2. Fig. 1-VII (b), shows the variation of wing chord, C, with the span. The values of C are entered in table 1-Ia as item (2). The area of the figure should be accurately determined and converted to the proper units. It should be one-half the value of design wing area.

3. Fig. 1-VII (c), represents an assumed span distribution curve. The factor R, represents the ratio of the actual C, at any point to the value of C2, at the root of the wing. Values of R, from this curve are entered in table 1-Ia under item (3).

4. Fig. 1-VII (d), is obtained by plotting RC (item (4)) in table 1-Ia against span. The ordinates of this curve are proportional to the actual force distribution over the span. The area under curve 1-VII (d) should be accurately determined and expressed in the proper units. Ko, the ratio of the mean effective C to the value of Cn. (at the root), is obtained by dividing the area under curve 1-VII (d) by the area under curve 1-VII (b), using the same units of measurement for each area. This value of K, is indicated by the dotted line on curve 1–VII (c).

5. To determine the location of the mean aerodynamic center along the span, fig. 1-VIII is drawn. The ordinates are obtained by multiplying the ordinates of curve 1-VII (d) by their distance. along the span, as shown in item (5), of table 1-Ia. The area under curve 1-VIII (a), divided by the area under curve 1-VII (d), gives the distance from the wing root to the chord on which the mean aerodynamic center of the wing panel is located. This distance is indicated on fig. 1-VII (a) by the dimension b.

6. The locus of the aerodynamic centers of each individual wing chord is plotted on fig. 1-VII (a) as the dotted line A-B. In table 1-Ia the distance "x" from the base line O-E to the line A-B is entered under item (6).

Figure 1-VII. Determination of effective normal force coefficient.

7. Fig. 1-VIII is now plotted, using as ordinates the values of R C obtained from item (7) of table 1-Ia. The area under curve 1-VIII (b), divided by the area under curve 1-VII (d), gives the distance of the mean aerodynamic center from the base line O-E in fig. 1-VII (a). This distance is indicated as x on that figure.

8. If it is assumed that the moment coefficient about the aerodynamic center of each individual chord is constant over the span, the magnitude of the mean aerodynamic chord is determined by means of fig. 1-VIII (c). The ordinates for this curve are

determined from item (8) of table 1-Ia. The area under curve 1-VIII (c), divided by the area under curve 1-VII (c), gives the value of the mean aerodynamic chord. By way of illustration, it is drawn on fig. 1-VII (a), so that its aerodynamic center coincides with the location of the mean aerodynamic center of the wing panel.

Figure 1-IX. Determination of mean effective moment coefficient.

9. In cases in which wing flaps or other auxiliary high-lift devices are used over a portion of the span it is desirable to obtain the mean effective moment coefficient. This is the coefficient to be used for balancing purposes in connection with the mean aerodynamic chord previously determined under the assumption of a uniform moment coefficient distribution. In table 1-Ia under item (9) the local values of the moment coefficient

about the aerodynamic center are entered. These are also plotted as fig. 1-IX, a, to illustrate a type of distribution which might exist.

10. Fig. 1-IX (b) is plotted from the values indicated under item

(10) of table 1-Ia. The area under this curve divided by the area under curve 1-VIII (c) gives the mean effective value of the moment coefficient for the entire wing panel.

11. In the case of twisted wings a different span distribution exists for each angle of attack. The location of the resultant forces can, however, be determined in the above manner for any known span distribution.

BALANCING LOADS

The balancing loads referred to in this chapter should be computed by a rational method or by a suitable arbitrary method.

Compliance Suggestion

METHOD OF ANALYSIS

a. The basic design conditions must be converted into conditions representing the external loads applied to the glider before a complete structural analysis can be made. This process is commonly referred to as "balancing" the glider and the final condition is referred to as a condition of "equilibrium." Actually, the glider is in equilibrium only in steady unaccelerated (constant speed) flight; in accelerated conditions both linear and angular accelerations change the velocity and attitude of the glider. It is customary to represent a dynamic condition, for structural purposes, as a static condition by the expedient of assigning to each item of mass the increased force with which it resists acceleration. Thus, if the total load acting on the glider in a certain direction is "n" times the total weight of the glider, each item of mass in the glider is assumed to act on the glider structure in exactly the opposite direction and with a force equal to "n" times its weight.

b. If then the resultant moment of the air forces acting on the glider is not zero with respect to the center of gravity, an angular acceleration results. An exact analysis would require the computation of this angular acceleration and its application to each item of mass in the glider. In general, such an analysis is not necessary except in certain cases for unsymmetrical flight conditions. The usual expedient in the case of the symmetrical flight conditions is to eliminate the effects of the unbalanced couple by applying a balancing load near the tail of the glider in such a way that the moment of the total force about the center of gravity is reduced to zero. This method is particularly convenient, as the balancing tail load can then be thought of either as an aerodynamic force from the tail surfaces or as a part of a couple approximately representing the angular inertia forces of the masses of and in the glider. Considering a gust condition, it is proba