21 If the slope of the C versus CL curve is 015 and the pitc

2.1 If the slope of the C versus C_L curve is -0.15 and the pitching moment at zero lift is equal to 0.08, determine the trim lift coefficient. If the center of gravity of the plane is located at X_cg /c=0.3, determine the stick fixed neutral point.

2.6 If the airplane in Example Problem 2.1 has the following hinge moment characteristics, find stick free neutral point.

C_L,w= 0.09/deg                C_h= -0.03/deg     Ch_{= -0.005/deg}              V_h=0.4

C_Lt = 0.08/deg         C_h0 =0.0          S_e/S_t=0.35        de/d=0.4

2.8 If the control characteristics of the elevator used in Example Problem 2.1 are as given below, determine the forward most limit on the center of gravity travel so that the airplane can be controlled during landing i.e. at C_Lmax . Neglect ground effect on the airplane’s aerodynamic characteristics.

C_me=-1.03/rad                                          _emax= +10 deg

-20 deg C_Lmax=1.4

Solution

Solution for problem 2.1

The trim lift coefficient is as follows

using an equation, Cm cg = Cm |CL=0 + (dCm / dCL) CL trim

where, Cm cg = 0

CLtrim = - Cm |CL=0 / dCm / dCL { eq.1 }

where, Cm |CL=0 = 0.08 and dCm / dCL = - 0.15

inserting these values in eq.1,

CLtrim = (0.08) / (0.15)

CLtrim = 0.53

The stick fixed neutral point is thus found

using an equation, dCm / dCL = [(Xcg / \\bar{c}) - (XNP / \\bar{c})] { eq.2 }

where, Xcg / \\bar{c} = 0.3 and dCm / dCL = - 0.15

inserting the values in eq.2,

- (0.15) = [(0.3) - (XNP / \\bar{c})]

XNP / \\bar{c} = (0.15) + (0.3)

XNP / \\bar{c} = 0.45