By John M. Campbell
Classic WWII softcover
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Extra resources for P-51 Mustang Nose Art Gallery
26) - The rotor i is assumed to have a moment of inertia IR; about its own spin axis. _ _ " ---<~ Angular momentum of airplane .. Chapter 1 with rotors fixed. 30c) ORIENTATION OF THE AIRPLANE RELATIVE TO THE EARTH FIXED COORDINATE SYSTEM X'Y'Z' .. ~ To define the orientation of an airplane relative to theeartlrfixed coordinate system X'Y'Z' it suffices to define the orientation of its body-fixed axis system XYZ. 1 shows the two axis systems without defining their interrelation. 5 show&axis system X'Y'Z' translated parallel to itself until its origin coincides with the center of mass, point P on the airplane.
3 CASE 3: EQUATIONS QF MOTlQN FOR STEADY SYl\QJETRICAL PULL-UP ',. 65) are used to study airplane controllability problems in the following conditions: * Symmetrical pull-up flight with all engines operating * Symmetrical pull-up flight with one or more engines inoperative * Ability to perform pull-up flight with certaiil failed systems Applications are disc~ssed in Chapter 4. 9 . S; V = VI + u ,. 68b) These substitutions are referred to as the 'Perturbation Substitutions'. At this stage, the magnitude of these perturbations is quite arbitrary!
By a process of elimination of variables it is also possible to think of these equations as a set of six differential equations of motion in six variables: either U, V, W, P, Q and R or U, V, W, qt, 9 and Ill. In either case, general solutions to the equations can be obtained only by numerical integration. However, from an airplane design and from a handling qualities viewpoint there are two special flight conditions for which solutions of these equations are of primary interest: 1. Steady state flight conditions 2.