LAB 2: VISUAL ODOMETRY
Minh Thai Tran
Texas A&M University
College Station, TX 77843, US.
Abstract
This report covers an experiment using visual odometry with the help of some modern equipment in order to find
the exact value of gravitational acceleration g in actual physics movements. As the tracking camera equipped at the
lab station measures objects in pixels unit, first the experiment will be made with a meter stick to determine the
conversion factor from pixels to SI unit of meters. Then a hockey punk labeled with colored sticker is utilized and
put to repeatedly slide down on the surface of an air lift table with an inclined degree of 3.6 and from the
experiment, the velocities, positions and accelerations of the punk at many different times can be measured and
calculated. Based from these measurements, the gravitational acceleration of the punk and its uncertainty can be
calculated which gives a value closely match the theoretical value of g equal to 9.81 𝑚/𝑠 2 .
Keywords: gravitational acceleration, inclined surface, odometry, uncertainty
1. Introduction
The goal of this lab is to provide a practical measurement of gravitational acceleration and its affect on the
movement of an object. From theoretical knowledge, it is known that gravitational acceleration is the acceleration
of an object in free fall within a vacuum. Every object on Earth are being affected by gravitational acceleration and
it can be defined as ratio of the object moving acceleration with the sine of the inclined angle as shown in
Equation 1 below
𝒂 = 𝒈 ∗ 𝐬𝐢𝐧 (𝜽) Equation 1
where a is the moving (or actual) acceleration of the object and g is the gravitational acceleration. It should be
noted that in order to use this formation, here the acceleration a must be the acceleration of y component, or 𝒂𝒚 .
For the lab the units of those properties are defined as m/s 2. From this lab, we can determine the positions with
their respectively times of the punk by utilizing simple physics Equation 2 and Equation 3 below
𝚫𝒔
𝒗= Equation 2
𝚫𝒕
where v is the velocity of the punk in m/s and equal to the change in positions (m) divide by the change in time (s).
Also:
𝚫𝒗
𝒂= Equation 3
𝚫𝒕
where a is the acceleration of the punk (m/s 2 ) and equal to the change in velocities (m/s) divide by the change in
time (s). In this lab, acceleration can also be determined as the second derivative of the velocity function. One
assignment of this experiment is to determine the uncertainty associated with this g measurement. Uncertainty can
be found by many different ways but in this report, uncertainty of g is calculated using an Excel function called
STDEV which is defined as the standard deviation from the data set of gravitational acceleration values and divides
that value with the square root of samples. This obtained value of g can also be compared with the actual
gravitational acceleration value of 9.81 m/s 2. Some Excel functions will be utilized for some calculations of this
lab.
2. Experimental Procedure
For this experiment, first we use a tracking camera equipped to The Visualization Studio to measure the average
length of a known value of millimeters on a meter stick (300 mm for this lab) in pixels using the tracking camera
measurement. The obtained value is sufficient to derive a conversion factor from pixels into millimeter or meter.
After that, a hockey punk labeled with colored sticker is utilized and put to repeatedly slide down on the surface of
an air lift table with an inclined degree of 3.6 with respect to the horizontal and from the experiment, positions of
the punk with their respective time can be captured in pixels and seconds. Using the conversion factor determined
previously, now the velocities and accelerations of the punk at many different times can be measured and
calculated. Based from these measurements, the gravitational acceleration of the punk and its uncertainty can be
calculated which gives a value closely match the theoretical value of g equal to 9.81 m/s^2.
This study source was downloaded by 100000850872992 from CourseHero.com on 02-22-2023 04:08:01 GMT -06:00
https://www.coursehero.com/file/84395884/ENGR-216-Lab-2-Reportpdf/
Minh Thai Tran
Texas A&M University
College Station, TX 77843, US.
Abstract
This report covers an experiment using visual odometry with the help of some modern equipment in order to find
the exact value of gravitational acceleration g in actual physics movements. As the tracking camera equipped at the
lab station measures objects in pixels unit, first the experiment will be made with a meter stick to determine the
conversion factor from pixels to SI unit of meters. Then a hockey punk labeled with colored sticker is utilized and
put to repeatedly slide down on the surface of an air lift table with an inclined degree of 3.6 and from the
experiment, the velocities, positions and accelerations of the punk at many different times can be measured and
calculated. Based from these measurements, the gravitational acceleration of the punk and its uncertainty can be
calculated which gives a value closely match the theoretical value of g equal to 9.81 𝑚/𝑠 2 .
Keywords: gravitational acceleration, inclined surface, odometry, uncertainty
1. Introduction
The goal of this lab is to provide a practical measurement of gravitational acceleration and its affect on the
movement of an object. From theoretical knowledge, it is known that gravitational acceleration is the acceleration
of an object in free fall within a vacuum. Every object on Earth are being affected by gravitational acceleration and
it can be defined as ratio of the object moving acceleration with the sine of the inclined angle as shown in
Equation 1 below
𝒂 = 𝒈 ∗ 𝐬𝐢𝐧 (𝜽) Equation 1
where a is the moving (or actual) acceleration of the object and g is the gravitational acceleration. It should be
noted that in order to use this formation, here the acceleration a must be the acceleration of y component, or 𝒂𝒚 .
For the lab the units of those properties are defined as m/s 2. From this lab, we can determine the positions with
their respectively times of the punk by utilizing simple physics Equation 2 and Equation 3 below
𝚫𝒔
𝒗= Equation 2
𝚫𝒕
where v is the velocity of the punk in m/s and equal to the change in positions (m) divide by the change in time (s).
Also:
𝚫𝒗
𝒂= Equation 3
𝚫𝒕
where a is the acceleration of the punk (m/s 2 ) and equal to the change in velocities (m/s) divide by the change in
time (s). In this lab, acceleration can also be determined as the second derivative of the velocity function. One
assignment of this experiment is to determine the uncertainty associated with this g measurement. Uncertainty can
be found by many different ways but in this report, uncertainty of g is calculated using an Excel function called
STDEV which is defined as the standard deviation from the data set of gravitational acceleration values and divides
that value with the square root of samples. This obtained value of g can also be compared with the actual
gravitational acceleration value of 9.81 m/s 2. Some Excel functions will be utilized for some calculations of this
lab.
2. Experimental Procedure
For this experiment, first we use a tracking camera equipped to The Visualization Studio to measure the average
length of a known value of millimeters on a meter stick (300 mm for this lab) in pixels using the tracking camera
measurement. The obtained value is sufficient to derive a conversion factor from pixels into millimeter or meter.
After that, a hockey punk labeled with colored sticker is utilized and put to repeatedly slide down on the surface of
an air lift table with an inclined degree of 3.6 with respect to the horizontal and from the experiment, positions of
the punk with their respective time can be captured in pixels and seconds. Using the conversion factor determined
previously, now the velocities and accelerations of the punk at many different times can be measured and
calculated. Based from these measurements, the gravitational acceleration of the punk and its uncertainty can be
calculated which gives a value closely match the theoretical value of g equal to 9.81 m/s^2.
This study source was downloaded by 100000850872992 from CourseHero.com on 02-22-2023 04:08:01 GMT -06:00
https://www.coursehero.com/file/84395884/ENGR-216-Lab-2-Reportpdf/
