Flight Dynamics Research Papers - Academia.edu (original) (raw)

Almost all of the research on ight dynamics of unguided missiles with wraparound ns is based on linear system models. This is in sharp contrast with the research on ight dynamics of planar nned unguided missiles, which has focused mostly on nonlinear problems since the 1950s. A general fth-order nonlinear autonomousdynamicsystem model is developed for unguided missiles with four wraparound ns. Aerodynamic characteristics of a basic planar nner and a basic wraparound nner are obtained by using a panel code, Missile DATCOM empirical database, and published experimental data. Effects of nonlinear aerodynamic terms on location and stability of equilibrium points of a basic planar nner and a basic wraparound nner are investigated. It is shown that wraparound and planar nned unguided missiles have different aerodynamic and ight dynamic characteristics. Nomenclature a D = quadratic drag force coeff cient a F , b F = cubic transverse static force coef cients a t , b t = cubic transverse static moment coeff cients a 1 = freestream speed of sound, m/s C D = drag force coef cient C D0 = drag force coef cient for d = 0 C F = C Y + iC Z C l , C m , C n = aerodynamic moment coef cients C lp = roll damping moment stability derivative, [@C l / @(pk / 2v C)] C l0 = induced roll moment coeff cient C ld f = roll moment stability derivative with respect to n cant C M0 = p (C 2 m 0 + C 2 n0) C mq , C mr = transverse damping moment stability derivatives C m 0 , C n0 = asymmetry moment coeff cients C m a , C mb = transverse static moment stability derivatives C m a p , C m b p = Magnus moment stability derivatives C m Ç a , C m Çb = transverse lag moment stability derivatives C m d 2 c = transverse induced moment coef cient C t = C m + iC n C X , C Y , C Z = aerodynamic force coeff cients C Y0 , C Z0 = asymmetry force coeff cients C Zq , C Zr = transverse damping force stability derivatives C Za , C Z b = static force stability derivatives C Za p , C Zb p = Magnus force stability derivatives C Z Ça , C Z Çb = transverse lag force stability derivatives C Z d 2 c = transverse induced force coef cient c = p [¡ M 0 / (1 ¡ r)] c F , d F = cubic transverse damping force coef cients c t , d t = cubic transverse damping moment coeff cients D m = missile diameter, m e F , f F = cubic Magnus force coef cients e t , f t = cubic Magnus moment coef cients F b = body-xed reference frame g 2 + ig 3 = transverse components of gravitational acceleration vector, m/s 2 I a , I t = axial and transverse moments of inertia, kg m 2 k a , k t = nondimensional axial and transverse radii of gyration M 1 = freestream Mach number m = mass, kg p, q, r = rotational velocity components, rad/s r C = nondimensional transverse distance of center of mass from geometrical center of missile cross section S m = reference area, (p / 4)k 2 , m 2 s = nondimensional distance variable, s = 1 k t t0 v C dt t = time, s u, v, w = translational velocity components, m/s u (b) 1, 2,3 = unit vectors of F b v C = speed of missile, p (u 2 + v 2 + w 2), m/s x cm = center of mass location from missile nose tip, m a = w / v C b = v / v C d f = n cant angle f = n / d TR = d s e ic k = reference length, missile diameter, D m , m l = (qk / 2v C) + i (rk / 2v C) = e e ig n = b + i a = d e ic q 1 = freestream density, kg/m 3 r = I a / I t s = nondimensional distance variable; Eq. (48) u M = tan ¡ 1 (C n0 / C m0) w , h , u = Euler yaw, pitch, roll angles Superscripts (I) = imaginary component (R) = real component T = matrix transpose ¤ = multiplication with q 1 S m k / 2m ! = division by c ¡ = complex conjugate ¢ = differentiation with respect to t or s