Thin-ship theory and influence of rake and flare

Abstract

The basic computational task of the thin-ship theory of free-surface potential flow about a ship that advances at constant speed along a straight path in calm water, of large depth and lateral extent, is considered. Specifically, a straightforward method for evaluating the pressure and the wave profile at a ship hull (the wave drag, hydrodynamic lift and pitch moment, and sinkage and trim are also considered) in accordance with Michell's thin-ship theory is given. A main ingredient of this method is a simple analytical approximation to the local-flow component in the expression for the Green function (associated with the classical Michell-Kelvin linearized freesurface boundary condition) of thin-ship theory. This practical Green function is used to evaluate and analyze steady flow about a four-parameter family of ship bows with rake and flare. In particular, the variations of the bow-wave height and location with respect to the draft-based Froude number, the entrance angles at the top and bottom waterlines, and the rake angle are explored via a systematic parametric study. This parametric study provides estimates-immediately useful for design-of the influence of rake and flare on the height and the location of a ship bow wave, and shows that rake and flare effects can be significant, especially at low Froude numbers. 123 50 F. Noblesse et al. δ = 45°, α = 15°, α' = 5°δ = -45°, α = 5°, α' = 15°Fig.

Practical mathematical representation of the flow due to a distribution of sources on a steadily advancing ship hull

“…The Green function defined by the integral representation (7) and (8) is considered for the two special cases y − y = 0 or z + z = 0 in [15] and [16], respectively. In these two special cases, simple approximations-valid in the entire flow region-for the local flow component G L in (7) have been obtained.…”

“…Thus, the Green function of thin-ship theory corresponds to the special case y − y = 0 of the Green function G( x, x). This thin-ship-theory Green function is simplified in [15] as…”

“…The gradients of the Green functions (9) and (10) are given in [15,16]. These two studies show that flow calculations based on the gradients of the highly simplified Green functions (9) or (10) or corresponding more accurate Green functions are practically indistinguishable.…”

“…Simple analytical approximations-valid within the entire flow region-to the local flow component are given for two special cases that correspond to flows due to thin ships [15] and air-cushion vehicles or planing boats [16], for which we have y − y = 0 or z + z = 0, respectively. The simple expressions given in [15,16] are extended here to the general case when the source point x and the flow-field point x in the Green function G( x, x) are arbitrary.…”

“…The simple expressions given in [15,16] are extended here to the general case when the source point x and the flow-field point x in the Green function G( x, x) are arbitrary.…”