The purpose of this experiment was to determine what formula would most accurately represent the velocity of an individual’s walking, speed walking, or jogging pace based on the length of their leg. Finding the correct formula could give amputees as easier transition to their new leg.
Contents
Introduction
Materials
Methods/Procedure
Data
Results/Findings
Graphs
Conclusion
Acknowledgements
Introduction
Prosthetic legs provide people with mobility after a life changing disaster. Adjusting to an aboveknee prosthetic leg is especially hard because an individual is missing both knee and ankle joints, which restricts their range of mobility. This Velocity Intended formula was created to help people who had gone through a dramatic change adjust to their new lives by providing a way for them to potentially customize the prosthetic leg to each person’s specific gait.
In a discussion about prosthetic legs, my physics teacher informed me of a human gait formula that I eventually based my experiment on. The formula 2.2 ·√l was created to predict the velocity of an individual’s walk based on the length of their leg in meters. The purpose of my experiment was to determine if the Velocity Intended formula 2.2 · √l would best fit the velocity of someone’s walking speed or if the Velocity Intended formula would better fit a speed walking or jogging gait.
Three variables –walking, speed walking, and jogging – were used to test if the Intended Velocity formula truly represented the velocity of an individual’s walk, or more closely represented an individual’s speed walk. I hypothesized that the formula would better represent a speed walk because the Velocity Intended formula was created from a pendulum formula meaning that the straighter the leg the more accurate the formula. Jogging was included as a control group for the experiment. When humans jog, they bend their knees allowing them greater mobility thus ignoring the straight leg motion the Velocity Intended formula was emphasizing.
Materials
Method/Procedure
The experiment was set up so the fortyeight students that participated could collect and calculate their data anonymously eliminating any legal restrictions. I demonstrated how to collect the data then supervised the fortyeight students while they completed the lab.
In order to find the correct spot to measure the proper length of leg, the students stood on one foot and swung their other leg back and forth feeling for the exact spot where their hipbone moved in its socket. The students then proceeded to cut a length of string from their hipbone to the floor. Each student measured their string with a meter stick to the nearest centimeter providing them with a very accurate representation of their leg length. String was used because it is a better technique for measuring something that is not completely straight. The students recorded their leg lengths on their lab papers.
Next, the class went into the hall where there was a 10meter stretch marked by tape for each student to walk, speed walk and jog down. Three student timers stood at the finish line and timed each student’s walk, speed walk, and jog. All three times for a particular gait were recorded and averaged to create a better more accurate representation of the time it took each student to cover the 10 meters. This was done for the three different gates. Each test was only run once per person due to time restraints.
Once the data was collected, the students calculated their average time by adding their times and dividing by three. They found their velocity by dividing the distance (10m) by their averaged time, and were able to predict their potential Velocity Intended with the formula 2.2 ·√l (meters). Each student’s data was anonymously recorded and documented on their individual lab sheet.
Before creating graphs, I reviewed and corrected any calculations that were incorrect. Then, I entered the fortyeight student’s data into Excel and created graphs comparing the Velocity Intended (2.2 ·√l ) versus the Velocity Measured (field data).
In order to determine if there was a correlation between the Velocity Measured (field data) and the Velocity Intended data, I took one standard deviation, 68.2%, of the collected data to determine if there was any overlap between the Velocity Intended formula and any of the Velocity Measured values.
In addition, I decided to calculate the R^{2 }values for the Velocities Measured which determines how closely the data represents a linear line for each of the walking, speed walking, and jogging data values. I then calculated the R^{2 }value for the Velocity Intended formula to see if there was any correlation between the Velocities Measured and Velocity Intended.
Results and Findings
When a line of best fit was drawn for each set of data on the graphs, the Velocity Intended was most consistent with the speed walk, as I had predicted.
Mathematically, I proved my hypothesis by averaging the data in each category and taking one standard deviation of the original data. I combined the averages and their respected standard deviations to see if there was any overlap. There was a considerable overlap between the speed walk and the velocity intended formula values. (See Table)
I continued to analyze my data by finding the R^{2} of each of the linear lines. This allowed me to see how accurate the line was to the data. The closer the decimal is to one, the more accurate the data is to the line of best fit. Although the Velocity Measured R^{2} values are very low, the speed walking R^{2} value was slightly higher than the walking and jogging values, which indicates that the data for the speed walking is more consistent than the walking and jogging values. (See Table)

Average Time 
1 standard deviation 
Range 
R^{2} 
Walk 
1.309 m/s 
+/ 0.161 m/s 
1.148 m/s – 1.47 m/s 
0.128 
Speed Walk 
2.315 m/s 
+/0.391 m/s 
1.924 m/s – 2.706 m/s 
0.190 
Jog 
2.693 m/s 
+/0.394 m/s 
2.299 m/s – 3.087 m/s 
0.123 
Velocity Intended Formula 
2.108 m/s 
+/0.071 m/s 
2.037 m/s – 2.179 m/s 
0.999 
Discussion and Conclusion
An analysis using one standard deviation showed an overlap between the speed walking and the Velocity Intended data values. In addition, it was noted that the R^{2 }values were slightly higher for the speed walk than for the walking and jogging values. The analysis proved my hypothesis that speed walking velocities best fit the Velocity Intended formula velocities.
Human error could have occurred throughout this study including timing and abnormal walking. The participants were told to walk normally, but subconsciously they may have walked slower in order to ensure they were walking “normally”. This issue could have been resolved if the participants did not know how far they were going, where the timing started, or if they walked a much greater distance than 10 meters.
Timing issues could have occurred including not starting together or not stopping once the person crossed the finish line. The experiment could also become more accurate if an automatic timer was used thus eliminating any human timing error.
With the data collected from these three tests I now know the Velocity Intended formula would have to be revised in order for prosthetic leg manufactures to better fit prosthetic legs to humans that have abovetheknee amputations. A revised formula could give amputees as easier transition to their new leg.
Acknowledgements
I would like to thank Wayne Latchford, my high school physics teacher, for guiding me as I went through this experiment. I would also like to thank the students in Anatomy & Physiology at Lewisburg Area High School for anonymously participating in my experiment, as well as Brandi Spotts, the high school Anatomy & Physiology teacher, for providing class time for her students to complete the calculations needed for my experiment.
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The purpose of this experiment was to determine what formula would most accurately represent the velocity of an individual’s walking, speed walking, or jogging pace based on the length of their leg. Finding the correct formula could give amputees as easier transition to their new leg.
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