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LAW OF COSINES EXAMPLES
Field Measuring for Ductwork Using the Law of Cosines —
Introduction
Dimensions taken when measuring objects in the field are taken
from the plan or horizontal plane and the elevation or vertical plane
of the objects. The purpose is to find the dimensional relationship of
distance and alignment between two or more objects. In the Sheet
Metal Industry, these specific dimensions are identified as
Length
,
Offset
, and
Angle
.
Relationships can be established between any two objects such as
ductwork, structural, penetrations, units or terminal devices. The
objects are not as important as an understanding of the information
required to achieve the ultimate goal of “the ability to develop the
required fittings and/or parts for the system.”
Example:
Two duct lines, both 18 Inches x 12 Inches as shown in the sketch
on the next page, are to be measured for a fill-in piece. Measurements
of the plan view or horizontal plane are taken from both ducts to a
parallel stationary object such as a wall or a structural member. The
difference between these two measurements establishes the hori-
zontal offset between the two duct lines, if any exists. The process is
repeated for the elevation measurements typically using the floor
below the objects (upper at 8 Feet 8 Inches, the lower 8 Feet 10-
9/16 Inches). A measurement between the two duct lines will estab-
lish length. These measurements and calculations are used to devel-
op the duct and/or fittings required to fill the space.
Using this method we find the fill-in piece will need to be 24 Inches
in length with a 9 Inch horizontal offset and a 2-9/16 Inches vertical
offset.
