Engineers are often
math enthusiasts who got bored with the abstract. Even though number crunching
is significant to engineers’ work, math is no more than a convenient means to
arrive at a physical end. The type of math an engineer uses will depend on the type
of engineer he is and the type of project in which he's involved.
Basic Arithmetic
All math is based on the idea that 1
plus 1 equals 2, and 1 minus 1 equals 0. Multiplication and division –2 times 2
and 4 divided by 2 – are variations used to avoid multiple iterations of either
subtraction or addition. One example of an engineer's use of basic arithmetic
is the civil engineer's calculations for describing water flow across an open
basin. The flow is reckoned in cubic feet per second, or Q, where Q equals the
runoff coefficient times the intensity of the rain for a specified period,
times the area of the basin. If the runoff coefficient is 2, the intensity, in
inches of rain, is 4 and the basin – a specified area of land – is 1/2 acre,
the engineer's formula resembles this: (2x4)/(.5x43,560), or 8/21,780. The
result, 0.0003673, is the volume of water, in cubic feet per second, flowing
across the land.
Algebra and Geometry
When several of the factors of a
problem are known and one or more are unknown, engineers use algebra, including
differential equations in cases when there are several unknowns. Because
engineers work to arrive at a solution to a physical problem, geometry – with
its planes, circles and angles – determines such diverse things as the torque
used to turn a wheel, and reduces the design of a roadway's curve to an
accurate engineering or construction drawing.
Trigonometry
Trigonometry is the science of
measuring triangles. Engineers may use plane trigonometry to determine the size
of an irregularly shaped parcel of land. It may also be used or to determine
the height of an object based solely on the distance to the object and the
angle, up or down, from the observer. Spherical trigonometry is used by naval
engineers in ship design and by mechanical engineers working on such arcane
projects as the design of mechanical hand for an underwater robot.
Statistics
We all love statistics. They tell us
where we stand in the world, among our peers and even in our family. They tell
us who's winning. The engineer uses them for the same reasons – by statistical
analysis of the design, the engineer can tell what percentage of a design will
need armor or reinforcement or where any likely failures will occur. For the
civil engineer, statistics appear as the concentration of rainfall, wind loads
and bridge design. In many locations, engineers designing drainage systems must
design for a 50- or 100-year storm in their calculations, a significant change
from the normal rain concentration.
Calculus
Calculus is used by engineers to
determine rates of change or rates by which factors, such as acceleration or
weight, change. It might tell NASA scientists at what point the change in a
satellite's orbit will cause the satellite to strike an object in space. A more
mundane task for calculus might be determining how large a box must be to
accommodate a specific number of things. An engineer who designs packaging, for
example, might know that a product of a certain weight must be packaged in
groups of no more than 10 because of their weight. Using calculus, he can
calculate both the optimum number of objects per box, plus the optimum size of
the box.
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