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Table of Contents
Introduction........................................................................................................... 1
Review of Literature...............................................................................................4
Problem Statement..............................................................................................10
Experimental Design...........................................................................................11
Data and Observations........................................................................................16
Data Analysis and Interpretation.........................................................................21
Conclusion...........................................................................................................33
Works Cited.........................................................................................................39
Lewandowski – Lidwell
Introduction
Soccer is a common pastime throughout the world, and possibly the
world’s most popular sport. The 2010 FIFA World Cup in South Africa in-home
television coverage reached 3.2 billion people (FIFA). Though many argue over
when the sport originated, the most widely accepted idea of its origin is in China
in 300 B.C. The Chinese called the game "Tsu Chu," which involved using no
hands to place a leather ball in a small hole (Blain). The game has now evolved
to the sport it is today, played with the approved ball type of the International
Federation of Association Football (FIFA), made out of synthetic leather at
standard sizes consisting of a cover, lining, stitching, and bladder, which is the
inside of the ball that holds the air in (Monet). Now, a soccer ball may seem like
any average ball, but many factors contribute to its performance. Some of these
factors include the ball’s diameter, air pressure, and the surface the balls roll on.
Knowledge of how a soccer ball travels on the ground is crucial to a quality
soccer game, for much of the ball’s traveling is done on the ground, as players
dribble the ball across the soccer field. The experiment that was performed
tested how these important factors affected the distance a soccer ball travels
when rolled from a ramp.
In the experiment that was conducted, different types of soccer balls were
used. The soccer balls used were size 3, size 4, and size 5, with diameters 7
inches, 8 inches, and 9 inches, respectively (Parrish). These sizes are
representative of the standard sizes of soccer balls that are most commonly
used, with smaller soccer balls being for young kids, and the larger soccer balls
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used in adult or professional soccer games. The recommended air pressure of a
soccer ball ranges from 6 psi to 12 psi (Parrish). The air pressure values of 6 psi,
9 psi, and 12 psi, were determined by using the high, low, and middle value of
the standard air pressure range of a soccer ball. The third factor in the
experiment was ground surface. Different surfaces cause different amounts of
friction between the soccer ball and ground surface. Because soccer balls and
other balls often roll on different surfaces, depending on where the game is being
played, whether it is in the streets, on the grass, or any other location such as
artificial turf, it is important to be aware of how the ball will perform on the
different surfaces. The surfaces of grass, dirt, and asphalt were chosen to test
the effect different coefficients have on the performance of soccer balls. Different
air pressures were used to determine how inflating the ball more would change
the distance, and different sizes were used to see how different size soccer balls
would travel. During the experiment, high and low levels of air pressure,
diameter, and ground surface were tested as the ball rolled down a wooden
ramp. The distance from the end of the ramp to the stopping point of the ball was
measured and analyzed so that the effects of the three factors could be
determined and then applied to the performance of a soccer ball.
The results from this experiment have many applications to various types
of people. First and foremost, the results can be used to improve the
performance of soccer players. A greater knowledge of how ground surface, air
pressure, and diameter affect the distance a soccer ball travels can help a soccer
player better prepare his ball for a game, better judge the distance that ball will
Lewandowski – Lidwell
travel as he is playing, and better transition from surface to surface when playing
in different places. For example, when he is playing on a grass surface, a soccer
player will know that he needs to account for a greater amount of friction in order
to achieve the necessary distance when dribbling the soccer ball. With an
increased awareness on soccer ball, the quality of players and the game itself
will increase. This knowledge can extend far past just the world of soccer into the
world of other sports that use balls, such as baseball. Although air pressure does
not apply, diameter and ground surface are important to baseball. Differences in
diameter would apply to softballs versus baseballs, and ground surfaces changes
as a ball rolls from the infield to the outfield. The results of this experiment can
improve the quality of baseball players. From a business standpoint, it is
important to make products that are as high-quality performing as possible.
Knowledge of the effects of ground surface, air pressure, and diameter can allow
manufacturers to create products that are best prepared for the different
conditions balls, or any other rolling product such as tires, may be exposed to
outside. They may even be inspired to research other factors that may affect the
performance of balls as well such as ball material. Whether people are athletes,
sports fans, businessmen, or just interested in science, the results of this
experiment can be applied to their lives.
Lewandowski – Lidwell
Review of Literature
The experiment conducted included a wide range of scientific topics and
applications. These topics and many previous experiments were examined in
order to determine the hypothesis of this experiment. The main topics that were
investigated were size of a soccer ball, air pressure of a soccer ball, and friction
of the ground surface on which the ball rolls.
One of the factors in the experiment was the air pressure of the soccer
ball. Air pressure is the force exerted by air on any surface in contact with it
(Benson). In this case, the air inside the soccer ball exerts a force on the surface
of the soccer ball. If there is more air and therefore more pressure, the ball will be
harder and more solid. The higher the pressure inside the ball, the farther the ball
should roll (Gibbs). If the ball has a higher psi (pounds per square inch), and
therefore more pressure, the soccer ball will have a smaller contact area with the
ground because it is inflated more and will flatten out less when coming in
contact with a surface. The laws of friction state that the area of contact between
the ball and the ground does not affect the friction between the surfaces, but it
will affect how far the ball travels. This law of friction changes when the surface
areas are small, because the coefficient of friction increases since the object may
sink into the surface somewhat (Nave). The ball has a very small contact area
with the ground, so the coefficient increases and the ball does not go as far.
Think of a ball that has been almost completely deflated. The ball will not roll far
because the bottom of the ball is flat and it must “roll over itself.” This can also be
seen in a rolling tire. The more a tire is inflated, the better it is able to roll (Barry).
Lewandowski – Lidwell
When the ball has a higher psi, it should travel farther because it would be easier
for it to roll over the surface.
One part of this experiment was determining what effect the diameter of
the ball would have on the distance traveled. The moment of inertia of an object
defines its resistance to a change in angular motion (Nave). The moment of
inertia of a soccer ball, measured in kg × m2, is found using the formula for the
moment of inertia of a hollow sphere I = ⅔mr2 where moment of inertia, I, is equal
to 2/3 times the mass of the ball, m, times the radius of the ball, r, squared
(McWeeny 66).
I = ⅔mr2
A smaller moment of inertia means that the ball would have a lower resistance to
a change in rotational motion, so it would rotate easier (Robertson). The less
mass and smaller radius a ball has, the less momentum it has. Momentum is
defined as the quantity of motion of a moving body. A smaller moment of inertia
and less momentum also means that an object will slow down easier. Lower
resistance to a change in motion works both ways, meaning that it is both easier
to start something in motion and slow it down. The smallest diameter soccer ball
would have the smallest moment of inertia because it has the smallest radius and
also a smaller mass than the other two. Because it is able to rotate more easily, it
will have a higher velocity than the larger soccer balls, and therefore travel
farther because of it going at a faster speed.
Ground surface was another factor in the conducted experiment. The ball
would roll farther on a surface with less friction. The type of friction that is
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primarily shown in this experiment is rolling friction. Rolling friction works in
largely the same way as kinetic friction except the object is not just sliding
forward, it is rolling. This is shown in Figure 1 below. A force acts on the rolling
object, causing it to roll and move forward. The force of friction that comes from
the ground opposes this motion, acting in the opposite direction, forcing it to slow
down.
Figure 1. Rolling Friction Diagram (Piccolo)
The surfaces from the lowest coefficient of friction to the highest are asphalt, dirt
(such as on a baseball diamond), and grass. Coefficient of friction is the frictional
force that resists the motion of an object. A higher coefficient of kinetic friction
between two objects means that the surface resists motion more (Schlager).
Newton’s first law states that an object in motion remains in motion until acted
upon by an unbalanced force, such as friction (“Newton’s First Law”). The grass
would act on the ball with the greatest frictional force, because it has the highest
coefficient, stopping it in the shortest distance. The distance traveled by the
soccer ball can also be determined by looking at how hard surfaces, such as
asphalt, and softer surfaces, such as grass, act on a hard or soft object. The
combination that would result in the farthest distance traveled is a hard object on
a hard surface (Kurtus). When a ball is rolling on grass, or when any object is
sliding on grass, there is more work being done. The ball must work to bend the
grass down to move over it and it could also get pushed slightly into the dirt
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below it. With asphalt, this is not the case. It is a flat surface with nothing on it, so
the ball can move over it easier. In the current experiment, the hardest object is
the most inflated ball and the hardest surface is asphalt, so the ball is likely to
travel the farthest under these circumstances.
An experiment related to the one conducted is an experiment performed
by Yusaka Tsuji and Yoshitsugu Muguruma in the Department of Mechanical
Engineering at Osaka University in Japan. The experiment tested the effect of
ball diameter on the motion of table tennis balls. The balls being tested, with
diameters of 38 mm, 39 mm, and 40 mm to represent standard table tennis ball
sizes, were placed at a uniform point on a table tennis table, and then set off at a
constant initial velocity and angle. Then, the velocity of the balls was measured
at key points along the table, including before the first bounce and directly after
the first bounce of the balls (Tsuji and Muguruma 42). After all the trials, it was
concluded that an increase in ball size lead to a decrease in the ball’s velocity at
the measured points along the table (Tsuji and Muguruma 53). This experiment
relates to the conducted experiment because diameter is a factor in both
experiments, and both involve the motion of balls. However, in the table tennis
balls experiment, velocity was measured after air travel, while in the soccer balls
experiment that was conducted, distance was measured after rolling on the
ground. Nonetheless, it was inferred that a velocity decrease in a ball travelling
through the air would lead to a velocity decrease rolling on the ground. A velocity
decrease would result in a decrease in the distance traveled by the ball,
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supporting the experiment’s hypothesis that the low ball diameter of 7 inches
would result in the greatest distance traveled by the soccer ball on the ground.
An experiment was done relating to moment of inertia by Hans J. Kolitzus
from the International Association for Sports Surface Sciences (ISSS). The
experimenter rolled a ball from a ramp onto a surface and determined moment of
inertia from that. The moment of inertia from this experiment can be used for the
soccer ball experiment. Both experiments use the moment of inertia for a hollow
sphere. The experiment helps determine the hypothesis for the conducted soccer
ball experiment because it shows that the smaller moment of inertia of a smaller
ball causes it to roll faster and farther. The conclusion for the experiment also
explains that the properties of a ball determine its speed.
Another experiment related to the soccer ball experiment conducted is an
experiment performed by Nancy K. O’Leary and Susan Shelly in one of O’Leary’s
college classrooms. O’Leary is working on a Ph.D. in both biology and chemistry,
and also teaches at both the high school and college level, whereas Shelly is a
journalist. The experiment tested how various amounts of air pressure in a
basketball affected its bounce. By starting with a standard pressure of 8 psi, the
ball was dropped from a set height and its bounce height was measured with a
meter stick. Then the psi of the basketball was increased or decreased by 1 psi,
and the ball was bounced again as the new bounce heights were recorded. After
the data was analyzed it was concluded that the higher the air pressure, the
higher the basketball bounced (O’Leary and Shelly). This experiment is similar to
the soccer ball experiment conducted because both tested the effect of air
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pressure in a ball. Also, both experiments measured the effect by releasing them
from a set point and measuring a distance, although the basketball’s bounce
height was measured versus the soccer ball’s rolling distance. The conclusion
from the basketball experiment proved that air pressure has a positive effect on
the performance of balls, within reason. This was applied to the soccer ball
experiment in the idea that a higher air pressure would lead to a greater distance
traveled by the soccer ball when rolled on the ground. Although the basketball
was bounced and the soccer ball was rolled, this experiment still provided a
general idea of how the soccer ball would perform in the experiment.
From the detailed scientific concepts along with the presence of various
similar experiments that were conducted by other researchers, it is obvious that
there is much science behind the performance of balls that can be applied to the
soccer ball experiment that was conducted. Whether it is soccer balls,
basketballs, or even table tennis balls, factors such as air pressure, diameter,
and ground surface play a key role in affecting ball velocity, bounce height, and
distance traveled. The science behind these factors and the previously
conducted experiments all lead to the hypothesis in the soccer ball experiment
that high air pressure, low diameter, and the hardest ground surface, would result
in the greatest distance traveled by the soccer ball. The findings of this
experiment can be helpful for a better understanding of the soccer ball and how it
works.
Lewandowski – Lidwell
Problem Statement
Problem:
To determine the effect of diameter, air pressure, and ground surface on
the distance traveled by soccer balls rolled down a ramp.
Hypothesis:
The high air pressure value, low diameter, and low ground surface will
cause the soccer ball to travel the farthest distance.
Data Measured:
The experiment was set up as a Three Factor DOE, with three runs of the
DOE. The factors, or independent variables, in the experiment were diameter of
the soccer, air pressure, and ground surface. The diameter was measured in
inches, the air pressure in pounds per square inch (PSI), and the ground surface
by the level of friction. The diameter values were 7” for the low, 8” for the
standard, and 9” for the high. The pressure values were 6 psi for the low, 9 psi
for the standard, and 12 psi for the high. The ground surfaces were asphalt for
the low, dirt for the standard, and grass for the high. The dependent variable, or
response variable, was the distance traveled by the soccer ball on the ground,
which was measured in meters.
Lewandowski – Lidwell
Experimental Design
Materials:
Franklin Sports MLS Ball Maintenance Kit 7.5-Inch Inflating PumpPressure GaugeExtender Piece(3) Metal Needles
Grass Surface Dirt Surface (Baseball Diamond Infield)Asphalt Surface (Parking lot)7” Diameter Size 3 Franklin Soccer Ball 8” Diameter Size 4 Baden Classic Soccer Ball 9” Diameter Size 5 Classic Sport Soccer Ball Empire Level 100' Open Reel Fiberglass Tape MeasureMMSTC Wooden Bowling RampTI-nspire Calculator
Procedures:
Randomization
1. Go to the random integer function on the calculator by pressing menu,
probability, random, and then integer.
2. In the randInt(), type in 1, 8, 8, to represent choosing the order of the eight
non-standard trials in a Three Factor DOE.
3. Record the trial order in the trial column of the data table, and follow that
order when testing the different high and low values for each ground
surface, air pressure, and diameter.
Experiment
1. Locate the three level surfaces (asphalt, dirt, and grass) on which to place
the ramp. Make sure that the chosen areas are as level as possible so the
soccer ball travels in a straight path.
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2. Mark the start position on the ground surfaces chosen to ensure that when
placing the ramp, the same area of ground surface is used.
3. Use data table to find the surface that is to be used, and place the ramp
on that surface.
4. To check psi level of ball, attach needle to pressure gauge from ball
maintenance kit. The low level pressure is 6 psi, the standard is 9 psi, and
the high air pressure is 12 psi.
5. Moisten needle and insert gauge slowly into ball. Read pressure gauge
and remove from ball.
6. If pressure is too low, attach other needle to pump. Moisten needle and
insert pump slowly into ball. Inflate ball and recheck air pressure.
7. If pressure is too high, attach other needle to extender piece, moisten, and
insert into ball so that air can escape. Take piece out and recheck air
pressure.
8. Take one end of the tape measure and place it at the end of the ramp, and
pull the tape measure out in a straight path from the bottom of the ramp as
someone holds the other end. For the grass trials pull the tape measure
out around 30 feet and for the high air pressure pull the tape measure out
around 55 feet.
9. Straighten the tape measure out as much as possible so that it acts as a
guide to monitor how straight the ball is rolling, and then place the tape
measure onto the ground surface.
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10. Take the soccer ball with the diameter that matches the trial number (7”
for low, 8” for standard, and 9” for high), and hold it at the top of the ramp
in the center.
11. Release the ball from the top of the ramp and allow it to roll until stopping.
12. When the ball stops, walk over to where the ball stopped rolling and read
on the tape measure where the ball stopped rolling. Use the center of the
ball as the point to match up with the measurement to ensure consistent
tape measure reading. See Figure 4.
13. Record the measurement in the data table.
14. Repeat steps 3-13 at the different high, low, and standard ground surface,
air pressure, and diameter values until the 3 Factor DOE is finished, and
then perform 2 more DOEs.
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Diagrams:
Figure 2. Experimental Materials
Figure 2 above shows the various materials used in the experiment,
excluding the ramp and the ground surfaces. The ramp is shown later in Figure
3. Labels indicate what each material is.
Figure 3. Experimental Setup
Figure 3 above shows the format of the experiment. The ball is released
from the top of the ramp after being placed in the center as shown in the soccer
balls position in the figure. The ball is released and rolls down the ramp in a
straight path next to the tape measure laid out as shown above. Then, the
distance from the end of the ramp to the soccer ball is measured.
Lewandowski – Lidwell
Figure 4. Measuring the Distance Traveled
Figure 4 above shows the point where the ball stopped rolling, at the end
of a trial. This is the point where the distance rolled by the ball was measured
and recorded by looking at the measuring tape. In this trial, the distance traveled
by the ball was near 17.7 feet.
Lewandowski – Lidwell
Data and ObservationsTable 1Experiment Data
Trial Number
Ground Surface(Friction)
Air Pressure
(PSI)
Diameter(Inches)
Distance (feet)Run
1Run
2Run
3 Average
***** standard standard standard 28.5 29.4 30.7 29.58 + + + 17.7 18.7 20.3 18.94 + + - 20.2 17.6 18.6 18.85 + - + 21.5 19.2 19.8 20.26 + - - 16.8 18.3 18.9 18.0
***** standard standard standard 28.7 29.8 31.0 29.82 - + + 36.5 38.0 36.9 37.11 - + - 43.8 46.0 44.1 44.63 - - + 47.6 39.9 44.0 43.87 - - - 52.3 44.2 48.3 48.3
****** standard standard standard 24.3 30.0 25.0 26.4
Table 1 above shows the data collected from the soccer ball trials. A total
of three 3 Factor DOEs were performed. The trial number column shows the
order each of the trials were performed due to randomization. The ground
surface, air pressure, and diameter columns all list whether a high, low, or
standard value was used for that factor when performing the trial. The total
distances traveled in each of the three DOEs are shown in the run columns. The
distances were found by just reading the measurement off the tape measure.
Then, the average of all three trials for each set of high, low, and standard values
is shown in the average column.
Table 2
Lewandowski – Lidwell
DOE Run 1 ObservationsDate Trial Observations4/23 1 Researcher 1 inflated the low diameter ball to the high air pressure
and rolled the ball down the ramp. Researcher 2 measured and recorded the distance the ball traveled.
4/23 2 Researcher 1 inflated the high diameter ball to the high air pressure and allowed ball to roll down the ramp. Research 2 measured and recorded the distance traveled.
4/23 3
Researcher 1 inflated the high diameter ball to the low air pressure and released the ball from the top of the ramp. Researcher 2 measured and recorded the distance traveled. It was very windy outside during this trial. The ball's path was not perfectly straight.
4/23 4
Researcher 1 inflated the low diameter ball to the high air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance the ball traveled. There was a large gust of wind during this trial. The grass was dry but the ground beneath it was slightly wet.
4/23 5
Researcher 1 inflated the high diameter ball to the low air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled by the ball. The grass was dry but the ground beneath it was slightly wet.
4/23 6
Researcher 1 inflated the low diameter ball to the proper air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled by the ball. The grass was dry but the ground beneath it was slightly wet.
4/23 7 Researcher 1 inflated the low diameter ball to the low air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled by the ball.
4/23 8
Researcher 1 inflated the high diameter ball to the high air pressure, rolled the ball down the ramp, measured the distance traveled by the ball. Researcher 2 recorded the distance traveled by the ball. The grass was dry but the ground beneath it was slightly wet.
Table 2 above shows the observations taken during the first DOE
performed. Significant occurrences were noted. All the trials of this DOE were
performed on the same day, April 23, 2013, which was a relatively dry, sunny
day.
Table 3
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DOE Run 2 Observations
Date Trial Observations
4/26 1
Researcher 1 inflated the low diameter ball to the high air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled. There was slight wind during this trial.
4/26 2
Researcher 1 inflated the high diameter ball to the high air pressure and allowed ball to roll down the ramp. Research 2 measured and recorded the distance traveled. The wind was blowing a lot during this trial.
4/26 3Researcher 1 inflated the high diameter ball to the low air pressure and released the ball from the top of the ramp. Researcher 2 measured and recorded the distance traveled.
4/26 4
Researcher 1 inflated the low diameter ball to the high air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance the ball traveled. The grass that the ball rolled on was wet and muddy.
4/26 5
Researcher 1 inflated the high diameter ball to the low air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled by the ball. The grass was wet and the ground was muddy.
4/26 6
Researcher 1 inflated the low diameter ball to the proper air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled by the ball. The grass was wet.
4/26 7Researcher 1 inflated the low diameter ball to the low air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled by the ball.
4/26 8
Researcher 1 inflated the high diameter ball to the high air pressure, rolled the ball down the ramp, measured the distance traveled by the ball. Researcher 2 recorded the distance traveled by the ball. The grass was wet and muddy.
Table 3 above shows the observations taken during the second DOE
performed. Significant occurrences were noted. All the trials of this DOE were
performed on the same day, April 26, 2013, which was a windy, wet day.
Between the day of the first DOE and second DOE it rained and the grass was
cut outside. Also, it was significantly colder than the day of the first DOE.
Table 4
Lewandowski – Lidwell
DOE Run 3 ObservationsDate Trial Observations
4/26 1
Researcher 1 inflated the low diameter ball to the high air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance the ball traveled. The wind picked up slightly during this trial. The ball curved slightly while rolling.
4/26 2Researcher 1 inflated the high diameter ball to the high air pressure and allowed ball to roll down the ramp. Research 2 measured and recorded the distance traveled. It was very windy during this trial.
4/26 3Researcher 1 inflated the high diameter ball to the low air pressure and released the ball from the top of the ramp. Researcher 2 measured and recorded the distance traveled
4/26 4
Researcher 1 inflated the low diameter ball to the high air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance the ball traveled. The grass was still wet and footprints started to form around the measuring tape where the ball rolled.
4/26 5
Researcher 1 inflated the high diameter ball to the low air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled by the ball. More footprints formed around the ball's rolling path.
4/26 6
Researcher 1 inflated the low diameter ball to the proper air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled by the ball. The wet ground was very muddy during this trial. The wind picked up a bit during this trial.
4/26 7Researcher 1 inflated the low diameter ball to the low air pressure and rolled the ball down the ramp. Researcher 2 measured and recorded the distance traveled by the ball.
4/26 8
Researcher 1 inflated the high diameter ball to the high air pressure, rolled the ball down the ramp, measured the distance traveled by the ball. Researcher 2 recorded the distance traveled by the ball. The ground was very muddy during this trial. It was very windy.
Table 4 above shows the observations taken during the third DOE
performed. Significant occurrences were noted. All the trials of this DOE were
performed on the same day, April 26, 2013, which was a windy, wet day. The
trials from the third DOE were all performed on the same date as the trials from
the second DOE.
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Figure 5. Ball’s Initial Release
Figure 5 above shows the initial release of the ball down the ramp. The
distance measured in the experiment was from where the ball left the ramp to the
point where the ball stopped moving. This initial point of where the ball left the
ramp is what is shown in the figure.
Figure 6. Soccer Ball Rolling
Figure 6 shows the middle of a trial of the experiment. The high diameter
soccer ball is rolling in a straight path along the measuring tape. In all the trials,
the ball was allowed to roll in a near straight path, and this is what the figure
above captures.
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Data Analysis and Interpretation
Data was collected using a comparative experiment to find the distance
traveled by a soccer ball and how it was affected by ground surface, air pressure,
and diameter. In order to ensure accuracy in the data collected, a control,
randomization, and replication were used. The control was the standard trials. No
experiment will be free of error; therefore, a control was used to limit the effect of
lurking variables on the data. Randomization was done in order to further reduce
any possible bias, and replication was used to ensure that the most accurate
measurement possible was taken. The replication was achieved by performing
three DOEs and then averaging the data from each one. Averaging many data
points accounts for any trials where there might have been an error. The
experiment that was done was analyzed using a three-factor Design of
Experiment.
Table 5Factors
Factors (-) Values Standard (+) Values
Ground Surface (friction) asphalt dirt grass
Pressure of Ball (psi) 6 9 12
Diameter of Ball (inches) 7 8 9
Table 5 shows the experimental values that were used in the experiment.
The three factors were ground surface, pressure, and diameter. The low,
standard, and high levels for ground surface were asphalt, baseball infield dirt,
and grass. The low, standard, and high values for pressure were 6 psi (pounds
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per square inch), 9 psi, and 12 psi, and the low, standard, and high values used
for diameter of the ball were 7”, 8” and 9”. The air pressure values were picked
using the recommend air pressure for any given soccer ball, which is between 6
and 12 psi (Parrish). The diameter values were picked using the three basic
soccer ball sizes, which are size 3 (7 inch diameter), size 4 (8 inch diameter),
and size 5 (9 inch diameter). The ground surface valued were picked by taking
common ground surfaces a soccer ball may be rolled on outside, and then
ranking them by increasing pressure.
Single Factor Effects:
Factor: Ground Surface (G)
Table 6Effect of Ground Surface
- +37.1 18.944.6 18.943.8 20.248.3 18.0
Avg: 43.5 Avg: 19.0
Effect = (19.0 - 43.5)/2 = 12.25
Figure 7. Effect of Ground Surface
Table 6 shows the resulting distances when ground surface was low and
when ground surface was high. Figure 7 shows how distance changed as ground
surface went from low to high. As ground surface (friction) increases, distance
traveled decreases by 12.25 feet.
-1 10.04.08.0
12.016.020.024.028.032.036.040.044.048.0
43.5
19.0
Ground Surface
Ground Surface
Dis
tanc
e (ft
)
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Factor: Pressure (P)
Table 7Effect of Pressure
- +20.2 18.918.0 18.843.8 37.148.3 44.6
Avg: 32.6 Avg: 29.9
Effect = (29.9 – 32.6)/2 = -1.35
Figure 8. Effect of Pressure
Table 7 shows the resulting distances when pressure was low and when
pressure was high. Figure 8 shows how distance changed as pressure went from
low to high. As pressure increases, distance traveled decreases by 1.35 feet.
-1 10.04.08.0
12.016.020.024.028.032.036.040.044.048.0
32.629.9
Pressure
PressureD
ista
nce
(ft)
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Factor: Diameter (D)
Table 8Effect of Diameter
- +18.8 18.918.0 20.244.6 37.148.3 43.8
Avg: 32.4 Avg: 30.0
Effect = (30.0 – 32.4)/2 = -1.2
Figure 9. Effect of Diameter
Table 8 shows the resulting distances when diameter was low and when
diameter was high. Figure 9 shows how distance changed as diameter went from
low to high. As diameter increases, distance traveled decreases by 1.2 feet.
-1 10.04.08.0
12.016.020.024.028.032.036.040.044.048.0
32.430.0
Diameter
DiameterD
ista
nce
(ft)
Lewandowski – Lidwell
Interaction Effects:
Interaction of Pressure and Ground Surface
Table 9Pressure and Ground Surface
Ground Surface (-)
Ground Surface (+)
Pressure (+)(solid segment)
37.144.6 Avg: 40.9
18.918.8 Avg: 18.9
Pressure (-)(dotted segment)
43.848.3 Avg: 46.1
20.218.0 Avg: 19.1
Effect =(18.9 – 40.9)/2 – (19.1 – 46.1)/2= 2.5
Figure 10. Pressure and Ground Surface
Table 9 shows the resulting distances and averages when pressure and
ground surface are low and high. Figure 10 shows the interaction between
pressure and ground surface. Segment P(-) is the dotted line segment for when
pressure is low and ground surface goes from low to high. Segment P(+) is the
solid line segment for when pressure is high and ground surface goes from low to
high. The line segments for both low and high pressure show that there is a
possible interaction between pressure and ground surface since their slopes are
not equal, so the line segments are not parallel. The expected distance for low
-1 10.04.08.0
12.016.020.024.028.032.036.040.044.048.0
40.9
18.9
46.1
19.1
Pressure and Ground Surface
Ground Surface
Dis
tanc
e (ft
)
P(+)
P(-)
Lewandowski – Lidwell
pressure is around 32.6 feet (Figure 8), but when ground surface goes from low
to high, low pressure goes from 46.1 to 19.1, which is not very close to 32.6,
meaning that ground surface likely had an effect. This is similar to the expected
distance for high pressure, meaning that there is a possible interaction between
ground surface and pressure.
Lewandowski – Lidwell
Interaction of Diameter and Ground Surface
Table 10Diameter and Ground Surface
Ground Surface (-)
Ground Surface (+)
Diameter (+)(solid segment)
37.143.8 Avg: 40.5
18.920.2 Avg: 19.6
Diameter (-)(dotted segment)
44.648.3 Avg: 46.5
18.818.0 Avg: 18.4
Effect =(19.6 – 40.5)/2 – (18.4 – 46.5)/2= 3.6
Figure 11. Diameter and Ground Surface
Table 10 shows the resulting distances and averages when diameter and
ground surface are low and high. Figure 11 shows the interaction between
diameter and ground surface. Segment D(-) is the dotted line segment for when
diameter is low and ground surface goes from low to high. Segment D(+) is the
solid line segment for when diameter is high and ground surface goes from low to
high. The line segments for both low and high diameter show that there is a
possible interaction between diameter and ground surface since their slopes are
not equal, so the line segments are not parallel. The expected distance for low
diameter is around 32.4 feet (Figure 9), but when ground surface goes from low
-1 10.04.08.0
12.016.020.024.028.032.036.040.044.048.0
40.5
19.6
46.5
18.4
Diameter and Ground Surface
Ground Surface
Dis
tanc
e (ft
) D(-)
D(+)
Lewandowski – Lidwell
to high, low diameter goes from 46.5 to 18.4, which is not very close to 32.4,
meaning that ground surface likely had an effect. This is similar to the expected
distance for high diameter, meaning that there is a possible interaction between
ground surface and diameter.
Lewandowski – Lidwell
Interaction of Diameter and Pressure
Table 11Diameter and Pressure
Pressure (-) Pressure (+)Diameter (+)(solid segment)
20.243.8 Avg: 32.0
18.937.1 Avg: 28.0
Diameter (-)(dotted segment)
18.048.3 Avg: 33.2
18.844.6 Avg: 31.7
Effect =(28.0 – 32.0)/2 – (31.7 – 33.2)/2= -1.25
Figure 12. Diameter and Pressure
Table 11 shows the resulting distances and averages when diameter and
pressure are low and high. Figure 12 shows the interaction between diameter
and pressure. Segment D(-) is the dotted line segment for when diameter is low
and pressure goes from low to high. Segment D(+) is the solid line segment for
when diameter is high and pressure goes from low to high. The line segments for
both low and high diameter show that there is probably little to no interaction
between diameter and pressure. The expected distance for low diameter is
around 32.4 feet (Figure 9), and when pressure goes from low to high, low
diameter goes from 33.2 to 31.7, which is close to 32.4, meaning that pressure
-1 10.04.08.0
12.016.020.024.028.032.036.040.044.048.0
32.028.0
33.231.7
Diameter and Pressure
Pressure
Dits
ance
(ft) D(-)
D(+)
Lewandowski – Lidwell
likely had no effect. This is similar to the expected distance for high diameter,
meaning that an interaction between diameter and pressure is not likely.
Grand Average of all trials = 31.2
Overall Effects of Single Factors:
Effect of Ground Surface (G) = 12.25
Effect of Pressure (P) = -1.35
Effect of Diameter (D) = -1.2
Interactions Between Factors:
Effect of Pressure and Ground Surface (PG) = 2.5
Effect of Diameter and Ground Surface (DG) = 3.6
Effect of Diameter and Pressure (DP) = -1.25
Prediction Equation:
Ŷ=Grand Average+G+P+D+PG+DG+DP+noise
Ŷ=31.2+12.25 (G )±1.35 (P )±1.2 (D )+2.5 (PG )+3.6 (DG )±1.25 (DP )+noise
Figure 13. Prediction Equation
Figure 13 shows the Prediction Equation used to predict experimental
values. This equation includes the grand average of all trials except standards,
the three main effects, the three interaction effects, and noise.
Graph of Standards:
Lewandowski – Lidwell
0 1 2 3 4 5 6 7 8 9 100
8
16
24
32
40
48Nine Standard Trials
Trial Number
Dis
tanc
e (ft
)
Figure 14. Graph of Standards
Figure 14 shows a graph of all nine standard trials that were performed.
The standards do not show any pattern and are consistent, which led to the
conclusion that the experimental results are valid because there was a consistent
control.
Figure 15. Dot Plot of Effects
Figure 15 shows a dot plot of all six effects. All of the effects are less than
4 away from zero, with the exception of ground surface, which has an effect of
12.25. This suggests that ground surface had a more significant effect than all
other single effects and interaction effects.
Test of Significance:
Lewandowski – Lidwell
2×|Rangeof Standards|
2×|31.0−24.3|
2×|6.7|=13.4
Figure 16. Test of Significance
Using the test of significance shown in Figure 16, the range of standards
and the rules of determining significant effects, only ground surface (G) was
identified as a significant effect. An effect was considered significant if the
absolute value of the effect was greater than twice the range of standards.
Though 12.25 is within twice the range of standards, it clearly stands out from all
the other effects, which are all between -2 and 4, therefore it is considered
significant.
Parsimonious Prediciton Equation:
Ŷ=31.2+12.25 (G )+noise
Figure 17. Parsimonious Prediction Equation
Figure 17 shows the Parsimonious Prediction Equation. This shows the
same thing as the Prediction Equation but only includes effects that were
determined to be significant, the grand average, and noise. The only effect that
was determined to be significant was ground surface (G), therefore it is the only
effect used in this equation. The effects of diameter, pressure, and the three
interaction effects of these single factors were not significant.
Conclusion
Lewandowski – Lidwell
An experiment was conducted using a three-factor Design of Experiment
that tested the effect different factors had on the distance a soccer ball rolled.
These factors were the ground surface the ball was rolled on, the diameter of the
ball, and the air pressure of the ball. A ramp was placed on three different
surfaces – asphalt, dirt, and grass. Three different ball diameters were used. The
ball was inflated to one of the three psi levels and was rolled down the ramp, and
the distance it took to stop was measured.
The original hypothesis was that the low diameter ball with high pressure
on asphalt would roll the farthest. This hypothesis was rejected. The factors that
led to the ball going the farthest were low diameter, low pressure, and asphalt.
The factors that led to the ball traveling the shortest distance were grass, low
pressure, and low diameter. The hypothesis was partially correct but since low
pressure and not high pressure caused it to roll farther, it was rejected.
Diameter did have a small, negative effect on rolling distance, meaning
that as ball diameter increased, distance traveled decreased slightly. Diameter of
the ball should not have an effect on distance a ball travels. When the velocity of
a rolling object is found, two expressions including mass are set equal to each
other, so the mass cancels out and does not matter. The diameter (radius) also
does not matter because when angular velocity is changed to velocity squared
over radius squared, this is multiplied by the moment of inertia, which includes
radius squared, so radius cancels out and does not affect velocity. Although
diameter does have some effect on distance, it did not have a huge effect. Balls
should not go dramatically farther or less far just because of what size they are.
Lewandowski – Lidwell
Different sizes are used in various levels of play but generally soccer balls will
travel similar distances unless there is another variable affecting it.
Higher air pressure also had a negative effect on distance. This went
against the hypothesis. This result could have been slightly altered if different psi
levels were used, because the effect air pressure had was small. The
recommended inflation values for the smallest ball were 6 psi to 8 psi, so inflating
this ball to the high psi value, 12 psi, could be the reason pressure had a
negative effect. This ball would have performed best when inflated to a pressure
within its range. The recommended inflation level for the largest diameter ball
was 10 to 12 psi. Inflating this ball to the high pressure would cause it to perform
normally, but inflating it to the low pressure had a negative effect. This is likely
the reason why pressure had such a small effect. The low psi caused the smaller
soccer ball to roll farther, but the high psi caused the larger ball to roll farther.
The effects somewhat offset each other, but pressure still had an overall negative
effect, leading to the conclusion that inflating a ball to a very high pressure or
over-inflating it will cause it to go a shorter distance. This does agree with current
findings because it is widely acknowledged that any kind of ball should always be
inflated to a psi within its designated range.
Ground surface was the last factor in the experiment. As the coefficient of
friction of each surface increased, the distance traveled decreased. Asphalt
cause the ball to go the farthest, dirt was in the middle, and grass caused it to go
the least far. In this order, the surfaces have increasing coefficients. A higher
coefficient means that the frictional force opposing the motion is greater. When
Lewandowski – Lidwell
there was a greater force going against the ball rolling, the ball, as expected,
went a shorter distance. There was a greater negative acceleration because of
the greater force, so the ball lost speed more quickly and did not go as far. Also,
as the surfaces became harder – grass, dirt, asphalt – the ball traveled farther.
This occurred because the ball could simply roll over the ground on the asphalt,
while on the grass it had to push down each blade in order to roll over it. Another
contributing factor was the ball being slightly pushed down into the ground. The
ball could not be pushed into the asphalt, but it could have sunk into the dirt and
the grass (or the dirt under the grass), causing it to have to work against the
ground even more instead of just rolling forward. The grass was an uneven
surface, and when objects roll on uneven surfaces they can be affected greatly
by the small bumps. The asphalt has much smaller deformities, though, so the
ball was much less affected by the surface and could travel farther. Overall,
ground surface was determined to be the only significant effect, meaning that
when determining the distance a ball rolls, ground surface is the only largely
contributing factor.
The results from the experiment agree with most of the current work in the
field. The diameter and ground surface experiments mentioned earlier (Review of
Literature) matched the results of the experiment that was conducted. However,
the air pressure results did not match, due to the fact that the air pressure
variable was difficult to manage with the different designated pressure ranges for
each ball. Still, the results can be combined to help determine how the soccer
ball would perform in other ways than just rolling in the ground. The table tennis
Lewandowski – Lidwell
experiment conducted by Yusaka Tsuji and Yoshitsugu Muguruma illustrated
how different diameter balls perform in air travel (Tsuji and Muguruma 53). Since
both their experiment and the one that was conducted here showed that
increased diameter decreases velocity and distance traveled, the results could
be combined to predict how the soccer ball would perform in air travel, such as
after being kicked rather than rolled off a ramp. It can most definitely be
hypothesized that diameter would continue to have a negative effect on the
soccer ball’s distance traveled. Also, the results from the air pressure experiment
from Nancy K. O’Leary and Susan Shelly showed air pressure had a positive
effect (O’Leary and Shelly). If the soccer ball experiment was conducted with
different air pressures that were proportional to the ball diameter rather than just
the same high, low, and standard values for all diameter balls, then the results
could be combined to predict how the soccer ball would travel when being
bounced off the ground. From combining these results from all the experiments,
a prediction of how a soccer ball would travel in all aspects of the game could be
achieved, whether the ball is traveling through the air, bouncing off the ground, or
rolling on the ground.
Though the overall experiment was successful, there were some
weaknesses and sources of error in the experiment. One of these flaws was in
the air pressure variable. The low air pressure level for the experiment was not
actually a low air pressure for the low diameter ball. Also, the high pressure level
in the high diameter ball was at the top of its pressure range, but the level was
well above the accepted pressure range for the low diameter ball. This caused
Lewandowski – Lidwell
the air pressure results to go against the science supporting that air pressure has
a positive effect on the distance traveled by a soccer ball. Another weakness in
the experiment was that the experiment was conducted outside in Michigan in
the month of April. April weather in Michigan is very inconsistent, meaning that
there were storms and rain on the different days of experimentation causing
differences in the ground surface. Even though most trials were conducted on the
second day of experimentation, that day was right after it had rained the day
before so the ground was wet and muddy. The fact that the ground was wet and
muddy could have limited the distance that the ball traveled, especially on the
grass trials as the ball made indentations in the ground surface and had some
mud on it which could have inhibited ball motion. This effect would be much
higher in the grass trials, so the gap between the asphalt and grass surfaces
could have been enlarged, which could have led to a significant effect for the
ground surface factor. Also, in all the trials, the wind could have affected ball
motion. The wind may have carried the soccer ball further in certain trials than in
trials where the wind was calmer. The wind could have caused the ball to travel
in less of a perfectly straight path. Though the trials should have been performed
in times of low wind, the wind was present throughout all trials at various speeds,
and due to time constraints, trials could not be held off to a less windy day.
To further research the topic of soccer ball performance, one thing that
could be done is testing the soccer ball when being kicked in the air. Ground
travel is only a part of the soccer game, and a knowledge of different factors such
as air pressure and diameter would help lead to a better understanding of the
Lewandowski – Lidwell
soccer ball's performance. Also, the experiment could be repeated using
proportional air pressure rather than just set air pressures of 6, 9, and 12 psi.
This would create more accurate results and more information about how air
pressure affects the distance traveled by a soccer ball since the levels would be
proportional to the accepted range of pressures for that specific ball diameter
rather than just the accepted overall range for all balls. This would lead to more
accurate results and a better scientific representation of how air pressure does
affect a soccer ball when rolling down a ramp, possibly leading to results actually
supporting the science in field. Also, other factors could be tested. In the Three-
Factor DOE, only ground surface, air pressure, and diameter were tested.
However, other factors affect how a soccer ball travels such as ball material.
Though all soccer balls are made from synthetic leather, there are many different
variations of it such as microfiber or ducksung (Monet). Adding additional factors
such as ball material would allow athletes to do everything in their power to both
understand their soccer ball, and to prepare their soccer ball in all aspects
including air pressure, ball material, and the other possible test factors. One final
idea for final research is to test different types of balls. Soccer balls were used so
that the effect of air pressure could be researched, however ground surface and
diameter effects can be applied to any ball-using sport. Basketballs, baseballs,
softballs, and more could be tested in further research so that not only will the
research benefit the field of soccer players, but it will benefit all sports that
involve balls, reaching an even larger audience.
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