Category AIRCRAF DESIGN

The most critical case is when an aircraft must land at its maximum landing weight of 0.95 MTOW. In an emergency, an aircraft lands at the same airport for an aborted takeoff, assuming a 5% weight loss due to fuel burn in order to make the return

circuit. Pilots prefer to approach as slow as possible for ease of handling at landing. For this class of aircraft, the approach velocity, Vapp (FAR requirement at 1.3 Vstau) is less than 125 kts to ensure that it is not constrained by the minimum control speed, Vc. Wing CLstaii is at the landing flap and slat setting.

For sizing purposes, an engine is set to the idle rating to produce zero thrust.

At approach:

or (Vapp)2 x Cbstall = 3.211 x (W/Sw)/P

or (W/Sw) = 0.311 x P x (Vapp)2 x Cbstall

There are no FAR or MILSPECS regulations to meet the initial cruise speed; initial cruise capability is a user requirement. Therefore, both civil and military aircraft sizing for initial cruise use the same equations. At a steady-state level flight, thrust required (airplane drag, D) = thrust available (Ta); that is:

D = Ta = 0.5pV2Cd x Sw (11.16)

Dividing both sides of the equation by the initial cruise weight, Wincr = к x MTOW due to fuel burned to climb to the initial cruise altitude. The factor к lies between 0.95 and 0.98, depending on the operating altitude for the class of aircraft, and it can be fine-tuned through iteration – in the coursework exercise, one round of iterations is sufficient. The factor cancels out in the following equation but is required later. Henceforth, in this part of cruise sizing, W represents the MTOW, in line with the takeoff sizing:

0.5p V2Cd x Sw/ W = Ta/ W (11.17)

The drag polar is now required to compute the relationships given in Equation 11.17. Use the Cd value to correspond to the initial cruise Cl (because they are nondimen­sional, both the FPS and SI systems provide the same values). Initial cruise:

Cl = к x MTOW/(0.5 x p x V2 x Sw) (11.18)

The thrust-to-weight ratio sizing for initial cruise capability is expressed in terms of TSlS. Equation 11.18 is based on the maximum-cruise thrust rating, which is lower than the TSlS. Equation 11.18 must be written in terms of TSlS. The TSLS/Ta ratio (factor кй see Section 10.11.3 and Figure 10.47) varies depending on the engine BPR. The factor ki is computed from the engine data supplied. Then, Equation 11.18 can be rewritten as:

Tsls/ W = к x 0.5pV2 x Cd/(W/Sw) (11.19)

Variation in wing size affects aircraft weight and drag. The question now is: How does the Cd change with changes in W and Sw? (Ta changes do not affect the drag because it is assumed that the physical size of an engine is not affected by small changes in thrust.) The solution method is to work with the wing only – first by scaling the wing for each case and then by estimating the changes in weight and drag and iterating – which is an involved process.

This book simplifies the method by using the same drag polar for all wing – loadings (W/S) with little loss of accuracy. As the wing size is scaled up or down (the AR invariant), it changes the parasite drag. The induced drag changes as the aircraft weight increases or decreases. However, to obtain the Cd value, the drag is divided by a larger wing, which keeps the Cd change minimal.

The initial rate of climb is a user specification and not a FAR requirement. In gen­eral, the FAR requirement for the one-engine inoperative, second-segment climb gradient provides sufficient margin to give a satisfactory all-engine initial climb rate. However, from the operational perspective, higher rates of climb are in demand when it is sized accordingly. Military aircraft (some with a single engine) require­ments stipulate faster climb rates and sizing for the initial climb rate is important. The methodology for aircraft sized to the initial climb rate is described in this sec­tion. Figure 11.2 shows a typical climb trajectory.

For a steady-state climb, the expression for rate of climb, RC = V x sin у. Steady-state force equilibrium gives T = D + W x sin у or sin у = (T – D)/ W. This gives:

RC = [(T – D) x V]/W = (T/ W – D/ W) x V (11.12)

Equation 11.12 is written as:

T/ W = RC / V + (D/ W)

or T/ W = RC/ V + [(Cd x 0.5 x p x V2 x Sw)/ W] (11.13)

Equation 11.13 is based on a climb-thrust rating that is lower than the TSLS; it must be written in terms of TSLS. The TSLS/ T ratio (factor k2; see Section 10.11.3 and Figure 10.46) varies depending on the engine BPR.

[Tsls/W]/кг = RC/V + [(Cd x 0.5 x p x V2)Sw/ W] (11.14)

[Tsls/ W] = k2 x RC/V + k2 x [(Cd x 0.5 x p x V2)Sw/ W] (11.15)

The drag polar is now required to compute the relationships given in Equation 11.15.

Because military aircraft mostly have a single engine, there is no requirement for one engine being inoperative; ejection is the best solution if the aircraft cannot be landed safely. Therefore, Equation 11.6 can be directly applied (for a multiengine design, the one-engine inoperative case generally uses measures similar to the civil – aircraft case).

In the FPS system, this can be written as:

(W/S) = (TOFL x (T/ W)(1 – D/ T – лW/ T + лЦ T)] x CLtaii)/18.85 (11.10a) In the SI system, it becomes:

(W/S) = 8.345 x (TOFL x (T/ W)(1 – D/T – ^W/ T + лЦ T)] x CLstaii) (11.10b)

Military aircraft have a thrust, TSLS/W, that is substantially higher than civil aircraft, which makes (D/T – л^/T + лЦ/T) even smaller. Therefore, for a single-engine

Figure 11.2. Aircraft climb trajectory

aircraft, no correction is needed and the simplified equations are as follows:

In the FPS system, this can be written as:

(W/S) = [TOFL x (T/W) x Cbstaii]/18.85 (11.11a)

In the SI system, this becomes:

(W/S) = 8.345 x (TOFL x (T/ W) x C^taii) (11.11b)

The contribution of the last three terms (-D/ T – лW/ T + /лL/ T) in Equa­tion 11.4 is minimal and can be omitted at this stage for the sizing calculation. In addition, for the one-engine inoperative condition after the decision speed (V1; see Section 13.4), the acceleration slows down, making the TOFL longer than the all – engines-operative case. Therefore, in the sizing computations to produce the spec­ified TOFL, further simplification is possible by applying a semi-empirical correc­tion factor primarily to compensate for loss of an engine. The correction factors are as follows (see [4]); all sizing calculations are performed at the MTOW and with Tsls:

For two engines, use a factor of 0.5 (loss of thrust by a half). Then, Equation 11.6 in the FPS system reduces to:

(W/S) = (TOFL x (T/ W) x CLstau)/3.15 (11.7a)

For the SI system:

(W/S) = 4.173 x TOFL x (T/ W) x CLstaii (11.7b)

For three engines, use a factor of 0.66 (loss of thrust by a third). Then, Equation 11.6 in the FPS system reduces to:

(W/S) = (TOFL x (T/ W) x CLstaii)/28.5 (11.8a)

For the SI system:

(W/S) = 5.5 x TOFL x (T/ W) x CLstaii (11.8b)

For four engines, use a factor of 0.75 (loss of thrust by a fourth). Then, Equation 11.6 in the FPS system reduces to:

(W/S) = (TOFL x (T/ W) x CLstaii)/25.1 (11.9a)

For the SI system:

(W/S) = 6.25 x TOFL x (T/W) x CLstaii (11.9b)

TOFL is the field length (i. e., runway plus clearway; Figure 11.1) required to clear a 35-ft (10-m) obstacle in the clearway while maintaining a specified minimum climb
gradient, y, with one engine inoperative and flaps and undercarriage extended. The FAR requirement for a two-engine aircraft minimum climb gradient is 1.2 (see Table 13.3 for aircraft with more than two engines).

For sizing, field-length calculations are at the sea-level standard day (no wind) and at a zero airfield gradient of paved runway. For further simplification, drag changes are ignored during the transition phase of liftoff to clear the obstacle (flar­ing after liftoff takes less than 3 s); in other words, the equations applied to Vuft-off are extended to V2 = 1.2Vstan. This gives V22 = [2 x 1.44 x (W/S)]/(pCLstaii). An aircraft stalls at CLmax. Chapter 13 addresses takeoff performance in detail.

A simplified expression for all engines is:

where dV/dt = a and V and a are instantaneous velocity and acceleration of the aircraft on the ground encountering friction (coefficient p = 0.025 for a paved, met­aled runway). Average acceleration, a, is taken at 0.7V2. By replacing V2 in terms of CLstall, Equation 11.1 reduces to:

fV2 „ 1 44W/S

TOFL = (1 /a) VdV = (V22/2a) = ——(11.2)

0 PCLstalla

In terms of wing-loading, Equation 11.2 can be written as:

(W/S) = (TOFL x p x a x CLstaii)/1.44 (11.3)

where average acceleration, a = F/m and applied force F = (T – D) – p(W-L). Until liftoff is achieved, W > L and F is the average value at 0.7 V2. Therefore:

a = [(T – D) – p(W – L)]g/ W = g(T/ W)[1 – D/ T – pW/ T + pL/ T] (11.4)

Substituting Equation 11.3, it becomes:

(W/S) = (TOFL x p x [g(T/ W)(1 – D/ T – pW/T + pL/ T)] x CLstaii)/1.44

(11.5)

In the FPS system, it can be written as p = 0.00238 slugs and g = 32.2 ft/s2. Therefore:

(W/S) = (TOFL x (T/ W)(1 – D/ T – pW/ T + pL/ T)] x CLai)/18.85 (11.6a)

In the SI system, it becomes p = 1.225 kg/m3 and g = 9.81 m/s2. Therefore,

(W/S) = 8.345 x (TOFL x (T/ W)(1 – D/ T – pW/ T + pL/ T)] x CLstaii)

(11.6b)

where W/S is in Newton/m2 to remain in alignment with the units of thrust in Newtons.

Checking of the second-segment climb gradient occurs after aircraft drag esti­mation, which is explained in Sections 13.5.1 and 13.5.3. If it falls short, then the TSLS must be increased. In general, TOFL requirements are not generous; there­fore, satisfying the TOFL is also likely to satisfy the second-segment climb gradient.

The parameters required for aircraft sizing and engine matching derive from market studies that reflect user requirements. In general, both civil and military aircraft use similar specification parameters, as discussed herein, as the basic input for aircraft sizing. All performance requirements in this chapter are at ISA day and all field performances are at sea level. The parameters are as follows:

1. Payload and range (fuel load): These determine the MTOW. This is not a sizing exercise but needs to be substantiated (see Chapter 13).

2. Takeoff field length (TOFL): This determines the engine-power ratings and wing size.

3. Landing field length (LFL): This determines wing size (baulked landing included).

4. Initial maximum cruise speed and altitude capabilities determine wing and engine sizes.

5. Initial rate of climb establishes wing and engine sizes.

These five requirements must be satisfied simultaneously. The governing parame­ters to satisfy TOFL, initial climb, initial cruise, and landing are wing-loading (W/S) and thrust-loading (TSLS/W).

Additional parameters for military aircraft sizing are as follows: [24]

These three parameters are primarily dependent on control-surface sizing (as well as engine sizing, to an extent), which is not addressed in this book. It is assumed that engine size for fast initial climb rates are sufficient and that enough control surface is available to perform the g requirements. A lower aspect ratio for the wing is considered for higher roll rates to reduce the wing-root bending moments.

As mentioned previously, an aircraft must simultaneously satisfy the takeoff field length, initial climb rate, initial maximum cruise speed-altitude capabilities, and LFL. Low wing-loading (i. e., a larger wing area) is required to sustain low speed at liftoff and touchdown (for a pilot’s ease), whereas high wing-loading (i. e., a low wing area) is suitable at cruise because high speeds generate the required lift on a smaller wing area. The large wing area for takeoff and landing results in excess wing for high-speed cruise. To obtain the minimum wing area and satisfy all require­ments, a compromise for sizing of the wing area must be found; this may require suitable high-lift devices to keep the wing area smaller. The wing area is sized in conjunction with a matched engine for takeoff, climb, cruise, and landing; landing is performed at the idle-engine rating.

In general, W/S varies with time as fuel is consumed and T/W is throttle – dependent. Therefore, a reference design condition of the MTOW and TSLS at ISA + SL are used for sizing considerations. This means that the MTOW, TSLS, and SW are the only parameters considered for aircraft sizing and engine matching. In general, wing-size variations are associated with changes in all other affecting parameters (e. g., AR, X, and wing sweep). However, at this stage, they are kept invariant – that is, the variation in wing size only scales the wing span and chord, leaving the general planform unaffected (like zoom in/zoom out).

At this point in the discussion, readers require knowledge of aircraft perfor­mance, and the important derivations of the equations used are provided in Chap­ter 13. References [2] through [6] are textbook sources for the detailed derivation of the performance equations. Other proven semi-empirical relations are in [4]. Although the methodology described herein is the same, the industry practice is more detailed and involved in order to maintain a high degree of accuracy.

Worked-out examples continue with the Learjet 45 Bizjet class for civil aircraft and the BAe Hawk class for military aircraft. Throughout this chapter, wing-loading (W/S) in the SI system is in N/m2 to align with the thrust (in Newtons) in thrust loading (TSLS/W) as a nondimensional parameter.

11.1 Overview

Chapter 6 proposes a methodology with worked-out examples to conceive a “first – cut” (i. e., preliminary) aircraft configuration, derived primarily from statistical infor­mation except for the fuselage, which is deterministic. A designer’s past experience is vital in making the preliminary configuration. Weight estimation is conducted in Chapter 8 for the proposed first-cut aircraft configuration, revising the MTOM taken from statistics. Chapter 9 establishes the aircraft drag (i. e., drag polar), and Chapter 10 develops engine performance. From these building blocks, finally, the aircraft size can be fine-tuned to a “satisfactory” (see Section 4.1) configuration offering a family of variant designs. None may be the optimum but together they offer the best fit to satisfy many customers (i. e., operators) and to encompass a wide range of payload-range requirements, resulting in increased sales and profitability.

The two classic important sizing parameters – wing-loading (W/S) and thrust­loading (TSls/W) are instrumental in the methodology for aircraft sizing and engine matching. This chapter presents a formal methodology to obtain the sized W/S and Tsls/W for a baseline aircraft. These two loadings alone provide sufficient infor­mation to conceive of aircraft configuration in a preferred size. Empennage size is governed by wing size and location on the fuselage. This study is possibly the most important aspect in the development of an aircraft, finalizing the external geometry for management review in order to obtain a go-ahead decision for the project.

Because the preliminary configuration is based on past experience and statistics, an iterative procedure ensues to fine-tune the aircraft for the correct size of the wing reference area for a family of variant aircraft designs and matched engines selected after discussion with engine manufacturers. Reference [1] provides an excellent pre­sentation on the subject.

11.1.1 What Is to Be Learned?

This chapter covers the following topics:

Section 11.2: Introduction to the concept of aircraft sizing and engine matching

Section 11.3: Theoretical considerations

Coursework exercises for civil aircraft Coursework exercises for military aircraft Sizing analysis and variant designs of civil aircraft Sizing analysis and variant designs of military aircraft Sensitivity analysis Future growth potential

11.1.2 Coursework Content

This chapter is important for continuing the coursework linearly. Readers compute the parameters that establish the criteria for aircraft sizing and engine matching. The final size is unlikely to be identical to the preliminary configuration; the use of spreadsheets facilitates the iterations.

11.2 Introduction

In a systematic manner, the conception of a new aircraft progresses from generating market specifications followed by the preliminary candidate configurations that rely on statistical data of past designs in order to arrive at a baseline design. In this chap­ter, the baseline design of an aircraft is formally sized with a matched engine (or engines) along with the family of variants to finalize the configuration (i. e., external geometry). An example from each class of civil (i. e., Bizjet) and military (i. e., AJT) aircraft is used to substantiate the methodology.

As of the circa 2000 fuel prices, the aircraft cost contributes to the DOC three to four times the contribution made by the fuel cost. (Fuel price fluctuates consid­erably. Of late, fuel price has shot up, making its contribution to DOC substantially higher. In this book, circa 2000 price level is maintained. That level of price held for a long time and large number of literature use this approximate value.) It is not cost-effective for aircraft manufacturers to offer custom-made new designs to each operator with varying payload-range requirements. As discussed previously, aircraft manufacturers offer aircraft in a family of variant designs. This approach maintains maximum component commonality within the family to reduce development costs and is reflected in aircraft unit-cost savings. In turn, it eases the amortization of non­recurring development costs, particularly as sales increase. It is therefore important for the aircraft-sizing exercise to ensure that the variant designs are least penalized to maintain commonality of components. This is what the introductory comments in Section 4.1 referred to in producing satisfying robust designs; these are not nec­essarily the optimum designs.

Multidisciplinary optimization is not easily amenable to this type of industrial use; it is currently explored more as research work. The industry uses a more sim­plistic parametric search for satisfying robust designs.

To generate a family of variant civil aircraft designs, the tendency is to retain the wing and empennage almost unchanged while plugging and unplugging the con­stant fuselage to cope with varying payload capacities (see Figure 11.4). Typically, the baseline aircraft remains as the middle design. The smaller aircraft results in a wing that is larger than necessary, providing better field performances (i. e., takeoff and landing); however, cruise performance is slightly penalized. Conversely, larger aircraft have smaller wings that improve the cruise performance; the shortfall in

takeoff is overcome by providing a higher thrust-to-weight ratio (TSLS/W) and pos­sibly with better high-lift devices, both of which incur additional costs. The baseline – aircraft approach speed, Vapp, initially is kept low enough so that the growth of Vapp for the larger aircraft is kept within the specifications. Of late, high investment with advanced composite wing-manufacturing method is in a position to produce sepa­rate wing sizes for each variant (large aircraft), offering improved economics in the long run. However, for some time to come, metal wing construction will continue with minimum change in wing size to maximize component commonality.

Matched engines are also in a family to meet the variation of thrust (or power) requirements for the aircraft variants (see Chapter 10). The sized engines are bought-out items supplied by engine manufacturers. Aircraft designers stay in con­stant communication with engine designers in order to arrive at the type of family of engines required. A variation of up to ±30% from the baseline engine is typically sufficient for larger and smaller aircraft variants from the baseline. Engine design­ers can produce scalable variants from a proven core gas-generator module of the engine – these scalable projected engines are known loosely as rubberized engines. The thrust variation of a rubberized engine does not affect the external dimensions of an engine (typically, the bare engine length and diameter change only around ±2%). This book uses an unchanged nacelle external dimension for the family vari­ants, although there is some difference in weight for the different engine thrusts. The generic methodology presented in this chapter is the basis for the sizing and matching practice.

Turbofan performance. An engine-matching and aircraft-sizing exercise that gives the TSLS is conducted in Chapter 11. Chapters 11 and 13 work out the installed thrust and fuel flow for the matched engines of the sized aircraft under study.

Takeoff Rating. Figure 10.45 shows the takeoff thrust in nondimensional form for the standard day for turbofans with a BPR of 4 or less. The fuel-flow rate remains nearly invariant for the envelope shown in the graph. Therefore, the sfc at the take­off rating is the value at the TSLS of 0.498 lb/lb/hr per engine.

Maximum Climb Rating. Figure 10.46 gives the maximum climb thrust and fuel flow in nondimensional form for the standard day up to a 50,000-ft altitude for three Mach numbers. Intermediate values may be linearly interpolated. There is a break in thrust generation at an approximate 6,000- to 10,000-ft altitude, depending on the Mach number, due to fuel control to keep the EGT low.

Equation 11.14 (see Chapter 11) requires a factor k2 to be applied to the TSLS to obtain the initial climb thrust. In the example, the initial climb starts at an 800-ft altitude at 250 VEAS (Mach 0.38), which gives T/ TSLS = 0.67 – that is, the factor k2 = TSLS/ T = 1.5. At a constant EAS, the Mach number increases with altitude; in

Figure 10.45. Uninstalled takeoff per­formance (^<BPR4)

Altitude (feet)

(a) Nondimensional Thrust

Figure 10.46. Uninstalled maximum climb rating (^<BPR 4)

the example, when it reaches 0.7 (depending on the aircraft type), the Mach number is held constant. Fuel flow at the initial climb is obtained from Figure 10.46b.

With varying values of altitude, climb calculations are performed in small incre­ments of altitude within which the variation is taken as the mean and is kept constant for the increment.

Maximum Cruise Rating. Figure 10.47 shows the maximum cruise thrust and fuel flow in nondimensional form for the standard day from a 5,000- to 50,000-ft altitude for Mach numbers varying from 0.5 to 0.8, which is sufficient for this class of engine-aircraft combinations. Intermediate values may be linearly interpolated.

The coursework example of the design initial maximum cruise speed is Mach 0.7 at 41,000 ft. From the graph, that point is T/ Tsls = 0.222, which has Tsls/ T =

4.5 (i. e., k2 in Chapter 11). Chapter 11 verifies whether the thrust is adequate for attaining the maximum cruise speed. Fuel flow per engine can be computed from Figure 10.47b.

Figure 10.48. Uninstalled takeoff perfor­mance (^>BPR 5)

(a) Nondimensional Thrust (b) Specific Fuel Consumption

Figure 10.50. Uninstalled maximum cruise rating (^>BPR 5)

Turbofans with a BPR around 5 or 7 (Larger Engines; e. g., RJs and Larger)

Turbofan performance. Larger engines have a higher BPR. The currently opera­tional larger turbofans are at a 5 to 7 BPR, which has nondimensional engine perfor­mance characteristics slightly different than smaller engines, as shown by comparing Figures 10.48 through 10.50.

The engine-matching and aircraft-sizing exercise in Chapter 11 gives the TSLS. Estimation of fuel flow is shown in the graph. Coursework follows the same routine as given herein.

Takeoff Rating. Figure 10.48 shows the takeoff thrust in nondimensional form for the standard day. The fuel flow rate remains nearly invariant for the envelope shown in the graph.

Maximum Climb Rating. Figure 10.49 shows the maximum climb thrust and fuel flow in nondimensional form for the standard day up to a 50,000-ft altitude for three Mach numbers. Intermediate values may be linearly interpolated.

Maximum Cruise Rating. Figure 10.50 shows the maximum cruise thrust and fuel flow in nondimensional form for the standard day from a 5,000- to 50,000-ft altitude for Mach numbers varying from 0.5 to 0.8, which is sufficient for this class of engine-aircraft combinations. Intermediate values may be linearly interpolated.

10.11.2 Turbofan Engine – Military Aircraft

This extended section of the book can be found on the Web at www. cambridge .org/Kundu and presents a typical military turbofan-engine performance in non­dimensional form (with and without reheat) at maximum rating suited to the class­room example of an AJT and a derivative in a CAS role. Figure 10.51 gives the thrust ratios from sea level to 36,000 ft altitude in an ISA day. Sfc is worked out.

Figure 10.51. Military turbofan engine with and without reheat (BPR = 0.75)

All thrusts discussed in this section are uninstalled thrust. There is loss of power when an engine is installed in an aircraft, as discussed in Section 10.10, from 7 to 10% at the takeoff rating depending on how the ECS is managed. At cruise, the loss discreases to 3 to 5%. For simplicity, both military and civil aircraft installation losses are kept at a similar percentage, although the off-take demands are signifi­cantly different.

Figures 10.45 through 10.51 show the turbofan power at the three ratings in a nondimensional form for civil aircraft engines with low and high BPRs. Civil – aircraft turbofan performance is also divided into two categories: one for a lower BPR on the order of 4 and the other at 5 and above. The most recent engines (i. e., engines for the newer Boeing787, Airbus350, and Bombardier Cseries) have

reached a BPR of 8 to 12; however, the author could not obtain realistic data for this class of turbofans.

The higher the BPR, the less is the specific thrust (TSLS/ma, lb/lb/s). There is a similar trend for the specific dry-engine weight (TSLS/dry-engine weight, nondimen­sional). Table 10.7 may be used for the computations.