Review Figure 4-13 noting that if the offset
(opposite side) had been 1″, the travel
(hypotenuse) 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 calcu-
late travel. Also, note that Figure 4-14 provides
constants for common offset angles.
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 U.S. customary
ruler. The other side is an offset scale in which
the units are less than one inch; in fact, 1.414 of
these units is equal to one inch, Figure 4-19. To
use the 45° scale, measure as you would when
measuring the run, except use the other side of
the rule.
It is important to remember that in all cases,
travel (hypotenuse) is greater than the actual
length of the pipe that must be cut. Fitting
allowances must be subtracted from the travel
to obtain the actual pipe length. Fitting
allowances vary by size of pipe and are
discussed in Chapters 19 and 20.
Computing Area and
Volume
The surface area of a square or rectangular
surface can be computed by multiplying the
length times the width, Figure 4-20. However,
94
Section 1 Introduction to Plumbing
Plumber’s rule: A measuring device that has a stan-
dard scale on one side and a scale for measuring the
length of 45º offsets on the other side.
Figure 4-15. Compute the horizontal distance
between the ends of parallel pipes using the tangent
ratio.
45°
A C
10″
Tangent A =
Opposite side
Adjacent side
Tangent 45° =
10″
Adjacent side
1.000 =
10″
Adjacent side
Adjacent side =
10
1.000
Adjacent side = 10″
Adjacent
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
221∕2° .4142
30° .5774
45° 1.000
60° 1.732
Figure 4-17. A plumber commonly uses the terms
travel, run, and offset. Compare these terms to the
ones used in Figure 4-13.
45°
A
Run
Travel
Offset
Figure 4-18. Calculating the travel for 45° offsets
using a constant.
Travel = Offset × Constant
Travel = 10″ × 1.414
Travel = 14.14″