Quantifying Gun Barrel Curvature: From Derivation of the Basic Formulas to Evaluating Derivatives, Estimating Errors, and Selecting Measurement Intervals.

Abstract

Following a discussion on the need to measure the curvature of gun barrels are given the derivations of the unit tangent and normal vectors; and the definitions of the binormal vector, and the curvature and torsion of a space curve. Formulas for curvature and torsion and the tangent, normal, and binormal vectors are given in terms of cartesian coordinate derivatives. The derivatives in these formulas must be evaluated numerically using measurements of the deviation from straightness of the barrel centerlines. Various methods for obtaining derivative formulas (e.g. Taylor's series, and differentiating interpolating polynomials derived by finite difference and least squares methods) and the requirements of a derivative formula are given origins and definitions of types of error are given as an introduction to error estimation and measurement interval selection. Finally a new method for selecting derivative formulas and measurement intervals based on the treatment of error as a random variable is introduced.

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1993
Accession Number
ADP009078

Entities

People

  • David F. Finlayson

Organizations

  • United States Army Armament Research, Development and Engineering Center

Tags

DTIC Thesaurus Topics

  • Cartesian Coordinates
  • Curvature
  • Dynamics
  • Geometry
  • Gun Barrels
  • Guns
  • Intervals
  • Least Squares Method
  • Mathematics
  • Measurement
  • Polynomials
  • Random Variables
  • Rhode Island

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Regression Analysis.
  • Structural Dynamics.

Technology Areas

  • Space