Category AIRCRAF DESIGN

This section defines various terms used in jet-engine performance analysis. Refer­ences [3] through [6] may be consulted for derivations of the expressions.

SFC: The fuel-flow rate required to produce one unit of thrust, or shaft horse­power (SHP):

SFC = (fuel flow rate)/(thrust or power) (10.1)

Units of SFC are in lb/hr per pound of thrust produced (in SI units, gm/s/N) – the lower the better. More precisely, reaction-type engines use TSFC and propeller – driven engines use PSFC, where T and P denote thrust and power, respectively.

For turbofan engines (see Section 10.4.2):

Following are the definitions of various types of jet engine efficiencies. The subscripts indicate the gas turbine component station numbers, as shown in Fig­ure 10.4 (in the figure, 5 represents e).

mechanical energy produced by the engine

heat energy of (air + fuel)

V2 – V2 / 1-Y

e ^ = 1 – PR~

2Cp(T — T2) V )

For a particular aircraft speed, VTO, the higher the exhaust velocity Ve, the better is the nt of the engine. Heat addition at the combustion chamber, q2-3 = Cp(T3 — T1) « Cp(Tt3 — Tt 1).

useful work done on airplane mechanical energy produced by the engine Wa = 2VTO

We Ve + VTO

For subsonic aircraft, Ve > VTO. Clearly, for a given engine exhaust velocity, Ve, the higher the aircraft speed, the better is the propulsion efficiency, np. A jet aircraft

flying below Mach 0.5 is not preferred – it is better to use a propeller-driven aircraft flying at or below Mach 0.5.

It can be shown (see [2] through [4]) that, ideally, for nonafterburning engines, the best overall efficiency, no, is when the engine-exhaust velocity, Ve, is twice the aircraft velocity, VO. Bypassed turbofans provide this efficiency at high-subsonic aircraft speeds.

Gliders were flying long before the Wright brothers first flew, but an engine could not be installed even when automobile piston engines became available – they were too heavy for gliders. The Wright brothers made their own lightweight gaso­line engine with the help of Glenn H. Curtiss. Until World War II, aircraft were designed around available engines. Aircraft sizing was a problem – it was not opti­mized for the mission role but rather based on the number and/or the size of the engine installed.

During the late 1930s, Frank Whittle in the United Kingdom (who died in Eng­land in 1996) and Hans von Ohain in Germany (who died in the United States in 1998) were working independently and simultaneously on reaction-type engines using vane-blade-type precompression before combustion. Their efforts resulted in today’s gas turbine engines; however, at the time, it was difficult for Whittle to con­vince his peers. By the end of World War II, gas-turbine-powered jet aircraft were in operation.

Post-World War II research led to the rapid advancement of gas turbine devel­opment such that from a core gas-generator module, a family of engines can be designed using a modular concept (Figure 10.1); this allowed engine designers to offer engines as specified by aircraft designers. Similar laws in thermodynamic – design parameters permitted power plants to be scaled (i. e., rubberized) to the requisite size around the core gas-generator module to meet the demands of the
mission requirements. The size and characteristics of an engine are determined by matching them with the aircraft mission. It is now possible for both the aircraft and the engine to be sized to the mission role, thereby improving operational economics. Modular engine design also favors low downtime for maintenance.

The potential energy locked in fuel is released through combustion. In gas – turbine technology, the high energy of the combustion product can be used in two ways: (1) converted to an increase in the kinetic energy of the exhaust to produce the reactionary thrust (i. e., turbojet and turbofan); or (2) further extracted through an additional turbine to drive a propeller (i. e., turboprop) to generate thrust.

Initially, reactionary-type engines were simple straight-through airflow turbo­jets (see Figure 10.4). Subsequently, turbojet development improved with the addi­tion of a fan (i. e., long compressor blades that are visible from the outside) in front of the compressor; this is called a turbofan. The intake airmass flow is split into two streams (see Figure 10.5): the core airmass flow passes through the engine as primary flow and is made to burn; the secondary flow through the fan is bypassed (hence, also called the bypass engine) around the engine and remains as cold flow. For this reason, the primary flow is known as hot flow and the secondary bypassed flow is known as cold flow.

Significant general progress has been made in the aircraft power plant design. Engine technology is substantially more complex than aircraft technology. A gas- turbine operating environment demands more aerodynamic considerations than an aircraft. Stringent design considerations must accommodate very high stress lev­els on an engine at elevated temperatures, yet it must be as lightweight as possi­ble. The manufacture of gas turbine parts is also a difficult task – a tough material must be machined in a complex 3D shape to a tight tolerance level. These consid­erations make gas turbine design a complex technology and requires an involved microprocessor-based management.

Gas turbine engines have a wide range of applications, from land-based, large prime movers for power generation and ships (both civil and military) to weight – critical airborne applications. The theory behind all the types has a common base; however, the hardware design differs, driven by the application requirements and technology level adopted. For example, land-based engines are not weight-critical and do not need to stand alone; therefore, they are less constrained in design. Surface-based gas turbines must run economically for days and/or months, generat­ing significant power compared to standalone, lightweight aircraft engines that run for hours on varying power, altitude, g-load, and airflow demands. Even the largest aircraft gas turbine engines are small compared to land-based engines.

The success of a new gas turbine design is achieved by fully understanding and appreciating previous designs. Progress is made in increments by incorporating proven, newer technologies that emerge in the interim. Gas turbine development has a long gestation period compared to aircraft and it depends on previous designs. Typically, a technology demonstrator leads the way in introducing a new design.

Gas turbine designs have advanced to incorporate sophisticated micro­processor-based control systems with automation, which are called full authority digital electronic control (FADEC) and work in conjunction with the FBW con­trol of aircraft. CAD, CAM, CFD, and FEM are now the standard tools for engine design.

Liquid-cooled aircraft piston engines of more than 3,000 HP have been built. However, except for a few types, they are no longer in production because they are too heavy for the power they generate; in their place, gas turbines predominate. Gas turbine engines have a better thrust-to-weight ratio. Two successful pistons were the World War II types: the Rolls Royce (RR) Merlin and the Griffon, which pro­duced 1,000 to 1,500 HP and weighed approximately 1,500 lb dry. Also, AVGAS is considerably more expensive than aviation turbine fuel (i. e., kerosene) (AVTUR). Today, the biggest piston engine in production is approximately 500 HP. Recently, diesel-fuel piston engines (i. e., less than 250 HP) have entered the general-aviation market. In the homebuilt market, motor gasoline (MOGAS)-powered engines have been used and are approved by the certifying agencies.

Chart 10.1 classifies all types of aircraft engines in current use; this book is con­cerned only with the air-breathing types.

The application domains of the types addressed in this book are shown in Figure 10.2. High BPR turbofans are intended for high-subsonic speeds. At super­sonic speeds, the BPR is less than 3. Typically, turboprop-powered aircraft speeds are at and below Mach 0.5. Piston-engine-powered aircraft are at the lowest end of the speed range.

Typical levels of specific thrust (F/ma, lb/lb/s) and specific fuel consumption (sfc, lb/hr/lb) of various types of gas turbine engines are shown in Figure 10.3.

Table 10.1 lists various efficiencies of the different classes of aircraft engines. Table 10.2 shows the progress made in the last half-century, indicating the advances made in engine-weight savings. Since the 1970s, compliance regarding engine-noise levels has been a requirement of the certifying agencies. Pollution levels due to noise and emissions are steadily decreasing (see Chapter 14).

If required (or preferred), the internal contours of the intake and exhaust of a civil aircraft nacelle pod are designed by engine designers in consultation with airframe designers. Shaping of the nacelle’s external contour is the responsibility of aircraft designers. Military aircraft intakes and exhausts have higher degrees of

complexity and are design-specific. Military aircraft intake and exhaust ducts are developed by aircraft designers in consultation with engine designers.

The engine may be considered the heart of any powered-aircraft system. This book is not concerned with engine design, but it covers the information needed by air­craft designers to find a matched engine, install it on an aircraft, and evaluate its performance. The chapter begins with an introduction to the evolution of an engine followed by the classification of engine types available and their domain of applica­tion. This chapter primarily discusses gas turbines (both jet – and propeller-driven) and – to a lesser extent – piston engines, which are used only in smaller general – aviation aircraft. Therefore, a discussion of propeller performance is also included in the chapter. The derivation of thrust equations precedes propeller theory.

It is difficult to obtain industry-standard engine-performance data for course- work because the information is proprietary. The performance of some types of engines in nondimensional form is described in Section 10.11. Readers must be care­ful when applying engine data – an error could degrade or upgrade the aircraft per­formance and corrupt the design. Verification and substantiation of aircraft design are accomplished through performance flight tests. It is difficult to locate the source of any discrepancy between predicted and tested performance, whether the discrep­ancy stems from the aircraft, the engine, or both. The author suggests that appropri­ate engine data may be obtained beyond what is provided in the scope of this book. As mentioned previously, the U. S. contribution to aeronautics is indispensable and its data are generated using the FPS system. Much of the data and worked-out exam­ples in this book are in the FPS system. An extensive list of conversion factors is in Appendix A.

10.1.1 What Is to Be Learned?

This chapter covers the following topics:

Section 10.2: Background on and classification of aircraft engines

Section 10.3: Definitions

Section 10.4: Introduction to air-breathing aircraft engine types

Section 10.5: Engine cycles

Section 10.6: Theories involved in engine-performance analysis

Figure 10.1. Modular concept of gas turbine design

Considerations for engine installation Intake and nozzle design Nozzle and thrust reversers Propeller

Engine-performance data

10.1.2 Coursework Content

This chapter creates engine-performance graphs that are used in Chapter 11 for aircraft-performance analysis. In this chapter, readers generate thrust and fuel-flow levels for matched engines at various power settings, speeds, and altitudes, all in a standard atmosphere.

The total Vigilante drag at the three Mach numbers is tabulated in Table 9.24. Figure 9.18 shows the Vigilante drag polar at the three aircraft speeds. Figures 9.20 through

9.26 are replotted at the end of this chapter from [3].

9.20 Concluding Remarks

Unlike other chapters, this important chapter warrants some concluding remarks. Drag estimation is state of the art and encompasses a large territory, as described herein. The tendency to underestimate drag is primarily due to failing to note some of the myriad items that must be considered in the process of estimation. The objec­tives of this chapter are to make readers aware of the sources of drag and to provide a methodology in line with typical industrial practices (without CFD results).

Some of the empirical relations are estimates based on industrial data available to the author that are not available in the public domain. The formulation could not possibly cover all aspects of drag estimation methodologies and therefore must be simplified for coursework. For example, the drag for high-lift devices is only approx­imate to give some idea.

Readers are advised to rely on industrial data or to generate their own databank through CFD and tests. The author would gratefully receive data and/or substanti­ated formulations that would improve the accuracy of future editions of this book (with acknowledgment).

Figures 9.19 through 9.26 are replotted from the NASA report in [3].

The data for ACDp given in Table 9.21 were extracted from [3] and are approximate.

9.19.1 Induced Drag

The formula for induced drag used is:

CDi = Cl2/(3.14 x 3.73) = CL/11.71 (Table 9.22)

9.19.2 Supersonic Drag Estimation

Supersonic flight would have a bow shock wave that is a form of compressibility drag, which is evaluated at zero CL. Drag increases with a change of the angle of attack. The difficulty arises in understanding the physics involved with an increase in the CL. Clearly, the increase – although lift-dependent – has little to do with viscosity unless the shock interacts with the boundary layer to increase pressure drag. Because the very purpose of design is to avoid such interaction up to a certain CL, this book addresses the compressibility drag at a supersonic speed composed of compressibility drag at a zero CL (i. e., CDshock) plus compressibility drag at a higher Cl (i. e., ACdw).

To compute compressibility drag at a zero CL, the following empirical proce­dure is adopted from [3]. The compressibility drag of an object depends on its thick­ness parameter; for the fuselage, it is the fineness ratio and for the wing it is the t/c ratio. The fuselage (including the empennage) and wing compressibility drags are computed separately and then added in with the interference effects. Graphs are used extensively for the empirical methodology (Figures 9.19 through 9.26). Com­pressibility drag at both Mach 0.9 and Mach 2.0 is estimated.

Drag estimation at Mach 0.9 follows the same method as worked out in the civil aircraft example and is tabulated in Section 9.19.8. For the fuselage compressibility drag (including the empennage contribution) at Mach 2.0, the thickness parameter is the fuselage fineness ratio.

Stepl: Plot the fuselage cross-section along the fuselage length as shown in Figure 9.17 and obtain the maximum cross-section Sn = 45.25 ft2 and the fuselage base Sb = 12 ft2. Find the ratios (1 + Sb/Sn) = 1 + 12/45.25 = 1.27 and S„/Sw = 45.25/700 = 0.065.

Step 2: Obtain the fuselage fineness ratio l/d = 73.3/7.788 = 9.66 (d is minus the intake width). Obtain (l/d)2 = (9.66)2 = 93.3.

Step3: Use Figure 9.21 to obtain Cm (l/d)2 = 18.25 at Mto = 2.0for(1 + SD/Sn) = 1.27. This gives Cm = 18.25/93.3 = 0.1956. Convert it to the fuselage contribution of compressibility drag expressed in terms of the wing reference area: CDwf = CDn x (Sn/Sw) = 0.1956 x 0.065 = 0.01271.

For the wing compressibility drag at Mach 2.0, use the following steps:

Step 1: Obtain the design CLDES from Figure 9.22 for the supersonic aerofoil for the AR x (t/c)1/3 = 3.73 x (0.05)1/3 = 1.374. This gives CLDES = 0.352. Test data of CLDES from [3] gives 0.365, which is close enough and used here.

Step 2: Obtain from Figure 9.23 the two-dimensional design Mach number, MDES^D = 0.784. Using Figure 9.24, obtain AMar = 0.038 for 1/AR = 0.268. Using Figure 9.24, obtain AMda/ = 0.067 for А/ = 37.5 deg.

Figure 9.17. Vigilante RA-C5 fuselage cross-section area distribution

Step 3: Make the correction to obtain in the design Mach as MDES = Mdes_2d + AMar + AMda1/4 or Mdes = 0.784 + 0.0.038 + 0.067 = 0.889. Then, AM = MTO – MDES = 2.0 – 0.889 = 1.111.

Step 4: Compute (t/c)5/3 x [1 + (h/c)/10)] = (0.05)5/3 x [1 + (0)/10)] = 0.00679.

Step 5: Compute AR tan ALE = 3.73 x tan 43 = 3.73 x 0.9325 = 3.48.

Step 6: Use Figure 9.25 and the values in Step 5 to obtain [ACDc_wing/ {(t/c)5/3 x [1 + (h/c)/10]}] = 0.675. Compute ACdc_wing = 0.675 x 0.00679 = 0.00458.

Finally, the interference drag at supersonic speed must be added to the fuselage and wing compressibility drag. Following is the procedure for estimating the wing – fuselage interference drag:

Step1: Compute (fuselage diameter at maximum area/wing span) = 7.785/53.14 = 0.1465.

Figure 9.20. Corrections for laminari – zation

Step 2: With the taper ratio, X = 0.19, compute (1 – X) cos Ai/4 = (1 – 0.19) cos 37.5 = 0.643.

Step3: Using Figure 9.26, obtain ACd_[NT x [(1 – X)cos Ai/4] = 0.00048. Compute ACd_[NT = 0.00048/0.643 = 0.00075.

The compressibility drag of the Vigilante aircraft at zero lift is summarized in Table 9.23.

The compressibility drag at Mach 0.9 is computed as for the civil aircraft example and is given in Table 9.24 along with the drag at both Mach 0.6 and Mach 2.0.

The wing reference area Sw = 700ft2, CDpmi„ = f/Sw. Table 9.20 summarizes the Vigilante parasite drag. As indicated in Section 9.16, [3] provides a correlated fac­tor of 1.284 to include all the so-called other effects. Therefore, the final flat-plate equivalent drag is faircraft = 1.284 x 8.87 = 11.39 ft2, 28.4% = 11.62ft2, to include military aircraft excrescence. This gives CDpmin at Mach 0.6 = 11.39/700 = 0.01627 ([3] uses 0.1645). This is the CDpmin at the flight Mach number before compressibil­ity effects begin to appear; that is, it is seen as the CDpmin at incompressible flow. At higher speeds, there is a CF shift to a lower value. The CDpmin estimation must be repeated with a lower CF at Mach 0.9 and Mach 2.0. To avoid repetition in account­ing for compressibility, a factor of 0.97 is used (i. e., a ratio of values at Mach 0.9 and Mach 0 in Figure 9.20b – a reduction of 3%) is taken at 0.9 Mach. A factor of 0.8 (i. e., a reduction of 20%) is taken at Mach 2.0, as shown in Table 9.16. At

the compressible flow, the wave drag is added. At supersonic speed, shock waves contribute to it.

To correlate with the methodology presented herein, the following values of ACDp were extracted from [3].

Fuselage

From the previous section, at Mach 0.6, the basic CFf = 0.0021. [23]

The total ACFf increment is provided in Table 9.11. Table 9.18 lists the compo­nents of the Vigilante fuselage ACFf.

Therefore, in terms of the equivalent flat-plate area, f, it becomes = CFf x AwF:

f = 1.067 x 0.0021 x 1,474 = 3.3 ft2

Add the canopy drag, C^ = 0.08 (approximated from Figure 9.4).

Therefore, canopy = 0.08 x 4.5 = 0.4 ft2; ff = 3.3 + 0.36 = 3.66 ft2

Wing

From the previous section, at Mach 0.06, the basic CF = 0.00257.

• 3D effects (Equations 9.14,9.15, and 9.16):

• Supervelocity:

ACFw = CFw x 1.4 x (aerofoil t/c ratio)

= 0.00257 x 1.4 x 0.05 = 0.00018 (7% ofbasic Cfw)

Table 9.18 gives the components of the Vigilante fuselage ACFf. • Pressure:

/ 6 0.125

ACFw = CFw x 60 x (aerofoil t/c ratio)4 x

= 0.00257 x 60 x (0.05)4 x (6/3.73)0125 = 0.1542 x 0.00000625 x 1.06 = 0.00000102(0.04 % ofbasic Cfw )

• Interference: AFw for a thin high wing, use 3% of CFw • Other effects:

Excrescence (nonmanufacturing; e. g., control surface gaps):

• flap and slat gaps: 2%

• others (increased later): 0%

• total ACFw increment: 12.04%

Table 9.19 lists the components of the Vigilante wing ACFw.

Therefore, in terms of the equivalent flat-plate area, f, it becomes =

CFw x A w

f w = 1.12 x 0.00257 x 1,144.08 = 3.3 ft2

Empennage

Because it is the same procedure as for the wing, it is not repeated. The same per­centage increment as for the wing is used for the coursework exercise. In the indus­try, engineers must compute systematically as shown for the wing.

• V-tail:

• wetted area, AwVT = 235.33 ft2

• basic Cf_V-tail = 0.00277

• fVT = 1.12 x 0.00277 x 235.33 = 0.73 ft2

• H-tail:

• wetted area, AwHT = 388.72 ft2

• basic Cf_H-tail = 0.002705

• fHT = 1.12 x 0.002705 x 388.72 = 1.18 ft2

The aircraft is first dissected into isolated components to obtain the Re, wetted area, and basic 2D flat-plate CF of each component, as listed herein. There is no correc­tion factor for CF at Mach 0.6 (i. e., no compressibility drag). The CF compressibility correction factor (computed from Figure 9.19b) at Mach 0.9 and at Mach 2.0 is applied at a later stage.

Figure 9.16. North American RA-C5 Vigilante aircraft (no pylon shown)

Fuselage

• fuselage wetted area = Awf = 1,474 ft2

• fuselage Re = 69 x 1.381 x 106 = 9.53 x 107 (length trimmed to what is perti­nent for Re)

• use Figure 9.19b to obtain basic CFf = 0.0021 Wing

• wing wetted area = Aww = 1,144.08 ft2

• wing Re = 15.19 x 1.381 x 106 = 2.1 x 107

• use Figure 9.19b to obtain basic CFw = 0.00257

Empennage (same procedure as for the wing)

• V-tail wetted area = AwVT = 235.33 ft2

• V-tail Re = 8.35 x 1.381 x 106 = 1.2 x 107

• use Figure 9.19b to obtain basic CF_V-tail = 0.00277

• H-tail wetted area = Awht =

• H-tail Re = 9.73 x 1.381 x 106 = 1.344 x 107

• use Figure 9.19b to obtain basic CFh-tail = 0.002705

A three-view diagram of an RA-C5 Vigilante aircraft is shown in Figure 9.16. The following pertinent geometric and performance parameters are from [3]: two crew; engine: 2 x turbo-jet GE J-79-8(N), 75.6 kN; wingspan: 16.2 m; length: 22.3 m; height:

5.9 m; wing area: 65.0 m2; start mass: 27,300 kg; max speed: Mach 2+; ceiling: 18,300 m; range: 3,700 km; armament: nuclear bombs and missiles (only a clean configuration is evaluated).

Fuselage

• fuselage length = 73.25 ft

• average diameter at the maximum cross-section = 7.785 ft

• fuselage length/diameter = 9.66 (fineness ratio)

• fuselage upsweep angle = 0 deg

• fuselage closure angle « 0 deg

Wing

• planform reference area, SW = 65.03 m2 (700 ft2)

• span = 16.2 m (53.14 ft)

• aspect ratio = 3.73 deg

• t/c = 5%

Figure 9.14. Drag polar of Figure 9.1 plotted C2l versus CD

• taper ratio, X = 0.19

• camber = 0

• wing MAC = 4.63 m (15.19 ft)

• А/ = 37.5 deg

• Ale = 43 deg

• root chord at centerline = 6.1 m (20 ft)

• tip chord = 1.05 m (3.46 ft)

Empennage

• V-tail

• Sv = 4.4 m2 (47.34 ft2)

• span = 3.6 m (11.92 ft)

• MAC = (8.35 ft)

• t/c 4%

• H-tail

• Sh = 6.063 m2 (65.3 ft2)

• span = 9.85 m (32.3 ft)

• MAC = (9.73 ft)

• t/c = 4%

Nacelle/pylon (the engine is buried in the fuselage – no nacelle pylon)

• aircraft cruise performance, where the basic drag polar must be computed

• drag estimated at cruise altitude = 36,152 ft

• Mach number = 0.6 (has compressibility drag)

• ambient pressure = 391.68 lb/ft2

• Re/ft = 1.381 x 106

• design CL = 0.365

• design Mach number = 0.896 (Mcrit is at 0.9)

• maximum Mach number = 2.0

Table 9.13 provides an aircraft parasite drag buildup summary in tabular format. The surface roughness effect of the 3% increase (see Equation 9.27) in f is added in the table for all surfaces. The wing reference area Sw = 323 ft2; the CDpmin = f/Sw; ISA day; 40,000-ft altitude; and Mach 0.65.

9.18.4 ACDp Estimation

Table 9.14 gives the Bizjet ACDp taken from Figure 9.8.

9.18.5 Induced Drag

The formula used for induced drag is Cm = Cl2/(3.14 x 7.5) = CL/23.55.

The Bizjet induced drag is given in Table 9.15.

9.18.6 Total Aircraft Drag at LRC

The drag polar at LRC is summarized in Table 9.16. The drag polar at HSC (Mach 0.74) requires the addition of wave drag from Figure 9.8b. (As discussed in Section 9.7.1, the CDpmin at only LRC is sufficient.) This drag polar is plotted in Figure 9.2. The CL2 versus the CD is plotted in Figure 9.14; the nonlinearity at low and high CLis of interest.

9.13 Coursework Example: Subsonic Military Aircraft

The coursework example of military aircraft was conducted for the subsonic AJT/CAS-type aircraft of the class BAe Hawk, which uses the same procedure as

in the civil aircraft drag estimation method. To avoid repetition, only the drag polar and other drag details of the AJT are shown in Figure 9.15. The drag polar at Mach 0.7 and at Mach 0.8 is tabulated in Table 9.17 and plotted in Figure 9.16.

To demonstrate the proper supersonic drag estimation method, a North Amer­ican RA-C5 Vigilante aircraft, shown in Figure 9.16, is used as an example here. Reference [3] provides the Vigilante drag polar for comparison. The subsonic drag estimation of a Vigilante aircraft follows the same procedure as in the civil aircraft example. Therefore, the results of drag at Mach 0.6 (i. e., no compressibility) and at Mach 0.9 (i. e., at Mcrit) are worked out briefly and tabulated. The supersonic drag estimation is worked out in detail using the empirical methodology described in [3].