficient:

CLclimb = W/(0.5 x 0.002378 x 4222 Sw) = 0.004723 x W/Sw Using Equation 11.14:

[Tsls/ W]/1.5 = 43.33/422 + (CD x 0.5 x 0.00232 x 4222 Sw)/W)

Tsls/ W = 0.154 + 310 x Cd x (Sw/ W)

11.4.3 Cruise

Requirements: Initial cruise speed must meet the high-speed cruise (HSC) at Mach 0.74 and at 41,000 ft (flying higher than bigger jets in less congested traffic corridors) using k = 0.972 in Equation 11.14.

In FPS at 41,000 ft:

p = 0.00056 slug/ft2 and V2 = (0.74 x 968.076)2 = 716.382 = 513,195 ft2/s2 In SI at 12,192 m:

p = 0.289 kg/m3 and V2 = (0.74 x 295.07)2 = 218.352 x 47,677.5 m2/s2 Equation 11.18 gives the initial cruise:

Cl = 0.972 MTOW/(0.5 x 0.289 x 47,677.5 x Sw)

= 0.0001414(W/ Sw)

where W/Sw is in N/m2.

Equation 11.19 gives:

Tsls/ W = k x 0.5p V2 x Cd/(W/Sw)

(Use factor ki = TSLS/ Ta = 4.5 from Figure 10.47.)

In FPS:

Tsls/ W = 4.5 x 0.5 x 0.00056 x 459,208.2 x Cd/(W/Sw) = 565.73 x Cd/(W/Sw)

In SI:

Tsls/ W = 4.5 X 0.5 X 0.289 x 42,662.5 x Cd/(W/Sw) = 27,741.3 x Cd/(W/Sw)

Both the FPS and the SI units are worked out in the examples. Sizing calcula­tions require the generic engine data in order to obtain the factors used (see Sec­tion 10.11.3). The Bizjet drag polar is provided in Figure 9.2.

11.4.1 Takeoff

Requirements: TOFL 4,400 ft (1,341 m) to clear a 35-ft height at ISA + sea level. The maximum lift coefficient at takeoff (i. e., flaps down, to 20 deg, and no slat) is CLstall(TO) = 1.9 (obtained from testing and CFD analysis). The result is computed in Table 11.1. Using Equation 11.7a, the expression reduces to:

W/S = 4,400 x 1.9 x (T/ W)/37.5 = 222.9 x (T/ W)

Using Equation 11.7b, it becomes:

W/S = 4.173 x 1,341 x 1.9 x (T/ W) = 10,633.55 x (T/ W)

The industry must also examine other takeoff requirements (e. g., an unprepared runway) and hot and high ambient conditions.