Lecture 9 : Understanding MIL-F-8785COr the flying qualities of piloted airplanes G. Leng, Flight Dynamics, Stability & Control 1.0 The concept of a reduced order approximation 1.1 Each stable real eigenvalue define a reduced (first) order approximation of the form: x’ T : + (1/T) x = 0 time constant The real eigenvalue is of the form: G. Leng, Flight Dynamics, Stability & Control 1 : 1st order system x(t)/x(0) = exp(-t/T) t/T G. Flight Dynamics. Leng. Stability & Control .Figure 1. 2 Each complex pair of eigenvalues define a reduced (second) order approximation of the form: x’’ + (2) x’ + 2 x : : damping ratio 01 = 0 undamped natural frequency 2. The complex pair of eigenvalues is of the form: G. Flight Dynamics. Leng.1. Stability & Control . Flight Dynamics. Leng.2 : 2nd order system x(t)/x(0) = exp[.Fig 1.() t ] cos(dt) dt/ 2 G. Stability & Control . the damping ratio and the undamped natural frequency for a complex eigenvalue can be deduced as follows: j x (1 . Stability & Control . G.2 ) . Flight Dynamics. Leng.In the complex plane. 3. G.Important note 1. 2. Leng. Flight Dynamics. Eigenvalues with the same damping ratio make the same angle with the imaginary axis. Eigenvalues with the same natural frequency are at the same distance from the origin. MIL-F-8785C specifies flying qualities using these concepts. Stability & Control . . Flight Dynamics. Leng.2. Indicate these boundaries on the complex plane G.0 MIL-F-8785C requirement for phugoid mode Recall that the phugoid mode is marginally stable or unstable.. Stability & Control . Flight Dynamics.1 MIL-F-8785C. Leng. Stability & Control .2. Section 1.5 : Levels of Flying Qualities G. Stability & Control .2 MIL-F-8785C boundaries for phugoid mode The angle of the constant damping with the imaginary axis is = = G. Flight Dynamics.2. Leng. 25 0. Leng.15 angle with imaginary axis (o) G.0 MIL-F-8785C : Short period damping requirements Note damping ratio 0.3.35 0. Flight Dynamics. Stability & Control . no precise tracking. ex : CR . LO . Stability & Control .4 Flight Phase Categories Cat A : non terminal flight phase. gradual maneuvers. ex: CO .takeoff. L . D .cruise. Section 1. may need precise flight path control. Leng.landing G.climb. Flight Dynamics. rapid maneuvering.loiter Cat C : terminal flight phases.air to air combat. CL .3. GA ground attack Cat B : non terminal flight phase .descent. ex : TO .1 MIL-F-8785C. accurate flight path control. precision tracking. precise flight path control. gradual maneuvers. 0 MIL-F-8785C 3.1 Dutch roll requirements G. Leng. Flight Dynamics.1.4.3. Stability & Control . 1 MIL-F-8785C 1. Leng.3 Classification of Airplanes G.4. Flight Dynamics. Stability & Control . The most demanding class of airplanes… G. Stability & Control . Leng. Flight Dynamics. 0 MIL-F-8785C 3.1. Leng. Stability & Control .3.5. Flight Dynamics.2 Roll mode requirements G. .3.0 MIL-F-8785C 3.1.. G. Flight Dynamics. Leng.6.3 Spiral mode requirements Recall that the spiral mode affects the roll (bank) angle. Stability & Control . 0 MIL-F-8785C 3. Flight Dynamics.4.1 Roll performance (class IV airplanes) G.7. Stability & Control . Leng.1.3. 3.1 MIL-F-8785C 3. Stability & Control .4.1 Speed ranges for roll performance Vmax . Flight Dynamics. Leng.7. Vmin : maximum (minimum) service speed Vo : above as adjusted by a factor in Table 1 G. Leng. Flight Dynamics.Question : Is there life after MIL-F-8785C ? G. Stability & Control .