State of the Arc (Mapping)

NFPA 921 Guide for Fire and Explosion Investigations considers the technique arc mapping to be one of the methodologies used in isolating a fire’s origin and spread. Provided the technique is used properly and understanding its limitations, it is a tool for investigators. Synthesized here is the latest peer-reviewed research and discussions on the implications of increased use of ground- and arc-fault circuit interrupters on arc mapping analysis. Incorporated are case studies and evaluations of recent legal decisions. The goal is to arm investigators with what’s needed to maximize the arc mapping’s efficacy and best present its use and results.

Forensic Engineering Analysis of an Explosion Allegedly Caused by an Overfilled Propane Cylinder

Analyzing the origin and cause of fires or explosions for the purposes of legal proceedings requires the smooth integration of a reliable fire investigative methodology with sound engineering principles and practices. The origin of a building fire was first determined based on the methodology of NFPA 921 Guide for Fire and Explosion Investigations. Engineering analysis was applied to witness observations, arc mapping, fire dynamics, and the evaluation of fire patterns. The fire cause was then evaluated considering NFPA 921 and integrated applied engineering analysis and calculations. The allegations of an overfilled propane cylinder as the cause of the fire were considered. Spoliation issues, poor investigation methodology, and the lack of sound engineering principles (resulting in unreliable opinions) are also contrasted and discussed.

Five-Axis Manufacturing Simulation Based on Normal Arc Mapping and Offset Volume Computation

This paper presents a general manufacturing simulation method for 5-axis manufacturing processes including both numerical controlled (NC) machining and additive manufacturing (AM). The method is based on three major steps: (1) normal arc mapping that is general for computing critical curves, (2) computing the cutter swept volume (SCV) along a 5-axis tool paths based on the critical curves, and (3) computation of simulation results based on a set of sampling points from the cutter swept volume. The first two steps are discussed in details. Based on the properties of the envelop theory, we first present a normal arc mapping method that is general and intuitive. Accordingly the critical curves can be computed for any position and orientation of a tool on a 5-axis tool path. We test various tool shapes including three typical cutters in NC machining and a laser ellipsoid tool in Stereolithography apparatus (SLA). Based on the critical curves, the envelope surfaces of the cutter swept volume related to given tool motions can be determined. We compute a closed continuous surface to approximate the cutter swept volume. The approximation error in computed result has been analyzed. Finally we use a discrete representation, layered depth normal images (LDNIs), to convert a set of cutter swept volumes into a booleaned solid model. The discrete computation based on LDNIs enables us to compute the simulation result robustly and effectively. We demonstrate our method for both NC machining and additive manufacturing processes. Five-axis tool paths can also be given in both curves and surfaces. Various test cases have been presented to illustrate the effectiveness of our method.

Conformal mappings to a doubly connected polycircular arc domain

The explicit construction of the conformal mapping of a concentric annulus to a doubly connected polygonal domain was first reported by Akhiezer in 1928. The construction of an analogous formula for the case of a polycircular arc domain, i.e. for a doubly connected domain whose boundaries are a union of circular arc segments, has remained an important open problem. In this paper, we present this explicit formula. We first introduce a new method for deriving the classical formula of Akhiezer and then show how to generalize the method to the case of a doubly connected polycircular arc domain. As an analytical check of the formula, a special exact solution for a doubly connected polycircular arc mapping is derived and compared with that obtained from the more general construction. As an illustrative example, a doubly connected polycircular arc domain arising in a classic potential flow problem considered in the last century by Lord Rayleigh is considered in detail.