The motion of an aircraft along a straight flight path inclined to the vertical is considered from an arbitrary initial velocity which may be far from steady flight speeds. The velocity and incidence, as a function of distance or time, provide a solution to the ‘inverse phugoid problem’ of finding the control laws that keep an aircraft on a straight flight path by exactly cancelling the phugoid instability (the short period mode is omitted by neglecting the rotational inertia of the aircraft). This is a non-linear problem, namely finding the motion of an aircraft from an initial condition far removed from a stable steady state, or finding the large amplitude deviations from an unstable equilibrium. The stability and instability problems are solved analytically using the following assumptions:

1. (i) the aircraft flies subsonically so that only form and induced drag need be considered;

2. (ii) the thrust consists of a constant term, minus a term specifying a dependence on velocity similar to that of the total drag; and

3. (iii) the aircraft incidence is away from stall so that lift is a linear function of incidence.

The response curves show that:

1. (i) flight at velocities below the lower steady flight speed, which is unstable, is difficult to maintain due to fast divergence towards the stall; and

2. (ii) for an initial velocity above the lower steady flight speed, there is convergence towards the higher steady flight speed.

The convergence, in the latter case (ii), may be slow along a straight flight path, although it can be hastened by suitable manoeuvres.

An asymptotic theory valid for large Reynolds number is developed for describing the oscillatory properties of a turbulent boundary layer in a free stream whose velocity varies harmonically with time around a non-zero mean value. The theory identifies two frequency parameters in terms of which four different regimes of oscillation frequency are defined. Similarity laws are identified for each of these frequency regimes and for the different layers of the periodic boundary layer. The theory seems to bring together the available data on unsteady wall bounded flows into a general framework.

Affine transformation and similarity rules has been used to solve the classical bending, buckling, and vibration problems of orthotropic plates. The present work extends these concepts to antisymmetric angle-ply laminated plates by employing a simple transformation, utilising previous material constant definitions by Tsai and Brunelle, and a similarity parameter. With the help of certain defined characteristic and bounded quantities, comprehensive solutions are found to this problem; hence, the curves presented in the text are generic rather than specific. The results indicate that the frequency parameters and buckling coefficients increase with increasing generalised rigidity ratio D* and decrease with increasing generalised Poisson’s ratio ε, and the static deflection coefficients decrease with increasing D* and increase with increasing ε. The results of a reduced set of equations agree with those obtained by previous investigators.

A method has been developed for calculating the load distribution, overall forces and moments on a thin wing of arbitrary shape undergoing small amplitude simple harmonic motion in inviscid, incompressible flow. The method is compared with experimental data and other theoretical methods for wings and control surfaces in pitching oscillation and wings going through a sinusoidal vertical gust.