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 = L_{CoG}/Chord + ((L_{CoG} - ^/Chord) X (A^/A wing)
X(1 + 2/(3AR/4))/(1 + 2/(3ARail/4)) X (1 - й_{ц} /d_{a})
where L_{CoG} is the longitudinal position of the center of gravity forward (positive) of the main wing quarter chord point, L_{tail} 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 d_{n}/d_{a} can be estimated from data provided in Raymer [11] (p. 482) and depends on wing aspect ratio (span^{2}/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 |
m^{2} |
AR |
Aspect ratio (span~2/area) |
9.00 |
— |
Thick |
Aerodynamic mean thickness |
62.1 |
mm |
Atail |
Tailplane area |
226 222 |
_{2} _{mm}^{2} |
Afin |
Fin area |
203 600 |
_{2} _{mm}^{2} |
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.