A MATERIALS APPROACH TO THE REDESIGN OF
LACROSSE HELMETS
by
Robert I. Park
SUBMITTED TO THE DEPARTMENT OF MATERIALS
SCIENCE AND ENGINEERING IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF
BACHELOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May 1988
Copyright (c) 1988 Massachusetts Institute of Technology
Signature redacted
Signature of Author
Department of Materials Science and Engineering
May 27, 1988
Signature red acted
Certified by
David K) Roylance
Thesis Supervisor
Signature redacted
Accepted by
David
O O
Y
JUL o0i 1988
M~CI-
k. Roylance
Chairman, Undergraduate Thesis Committee
A Materials Approach to the Redesign
of Lacrosse Helmets
by
Robert I. Park
Submitted to the Department of Materials Science and Engineering
on 27 May, 1988 in partial fulfillment of the Requirements for
the Degree of Bachelor of Science in Materials Science and Engineering
Abstract
The redesign of lacrosse helmets is approached from a materials science
viewpoint. The forces on a helmet during the National Operating Committee on
Standards for Athletic Equipment (NOCSAE) tests are translated into energies and
momenta and applied to a model of the human head. A computer finite element
analysis is used to approximate the effective area of impact on the helmet. 0.50 inches
of high density polyurethane foam is determined to be the thickness of foam required
for absorption of impact energy for a 60 inch drop test of a 10.5 pound headform. A
strain gage mounted modified Izod-Charpy impact testing machine is used to
determine peak accelerations of various combinations of densities and thicknesses of
liners and shells and to characterize the polymers chosen for the shell and liner.
Thesis Supervisor:
Title:
David K. Roylance
Associate Professor of Materials Science and Engineering
2
Table of Contents
a=e
Abstract
2
Figures and Illustrations
4
List of Tables
5
Acknowledgements
6
Introduction
7
Literature Survey
9
Outline and Plan of Work
14
Experimental Apparatus and Procedure
16
Results
19
Discussion
24
Summary and Conclusion
28
Suggestions for Further Work
29
References
31
Appendix I:
Translation of NOCSAE Standard
32
Appendix II: Description of FEAP
35
Appendix III: Determination of Liner Thickness
37
Appendix IV: Properties of Shell Materials
38
Appendix V: Modified Izod-Charpy Machine
39
Appendix VI: Catastrophic Injuries in Lacrosse
40
Appendix VII: Mechanism of Head Injuries
42
Bibliography
45
3
Figures and Illustrations
Figure I:
Stress-strain behavior of a buckling column and a
compressed open cell foam.
11
Figure II:
Normalized peak acceleration versus impact energy
for urethane foams.
13
Figure III: Modified section of Izod-Charpy impact tester.
16
Figure IV: Simulated deflecton for a point load applied at the top
of the helmet.
19
Figure V:
Representation of deformations produced in helmet
during application of a point load.
20
Figure VI: Acceleration vs time for a high density 0.25" urethane
foam.
21
Figure VII: Acceleration vs time for a PVC/Acr shell with a 0.25"
high density polyurethane foam liner.
21
Figure VIII: Acceleration vs time for a PC/ABS shell with a 0.25"
high density polyuethane foam liner.
22
Figure IX: Acceleration vs time for a 0.5" high density polyurethane
foam.
22
Figure X: Acceleration vs time for a PVC/Acr shell with a 0.5" high
density polyurethane foam liner.
22
Figure XI: Acceleration vs time for a PC/ABS shell with a 0.5" high
density polyurethane foam liner.
22
Figure XII: Acceleration vs time for a 0.25" high density and 0.325"
medium density polyurethane foam liner.
23
Figure XIII: PVC/Acr shell with the foam in Figure XII.
23
Figure XIV:PC/ABS with the foam in Figure XII.
23
4
Tables
Page
Table I:
Samples prepared for testing.
17
Table Il:
Combinations of shell and liner materials tested.
17
Table Ill:
Translation of NOCSAE lacrosse standard.
19
Table IV:
Theoretical required thicknessses of polyurethane foams.
20
Table V:
Optimum range of energy densities for urethane foams.
20
Table VI:
Energy absorption and peak acceleration for samples tested
21
5
Acknowledaements
Many people helped me to complete this thesis. I would like to thank Professor
Roylance for his patience in dealing with all of my questions while I was developing
and writing this thesis. I also owe thanks to:
1. Gwen Sturdy (and her husband Jim) whose already modified Izod machine I further
modified.
2. Mark Shudt and Mark Russman who helped me in the data collection process.
3. Joey Mead who helped me to locate information about impact absorbing foams.
4. The Rogers Corportion for supplying me with Poron polyurethane foam
specifications and samples for testing.
5. The Borg-Warner Corporation for supplying specifications for and samples of
PC/ABS for testing.
6. Rohm and Haas, Inc. for suppling specifications for and samples of PVC/ABS for
testing.
Finally, thanks Mom and Dad for sending me to MIT.
6
Introduction
The lacrosse helmets presently in use by teams throughout the United
States and the world are inadequate when the forces involved in playing lacrosse are
considered. The lack of a well established professional lacrosse league has led to
neglect in the development of lacrosse helmet designs which meet the needs of the
sport. The establishment of a lacrosse helmet standard by the National Operating
Committee on Standards for Athletic Equipment (NOCSAE) has led to improvements in
lacrosse helmets, but the reluctance of present helmet manufacturers to retool factories
has led to few major changes in the design of lacrosse helmets.
Minimum requirements of lacrosse helmets are interpreted from the
NOCSAE standard and from the mechanism of head injuries and are translated into
minimum requirements for materials used in the shell and the liner of lacrosse helmets.
The design of the facemask was not considered in this paper as the added complexity
in design would entail more time than was available. Instead, the emphasis is on
energy absorption by the shell and liner and characterization of the polymers involved.
The design of lacrosse helmets entails several parameters beyond the
impact factors established by NOCSAE. Lacrosse helmets must be light to
accomadate players who run up to five miles in a game, must be as close fitting as
possible to minimize rotational accelerations which are the primary mechanism of
concussion, and must have a smooth surface to minimize binding of the helmet to other
players' equipment during collision. With the weight of the helmet and the fit
considered, the NOCSAE standard is applied.
The parameters for possible materials chosen for use in the lacrosse helmet
are analysed in a four step process. First, forces interpreted from the NOCSAE
7
program mounted on Project Athena was used to determine stresses in the helmet
shell and liner and to approximate the effective area of application of stress to the
headform model.
Third, the necessary thickness of liner was calculated from
specifications provided from the manufacturers specifications. Finally, a modified Izod
testing apparatus was used to determine the accuracy of the theoretical effectiveness
for shock absorption.
8
Literature Survey
NOCSAE Standard:
The National Operating Committee on Standards for Atheletic Equipment
(NOCSAE) was founded in 1969 to provide helmet manufacturers with a set of
requirements which would minimize head and facial injuries in sports. The football
standard was introduced in 1970 and the lacrosse standard in 1986.
The NOCSAE standards are based on the 1500 Severity Index (SI)
developed by C.W. Gadd. 1 The SI is a standard derived from tests on cadavers and
primates in which the acceleration and duration of an acceleration pulse are used to
determine when concussion will occur. The SI is defined as:
SI =
A2 .5 dt
s 1500
where: A
2.5
t
T
= acceleration in g's
= weighting factor
- time
= pulse duration in seconds
0.0025<T<0.050
Gadd detrmined a SI of 1500 to be the limit of human attenuated impact tolerance. The
NOCSAE standards require a helmet to maintain a SI below 1500.
The NOCSAE lacrosse standard 2 consists of three tests on a helmet mounted
headform. Three different sized headforms are used to approximate human ranges;
the dimensions for the headforms appear in Appendix. To simplify design parameters,
I used the medium headform for all calculations and dimensioning. Each headform in
the NOCSAE tests is equipped with a triaxial acccelerometer mounted at the center of
mass of the headform. Signals from the accelerometer are converted into SI. The
three tests in the NOCSAE lacrosse standard are:
1. Drop test: The helmet mounted headform is dropped from a height of 60
9
inches onto a rigid surface. The impact is repeated for different sites on the
helmet.
2. Ball - Head Impact test: A lacrosse ball (weight = 5.5oz) is propelled at 70 mph
to various sites on the helmet.
3. Stick - Head Impact test: A lacrosse stick with a wooden shaft (weight = 1.5 lbs,
length = 60 inches) with a tip speed of 50 mph is impacted at various sites on
the helmet mounted headform.
Impact Behavior of Polymeric Foams:
Flexible polymer foams which are intended for use in impact aborbing
applications must be able to absorb and dissipate energy and exhibit consistent stress
- strain behavior. Polymers which are used in liners of helmets must ideally be able to
decelerate the head at a constant rate. If a constant deceleration is not imparted to the
head, but instead a peak deceleration or force is applied, diffuse and/or focal brain
injury (see Appendix
for the mechanism of head injuries) may occur. Foams which
exhibit plateau regions on their stress-strain curves absorb energy at a rate which
gives constant deceleration. In addition to absorbing energy, polymer foams used for
impact purposes must be able to dissipate energy; should the energy of impact be
returned to the head after impact, head injury could occur.
Several models have been developed to predict the compressive behavior of
polymer foams.
Open cell polymers are modeled as assemblies of small columns
arranged in a three dimensional network3 .
The stress-strain behavior of a buckling
column with fixed ends is similar to the behavior of an open cell foam. Initially, a large
stress is necessary to induce buckling in the fixed column, but the force necessary for
.
further deformation decreases as the bending moment factor becomes important 4
Likewise, compressed polymer foams exhibit an initial rise in the stress necessary for
deformation followed by a decrease in modulus. At large deformations, the modulus of
10
the compressed foam approaches the compressive modulus of the solid polymer as
the polymer strands are pressed together. The stress-strain curves of an open cell
natural rubber and a buckling column appear below:
1.6-2
0
0
0.6
Q0a
0.
0
-40
-ao
C N%
0 buckling column
o c ompressed foam
.
Figure I: Stress-strain behavior of a buckling column and a compressed open cell
foam5
The presence of closed cells in polymer foams complicates the model of
interconnected threads of polymer. Several models have been proposed to predict the
behavior of open cell polymer foams at low strains, but the prediction of the behavior
of open cell foams is impossible without empirical functions.
The behavior of closed cell foams differs from that of open cell foams in that the
presssure of the entrapped gasses must be taken into account in the analysis.
Skochdopole and Rubens8 designed a model using
the ideal gas law to predict the
behavior of closed cell foams. Their results correlated fairly well with empirical results.
At low strains, the stress was dominated by the modulus of the threads in the model; at
intermediate strains, the foam behaved as predicted by the ideal gas law -the modulus
leveled off; at high strains, the foam behaved like a solid polymer, exhibiting the
modulus of the solid polymer.9
Energy dissipation in polymer foams can be measured as the area between the
loading and unloading curves during and after impact. Energy dissipation occurs in
four ways. First, energy is lost in straining the polymer matrix. The four types of strain
11
are compression, tension, buckling, and shear. Second, energy is expended through
Third, energy is lost in the irreversible
friction within the matrix of the foam.
compression of gasses within the cells of the foam. Finally, energy is lost through the
viscous flow of gasses through open cells in the foam. 10
Mathematical and mechanical models of polymer foams exist, but due to the
complexity of the models, empirical properties from the manufacturers are used to
predict the impact behavior of polymer foams in the lacrosse helmet design.
Prediction of Impact Behavior of Polymer Foams from Empirical Data:
Plots of impact energy density versus normalized peak deceleration are available
from the manufacturers of impact absorbing foams. The impact energy density is
defined as:
WxH
AxT
where: W = drop weight (lbs)
H - drop height (in.)
A - impact are ( in2
)
Impact energy density = U
T - sample thickness
(in.)
Normalized Peak Deceleration is defined as:
Normalized peak deceleration = J =
P
(H/T)
where: P = peak deceleration
(g's)
H = drop height ( in.)
T = sample thickness
(in.)
Once the impact energy density (U) is known, the "J Curves" or plots of
normalized peak deceleration versus impact energy density can be used to choose the
polymer foam which gives the optimal impact absorption. The "J Curve" for high and
12
medium density polyurethane foams appears below:
10
a
619
4
F
00
10
P3
2
0109
102
10
103
Figure [I: Normalized peak deceleration versus impact energy density for high and
medium density cellular urethane. (Courtesy of the Rogers Corporation)
The J curve gives a plot of normalized peak deceleration vs impact energy density for
different polymer foams.
To determine the effectiveness of a polymer in shock
absorption, the energy density is calculated from test parameters and the normalized
peak acceleration is read from the J curve.
The lower the normalized peak
acceleration, the more effective the polymer foam. The J curve can also be used to
determine the necessary thickness for a given polymer foam.
To determine the
necessary thickness of a polymer foam, the J curve is used to find the energy density
which corresponds to the minimum normalized peak acceleration.
Determining the
foam thickness from the J curve ensures operation of the foam within its optimal range.
13
Outline and Plan of Work
A. Determination of Impact Energies and Forces
From the NOCSAE standard, the momentum of the headform and the impact
forces and energies are calculated using the following assumptions:
1. The ball-head and stick-head collisions, are elastic.
2. The duration of the impulse is seven milliseconds. (This is a conservative
estimate. Actual impulse times range from 7-12 milliseconds) 1
3. The medium headform is used.
4. The head and helmet do not rebound during the drop test.
B. Selection of Possible Materials for Use in Shell and Liner
The candidates for the shell material are chosen through examination of the
following parameters:
1. Density
2. Flexural Strength
3. Flexural Modulus
4. Izod impact test
The materials with the lowest density, highest flexural strength and modulus, and
greatest toughness were chosen as candidates for use in the shell. The selected
materials are PC, PVC/Acr, and PC/ABS.
Only two materials were chosen for consideration in the liner. EVA and
polyurethane are the two flexible foams reccommended by manufacturers for use in
helmets. Polyurethane was chosen for its greater shock absorbing characteristics at
low strains.
14
FEAP, a Finite Element Analysis Program developed by R.L. Taylor at the
University of California at Berkeley 12 was used to simulate the head, liner, and shell,
and was used to approximate the effective area of influence during loading and to
examine the distribution of stresses on the head during impact.
D. Determination of Volume of Liner necessary to Absorb Impact
From the effective area of impact and the J curves, the necessary thickness of
foam necessary to absorb the impact is determined.
E. Characterization of Energy Absorption of Shell and Liner via Modified Izod Device
A modified Izod device is used in conjunction with an IBM PC XT to determine the
acceleration vs. time imparted to the head during impact. The properties of the liner,
and shell and liner, are determined by acceleration-time distribution. The experimental
results are correlated with the theoretical results.
15
Experimental Apparatus and Procedure
The mechanical testing of the shell and liner was done on a modified Satec
Systems Model BLI Izod testing machine. The modifications to the Izod device are: the
replacement of the hammer with a larger steel hammer to impact the sample over one
square inch; replacement of the sample holder with a larger steel base on which was
mounted the samples for testing; strain gages mounted to the steel base to measure
strain in the base during impact; and a trigger circuit which allows measurement of a
time interval of ~eight milliseconds. The modified region of the Izod machine appears
below:
symple
strain gauge
hammer
BASE
Figure III: Modified section of Izod impacter.
16
Procedure:
One square inch samples of the following materials were prepared for testing:
Liner
Shell
Material
PC/ABS
Polyurethane
PC/PVC
1
Thickness
0.125"
0.125"
5
0.250" 0.375" 0.500"
0.250"
0.500"
Table 1: Samples prepared for testing.
The following combinations of shells and liners in the grades and thicknesses
shown below were mounted on the base of the Izod impact machine and impacted with
an kinetic energy of 2.10 ft lbs. The modified hammer added 41 grams to the mass of
the pendulum at the point of impact, increasing the energy of impact from 2.02 ft lbs to
2.10 ft lbs.
Uner
Shell
Sampjle Material Thickness
1
Materiall Thickness Grade Material2 Thickness Grade
urethane
0.25"
h.d.
none
0. 125"
urethane
0.25"
h.d.
none
urethane
0.25"
h.d.
none
urethane
0.50"
h.d.
none
2
none
PVC/Acr
3
4
PC/ABS
none
0.125"
5
PVC/Acr
0.125"
urethane
0.50"
h.d.
none
6
PC/ABS
0. 125"
urethane
0.50"
h.d.
none
7
none
urethane
0.25"
h.d.
urethane
0.25"
m.d.
8
PVC/Acr
0.125"
urethane
0.25"
h.d.
urethane
0.25"
m.d.
9
PC/ABS
0.125"
urethane
0.25"
h.d.
urethane
0.25"
m.d.
Table II: Combinations of shell materials and liner materials tested.
17
Impact tests were executed at T = 690 F. Each sample was tested five times with
a five minute recovery period between tests. Energy loss during the impact was
estimated from the height to which the pendulum arm returned. The signal from the
strain gage mounted in the base was frozen on an oscilloscope and transferred to an
IBM PC XT and stored in data files. The data files were interpreted in a FORTRAN
program which correlated the total energy losses during impact to the strain gage
voltages, converted the total energy loss to total acceleration and integrated over the
voltage vs time curves to give the acceleration vs time curves. See Appendix V for
details on conversions. Finally, the peak acceleration from the acceleration vs. time
curve was compared to theoretical data, and the loading distributions examined.
18
Results
Translation of NOCSAE Standard
Kinetic Energy
Test (NOCSAEI
Head-ground
Stick- Head
Ball-Head
absorbed during impact
F (time av.)
Kinetic energy
absorbed per inr
834.6 lb
52.3 ft lb
2.04 ft lb/in2
366.1 lb
26.2 ft lb
10.02 ft lb/in2
183.5 lb
6.12 ft lb
0.239 ft lb/in2
Table Ill: Translation of NOCSAE Standard
Computer Simulation (FEAP)
FEAP was used to approximate the effective area of foam which absorbs energy
during impact. See Appendix I for details on FEAP.
T
Figure IV: Deflection caused by application of a point force at the top of the head and
helmet.
The representation of the application of a point force appears below:
19
Figure V: Representation of deformation in helmet during application of a point load.
Theoretical required thicknesses of urethane foam:
Test
Energy
/n2
EnergyDensity
Thickness (h.d.4
Thickness (m.d.)
Head-ground
2.04 ft lb
4.0 ft lb/in3
0.51 in
3.06 in
Stick-head
1.02 ft lb
4.0 ft Ib/in 3
0.26 in
1.53 in
Ball-head
0.239 ft lb
4.0 ft lb/in3
0.06u in
0.359 in
Table IV: Theoretical required thicknessses for urethane foam.
Optimal range of loading for urethane foams:
Energy Density
Densy
Medium
High
0.417 ft IbAn3 <U< 4.16 ft IbAn 3
1.25 ft lb/in3 <U< 12.5 ft Ib/n 3
Table V: Optimal range of energy densities for urethane foams.
20
Modified Izod Test Results
Peak Acceleration (a)
Eneray absorbed (ft Ib)
1
g
1.61 0.05
13.79
0.28
2
pg
1.67 0.05
11.44
0.16
3
ag
1.50 0.05
11.04
0.16
4
gg
1.48 0.05
4.210
0.10
5
1.54 0.05
4.030
0.06
6
pgg
agg
1.50 0.05
4.020
0.08
7
gb
1.44 0.05
4.370
0.19
8
pgb
1.44 0.05
4.140
0.17
9
agb
1.47 0.05
4.460 V0.44
Table VI: Energy absorption and peak accelerations for liner and shell, and liner
samples. See procedure for sample descriptions.
The acceleration versus time distributions appear below:
341.37,
(Ni
0
MA
VV
ci)
Q
C's
.
Ome (sec)
10
.5
..
.81
ime (sec)
Figure VII: Acceleration vs. time PVC/Acr shell
with .25" high density urethane foam.
Figure VI: Acceleration vs. time for 0.25"
high density foam.
21
______________
_
uIrc,
g__al
I
____________.___9
Ri
It~
tog 187-7-
285.1
1
?
213.90-
'V
V.
/
142.6-~-
T
I"
/
/
as
I
.0
.888
.885
.8Am
.882
i
ill,r~ A.
I
-- T-
-r-
tkne (sec)
.883
.88s
.887
129.2
131.5
183.3T
.As.2-
5
52.6
-
-8 51.7
2.3
V, i ,
F
.885
Aa
.
Z.88
2.He
.982
A8
ass
.887
.888
tkme (sec)
Figure IX: Acceleration vs. time for .5", high
density urethane foam.
Figure VIII: Acceleration vs. time for PC/ABS
with 0.25" high density urethane liner.
(N77.
.882
.888
.888
.88V
LA ~4 L.4AA
-
.4,
, I
.888
.088
tkme (sec)
Figure X: Acceleration vs time for PVC/Acr shell
with .5" urethane foam liner.
ure
.am
.833
.8849 .8866 .8882
time (sec)
gure XI: Acceleration vs time for PC/ABS shell
with .5" urethane foam liner.
22
146./
141.2-
U17. S
112.91
'
r
84.7-
Alfl
56
Z9.4-
2B.2
-
-
5S8.8t
.8888
.8816
.898
.88 82
.8866
.8849
.2*33
.882
.883
.885
.887
Ome (sec)
tkme (sec)
Figure XIII: Acceleration vs time for PVC/Acr
shell with dual density foam in Fig. XI.
Figure XII: Acceleration vs time for urethane foam,
.25" high density, .375" medium density.
~gFk ~
I,~j
.6
-1
125.8
I
6
/i
.s t
j
I
~
'I
-1
0t
31.31
~
-F
4,~d4~
,JT~.
1
I
.899
.892
4
'~
*
.883.Afs
4~~ III
~r
.8V97.I
fme (sec)
Figure XIV: PC/ABS shell with dual, .375" medium density and .25" high density polyurethane liner.
23
.888
Discussion
The choice of materials for use in the shell and liner of lacrosse helmets depends
on the shape of the accceleration curve of the polymer foam, as well as the peak
accelerations achieved during impact. The optimal choice for helmet liner material,
when the peak acceleration data is examined, is either 0.5 inch high density urethane
foam or 0.25 inch high density urethane foam combined with 0.325 inch medium
density urethane foam. Examination of the acceleration vs. time curves for the various
combinations of materials yields information concerning the mechanism of energy
absorption during impact.
The 2.10 lb Izod impact test was used to test the validity of calculations and
assumptions about the behavior of impact absorbing polymer foams during the 60"
head-ground imapct test, the most energetic impact. During the head-ground impact
simulation, it is assumed that the height to which the head rebounds after striking the
ground is negligiible, indicating that a majority of the kinetic energy of the head is
absorbed by the liner and shell. From the computer simulation, the effective impact
area for a top of head strike is estimated to be 25.6 in 2. Simulated point load
deformations appear in Figures IV and V. Extension of the model leads to
approximation of the effective area.
The theoretical energy absorption per square inch of effective impact area
appears in Table Ill. From the J curve in Figure 1I, the necessary thickness of liner was
determined to be 0.51 inches for optimum performance of the high density foam. Table
VI indicates that the 0.50 inch high density polyurethane foam absorbs an average of
1.51 ft lbs of the original 2.10 ft lbs of energy during impact and exerts a peak force of
~4 g on the headform. The J curve is at a minimum when U = 4.0 ft Ibs/in 3 and
maintains a slowly changing slope in a fairly large region surrounding the minimum.
24
large range of energy densities, indicating that approximations and assumptions made
during calculation of the energies will not significantly effect peak accelerations.
Consideration of the curves in Figures VI through XIV is necessary to understand
the effectiveness of different grades and combinations of grades of polyurethanes in
shock absorption. In Figure VI, the acceleration distribution curve for a 0.25" sample of
high density polyurethane foam, a thin sharp spike is seen with a peak acceleration
corresponding to ~13.79 g. The urethane foam in Sample 1 does not exhibit the
plateau acceleration region expected for a flexible impact absorbing urethane foam
operating in its optimum region. Sample 1 instead behaves as a solid polyurethane,
exhibiting a fairly constant slope. From the curve in Figure VI, we can conclude that the
polyurethane in sample 1 is almost immediately strained beyond the effective regions
of impact absorption.
The polyurethane passes rapidly through the regions
corresponding to buckling of the cell walls and gas compression within the cells and
cannot absorb the kinetic energy of impact.
Figures Vil and Vill, corresponding to PVC/Acr with 0.25" high density
polyurethane and PC/ABS with 0.25" high density polyurethane, show behavior
similar to Sample 1. In both Samples 2 and 3, a sharp spike with a fairly constant
slope is appears. The lower peak acceleration of Samples 2 and 3 can be attributed to
deformation of the shell material after the polyurethane has bottomed out. Samples 1,
2, and 3 can be considered unacceptable due to inability to absorb the energy of
impact.
Sample 4, a 0.50" sample of high density polyurethane, whose acceleration vs
time curve appears in Figure 9, exhibits a maximum acceleration of 4.21 g, an
acceptable acceleration for use in helmets.
The curve in Figure 9 exhibits the
predicted plateau region of acceleration which corresponds to a plateau in the stress
vs strain curve during gas compression in polymer foams. Beyond the plateau region,
the acceleration rises gradually, peaking at 4.21 g. Sample 4 acts in the predicted
25
fashion, absorbing energy over a much longer time period than in sample 1, 2, and3.
Sample 4 can, as expected, absorb the impact energy of a 60 inch drop test of a
NOCSAE headform.
Samples 5 and 6, corresponding to Figures 10 and 11, PVC/Acr with 0.50" high
density polyurethane foam and PC/ABS with 0.50" high density polyurethane foam,
respectively, behave similarly to Sample 4.
The peak accelerations are fairly low,
4.03g and 4.02 g respectively, well within acceptable bounds; the regions
corresponding to the plateau in the stress-strain curve appear in both samples,
resulting in predicted behavior. The material combinations in Sample 5 and 6 could
be used in the design of lacrosse helmets.
Samples 7, 8, and 9 exhibit fairly low peak accelerations, but the curves
corresponding to the samples exhibit deviations from predicted behavior.
The
expected linear region is very small, with the the acceleration increasing rapidly over a
short period. After the peak acceleration, instead of dropping off rapidly, as in the
previous samples, the acceleration drops off gradually.
Unexpected energy
absorption phenomena in the dual density liners can be attributed to a combination of
the responses of the two densities of foams under simultaneous loading.
The PC/ABS shell is chosen for use in the shell of the lacrosse helmet due to the
higher flexural modulus and lighter weight when compared to PVC/Acr and PC. Data
for potential shell materials appear in Appendix 3. As demonstrated by the results in
Table VI, the materials tested for the shell do not significantly influence the impact
properties of the liner material so long as the moduli of the shell material candidates
are similar. A 0.5 " high density polyurethane foam is chosen as the liner material.
The impact energy absorption capabilities of the high density urethane foam are
reflected in the low peak accelerations in Table VI as well as in the plots of
acceleration vs time in Figures IX, X, and XI. Higher impact rates than in the executed
tests may change the impact absorbing abilities of the foams , but at the applied
26
energy density (corresponding to the minimum region of the J curve), the peak
accelerations are sufficiently low to allow use of the indicated thicknesses with
confidence.
27
Summary and Conclusion
The suggested materials for lacrosse helmet shells and liners are, respectively,
0.25" PC/ABS and 0.50" high density polyurethane foam.
The conversion of the
NOCSAE lacrosse standard to engineering terms results in a loading of 2.04 ft lbs/in 2
on the surface of the helmet. The J curve was used to approximate the necessary
thickness of foam liner. A modified Izod-Charpy testing machine was used to simulate
the loading on helmet surfaces and measure imparted accelerations. Data from the
modified Izod testing machine shows peak acceleration for a 0.50" high density
polyurethane liner to be ~4.00 g. The acceleration vs. time plots were used to further
characterize the polyurethane liners and determine the accuracy of approximations.
0.50" high density polyurethane is found to be appropriate for use in lacrosse helmets.
28
Suggestions for further work:
Actual design and production of a prototype lacrosse helmet would entail the
following steps:
1.
Higher rate impact tests -the tests executed on the modified Izod Charpy impact
machine had a hammer speed of only 11.35 ft/sec whereas real impacts occur at
17 to 260 ft/sec. Drop tests from a height of sixty inches onto a strain gage
mounted surface would give better characterization of actual loading conditions.
2.
Addition of strain rate monitor to testig devices to give macroscopic strain as a
function of time and load or acceleration.
3.
Lower net force impact tests to characterize the impacts of the ball and stick from
the NOCSAE tests. Polyurethane foams are tested in this paper for high energy
impacts, but polymer foams which perform efficiently at high energies may not be
efficient at lower energies and vice versa.
4.
Determination of estimated parameters
a. measurement of ball speed before and after impact to determine kinetic
energy loss.
b. measurement of rebound of helmet after impact with gorund to determine
kinetic energy loss.
c. measurement of rebound of stick to approximate kinetic enrgy transfer and
loss.
5.
Flexural tests of shell materials to determine shell energy absorption.
29
6.
Design of close fitting, light weight facemask.
30
References
1. C.W. Gadd , "Use of Weighted Impulse Criterion for Estimating Injury Hazard,"
1 OthStapp Car Crash Conference Proceedings. New York, Society of Automotive
Engineers, November, 1966.
2. NOCSAE, "Standard method of Impact Test and Performance Requirements for
Lacrosse Helmets and Faceguards." National Operating Committee on
Standards for Athletic Equipment, Wayne State University, Detroit; 1987.
3. D. M. Schwaber, "Impact Behavior of Polymeric Foams," Polvmer-Plastic Technology
and Enineering. 2(2), 231-249, 1973.
4. Schwaber, p.233.
5. Schwaber, p.233.
6. A.N. Gent and A.G. Thomas, Journal of Applied Polymer Science. 1,107 (1959).
7. W.L. Ko, Journal of Cellular Plastic, 1, 45 (1965).
8. R.E. Skochdopole and L.C. Rubens, Journal of Cellular Plastic. 1, 91, 1965.
9. Skochdopole and Rubens.
10. Schwaber, p.240.
11. Hodgson, V., NOCSAE, Wayne State Universtiy, Detroit, 1988.
12. Zienkiewicz, O.C., The Finite Element Method. 3rd ed., McGraw-Hill Book Co., New
York, 1977.
31
Appendix I: Translation of the NOCSAE Standard
The NOCSAE standard consists of three tests on helmet mounted standard
headforms to establish the helmets impact absorbing abilities. The headforms are
equipped with a triaxial accelerometer at the center of mass.
are available in the NOCSAE standard.
Headform dimensions
The medium headform is used in all
calculations in this report. Weight = 10.5 lbs.
Tests:
1. 60" Drop test: A helmet mounted headform is dropped from a height of 60" on
to standard sites on the helmet. To simplify the test, only the impact on
the top of the headform was considered.
2. 70 mph ball impact test: A lacrosse ball (maximum weight = 5.5 oz) is propelled
at 70 mph on to several sites on the helmet. To represent the ball impact
test, the head and ball are represented as point masses undergoing an
elastic collision.
3. Stick-head impact test: A lacrosse stick (weight = 1.5 lbs) is propelled to a tip
speed of 50 mph and impacted onto the headform at a point just below
the head of the stick. The stick is represented as a distributed mass with
a point mass attached undergoing an elastic collision.
Translation of NOCSAE Tests:
Head-ground impact
mi = mass of headform = 10.5 lbs ~0.328 slugs
vi = velocity of head at impact = gt
s = 60 inches = 0.5 g t 2
g = gravitational constant = 32.2 ft/sec 2
t = 0.557 sec.
32
Kinetic energy* =0.5 mv2
v= 17.9 ft/sec
= 52.3 ft lb
*assuming that the head rebound after impact is negligible.
Ball-head collision
ml = mass of ball
= 0.344 lbs =0.01 07 slugs
m2 = mass of head
= 0.328 slugs
v, =initial velocity of ball
= 96.4 ft/sec
v= final velocity of ball
V2= initial velocity of head
=0.00
V= final velocity of head
For an elastic collision,
v1' =
vi =
1.-_M,
-90.3 ft/sec
v2' =-2m,__ v, = 6.11 ft/sec
mi + M2
Kinetic Energy = 0.5 ( m2 v2 2 )
(absorbed by liner)
=
6.11 ft/sec
Stick-head impact
(since kinetic energy is .5( 1 w2 ), treat as total mass at center of mass at velocity of
center of mass)
I = moment of inertia
w = angular velocity
then treat as point masses in elastic collisions
v1 = velocity of stick = R w = 44.52 ft/sec
R = radius of center of mass
v2 =initial velocity of head = 0
v2' =
2 mi _ v, = 12.65 ft/sec
33
m 1 +M 2
Kinetic Energy = 26.2 ft lbs
This value is only an approximation of the energy transferred.
34
Appendix II: Finite Element Analysis Program (FEAP)
FEAP is mounted under the directory of 3.11 on Project Athena. FEAP is a
program written by R.L. Taylor at the University of California at Berkeley. The system
consists of three primary programs. PREP (written by Art Nava, MIT) creates a data file
which is readable by FEAP through the generation of an illustration of the nodes
whose information is written into the file. Nodes are connected by two or four element
nodes which are assigned material sets. Material sets contain the information (e.g.
Young's modulus, Poisson's ratio) about the material an element is to be created from.
Boundary conditions are assigned and forces or deformations are assigned to the
loaded nodes. FEAP carries out the finite element analysis and writes data files which
can be interpreted by a postprocessor (POST) which creates graphical representations
of the loaded structure. FEAP analyses a PREP file by using the applied forces (at
nodes) to calculate deformations of individual nodes and the stresses and strains
created. From the deformations created by a point force, an area of influence is
determined. The effective area of influence during the drop test was determined by
loading the nodes along the top, relatively planar, section of helmet. From the point
force applied, we know that the nodes beyond loading nodes which are effected due to
edge effects. From the radius of influence, the effective impact area is calculated. To
properly model the impacts applied to a head, a three dimensional representation of a
helmet and headform, and an infinite number of nodes would be required. However,
the FEAP program gives a usable approximation of the effectiv impact area.
Below appears the nodal setup and nodes with elements assigned. Deformation
di=-graIs
a
In
FIgwues
I V
4an
V.
35
Nodal Representation of Helmet and Head
.g9
114
8-8OI
-2 -3 -4 -5
-Ig 3 -92
-
-14 -36.5
-15 -37
*I6
#
-1j5 94
-tgy-g *19 -M6
ElementNodalR4e
e4a4s4e414n4t4a6ton&6767
20-42
7-727374797e777R
-423
Element Nodal Representation
43
676543
62 61
58 57 41
43 44
4
as
36
17
FO ft
72
PS
2
3
Appendix Ill: Determination of Liner Thickness
The total kinetic energy absorbed by the head and helmet is taken from the
translation of the NOCSAE standard. The total kinetic energy is divided by the total
area, that is the effective area of impact, to get the energy absorbed per square inch.
The optimum energy densities (which produce the lowest J) are read from the J curves.
The energy per square inch is divided by the optimum energy density to produce the
thickness of foam necessary for optimal energy absorption during impact. The J curves
appear below.
For the most rigorous test, the head drop test, the adjusted kinetic
energy is 2.04 ft lbs which corresponds to 0.51 inches of 5-20 (high density) foam. Low
density liners are not tested because their range of operation is not within the range of
the energy density produced by the drop test.
37
Appendix IV: Properties of Shell Material Candidates
Possible materials fo the shell were chosen by several criteria; flexural modulus,
flexural strength, density, and notche Izod toughness. The properties appear below:
Material
Sp Gravity
Flexural Strenogth
Flexural modulus
Izod Impact Streng.
ABS
1.01 -1.05
5400-11000 psi
PC/ABS
1.07- 1.12
12000-13000 psi 3.20E5 - 3.70E5 psi
6.4
Acr//ABS
1.35
10700 psi
3.30E5 - 4.00E5 psi
15.0
PC
1.2
13500 psi
3.40E5 psi
14
1.79E5 -3.75E5 psi
6.1 -9.3
-
10.5
ABS was eliminated almost immediately due to its susceptibility to environmental
stress cracking. The others were considered and PC/ABS chosen.
38
Appendix V: Modified Izod-Charpy Impact Machine:
The following modifications are made to a standard Izod-Charpy impact device:
1. The base is expanded to include rigid .325" fixed steel plate to which is mounted
samples of liner and shells.
2. A hammer of mass = 41 grams is mounted in place of the standard hammer. Total
mass of arm is 1.09 lbs, corresponding to a kinetic energy of 2.18 ft lbs.
3. A strain gage is mounted on a the base of the testing apparatus immediately
behind the point of impact. Signals from the strain gage are temporarily stored
in an oscilloscope and then sent to an IBM PC XT for interpretation.
The signal from the strain gage is converted into accb!eration vs. time curves for the
various samples.
The energy absorbed in impact (found through measurement of
height to which the pendulum arm returns after impact) is correlated to the voltage from
the strain gage. The total energy is integrated over the entire curve to give a force vs
time curve. Division of the force by effective mass of head (accelerated by 1 square
inch) yields the acceleration vs time curve for a material.
device appears below:
symple
strain gauge
hammer
BASE
39
A schematic of the modified
Appendix VI: Catastrophic Injuries in Lacrosse
Statistics regarding injuries other than catastrophic injuries are not available due
to lack of an organized injury data collection method (not only for lacrosse, but for
many sports) at the ilntercollegiate level. As there are no established professional
lacrosse leagues, professional data are not available. Thus, only catastrophic injury
data are available and appears below for three collegiate sports; lacrosse, football
and ice hockey.
Fred Mueller reports statistics of direct and indirect injuries in college sports:
Serious
Non-Fatal
Lacrosse
0.00
4.00
8.00
Football
0.80
2.13
6.67
Ice Hockey
0.00
0.00
4.59
Figure I: Direct Iniuries per 100,000 participants 1982-87.
Data is for male participants in intercollegiate sports.
Sport
Lacrosse
Football
Ice Hockey
Fatal
0.00
2.13
4.59
Non-Fatal
0.00
0.00
0.00
Serious
0.00
0.00
0.00
Figure II: Indirect injuries per 100,000 1982-83 - 1986-87.
Data is fkor male participaints in intercollegiate sports.
Definition of terms:
Direct injuries-"those fatalities which result directly from participation in the skills
of the sport."
Indirect injuries-"those fatalities which were caused by systematic failure as a
result of exertion while participating in a sport activity or by a
40
complication whilch was secondary to a non-fatal injury."
Fatality-death
Non-fatal-"permanent severe functional disability."
Serious-"no permanent functional disability but severe injury. An example would
be a fractured cervical vertebra with no paralysis."
Lacrosse, with limited contact, has an inordinately high percentage of serious
injuries, due in part to the equipment used. Though non-serious injuries have not
been reported in lacrosse. Jim Group, representing the Lacrosse Coaches Association,
called for the establishment of a lacrosse helmet standard to prevent further injuries.
Serious and fatal injuries as well as non-serious injuries such as concussions could be
prevented with the development of better helmets.
In 1986, the National Operating
Committee for Athletic Equipment
published such a standard.
(NOCSAE)
Establishment of the NOCSAE standard in football caused a 42% reduction in the
number of deaths over a period of eight years.
41
Appendix VII: Mechanisms of Head Injury:
Design of a helmet requires an understanding of the mechanisms of head injury.
Head injuries can be categorized in three basic types:
1. Skull fracture: fracture of the cranium which may or may not be accompanied
by one or both of the following mechanisms.
2. Focal injury: localized damage to brain matter characterized by hemorrhaging,
edema, or ischemia.
3. Diffuse injury: no localized injury, but "widespread disruption of the structure or
function of the brain.
Focal injury causes an increase in the local brain tissue pressure, resulting in
herniation of the tissue. The brain may shift, causing compression of the brain stem
and may cause secondary hemorrhaging of the brain stem.
Centers controlling
respiration and cardiac functions may be damaged permanently and the patient may
die. Focal injury is most commonly seen as a result of skull fracture and is the cause of
approximately two-thirds of all deaths from head injury,
In diffuse injury, local damage is not seen, but the damage is spread through the
entire brain. Diffuse injury is primarily the result of rapid acceleration of the brain, either
translationally or rotationally and may cause temporary neurological disorders.
However, if the injury is more sever, diffuse swelling of the brain causes an increse in
the intracranial pressure, resulting in extensive axon damage and "permanent
functional dysfunction."
The mechanisms of head injury can be divided into two basic categories:
1. Static loading: forces applied o 'er an interval of >200-500 msec.
Static loading is not common in sports related injuries and will not
be discussed here.
42
2. Dynamic loading: forces applied over an interval <200 msec.
Dynamic loading can be separated into two components, impact
and impulsive loading. The two types of dynamic loading are somewhat related.
Impact is an inertial loading (acceleration) of the head accompanied by contact
phenomena and may result in focal and/or diffuse injuries. Impulsive loading. is rapild
acceleration or deceleration of the head which results most commonly in diffuse injury,
but may also result in focal injury.
Both impact and inertial loading of the brain include the inertial effects whilch are
responsible for many head injuries in sports. Inertial effects may be categorized as
translational or rotational acceleration of the brain, both of which result in shear,
tensile, or compressive strain in brain tissue. Translational acceleration of the brain
induces "focal structural lesions" in the brain, but the accelerations necessary to induce
concussion are significantly higher in translational acceleration than in rotational
acceleration.
Rotational acceleration of the brain induces diffuse injuries in the brain and
results in concussive effects at lower levels than translational acceleration. In
summary, acceleration effects, both translational and rotational, are the primary
mechanism for brain damage when skull fracture is not involved. Thus, though it is
difficult for head gear to protect against acceleration effects, helmets must bse
designed to minimize the local effects of impact forces by distributing them over the
entire head, to prevent skull fractures, and to minimize the effect of acceleration by
translating a pulse of high magnitude over a short period to a pulse of tolerable
magnitude over a longer period.
Neck injury is a second effect of dynamic loading of the head and can be
seperated into two mechanisms:
1. Hyperextension: movement of the head angularly and posteriorly, resulting in
shearing of the spional cord by vertebrae or seperation of
43
vertebrae.
2. Hyperflexion: axial loading of the vertabrae, whilch act as a segmented
column, resulting in buckling and/or fracture of the vertebrae.
Hyperflexion is the most common mechanism for fractur or dislocation of the neck
and requires a load of 750-1000 lbs. to induce serious damage. Albert Burstein at al
write that a "structure such as a helmet cannot be relied upon to absorb tlhe kinetic
energy from the torso. Moreover, if the primary function of the helmet is to provide
protection for the skull (head), a redesigned helmet which would also be capable of
absorbing all the kinetic energy of the body would be a disproportionate and totally
useless structure." Thus, I focused my design of the lacrosse helmet on protection of
the head and will not concern myself to a great degree witro the neck. Furthermore, I
was not concerned in this thesis with injuries which are related to the facemask design.
44
Bibliography
1. Gadd, C. W., "Use of a Weighted Impilse Criterion for Estimating Injury Hazard," in
the Tenth Stapp Car Crash Conference Proceedings, New York, Society of
Automotive Engineers, Nov. 1986.
2. Gadd, C. W., "Tolerable Severity Index in Whole Head, Nonmechanical Impact,"
Fifteenth Stapp Car Crash Conference Proceedings. New York, Society of
Automotive Engineers. Nov., 1986.
3. Gent, A.N. and A.G. Thomas, Journal of Applied Polymer Science, 1, 107, 1959.
4. Gurdjian, E.S. and Webster, J.E., Head Injuries: Mechanisms. Diagnosis. and
Management. Boston, Little, Brown, and Co., 1958.
5. Hilyard, N.C., editor, Mechanics of Cellular Plastics; Macmillan Publishing Co., New
York, 1982.
6. Ko, W. L., Journal of Cellular Plastics !, 45, 1965.
7. Meinecke, E., Mechanical Properties of Polymeric Foams; Technomic Publishing
Co., Westport, Conn., 19M
8. Mueller. F.O. and Blyth. C.S.. Fifth Annual Report of the National Center for
Catastrophic Sports Injury Research; University of North Carolina at Chapel
Hill, 1982-1987.
9. National Operating Committee on Standards for Athletic Equipment, Standard
Method of Impact Test and Performance Requirements for Lacrosse Helmets
and Faceguards; Wayne State University, 1987.
10. Ohanian, H. C., Physics Vol. 1; W W Norton and Co., New York, 1985.
11. Rogers Corporation, "Specification Sheets for the Use of Poron", 1987.
12. Schwaber, D. M., "Impact Behavior of Polymeric Foams, a Review,"
Polymer-Plastic Technology and Engineering, 1973.
13. Slochdopole, R.E., and Rubens, L.C., Journal of Cellular Plastics, 1, 91 ; 1965.
14. Torg, J.S., MD, Athletic Injuries to the Head. Neck. and Face; Leu and Febiner,
Philadelphia, 1982.
15. Zienkiewicz, O.C., The Finite Element Method, 3d edition, McGraw-Hill, New York,
1977.
45