Drag Due to Lift

The methods used in Chapter 6 are applicable here. The lift coefficient for level, unaccelerated flight follows directly from the information in Table 9.1 because the lift must equal the weight. We find:

W

CL = W = 021.

L qS

Then, the induced-drag coefficient is found from:

C CL (0.21)2

CDi KeAR n(0.98)5.8

where the effective AR was reduced by Hoerner from 6.1 to 5.8 to account for planform losses related to the wing-tips shape. Thus, the drag area representing the induced drag is:

(drag area)mduced = CDiS = 0.42 ft2.

Adjustment of the AR represents an unusual method for handling the effect of the planform shape. The departure from the ideal (i. e., elliptic) lift distri­bution usually is accounted for entirely by the efficiency factor, e. Hoerner used a value of 0.98, which appears too large—although it may have been the value for which the designers were striving. If the actual AR is used in the formula

and the efficiency factor is adjusted (assuming that the final calculated induced – drag coefficient is correct), then we find that e should be 0.93. This seems to be in reasonable agreement with values of span efficiency based on the work of Glauert and others for straight-tapered wings with rounded tips.

1. Wing Contribution to Parasite Drag

Parasite drag on the wing is the sum of the profile drag, skin friction, drag due to flow separation in various gaps (i. g., around the landing-gear fairings), and sur­face imperfections (e. g., protruding rivet and bolt heads). The drag areas for each is summarized in Table 9.2. In estimating the skin-friction drag, Hoerner noted that the sheet-metal gaps behind the leading-edge slats (which opened automati­cally at low speed to improve stalling characteristics) render the boundary-layer flow fully turbulent. He also indicated that the camouflage paint used for these aircraft exhibited a roughness height on the order of 1 mil. With this in mind, he then estimated that the skin-friction drag coefficient is Cf = 0.0035, which is considerably larger than an estimate (0.0028) assuming a smooth surface with a Re number of 1.1 x 107. The projected surface area of the part of the wing out­side of the fuselage is adjusted by a factor of 1.28 to account for the influence of the wing-section thickness. These considerations lead to the skin-friction drag area shown in the table. Most of the table entries are based on drag data from wind-tunnel tests simulating each type of drag source or surface imperfection. Hoerner’s book is a useful compendium of such data, with practical techniques for application in drag estimation.

2. Fuselage Drag

In estimating the skin friction drag, the boundary layer is assumed to be every where turbulent due to the propeller slipstream. Again, the rough cam­ouflage-paint surface is taken into account. This yields a skin-friction coefficient of Cf = 0.0025. Account also must be taken of various appendages, as listed in Table 9.3.

The fuselage wetted area is 250 ft2, so the basic drag area for the fuselage is 0.625 ft2. This must be adjusted to account for rivet and bolt heads and the dynamic-pressure increase along the fuselage sides (Hoerner multiplied the result by 1.07 to account for this). Therefore, the adjusted drag area is 1.75 ft2, as shown in Table 9.3.

A various “appendages” must be accounted for in the drag estimate. Table 9.3 shows the estimates for the canopy, tail wheel, and antenna components. The canopy has numerous edges around the window panes so that the drag of the canopy is almost double that of the same shape without these irregularities. Again, the estimates are based on wind-tunnel studies of many different shapes. A correction must be added to account for the increase in dynamic pressure because the fuselage flow field is within the slipstream of the propeller. Hoerner estimated that there is a 10 percent increase in q, as indicated in Table 9.3.

3. Engine Installation Drag

Some of these effects are due to fuselage appendages and usually are included with the fuselage drag; others are additions to the wing drag. Hoerner chose to include them in a detailed estimate of the drag caused by the various air scoops for the radiators and oil coolers, as well as exhaust stacks needed for the engine installation, as tabulated in Table 9.4. The high-drag contribution from the two

Table 9.2. Contributions to Bf-109G wing pvarasite drag (Hoerner, 1993.) Drag Source Drag Area, ft2 Wing skin friction (turbulent, rough surface) 1.350 Surface imperfections common to both upper and lower surfaces: Aileron gaps 0.018 Aileron hinges 0.030 Aileron balance weights 0.027 Side gaps on slots 0.090 Side gaps at ailerons and flaps 0.030 Pitot-static tube 0.010 Position lights at wing tips 0.002 Upper-wing side blisters 0.020 Holes around landing gear 0.140 Subtotal 0.367 Upper-wing surface imperfections: 0.011 (1.16)* 0.013 Lower-wing surface imperfections: Lateral sheet-metal edges (29 ft) 0.013 Lateral surface gaps (36 ft) 0.038 Longitudinal sheet edges (50 ft) 0.001 Bolt heads (500) 0.004 Flush rivet heads (3,500) 0.002 Sheet-metal blisters (e. g., over cannons.) 0.007 Subtotal 0.075(1.42)* 0.107 Additional skin friction due to surface imperfections: 0.090 Total Wing-Parasite Drag Area: 1.927

* Factors in parentheses are corrections for dynamic pressure on upper and lower-wing surfaces above the freestream reference value.

wing-mounted radiators, according to Hoerner, is due to “poor aerodynamic design and considerable internal leakage.” Much work was accomplished more recently by NACA (and later NASA), as well as the aircraft industry, in reducing drag of air intakes, motivated mainly by the advent of jet propulsion. Compress­ibility effects are important in the design process for high-speed flight.

Table 9.3. Contributions to Bf-109G fuselage-parasite drag (Hoerner, 1993) Drag Source Drag Area, ft2 Fuselage skin friction (based on wetted area) 0.750 Fuselage appendages: Canopy 0.120 Tail wheel 0.290 Antenna mast 0.030 Antenna wires, etc. 0.030 Direction finder 0.050 Gun installation 0.030 Other irregularities 0.080 Subtotal 0.630 Wing/fuselage interference 0.220 Total 1.600 Correction for increase in dynamic pressure due to propeller slipstream (q is 10 percent higher on fuselage and wing fillets); therefore, multiply 1.6 by 1.1=1.75 Total Fuselage-Parasite Drag Area: 1.750

Table 9.4. Contributions to Bf-109G engine-installation drag Drag Source Drag Area, ft2 Engine appendages: Fuselage appendages: Carburetor air scoop 0.067 Intake momentum drag 0.080 Exhaust stacks 0.056 Oil cooler 0.168 Ventilation openings 0.100 Wing radiators 0.660 Subtotal 1.131 Correction for increase in dynamic pressure due to propeller slipstream (q higher on engine parts); therefore, multiply 1.131 X 1.1 = 1.24 is 10 percent Total Engine-Installation Drag Area: 1.240