A Fire Fighter's Problem

Suppose that a circular fire spreads in the plane at unit speed. A single fire fighter can build a barrier at speed $v>1$. How large must $v$ be to ensure that the fire can be contained, and how should the fire fighter proceed? We contribute two results. First, we analyze the natural curve \mbox{FF}_v that develops when the fighter keeps building, at speed $v$, a barrier along the boundary of the expanding fire. We prove that the behavior of this spiralling curve is governed by a complex function $(e^{w Z} - s \, Z)^{-1}$, where $w$ and $s$ are real functions of $v$. For $v>v_c=2.6144 \ldots$ all zeroes are complex conjugate pairs. If $\phi$ denotes the complex argument of the conjugate pair nearest to the origin then, by residue calculus, the fire fighter needs $\Theta( 1/\phi)$ rounds before the fire is contained. As $v$ decreases towards $v_c$ these two zeroes merge into a real one, so that argument $\phi$ goes to~0. Thus, curve \mbox{FF}_v does not contain the fire if the fighter moves at speed $v=v_c$. (That speed $v>v_c$ is sufficient for containing the fire has been proposed before by Bressan et al. [7], who constructed a sequence of logarithmic spiral segments that stay strictly away from the fire.) Second, we show that any curve that visits the four coordinate half-axes in cyclic order, and in inreasing distances from the origin, needs speed $v>1.618\ldots$, the golden ratio, in order to contain the fire. Keywords: Motion Planning, Dynamic Environments, Spiralling strategies, Lower and upper boundsComment: A preliminary version of the paper was presented at SoCG 201

Evaluation of Moisture Barriers for Fire Fighting Turnout Gear Assessment of Product Failure and Test Method Development Predicting Failure Modes

The purpose of this study was to investigate the failures seen in the moisture barrier of fire fighting turnout gear. Moisture barriers taken from garments in field were evaluated to establish a baseline for comparison. Moisture barriers were exposed as part of a three-piece ensemble and as a single layer moisture barrier to instrumental light exposure in a Carbon Arc Fade-ometer and natural sunlight exposure according to AATCC and ASTM test methods. After exposure, moisture barriers were visually examined using stereo and compound microscopes. A performance measurement was conducted on the exposed moisture barriers using a modified NFPA Hydrostatic Water Penetration Resistance Test. Results of the instrumental and natural sunlight exposures were compared to the failed garments from the field. The results showed that moisture barriers were degraded by ultraviolet light and replicated some of the results seen in the field to predict failures. Based on the results of this study, suggestions were made for future research for developing a test method for predicting moisture barrier failures

Extensions of the classical fighter-bomber duel

In this dissertation, we consider a two-person zero-sum game in which a fighter with a missile wishes to destroy a bomber. The bomber has much small-caliber ammunition for protecting itself from the fighter. And the fighter possesses a missile for attacking the bomber. We develop models for the behavior of the fighter, in terms of missile launch time, and of the bomber, in terms of ammunition firing rate, in several situations. In particular, we examine extensions of the Weiss-Gillman model and the Karlin model

Issues related to occupational exposure to fire fighters, 1990 to 2001

"This document contains a summary of 30 Health Hazard Evaluations (HHEs) related to fire fighting that involved a site visit between 1990 and 2001, categorized by the focus. Of the 30 HHEs, 7 were related to respiratory health effects and safety and health programs and procedures, 8 to diesel exhaust, 5 to forest fire fighting, 6 to chemical fires, 2 to communicable diseases, 1 to arsenic poisoning, and 1 to inspecting fire scenes at buildings with chromated copper arsenic (CCA)-treated lumber ... none were related to noise exposure"--P. iii."Fire fighting continues to be one of the more hazardous industries in this country. l The occupational environment for fire fighters is somewhat unique: exposures are varied, often high, and intermittent. They occur in circumstances of extreme physical and mental stress where the only means of exposure control is self- contained breathing apparatus (5CBAs). Exposures can include smoke and particulate matter, carbon monoxide (CO), nitrogen dioxide (N02), hydrogen chloride, hydrogen cyanide, sulfur dioxide (502) / sulfuric acid, acrolein, formaldehyde and acetaldehyde, benzene and many other organic chemicals, and any chemicals that might be located at the fire scene. . Many of these exposures cause acute effects, but others may cause chronic effects, such as respiratory health effects and decreased lung function from repeated smoke exposures or cancer from repeated exposures to diesel exhaust, benzene, polycyclic aromatic hydrocarbons (PAHs), asbestos, or formaldehyde. A high potential exists for burns, acute trauma, and musculoskeletal injuries. Communicable diseases are becoming a major concern, especially blood-borne pathogens and tuberculosis (TB). Other health effects associated with fire fighters are cardio- vascular disease, reproductive hazards, hearing loss, and occupational stress. A detailed summary of these exposures and health effects can be found in Occupational Medicine: State of the Art Reviews: Fire Fighters' Safety and Health. The 30 Health Hazard Evaluations (HHEs) summarized in this document are grouped into the following six categories: 1. Respiratory health effects and safety and health programs and procedures (7). 2. Diesel exhaust exposures (8). 3. Forest fire-fighting (5). 4. Chemical diseases (6). 5. Communicable diseases (2). 6. Other (2). Along with conducting fire-fighting HHEs, the Hazard Evaluations and Technical Assistance Branch (HETAB) began a project under the Fire Fighter Fatality Investigation and Prevention Program (FFFI&PP) during fiscal year (FY) 1998 to investigate line-of-duty cardiovascular fatalities suffered by fire fighters. Approximately 45 fire fighters suffer fatal heart attacks each year, and NIOSH is investigating these fatalities to generate hypotheses for prevention and intervention activities. Each investigation includes an assessment of the physiologic and psycho logic demands of the job, workplace organization factors, and individual risk factors. Each investigation results in a succinct report for the affected fire department as well as the country's fire service and is included as part of the larger annual report. From 1998 to 2001, 62 investigative reports have been completed, with an additional 13 pending completion. These reports have been distributed to more than 30,000 fire departments representing more than 1 million fire fighters. They are also available on the NIOSH fire fighter Web site www.cdc.gov/niosh/firehome.html. One peer-reviewed journal article has been published, and seven presentations have been given at national meetings. Finally, as an expert of cardiovascular disease (CVD) among those employed in the fire service, one program member was invited to become a member of the National Fire Protection Association (NFPA) Standard 1582, Medical Requirements of Fire Fighters and Information for Fire Department Physicians." - NIOSHTIC-2"January 2004.""Prepared by Beth Donovan Reh; editor, Jane Weber." - p. ivAlso available via the World Wide Web.Includes bibliographical references (p. 27)

Power of Municipal Corporations to Lay Off Employees, Atwood v. Judge

At a time when the future of the American economy appears bleak, and the necessity to curtail vital urban services becomes commonplace in our cities, the significance of the decision rendered by the Ohio Court of Appeals for Columbiana County in Atwood v. Judge\u27 deserves to be noted. The tension between the public interest in maintaining vital services within the community and the state mandate\u27 that a city operate within its budget is not satisfactorily resolved by the court

Design of a Low Cost Short Takeoff-vertical Landing Export Fighter/attack Aircraft

The design of a supersonic short takeoff and vertical landing (STOVL) aircraft is presented that is suitable for export. An advanced four poster, low bypass turbofan engine is to be used for propulsion. Preliminary aerodynamic analysis is presented covering a determination of CD versus CL, CD versus Mach number, as well as best cruise Mach number and altitude. Component locations are presented and center of gravity determined. Cost minimization is achieved through the use of developed subsystems and standard fabrication techniques using nonexotic materials. Conclusions regarding the viability of the STOVL design are presented

Technology utilization program report, 1974

The adaptation of various technological innovations from the NASA space program to industrial and domestic applications is summarized