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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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