Category AIRCRAF DESIGN

The discussion on subsonic aircraft continues linearly from previous chapters.

9.18.1 Geometric and Performance Data

The geometric and performance parameters discussed herein were used in previous chapters. Figure 9.13 illustrates the dissected anatomy of the coursework baseline aircraft.

Aircraft cruise performance for the basic drag polar is computed as follows:

• cruise altitude = 40,000 ft

• LRC Mach = 0.65 (630 ft/s)

• ambient pressure = 391.68 lb/ft2

• ambient temperature = 390 K

• ambient density = 0.00058 sl/ft3

• ambient viscosity = 2.96909847 x 10-7lbs/ft2

• Re/ft = 1.2415272 x 106 (use the incompressible zero Mach line, as explained in Section 9.7.1)

• CL at LRC (Mach 0.65) = 0.5

• Cl at HSC (Mach 0.7) = 0.43

Fuselage (see Figure 9.13)

• fuselage length, Lf = 15.24 m (50 ft)

• average diameter at the constant cross-section barrel, Df = 1.75 m (5.74 ft)
. Lf IDf = 8.71

• fuselage upsweep angle = 10 deg

• fuselage closure angle = 10 deg

Wing (see Figure 9.13)

• planform reference area, SW = 30 m[17] [18] [19] (323 ft2)

• span = 15 m (49.2 ft)

• aspect ratio = 7.5

• wing MAC = 2.132 m (7 ft)

• root chord at centerline = 2.86 m (9.38 ft)

• tip chord = 1.143 m (3.75 ft)

• quarter-chord wing sweep = 14 deg

• aerofoil: NACA 65-410 with 10% tic ratio for design CL = 0.4

Empennage (see Figure 9.13)

• V-tail: SF = 4.4 m2 (47.34 ft2)

• span = m (ft)

• MAC = (7 ft)

• H-tail: Sh = 6.063 m2 (65.3 ft2)

• span = 5 m (ft)

• MAC = (4.2 ft)

Nacelle (see Figure 9.13)

• nacelle length = 2.62 m (8.6 ft)

• nacelle diameter = 1.074 m (3.52 ft)

• nacelle fineness ratio = 2.62I1.074 = 2.44

9.18.2 Computation of Wetted Areas, Re, and Basic CF

An aircraft is first dissected into isolated components, as shown in Figure 9.15. The Re, wetted area, and basic 2D flat-plate CF_baSiC of each component are worked out herein.

Fuselage

The fuselage is conveniently sectioned into three parts:

• total wetted area, Awf = 110 + 340 + 170 + 50 = 670 ft2

• fuselage Re = 50 x 1.2415272 x 106 = 6.2 x 107

• from Figure 9.19b (fully turbulent) at LRC, the incompressible basic CFf =

0. 0022

Wing

• wing exposed reference area = 323 – 50 (area buried in the fuselage) = 273 ft2

• MAC = 2.132 m (7 ft), AR = 7.5

• For t/c = 10% of the wing wetted area, Aww = 2.024 x 273 = 552.3 ft2

• root chord, CR = 2.86 m (9.38 ft)

• tip chord, CT =1.143 m (3.75 ft)

• wing Re = 7 x 1.2415272 x 106 = 8.7 x 106

• from Figure 9.19b at LRC, the incompressible basic CFw = 0.003

Empennage (same procedure as for the wing)

• V-tail

• reference area, SV = 4.4 m2 (47.34 ft2)

• exposed reference area = 47.34 – 7.34 (area buried in the fuselage) = 40 ft2

• for t/c = 10% the V-tail wetted area, AwVT = 2.024 x 40 = 81 ft2

• taper ratio = 0.6

• MAC = 2.132 m (7 ft)

• V-tail

• Re = 7 x 1.2415272 x 106 = 8.7 x 106

• from Figure 9.19b (fully turbulent) at LRC, the incompressible basic

CF_V-tail = 0.003

• H-tail

• reference area, SH = 6.063 m2 (65.3 ft2); it is a T-tail and it is fully exposed

• for t/c = 10%, the H-tail wetted area, AwHT = 2.024 x 65.3 = 132.2 ft2

• taper ratio = 0.5

• MAC = 1.28 m (4.22 ft)

• H-tail Re = 4.22 x 1.2415272 x 106 = 5.24 x 106

From Figure 9.19b (fully turbulent) at LRC, the incompressible basic CF_H-tail = 0.003185.

Nacelle

• length = 2.62 m (8.6 ft)

• maximum diameter = 1.074 m (3.52 ft)

• fineness ratio = 2.45

• nacelle Re = 8.6 x 1.2415272 x 106 = 1.07 x 107

• two-nacelle wetted area, Awn = 2 x 3.14 x 3.1(Dave) x 8.6 – 2 x 5 (two pylon cutouts) = 158 ft2

• from Figure 9.19b (fully turbulent) at LRC, the incompressible basic CFnac =

0. 0029

Pylon

• each pylon exposed reference area = 14 ft2

• length = 2.28 m (7.5 ft)

(d) aft-end cross-sectional shape – circular: 6

• cabin pressurization leakage (if unknown, use higher value): 5%

• excrescence (nonmanufacturing types; e. g., windows)

(a) windows and doors (higher values for larger aircraft): 2%

(b) miscellaneous: 1%

• wing-fuselage-belly fairing, if any (higher value if it houses undercarriage):

5%

• ECS (see Section 9.8) gives 0.06 ft2: 3.6%

• Total ACFf increment: 41.8%

Table 9.10 gives the Bizjet fuselage ACFf components.

Add the canopy drag for two-abreast seating f = 0.1 ft2 (see Section 9.8.1). Therefore, the equivalent flat-plate area, f, becomes = CFf x AwF + canopy drag.

ff = 1.416 x 0.0022 x 670 + 0.1 = 2.087 + 0.1 = 2.187 ft2

Surface roughness (to be added later): 3%

Wing

The basic CFW = 0.003.

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

• Supervelocity

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

= 0.003 x 1.4 x 0.1 = 0.00042(14% ofbasic Cfw) [20]

• Interference

= 9.382 x 0.6 x [{0.75 x (0.1)3 – 0.0003}/552.3]

= 87.985 x 0.6 x (0.00075 – 0.0003)/552.3 = 0.02375/552.3 = 0.000043 (1.43% of basic CFv,)

• Other effects. For excrescence (nonmanufacturing; e. g., control-surface gaps):

flap gaps: 5% others: 5%

total ACFw increment: 25%

Table 9.11 gives the Bizjet wing ACFw components.

Therefore, the equivalent flat-plate area, f, becomes = CFw x Aww.

ff = 1.26 x 0.003 x 552.3 = 2.09 ft2

• surface roughness (to be added later): 3%

Empennage

Because the procedure is the same as for the wing, it is not repeated. The same per­centage increment as the wing is used for the coursework exercise. In the industry, engineers must compute systematically as shown for the wing. [21]

Nacelle

• fineness ratio = 2.45

• nacelle Re = 1.07 x 107

• wetted area of two nacelles, Awn = 158 ft2

• basic CFnac = 0.0029

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

• Wrapping (Equation 9.9):

ACFn = CFn x 0.025 x (length/diameter) x R-02 = 0.025 x 0.003 x 2.45 x (1.07 x 107)-02 = 0.000184 x 0.0393 = 0.0000072(0.25% ofbasic CFf)

• Other increments are shown in Table 9.4 for one nacelle. For two nacelles (shown in wetted area):

fn = 1.8325 x 0.0029 x 158 = 0.84 ft2 • surface roughness (to be added later): 3%

Pylon

Because the pylon has the same procedure as the wing, it is not repeated. The same percentage increment as for the wing is used in the coursework exercise. There is interference on both sides of the pylon. [22]

A well-substantiated reference for industrial use is [3], which was prepared by Lockheed as a NASA contract for the National Information Service, published in 1978. A comprehensive method for estimating supersonic drag that is suitable for coursework is derived from this exercise. The empirical methodology (called the Delta Method) is based on regression analyses of eighteen subsonic and supersonic military aircraft (i. e., the T-2B, T37B, KA-3B, A-4F, TA-4F, RA-5C, A-6A, A-7A, F4E, F5A, F8C, F-11F, F100, F101, F104G, F105B, F106A, and XB70) and fifteen advanced (i. e., supercritical) aerofoils. The empirical approach includes the effects of the following:

• wing geometry (AR, Л, t/c, and aerofoil section)

• cross-sectional area distribution

• CD variation with CL and Mach number

The methodology presented herein follows [3], modified to simplify ACDp esti­mation resulting in minor discrepancies. The method is limited and may not be suitable to analyze more exotic aircraft configurations. However, this method is a learning tool for understanding the parameters that affect supersonic aircraft drag buildup. Results can be improved when more information is available.

The introduction to this chapter highlights that aircraft with supersonic capabil­ities require estimation of CDpmi„ at three speeds: (1) at a speed before the onset of wave drag, (2) at Mcrit, and (3) at maximum speed. The first two speeds follow the same procedure as for the high-subsonic aircraft discussed in Sections 9.7 through 9.14. In the subsonic drag estimation method, the viscous-dependent ACDp varying with the CL is separated from the wave drag, CDw (i. e., transonic effects), which also varies with the CL but independent of viscosity.

For bookkeeping purposes in supersonic flight, such a division between the ACDp and the CDw is not clear with the CL variation. In supersonic speed, there is little complex transonic flow over the body even when the CL is varied. It is not

clear how shock waves affect the induced drag with a change in the angle of attack. For simplicity, however, in the empirical approach presented here, it is assumed that supersonic drag estimation can use the same approach as the subsonic drag estimation by keeping ACDp and CDw separate. The ACDp values for the worked – out example are listed in Table 9.13. Here, drag due to shock waves is computed at CL = 0, and CDw is the additional shock-wave drag due to compressibility varying with CL > 0. The total supersonic aircraft drag coefficient can then be expressed as follows:

Cd = Cupmin + ACup + C2L/n AR + (Cu^hock@CL = 0) + Cdw (9.37)

It is recommended that in current practice, CFD analysis should be used to obtain the variation of ACDp and ACDw with CL. Reference [3] was published in 1978 using aircraft data before the advent of CFD. Readers are referred to [1], [4], and [5] for other methods. The industry has advanced methodologies, which are naturally more involved.

The aircraft cross-section area distribution should be as smooth as possible, as discussed in Section 3.13 (see Figure 3.23). It may not always be possible to use narrowing of the fuselage when appropriate distribution of areas may be carried out.

The stepwise empirical approach to estimate supersonic drag is as follows:

Step 1: Progress in the same manner as for subsonic aircraft to obtain the

aircraft-component Re for the cruise flight condition and the incom­pressible CFcomponent.

Step 2: Increase drag in Step 1 by 28.4% as the military aircraft excrescence

effect.

Step 3: Compute CDpmin at the three speeds discussed previously.

Step 4: Compute induced drag using CDi = C2JnAR.

Step 5: Obtain ACDp from the CFD and tests or from empirical relations.

Step 6: Plot the fuselage cross-section area versus the length and obtain the

maximum area, Бл, and base area, Sb (see example in Figure 9.17).

Step 7: Compute the supersonic wave drag at zero lift for the fuselage and

the empennage using graphs; use the parameters obtained in Step 6.

Step 8: Obtain the design CL and the design Mach number using graphs (see

example in Figure 9.19).

Step 9: Obtain the wave drag, CDw, for the wing using graphs.

Step 10: Obtain the wing-fuselage interference drag at supersonic flight using graphs.

Step 11: Total all the drags to obtain the total aircraft drag and plot as CD versus CL.

The worked-out example for the North American RA-5C Vigilante aircraft is a worthwhile coursework exercise. Details of the Vigilante aircraft drag are in [3]. The subsonic drag estimation methodology described in this book differs with what is presented in [3] yet is in agreement with it. The supersonic drag estimation fol­lows the methodology described in [3]. A typical combat aircraft of today is not too different than the Vigilante in configuration details, and similar logic can be applied. Exotic shapes (e. g., the F117 Nighthawk) should depend more on information gen­erated from CFD and tests along with the empirical relations. For this reason, the

exposed areas

ate shaded

author does not recommend undertaking coursework on exotic-aircraft configura­tions unless the results can be substantiated. Learning with a familiar design that can be substantiated gives confidence to practitioners. Those in the industry are for­tunate to have access to more accurate in-house data.

Although military aircraft topics are not discussed here, and instead are found in the Web at www. cambridge. org/Kundu, this important topic of military aircraft drag estimation is kept here.

Military aircraft drag estimation requires additional considerations to account for the weapon system because few are carried inside the aircraft mould lines (e. g., guns, ammunition, and bombs inside the fuselage bomb bay, if any); most are exter­nal stores (e. g., missiles, bombs, drop-tanks, and flares and chaff launchers). With­out external carriages, military aircraft are considered at typical configuration (the pylons are not removed – part of a typical configuration). Internal guns without their consumables is considered a typical configuration; with armaments, the aircraft is considered to be in a loaded configuration. In addition, most combat aircraft have a supersonic-speed capability, which requires additional supersonic-wave drag.

Rather than drag due to passenger doors and windows as in a civil aircraft, mil­itary aircraft have additional excrescence drag (e. g., gun ports, extra blisters and antennas, and pylons) that requires a drag increment. To account for these addi­tional excrescences, [3] suggests an increment of the clean flat-plate equivalent drag, f, by 28.4%.

Streamlined external-store drag is shown in Table 9.8 based on the frontal max­imum cross-sectional area.

Bombs and missiles flush with the aircraft contour line have minor interference drag and may be ignored at this stage. Pylons and bomb racks create interference, and Equation 9.17 is used to estimate interference on both sides (i. e., the aircraft and the store). These values are highly simplified at the expense of unspecified inac­curacy; readers should be aware that these simplified values are not far from reality (see [1], [4], and [5] for more details).

Military aircraft engines are buried into the fuselage and do not have nacelles and associated pylons. Intake represents the air-inhalation duct. Skin friction drag and other associated 3D effects are integral to fuselage drag, but their intakes must accommodate large variations of intake air-mass flow. Military aircraft intakes operate supersonically; their power plants are very low bypass turbofans (i. e., on the order of less than 3.0 – earlier designs did not have any bypass). For speed capa­bilities higher than Mach 1.9, most intakes and exhaust nozzles have an adjustable mechanism to match the flow demand in order to extract the best results. In gen­eral, the adjustment aims to keep the Vi„take/Vm ratio more than 0.8 over opera­tional flight conditions, thereby practically eliminating spillage drag (see Figure 9.7). Supersonic flight is associated with shock-wave drag.

Mandatory requirements by certifying agencies (e. g., FAA and CAA) specify that multiengine commercial aircraft must be able to climb at a minimum specified gra­dient with one engine inoperative at “dirty” configuration. This immediately safe­guards an aircraft in the rare event of an engine failure; and, in certain cases, after liftoff. Certifying agencies require backup for mission-critical failures to provide safety regardless of the probability of an event occurring.

Asymmetric drag produced by the loss of an engine would make an aircraft yaw, requiring a rudder to fly straight by compensating for the yawing moment caused by the inoperative engine. Both the failed engine and rudder deflection substantially increase drag, expressed by ACD_engine out+ruddert. Typical values for coursework are in Table 9.7.

9.12 Propeller-Driven Aircraft Drag

Drag estimation of propeller-driven aircraft involves additional considerations. The slipstream of a tractor propeller blows over the nacelle, which blocks the resisting flow. Also, the faster flowing slipstream causes a higher level of skin friction over the downstream bodies. This is accounted for as a loss of thrust, thereby keeping

the drag polar unchanged. The following two factors arrest the propeller effects with piston engines (see Chapter 10 for calculating propeller thrust):

1. Blockage factor, fb, for tractor-type propeller: 0.96 to 0.98 applied to thrust (for the pusher type, there is no blockage; therefore, this factor is not required – i. e., fb = 1.0)

2. A factor, fh, as an additional profile drag of a nacelle: 0.96 to 0.98 applied to thrust (this is the slipstream effect applicable to both types of propellers)

Turboprop nacelles have a slightly higher value of fb than piston-engine types because of a more streamlined shape. However, the slipstream from a turboprop is higher and therefore has a lower value of fh.

To decrease aircraft speed, whether in combat action or at landing, flat plates – which are attached to the fuselage and shaped to its geometric contour when retracted – are used. They could be placed symmetrically on both sides of the wing or on the upper fuselage (i. e., for military aircraft). The flat plates are deployed dur­ing subsonic flight. Use CDnbrake = 1.2 to 2.0 (average 1.6) based on the projected frontal area of the brake to air stream. The force level encountered is high and con­trolled by the level of deflection. The best position for the dive brake is where the aircraft moment change is the least (i. e., close to the aircraft CG line).

9.14.1 Undercarriage Drag

Undercarriages, fixed or extended (i. e., retractable type), cause considerable drag on smaller, low-speed aircraft. A fixed undercarriage (not streamlined) can cause

up to about a third of aircraft parasite drag. When the undercarriage is covered by a streamlined wheel fairing, the drag level can be halved. It is essential for high-speed aircraft to retract the undercarriage as soon as it is safe to do so (like birds). Below a 200-ft altitude from takeoff and landing, an aircraft undercarriage is kept extended. Again, it is cautioned that the data in this book are intended for coursework so readers have some sense of the order of magnitude involved.

The drag of an undercarriage wheel is computed based on its frontal area: An_wheei product of wheel diameter and width (see Figure 7.15). For twin side-by­side wheels, the gap between them is ignored and the wheel drag is increased by 50% from a single-wheel drag. For the bogey type, the drag also would increase – it is assumed by 10% for each bogey, gradually decreasing to a total maximum 50% increase for a large bogey. Finally, interference effects (e. g., due to doors and tub­ing) would double the total of wheel drag. The drag of struts is computed separately. The bare single-wheel CD_wheel based on the frontal area is in Table 9.6 (wheel aspect ratio = D/Wb).

For the smooth side, reduce by half. In terms of an aircraft:

CDp_wheel — (CDn_wheel X An_wheel)/SW

A circular strut has nearly twice the amount of drag compared to a stream­lined strut in a fixed undercarriage. For example, the drag coefficient of a circular strut based on its cross-sectional area per unit length is CDn_jtrut — 1-0 because it

operates at a low Re during takeoff and landing. For streamlined struts with fair­ings, it decreases to 0.5 to 0.6, depending on the type.

Torenbeek [10] suggests using an empirical formula if details of undercarriage sizes are not known at an early conceptual design phase. This formula is given in the FPS system as follows:

Cd_uc = 0.00403 x (MTOW0’785)/Sw (9.36)

Understandably, it could result in a slightly higher value (see the following example).

worked-out example. Continue with the previous example using the largest in the design (i. e., MTOM = 24,200 lb and SW = 323 ft2) for the undercarriage size. It has a twin-wheel, single-strut length of 2 ft (i. e., diameter of 6 inches, An_strui ^ 0.2 ft2) and a main wheel size with a 22-inch diameter and a 6.6-inch width (i. e., wheel aspect ratio = 3.33, Anwheel ^ 1 ft2). From Table 9.6, a typical value of CDnwheel = 0.18, based on the frontal area and increased by 50% for the twin-wheel (i. e., CD0 = 0.27). Including the nose wheel (although it is smaller and a single wheel, it is better to be liberal in drag estimation), the total frontal area is about 3 ft2:

fwheel = 0.27 x 3 = 0.81 ft2 fstmt = 1.0 x 3 x 2 x 0.2 = 1.2 ft2

Total fUc = 2 x (0.81 + 1.2) = 4.02 ft2 (100% increase due to interference, doors, tubing, and so on) in terms of CDpmi„_Uc = 4.02/323 = 0.0124. Checking the empirical relation in Equation 9.36, CduC = 0.00403 x (24,200a785)/323 =

0. 034, a higher value that is acceptable when details are not known.

High-lift devices are typically flaps and slats, which can be deployed independently of each other. Some aircraft have flaps but no slats. Flaps and slats conform to the

Figure 9.9. NACA 632-118 aerofoil

aerofoil shape in the retracted position (see Section 3.10). The function of a high-lift device is to increase the aerofoil camber when it is deflected relative to the baseline aerofoil. If it extends beyond the wing LE and trailing edge, then the wing area is increased. A camber increase causes an increase in lift for the same angle of attack at the expense of drag increase. Slats are nearly full span, but flaps can be anywhere from part to full span (i. e., flaperon). Typically, flaps are sized up to about two thirds from the wing root. The flap-chord-to-aerofoil-chord (cc/c) ratio is in the order of 0.2 to 0.3. The main contribution to drag from high-lift devices is proportional to their projected area normal to free-stream air. The associated parameters affecting drag contributions are as follows:

• type of flap or slat (see Section 3.10)

• extent of flap or slat chord to aerofoil chord (typically, flap has 20 to 30% of wing chord)

• extent of deflection (flap at takeoff is from 7 to 15 deg; at landing, it is from 25 to 60 deg)

• gaps between the wing and flap or slat (depends on the construction)

• extent of flap or slat span

• fuselage width fraction of wing span

• wing sweep, t/c, twist, and AR

The myriad variables make formulation of semi-empirical relations difficult. Refer­ences [1], [4], and [5] offer different methodologies. It is recommended that prac­titioners use CFD and test data. Reference [14] gives detailed test results of a double-slotted flap (0.309c) NACA 632-118 aerofoil (Figure 9.9). Both elements of a double-slotted flap move together, and the deflection of the last element is the overall deflection. For wing application, this requires an aspect-ratio correction, as described in Section 3.13.

Figure 9.10 is generated from various sources giving averaged typical values of ACl and ACoflap versus flap deflection. It does not represent any particular aero­foil and is intended only for coursework to be familiar with the order of magnitude involved without loss of overall accuracy. The methodology is approximate; practic­ing engineers should use data generated by tests and CFD.

The simple semi-empirical relation for flap drag given in Equation 9.32 is gener­ated from flap-drag data shown in Figure 9.10. The methodology starts by working on a straight wing (Л0) with an aspect ratio of 8, flap-span-to-wing-span ratio (bf/b) of two-thirds, and a fuselage-width-to-wing-span ratio of less than one-fourth. Total flap drag on a straight wing (Л0) is seen as composed of two-dimensional para­site drag of the flap (CDpjap2D), change in induced drag due to flap deployment (ACoi. flap), and interference generated on deflection (ACDi„tflap). Equation 9.33 is

intended for a swept wing. The basic expressions are corrected for other geometries, as given in Equations 9.34 and 9.35.

Straight wing:

CD-flap-A0 — ACD-flap-2D + ACDi-flap + ACDintflap (9.32)

Swept wing:

CD-flap_A1/4 — CD-flaP-A0 X cos Л14 (9.33)

The empirical form of the second term of Equation 9.32 is given by:

ACDiflap — 0.025 X (8/AR)03 x [(2b)/(3bf)]05 x (ACl)2 (9.34)

where AR is the wing-aspect ratio and (bf/b) is the flap-to-wing-span ratio.

The empirical form of the third term of Equation 9.32 is given by:

ACDintflap — к X CD_flap^D (9.35)

where к is 0.1 for a single-slotted flap, 0.2 for a double-slotted flap, 0.25 to 0.3 for a single-Fowler flap, and 0.3 to 0.4 for a double-Fowler flap. Lower values may be used at lower settings.

Figure 9.10 shows the CDjap2D for various flap types at various deflection angles with the corresponding maximum ACL gain given in Table 9.1. Aircraft fly well below CLmax, keeping a safe margin. Increase ACDi_flap by 0.002 if the slats are deployed.

worked-out example. An aircraft has an aspect ratio, AR — 7.5, Л/ — 20 deg, (bf/b) — 2/3, and fuselage-to-wing-span ratio less than 1/4. The flap type is a single-slotted Fowler flap and there is a slat. The aircraft has CDpmin — 0.019. Construct its drag polar.

At 20 deg deflection:

It is typical for takeoff with CL — 2.2 (approximate) but can be used at landing.

From Figure 9.10:

ACD_fl. ap.2D = 0.045 and ACl = 1.46.

From Equation 9.34:

ACDiflap = 0.025 x (8/7.5)0’3 x [(2/3)/(3/2)f5 x (1.46)2 = 0.025 x 1.02 x 2.13 = 0.054

From Equation 9.35:

ACDtntflap = 0.25 x 0.045 = 0.01125;

CDflap-A0 = 0.045 + 0.054 + 0.01125 = 0.11, with slat on C^hightift = 0.112

For the aircraft wing:

CDflap-A1 = CDflap-A0 x cos A0 = °.112 x cos 20 = °.1-°5

Induced drag:

Cdi = (C2L)/(nAR) = (2.2)2/(3.14 x 7.5) = 4.48/23.55 = 0.21 Total aircraft drag:

Cd = 0.019 + 0.105 + 0.21 = 0.334

At 45 deg deflection:

It is typical for landing with CL = 2.7 (approximate).

From Figure 9.10:

ACDflap-2D = 0.08 and ACl = 2.1

From Equation 9.34:

ACDfl = 0.025 x (8/7.5)03 x [(2/3)/(3/2)]05 x (2.1)2 = 0.025 x 1.02 x 4.41 = 0.112

From Equation 9.34:

ACDintflap = 0.3 x 0.08 = 0.024 CDpflapAo = 0.08 + 0.112 + 0.024 = 0.216

With slat on:

CDp-highUft = 0.218

For the aircraft wing:

CDflapA1/4 = CDflap_Ao x cos A0 = 0.218 x cos 20 = 0.201 x 0.94 = 0.205 Induced drag:

Cdi = {CL)/(nAR) = (2.7)2/(3.14 x 7.5) = 7.29/23.55 = 0.31

Figure 9.11. Typical drag polar with high-lift devices

Cd = 0.019 + 0.205 + 0.31 = 0.534

Drag polar with a high-lift device extended is plotted as shown in Figure 9.11 (after Figure 9.1) at various deflections. It is cautioned that this graph is intended only for coursework; practicing industry-based engineers must use data generated by tests and CFD.

A typical value of Cl/Cd for high-subsonic commercial transport aircraft at takeoff with flaps deployed is on the order of 10 to 12; at landing, it is reduced to 6 to 8.

A more convenient method is shown in Figure 9.12, and it is used for the course – work example (civil aircraft) worked out in Section 9.19.

Total aircraft drag is the sum of all drags estimated in Sections 9.8 through 9.12, as follows for LRC and HSC:

At LRC,

C2

Cd — CDpmin + &Cdd + ПІК (9’30)

At HSC,

C2

( Merit )CD ‘ + CDw (9.31)

п AK

At takeoff and landing, additional drag exists, as explained in the next section.

9.11 Low-Speed Aircraft Drag at Takeoff and Landing

For safety in operation and aircraft structural integrity, aircraft speed at takeoff and landing must be kept as low as possible. At ground proximity, lower speed would provide longer reaction time for the pilot, easing the task of controlling an aircraft at a precise speed. Keeping an aircraft aloft at low speed is achieved by increas­ing lift through increasing wing camber and area using high-lift devices such as a flap and/or a slat. Deployment of a flap and slat increases drag; the extent depends on the type and degree of deflection. Of course, in this scenario, the undercarriage remains extended, which also would incur a substantial drag increase. At approach to landing, especially for military aircraft, it may require “washing out” of speed to slow down by using fuselage-mounted speed brakes (in the case of civil air­craft, this is accomplished by wing-mounted spoilers). Extension of all these items is known as a dirty configuration of the aircraft, as opposed to a clean configuration at cruise. Deployment of these devices is speed-limited in order to maintain structural integrity; that is, a certain speed for each type of device extension should not be exceeded.

After takeoff, at a safe altitude of 200 ft, pilots typically retract the undercar­riage, resulting in noticeable acceleration and gain in speed. At about an 800-ft alti­tude with appropriate speed gain, the pilot retracts the high-lift devices. The air­craft is then in the clean configuration, ready for an enroute climb to cruise altitude; therefore, this is sometimes known as enroute configuration or cruise configuration.

Wave drag is caused by compressibility effects of air as an aircraft approaches high subsonic speed because local shock (i. e., supervelocity) appears on a curved surface as aircraft speed increases. This is in a transonic-flow regime, in which a small part of the flow over the body is supersonic while the remainder is subsonic. In some cases, a shock interacting with the boundary layer can cause premature flow separation, thus increasing pressure drag. Initially, it is gradual and then shows a rapid rise as it approaches the speed of sound. The industry practice is to tolerate a twenty-count (i. e., ACd = 0.002) increase due to compressibility at a speed identified as Mcrit (Figure 9.8b). At higher speeds, higher wave-drag penalties are incurred.

A typical wave drag (CDw) graph is shown in Figure 9.8b, which can be used for coursework (civil aircraft) described in Section 9.19. Wave-drag characteristics are design-specific; each aircraft has its own CDw, which depends on wing geometry (i. e., planform shape, quarter-chord sweep, taper ratio, and aspect ratio) and aero­foil characteristics (i. e., camber and t/c). Wind-tunnel testing and CFD can predict wave drag accurately but must be verified by flight tests. The industry has a large
databank to generate semi-empirically the CDw graph during the conceptual design phase. Today, CFD can generate wave drag accurately and is an indispensable tool (see Chapter 14), replacing the empirical/semi-empirical approach. CFD analysis is beyond the scope of this book. It is suggested that practitioners use data from tests or from CFD analysis in conjunction with an empirical approach.

The aircraft CDpmin can now be obtained from faircmft. The minimum parasite drag of the entire aircraft is CDpmin — (1 /Sw)J2fi, where is the sum of the total fs of

the entire aircraft:

CDpmin — faircraft/Sw

9.10 ACDp Estimation

Equation 9.2 shows that ACDp is not easy to estimate. ACDp contains the lift – dependent variation of parasite drags due to a change in the pressure distribution with changes in the angle of attack. Although it is a small percentage of the total air­craft drag (it varies from 0 to 10%, depending on the aircraft Cl), it is the most diffi­cult to estimate. There is no proper method available to estimate the ACDp-versus – Cl relationship; it is design-specific and depends on wing geometry (i. e., planform, sweep, taper ratio, aspect ratio, and wing-body incidence) and aerofoil character­istics (i. e., camber and t/c). The values are obtained through wind-tunnel tests and, currently, by CFD.

During cruise, the lift coefficient varies with changes in aircraft weight and/or flight speed. The design-lift coefficient, Cld, is around the mid-cruise weight of the

I

I

»

I

LRC. Let CLP be the lift coefficient when ACDp = 0. The wing should offer CLP at the three-fourths value of the designed CLD. This would permit an aircraft to oper­ate at HSC (at McrU; i. e., at the lower CL) with almost zero ACDp. Figure 9.8a shows a typical ACDp-versus-CL variation. This graph can be used only for coursework in Sections 9.18 and 9.19.

For any other type of aircraft, a separate graph must be generated from wind – tunnel tests and/or CFD analysis. The industry has a large databank to generate such graphs during the conceptual design phase. In general, the semi-empirical method takes a tested wing (with sufficiently close geometrical similarity) ACDp – versus-CL relationship and then corrects it for the differences in wing sweep (ф), aspect ratio (ф), t/c ratio (t), camber, and any other specific geometrical differences (Figure 9.8a).

In addition to excrescence drag, there are other drag increments such as ECS drag (e. g., air-conditioning), which is drag at a fixed value depending on the number of passengers); and aerials and trim drag, which are included to obtain the minimum parasite drag of the aircraft.

Air-Conditioning Drag

Air-conditioning air is inhaled from the atmosphere through flush intakes that incur drag. It is mixed with hot air bled from a midstage of the engine compressor and then purified. Loss of thrust due to engine bleed is accounted for in the engine- thrust computation, but the higher pressure of the expunged cabin air causes a small amount of thrust. Table 9.4 shows the air-conditioning drag based on the number of passengers (interpolation is used for the between sizes).

Trim Drag

Due to weight changes during cruise, the CG could shift, thereby requiring the air­craft to be trimmed in order to relieve the control forces. Change in the trim-surface angle causes a drag increment. The average trim drag during cruise is approximated

as shown in Table 9.5, based on the wing reference area (interpolation is used for the between sizes).

Aerials

Navigational and communication systems require aerials that extend from an air­craft body, generating parasite drag on the order 0.06 to 0.1 ft2, depending on the size and number of aerials installed. For midsized transport aircraft, 0.075 ft2 is typ­ically used. Therefore:

9.9 Notes on Excrescence Drag Resulting from Surface Imperfections

This section may be omitted because there is no coursework exercise involved. Semi-empirical relations discussed in Sections 9.8.4 and 9.8.5 are sufficient for the purpose. Excrescence drag due to surface imperfections is difficult to estimate; therefore, this section provides background on the nature of the difficulty encoun­tered. Capturing all the excrescence effects over the full aircraft in CFD is yet to be accomplished with guaranteed accuracy.

A major difficulty arises in assessing the drag of small items attached to the air­craft surface, such as instruments (e. g., pitot and vanes), ducts (e. g., cooling), and necessary gaps to accommodate moving surfaces. In addition, there is the unavoid­able discrete surface roughness from mismatches and imperfections – aerodynamic defects – resulting from limitations in the manufacturing processes. Together, all of these drags, from both manufacturing and nonmanufacturing origins, are collec­tively termed excrescence drag, which is parasitic in nature. Of particular interest is the excrescence drag resulting from the discrete roughness, within the manufactur­ing tolerance allocation, in compliance with the surface-smoothness requirements specified by aerodynamicists to minimize drag.

Mismatches at the assembly joints are seen as discrete roughness (i. e., aerody­namic defects) – for example, steps, gaps, fastener flushness, and contour deviation – placed normal, parallel, or at any angle to the free-stream air flow. These defects generate excrescence drag. In consultation with production engineers, aerodynami – cists specify tolerances to minimize the excrescence drag – on the order of 1 to 3%

of the CDpmin.

The “defects” are neither at the maximum limits throughout nor uniformly dis­tributed. The excrescence dimension is on the order of less than 0.1 inch; for com­parison, the physical dimension of a fuselage is nearly 5,000 to 10,000 times larger. It poses a special problem for estimating excrescence drag; that is, capturing the resulting complex problem in the boundary layer downstream of the mismatch.

The methodology involves first computing excrescence drag on a 2D flat surface without any pressure gradient. On a 3D curved surface with a pressure gradient, the excrescence drag is magnified. The location of a joint of a subassembly on the 3D body is important for determining the magnification factor that will be applied on the 2D flat-plate excrescence drag obtained by semi-empirical methods. The body is divided into two zones (see Figure 16.5): Zone 1 (the front side) is in an adverse pressure gradient, and Zone 2 is in a favorable pressure gradient. Excrescences in Zone 1 are more critical to magnification than in Zone 2. At a LRC flight speed (i. e., below McrU for civil aircraft), shocks are local, and subassembly joints should not be placed in this area (Zone 1).

Estimation of aircraft drag uses an average skin-friction coefficient CF (see Fig­ure 9.19b), whereas excrescence-drag estimation uses the local skin-friction coef­ficient Cf (see Figure 9.19a), appropriate to the location of the mismatch. These fundamental differences in drag estimation methods make the estimation of aircraft drag and excrescence drag quite different.

After World War II, efforts continued for the next two decades – especially at the RAE by Gaudet, Winters, Johnson, Pallister, and Tillman et al. – using wind – tunnel tests to understand and estimate excrescence drag. Their experiments led to semi-empirical methods subsquently compiled by ESDU as the most authoritative information on the subject. Aircraft and excrescence drag estimation methods still remain state of the art, and efforts to understand the drag phenomena continue.

Surface imperfections inside the nacelle – that is, at the inlet diffuser surface and at the exhaust nozzle – could affect engine performance as loss of thrust. Care must be taken so that the “defects” do not perturb the engine flow field. The internal nacelle drag is accounted for as an engine-installation effect.