2.671 Measurement and Instrumentation
Friday PM
Professor Thomas Peacock
05/12/09
ENERGY TRANSFER IN VARIOUS TYPES OF SOCCER KICKS
Joshua B. Gafford
Massachusetts Institute of Technology
Cambridge, MA, USA
ABSTRACT
In an effort to quantify the efficiency with which
different types of kick transfer energy to a soccer ball,
velocity profiles for a soccer ball during various types of
kicks (instep, inside, and toe) were derived using highspeed imaging and an accelerometer. The efficiency of
energy transfer from foot to ball was described in terms
of a lumped constant meff. The values for this constant
were found to be 0.298 ± 0.123 kg for the instep, 0.381 ±
0.199 kg for the inside, and 0.225 ± 0.077 kg for the toe.
Ultimately, it was found that the instep and inside of the
foot were most efficient at transferring energy, with the
inside of the foot having the slight edge. As expected, the
toe kick was least efficient, due in part to the smaller
contact area, concentrated force, and amount of energy
dissipated by way of ball deformation.
INTRODUCTION
The sport of soccer is a fast-paced, dynamic game in
which players rely on a variety of strategies to gain the
upper-hand on their opponent. One of these strategies,
which may seem trivial to any practiced player of the
game, but is extremely fundamental, is knowing which
style of kick to employ in different situations. The inside
of the foot is primarily used at close-range when accuracy
and finesse are desired. Players use the instep of the foot
for longer-range passes or shots, when accuracy is
sacrificed for power and elevation if necessary. The toe is
usually a last-resort, employed when players find
themselves in a tight situation and need to “poke” the ball
out of harm’s way. The three kick styles mentioned above
are represented pictorially in Figure 1. Other
circumstances might call for the use of the outside of the
foot or the heel, but these extraneous situations are
beyond the scope of this report.
(a)
(b)
(c)
Figure 1: Pictures of (a) inside of the foot kick, (b) instep
kick, and (c) toe kick
The way in which the foot contacts the ball in each
situation corresponds to a different contact area, which
ultimately affects the velocity of the ball during the kick,
as well as the accuracy. During an inside-of-the-foot kick,
contact area is optimized, leading to a more uniform
distribution of force across the contact surface of the ball.
Additionally, the concave arc described by the inside of
the foot roughly conforms to the curvature of the ball,
helping to focus contact forces on a line perpendicular to
the longitudinal axis of the foot for optimal accuracy.
When a player kicks with his instep, the aim is to strike
the ball with the “bony” region of the top of the foot in
order to maximize power. However, the convex arc
described by the instep results in a smaller contact area,
which hinders accuracy. Finally, a toe-kick is an extreme
case, in which contact area is minimal; if the kick is not
applied at the exact geometric center of the ball, the ball
will not follow a straight path.
The reaction of the ball when exposed to the three
kicks shown in Figure 1 is directly related to the way in
which energy is transferred from the foot to the ball
during the kick. Section 1 introduces the physics
underlying a soccer kick, and outlines the principles of
energy transfer. Section 2 explains the experimental setup
that was used to gain insight into how energy is
transferred to the ball depending on kick type. Because
the instep of the foot is most widely used for shots and
kicks that require more power, it may be expected that
use of the instep of the foot will result in a greater
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2.671 Go Forth and Measure
amount of kinetic energy transfer to the ball. The purpose
of this report is to quantify this expectation using
experimental and theoretical data, and compare the
energy transfer capabilities of the instep kick with the
inside-foot and toe kick. These quantifications are
presented in Section 3.
I.
UNDERLYING PHYSICS OF A KICK
A soccer kick is effectively an imperfect elastic
collision between the foot and the ball where energy is
lost in several ways. The complexity of the collision
prohibits it from being modeled as a collision between
two free-moving bodies: this will be discussed more indepth later. A simplified physical model of a soccer ball
being kicked is presented in Figure 2. Three forces act on
the ball: the force of the kick F(t), a frictional force
Ffriction, and a drag force Fdrag.
y
x
Figure 2: Simplified Physical Model of a Kick
It is assumed that all relevant velocities and forces
only occur in the x-direction throughout the duration of
impact. The second-order nonlinear differential equation
corresponding to Figure 1 is presented in Equation (1):
dvball (t )
(1)
m
 C v (t ) 2 R 2  m g  F (t )
ball
dt
D
ball
ball
f
where CD is the drag coefficient, ρ is the density of air, R
is the radius of the ball, g is the gravitational constant
(9.81m/s2), μf is the coefficient of friction between the
ball and the surface, and F(t) is the applied force from the
foot as a function of time.
However, because the force is applied over a very
short amount of time, it is effectively an impulse force.
As a result we can simplify the model further in saying
that neither drag nor friction has a significant impact on
the motion of the ball throughout the duration of the kick,
which results in Equation (2):
mball
dvball
 F (t )
dt
(2)
Now that the differential equation describing the
motion of the ball is linear and first-order, we can
separate variables and integrate twice to obtain the
equation for change in kinetic energy of the ball, as
shown in Equation (3):
ball
Ekinetic

1
mball (v 2f ,ball  vi2,ball )
2
(3)
However, as we know from intuition, and as we will
show in this report pictorially, the ball can undergo
significant deformation during a kick, which ultimately
results in energy loss. In a realistic case, the ball is not
infinitely stiff and complies with the foot, and the force
felt by the ball is a function of the relative stiffness
constant of the ball, which is not easily computed. In
addition, several other factors can affect the energy
transfer efficiency of the kick, which are not easily
quantifiable. These include but are not limited to the
effective mass of the foot, frictional losses, material
properties of the ball and cleat (more specifically the
compliance of each to an applied force), and the quality
of contact between the foot and the ball.
Although we can’t really quantify how much energy
is lost between the foot and the ball due to the foot not
being a free body, it is possible to gain some insight into
how the velocity of the foot pre-collision affects the
energy change in each kicking case. In an effort to
quantify the efficiency of energy transfer to the ball, for
the purpose of this report it is assumed that the change in
kinetic energy of the ball is a function of the pre-collision
foot velocity, according to Equation (4):
ball
E kinetic
 f (vi , foot )  meff vi2, foot
(4)
where meff is a lumped correction coefficient (with units
of mass) that takes into account all of the loss
mechanisms discussed earlier. The purpose of this report
is to quantify meff for each of the three kick types and
discuss the discrepancies that will arise between each.
II.
EXPERIMENTAL SETUP
A schematic of the experimental setup can be seen in
Figure 3. A Vernier 25-g Accelerometer was rigidly
attached to the ball and zeroed prior to each kick. For this
experiment, it was assumed that the ball would primarily
undergo 1-dimensional translation in the x-direction so
that any other translations and rotational components
picked up by the accelerometer would be negligible in
comparison (this assumption was justified by inspection
of high-speed video data). The accelerometer uploads its
information to the Vernier LabPro, which is a data
collection interface. The LabPro converts the sensor’s
voltage output into the desired units of m/s2. Data was
recorded at a rate of 1000 Hz, with an accuracy of ±2.45
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2.671 Go Forth and Measure
(a)
Acceleration(m/s2)
m/s2 and resolution of 0.1 m/s2. The accelerometer was
calibrated during manufacturing, so there was no need for
manual calibration during setup.
Good Data
(b)
Acceleration (m/s2)
Time [s]
Poor Data
Time [s]
Figure 3: Picture of experimental setup
Connected in parallel with the LabPro setup is a
Fastec In-Line High-Speed Imaging camera. The camera
captures the collision between the foot and the ball at a
rate of 500 frames-per-second, giving it a resolution of 2
milliseconds. The camera collects information
continuously and stores it in what is called a “revolving
memory buffer,” and once an external trigger is applied,
the data is recorded using FIMS software. Ultimately, a
video recorded with the Fastec is uploaded into
LoggerPro, where it can be scaled (to the diameter of the
ball, measured to be 21.94 ± 0.077 cm, using 95%
uncertainty) and analyzed frame-by-frame. Using built-in
functions in LoggerPro, analysis can be done to obtain
the displacement and velocity profiles underwent by the
ball during a kick.
An experienced soccer player (+15 years
experience) was used as the subject of this experiment.
Proper soccer apparel was worn by the subject. A Nike
Brasil 2008 soccer ball weighing 409 ± 13 grams, and
somewhat worn from previous use, was used.
Figure 4: Representative accelerometer graphs
comparing (a) good data within the range of the
accelerometer and (b) poor data that exceeds the
range of the accelerometer
Data was recorded for low-acceleration kicks using
the accelerometer and the high-speed camera
simultaneously in parallel. The acceleration curve
obtained by the accelerometer was integrated over the
time of contact to obtain the velocity profile of the ball
during the duration of the kick. In addition, the recorded
video of the kick was analyzed frame-by-frame to obtain
the velocity profile of the ball, and ultimately the overall
change in kinetic energy. Two velocity profiles, one
found from the high-speed camera, and the other found
by integrating accelerometer data, were superimposed on
the same graph to get an idea of the differences between
the two. In addition, the changes in kinetic energy of the
ball measured by each instrument were compared, and an
error was established between the two. The purpose of
the error calculation is to compare discrepancies between
measured values with 95% confidence intervals.
2.2
2.1
LOW-ACCELERATION ENERGY TRANSFER
Figures 4a and 4b graphically demonstrate the
accelerometer upper-bound. The range of the
accelerometer is ~±310 m/s2, which corresponds to a
maximum ball velocity of around 4 m/s.
HIGH-ACCELERATION ENERGY TRANSFER
In order to estimate the energy change typical in
higher-acceleration kicks (>310 m/s2), the use of the
accelerometer was discontinued. This allowed for a more
realistic setting for a typical soccer kick, as the ball was
no longer “tethered” by the accelerometer cable.
Additionally, damage to the accelerometer was no longer
a concern, so kicks could be taken with a greater velocity
to simulate gameplay conditions.
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2.671 Go Forth and Measure
5
The three styles of kick were recorded with the highspeed camera, and analyzed via LoggerPro to find the
pre-kick velocity of the foot and final velocity of the ball.
All kicks were taken from a standing position (no
approach). Graphs of foot velocity, ball velocity, and ball
deformation as a function of contact time were
constructed in MathCAD using recorded data in
LoggerPro.
Velocity [m/s]
4
3
2
1
0
III.
RESULTS AND DISCUSSION
3.1
LOW-ACCELERATION ENERGY TRANSFER
0.01
0.02
Time [s]
Data were recorded with both the Fastec camera and
the accelerometer for the three kick styles. The velocity
profile of the ball was found directly from video analysis,
and theoretically by integrating accelerometer data to
obtain the velocity profile over the time of contact. For
the purpose of this report, ball velocity profiles from
kicks taken with the instep will be represented in blue,
the inside will be represented in red, and the toe will be
represented in green. The results of the low-g tests are
displayed in Figures 5a, 5b, and 5c. As can be seen from
the graphs, the velocity profiles recorded from the highspeed camera (the actual velocity of the ball) are very
comparable to the accelerometer results, and the two
methods of measurement agree with each other.
(c)
Figure 5: Comparison of accelerometer data and
high-speed video data at various kick speeds for (a)
instep, (b) inside, (c) toe.
Using Equation (3), the change in kinetic energy of
the ball at three different speeds was calculated from data
obtained from both the Fastec and the accelerometer for
each kick type. Table 1 presents a comparison of the
results obtained by each method, as well as the difference
between the results. It is evident that the margin of error
between the two methods is small in each case, and any
discrepancy present falls within the 95% confidence
interval of each result (the toe kick and the inside kick at
slow speeds were the only scenarios where the margin of
error was greater than the confidence interval).
Table 1: Comparison of results for change in kinetic
energy undergone by the ball, measured by both highspeed video and the accelerometer, at (a) slow velocity, (b)
medium velocity, and (c) fast velocity.
3
Velocity [m/s]
0
(a)
2
Eball (Slow Velocity)
1
0
0
510
3
0.01
0.015
0.02
Time [s]
(a)
Instep
Inside
Toe
Accel.
Data [J]
Camera
Data [J]
Difference
[J]
0.53±0.17
0.45±0.02
0.47±0.17
0.53±0.05
0.65±0.06
0.77±0.07
0.01
0.20
0.30
3
Velocity [m/s]
(b)
Eball (Medium Velocity)
2
Accel.
Data [J]
Camera
Data [J]
Difference
[J]
0.94±0.28
1.49±0.28
1.35±0.16
1.12±0.10
1.53±0.12
1.41±0.13
0.18
0.04
0.06
1
0
0
510
3
0.01
0.015
0.02
Instep
Inside
Toe
Time [s]
(b)
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Instep
Inside
Toe
Accel.
Data [J]
Camera
Data [J]
Difference
[J]
2.44±0.36
0.24±0.35
0.07±0.51
2.23±0.15
2.21±0.15
4.96±0.31
0.21
0.03
0.89
15
30
Deformed Diameter d
HIGH-ACCELERATION ENERGY TRANSFER
As mentioned earlier, use of the accelerometer was
discontinued for kicks at higher velocities. High-speed
video analysis of an instep kick resulted in the data
presented in Figure 6. In the figures that follow, the same
color scheme is used for ball velocity (blue for instep, red
for inside and green for toe), but in addition each graph
shows foot velocity in black and relative ball
deformation in purple as a function of time.
The velocity profile of both the ball and the foot
during the collision were fit with 4th order polynomial
functions, and the deformation of the ball was fit with a
2nd order polynomial. Because the contact surface of the
ball is spherical and the surface of the foot can be
modeled as flat, ball stiffness (which is a function of the
internal pressure and material makeup of the ball) varies
quadratically as a function of deformation, so we expect a
parabolic response in ball deformation, with peak
deformation at the highest applied force. As one would
expect, and as Figure 6 somewhat reflects, ball
deformation is highest when the two velocities equalize.
After this point, the foot no longer directly influences the
velocity of the ball; rather, the ball is undergoing
“springback” and accelerates its way away from the
surface of the foot1.
15
5
10
Ball Velocity Data
Ball Velocity Fit
Foot Velocity Data
Foot Velocity Fit
Deformation Data
Deformation Fit
0
510
0
0
3
0.01
Time [s]
Figure 7: Impact velocity profiles for the ball and
foot during an inside kick, superimposed with ball
deformation.
Finally, Figure 8 shows the results of the toe-kick.
As expected, ball deformation for the toe kick was the
greatest, since the contact area is smaller and the force is
more concentrated.
Figure 8: Impact velocity profiles for the ball and
foot during a toe kick, superimposed with ball
deformation.
15
30
10
20
Velocity [m/s]
3.2
20
Velocity [m/s]
10
Deformation [mm]
Eball (Fast Velocity)
Figure 7 presents the results of the inside-of-the-foot
kick. The magnitude of ball deformation is very
comparable to that of the instep, which is expected since
the contact areas are generally pretty similar.
30
5
Deformation [mm]
(c)
10
20
Velocity [m/s]
10
5
Deformation [mm]
Ball Velocity Data
Ball Velocity Fit
Foot Velocity Data
Foot Velocity Fit
Deformation Data
Deformation Fit
10
Ball Velocity Data
Ball Velocity Fit
Foot Velocity Data
Foot Velocity Fit
Deformation Data
Deformation Fit
0
0
3
510
0
0.01
Time [s]
Figure
6:
Impact
velocity
profiles for the ball and foot during an instep kick,
superimposed with ball deformation.
0
0
510
0
3
0.01
0.015
Time [s]
Figure 9 shows how ball deformation was estimated.
The determination of ball deformation was highly
qualitative, and any error associated with its estimation is
difficult to quantify. Conservative uncertainty estimates
were assumed during video analysis, and this error was
propagated through any relevant calculations to
determine the 95% confidence interval associated with
deformation.
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2.671 Go Forth and Measure
Undeformed Diameter D
Deformed Diameter d
δ=D-d
Figure 9: Determination of ball deformation δ
Figures 6-8 are representative graphs. The
experiment was performed four times at various speeds
for each type of kick in order to obtain a greater pool of
data with which to quantify energy transfer efficiency
meff. This process is explained in Section 3.3.
3.3
DETERMINATION OF EFFICIENCY MEFF
Using data obtained during the low velocity and high
velocity experiments, as well as Equation (4), Figure 9
was constructed, which displays the change in kinetic
energy of the ball as a function of the pre-collision foot
velocity squared. According to Equation (4), the energy
transfer efficiency coefficient meff is simply the slope of
the fitted line for each type of kick.
Because video analysis and its associated uncertainty
both depend on several qualitative factors, all uncertainty
estimates were conservative, lending to a rather large
95% confidence interval.
It is shown in Figure 9 that the inside of the foot is
most efficient at transferring energy to the ball. This is a
particularly surprising result, as it was expected that the
instep of the foot would result in greater energy transfer
efficiency.
If the inside of the foot yields greater energy transfer
than the instep at a given pre-collision foot velocity, why
don’t players use the inside more often for shots? Ask
any soccer player and he or she will tell you that a kick
made with the inside of the foot feels quite unnatural and
restricted. When the foot is forced outward to expose the
inside of the foot, rotation about the knee is severely
inhibited; as a result, the maximum angular momentum
that can be achieved is greatly hindered. Instep kicks are
much more natural and fluid, allowing for a much greater
range of motion. In addition, the plantar flexion of the
foot during an instep kick allows for rotation about the
knee and greater angular momentum can be achieved. As
a result, greater foot velocities can be achieved for instepkicks rather than inside-kicks. A simple schematic of the
dynamics of a leg during each of these scenarios is
presented in Figure 10a and 10b.
 hip
60
Instep Data
inside
meff
 0.38  0.20 kg
Inside Data
lthigh
Toe Data
50
 hip
 knee
lthigh
l shank
Ball Kinetic Energy (J)
Instep Linear Fit
Inside Linear Fit
Toe Linear Fit
40
l shank
30
instep
meff
 0.30  0.12 kg
20
Figure 10: Schematic of kicking dynamics for (a)
the inside of the foot and (b) the instep of the foot
toe
meff
 0.22  0.08 kg
10
0
0
50
100
150
Square of Pre-Collision Foot Velocity
Figure 9: Graph showing the change in kinetic
energy of the ball as a function of the pre-collision
foot velocity squared.
Uncertainties in meff for each kick were calculated in
the following way: conservative “eyeball error” was
estimated from video analysis and inserted into
propagation of uncertainty for each data point, and linear
relationship uncertainty was calculated for each linear fit.
As is demonstrated in Figure 10, for the same
angular velocity Ωhip about the hip joint, the velocity of
the foot has the added component of angular velocity
Ωknee about the knee in the case of the instep kick. In the
simple case that the angular velocities Ωhip and Ωknee are
equal, the knee is at the midpoint of the leg, and the kick
is performed so that the thigh and the shank are parallel
at the striking point, the linear velocity of the foot at the
striking point is twice as much in the instep case than in
the inside case, where Ωknee ~ 0 rad/s. Therefore, the
added rotation about the knee allows for the instep kick
to yield much greater pre-collision foot velocities, which
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2.671 Go Forth and Measure
is why the instep is more widely used for shots and kicks
where power is desired.
The toe kick was the least efficient in transferring
energy to the ball. Although the same range of motion of
the instep kick can be achieved with a toe kick, the
smaller energy transfer efficiency can be explained by the
significantly greater amount of deformation underwent by
the ball. This claim is realized in Figure 11, which is a
graph of the ball velocity immediately after impact as a
function of the maximum deformation experienced by the
ball. It can be seen that instep and inside kicks resulted in
comparable ball velocities at a given deformation,
whereas the toe kick resulted in a much less-efficient
response at a given deformation. Data in Figure 11 helps
to qualify the conclusion that the toe is the least-efficient
kick for energy transfer and explains why meff for the toe
is the smallest. More energy was dissipated by way of
ball deformation, and as a result, less of the foot’s kinetic
energy was transferred to the ball.
16
 vball 


 764  227 s 1
  max instep
Instep
Inside
14
 vball 


 712  120 s 1
  max inside
Toe
Instep Linear Fit
12
Ball Exit Velocity [m/s]
energy of the ball using two different media revealed
comparable results, lending validity to each method of
measurement. The efficiency of energy transfer for each
type of kick was described in terms of a lumped constant
meff, which takes into account loss mechanisms and other
factors that adversely affect the transfer of energy from
the foot to the ball. The values for this constant were
found to be 0.298 ± 0.123 kg for the instep, 0.381 ± 0.199
kg for the inside, and 0.225 ± 0.077 kg for the toe.
Surprisingly, it was shown that the inside of the
foot proved to be the most efficient kick for transferring
kinetic energy to the ball, although biological limitations
(such as the inability to bend the knee for greater angular
momentum) inhibit the use of the inside of the foot when
higher-velocity responses are necessitated.
Plantar
flexion characterized by the instep kick allows for greater
angular velocity about both the hip and knee.2 As
expected, the toe kick resulted in the least amount of
energy transfer despite its dynamic similarity to an instep
kick. It was shown that the ball deforms the most in a toe
kick, which means that more of the foot’s kinetic energy
was dissipated by way of ball deformation.
Inside Linear Fit
ACKNOWLEDGMENTS
Toe Linear Fit
10
8
I would like to thank Professor Thomas Peacock for
pointing me in the right direction and offering valuable
insight for this investigation. Additionally, I would like to
thank Dr. Barbara Hughey for offering advice in
calculating the uncertainty of my measurements.
 vball 
1
    432  180 s
 max toe
6
4
2
0
0
5
10
15
20
25
30
Maximum Ball Deformation [mm]
Figure 11: Ball velocity immediately after impact
vs. maximum deformation for each kick at various
velocities
The relative energies associated with each kick are
on the order of tens of Joules, which is relatively small.
To get an idea of an upper-bound for energy transfer to a
soccer ball, the fastest soccer kick ever recorded, at
around 132 mph (~59 m/s), corresponds to 711 J of
energy transfer. With this in mind, the energy a soccer
ball receives from a kick isn’t even on the same order of
magnitude as, say, the energy a person receives from
eating a single peanut (~3.8 kJ).
IV.
REFERENCES
1. Shinkai, Hironari et al. “Ball-Foot Interaction in
Impact Phase of Instep Soccer Kick.” Journal of
Sports Science and Medicine 10 (2007): 26-29
2. Kellis, E. and Kattis, A. “Biomechanical
Characteristics and Determinants of an Instep Soccer
Kick.” Journal of Sports Science and Medicine 6
(2007): 154-1
CONCLUSIONS
An analysis of a soccer ball under the influence
of a kick both revealed and confirmed insights into how
different styles of kick transfer energy to the ball
differently. An attempt at measuring the change in kinetic
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