Equations 8.19 to 8.23 apply to any of these configurations if i, is taken to mean the incidence angle of the tail’s zero lift line. To pursue this further, we know from Chapter Three that the lift coefficient for a flapped airfoil can be

expressed as

С/ = a(a + tS)

Here, t is the actual value of the flap effectiveness value and equals т obtained from Figure 3.32 multiplied by 17 from Figure 3.33. Thus, referring to the tail configuration of Figure 8.7b, if the elevator is deflected downward through the angle 8e, the incidence angle of the zero lift line is decreased by the amount t 8e, If ihS denotes the incidence angle of the fixed horizontal stabilizer, then the incidence angle of the tail zero lift line will be

it = ihs — t 8e (8.24)

The coefficients CM, and Cl, then become

дСм _ дСм d 8e dit d 8e dit



Using Equations 8.22, 8.24, and the above expressions for Cm, and CLl results in


Thus, as a function of CL, Se has the same form as it, except that the slope of Se versus Cl will be negative, since the positive rotation of the elevator is opposite to that for the incidence angle.


Now consider the configuration in Figure 8.7c. Let 4, (which is now variable) and 8e be related by

Using Equation 8.24, i, now becomes

і, = 4,(1 – rke)

This is identical to Equation 8.22, except for the factor 1/(1 – rk3). By varying ke, one is able to alter the rate of change of the tail incidence angle with CL – Usually a negative value of ke is used to make the tail more effective for a given displacement. This increases the tail lift curve slope since, for the linked elevator,

a( 1 – тке)

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