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Reduction of Non-Monomial Basis in the Dimensional Analysis of a Dynamical System

[+] Author Affiliations
Srikanth Tadepalli, Kristin L. Wood

University of Texas at Austin, Austin, TX

Paper No. DETC2007-35504, pp. 685-697; 13 pages
doi:10.1115/DETC2007-35504
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 33rd Design Automation Conference, Parts A and B
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4807-8 | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

Dimensional Analysis (DA) is a tool often used to relate models and specimens to the actual product or system based on the hypothesis that the two regimes follow the same physical laws and are hence dimensionally equivalent. While this has been a conventional use of the process, we extend the technique to dynamic systems to develop state equations that allow for design studies and optimization. A methodical approach is detailed coupled with an example of a toy water-rocket assembly. A modified methodology (heuristic) is also discussed to condense non-monomial basis systems using simple physical laws and a novel reduction process. Experimental verification is provided to complement the analysis procedure. Efficacy of the process is highlighted in comparison with the conventional close-form approach.

Copyright © 2007 by ASME

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