Chapter 6: stability and control
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- Figure 6.11 Trim Diagrams for Positive, Neutral, and Negative Static Longitudinal Stability Calculating C
Figure 6.10 Trim Diagram Note that the CMcg vs a curve slope, CM, is constant. This is typical at low angles of attack. The pitching moment coefficient at a = 0 (and CL = 0) is given the symbol Cmo . The angle of attack where CMcg = 0 is the trim angle of attack, e . The subscript e (for equilibrium) is used to denote the trim angle of attack because the subscript t is usually reserved for quantities associated with the horizontal tail. Figure 6.10 immediately makes obvious another requirement for an aircraft with positive longitudinal stability. Since aircraft must produce lift in most cases for equilibrium, only positive absolute angles of attack are useful as trim angles of attack. Since CM < 0 for stability, it follows that  must be greater than 0 if the aircraft is to trim at a useful e . This is not strictly a stability criterion, but it is a required characteristic of aircraft which have positive static longitudinal stability and useful trim angles of attack.
Figure 6.11 shows CMcg vs a curves for aircraft with neutral and negative static longitudinal stability. CM = 0 for neutral stability, and CM > 0 when static stability is negative. Clearly, for an aircraft with neutral static longitudinal stability to have a useful e , CMomust equal zero, and then all values of a are trim angles of attack. Likewise, if the aircraft has negative static stability, CMomust be less than zero for any useful value of e . 
Figure 6.11 Trim Diagrams for Positive, Neutral, and Negative Static Longitudinal Stability Calculating Cmo and CM The methods for calculating the zero-lift pitching moment and moment curve slope for an airplane are based on the methods used in Chapter 4 to calculate the lift of the whole airplane. Figures 6.6 and 6.12 illustrate the typical geometry which must be included in the analysis. 
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