All airplane has the following stability and inertia characteristics: W = 564 00

Question

All airplane has the following stability and inertia characteristics: W = 564 000 lb C_L = 1.11 l_x = 13.7 Times 10^6 slug middot ft^2 C_D = 0.102 I_y = 30.5 Times 10^6 slug middot ft^2 C_L_u = 5.7 rad^-1 I_z = 43.1 Times 10^6 slug middot ft^2 C_D_n = 0.66 rad^-1 h = sea level C_m_a = -1.26 rad^-1 S = 5500 ft^2 C_m_a = -3.2 rad^-1 b = 195.68 ft C_m_g = -20.8 rad^-1 c = 27.3 ft V = 280 ft/s Find the frequency and damping ratios of the short- and long-period modes. Find the time to half-amplitude for each mode. Discuss the influence of the coefficients C_m_q and C_m_a on the longitudinal motion.

Explanation / Answer

a) frequencies   =   2 * 3.14/0.693 = 9.062 Hz         (short term)

                           =   2 * 3.14/0.314 = 20 Hz         (long term)

   damping ratio =   0.524   (short term)

                           = 0.456   (long term)

b)    time to half amplitude =   20/52 = 0.384 sec            (short term)

                                           = 20/66   =   0.303 sec            ( long term)

c)    damping ratio of longitudinal motion increases with the increase in value of coefficients .

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