High-Lift Device Drag

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.

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