For 45° offsets, it is possible to obtain the travel by measuring directly from the pipes with a plumber’s rule. One side of the plumber’s rule is a standard US customary ruler. The other side is Simple Methods for Computing Offsets Plumbers typically do not use the language of trigonometry when calculating offsets. Figure 4-17 illustrates the names commonly used. Note that offset and run will be equal if a 45° offset is being fabricated. Review Figure 4-13 noting that if the offset (opposite side) had been 1″, the travel (hypote- nuse) would have been 1.414″. This value can be used as a constant to calculate the travel for any 45° offset because for every inch of offset the travel must be 1.414″. Figure 4-18 gives an example of using the constant to calculate travel. Also, note that Figure 4-14 provides constants for common offset angles. Life Cycle Assessment A life cycle assessment is a tool used to evaluate the environmental impact associated with the production, utilization, maintenance, repair, and recycling or disposal of a product. The results of the assessment are interpreted and used by designers, contractors, and consumers to choose products that have minimal impact on the environment. To get a better idea of what is involved in a life cycle assessment, consider the stages in the life of copper pipe that would need to be assessed: • Obtaining raw materials. Large earthmoving machines, explosives, and trucks are required to extract ore and move it to the processing plant. Using recycled copper reduces the environmental cost, but it is still necessary to collect, disassemble, sort, and transport this raw material. • Producing pipe. Huge furnaces and large amounts of fuel are required to melt the copper. Chemicals are needed to remove impurities from molten copper. The molten copper is cast into billets from which pipe is made using extruders. All of this equipment is very large and requires a lot of energy to produce the copper pipe. Large quantities of copper pipe are shipped from the factory to wholesale companies who sell the pipe to retailers. Both of these steps require transportation. • Installing and using pipe. In addition to pipe, supplies such as fittings, valves, solder, and gas for the torch need to arrive at the jobsite along with the plumbers who will install, maintain, repair, and replace the pipe throughout its useful life. • Recycling or disposing. Recycling requires that the pipe be removed from the structure, separated from other types of material and delivered to the recycling company. Disposing means that the copper is sent to the landfill. A complete life cycle assessment would con- sider everything involved in each stage of the life of the copper pipe. For example, what impact does making, operating, and recycling each of the machines used to quarry copper ore have on the environment? Are the gases given off by the fur- nace used to melt the copper ore damaging to the environment? What other questions do you think should be included in the life cycle assessment of copper pipe? The fact that copper pipe lasts a long time and requires little maintenance will improve its assessment. However, the growing demand for copper and the limited availability of high-quality copper ore make the efficient use of this material essential. Goodheart-Willcox Publisher Figure 4-16. In this case, the relationship of the angle’s adjacent side and its opposite side is 1:1. Therefore, the two sides are equal. Brief Table of Tangent Ratios Angle Tangent 22½° 30° 45° 60° .4142 .5774 1.000 1.732 78 Section 1 Introduction to Plumbing Copyright Goodheart-Willcox Co., Inc.