Mathematically Speaking

March 1, 1999
Powerful math aids are available for the occupational safety and health professional.

Success as an occupational health and safety professional doesn't require a degree in mathematics, but it does demand working knowledge of an extensive and growing body of equations and mathematical models. Mathematical demands in the safety and health profession range from simple exposure calculations and conversions to more complex engineering design and exposure modeling equations.

Fortunately, powerful tools are available to simplify our calculations: pocket calculators, computer spreadsheets and mathematics software. We'll examine the capabilities of these tools by applying them to modeling an exposure to acetone vapors from a small acetone spill in a room, assuming well-mixed air.

Pocket Calculators

The scientific pocket calculator - small, portable, and extremely powerful - remains the mathematical tool of choice for most safety and health professionals. Unfortunately, many professionals still use their calculators the old-fashioned way: problems are set up using pencil and paper, with the calculator relegated to the final keyboard calculation. It doesn't have to be this way. With the right calculator, you can put pencil and paper aside and use the calculator to both set up the equation and perform the final calculation.

Hewlett-Packard's HP-48G ( calculator couples a visually appealing Equation editor with a powerful Solve function, making it my favorite math tool. Setting up an equation is a snap with the Equation editor. Simply enter the equation exactly as it appears in print and save it to the calculator's memory.

The HP 48's powerful Solve function eliminates the need to learn calculator programming. The Solve function takes an equation and creates an entry screen for the equation's variables. Simply enter the values for the known variables, and the calculator automatically solves the equation for the remaining unknown. No muss, no fuss, no programming.

Since the HP48 shares variables within a directory, it is easy to set up a directory of related equations so that the variables calculated by one equation are available for use by other equations within the directory. For example, the time calculated when acetone levels reach their maximum air concentration can be used by the modeling equation to calculate the maximum concentration.

The HP48 is filled with great features, including powerful statistics, symbolic algebra, calculus, unit conversion and plotting functions. With 148 different units in 16 different categories, OHS professionals will find the HP48's Units function indispensable for converting cubic feet to cubic meters, feet/sec. to meters/sec. or inches of water to pounds/in2.

Thanks to great user support, the HP 48 has another appeal to geeks like me: it can be cloned to run on Windows, Windows CE, and Macintosh computers. The necessary free software is available at the web site's ( HP Calculator Emulators page (


Found on computers large and small, computer spreadsheets have become a standard tool for general problem solving on personal computers. Spreadsheets are a popular choice for OHS mathematics.

Frankly, I don't like using spreadsheets for general mathematical work. Spreadsheets require careful planning and logistical work. Separate equations must be established for each variable to be solved, known variables must be assigned to specific cells in the spreadsheet and the solution equations programmed into the spreadsheet, using arcane cell references.

Don't get me wrong. Spreadsheets can do extremely powerful math and present results in an attractive manner. It's just that it takes a lot of work to get there. There must be an easier way.


Mathcad 8 (Mathsoft, Inc., telephone (617)577-1017, eliminates the logistical headaches of spreadsheet mathematics. Mathcad is a live interactive math tool that lets the user instantly solve complex technical problems, using standard mathematical notation. Like the HP48, equations are entered into Mathcad just as they appear in print. But Mathcad goes beyond the HP48, taking full advantage of the power of desktop computing to provide easier equation entry, a larger work area, word processing capabilities, and much faster equation-solving.

Setting up our simple spill model using Mathcad was almost a trivial task (Figure 3). The equations were entered quickly from the keyboard and the model, its application and limitations and variables clearly described using Mathcad's word processing capabilities. The graph was a cinch to create with a few clicks of the mouse.

Mathcad 8 provides a complete range of math tools, including symbolic algebra, calculus, vectors, matrices, statistics, Boolean algebra, and unit conversions. Despite the complexity of the math that it manages, Mathcad is easy to learn and use. Mathcad comes with an excellent interactive Resource Center that quickly brings the new user up to speed and provides a ready review for the experienced user. The Resource Center also includes extensive reference tables, links to a Web-based library of Mathcad documents and an online Mathcad Collaboratory discussion group.

Mathcad 8 Professional, priced at $500, includes custom programming support, more advanced functions, document sharing support, and additional "quicksheets" covering a broad range of disciplines, and other advanced features. Most occupational health and safety professionals will find Mathcad 8 Standard edition fills their needs at a more modest $99.95 price. A free Mathcad Explorer which lets you read and interact with Mathcad-based worksheets and electronic books is available at the Mathsoft Web site (www.mathsoft. com/mathcad/explorer/).

How to Comply with Federal Employee Laws

Operating a business is a challenge, especially when confronted with managing compliance with federal and state employment regulations. While it won't help with state employment regulations, How To Comply With Federal Employee Laws, by Sheldon I. London, provides the information you need to stay on the right side of the law.

How To Comply contains plain English explanations of every significant federal employee law, including the Family and Medical Leave Act, Health Insurance Portability, OSHA, Fair Labor Standards Act, and Equal Opportunity and Anti-Bias Laws. Helpful checklists, examples, tables, charts and frequently asked questions help unravel the complexities of federal labor laws. The book includes a bulletin board poster containing the five federally mandated notices required in most workplaces.

This well-written guidebook comes in both print and CD-ROM versions. The CD-ROM version contains the complete text of the printed version in Folio View format. Folio View provides a solid set of search tools, electronic bookmarks, electronic highlighting, and hyperlink browsing.

Copies of both the print and CD-ROM versions are available for $119 from the publisher, Vizia Enterprises LLC, Rochester, N.Y. Vizia may be contacted by telephone at (716)328-8189, email at [email protected], or on the World Wide Web at

Contributing Editor Michael Blotzer, MS, CIH, CSP, author of "Internet User's Guide for Safety and Health Professionals," is an occupational hygiene and safety professional, writer, and computer enthusiast who brakes for animals on the information superhighway. Mike can be reached by mail addressed to Occupational Hazards, by fax at (216)899-1581 or by electronic mail at [email protected]. Visit Mike's World Wide Web page at

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