MECHANICS OF FLIGHT I Project no. 2 Aerodynamic Characteristics of the Wing

Transcription

1 MECHANICS OF FLIGHT I Project no. 2 Aerodynamic Characteristics of the Wing Geometry of the wing 1. Take from the airplane's drawing following basic dimensions of the airplane wing (fig. 2.1): wing span b, root chord, tip chord, x N c a x(y) y /2 /2 c(y) x b Fig. 2.1 Geometrical parameters of a wing 2. You need also the wing area S which usually is presented in the technical data set. If not, calculate it based on the wing dimensions. 3. Calculate (see fig. 2.1): wing aspect ratio wing taper ratio = b2 S, =, mean aerodynamic chord (MAC) c a, and coordinate of the tip of mean aerodynamic chord x N : Mechanics of Flight 1 / 5

2 Note: for straight, moderate sweep tapered wings following formulas can be used: c a = , x n = b tg x where x 0 denotes the sweep angle of the leading edge of the wing. Aerodynamic characteristics of the airfoil and the wing 1. Let assume that the wing of the airplane was designed using one of NACA wing sections published in NACA Report 824 ( also available on home page ). 2. From the technical description of the airplane take the minimum speed of the aircraft V S 1 (stall speed). If this speed is not in the data set then calculate it using formula: V S 1= 2 m g S C Lmax where: m total take-off mass of the airplane, g - normal Earth acceleration, - normal air density for altitude = 0 m STD, S - wing area, C L max maximum of lift coefficient, see airfoil data in NACA Report Using V S1 calculate Reynold number Re 1 for the wing where 0 = m 2 0 m STD. s Re 1 = V S1 c a 0 is the kinematic viscosity coefficient of the air for flight altitude 4. Take from the NACA Report 824 aerodynamic characteristics C Dꝏ, C Lꝏ of chosen airfoil as a function of the airfoil angle of attack. Use data for the Reynolds number closest to calculated Re 1 (ie. if you obtain Re 1 =5,28*10 6 then use values of C Dꝏ and C Lꝏ for Re=6*10 6 ). Take values of aerodynamic center position x a.c. and z a.c., the value of pitching moment coefficient (referenced to aerodynamic center) C ma.c., and calculate very important aerodynamic coefficient - airfoil lift slope a - defined as a = d C L d It can be easy done using standard linear approximation (or linear regression) function of a hand-held scientific calculator or a PC spreadsheet (ie. the function REGLINP in Open Office Calc). Please exclude from this calculation the non-linear part of the function C L close to C L min. and C L max. Remark Due to convenience of future calculations the airfoil data should be collected as a function of lift coefficient C Lꝏ rather than angle of attack α ꝏ, see table 2.1 bellow. Mechanics of Flight 2 / 5

3 1 2 Tabe Aerodynamic Characteristics of the Wing airfoil type:... wig area:... m 2 wing aspect ratio:... Airfoil Wing C Lꝏ α ꝏ C Dꝏ 1 ΔC Dꝏ C ' Dꝏ 2 α i α C D i C`D w n 5. If the value of Re 1 is less than 10*10 6 (ie. Re 1 = 5.28*10 6 is rather far from ten millions) then compute the correction of the airfoil drag coefficient C D due to changes of Reynolds number for high speed regimes of flight using formulas: 0.11 Re C D min2 =C D min C D C L = C D min2 C D min1 1 C L C L max and compute final value of the wing section drag coefficient: ' C D 2 =C D 1 C D C L Assume that for this calculations as well as in future computations of wing and airplane characteristics, the independent variable is C L, not the angle of attack (see remark on previous page). Please note that for the negative region of C L (ie. from 0.0 up to -1.1) use in above expression C L min instead of C L max (i.e ). Please note that values of C D are negative and are equal to zero for C L min and C L max. 6. Compute Glauert's correctional coefficients, as follows: Mechanics of Flight 3 / 5

4 3 = where 25 is the wing quater-chord line sweep angle, in degrees. Please note that: in above expressions lift slope a units should be 1/radian, not 1/degree! for typical rectangular and straight tapered wings and for elliptic wing (ie. Supermarine Spitfire) = = Calculate induced angle of attack i and induced drag coefficient C Di : i = C L 1, 2 C D i = C L Now you can calculate aerodynamic characteristics for the wing: C L =f 1 w,c D =f 2 C L : the wing angle of attack as a sum of and i : w = i, total drag coefficient as the sum: ' ' C Dtech C Di. C Dw =C D 2 Second component of the sum above, C Dtech, is called as drag increment due to manufacturing (technological) effects on a real wing of an airplane. It can be estimated as: 0.15 C D 2 min for all-metal or fiberglass composite wings 0.50 C D 2 min for wings of old-style airplanes made of wood and fabric (World War I and ). 9. Results of the calculations have to be shown on graphs consists of C L and C D both for airfoil (with Re effect) and for the wing. Mechanics of Flight 4 / 5

5 Fig Lift and drag characteristics of the wing Notes for the figure 2.2: C x == C D drag coefficient, C z == C L lift coefficient; the symbol denotes data valid for wing section (airfoil), the subscript kr by angle of attack symbol is equivalent to cr (critical); lower values of C L min and C L max for the wing you can see on the graph were obtained from more sophisticated method taking into account effects of variable distribution of angle of attack and lift force along wing span; simple method described in this paper does not "see" all these effects and because of this for our characteristics always C L min ꝏ = C L min wing as well as C L max ꝏ = C L max wing. [end-of-text] Mechanics of Flight 5 / 5