PEP 294: Web-Based Labs

Lab #8: Ground Reaction Force

Before you start this lab, first read the general instructions for the PEP 294 web-based labs.

Procedures

According to the Newton's Law of Gravitation, any two objects with masses attract each other and the magnitude of this attracting force is proportional to the product of the masses and inversely proportional to the square of the distance. This also holds for the gravitation between the earth and an object on the earth. The gravitational force acted upon an object by the earth is called gravity or weight of the object.

Since we always have contact with the ground due to this gravity there always is an interaction between our bodies and the ground. According to the Newton's Law of Reaction, there is an equal and opposite reaction to every action. In other words, the action to the ground is always accompanied by a reaction from it. This reaction force from the ground is called the ground reaction force (R in Figure 1). The ground reaction force is an important external force acting upon the human body in motion. We use this force as propulsion to initiate and to control the movement.

According to the Newton's Law of Acceleration, the external forces acting on the body causes an acceleration:

F = ma   [1]

where, F = sum of the external forces (vector), m = mass of the subject (scalar), and a = acceleration (vector) of the subject's center of mass (COM). In Figure 1, the two external forces acting on the subject's body are the weight of the jumper (W) and the ground reaction force from the ground (R). Therefore:

F = R + W    [2a]

Here, note that weight W always acts downward. Considering only the vertical forces and their directions:

Fz = Rz - W    [2b]

where Fz = net vertical force acting on the body, Rz = the vertical ground reaction force, and W = weight of the body. From [1] and [2b]:

Rz - W = maz    [2c]

where az = magnitude of the vertical acceleration. Or

az = ( Rz - W ) / m    [3]

Now, let's focus on the relationship between Rz and W, and the resulting az:

Rz vs. W az
Rz > W az > 0
Rz = W az = 0
Rz < W az < 0

By measuring the ground reaction force you will be able to compute the acceleration of the COM and predict its motion.

The purpose of this lab is to understand the nature of the interaction between the human foot and the ground in running. The vertical component of the ground reaction force (Rz in [3]) will be examined and its properties will be discussed.

Step 1: Force Plate

A force plate is normally used in measuring the ground reaction force. There are four 3-axial force sensors embedded in the plate so that one can measure the ground reaction force in 3 axes: transverse axis (X axis shown in Figure 2a), antero-posterior axis (Y axis), and vertical axis (Z axis)

Figure 2b shows the reactions from the ground to the foot. The sum of all the reactions from the ground shown in Figure 2b is equivalent to the sum of the forces measured by the four force sensors in the plate (R1 + R2 + R3 + R4) shown Figure 2c. The ground reaction force (R) is the sum of these forces as shown in Figure 2d.

The ground reaction force has three components: X-, Y- and Z-components (Rx, Ry & Rz). Among these, the Y-component is along the direction of the motion which reflects the propulsion or the braking force. The Z-component is used to support the body so that to prevent the body from collapsing, and also to thrust the body upward in jumping motion. We, in this lab, will focus on the vertical component of the ground reaction force (Rz).

Step 2: Rz Pattern in Jogging

wpe15.jpg (9346 bytes)Figure 3 shows a typical Rz pattern during jogging. There are two peaks in the vertical ground reaction force. The first peak is called the impact peak (P1) while the second is called the propulsion peak (P2). The impact peak is associated with the impact of the foot to the ground during early foot contact phase. The propulsion peak is associated with the propulsion of the body forward. It has always been the main focus of the shoe engineers that how to design the shoe-sole to reduce the impact peak while maintaining the propulsive characteristics.

The max. vertical ground reaction force in jogging reaches 2 to 3 times the body weight. The factors affecting the magnitude of the ground reaction force are running style (rearfoot, midfoot or forefoot strike), running speed, footwear, ground surface, inclination of the ground, etc.

T1 in Figure 3 is the impact peak time, the instant when P1 occurs, while T2 is the propulsion peak time. The time periods involved in ground reaction force development are also very important since these determine the rate of impact or force development.

[Example]   Vertical Ground Reaction Forces in Jogging

Table 1 shows the results from a jogging trial. The vertical ground reaction forces are provided in the table. Click here to download the worksheet file for this example.

Table 1. Vertical Ground Reaction Force in Jogging

Time (s) Rz (N)
0.00 4.4
0.01 44.5
0.02 111.2
0.03 849.6
0.04 1832.6
0.05 1507.9
0.06 1894.8
0.07 2277.4
0.08 2624.3
0.09 2833.4
0.10 3104.7
0.11 3135.8
0.12 3064.7
0.13 2900.1
0.14 2579.8
0.15 2188.4
0.16 1708.0
0.17 1241.0
0.18 818.4
0.19 507.1
0.20 302.5
0.21 146.8
0.22 40.0
0.23 4.4
0.24 0.0

Note that the sampling rate of data collection was 100 samples/s so that the Time Constant is 0.01 s/sample.

1. Weight of the Subject: Subject's mass is 94 kg, so his weight (in N) is:

W = mg = (94)(9.81) = 922.14 N

where g = gravitational acceleration.

2. Vertical acceleration of the Subject's COM: Using [3b], compute the vertical accelerations (az). For example, the acceleration at t = 0.00 s is

az = ( Rz - W ) / m = ( 4.40 - 922.14 ) / 94.0 = -9.76 m/s2.

See the complete acceleration table found in the exemplar worksheet.

3. Rz-time curve & az-time curve: Use proper scales for the horizontal (time) & vertical (Rz & az) axes.

4. Peak Forces (P1 & P2): Find the impact peak (P1) and the propulsion peak (P2). Also find the impact peak time (T1) and the propulsion peak time (T2):

P1 = 1832.6 N

T1 = 0.04 s

P2 = 3135.8 N

T2 = 0.11 s

5. Loading Rate (R1). First, find the sample whose Rz gets larger than 50 N for the first time, and read its value (F50+) and time (T50+):

F50+ = 111.2 N

T50+ = 0.02 s

Then use the following equation to compute the loading rate:

= 86070.00 N/s

The loading rate is important since it reflect the force development rate during impact phase of running. Loading rate is closely related to the hardness of the shoe sole and the running speed.

6. Decay Rate (R2): Find the sample whose Rz gets smaller than 50 N for the first time after P2, and read its value (F50-) and time (T50-):

F50- = 40.00 N

T50- = 0.22 s

Use the following equation to compute the decay rate:

= -28143.64 N/s

The decay rate is closely related to the running speed. It is smaller than the loading rate by a factor of approximately 5. If the decay time (T50- - T2 in the above equation) is too long with relatively low Rz, there is a danger of slipping.

Stage 3: Data Collection (5 points)

Data collection will be performed at the Biomechanics Lab during the lab session. Students will be divided into groups. The Rz-time data will be posted on the web.

Summary

1. The ground reaction force is the reaction to the force you exert on the ground.

2. The ground reaction force is an important external force affecting human motion.

3. The two external forces acting on a running subject are the ground reaction force and the subject's weight.

4. The acceleration of the subject's COM is determined by the relative magnitudes of the ground reaction force and the weight.

5. According to the Newton's Law of Acceleration, sum of the external forces acting on a body is equal to the product of the object's mass and the acceleration of its COM.

6. The vertical ground reaction force (Rz) pattern in running typically shows two peaks: impact peak and propulsion peak.

7. The loading rate and the decay rate are computed from the peak forces and the time information and reflect the interaction conditions between the foot and the ground.

Questions (15 points)

Download the worksheet file of your group:

294.2: Group 1, Group 2, Group 3, Group 4
294.4: Group 1, Group 2, Group 3

Attach the completed worksheet to the lab report.

1. Compute the vertical acceleration of subject's COM due to Rz. (2 points)

2. Draw the Rz-time & az-time graphs. Insert the graphs in your lab report. Hint: Use the scatter-gram. (4 points)

3. Find the impact peak (P1), the impact peak time (T1), the propulsion peak (P2), and the propulsion peak time (T2). Describe also the impact peak and the propulsion peak in subject's body weight. (6 points)

4. Compute the loading rate (R1) and the decay rate (R2). (2 points)

5. What is ground reaction force? Discuss the importance of the ground reaction force in human motion. (2 points)