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Exploring the brachistochrone (shortest-time) path in fire spread.

Peiyi Sun1, Yanhui Liu1, Xinyan Huang2

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This summary is machine-generated.

This study investigates the shortest-time fire spread paths between two points. Optimal fire spread paths depend on fuel type, with vertical upward spread maximizing speed for both thin and thick fuels.

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Area of Science:

  • Fire Science
  • Fluid Dynamics
  • Combustion Science

Background:

  • The brachistochrone curve defines the path of shortest travel time.
  • Understanding fire spread dynamics is crucial for safety and optimization.

Purpose of the Study:

  • To determine the brachistochrone path for fire spread between two points.
  • To analyze how fuel type (thermally thin vs. thick) affects the shortest-time fire spread path.

Main Methods:

  • Experimental investigation of flame spread over various fuel geometries (triangular, rectangular, circular).
  • Utilizing thin wires and polymethyl methacrylate (PMMA) bars to represent different fuel thermal properties.
  • Theoretical analysis to validate experimental findings on fire spread dynamics.

Main Results:

  • Local maxima in flame spread rate do not guarantee the shortest overall travel time.
  • For thin fuels, vertical upward spread maximizes overall speed.
  • For thick fuels (PMMA), maximum vertical upward path length is key due to significantly faster upward than downward spread.

Conclusions:

  • The brachistochrone path for fire spread is influenced by fuel thermal thickness.
  • Findings can inform fuel arrangement optimization in built environments.
  • Results aid in estimating safe egress times during building and wildland fires.