Lecture 3 - Illinois Institute of Technology
Lecture 3 - Illinois Institute of Technology
Lecture 3 - Illinois Institute of Technology
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Static Longitudinal Stability<br />
Characteristic Equation<br />
The displacement dynamics are<br />
d 2<br />
dt 2∆α(t) = C QSl<br />
Mα<br />
I ∆α(t)<br />
Thus the characteristic equation is s 2 − CMαQSl<br />
I<br />
, which has roots at<br />
√<br />
CMα QSl<br />
s 1,2 = ± 1 2<br />
I<br />
• We want to know if any roots have positive real part.<br />
Since Q, S, l and I are all positive, there are two cases.<br />
Case 1:<br />
Case 2:<br />
• C Mα ≥ 0<br />
• C Mα < 0<br />
Aircraft is Unstable! Aircraft is Stable, but oscillates.<br />
M. Peet <strong>Lecture</strong> 3: Nomenclature 26 / 36
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