Semi-empirical Relations to Estimate Aircraft Component Parasite Drag

Isolated aircraft components are worked on to estimate component parasite drag. The semi-empirical relations given here embed the necessary corrections required for 3D effects. Associated coefficients and indices are derived from actual flight – test data. (Wind-tunnel tests are conducted at a lower Re and therefore require correction to represent flight-tested results.) The influence of the related drivers is shown as drag increasing byt and drag decreasing by^. For example, an increase of the Re reduces the skin-friction coefficient and is shown as Re (ф).

9.8.1 Fuselage

The fuselage characteristic length, Lfus, is the length from the tip of the nose cone to the end of the tail cone. The wetted area, Awf (t), and fineness ratio (length/ diameter) (ф) of the fuselage are computed. Ensure that cutouts at the wing and

Ml і гагу Aircraft

area shaded

Bubble canopy – long length _|

Civil Aircraft

Figure 9.4. Canopy types for drag estimation empennage junctions are subtracted. Obtain the Ref (^). The corresponding basic CFf for the fuselage using Figures 9.19 and 9.20 is intended for the flat plate at the flight Mach number. Figure 9.19 is accurate and validated over time.

The semi-empirical formulation is required to correct the 2D skin friction drag for the 3D effects and other influencing parameters, as listed herein. These are incre­mental values shown by the symbol A. There are many incremental effects and it is easy to miss some of them.

1. 3D effects [1] are due to surface curvature resulting in a change in the local flow speed and associated pressure gradients, as follows:



ACFf = CFf x [k x (length/diameter) x Re-02]


where k is between 0.022 and 0.025 (use the higher value) and Re = the Re of the fuselage



ACFf = CFf x (diameter/length)1′[12]




ACFf = CFf x 7 x (diameter/length)[13] [14] [15]


coefficient CDn is based on the frontal cross-sectional area shown in the military type aircraft in Figure 9.4 (the front view of the raised canopy is shaded). The extent of the raised frontal area contributes to the extent of drag increment and the CDn accounts for the effects of canopy rise. CDn is then converted to ACFfcanopy = (A„ xCDn)/Awf, where Awf is the fuselage wetted area. The dominant types of a raised or bubble-type canopy and their associated CDn are summarized in Table 9.1.

(ii) Windshield-type canopy for larger aircraft. These canopies are typi­cally associated with payload-carrying commercial aircraft from a small Bizjet and larger. Flat panes lower the manufacturing cost but result in a kink at the double-curvature nose cone of the fuselage. A curved and smooth transparent windshield avoids the kink that would reduce drag at an additional cost. Smoother types have curved panes with a single or double curvature. Single-curvature panes come in smaller pieces, with a straight side and a curved side. Double-curvature panes are the most expensive and considerable attention is required during manufacturing to avoid distortion of vision. The values in square feet in Table 9.2 are used to obtain a sharp-edged windshield-type canopy drag.

(b) Body pressurization-fuselage surface waviness (use 5.5%), 5 to 6%

(c) Nonoptimum fuselage shape (interpolate the in-between values)

(i) Nose fineness ratio, Fcf (see Figure 4.17 and Table 4.5)

For Fcf < 1.5: 8%

For 1.5 < Fcf < 1.75: 6%

For Fcf > 1.75: 4%

For military aircraft type with high nose fineness: 3%

(ii) Fuselage closure – above Mach 0.6 (see Table 4.5)

Less than 10 deg: 0 11 to 12 deg closure: 1%

13 to 14 deg: 4%

(iii) Upsweep closure (see Section 3.21) use in conjunction with (iv)

No upsweep: 0 4 deg of upsweep: 2%

10 deg of upsweep: 8%

15 deg of upsweep: 15%

(interpolate in-between values)

(iv) Aft-end cross-sectional shape

Circular: 0 Shallow keel: 0 to 1%

Deep keel: 1 to 2%

(v) Rear-mounted door (with fuselage upsweep): 5 to 10%

(d) Cabin-pressurization leakage (if unknown, use higher value): 3 to 5%

(e) Excrescence (nonmanufacturing types such as windows)

(i) Windows and doors (use higher values for larger aircraft): 2 to 4%

(ii) Miscellaneous: 1%

(f) Wing fuselage belly fairing, if any: 1 to 5%

(use higher value if houses undercarriage)

(g) Undercarriage fairing – typically for high-wing aircraft (if any fairing): 2 to 6%

(based on fairing protrusion height from fuselage)

3. The interference drag increment with the wing and empennage is included in the calculation of lifting-surface drag and therefore is not duplicated when comput­ing the fuselage parasite drag. Totaling the CFf and ACFf from the wetted area AwF of the isolated fuselage, the flat-plate equivalent drag, ff (see Step 6 in Section 9.7.3), is estimated in square feet.

4. Surface roughness is 2 to 3%. These effects are from the manufacturing origin, discussed in Section 9.8.4. Because surface-roughness drag is the same percent­age for all components, it is convenient to total them after evaluating all com­ponents. In that case, the term ACFfrough is dropped from Equation 9.13 and it is accounted for as shown in Equation 9.27.

Total all the components of parasite drag to obtain CDpmin, as follows. It should include the excrescence-drag increment. Converted into the fuselage contribution to [CDpmin]f in terms of aircraft wing area, it becomes:

CFf = 1.03 x (basic CFf + J2ACFf)

ff = (CFf + ACFfwrap + ACFfsupervel + ACFfpress + ACFfother + ACFfrough) x Awf

[Copmin] f = ff / Sw (9.14)

See the worked-out examples.

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