image of the crown cut about the centerline. However, the keel-cut radius at LFB is 1.4 times Rfan = 1.4 × 0.716/2 = 0.5 m (1.64 ft).

The intake internal contour can be finalized by taking the inflexion point at about mid Ldiff, maintaining maximum θ within the range (i.e., 8 to 9 deg).

The average diameter at the maximum circumference = 0.41 + (0.5 − 0.41)/2 = 0.91 m (3 ft).

Nozzle Geometry

Use a nozzle length = 0.75 × fan-face diameter = 0.75 × 0.716 m = 0.537 m (1.76 ft). Once the control points for the geometry are established, the contour can be generated in CAD using splined curves (i.e., smooth fairing when drawn manually).

The total nacelle length = intake length + engine length + nozzle length = 0.565 + 1.547 + 0.537 = 2.65 m (≈ 8.7 ft), which is close to what was established in Chapter 6 from the statistical data.

The nacelle fineness ratio = 2.62/1.074 = 2.44 (i.e., within the range).

The author cautions that the empirical method presented from his industrial experience is coarse but nevertheless provides a representative geometry for the coursework exercise. This physical model serves as a starting point for further aerodynamic refinement to a more slimline shape through CFD and testing. To obtain the factors used in the example, significant nacelle geometric data are required for better substantiation. (Readers must study many designs to get a sense of the factors used here.) Each industry has its own approach based on past designs (which form the basis of statistical data) to generate a nacelle geometry. In the industry, nacelle design is an involved process that includes the points addressed herein.

10.9.4 Military Aircraft Thrust Reverser Application and Exhaust Nozzles

This extended section of the book can be found on the Web site www.cambridge

.org/Kundu and discusses important considerations involving typical military aircraft thrust reversers (TR) and exhaust nozzles. Associated figures include the following.

Figure 10.28. Military aircraft nozzle adjustment scheme (from [19])

(a)Mechanism for nozzle adjustment

(b)Individual petal movement

Figure 10.29. Supersonic nozzle area adjustment and thrust vectoring

10.10 Propeller

Aircraft flying at speeds less than Mach 0.5 are propeller-driven, larger aircraft are powered by gas turbines, and smaller aircraft are powered by piston engines. More advanced turboprops have pushed the flight speed to more than Mach 0.7 (e.g., the Airbus A400). This book discusses conventional types of propellers that operate at a flight speed of less than or equal to Mach 0.5. After introducing the basics of propeller theory, this section concentrates on the engineering aspects of what is required by aircraft designers. References [16], [18], and [22] may be consulted

Figure 10.30. Aircraft propeller

for more details. It is recommended that certified propellers manufactured by wellknown companies are used.

Propellers are twisted, wing-like blades that rotate in a plane normal to the aircraft (i.e., the flight path). The thrust generated by the propeller is the lift component produced by the propeller blades in the flight direction. It acts as a propulsive force and is not meant to lift weight unless the thrust line is vectored. It has aerofoil sections that vary from being thickest at the root to thinnest at the tip chord (Figure 10.30). In rotation, the tip experiences the highest tangential velocity.

A propeller can have from two blades to as many as seven or eight blades. Smaller aircraft have two or three blades, whereas larger aircraft can have from four to seven or eight blades. Propeller types are shown in Figure 10.31 with associated geometries and symbols used in analysis (see Section 10.10.1). The three important angles are the blade pitch angle, β; the angle subtended by the relative velocity, ϕ; and the angle of attack, α = (β − ϕ). Also shown in the figure is the effect of both coarse and fine propeller pitch, p. When a propeller is placed in front of an aircraft, it is called a tractor (Figure 10.21a); when it is placed aft, it is called a pusher (see Figure 3.47). The majority of propellers are the tractor type.

Blade pitch should match the aircraft speed, V, to keep the blade angle of attack α producing the best lift. To cope with aircraft speed changes, it is beneficial for the blade to rotate (i.e., varying the pitch) about its axis through the hub to maintain a favorable α at all speeds. This is called a variable-pitch propeller. For pitch variation, the propeller typically is kept at a constant rpm with the assistance of a governor, which is then called a constant-speed propeller. Almost all aircraft flying at higher speeds have a constant-speed, variable-pitch propeller (when

Figure 10.31. Multibladed aircraft propellers

operated manually, it is β-controlled). Smaller, low-speed aircraft have a fixed pitch, which runs best at one combination of aircraft speed and propeller rpm. If the fixed pitch is intended for cruise, then at takeoff (i.e., low aircraft speed and high propeller revolution), the propeller is less efficient. Typically, aircraft designers prefer a fixed-pitch propeller matched to the climb – a condition between cruise and takeoff – to minimize the difference between the two extremes. Obviously, for high- speed performance, the propeller should match the high-speed cruise condition. Figure 10.32 shows the benefits of a constant-speed, variable-pitch propeller over the speed range.

The β-control can extend to the reversing of propeller pitch. A full reverse thrust acts as all the benefits of a TR described in Section 10.9. The pitch can be controlled to a fine pitch to produce zero thrust when an aircraft is static. This could assist an aircraft to the washout speed, especially on approach to landing.

When an engine fails (i.e., the system senses insufficient power), the pilot or the automatic sensing device elects to feather the propeller (see Figure 10.30). Feathering is changing β to 75 to 85 deg (maximum course) when the propeller slows down to zero rpm – producing a net drag and thrust (i.e., part of the propeller has thrust and the remainder has drag) of zero.

Figure 10.32. Comparison of a fixedpitch and a constant-speed, variablepitch propeller

Windmilling of the propeller is when the engine has no power and is free to rotate, driven by the relative air speed of the propeller when the aircraft is in flight. The β angle is in a fine position.

10.10.1 Propeller-Related Definitions

The industry uses propeller charts that incorporate special terminology. The necessary terminology and parameters are defined in this section. Figure 10.30 shows a two-bladed propeller with a blade-element section, dr, at radius r. The propeller has a diameter, D. If ω is the angular velocity, then the blade-element linear velocity at radius r is ωr = 2π nr = π nD, where n is the number of revolutions per unit time. An aircraft with a true air speed of V and a propeller angular velocity of ω has the blade element moving in a helical path. At any radius, the relative velocity, VR, has an angle ϕ = tan−1(V/2π nr). At the tip, ϕtip = tan−1(V/π nD).

D = propeller diameter = 2× r n = revolutions per second (rps) ω = angular velocity

N = number of blades

b = propeller-blade width (varies with radius, r) P = propeller power

Cp = power coefficient (not to be confused with the pressure coefficient) =

P/(ρn3D5)

T = propeller thrust

CLi = integrated design lift coefficient (CLd = sectional lift coefficient) CT = propeller thrust coefficient = T/(ρn2D4)

β = blade pitch angle subtended by the blade chord and its rotating plane

p = propeller pitch = no slip distance covered in one rotation = 2π r tan β (explained previously) √

VR = velocity relative to the blade element = (V2 + ω2r2) (blade Mach number = VR/a)

ϕ= angle subtended by the relative velocity = tan−1(V/2π nr) or tan ϕ = V/π nD (This is the pitch angle of the propeller in flight and is not the same as the blade pitch, which is independent of aircraft speed.)

α = angle of attack = (β – ϕ)

J = advance ratio = V/(nD) = π tanϕ (a nondimensional quantity – analogues to α)

AF = activity factor = (105/16) (r/R)3(b/D)d(r/R)

TAF = total activity factor = N× AF (it indicates the power absorbed)

However, irrespective of aircraft speed, the inclination of the blade angle from the rotating plane can be seen as a solid-body, screw-thread inclination and is known as the pitch angle, β. The solid-body, screw-like linear advancement through one rotation is called pitch, p. The pitch definition is problematic because unlike mechanical screws, the choice of the inclination plane is not standardized. It can be the zerolift line (which is aerodynamically convenient) or the chord line (which is easy to locate) or the bottom surface – each plane has a different pitch. All of these planes