Windable Quasi-Geodesic Paths on Surfaces of Revolution.

Abstract

If r is the profile or radius function for a surface of revolution and ro is the polar radius function, a quasi-geodesic path on the surface can be defined by the generalized Clairaut relation rSin(w)=ro, where w is the meridional angle. An inequality involving r,r',rn,ro,and ro', is derived. The global satisfaction of this inequality guarantees the windability of the path on a convex (rn<0) surface by a filament winding machine. If the surface is concave anywhere (rn>0) and a more well known clinging inequality is also satisfied, windability is also guaranteed. By windable, we mean that the winding data produced from the path represents a single-valued function and that the wound filament does not bridge. In addition to this new windability criterion, simplified methods for generating quasi-geodesic paths and properly scaled winding data are also presented. (AN)

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1995
Accession Number
ADA294025

Entities

People

  • Royce W. Soanes

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Bandwidth
  • Demographic Cohorts
  • Differential Geometry
  • Displacement
  • Engineering
  • Equations
  • Filaments
  • Geometry
  • Guarantees
  • Inequalities
  • Information Security
  • Mathematics
  • Military Research
  • Numbers
  • Revolutions
  • Security

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