San Marin High School
Gait Analysis
Austin Marr, Ben Klinge, Liz King, Dean Kidder-Buell
Senior Engineering - Period 1
Mr. Tronconi
October 12, 2018
Abstract
In this experiment, the gait of four students was observed in order to analyze general walking patterns. The data was used to formulate an equation which derives height from leg length and step frequency. The program used to take data on the students’ gait was a mobile phone application called Physics Toolbox Accelerometer. The cell phone was attached to the students’ lower backs, while they each walked 10 steps in a straight line. The phone application took detailed data of the accelerations experienced in three axis, and automatically converted this information to a spreadsheet. The data was analyzed in order to make observations on the gait of the general population. The data collected in this experiment was not extensive enough to create and test the accuracy of equations that predict the height and frequency of steps taken in one second of any subject.
Table of Contents
Introduction 4
Method 4
Results 4
Discussion 14
Conclusion 14
References 15
Appendix 15
IntroductionA fundamental concept in gait analysis is oscillations, which is a repetitive motion about an equilibrium position, where the amplitude is the maximum displacement from equilibrium. Oscillations are seen everyday, in the pendulum of a clock, people’s natural gait, waves of the ocean, vibrations of guitar strings, etc. For this project, the repetitive motion is each of us walking. The equations that help represent oscillations are frequency and wave speed.
f = 1T, where f represents frequency, where Trepresents period
c = , where c represents wave speed, where represents wavelength, where represents frequency
In addition, the kinetic energy of each person can be calculated through the equation:
KE = 12mv2, where m represents mass in kg, where v represents velocity in m/s
In this experiment, the equations of frequency, wave speed, and kinetic energy will be used with relation to each of our natural gaits to help answer the question, “What is the relationship between the height and gait frequency for walking humans?”
MethodFirst we measured the height and weight of each person, as well as their shoe sizes and tried to describe their walk. We duct-taped the phone to the lower back of each person, in contact with the skin. In our first trial, each person walked in a straight line for 10 steps. Everyone started with their right foot and walked how they normally would. For the second trial we walked in a straight line for 10 steps and starting with the right foot again, but we had a backpack on our backs, using both straps, that weighed 16 lbs. The app we used to record the data was called Physics Toolbox Accelerometer.
ResultsTable 1.1 - Information about each test subject
Subject
Height (cm)
Weight (kg)
Shoe Size (US mens)
Description of walk
Dean
183
63.5
10
Upright, flat, tiptoes
Ben
177
69.85
11
Sways, flat, waddles a little, sways side to side
Austin
168
58.97
8
Bouncy, feet on ground for long time, sways side to side
Liz
176
62.14
6
Evenly spaced steps with no abnormal movements
Table 1.2 - Distance walked with and without a backpack
Subject
Meters walked in 10 steps
Meters walked in 10 steps with 16 pound backpack
Dean
6.73
7.29
Ben
7.83
7.40
Austin
7.88
7.52
Liz
6.97
7.03
Table 1.3 - Leg length
Dean
Ben
Austin
Liz
1.12m
1.09m
1.04m
1.08m
In the following charts, the subjects were not wearing the backpack. Blue represents gFx, red represents gFy, and yellow represents gFz.
(Dean)
Frequency: 1.56 steps/second
Kinetic Energy: 57.52 J
v = d (m)t (s)
v = 6.73 m5 s
v = 1.346 m/s
KE = 12mv2
KE = 12(63.50kg)(1.346m/s)2
KE = 57.52 J
(Ben)
Frequency: 1.67 steps/second
Kinetic Energy: 85.65 J
v = d (m)t (s)
v = 7.83 m5 s
v = 1.566 m/s
KE = 12mv2
KE = 12(69.85kg)(1.566/s)2
KE = 85.65 J
(Austin)
Frequency: 1.76 steps/seconds
Kinetic Energy: 73.23 J
v = d (m)t (s)
v = 7.88 m5 s
v = 1.576 m/s
KE = 12mv2
KE = 12(58.97kg)(1.576m/s)2
KE = 73.23 J
(Liz)
Frequency: 1.57 steps/second
Kinetic Energy:
v = d (m)t (s)
v = 6.97 m5 s
v = 1.394 m/s
KE = 12mv2
KE = 12(62.14kg)(1.458m/s)2
KE = 60.38 J
In the following charts, the subject was wearing a 7.26kg backpack. Blue represents gFx, red represents gFy, and yellow represents gFz.
(Dean)
Frequency: 1.67 steps/second
Kinetic Energy: 75.21 J
v = d (m)t (s)
v = 7.29 m5 s
v = 1.458 m/s
KE = 12mv2
KE = 12(70.76kg)(1.458m/s)2
KE = 75.21 J
(Ben)
Frequency: 2.3 steps/second
Kinetic Energy: 84.45 J
v = d (m)t (s)
v = 7.40 m5 s
v = 1.48 m/s
KE = 12mv2
KE = 12(77.11kg)(1.48m/s)2
KE = 84.45 J
(Austin)
Frequency: 1.67 steps/second
Kinetic Energy: 74.90 J
v = d (m)t (s)
v = 7.52 m5 s
v = 1.504 m/s
KE = 12mv2
KE = 12(66.22kg)(1.504m/s)2
KE = 74.90 J
(Liz)
Frequency: 1.54 steps/second
Kinetic Energy: 68.60 J
v = d (m)t (s)
v = 7.03 m5 s
v = 1.406 m/s
KE = 12mv2
KE = 12(69.40kg)(1.406m/s)2
KE = 68.60 J
(Reference Tables 1.1 and 1.2)
After performing basic calculations, we were able to derive a predictive model that predicts frequency: f=(m[kg])/(23(h[m])
It works by plugging in an individual’s mass and height and retrieving the frequency as an output. The model is most likely not very accurate as we used the averages of only four people. Also, our range of age among test subjects was very small, so this model is likely even less reliable when used to calculate the step frequency of a person with large age variance. We found this model by graphing regressions of weight vs. height and weight v frequency, and comparing the lines. We took basic observations in an attempt to deduct the best method of formulating a predictive model. After this we made a table of our weights, height, and frequency and compared the data. We multiplied frequency by height, and divided our weight by that product. We averaged the quotients of that function to find our constant K to be about 20. This equation allows us to predict the number of steps each subject took in one second, however we were unable to measure it accurately to allow us to determine if our equation is accurate.
(Reference Table 1.3) (L = leg length (m))
Height = L(1.64 steps/s) -0.0153
We are able to predict the height of someone by using their leg length and multiplying it by the average frequency. We then subtracted a constant, 0.0153, that was derived from the average standard deviation between all of our heights. This worked with Liz, who has a leg length of 1.08m and a height of 1.76m, and Ben, who has a leg length of 1.09m. The equation was slightly off with the predicted heights of Austin and Dean; it added an inch to Austin’s height and subtracted one from Dean’s. This may be because the measurements taken of the subjects’ legs is slightly off for these two subjects. Overall, this model equation is able to predict the height of a subject with a deviation of about one inch.
DiscussionOur data was inconsistent. Austin was the shortest person in our group, 168 centimeters, but he walked the second farthest length. Liz was the second shortest person, and she walked the second shortest length without the backpack, and the shortest length with it. Ben was the second tallest person, at 177 centimeters, and he walked the farthest in both trials. Dean was the tallest in the group, at 183 centimeters, and he walked the shortest length without the backpack, but with it, he walked the second shortest. The person who took the least steps per second walked the shortest distance, but the reason for this was unclear to us. Our data did not seem to correspond to height or weight. It may have been related to stride length. We should have done more trials with each person. We conducted three tests with each subject, but should have done it a few more times in order to determine whether or not our data was accurate. We only measured our subjects’ height, weight, shoe size, and the distance they walked in 10 steps. Because our data didn’t correspond with our results, this means we should have measured more to try to figure out what determines the gait. We could have measured stride, how long their foot is on the ground, and their waist circumference. In the future, we will conduct more tests, with more subjects, and will collect more data from each subject before the tests. Our predictive model was very accurate despite the inconsistent data we collected. Although we were unable to figure out what determines the gait frequency of each subject, it was correct because we were able to find the height of the subjects using our predictive equation.
ConclusionIn the end,we were unable to conclude what determines gait frequency of someone because the data that we gathered was very inconsistent in terms of our height, weight, and shoe size. We conducted multiple tests with and without us wearing a backpack. We were able to create an equation that predicts height, f=(m[kg])/(23(h[m]), because the data required to determine this was simple to record and we did so in a uniform fashion. Our group worked well together when conducting the trials. We communicated with one another other well and used our resources to benefit us. We learned that very specific data is hard to obtain consistently, especially with the measuring devices we had access to. Finding an equation for the height of the subject was one of the main challenges for we had. We learned that different variables coming together with one or more constants can determine the height of the subject. Our equation works but with a minute amount of inaccuracy.
ReferencesTronconi, Claudio. “Gait Analysis.” STEM Engineering, Mr. Tronconi, sites.google.com/students.nusd.org/stemse/unit-2/u2-gait-analysis?authuser=2.
Chrystian Vieyra. Physics Toolbox Accelerometer. Vieyra, October 5, 2018. Version 1.3.3.
Knight, Randall Dewey, et al. College Physics: a Strategic Approach. Pearson, 2018.
AppendixSee results section.
Gait Analysis
Austin Marr, Ben Klinge, Liz King, Dean Kidder-Buell
Senior Engineering - Period 1
Mr. Tronconi
October 12, 2018
Abstract
In this experiment, the gait of four students was observed in order to analyze general walking patterns. The data was used to formulate an equation which derives height from leg length and step frequency. The program used to take data on the students’ gait was a mobile phone application called Physics Toolbox Accelerometer. The cell phone was attached to the students’ lower backs, while they each walked 10 steps in a straight line. The phone application took detailed data of the accelerations experienced in three axis, and automatically converted this information to a spreadsheet. The data was analyzed in order to make observations on the gait of the general population. The data collected in this experiment was not extensive enough to create and test the accuracy of equations that predict the height and frequency of steps taken in one second of any subject.
Table of Contents
Introduction 4
Method 4
Results 4
Discussion 14
Conclusion 14
References 15
Appendix 15
IntroductionA fundamental concept in gait analysis is oscillations, which is a repetitive motion about an equilibrium position, where the amplitude is the maximum displacement from equilibrium. Oscillations are seen everyday, in the pendulum of a clock, people’s natural gait, waves of the ocean, vibrations of guitar strings, etc. For this project, the repetitive motion is each of us walking. The equations that help represent oscillations are frequency and wave speed.
f = 1T, where f represents frequency, where Trepresents period
c = , where c represents wave speed, where represents wavelength, where represents frequency
In addition, the kinetic energy of each person can be calculated through the equation:
KE = 12mv2, where m represents mass in kg, where v represents velocity in m/s
In this experiment, the equations of frequency, wave speed, and kinetic energy will be used with relation to each of our natural gaits to help answer the question, “What is the relationship between the height and gait frequency for walking humans?”
MethodFirst we measured the height and weight of each person, as well as their shoe sizes and tried to describe their walk. We duct-taped the phone to the lower back of each person, in contact with the skin. In our first trial, each person walked in a straight line for 10 steps. Everyone started with their right foot and walked how they normally would. For the second trial we walked in a straight line for 10 steps and starting with the right foot again, but we had a backpack on our backs, using both straps, that weighed 16 lbs. The app we used to record the data was called Physics Toolbox Accelerometer.
ResultsTable 1.1 - Information about each test subject
Subject
Height (cm)
Weight (kg)
Shoe Size (US mens)
Description of walk
Dean
183
63.5
10
Upright, flat, tiptoes
Ben
177
69.85
11
Sways, flat, waddles a little, sways side to side
Austin
168
58.97
8
Bouncy, feet on ground for long time, sways side to side
Liz
176
62.14
6
Evenly spaced steps with no abnormal movements
Table 1.2 - Distance walked with and without a backpack
Subject
Meters walked in 10 steps
Meters walked in 10 steps with 16 pound backpack
Dean
6.73
7.29
Ben
7.83
7.40
Austin
7.88
7.52
Liz
6.97
7.03
Table 1.3 - Leg length
Dean
Ben
Austin
Liz
1.12m
1.09m
1.04m
1.08m
In the following charts, the subjects were not wearing the backpack. Blue represents gFx, red represents gFy, and yellow represents gFz.
(Dean)
Frequency: 1.56 steps/second
Kinetic Energy: 57.52 J
v = d (m)t (s)
v = 6.73 m5 s
v = 1.346 m/s
KE = 12mv2
KE = 12(63.50kg)(1.346m/s)2
KE = 57.52 J
(Ben)
Frequency: 1.67 steps/second
Kinetic Energy: 85.65 J
v = d (m)t (s)
v = 7.83 m5 s
v = 1.566 m/s
KE = 12mv2
KE = 12(69.85kg)(1.566/s)2
KE = 85.65 J
(Austin)
Frequency: 1.76 steps/seconds
Kinetic Energy: 73.23 J
v = d (m)t (s)
v = 7.88 m5 s
v = 1.576 m/s
KE = 12mv2
KE = 12(58.97kg)(1.576m/s)2
KE = 73.23 J
(Liz)
Frequency: 1.57 steps/second
Kinetic Energy:
v = d (m)t (s)
v = 6.97 m5 s
v = 1.394 m/s
KE = 12mv2
KE = 12(62.14kg)(1.458m/s)2
KE = 60.38 J
In the following charts, the subject was wearing a 7.26kg backpack. Blue represents gFx, red represents gFy, and yellow represents gFz.
(Dean)
Frequency: 1.67 steps/second
Kinetic Energy: 75.21 J
v = d (m)t (s)
v = 7.29 m5 s
v = 1.458 m/s
KE = 12mv2
KE = 12(70.76kg)(1.458m/s)2
KE = 75.21 J
(Ben)
Frequency: 2.3 steps/second
Kinetic Energy: 84.45 J
v = d (m)t (s)
v = 7.40 m5 s
v = 1.48 m/s
KE = 12mv2
KE = 12(77.11kg)(1.48m/s)2
KE = 84.45 J
(Austin)
Frequency: 1.67 steps/second
Kinetic Energy: 74.90 J
v = d (m)t (s)
v = 7.52 m5 s
v = 1.504 m/s
KE = 12mv2
KE = 12(66.22kg)(1.504m/s)2
KE = 74.90 J
(Liz)
Frequency: 1.54 steps/second
Kinetic Energy: 68.60 J
v = d (m)t (s)
v = 7.03 m5 s
v = 1.406 m/s
KE = 12mv2
KE = 12(69.40kg)(1.406m/s)2
KE = 68.60 J
(Reference Tables 1.1 and 1.2)
After performing basic calculations, we were able to derive a predictive model that predicts frequency: f=(m[kg])/(23(h[m])
It works by plugging in an individual’s mass and height and retrieving the frequency as an output. The model is most likely not very accurate as we used the averages of only four people. Also, our range of age among test subjects was very small, so this model is likely even less reliable when used to calculate the step frequency of a person with large age variance. We found this model by graphing regressions of weight vs. height and weight v frequency, and comparing the lines. We took basic observations in an attempt to deduct the best method of formulating a predictive model. After this we made a table of our weights, height, and frequency and compared the data. We multiplied frequency by height, and divided our weight by that product. We averaged the quotients of that function to find our constant K to be about 20. This equation allows us to predict the number of steps each subject took in one second, however we were unable to measure it accurately to allow us to determine if our equation is accurate.
(Reference Table 1.3) (L = leg length (m))
Height = L(1.64 steps/s) -0.0153
We are able to predict the height of someone by using their leg length and multiplying it by the average frequency. We then subtracted a constant, 0.0153, that was derived from the average standard deviation between all of our heights. This worked with Liz, who has a leg length of 1.08m and a height of 1.76m, and Ben, who has a leg length of 1.09m. The equation was slightly off with the predicted heights of Austin and Dean; it added an inch to Austin’s height and subtracted one from Dean’s. This may be because the measurements taken of the subjects’ legs is slightly off for these two subjects. Overall, this model equation is able to predict the height of a subject with a deviation of about one inch.
DiscussionOur data was inconsistent. Austin was the shortest person in our group, 168 centimeters, but he walked the second farthest length. Liz was the second shortest person, and she walked the second shortest length without the backpack, and the shortest length with it. Ben was the second tallest person, at 177 centimeters, and he walked the farthest in both trials. Dean was the tallest in the group, at 183 centimeters, and he walked the shortest length without the backpack, but with it, he walked the second shortest. The person who took the least steps per second walked the shortest distance, but the reason for this was unclear to us. Our data did not seem to correspond to height or weight. It may have been related to stride length. We should have done more trials with each person. We conducted three tests with each subject, but should have done it a few more times in order to determine whether or not our data was accurate. We only measured our subjects’ height, weight, shoe size, and the distance they walked in 10 steps. Because our data didn’t correspond with our results, this means we should have measured more to try to figure out what determines the gait. We could have measured stride, how long their foot is on the ground, and their waist circumference. In the future, we will conduct more tests, with more subjects, and will collect more data from each subject before the tests. Our predictive model was very accurate despite the inconsistent data we collected. Although we were unable to figure out what determines the gait frequency of each subject, it was correct because we were able to find the height of the subjects using our predictive equation.
ConclusionIn the end,we were unable to conclude what determines gait frequency of someone because the data that we gathered was very inconsistent in terms of our height, weight, and shoe size. We conducted multiple tests with and without us wearing a backpack. We were able to create an equation that predicts height, f=(m[kg])/(23(h[m]), because the data required to determine this was simple to record and we did so in a uniform fashion. Our group worked well together when conducting the trials. We communicated with one another other well and used our resources to benefit us. We learned that very specific data is hard to obtain consistently, especially with the measuring devices we had access to. Finding an equation for the height of the subject was one of the main challenges for we had. We learned that different variables coming together with one or more constants can determine the height of the subject. Our equation works but with a minute amount of inaccuracy.
ReferencesTronconi, Claudio. “Gait Analysis.” STEM Engineering, Mr. Tronconi, sites.google.com/students.nusd.org/stemse/unit-2/u2-gait-analysis?authuser=2.
Chrystian Vieyra. Physics Toolbox Accelerometer. Vieyra, October 5, 2018. Version 1.3.3.
Knight, Randall Dewey, et al. College Physics: a Strategic Approach. Pearson, 2018.
AppendixSee results section.