EXSS 323 IMPULSE AND GROUND REACTION FORCE LAB

This lab was developed by Gerry Smith, Ph.D., formerly of Oregon State University, and is used by permission. Portions in italics are additions/modifications to the original and were made by Gary Christopher, M.S., A.T.C.

• INTRODUCTION

  In last week's lab, you measured the vertical ground reaction force during vertical jumps. The force-time curves which resulted were assessed qualitatively without detailing the relationships of force to resulting movement. This week's lab will continue with analysis of ground reaction forces (GRF) and the relationship of force, time, impulse and velocity.

  Newton's second law (F = ma) can be written in a form which includes the definition of acceleration:

  

  With simple algebraic rearrangement, this can be written as:

  

  or

  Impulse = Change of Momentum

  The "Impulse" part of this expression is a new quantity in our study of mechanics. It depends on both force and the time over which the force was applied. Units of impulse involve force and time: N*s.

  This impulse-momentum relationship is an important means of determining what motion results from an applied force. In the case of constant force application, impulse is particularly easy to calculate. However, if force is not constant (which is typical of most real situations) a slightly different understanding must be used. Consider the force-time graphs shown in figure 1.

  In the first graph, force is constant. The impulse of the force is just the value of the force times the time of application. On the graph, this corresponds to the shaded rectangular area below the force line (2 Ns).

  On the second graph, force is not constant. The impulse cannot be calculated based on a constant force times its period of application as was done in the first case. However, the idea of area under the force graph is still appropriate. If we could determine that area we would know the impulse (and consequently the change of momentum).

  So, how to determine the area under the force-time graph? Several ways of estimating the area under a graph are often used:

  1. Plot the graph on a grid and count the number of squares under the curve.
  2. Approximate the force-time curve using straight line segments. Then use formulas for the area of triangles and rectangles.
  3. Approximate the area as a set of vertical bars where the height of each bar is the average values of the data points at sides of the bar. The area of each bar (a rectangle) is then the product of its height and its width (time between measurements). The impulse is the sum of the areas of the bars.

     This is illustrated below for forces of 1, 1.2, 1.5, 1.9, 2.4 and 3.0 N at the times shown on the graph. The impulse of the first shaded bar can be found by first getting the average force of the two samples determining its height (1.2 and 1.5 N). The average force is 1.35 N over the interval of 0.2 seconds (0.2 to 0.4). Hence the impulse (shaded area) is 1.35 N times 0.2 seconds which is 0.27 Ns.

     For the second shaded bar the average force is 2.15 N and the impulse would be 0.43 Ns of impulse. If you follow this procedure for the whole area under these six data points, the impulse is 1.8 Ns.

  In general, this third method is most commonly used in determining the impulse of biomechanical forces.

• PART 1 METHODS

  A vertical jump force-time curve has been included for illustration. A body weight (BW) line has been added to the graph. The total force acting on the jumper is the ground reaction force minus gravitational force (BW). Thus to calculate the impulse, one must first subtract off body weight. In effect, this is as if the zero point for the force axis was shifted upward. The shaded regions of the graph sum to produce the impulse before takeoff and the impulse after landing. The regions below the BW line are "negative areas."

  In equation form this can be written out as follows:

  First, let Fi be the force at some instant in time. The total force acting on the person at that instant will be Fi - Body Weight (BW). The impulse of the force for samples Fi and Fi+1 would be:
  

            (Fi - BW) + (Fi+1 - BW)
  Impulse = ______________________ *(Time Interval between samples)  
                      2
  

  Note that this is the area or Impulse under just one strip or one interval from i to i+1. The Total Impulse would involve summing each of these strips up to the time of takeoff.

  To determine body weight (BW), take an average force from the first several (20-30) frames of "zero corrected" data. This average is the Body Weight (don't worry that it doesn't match your body weight precisely).

  Using force-time data from last week's lab, determine the vertical impulse up to the point of takeoff for both of your jumps (Squat & Countermovement). Then determine the impulse from the landing point in time to the end of the data collection. Use a spreadsheet to calculate the total impulse. Set up the spreadsheet as follows:

  Time (seconds)	GRF (N)	GRF - BW (N)	Average Force (N)	Area of strip (N*s)
  0.00
  0.01
  0.02
  0.03
  0.04
  etc.

  In your spreadsheet, write a formula to determine the impulse up to takeoff and the impulse from the landing point. Make note of the flight time of the jump.

• PART 2 METHODS

  On an attached page, Force-Time data are tabulated along with a graph to illustrate the characteristics of a standing long jump. Determine the vertical and horizontal impulse for the jump up to the point of takeoff. The mass of the jumper in this case was 63 kg.

• SUMMARY REPORT:

  Based on your data analysis and results, briefly summarize the procedures used to determine impulse of ground reaction force. In addition, discuss the meaning of impulse and how it relates to movement that it caused. In your summary and discussion, include responses to the following questions. Limit this writing to one page single spaced. Attach printouts of your Takeoff and Landing impulse calculations from your own jumps, plus the entire table created for the Standing Long Jump to the written paper and return these to your lab instructor at the beginning of the next lab meeting.

  1. For Part 1: From the impulse calculation, what was the vertical jumper's takeoff velocity? Based on this takeoff velocity, calculate the flight time and compare it with the measured flight time from the force lab. Explain any observed differences.
  2. For Part 1: How did the takeoff and the landing impulses compare for the vertical jumps (within jump, not across jumps)? Should these values be equal?
  3. For Part 2: From the impulse calculation, what was the long jumper's vertical and horizontal velocity at takeoff? What was the angle of projection of the long jump? (Based on the velocity components.)