## Interference and Nonplanar Lifting-Surface Theories

10- 1 Introduction

For a general discussion of interference problems and linearized theoretical methods for analyzing them, the reader is referred to Ferrari (1957). His review contains a comprehensive list of references, and although it was editorially closed in 1955 only a few articles of fundamental importance seem to have been published since that date.

The motivation for interference or interaction studies arises from the fact that a flight vehicle is a collection of bodies, wings, and tail surfaces, whereas most aerodynamic theory deals with individual lifting surfaces, or other components in isolation. Ideally, one would like to have theoretical methods of comparable accuracy which solve for the entire combined flow field, satisfying all the various boundary conditions simultaneously. Except for a few special situations like cascades and slender wing-body configurations, this has proved impossible in practice. One has therefore been forced to more approximate procedures, all of which pretty much boil down to the following: first the disturbance flow field generated by one element along the mean line or center surface of a second element is calculated; then the angle-of-attack distribution and hence the loading of the second element are modified in such a way as to cancel this “interference flow field” due to the first. Such interference effects are worked out for each pair of elements in the vehicle which can be expected to interact significantly. Since the theories are linear, the various increments can be added to yield the total loading.

There are some pairs of elements for which interference is unidirectional. Thus a supersonic wing can induce loading on a horizontal stabilizer behind it, whereas the law of forbidden signals usually prevents the stabilizer from influencing the wing. In such cases, the aforementioned procedure yields the exactly correct interference loading within the limits imposed by linearization. When the interaction is strong and mutual, as in the case of an intersecting wing and fuselage, the correct combined flow can be worked out only by an iteration process, a process which seems usually to be stopped after the first step.

Interference problems can be categorized by the types of elements involved. The most common combinations are listed below.

(1) Wing and tail surfaces.

(2) Pairs or collections of wings (biplanes or cascades).

(3) Nonplanar lifting surfaces (T – and V-tails, hydrofoil-strut combinations).

(4) Wing or tail and fuselage or nacelle.

(5) Lifting surface and propulsion system, especially wing and propeller.

(6) Tunnel boundary, ground and free-surface effects.

It is also convenient to distinguish between subsonic and supersonic steady flight, since the flow fields are so different in’the two conditions.

In the present discussion, only the first three items are treated, and even within this limitation a number of effects are omitted. Regarding item 4, wing-fuselage interference, however, a few comments are worth making. Following Ferrari, one can roughly separate such problems into those with large aspect-ratio, relatively unswept wings and those with highly-swept, low aspect-ratio wings. Both at subsonic and (not too high) supersonic speeds, the latter can be analyzed by slender-body methods along the lines described in Chapter 6. The wings of wider span need different approaches, depending on the Mach number [cf. Sections C, 6-11 and C, 35-50 of Ferrari (1957)]. For instance, subsonically it appears to be satisfactory to replace the fuselage with an infinite cylinder and work with two-dimensional crossflow methods in the Trefftz plane.[7] At supersonic speeds, however, the bow wave from the pointed body may have a major influence in modifying the spanwise load distribution.