A plan view of Boeing B747200 is depicted below with some ge

A plan view of Boeing B747-200 is depicted below with some geometric information and the eg location. Evaluate stick-fixed longitudinal static stability for low-altitude cruise, and determine the static margins. Assume that (i) the tail efficiency is nearly unity; (ii) the initial setting angle for the tail is 3 degree; and (iii) the wing platform area (5, 500ft^2)and the eg location remain the same. Provide your answer in SI units, and pay attention in the lift slope units (1/rad or 1/deg).

Solution

To determine the stick fixed static longitudinal stability of an airplane it is necessary to check for change in Coefficient of moment of gravity due to change in trim angle of the elevator.

CM_{,cg e},

where,

C_M,cg - change in moment coefficient of gravity and,

_e - change in trim angle

To determine, C_M,cg consider the relation of coefficient of lift over trim angle,

C_{M,cg e =} -V_h(C_{L e})

which gives C_{M,cg   =} -V_h(C_{L e}) _e

_{substitute the values in the above equation,}

C_{M,cg = - 214.5 (0.768) 2.5 x 0.0174}

CM,cg = - 7.166 rad. m / sec

The negative sign denotes positive longitudinal stability

V_{h -} horizontal velocity, C_{L e} - slope of lift curve

Rearrange the relation to determine C_M,cg