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Introduction to Engineering Linear and Logarithmic Scales: Concepts and Applications

This guide explores the principles of linear and logarithmic scales in engineering, emphasizing their importance in data analysis. Engineers frequently manage vast datasets to derive insights, and understanding scale selection can enhance data interpretation. We will discuss linear versus logarithmic plotting, including log-log and semi-log plots, through practical examples such as temperature expansion, wind force, and population growth. The choice of scale can significantly impact how relationships manifest graphically and illustrate data variations across orders of magnitude.

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Introduction to Engineering Linear and Logarithmic Scales: Concepts and Applications

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  1. Introduction to EngineeringLinear & Logarithmic Scales Agenda Linear & Logarithmic Scales Linear vs. Linear Plot Log-Log Plot Semi-log (log v. linear) plot

  2. 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.

  3. 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.

  4. -20 -15 -10 -5 0 5 10 15 20 0.1 1 10 100 Linear and Logarithmic Scaling Linear axis: Logarithmic axis:

  5. Three Examples • Temperature Expansion • Linear Y = mX + B • Wind Force • Power Equation Y = bXm • Population Growth • Y = bemX

  6. 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)

  7. 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)

  8. Y = bXm

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

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

  11. Exponential Relationship ExamplePopulationGrowth Y = bemX Linear Form: ln Y = ln b + m XY* = m X + b

  12. Assignment • Assignment #8 • Log and Semi-Log Review sheet • Bring a floppy disk to class tomorrow

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