iii Preface Twen ty years ago, I first stepped in front of a class of students who wanted to learn the HVACR trade. Over the next few days, it became apparent that some of the concepts I was trying to explain were lost on the students unless they had a good working knowledge of mathematics. Sensible and latent heat values, the measurement of heat versus temperature, and pressure/temperature relationships are all frequently used in our trade, and all of these involve mathematics. When I saw my students struggling to understand simple, yet critical computations, I decided to spend some time teaching math. The result was so amazing that I repeated the process with each subsequent trade school class I taught. Though the students groaned when I took away their calculators, they soon learned that success in our jobs as HVACR tradespeople depends on a complete working knowledge of mathematics—from basic arithmetic to algebra, geometry, and even a bit of trigonometry. I struggled through those classes for lack of a textbook that was directed toward the group I was trying to train. High school and college textbooks were generally too abstract, and grade school textbooks were too basic. So I improvised, and much of this book is a culmination of my time spent teaching students—from novices to professional engineers—how to apply mathematical concepts in real-world situations. The practical exercises used within this text are often ones I use in my classes. Most of these come from actual situations I encountered in over 25 years of working with commercial and industrial HVACR and boiler systems. This book begins with a review of the basic math operations and concepts, such as adding, subtracting, multiplying, dividing, fractions, decimals, and percentages. These are used by everyone from the apprentice installer to the master technician. The text continues with ratios, proportions, estimating, and measurement and then covers algebraic formulas, geometry, and trigonometry. Each of these chapters shows how these concepts and theories apply to everyday work in the mechanical trades. The book culminates in a series of practical applications of the material learned in each of the chapters. Measurement is of such importance that I devoted an entire chapter (5) to it. If initial measurements are fl awed, all calculations based on those values will be flawed as well. The potential for error in measurement and subsequent calculations and conversions is very real, and the consequences can be costly. This chapter covers dozens of measurement variables, and we work in both US Customary (I-P or inch-pound) and Systems International (SI) metric units. Also included are many charts for conversion within each system of measurement and also conversion between the two systems. Immediately following this is a chapter (6) that explains many HVACR formulas that are commonly needed but seldom memorized! These formulas are explained and example calculations are provided. While there are many good textbooks available that explain the fundamentals of heating, ventilation, air-conditioning, and refrigeration, there was, until now, a defi in the mathematical instructional tools available to those in our trade. Filling ficit that gap is the role of this text. Gary B. Xavier