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GT AE 3051 - GRAPHING

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Spring 2001 AE 3145 Measurements Lab 1Graphing• Graphs are one of the most effective ways to communicate experimental results…• Graphs are simple to construct but they are often constructed very poorly and this completely negates their benefit…• NOTE: these illustrations are from Beckwith, Marangoni & LienhardTime Pressure10:00 1009.011:30 984.21:00PM 999.82:15 989.03:40 977.14:40 981.25:40 990.0Time Pressure10:00 1009.011:30 984.21:00PM 999.82:15 989.03:40 977.14:40 981.25:40 990.0•Picture vs 1000 words•Clarity & logic•Picture vs 1000 words•Clarity & logicSpring 2001 AE 3145 Measurements Lab 2Make it Clear to Reader...Good:• y=values on log scale• x=every 20 years• Circle symbols• Linear trend...Good:• y=values on log scale• x=every 20 years• Circle symbols• Linear trend...Poor:• y=log()• x=too many values• No data symbols• What does line mean?Poor:• y=log()• x=too many values• No data symbols• What does line mean?Spring 2001 AE 3145 Measurements Lab 3Basic Types of Cartesian PlotsLinear• Both axes are linear• Symbols & curvesLinear• Both axes are linear• Symbols & curvesSemi-log• One axis is log• Symbols & curves• Error boundsSemi-log• One axis is log• Symbols & curves• Error boundsLog-log• Both axes are log (could use dB)• Symbols & curvesLog-log• Both axes are log (could use dB)• Symbols & curvesError bars show uncertaintyError bars show uncertaintySpring 2001 AE 3145 Measurements Lab 4Polar Chart• Useful for showing angular effectsSpring 2001 AE 3145 Measurements Lab 5Semi-log Shows a Trend• Cool-down data from liquid sample shows exponential trend when plotted using linear scales (left) and linear when plotted using log y scale.• Experimental data shown with symbols.• Theoretical results shown with smooth curves.• Use Legend to define each curve or symbol used.Spring 2001 AE 3145 Measurements Lab 6Changing Scales Can Show Structure• Replotting nonlinear data using nonlinear axes can often reveal underlying analytical forms• In this example, both asymptote and hyperbolic coefficient are revealed in intercept & slope of linear plot.• Usually, replotting is designed to create a linear curve whose slope & intercept can be related to underlying parameters.Nonlinear• y=1 + 2.5/x• Asymptotic behavior• Hyperbolic behaviorNonlinear• y=1 + 2.5/x• Asymptotic behavior• Hyperbolic behaviorNonlinear Axes• y=same; x →1/x• Slope = 2.5• Intercept = 1.0Nonlinear Axes• y=same; x →1/x• Slope = 2.5• Intercept = 1.0Spring 2001 AE 3145 Measurements Lab 7Transformations to Linear Forms• Some simple transformationsF(x) YXABy=a + b/x y 1/x a by=1/(a + bx) 1/y x a by=x/(a + bx) x/y x a by=abxlog y x log a log by=acbxlog y x log a b log cy=axblog y log x log a by=a + bxNyxNab(N=known)F(x) YXABy=a + b/x y 1/x a by=1/(a + bx) 1/y x a by=x/(a + bx) x/y x a by=abxlog y x log a log by=acbxlog y x log a b log cy=axblog y log x log a by=a +

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