INTRODUCTION

As discussed in class, many biomechnanical endeavors rely on the analysis of pictures, films or videos. These techniques can be used to analyze a variety of variables. We can measure the velocity of a kick or a pitch, the duration of foot contact with the ground of a sprinter, the stride length of a patient with artificial limb. This lab will track motion during a standing long jump. Horizontal and vertical positions 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 on 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:

                         (Real Length of Calibration Stick)
Conversion Factor (CF) = -----------------------------------
                         (Projected Length of Calibration Stick)

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:

       1 m
CF  = -----   =  0.125 m/mm
       8 mm

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 would be obtained by:

    64 mm      0.125 m
   -------  X  --------  =  8.00 m
      1          1 mm

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/t). 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 each 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:

            1              1
t  = --------------  =  ---------  =  0.01 seconds per frame
      camera speed       100 f/s

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 would be calculated in the following manner:

                    0.01 s
elapsed time  =  ( --------  )  X  (200 frames)  =  2.00 s
                     frame

From the displacement and the elapsed time, the runner's average velocity can be calculated:

        d        8.00 m
V  =  -----  =  ------- =  4.00 m/s
        t        2.00 s

METHODS

A video recording of a long jump has been include 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 beginning to end of the jump. Finally, determine the average velocity in both horizontal and vertical directions from image to image and over the whole jump.

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 may 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: It is best to use Firefox as the browser of choice for this lab. If the coordinates do not show up on your browser 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:

ANALYSIS OF THE JUMP:

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).

Then, calculate the horizontal and vertical velocity across time using the first central difference formula in the next columns of the spreadsheet.

Finally, to display your results, create graphs of position vs time and velocity vs time for the jump. On each graph include both horizontal and vertical components.

SUMMARY REPORT:

Based on your measured position data and calculations, briefly summarize, in your own words, the methodology and results of this experiment. Discuss how the method might be used for more general analysis of human motion. Include responses to the following questions in your discussion. Limit this writing to three pages double-spaced. Attach printouts of your graphs and spreadsheet to the written paper.

1. How did horizontal and vertical velocities change during the jump?

2. Through which frames was the jumper in flight without contact with the ground? How did the velocity components change during that period?

3. Based on the velocity graphs, qualitatively describe the acceleration of the jumper as a function of time. (Comment separately about horizontal and vertical components of acceleration.)

4. 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 more accurately be determined for describing jumping mechanics?