Translational Oscillations Research Articles

Kinetic Energy of a Liquid Surrounding a Prolate Spheroid Vibrating at Its Free Surface

This paper is the third of a series reporting the results of an investigation of the motion around semisubmerged prolate ellipsoids of revolution. The first paper [1]4 dealt with the general motion around a vibrating spheroid and with its applications to vertical ship vibrations; correction factors for the evaluation of the added mass were there calculated. The second paper [2] contained an analysis of the motion generated by a prolate spheroid under translatory horizontal oscillations and the resulting expressions and values for the added-mass coefficients. In the present work the expressions for the kinetic energy and the correction factors are derived for horizontal vibrations of the spheroid with any number of nodes. The values corresponding to certain horizontal vibrations with two and three nodes are given.

Portable Magnetic Field and Gradient Meter

A portable instrument for measuring magnetic fields and field gradients is described. The measurements depend on comparing the alternating emf's induced in two search coils oscillated synchronously at about 3 cps through angles of less than 3°, one in the field to be measured and the other in the reference field of a permanent magnet in the instrument. A precision Helipot is used as a potentiometer, in which a measured fraction of the signal from the reference coil is balanced against the signal from the probe coil. The null is obtained through an electronic amplifier and galvanometer. Tests of the instrument indicate 0.1% precision. A field gradient can be measured with the same instrument by use of a search coil which is given translatory oscillations in the direction of the gradient.

The aerodynamic forces on an aerofoil in non-uniform unsteady motion in a closed tunnel

The two-dimensional unsteady motion of an aerofoil, situated midway between parallel walls, and moving through an inviscid, incompressible fluid, is investigated. A completely general upwash distribution is taken, and expressions are obtained for the pressure on the aerofoil surface and the lift and moment about the mid-chord point. By a conformal transformation involving Jacobian elliptic functions the physical plane is mapped into a rectangle, and the theory is based on a solution of Laplace’s equation satisfying certain given boundary conditions on this rectangle. Special cases are considered in which the upwash is ( a ) sudden upgust, and ( b ) a harmonic oscillation. Detailed examination is made of a rigid-body aerofoil performing translational and rotational harmonic oscillations. The aerodynamic forces are expressed in terms of dimensionless ‘air-load coefficients’, which are then compared with corresponding coefficients for an aerofoil in an infinitely deep stream. The air-load coefficients are obtained in a form which readily enables first-order corrections for wall interference to be evaluated. It is shown that the formulae derived are at variance with corresponding results obtained by other authors using different methods.

A detailed refinement of the crystal and molecular structure of anthracene

A detailed refinement of Mathieson, Robertson & Sinclair's X-ray crystallographic data for anthracene is described. The many calculations needed were carried out on the Manchester University electronic computer. The difference maps indicate some channelling of the electrons along the lines of the bonds. The anisotropie vibrations of the carbon atoms are interpreted in terms of anisotropic translational and rotational oscillations of the molecules. The magnitudes of the angular oscillations agree well with those inferred from Raman spectra. C-C bond lengths with e.s.d.'s of about 0.004 A and bond angles with e.s.d.'s of about 12' are obtained. Close intermolecular approaches explain a very slight buckling of the molecules.

Absolute Thermal Decomposition Rates of Solids. Part II. The Vacuum Sublimation Rate of Molecular Crystals

The linear rates of sublimation of rhombic benzene and rhombic sulfur have been calculated by use of absolute reaction rate theory in reasonable agreement with rates derived from published experimental data. Required mean torsional oscillation and translational oscillation frequencies for the molecules in the crystal lattice were obtained by an analysis of the available heat capacity and Raman spectral data. A detailed comparison of this treatment with Penner's treatment of the sublimation process is included.

Some Simplified Methods in Airfoil Theory

T USE OF the acceleration potential in thin airfoil theory was introduced by L. Prandtl.'' The method has since been applied by several authors' to problems of stationary and non-stationary flow in both compressible and incompressible fluids. A striking feature of this method is that no use has to be made of vortex wakes because the acceleration potential is everywhere continuous in the fluid. Such concepts as the trailing vortices and the induced downwash play no direct part in this theory. The purpose of the present article is the treatment of two dimensional airfoil theory in an incompressible fluid by the combined use of conformal transformation and the acceleration potential. This method of approach greatly simplifies the solution of certain airfoil problems. First the reader is introduced to the fundamental properties of the acceleration potential in an incompressible fluid. Then it is shown how the problem of finding the acceleration potential can be solved by conformal representation of the airfoil on a circle and a simple relation is derived between the velocity and the stream corresponding to this potential. The method is next applied to the stationary airfoil with and without flap, and to the determination of the airfoil camber line and thickness function for a given pressure distribution along the chord. The simplicity of the method is especially apparent for the case of the oscillating airfoil which is the subject of the last treatment. For the sake of brevity only translatory oscillations are considered.