Home Engineering Small Unmanned Fixed-Wing Aircraft Design. A Practical Approach
Static longitudinal (pitch) stability calculations are always needed, which require suitable downwash data for the elevator surfaces. Here we take the main wing quarter chord point as the datum and center of lift of the main wing:
static margin = LCoG/Chord + ((LCoG - ^/Chord) X (A^/A wing)
X(1 + 2/(3AR/4))/(1 + 2/(3ARail/4)) X (1 - йц /da)
where LCoG is the longitudinal position of the center of gravity forward (positive) of the main wing quarter chord point, Ltail is the longitudinal position of the tail-plane quarter chord behind (negative) the main wing quarter chord point. The value of 2 used twice is from theoretically perfect inviscid two-dimensional thin airfoil theory of 2ж for the lift curve slope - in practice, a value of 1.9 is more likely. The value of 3/4 used twice is the Oswald span efficiency and this is on the pessimistic side, 0.85 might be more likely. However, since both the perfect slope value and the span efficiency are applied to both wing and tail terms, the errors tend to cancel; if the main wing and tail-plane aspect ratios are equal they cancel completely. The terms essentially penalize low-aspect-ratio tail-planes slightly. Also in the downwash term dn/da can be estimated from data provided in Raymer  (p. 482) and depends on wing aspect ratio (span2/area); wing semispan (assuming a rectangular wing); vertical position of tailplane compared to the main wing; longitudinal position of tail-plane quarter chord point behind wing quarter chord point; tail aspect ratio; r =tail-plane longitudinal position/semi-span; m =tail-plane vertical position/semispan. We leave consideration of
Table 11.4 Variables that might be used to estimate UAV weights.
dynamic stability until more detailed analysis is to take place, and instead rely on sensible tail volume coefficients to ensure a reasonable starting point has been chosen.
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