Constant acceleration exit of two-dimensional free-surface-piercing bodies

The forced constant acceleration exit of two-dimensional bodies through a free-surface is computed for various 2D bodies (symmetric wedges, asymmetric wedges, truncated wedges and boxes). The calculations are based on the fully non-linear time-stepping complex-variable method of Vinje and Brevig (1981). The model was formulated as an initial boundary-value problem (IBVP) with boundary conditions specified on the boundaries (dynamic and kinematic free-surface boundary conditions) and initial conditions at time zero (initial velocity and position of the body and free-surface particles). The formulated problem was solved by means of a boundary-element method using collocation points on the boundary of the domain and stepped forward in time using Runge–Kutta and Hamming predictor–corrector methods. Numerical results for the deformed free-surface profile, pressure along the wetted region of the bodies and force experienced by the bodies are given for the exit. The analytical added-mass force is presented for the exit of symmetric wedges and boxes with constant acceleration using conformal mappings. To verify the numerical results, the added-mass force and the numerical force are compared and give good agreement for the exit of a symmetric wedge at a time zero (t = 0) as expected but only moderate agreement for the box

Radiation hardening of components and systems for nuclear rocket vehicle applications

The results of the analysis of the S-2 and S-4B components, although incomplete, indicate that many Saturn 5 components and subsystems, e.g., pumps, valves, etc., can be radiation hardened to meet NRV requirements by material substitution and minor design modifications. Results of these analyses include (1) recommended radiation tolerance limits for over 100 material applications; (2) design data which describes the components of each system; (3) presentation of radiation hardening examples of systems; and (4) designing radiation effects tests to supply data for selecting materials

A complex variable method for the floating-body boundary-value problem

AbstractThis paper reviews the use of a method using Cauchy's theorem, which has recently formed the basis of very successful numerical schemes for considering the nonlinear water-wave problem, both with and without floating or submerged bodies. Outstanding problems, concerning the intersection point problem (where two boundary conditions are to be applied) and the treatment of radiation conditions, are outlined. Notwithstanding these difficulties, useful results for transient problems may be obtained; examples presented include new results for water exit of a wedge and horizontal motion of a submerged cylinder

maths e.g. as a learning resource

This update describes the use of the “maths e.g.” question database in enhancing any sort of learning material by easily including specific ‘Try one yourself’ links to any of the over 5000 individual (randomised) questions or allowing student selection from the numerous topics/sub-topics that span the school/university interface and selected service mathematics content. A new question type is also presented to facilitate the (partial) testing of more theoretical material.