EGR100- Engineering Seminar

1
EGR100- Engineering Seminar

• Engineering Graphics 2
• Analysis of Data by Graphical Means

2
EGR100- Engineering Seminar

• The most important equation from math class is
• Y mx b
• This is the point slope form of the linear
  equation where m represents the slope of the line
  and b represents the intercept along the y axis
  where x0.
• The slope is given by drawing a triangle with the
  line as the hypotenuse. The ratio is then
• m DY/ DX
• The value of b can be read directly from the
  graph.
• See next slide.

3
Hold a folded paper edge to the line above and
read off the value of b
Similarly, read off the values of DX and Dy from
the graph and find the slope.
4
Note that the computer found the values shown at
the left of Y 2x 3
5
EGR100- Engineering Seminar

• There are many situations where the data results
  in a straight line. Other times the variation
  from a straight line may be less than the
  acceptable errors in the data.

So over a limited range of values the curve may
be expressed by a straight line. The reason to
achieve this is that it addition to it being
simpler math it makes scaling with electronic
circuits easier. Most electronics operates in a
liner fashion.
In recent times this is being changed as digital
computers have grown faster and are easily able
to deal with non-linear equations.
6
Although this is a yx2 equation note that the
line fits to 99.5 accuracy. But this is over
a limited range the same curve is shown on the
next slide over a wider range of values.
7
Notice that the straight line is further from the
real curve when taken over a larger range of
values.
8
EGR100- Engineering Seminar

• Another technique to get a straight line is to
  use special graph paper. For example, if an
  equation like y 4x2 is graphed on log-log paper
  it will be a straight line! In such a graph if
  the scale is set equal in both directions, a
  triangle drawn on the line will produce the
  exponent of the curve. This will work on any
  power relation in general, the straight line will
  represent
• yb xm
• On the next slide is the above equation note how
  at x1 the y value will be the value of b.

9
EGR100 - Engineering Seminar
This is the curve on xy-coordinate paper. Notice
the common shape of the quadratic equation.
10
In a log-log graph the sections go by decades.
If you print out this slide and measure with a
ruler a triangle one the line the slope will be
2 The value of 4 is when X1. Remember the axis
is non-linear and 4 is a little above half the
decade as the log of 4 is 0.602
4
11
EGR100-Engineering Seminar
Well we are nearly done. The next lesson will
discuss some graphics program available in the
Engineering Technology Department some of which
are available to you for home use.
Complete your Quiz 14.