Introduction to engineering linear logarithmic scales
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Introduction to Engineering Linear & Logarithmic Scales PowerPoint PPT Presentation


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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:

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Introduction to Engineering Linear & Logarithmic Scales

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Introduction to engineering linear logarithmic scales

Introduction to EngineeringLinear & Logarithmic Scales

Agenda

Linear & Logarithmic Scales

Linear vs. Linear Plot

Log-Log Plot

Semi-log (log v. linear) plot


Working with data

Working With Data

  • Engineers often collect large amounts of data

  • Two common ways to analyze the data are:

    • Write an equation to fit the data.

    • Graph the data.


Working with equations describing engineering phenomena and 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

-20

-15

-10

-5

0

5

10

15

20

0.1

1

10

100

Linear and Logarithmic Scaling

Linear axis:

Logarithmic axis:


Three examples

Three Examples

  • Temperature Expansion

    • Linear Y = mX + B

  • Wind Force

    • Power Equation Y = bXm

  • Population Growth

    • Y = bemX


Linear relationship example temperature expansion of pipe

Length, L

a

L

1

Lo

dT

Linear Relationship Example Temperature Expansion of Pipe

L = a (T – To) + Lo

L = a (dT) + Lo

(Form : Y = mX + b)


Power relationship example wind force on road sign

Power Relationship ExampleWind 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)


Y bx m

Y = bXm


Y bx m linear form log y log b m log x y m x b

Y = bXm Linear Form: log Y = log b + m log X Y* = m X* + b


Y bxm linear form log y log b m log x y m x b

Y = bXm Linear Form: log Y = log b + m log X Y* = m X* + b


Exponential relationship example population growth

Exponential Relationship ExamplePopulationGrowth

Y = bemXLinear Form: ln Y = ln b + m XY* = m X + b


Assignment

Assignment

  • Assignment #8

    • Log and Semi-Log Review sheet

    • Bring a floppy disk to class tomorrow


  • Login