Beam Theory Wing

making it evident that 1 /0 is proportional to 1 /q (see Fig. 3.4). Therefore, for a model of this type only two data points are needed to extrapolate the line down and to the left until it

Data point 1

Id aT

Data point 2 Figure 3.5 Schematic of a sting-mounted wind tunnel model.

intercepts the 1 /q axis at a distance 1 /q¡> from the origin. As can be seen from the figure, the slope of this line can also be used to estimate qD. The form of this plot is of great practical value because estimates of qD can be extrapolated from data taken at speeds far below the divergence speed. This means that qD can be estimated even when the values of the model parameters are not precisely known, thus circumventing the need to risk destruction of the model by testing all the way up to the divergence boundary.

3.1.2 Sting-Moun ted Model

A second configuration of potential interest is a rigid model mounted on an elastic sting. A simplified version of this kind of model is shown in Figs. 3.5-3.7, where the sting is modeled as a uniform, elastic, cantilevered beam with bending stiffness EI and length 2c. The model is mounted in such a way as to have angle of attack of ar when the beam is undeformed. Thus, as before a — ar + 6, where 6 is the nose-up rotation of the wing resulting from bending of the sting, as shown in Fig. 3.6. Also in Fig. 3.6 we denote the tip deflection of the cantilever beam as S, although we do not need it for this analysis. One should note the equal and opposite directions on the force Fy and moment Mo at the trailing edge of the wing in Fig. 3.7 versus at the tip of the sting in Fig. 3.6.

From superposition one can deduce the total bending slope at the tip of the sting as the sum of contributions from the tip force Fu and tip moment M0, denoted by dF and 6M, respectively, so that

From elementary beam theory these constituent parts can be written as

Fo(2c)2 Zer,

OKI, ine

Zer,

 a I
0 0