Projeto Aerodinâmico Aplicado à Aeromodelos

...lift curve slope has been approximated to an (OL 8( on Figure 1. The section lift data needs to be corrected for 3D, finite wing effects. The low speed unswept finite wing lift curve slope is estimated as follows for AR 3 (see Reference 1, page 264 or Reference 2, page 8): dCL/d( CL( Cl( AR/(2 + (4 + AR2)) where Cl( section lift curve slope (typically 2( per radian) and AR wing aspect ratio (span)2/wing area Figure 1 shows the construction of a 3D AR 10 wing lift curve using the 2D (OL and the section lift curve slope. For large AR (ie AR 5) low speed, unswept wings, the wing CLmax ( 0.9 Clmax 1.67 (Reference 2, page 9-15). The 3D (stall is approximated using the 2D stall characteristics. The section drag polar data is used to estimate the following wing data: CLmin ( Clmin 0.7 CDmin ( Cdmin 0.0145 and the wing viscous drag-due-to-lift factor K 0.0137 as shown on Figure 2. Figure 2 Viscous drag-due-to-lift factor for the LMN-1 airfoil V ESTIMATING MODEL DRAG As mentioned earlier we will approximate the aircraft drag polar by the expression CD CDmin + (K + K)( CL CLmin)2 The CDmin term is primarily skin friction and the data on Figure 3 will be used in its estimation. The boundary layer can be one of three types: laminar, turbulent or separated. We eliminate the separated BL (except in the case of stall) by careful design. For Re 105 the BL is most likely laminar. At a Re 5x105 the BL is tending to transition to turbulent with a marked increase in skin friction. By Re 106 the BL is usually fully turbulent. Notice that our model Re is right in the transition region shown on Figure 3. Figure 3 Skin friction coefficient versus Reynolds Number We will demonstrate the methodology by estimating the drag of a notional R/C model with the following characteristics: Configuration: Fuselage/payload pod with a boom holding a horizontal and vertical tail. Fuselage/boom length 84 in, Fuselage length 25 in, Fuselage width 5 in Wing AR 10, Wing taper 0.5 Wing area SRef 1440 in2 10 ft2 Wing span 120 in Landing gear: tricycle Item Planform Wetted Reference Area Area Length (in2) (in2) (in) Fuselage 151 605 25 Engine /mount 15 100 na Horiz Tail 126 252 7 (MAC) Tail Boom 14 28 48 + fuselage Landing gear 12 24 na Wing (exposed) 1360 2720 12.4 (MAC) Vert Tail 0 189 9.8 (MAC) Fuselage Re 625,000, assume BL is turbulent Fuselage CDmin FF Cf SWet/SRef Where FF is a form factor (Reference 1, pg 281 or Reference 2, page 11-21) representing a pressure drag contribution. Form factors are empirically based and can be replaced with CFD or wind tunnel data. FF 1 + 60/(FR)3 + 0.0025 FR 1.49 FR fuselage fineness ratio fuselage length/diameter 25/5 5 Fuselage CDmin 0.0032 Wing Re 310,000 Wing CDmin FF Cf SWet/SRef Where FF [1 + L(t/c) + 100(t/c)4] R and L is the airfoil thickness location parameter (L 1.2 for the max t/c located at ( 0.3c and L 2.0 for the max t/c 0.3c)and R is the lifting surface correlation parameter. Thus L 1.2 and R is determined from Reference 1, page 281 or Reference 2, page 11-13 for a low speed, unswept wing to be 1.05. Since a wing Re 310,000 could be either laminar or turbulent, we will calculate the minimum drag coefficient both ways and compare with the section Cdmin 0.0145 (from Figure 1). If the BL is laminar, the wing Cf 0.00239 and wing CDmin 0.0057. If the BL is turbulent, the wing Cf 0.0059 and wing CDmin 0.014. Thus the wing boundary layer must be turbulent and we will use wing CDmin 0.0145. Horizontal Tail The Re 175,000, therefore well assume the BL is laminar. The tail (both horizontal and vertical) CDmin equation is the same as for the wing. For a t/c 0.09 airfoil with L 1.2 and R 1.05, the horiz tail CDmin 0.00046. Vertical Tail The Re 245,000, therefore assume the BL is laminar. For a t/c 0.09 airfoil with L 1.2 and R 1.05, the vert tail CDmin 0.00039. Tail Boom The reference length for the tail boom is the fuselage length plus the boom length since the BL will start on the fuselage and continue onto the boom. Thus the tail boom Re 1.825x106 and the BL is turbulent. Thus Tail Boom CDmin 1.05 Cf SWet/SRef 0.00009 Where the factor 1.05 accounts for tail/boom interference drag. Landing Gear From Reference 3, page 13.14 a single strut and wheel (4 inch diameter, 0.5 inch wide) has a CDmin 1.01 based upon frontal area. Thus the tricycle gear CDmin (3)(1.01)(2)/1440 0.0042. Engine From Reference 3, page 13.4, Figure 13 the engine CDmin 0.34 based upon frontal area. For a 6 in2 frontal area the engine CDmin 0.002. Total CDmin The total CDmin is the sum of all the components, thus total model CDmin 0.02484 Total Drag Expression Assuming a wing efficiency e 0.95 gives an induced drag factor K 1/(( AR e) 0.0335. Notice that the often omitted viscous drag factor K 0.0137 is 40% of the induced drag factor. The total drag expression is CD 0.02484 + 0.0472(CL 0.7)2 The untrimmed (neglecting the horizontal tail drag-due-to lift) model drag polar and L/D are shown on Figure 4. Figure 4 Notional model aircraft total d...

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