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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


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


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.


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).


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


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

http://wahs-biology.wikispaces.com/file/view/types_of_friction_diagram.png/282862736/288x296/types_of_friction_diagram.png


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,


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


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.


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.


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.


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.


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.


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.


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.


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


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


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 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


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 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.


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.


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


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

)


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)


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)


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(-)


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.


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(+)


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.


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(+)


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:


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:


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


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.


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


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


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


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


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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