High-aspect-ratio wings

Wing lift coefficient

Section 1. AERODYNAMICS OF LIFTING SURFACES

Topic 4. The aerodynamic characteristics of
Wings in a flow of incompressible fluid

The main aerodynamic characteristics of an aircraft moving with Mach numbers are considered in this lecture.

The dependence is linear on the segment of attached flow (Fig. 4.1).

In general . (4.1)

The angle of zero lift is determined by the airfoil shape and wing twist. For a flat wing

, degree. (4.2)

Fig. 4.1. Dependence of the lift coefficient on the angle of attack

Geometrical twist of a wing causes changing of by the value , which can be approximately estimated for the unswept wing by the formula

.

If the wing is swept then the absolute value of should be reduced by size .

The derivative depends on aspect ratio and sweep angle , influence of taper on derivative size is weak. The derivative does not depend on wing twist. It is possible to offer the following approximate formula for calculation of value of :

, (4.3)

Here the parameter takes into account the wing plan form and depends on , , . It is possible to assume in the first approximation (in general ),

. (4.4)

Parameter is a derivative for the airfoil (wing with ) and is calculated by the formula

. (4.5)

It follows from the formula, that at and if in addition , then .

It is also possible to use the following formula for calculation :

. (4.6)

Here - ratio of half-perimeter of the wing outline in the plan to span (Fig. 4.2). The significance of the last formula - its universality and capability to apply to any plan forms and aspect ratios (it is especially useful for wings with curvilinear edges or edges with a fractures).

Fig. 4.2.

It is possible to define parameter for a wing represented in a fig. 4.2, by the formula , or in case of tapered wing - by the formula .

Fig. 4.3.   Fig. 4.4.

Let's analyze the influence of wing geometrical parameters on value of .

1. With increasing of wing aspect ratio the derivative of a lift coefficient on an angle of attack grows (at conditions of and the value of a derivative tend to the airfoil characteristic (Fig. 4.3).

2. With increasing of sweep angle at half-line chord ( chord line ) the derivative value decreases (Fig. 4.4). (It occurs due to effect of slipping, at condition of , the sweep angles on the leading and trailing edges are identical , ).

3. The sweep influence on derivative value decreases with decreasing of aspect ratio (Fig. 4.5) (sweep practically does not influence on value of lift coefficient derivative on an angle of attack at small values of aspect ratio ).

Fig. 4.5.

4. The wing taper influences a little bit onto the value of a derivative (refer to formula (4.4), parameter ).

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