# Find the neutral point and static margin of an airplane.

Find the neutral point and static margin of an airplane if the location of the aerodynamic  center is at $$0.3$$ chord length, the location of center of gravity is at $$0.38$$ chord length, tail volume ratio is $$0.352$$, tail lift slope is $$0.12$$ per degree, lift slope of the wing body is $$0.085$$ per degree and $$\frac{{\partial \varepsilon }}{{\partial \alpha }}$$ from wind tunnel data is $$0.36$$. Here, $$\varepsilon$$ is the down wash angle, and $$\alpha$$ is the angle of attack.

Static margin is the distance between the center of gravity and neutral point of an aircraft. It is expressed as percentage in terms of mean aerodynamic chord of the wing. Neutral point of an aircraft is the point where aircraft is neutrally stable, when it is disturbed from its trim angle of attack longitudinally.

Neutral point is given as

${h_n} = {h_{ac,wb}} + {V_H}\frac{{{a_t}}}{a}\left( {1 – \frac{{\partial \varepsilon }}{{\partial \alpha }}} \right)$

$\Rightarrow {h_n} = 0.3 + \left( {0.352} \right)\frac{{0.12}}{{0.085}}\left( {1 – 0.36} \right)$

$\Rightarrow {h_n} = 0.3 + \left( {0.352} \right)\left( {1.41} \right)\left( {0.64} \right) = 0.618$

Static margin, $${h_n} – h = 0.618 – 0.38 = 0.238\,{\rm{chord}}\,{\rm{length}}$$