Introduction to Engineering
Linear & Logarithmic Scales
Agenda
Linear & Logarithmic Scales
Linear vs. Linear Plot
Log-Log Plot
Semi-log (log v. linear) plot
Working With Data
 Engineers often collect large amounts of
data
 Two common ways to analyze the data
are:
1. Write an equation to fit the data.
2. Graph the data.
Working with Equations Describing
Engineering Phenomena and Data
Plotting data with appropriate scales can
be very helpful in display of data and
interpretation
Choosing the right scale can make the
appear on a straight line
Choosing the right scale allows you to plot
data ranging over several orders of
magnitude on a single page.
Linear and Logarithmic Scaling
Linear axis:
-20 -15 -10
-5
0
5
10
15
20
Logarithmic axis:
0.1
1
10
100
Three Examples
 Temperature Expansion
 Linear
Y = mX + B
 Wind Force
m
 Power Equation Y = bX
 Population Growth
 Y = bemX
Linear Relationship Example
Temperature Expansion of Pipe
L = a (T – To) + Lo
L = a (dT) + Lo
(Form : Y = mX + b)
Length, L
L
a
1
Lo
dT
Power Relationship Example
Wind Force on Road Sign
Wind Force on a
Sign F = P A
P = 0.0036 V2
F = 0.0036 V2 A
 Where
P = pressure in lb/ft2
V = velocity in ft/sec
 (Form Y = bXm)
Linear Scale Plot
Pressure (lb/sqft)
Y=
m
bX
90
80
70
60
50
40
30
20
10
0
0
50
100
150
Wind Velocity (ft/sec)
200
Y = bXm
Linear Form: log Y = log b + m log X
Y* = m X* + b
log (Velocity) vs log (Pressure) Plot
on Linear Scale Plot
log (Pressure)
3
2
1
0
-1
-2
-3
0
0.5
1
1.5
log (Velocity)
2
2.5
Y = bXm
Linear Form: log Y = log b + m log X
Y* = m X* + b
Log/Log Scale Plot
Pressure (lb/sqft)
100
10
1
0.1
0.01
0.001
1
10
100
Velocity (ft/sec)
1000
Exponential Relationship Example
Population Growth
Y = bemX
Linear Form: ln Y = ln b + m X
Y* = m X + b
Exponential Growth on Linear vs. Linear
Scale
Exponential Growth 0n Log vs. Linear
Scales
10000
3500
1000
2500
Population
Population
3000
2000
1500
1000
100
10
1
500
0
0.1
0
50
100
Time (hrs)
150
0
50
100
Time (hrs)
150
Assignment
 Assignment #8
Log and Semi-Log Review sheet
Bring a floppy disk to class tomorrow