Question 7 (Total 10 marks) (a) The longitudinal dynamics of an aircraft at 15,000 ft at Mach 0.3 (U₁ = 335.00 ft/s) due to elevator input is considered. The equation of

motion for the level flight in the state-space is given by : (b) (1) Additionally, the pitch response to the elevator is given by : (ii) -0.0353 0.0046 0 -0.2309 -0.545 309.00 0.00185 -0.00767 -0.395 0 1 Gen (ii) -31.34 -27 0 0.00132 9 -4.51576 W 0 0 5.63 -23.8 (1) (2) (3) 8(s) -4.516 (s-0.008) (s +0.506) n (s) (s²+0.033s +0.02) (s² +0.902s +2.666) Analyse the longitudinal stability of the aircraft by evaluating the frequency and damping factor of the phugoid and short period modes. Appraise the steady state pitch response due a unit step elevator input. (iii) Analyse the time response graph of u and w together on the same graph to analyse the short period. Do likewise for the phugoid mode. From the graphs evaluate the following parameters for phugoid mode. Period of oscillation Time to damp to ½ amplitude Cycle to damp to ½ amplitude Using the time responses drawn in Part (a)(iii) above, (1) describe the key characteristic and differences between phugoid and short period modes. Assume a step elevator input is applied. Explain why the aircraft response (after 10 seconds or more) is very much like phugoid