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where: Cm, is the average moment coefficient about the aerodynamic
center (or at zero lift) for the airfoil section with flap completely extended. The average moment coefficient refers to a weighted average over the span when Cm is variable. (The wing area affected should be used in the weighting.) V, is the design speed with flaps extended. V, is the design gliding speed used in Conditions III and IV.
COMPUTATIONS NECESSARY When the above provisions are made, no balancing computations for the extended flap conditions need be submitted; hence these conditions can also be eliminated from the design of the horizontal tail surfaces. • The foregoing interpretation applies to normal installations in which the flap is inboard of the ailerons, or in which a full span flap is used and the flap is intended for conventional use, i.e., the relatively low speeds of approach and landing. For other arrangements it will be necessary to submit additional computations if it is
desired to prove that flap conditions are not critical. • In all cases an investigation is required of the local wing structure
to which the flap is attached, using the flap design loads as determined. The strength of special wing ribs used with split flaps, and the effect of flap control forces, should also be investigated. Reference should be made to current NACA reports for acceptable flap data.
UNSYMMETRICAL FLIGHT CONDITIONS In the required investigation for the effects of unsymmetrical flight loads, the following assumptions should be made: • Modify Conditions I and III (Chap. 1, pp. 9, 10) and the most critical negative condition by assuming 100 percent of the air load to be acting on one side of the glider and 40 percent on the other. Assume the moment of inertia of the entire glider is effective.
It will usually be convenient to separate the effects of the loads due to linear accelerations from the loads due to torque (T). It may be assumed that the stresses due to unsymmetrical loads can be obtained by adding algebraically the stresses due to 70 percent of the normal (symmetrical) loading to those determined by considering 30 percent of the normal total load to be acting upward on one wing panel and 30 percent to be acting downward on the other. The unbalanced moment or torque is caused by the differential of 60 percent of the normal total load on one wing panel times the distance from the longitudinal axis to the centroid of the load normally acting on the panel. (See fig. 1-IV.)
Figure 1-IV. Span load distribution for unsymmetrical flight conditions.
The angular acceleration “a” resulting from the torque “T” may be obtained as follows:
a = T (rad/sec.2)
where Iz = the moment of inertia of the glider (and contents) about
the X, or longitudinal axis. I, is in mass units, and may be computed in accordance with the procedure in NACA
Technical Note No. 575. The torque Tn resisted by any portion of the glider may be obtained from the following, assuming the angular acceleration to be constant for all parts of the glider:
Tn = In a (ft. lbs.) when Iz =My dna
where My = the mass of part N
dy = the distance from the longi
tudinal axis to the CG of part
SPECIAL FLIGHT CONDITIONS Wing load distribution.—The limit air loads and inertia loads acting on the wing structure should be distributed and applied in a manner closely approximating the actual distribution in flight.
SPAN DISTRIBUTION DETERMINATION (a) For wings having mean taper ratios equal to or greater than .33, the span distribution should be determined as follows: 1. If the wing does not have aerodynamic twist (that is, if the zero
lift lines of all sections are parallel), the span distribution for normal force coefficient (Cn) should be assumed to vary in accordance with figs. 1-V and 1-VI, which are assumed to represent two extreme cases of tip loading. Each case should be investigated, unless it is demonstrated that only one is critical. As an alternative method, it will be acceptable to investigate each design condition for only one span distribution using a rational distribution, except in the case of the high-angle-ofattack condition which gives the maximum forward chord loads (Condition I). For this condition the analysis should be made for both the rational distribution and that given in fig. 1-V.
2. If the wing has aerodynamic twist, the span distribution should
be determined by the alternative method given in 1, above. 3. For these purposes, the mean taper ratio is defined as the ratio
of the tip chord (obtained by extending the leading and trailing edges to the extreme wing tip) to the root chord (obtained by extending the leading and trailing edges to the plane of sym
metry). 4. Acceptable methods of determining a rational span distribution
are given in publication ANC-1 "Spanwise Air Load Distribu
tion,” and in NACA Technical Report Nos. 572, 585 and 606. b. For all wings having mean taper ratios less than .33 the span distribution should be determined by rational methods, unless it is shown that a more severe distribution has been used. Acceptable methods of determining rational span distribution are given in the aforementioned documents of a, 4, above.
c. When the normal force coefficient is assumed to vary over the span, the value used should be adjusted to give the same total normal force as the design value of Cn acting uniformly over the span.
d. When figs. 1-V and 1-VI are used, the chord coefficient should be assumed to be constant along the span.
e. For wings having aerodynamic twist (not geometric twist), it is very important that the effect of twist (wash-out) be considered in the investigation of the wings for the negative conditions.
DETERMINING CHORD DISTRIBUTION a. The approximate method of chord loadings outlined under "Rib Tests” in Chapter 2 for the testing of wing ribs is suitable for conventional two-spar construction if the rib forms a complete truss between the leading and trailing edges. An investigation of the actual chord loading should be made in the case of stressed-skin wings if the longitudinal stiffeners are used to support direct air loads. In some cases it is necessary to determine the actual distribution, not only for total load but for each surface of the wing. If wind tunnel data are not available, the methods outlined in NACA Reports Nos. 383, 411, 456, 631, and 634 are suitable for this purpose. These methods consist of determining the “basic” pressure distribution curve at the “ideal” angle of attack and the "additional” pressure distribution curve for the additional angle of attack. These curves can be coordinated with certain values of Cz so that the final pressure distribution curve can be obtained immediately for any Cl. Curves of this nature for several widely used air foils can be obtained directly from the NACA.
6. On high speed gliders the leading edge loads developed may be exceptionally severe, particularly the "down” loads which are produced by negative gusts when the glider is flying at the design gliding speed. The magnitude of such loads can be estimated without determining the entire chord distribution by the method outlined in NACA Report No. 413.
c. When a design speed higher than required is used in connection with wing flaps or other auxiliary devices it will be necessary to determine the chord distribution over the entire airfoil. The effect of any device which remains operative up to V, should be carefully investigated. This applies particularly to auxiliary airfoils, spoilers, and fixed slots.
Compliance Suggestion DETERMINATION OF RESULTANT AIR FORCES A general method is outlined below for determining the mean effective value of the normal force coefficient, the average moment coefficient, location of the mean aerodynamic center and value of the mean aerodynamic chord. These factors are needed in order to determine the balancing loads for various flight conditions. The most general case will be considered, so that certain steps can be omitted when simpler wing forms or span load distribution curves are involved.
a. In general, the summation of all forces acting on a wing can be expressed as a single resultant force acting at a certain point. If the point is so chosen that, at constant dynamic pressure, the moment of the air forces does not appreciably change with a change in the angle of attack of the airfoil, the point can be considered as the mean aerodynamic center of the wing. The resultant force can be resolved into the normal and chord components and represented by the average coefficient, Cr and Cc, while the moment is represented by the average moment coefficient, Cm, multiplied by a distance which can be considered to be the mean aerodynamic chord. The values of the above quantities and the location of the mean aerodynamic center will depend on the plan-form of the wing and the type of span distribution curve used.
6. For convenience and clarification, table 1-Ia has been developed and the various curves obtained as a part of this method are illustrated in figs. 1-VII, 1-VIII, and 1-IX. It should be particularly noted that when the area under a curve is referred to, the area should be expressed in terms of the product of the units (coordinates) to which the curve is drawn. The procedure is as follows: 1. Fig. 1-VII illustrates the actual wing planform, plotted to a
suitable scale. This should agree with the definition of design wing area.
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