PROBLEM 1(30pts) From AERE355 you might recall that an airplane has longitudinal static stability (positive pitch
stiffness), so long as the dimensionless stability derivative $C_{m_\alpha} < 0$. Consider the AOA stability derivative:
$C_{m_\alpha} = C_{L_{\alpha}}(h - h_{ac}) + C_{m_{\alpha f}} + C_{m_{\alpha r}}$
(1.1)
For the NAVION plane @ sea level, p.400 of Nelson for $h = h_0 = 0.295$ gives: $C_{m_\alpha} = -0.683$, $C_{L_\alpha} = 4.44$, and $h_{ac} = 0.25$.
On p.59 he gives: $C_{m_\alpha} = -1.42$. From these numbers, we have: $C_{m_{\alpha f}} = 0.537$. This number is quite different from the
value 0.12 that he gives on p.60. He claims that 0.12 was arrived at from (2.32) on p.53, along with the information given
on p.61 in Figure 2.17. However, he claims that sum of the elements of the rightmost column in that Figure is 85.1. Using
that sum in (2.32) gives $C_{m_{\alpha f}} = 0.0022$. That actual sum is169.8. Using that sum in (2.32) gives $C_{m_{\alpha f}} = 0.0044$. Clearly,
something is not correct. Assuming that $C_{m_\alpha} = -1.42$ is correct, then the only way that (1.1) can hold is for $C_{m_{\alpha f}} = 0.537$.
We point this out because of the importance of (1.1) in maintaining static stability.
(a)(3pts) Find the value for $h = h_{NP}$, such that $C_{m_\alpha} = 0$ (i.e. the plane has neutral static stability).
Solution:
