ES 422 Biomechanics of Human Movement ES 422 - Biomechanics of Human Movement Lab 1: Review of Trigonometry and Computation in Excel Reading Assignment: Appendix B (pp. 449-452) Introduction In biomechanics, we rely on concepts from trigonometry and calculus to help us analyze mechanical problems. Understanding of the basic mathematical tools will enhance your comprehension of lectures and labs and will improve your performance on quizzes and exams. Biomechanical analysis often involves large data sets, making hand calculations too time consuming to be practical. However, if you can properly execute the calculation once, commonly available computer programs, such as Microsoft Excel, can automate the repeated calculations. You can also use these programs to generate graphs of the results, simplifying the process of interpreting your data. Purpose: To learn how to execute trigonometric calculations using Microsoft Excel, and to generate graphs of the data and results. This will lay a computational foundation for the rest of the course since several subsequent labs will require the use of Excel. Using Formulas and Functions in Excel Excel allows you to enter your own formulas, select from a broad range of predefined functions, or to use predefined functions as part of your own formula. When entering your own formulas, a common mistake is to ignore the order of operations. Excel will evaluate anything inside of parentheses first, then exponents, then multiplication and division, and finally addition and subtraction. Many common mathematical operations are already defined by functions in Excel. AVERAGE, STDEV, SIN, COS, TAN, ASIN, ACOS, ATAN, DEGREES, and RADIANS are all functions that you will use often in this course. If you want to use a function but don’t know what it is called, you can search for a function by going to the insert menu and selecting function. You can enter a formula into a range of cells by copying a formula from another cell. When you do this, the cell references will change relative to cell you’re pasting the formula into. If you type a dollar sign before the column name and before the row number (i.e. “$A$1” instead of “A1”), Excel treats this as an absolute reference. This means that the value in that cell will be the only value used even if you copy that formula to another cell In-lab Assignment #1: Enter the sample data set (below). Calculate the mean race time, start time, split time (CS), and finish time. Calculate the standard deviation for each of the above categories. Determine the velocity for the race, start, CS, and finish. Velocity = Distance/Time Sample Data Set Graphing Your Results To graph your results, select the chart wizard from the Menu bar. Excel will present with many chart type options (column, bar, line, etc.), but for purposes of this class you should always choose “XY (Scatter)”. Next, you’ll be presented with a dialogue box to specify a series (a pairing of x and y values), followed by a dialogue box to enter the chart title, axes labels, and several appearance options. As a rule, all charts should have a title, axes labels (including the units of quantities being graphed), and only have a legend if there is more than one series being plotted. In-lab Assignment #2: Graph the three velocities vs. race time for sample data set above. This should be one graph with three series plotted on it: start velocity (y-axis) vs. race time (x-axis). CS velocity (y-axis) vs. race time (x-axis), and finish velocity (y-axis) vs. race time (x-axis). Trigonometric Functions In biomechanics, it is often necessary to use trigonometric functions to calculate segment lengths and joint angles. The Pythagorean Theorem is often used to find the length of segment. The sine, cosine, tangent functions can be used convert a vector into component from. Pythagorean Theorem C A B β α θ Trigonometric Functions In-lab Assignment #3: In the figure above, A = 3, B=2, and θ = 90°. Use Excel to find C. In the above diagram, θ is known to be 90°. If θ is not 90°, the law of cosines is used instead of the Pythagorean Theorem. Often, the law of cosines is solved for θ and used to find a joint angle. A B C β θ α Law of Cosines In-lab Assignment #4: In the figure above, A = 3, B = 2, and θ = 45°. Use Excel to determine what C equals. Name Date Section # Instructor Country Race Time (50 m) Start Time (10 m) CS Time (32.5 m) Finish Time (7.5m) RUS 22.13 3.37 15.27 3.5 USA 22.26 3.4 15.23 3.63 BRA 22.29 3.47 15.23 3.59 CHN 22.33 3.4 15.37 3.56 RSA 22.59 3.37 15.43 3.79 USA 22.68 3.4 15.53 3.75 VEN 22.72 3.4 15.73 3.59 PUR 22.73 3.53 15.5 3.7 3 Exercise Science ProgramDepartment of Exercise, Sport & Leisure Studies, University of Tennessee