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LONGITUDINAL CONTROL
Control Position as a Function of Lift Coefficient
According to Equation 8.7, the pitching moment coefficient can be written as a linear function of a.
См — Сщ + Cmjx
From Equation 8.10,
Cl — Cl„oc + Cii’t
where CLi = – r),a, S,IS. Substituting for a in the equation for CM and setting the result equal to zero gives
0 — Сщ + (Cl — Сції)
Сщ is given by Equation 8.5.
All-Movable Tail
If we now consider the tail incidence angle, it, to be a variable, we can write
Сщ = Смас + Сщі{ (8.21)
where CMi = r),VHa,.
Substitution of Equation 8.21 into Equation 8.20 results in the following equation for the trim tail incidence angle as a function of the lift coefficient.
Cm Cl + ClCm^ CmPl„ ~ СмСц
Сма is negative for a statically stable airplane and CL) is always negative. См, с is usually negative and CLa is always positive. It therefore follows, if
1,1 c > (h„ – h), that i, as a function of CL is of the form
i, — ACl + В
where A and В are positive constants. Notice that
dit _________ Сма_____
dCL (CMiCLa – CMCL) < J
This allows one to determine experimentally the neutral point for a given airplane. This is done by measuring i, as a function of Cl for different center-of-gravity locations. The slopes of the experimentally determined plots of i, versus Cl are then plotted as a function of center of gravity and are extrapolated to the value of the center of gravity that gives a zero slope. From Equation 8.23, CM„ for this center-of-gravity position is obviously zero. From Equation 8.13, it then follows that this center-of-gravity position corresponds to the neutral point.
The foregoing material applies strictly only to aircraft with all-movable tails. There are two variations on this configuration. The first is the fixed horizontal stabilizer-movable elevator configuration. The other is the movable horizontal stabilizer with a linked elevator (or trim tab). These three configurations are pictured in Figure 8.7. A variant on the configuration of Figure 8.7c is to input the control directly to the tab. Deflection of the tab produces a moment that rotates the rest of the tail. This configuration is referred to as a flying tail. Some persons refer to any all-movable tail as a flying tail.
