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EXSS 323
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This
lab was developed by Gerry Smith, Ph.D., formerly of Oregon State
University
· INTRODUCTION
The purpose of this lab is to provide you with an experience in analyzing video taken with a high speed camera. High speed filming is used for many different reasons in biomechanics. It can be used to measure the release velocity during a baseball pitch, duration of ball-foot contact during a kick or a sprinter's acceleration coming out of the blocks. In today's lab, you will track motion during a standing long jump. Horizontal and vertical positions, velocities, and accelerations of the body center of mass will be determined as a function of time.
In the process of making a film or video picture, the image entering the camera's lens is reduced to a fraction of its original size. In viewing the film or video, the images are either projected onto a screen, viewed on a computer monitor, or printed to paper. The images may be smaller or larger than real-life size. Because the images are seldom used at real-life size, any distance measured on the image must be multiplied by a constant conversion factor to expand it to its real-life value.
The standard procedure for determining the conversion factor is to place a meter stick in the camera's field of view during the filming. Knowing the calibration stick's real length and its length when projected, a constant conversion factor can be calculated with the following formula:
For example, if a 1 meter calibration stick was placed in the field of view during filming of a runner and then measured as 8 millimeters in the image that was projected from the film, the conversion factor would be:
The CF is used to convert distances measured in millimeters on the projected image to real life distance in meters. For instance, if a runner moved 64 mm from beginning to end of a cycle of pictures, the real-life displacement (d) would be obtained by:
Notice that the units cancel to yield a displacement in meters.
It is often necessary to be able to determine time between special events when analyzing high speed film or video. For example, if average running velocity is to be calculated from film images, time is in the denominator of the velocity equation (v = d / Dt). Measuring the time can be accomplished by knowing the number of frames of film between two points of interest and the time per frame.
High speed film cameras usually have adjustable frame rates which are frequently set to shoot between 50 and 200 frames per second (f/s). Video recording is less adjustable. Images can usually be analyzed at 60 or 30 f/s.
The time for one frame of film or video can be calculated from the camera speed setting. For example, if a camera speed of 100 f/s is used, the time per frame is:
This time constant (0.01 seconds per frame) can then be used to calculate time between events. For example, if the above runner (filmed at 100 f/s) took 200 consecutive frames to displace the 8 meters, then the elapsed time (Dt) would be calculated in the following manner:
From the displacement and the elapsed time, the runner's average velocity can be calculated:
While the average velocity over a period of time is often of interest, sometimes the velocity at a specific instant is of greater importance, particularly if one wishes to compute the acceleration over a period. To find the instantaneous velocity in the X direction (vX) in frame i, one typically uses the central difference method:
where x(i + 1) and x(i – 1) are the X positions in frames i+1 (= 1 frame into the future) and i – 1 (= 1 frame into the past), respectively. t(i + 1) and t(i – 1) are the times corresponding to frames i+1 and i – 1 and are found by multiplying the frame number minus 1 by the time per frame (tF). A similar formula is used to compute the instantaneous velocity in the Y direction from the Y position data. Note that, with this method, the instantaneous velocity cannot be computed for the first and last frames of data.
Once one has determined the instantaneous velocity in the X direction at different instants, one may compute the average acceleration in the X direction over a period of time (= DvX / Dt) or the instantaneous acceleration in the X direction at specific instants. To find the instantaneous acceleration in the X direction (aX) in frame i, one can again use the central difference method:
Equivalent processing can be performed to find the accelerations in the Y direction.
· METHODS
A video recording of a long jump has been included for your viewing of the movement pattern (NOTE: this file requires Quicktime MoviePlayer and is more than 600 Kbytes in length). Sixteen frames from the jump have been saved as individual images for analysis. These were recorded at 15 frames per second and thus have time intervals of 0.067 seconds between pictures.
Images displayed on a computer monitor are composed of very small dots which are referred to as "pixels." The images that you will be analyzing are smaller than real-life size and are scaled at 110 pixels per real-life meter.
Measure and record the horizontal and vertical position of the jumper's hip marker in each illustrated frame. Then, using the appropriate conversion factor, determine the real-life displacement from image to image.
Based on the frame numbers and time per frame, determine the time for each frame from the beginning to the end of the jump. Next, determine the instantaneous velocity in both the horizontal and vertical direction in each frame over the whole jump. Finally, compute the instantaneous horizontal and vertical acceleration in each frame.
Links to the jump images (below) will bring up a new page with the image included. When the mouse cursor passes over the image you will notice that at the bottom of the page a pair of numbers will be reported. These are the image coordinates of the cursor. Point to the hip marker and record the coordinates in a table for each frame.
NOTE: This technique for finding coordinates works on the web browser installed on the lab computers and on some but not all other web browsers. If on your browser the coordinates do not show up in the status bar at the bottom of the page, click on the image. The page will be reloaded and the coordinates will show up at the end of the location bar (with the URL or address).
Jump frames:
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1.
jump picture 2.
jump picture 3.
jump picture 4.
jump picture 5.
jump picture 6.
jump picture 7.
jump picture 8. jump picture |
9.
jump picture 10.
jump picture 11.
jump picture 12.
jump picture 13.
jump picture 14.
jump picture 15.
jump picture 16. jump picture |
· ANALYSIS OF THE JUMP
Enter the horizontal and vertical coordinates for each jump picture into a spreadsheet which will be used for the subsequent analysis. Configure the spreadsheet columns as illustrated in this example table.
An unusual characteristic of computer image coordinates that you have recorded is that the vertical coordinate increases as one goes down the image. This is opposite from the "normal" rectangular coordinate system used in mechanics, where up is taken as positive. We can easily convert the vertical data to a conventional system by writing a formula in the next column of the spreadsheet. The images you have analyzed had 240 pixels vertically. To set the origin at the bottom left corner, as is typical, simply subtract the measured vertical coordinate from 240: (240 - Vert Coord).
Next in the analysis is to convert to real-life dimensions in both horizontal and vertical directions. Use the conversion information described above (1 m = 110 pixels) to determine the conversion factor. Then write a formula in the spreadsheet for new columns of real-life horizontal and vertical positions (X and Y).
Calculate the horizontal and vertical velocity (Vx and Vy) across time using the first central difference formula in the next two columns of the spreadsheet.
From the computed velocities, use the first central difference formula to calculate the horizontal and vertical accelerations (Ax and Ay) across time. Place the answers in the next two columns of the spreadsheet.
Finally, to display your results, create graphs of :
· position vs. time
· velocity vs. time
· acceleration vs. time
for the jump. On each graph include both the horizontal and vertical components.
· SUMMARY REPORT
Based on your measured position data and calculations, briefly summarize the methodology and results of this experiment. Include responses to the following questions in your discussion. Limit this writing to one page single spaced. Attach printouts of your graphs and spreadsheet to the written paper and return these to your lab instructor at the beginning of the next lab meeting.
1. Through which frames was the jumper in flight, without contact with the ground?
2. How did the horizontal and vertical velocities change before the jumper left the ground? In which direction did the jumper accelerate with the greatest peak magnitude during take-off, forward or upward?
3. How did the velocity components change while the jumper was in flight? What should the acceleration components look like for the center of mass of a body in flight? Does this match the actual acceleration of the hip?
4. After landing, was the jumper propelling himself or braking himself in the horizontal and vertical directions? How can you tell?
5. Using a single point on the hip to characterize jumping mechanics was a simplification which made analysis of this jump easier to complete. What effect do you think this simplification had on the results? How could the whole body motion be determined more accurately for describing jumping mechanics?
6. How might this method be used for more general analysis of human motion?