Representation of Technical Information Lecture 9 Representation of Technical Data Chapter 4 References http://www.csun.edu/~vceed002/ref/measurement/data/ graph_paper.html If you don’t have PowerPoint loaded on your computer, the following site will give a free download that will allow you to read (not create) a PowerPoint document. http://www.microsoft.com/downloads/details.aspx?FamilyID=428d5727-43ab-4f24-90b7-a94784af71a4&DisplayLang=en Freshman Engineering Project Freshman engineering project – actual data Assignment: determine how temperature and air pressure vary with altitude Students: collected, recorded, plotted and analyzed the data University plane equipped with the latest Rockwell Collins avionics gear Using the plane and avionics gear, data on the next page was collected Recorded Data Data Plotted Freehand Legend: Temperature Pressure Class Data Excel Spreadsheet Excel Spreadsheet Graph Temp and Pressure vs Altitude Temperature T F Pressure lbf/in2 Height H, ft What’s wrong with this chart? How can it be improved? Plotting Data on 2-Axes in Excel Highlight data to be plotted in Excel Spreadsheet Click on Chart icon Select chart type (scatter chart in this case) Click option desired, Choose Next Check data range and click next Choose embedded chart or new sheet This gets us a chart but not the second axis Adding a Second Axis Highlight data to be plotted on 2nd axis Select Format, Selected Data Series Choose Axis tab Select Secondary Axis on which to plot data and OK Select Chart, Choose Chart Options. Select Secondary y-Axis. Type the Name (“Pressure”), Symbol (“P”), and units of measure (“lbf per sq in”) http://www.me.ua.edu/ME360/docs/Excel-WhatToKnow/AddSecondaryAxis.htm Air Temp & Press vs Altitude Height, h, ft Pressure, P, lbf/sq in Temp, T, degrees F Legend Temp Pressure Spreadsheet Software Excel Lotus123 Search: http:/www.google.com for: Spreadsheet software and/or Spreadsheets Some spreadsheets are free; some have a nominal cost – can make no recommendations on software- haven’t tried any of them. Excel and Lotus 123 are the industry standards with Excel dominating the market place Collecting and Recording Data Modern science founded on scientific measurements. Scientific experiments produced volume of data. That data had to be: Collected Recorded Documented Formal data sheets or notebooks Time, Date Observations Info on equipment Data Sheet Identify Test, Date, Observes. Note instruments used, date last calibrated, ect. Engr 107 Midterm 08 Mar 06 Sect 1 Data Sheet Title of Test: Test No: Foreman: Apparatus Tested: No Set: Rating: Date: Wiring check by: Data checked by: Instrument No: Shunt or CT No: Mult or PT No: Apparatus Tested: No Range used: Scale read: Factor: Data Acquisition Terminology Accuracy and Precision Accuracy – a measure of the nearness of a value to the correct or true value. Precision – refers to repeatability of a measurement, i.e., how close successive measurements are to each other. Accuracy and Precision ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤ Inaccurate & Imprecise Precise but inaccurate Accurate and precise Accurate but imprecise Accuracy & Precision are Relative ¤ ¤ ¤ ¤ ¤ ¤ What classification is this? Accurate or Inaccurate? Precise or Imprecise? Can’t tell without some comparison! Now what would you say? Accurate or Inaccurate? Precise or Imprecise? Accurate Precise Accuracy & Precision are Relative ¤ ¤ ¤ ¤ ¤ ¤ What classification is this? Accurate or Inaccurate? Precise or Imprecise? Again, we can’t tell without some comparison! Now what would you say? Accurate or Inaccurate? Precise or Imprecise? ¤ ¤ ¤ ¤ ¤ ¤ Accurate Imprecise Errors in Data Systematic errors Identifiable and correctable. e.g. – known instrumentation bias. e.g., metal tape measure susceptible to temperature. Need coefficient of thermal expansion to correct. Random Accidental or other nonidentifiable errors. Noise (e.g., white noise) superimposed on sensor signals. General Graphing Procedures 1. Select graph paper (rectilinear, semi-log, log-log) and grid spacing for best representation 2. Choose proper location of the horizontal and vertical axes 3. Determine the scale units (range) for each axis 4. Graduate and calibrate the axes using the 1,2,5 rule 5. Identify each axis completely (name, symbol, & units) General Graphing Procedures 6. Plot points using permissible symbols Observed data points are located by symbol Theoretical graphs are normally constructed smooth) 7. Check any point that deviates from the slope or curvature of the line 8. Draw the curve or curves 9. Identify each curve or curves, add title and necessary notes (write out coordinates of each pt. 10. Darken lines for good representation Commercial Graph Paper Graph paper is available in a wide variety of formats, styles, weights, and grades Both log-log and semi-log paper is available in 1 to 5 cycle axes Semi-Log Paper Two cycle paper Log-Log Paper Three x One cycle paper Graph Paper There are several websites that provide capability to print various graph papers. http://www.mathematicshelpcentral.com/graph_paper.htm http://www.csun.edu/~vceed002/ref/measurement/data/graph_paper.html Axes Location The axes of a graph consists of two intersecting straight lines Abscissa: the x-axis Ordinate: the y-axis Common practice is to plot the independent variable along the x-axis Locate the axes in a location to best present the data Commercial graph paper often does not provide adequate border space around the grids for axis labels The axes should be placed approximately 1 in. inside the printed edge to allow space for graduations, calibration, axis labels, reproduction, and binding Scale Graduation & Calibrations Scales – series of marks called graduations laid down along the axis. Calibrations – numerical values assigned to significant graduations Uniform scale – equal spacing along the stem Nonuniform scale – A scale is non-uniform when the scale represents a variable whose exponent is not equal to one or the variable contains trigonometric or logarithmic functions 0 10 20 30 0 1 2 3 4 Uniform Calibrations Nonuniform Calibrations Using the 1, 2, 5 Rule Use the 1, 2, 5 rule: Scale graduations are selected so that the smallest division of the axis is a pos or neg integer power of 10 times 1, 2, or 5. 0 10 20 30 0 10 20 30 Acceptable Graduations Unacceptable Graduations Smallest division = 5 Smallest division = 3.33 Exceptions to the 1, 2, 5 rule: - Days - Months - Years Axis Labeling Each axis should be clearly identified and contain: Variable name Variable symbol Variable units E.g. If the independent variable is time, the x-axis becomes: 0 10 20 30 Time, t, s Point Plotting Procedure Data can generally be characterized in one of three general ways: Observed data Empirical data Theoretical Observed and empirical data points are usually located by various symbols such as a small circle, a square, or a diamond around each data point. Theoretical curves or lines are smooth and without symbols. Every point on the curve is a data point. Plotting Data Title Axis Title Legend X-axis: Abscissa Y-axis: Ordinate Linear scale graph Data Annotation Test Flight 11] Altitude: 7K ft GW: 23,500 lbs Data Collection To understand a physical process or event. Measurements are observations of a physical process or event. We measure physical quantities such as length, time, temperature, force Sensors – any device that receives a signal or stimulus and generates measurements as a function of that stimulus. Thermometer, strain gage, accelerometer, etc. How do we obtain data? Simulation, e.g.; Simulation environments, e.g., Matlab. Custom simulation; C/C++, Fortran, Visual Basic, Java, etc. Experiment/testing, e.g.; Component or coupon testing. Sub-scale or full-scale testing. DAQ (‘dak’) – data acquisition. ABS Braking Simulation Model Simulation of the dynamic behavior of a vehicle under hard braking conditions ωv + Vv/ Rr , where, Vv = vehicle speed in terms of corresponding wheel angular velocity Slip = 1- ωW / ωv Vv = vehicle velocity Rr = wheel radius ωW = wheel angular velocity Relative Slip Testing - ABS Data Acquisition Full-Scale Structural Testing BMW Indy Car Tabulating Data Assignment Representation of Technical Data (Chapter 4, Eide, et al; pages 161– 174) Problem 2.3, 3.1, and 3.3 due 01 Oct Feb