# Estimation of Aerodynamic Hinge Moments

Reference 8.3, similar to Reference 5.5, is a comprehensive collection of data relating to aerodynamics, structures, and performance. If one requires an extensive treatment of the effects of airfoil thickness, aerodynamic balance, trailing edge angle, and other geometric parameters on the hinge moment coefficient, this reference should be consulted. The many geometric features that affect the aerodynamic performance of an elevator are pictured in Figure

8.10. These are all considered to some extent by the reference.

For illustrative purposes, a limited amount of data is presented here in Figures 8.11 to 8.15, based on Reference 8.2 and also Reference 8.3. Figures

(J) Aerodynamic balance, balance ratio, BR

(б) Trailing edge bevel

(6) Control horn balance

(7) Spanwise extent of elevator

(5) Total tail aspect ratio and taper ratio (¥) Ratio of ce to c

<b)

 Figure 8.13 Rate of change of elevator hinge moment coefficient with trim tab angle.

8.11 and 8.12 present factors kx and k2, from which b{ and b2 in Equation 8.37 can be obtained. These curves actually represent deviations from a norm defined by the following factors.

1. 10% thick, symmetrical 2-D airfoil.

2. The ratio of elevator chord-to-airfoil chord (cjc) equals 0.3.

3. No aerodynamic balance.

4. A round nose on the elevator.

Each curve in these figures represents the effect of varying one parameter while keeping the others at their nominal value. For the nominal case,

b = —0.55 b2=- 0.89

Thus,

b,.-OMk0y(LjuBR)kt{L)

b2 = -o. m2(^y2(ty2(BR)k2fy

For example, suppose the following is given for a horizontal tail.

b.

b

| = ».25 b

BR = 0

The notation is a little confusing, since the subscript t, denoting “tail,” has been dropped but added again to denote “tab.”

For this case, from Figure 8.11,

k2(BR) = 1.0

Ці) = 0.73

Thus, b and b2 are estimated to be

bx = -0.55(1.16X0.49)

= -0.31

b2 = -0.89(1.05X0.73)

= -0.68

The effect of the tab on the hinge moment is obtained from Figure 8.13. For a two-dimensional airfoil,

^=-0.83

к

к = 0.97 b3 = -0.81

Since most trim tabs are located near the midspan of the elevator, the correction for aspect ratio is assumed to be negligible. However, since the tab extends over only 25% of the tailspan, the value of b2 is reduced in propor­tion. Thus,

b2 = -0.20

For this example, it follows that

CH = -0.31a – 0.685, – 0.205,

The angles a, Se and 5, are in radians.

The foregoing relationships assume linear relationships between CH and the angles a, Se, and 8,. As the material relating to flaps in Chapter Three showed earlier, linear aerodynamics holds only up to some combination of flap angle and angle of attack, beyond which flow separation occurs. An estimate of these limits can be obtained from Figure 8.14 (taken from Ref. 8.4). This graph is for a NACA 0009 airfoil having a plain flap and operating at a Reynolds number of 3.41 x Ю6. This value of R is typical for the horizontal tail of a light to medium aircraft at landing speeds.

Figure 8.14 is not applicable to trim tabs. However, the reference notes on conventional control surfaces (elevator with trim tab), a satisfactory maximum for tab deflection exists between the angles of+/-15and +/—20° for

moderate flap deflections. Thus, for a constant tab chord, it is better to use a large-span tab’deflected to a small angle than a short-span tab deflected to a large angle.

The combination of the vertical and horizontal tails on an airplane, that is, its complete tail assembly, is called the empennage. On some airplanes the empennage consists of a vertical tail mounted at each tip of the horizontal tail. These “twin tails” act as end plates to the horizontal tail and effectively increase its aspect ratio. An estimate of this increase can be obtained from Figure 8.15. The effective aspect ratio equals the geometric value of A divided by the factor r. For example, a tail with A = 4.0 would have a lift curve slope of approximately 0.06CJdeg. If end plates having a height-to-span ratio of 0.4 were put on this tail, its effective aspect ratio would increase to 6.7. Thus a, would increase to approximately 0.073, an increase of 22%. Although possibly not as great, one would also expect a similar improvement in the effectiveness of the elevator.