Low aspect ratio wings

High-aspect-ratio wings

Wing lift coefficient

In general case .

At small angles of attack and the lift coefficient of a wing is determined by equality

. (5.5)

In compliance with the linear theory the lift coefficient in compressed gas is determined by the formula , where - lift coefficient of the deformed wing in incompressible gas. It follows from the last ratios, that

, . (5.6)

For incompressible fluid we have , where , (refer to section 4.1.1). As and , then . Now should be determined as , where .

If assumes that and , then we get a result of a thin airfoil theory , where .

Parameter .

Approximately , where and .

As non-linear lift component is absent for a wing of high aspect ratio , then .

It is possible to use the formula for determination of a derivative of a lift coefficient by angle of attack :

, (5.7)

where - parameter determined for a transformed wing.

Particularly, we have for a tapered wing:

.

Finally we shall write down the expression ,

where ,

.

The non-linear additive is calculated under the formula:

. (5.8)

It is necessary to note, that the conversion linear theory can not be used for connection between compressed and incompressible flows while calculation of the non-linear additive .

Thus: .

5.1.3. Extreme small-aspect-ratio wings().

In such case we have and , therefore derivative does not depend on Mach numbers .

The non-linear additive is determined by above mentioned formula (5.8).

Note: it is possible to notice in the above mentioned formulae for , that the ratio is a function of parameters , and .

Parameter - reduced aspect ratio.

These parameters can be considered as parameters of similarity and used for creation of the diagrams. So .

The analysis of wing lift in a subsonic gas flow:

1. The angle of zero lift does not depend on numbers (Fig. 5.2).

2. The derivative grows with increasing of numbers (Fig. 5.2).

3. The effect of a compressibility (influence of Mach numbers onto the derivative ) decreases with reduction of (it is the reason of spatial flow of low aspect ratio wings) (Fig. 5.3).

4. The non-linear component decreases with increasing of numbers .

Fig. 5.2. Influence of number onto dependence

Fig. 5.3. Influence of wing aspect ratio onto compressibility effect

5. The effect of a compressibility decreases with increasing of sweep angle (Fig. 5.4). The reason of it - with rising up of sweep angle , the speeds component normal to the leading edge from which depends the characteristic becomes less,.

6. The value of decreases with increasing of numbers (reason - more earlier flow stalling) (Fig. 5.5). For example, for the airplane : at - , and at - .

Fig. 5.4. Influence of a sweep angle onto effect of compressibility at

Fig. 5.5. Influence of number onto dependence

Using parameters of similarity the dependence looks like it is shown in fig. 5.6.

Fig. 5.6. Dependence of a factor on parameters of similarity

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