Glider Equilibrium

Away from high lift, a linear model of the glider in terms of the angle of incidence a (deg) and tail setting angle tt (deg) is given by:

CL (a, tt) = 0.1a + 0.01tt + 0.7
См,0(а, tt) = -0.02a – 0.01tt – 0.13

15.3.3.1 Definition

The aerodynamic center is the point about which the moment is independent of incidence.

15.3.3.2 Aerodynamic Center

As seen in class, the location of the aerodynamic center satisfies

^ ^ = 0.02/0.1 = 0.2

lref d a d a

hence xac = 0.3 m.

15.3.3.3 Moment at Aerodynamic Center

Using the transfer of moment formula one finds:

См, ac — См, о + ■— Cl — —0.02a — 0.01tt — 0.13 + -— (0.1a + 0.01tt + 0.7)

lref I ref

Using the result for xac this simplifies to:

См, ас — —0.008tt + 0.01

As expected, it is independent of a.

15.3.3.4 Moment at Center of Gravity

Using the transfer of moment formula one finds:
0.004a – 0.00841; – 0.018

The airplane is statically stable because the slope dCfacg < 0.

15.3.3.5 Equilibrium

At equilibrium, CM, cg —

a(tt) — 2.1t; 4.5

15.4 Solution to Problem 4