Home Engineering Small Unmanned Fixed-Wing Aircraft Design. A Practical Approach

# Longitudinal Stability

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 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 [11] (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.

 Name Long name/definition Typical value Unit Awing Total wing area 1.54 m2 AR Aspect ratio (span~2/area) 9.00 — Thick Aerodynamic mean thickness 62.1 mm Atail Tailplane area 226 222 2 mm2 Afin Fin area 203 600 2 mm2 y_ tail_ boom Horizontal position of tail booms 271.5 mm Span_ tail Tailplane span 951.3 mm Chord_ tail Tailplane mean chord 237.8 mm Height_ fin Fin height (or semispan) for two fins 390.8 mm Chord_ fin Fin mean chord 260.5 mm Vmax_ C Maximum cruise speed 30.0 m/s x_ main_ spar Long position of main spar 0.0 mm x_ fnt_ bkhd Long position of front bulkhead 240.3 mm x_ tail_ spar Long position of tailplane spar -1127.9 mm x_ rear_ bkhd Long position of rear bulkhead -200 mm x_ mid_ bkhd Long position of middle bulkhead 20.2 mm Depth_ Fuse Fuselage depth 250 mm Width_ Fuse Fuselage width 190 mm Len_ Nose Nose length (forward of front bulkhead) 200 mm Len_ Engine Length of engine 125 mm Mengine Engine mass 2.072 kg Dprop Propeller diameter 494 mm DTop Design topology 3 —

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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