NBSIR 76-1107

Considerations in Developing

Test Methods for Protective

Headgear

Robert E. Berger

Product Safety Engineering Section

Product Engineering Division

Center for Consumer Product Technology

August 1 976

This is an interim report

Issued September 1976

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 76-1107

CONSIDERATIONS IN DEVELOPING

TEST METHODS FOR PROTECTIVE

HEADGEAR

Robert E. Berger

Product Safety Engineering Section

Product Engineering Division

Center for Consumer Product Technology

August 1 976

This is an interim report

Issued September 1976

U.S. DEPARTMENT OF COMMERCE, Elliot L. Richardson, Secretary

Edward O. Vetter, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

I. Introduction

Protective headgear has long been used to reduce injury in such

activities as construction, mining, fire fighting, motorcycling, and

sports (including football, baseball, and hockey). In addition, the use

of protective headgear is becoming more widespread among some consumers

who were traditionally not associated with helmet wear (e.g., bicycle

riders)

.

Many manufacturers respond to this demand. Even for helmets designed

for the same activity there are large variations in style, materials, comfort and cost. There are at least 10 manufacturers who offer more than 50

different models of football helmets alone. The prospective purchaser of

this equipment, whether football coach, fire chief, industrial representative, or individual consumer, is faced with the monumental task of choosing

among the helmets offered for a particular activity. To further complicate this decision, the most important variable, the degree of protection

offered, is the least well understood and the most difficult to evaluate.

There exist many test methods for evaluating the protective

characteristics of the headgear, and standards have been proposed to maintain minimum performance levels. Some of these are promulgated by

authorized government agencies (National Highway Traffic Safety Administration, Occupational Safety and Health Administration, Law Enforcement

Assistance Administration); some are promulgated by long existing voluntary

standards organizations (American National Standards Institute, American

Society for Testing and Materials); others are promulgated by groups

established for specific purposes (National Operating Committee for

Standards in Athletic Equipment). These standards are presently in various

stages of completion. It is not unusual to find more than one test method

for the same type of protective headgear. Sometimes helmets rejected by

one method will be passed by another.

These difficulties are in part due to the limited information which

is available on head injury, especially internal head injury. Another

factor is that the relationship between a test method for protective

headgear and the amelioration of head injury has not been sati sfactori ly

explored. Also the importance of simulating the injury environment in the

test method is not well established.

The purpose of this report is to summarize the difficulties in the

evaluation of protective headgear and to suggest the existence of a relationship between test method and injury prevention. First, the state

of the art concerning the mechanisms of head injury and the relationship

of these injuries to the modes of energy input are briefly reviewed. Next

the general guidelines in the design of protective headgear are discussed

and present test methods for helmets are summarized. In order to provide

a quantitative framework, a simple model which incorporates many features

of present test methods is defined and executed. A rational approach to

the design of meaningful test methods for protective headgear is duscussed,

with reference to the results of the model.
Injuries

- 2 -

1 1 . Mechanisms of Injury

A cross section schematic of the head and its contents is shown in

figure 1. The brain, a viscoelastic, inhomogenous, and anisotropic material

is encased in the skull which is relatively rigid except for the opening

through which the spinal cord protrudes, the foramen magnum. The geometry

of the skull in the frontal regions is marked by small curvatures and bony

protuberances in contrast to the nearly spherical top and rear (occipital)

regions. For more details, the reader is referred to references 1/ and 2/.

The types of injuries that are likely to occur when the head is

impacted have been well documented ]_/

3/, and only general categories

will be mentioned here. Among the ways to classify head injury is by the

type of material damaged: namely, skull, blood vessels, and brain matter.

Skull fracture is the structural failure of the cranial bone, usually due

to the process of crack initiation and growth when tensile stresses arise

during impact. Linear fractures, for which the resulting skull geometry

is unchanged except for the appearance of a crack, are the most common 4/.

Internal bleeding, when it accompanies head trauma, may be found either

within the brain tissue (e.g. petechial hemorrhage) or between the brain

and skull (e.g. subdural hematoma). Nearly all such injuries are potentially

fatal and require surgical intervention 5/. The injuries to brain material

are usually divided into contusions and lacerations. Contusions are found

on the outer surface of the brain and are marked by a discoloration of the

brain material; a laceration is a tearing of brain material often found in

the regions of the bony protuberances of the skull ]_/. These injuries

may occur separately or may accompany one another.

When the impairment of function is immediate, the injury is usually

diagnosed as a concussion. There are about as many definitions of con- cussion as there are authors on the subject. Thomas 6/ reported that

concussion is - "characterized by immediate and transient impairment of

neural function, such as alteration of consciousness, disturbance of

vision, equil ibrium, etc., due to mechanical forces." 7/ He restricts his

attention to cases of unconsciousness and suggests that the ultimate cause

is mechanical input to the brain stem axis (by stretching or shear strain).

However, Ommaya 8/, quoting from Walker 9/ argues that "concussion involves

not only the brain stem but other loci in the brain." He then goes on to

say, quoting now from Symonds 1_0/ :

"Concussion should not be confined to cases in which there is

immediate loss of consciousness with rapid and complete recovery,

but should include the many cases in which the initial symptoms

are the same but with subsequent long continued disturbances of

consciousness, often followed by residual symptoms - concussion in

the above sense depends upon diffuse injury to nerve cells and

fibers sustained at the moment of the accident. The effects of

this injury may or may not be reversible."

In this sense the alteration of consciousness known as concussion will

include those cases in which the diffuse disturbance of functional

damage is accompanied by structural failure which may be irreversible.
- 3

-

Relation between gross head motions

and tissue level injuries

It is important to distinguish between the local disturbance of

function or structure and the gross head motions which accompany these

local disturbances. These local disturbances are always due to material

deformation which may be quantified by field variables such as strain,

stress, or pressure. The local deformation can be related to the gross

motion of the skull. Following an impact, three distinct motions occur*

(figure 2)

:

1. Skull bending

2. Translational component of the acceleration of the center

of gravity.

3. Rotational acceleration of the head about the center of

gravity.

The latter two modes of motion are inertial and may result without impact

to the head (say in the case of whiplash). The skull bending mode results

from the contact phenomena between a foreign object and the scalp, transmitting a local force distribution to the skull.

Each of these modes give rise to local deformations which, depending

upon the magnitude, are capable of producing internal head injuries. Only

the skull bending mode contributes to skull fracture. Many experimental

and analytical studies have attempted to understand the mechanisms by

which the energy of the gross motions is transferred to the local tissue

level. In the rest of this section, some of these results will be briefly

mentioned.

While all modes are operative in most impact situations, the experimental

and mathematical model studies tend to consider the rotational motion separately.

In many animal impact studies the translational component of acceleration

has been singled out as the most important variable for measurement.

Accordingly, most tolerance criteria for head injury have- been referred to

the translational acceleration.

The mechanism for tissue damage by the direct impact mode (skull bending

and translational acceleration) has been qualitatively explained as follows:

when the skull is impacted, pressure gradients arise in the fluid-like brain

(as in any accelerated fluid-filled container) 11/. Positive pressures

develop in the brain at the site of the blow, and negative pressures (normal

tensile stresses) develop at the opposite side of the brain (contre coup

site) 12/. Transient pressure waves in the brain and stress waves in the

skull also tend to magnify the amplitude of the negative pressures 1 3/.

It was postulated that the large negative pressures, which appear to exist

at the contre coup site, may cause cavitation in blood or brain tissue 11/-14/.

However, contracoup injuries are often observed for occipital impacts but

rarely for frontal impacts 15/, a descrepancy which cavitation theories often

fail to resolve 16/.

*If the direction of the blow does not pass through the neck axis, there will

also be a rotation about this axis.
- 4 -

In studies with water-filled cadaver skulls, it was shown that the

presence of the foramen magnum enhanced the resulting pressure gradients Y\J

It has been suggested that the established pressure gradients may force

brain material through the foramen magnum, causing shear stresses to develop

in the region of the brain stem 6/. Other displacements of brain material

have also been observed to occur 1J_/, 17/, 18/. Locations where these

relative motions are large are thought to be potential sites of injury. In particular, Gurdijian suggests that these "relative motions seem to be

the most likely mechanism for frontal and temporal lobe contusions rather

than negative pressures" 1J_/.

Figure 3 shows the Wayne State University Concussion Tolerance

Curve, first published in 1962 19/. These data were based on cadaver skull

fracture in the short duration range (because of the clinical association

of linear skull fracture and concussion) and on human volunteer studies for

impacts of long duration. It is seen that the average translational

acceleration required to produce the injury depends upon the time interval over which the acceleration is applied. Haut et. al noted that such

behavior is to be expected for viscoelastic material like the human brain 20/

While the short-comings of this tolerance curve have been rigoriously

discussed 21/- 23/, it remains the most widely accepted compendium of con- cussion tolerance.

Several indices of injury potential have been derived from the Wayne

State data, based on the near linearity of the data when plotted on log-log

paper. Gadd developed the severity index,

where a is the acceleration expressed as a multiple of the gravitational

acceleration and T is the duration of impact. According to Hodgson 4/:

"Gadd derived a critical value of 1000 (the units for SI are seconds) as being the threshold of danger to ^ife. . . He recognized that the Severity Index may be a function of contact area. . . Later on, Gadd suggested a critical value of SI equal to 1500 . . . for distributed impact" 24/.

a Arguing that the SI does not really match the Wayne State data, Versace 2

developed the head injury criterion:

where t-, and to are those times between 0 and T for which the above

expression is maximized. Again, "a HIC level of 1000 is assumed to be a threat to 1 ife" 4/.

t

2 • 2.5
5

Other tolerance criteria have been based upon 1 umped-parameter models

of the head 22/, 26/, 27/. One example, the maximum strain criterion (MSC),

is shown in figure 4a 26 / where parameters were chosen to match the

impedance response of animal or cadaver heads. The maximum strain in the

model was related to the onset of discernable structural damage in experimental animals. "The tolerable head strain for humans (found to be

.006 in/in) was calculated from the mathematical model" 27/based on scaling factors that were developed. An acceleration tolerance curve was developed and compared to the Wayne State curve (figure 4b). For side

impacts a different tolerance curve was indicated 28/

.

Ommaya and his associates 1_6/, 29/ -34/ have conducted a large part of

the experimental research to identify the contribution to injury by the

rotational component of acceleration. This mechanism of injury, originally

proposed by Hoi bourn 35/, involves the transfer of shear stresses to the

viscoelastic brain by the rotating skull.

In whiplash experiments with monkeys, rotational accelerations were

measured and tolerance curves for concussion were derived 29/ , 30/ (see

figure 5). It was found that the tolerance levels were reduced if the

resulting head rotation was- produced by direct impact, and suggested that

"skull distortion effects appear to reduce the level of head rotation

required for the production of cerebral concussion and contusions" 1 6/

.

When animals wearing protective helmets were impacted, no concussions were

observed at the same rotational levels 16/. Thus it was thought that the

gross head motion of skull bending contributed to the shear stress

mechanism of injury 29/. Reasoning from a scaling law, also attributed to

Holbourn (in which tolerable rotation levels for different species are inversely proportional to the brain mass raised to the 2/3 power), the

primate data was extrapolated to humans to obtain tolerances of rotational

acceleration for long duration impacts:

2 7500 rad/sec for concussion of 99% of population

1800 rad/sec^ for concussion of 50% of population

In another series of experiments 31_/, 32/ an attempt was made to

isolate the two inertial gross motions. By rigidly securing primate heads

in pots, the heads could be subjected to purely .rotational or translational

motions (the axis of rotation was not the center of gravity of the head;

therefore, a component of translational acceleration was present, which was comparable to that of the translated animals). All rotated animals

suffered concussions, while none of the translated animals were concussed.

On autopsy it was found "that a greater number of lesions occurred in a more diffusely widespread symmetrical manner in the rotated group, whereas

only a few asymmetrical ly placed focal lesions developed in the translated

group" 8/. This does not suggest that such focal lesions are not dangerous

(all are potentially fatal) but rather that they occur without concussion

(as diagnosed immediately) in the purely translated group.

To further quantify concussion, functional damage was assessed by a somatosensory evoked response (SER) method 32/, 33/ : "all animals in the

rotated group exhibited neurological evidence of experimental cerebral

concussion; in contrast, none of the translated group showed this effect."

At the local level, similar changes in the SER of individual nerve fibers

were observed under mechanical loads 34/.
- 6 -

Mathematical modeling of head injury

The usefulness of mathematical models lies in their ability to

quantitatively relate the gross head motions to local tissue deformation. The

effect of the various input modes can be isolated and studied. Of course,

they are limited by how well the material properties of the skull and brain

can be established. At this time the mechanical properties of the skull

(see e.g. 36/, 37/) are more reliably known than those of the structurally

more complicated brain (see e.g. 38/, 39/)

.

If, in addition, experiments can establish tissue level failure

criteria (including functional failure, say by experiments similar to

those of Thibault 34/ described earlier), then the models can be used to

establish tolerance limits for the gross head motions. This procedure would

be as follows:

1. Perform experiments on tissues that relate the severity of

damage to the history of the local deformation. This

relationship, expressed in functional notation* is

S

T =^(D)

where D is the deformation tensor.

2. Use the model to derive another functional which relates

severity to the history of the gross head motion X (itself a function of position and time):

S G^( X >

Two examples of these functionals, SI and HIC, were discussed earlier.

They relate the severity potential to an integral of the translational

component of the acceleration. In the MSC approach 26/ the acceleration

criteria is derived from a given injury index, mean strain. However, this

relationship is between two gross modes (translational acceleration and

skull inbending) instead of between a local injury mechanism and a gross

head motion.

The mathematical models to be discussed can be cateoorized accordinq

to whether or not skull rotation effects are included. Some of the studies,

which do not include rotation, have modelled the brain as an inviscid fluid

41/ - 47/ in order to identify areas which are likely to sustain large pres- sure cFanges (both positive or negative). They are also useful in predicting

sites of the skull at which fracture is likely. These models range from the

*A functional is an operation which maps histories of one variable onto a one dimensional space (see, e.g. Truesdell 40/). The simplest case is

where only the present value of the variable is important, in which case

the functional reduces to a simple function. Therefore, for skull fracture,

where failure occurs when the tensile stress exceeds a certain limit, the

local severity index would reduce to the maximum value of the tensile

stress.
7

rigid skull model of Guttinger 41/ to the sandwich skull model of Akkas 44/

and include the effects of non-sphericity 45/ and glancing blows 46/. The

finite element model of Shugar 1_5/ incorporates many complicated structural

features, including the foramen magnum. Goldsmith, using a physical

model, accounted for the effect of the neck 47/. Because of wave propagation effects, these models predict large values of negative pressures at or near (depending upon the sophistication of the model) both poles (impact

side and opposite site). However, in all of these studies, the duration of

loading is very small (one millisecond or less), a situation which magnifies the importance of the transient fluctuations 48/ . Advani and Owings 49/

have predicted that the impact duration of the skull against a rigid flat

surface is at least 3 msec.

Other investigators have accounted for the low shear modulus of

the brain material 41/- 48/ in order to identify sites of large shear

strain even in the absence of rotation. In these studies, the pressure

distribution results were similar to the inviscid studies described above.

Owings and Advani 49/, 50/ with an elastic brain model, predicted large

values of shear strain at both the midbrain area and the brain surface.

When viscous damping is accounted for 48/, 51/ , the magnitude of the shear

strain decreases and the locations shift slightly. Hickling and Wenner 48/

predicted shear strain values of about .025 rad for a 3 msec pulse with an average acceleration of about 150g. This is on the same order as the

shear strain for structural failure, .035 rad 38/

.

In the above studies, longer loading durations were considered (up to

20 msec). As the duration increases, the magnitude of both the negative

pressure and the shear strain decreases. This result would be contradictory

to the Wayne State Tolerance Curve (figure 3) if only the magnitudes of

these quantities were responsible for brain injury. However, the results

of these investigations also show that at the local level, there is also

an increase in the time duration for which negative pressures and shear

strains exist. Therefore, it is likely that the injury has some history

dependence at the tissue level itself.

In rotation studies the skull is modelled as a rigid sphere which is

subjected to prescribed rotational accelerations, either step functions 52/

,

53/ or finite pulses 54/- 57/ . When the brain is modelled as an elastic

material, Holbourn's 2/3 power scaling law, discussed earlier, was confirmed 54/. If viscous damping effects are included, the magnitude and

transient fluctuations of the shear strain are reduced 55/, and the 2/3

power scaling law applies only approximately 54/. Bycroft picked a specific

brain location for concussion injury (non-dimensional radius of 0.3) and

calculated the value of the maximum strain required for correlation with

experimental whiplash studies. For both squirrel and rhesus monkeys, this

strain value was .05 rad. Using this same location and shear strain level

for human concussion, a threshold level for concussion was calculated to

be 3500 rad/sec . Liu, Chandran, and von Rosenberg 55/ obtained similar

results using a finite difference procedure. Ljung's model 56/ accounted

for the effect of the falx, the near rigid portion which separates the two

hemispheres of the brain. Lowehhelm 57/ , using the results of this model,

calculated a tolerance curve based on a local injury criterion which was strain rate dependent.
- 8 -

III. Headgear

The preceeding summary of injury mechanisms is useful for suggesting

performance criteria for protective headgear. The experimental and

analytical studies confirm that all three modes of the gross head motion

are capable of producing local deformations which are potentially injurious.

At this time, no single mode can be identified as the most harmful. The

tolerance values for these gross motions, where they exist, are quite

sketchy, but some indications are clear. The dependence of the injury

potential on the history of the gross motions (effect of input duration)

is a factor, especially for impacts of shorter durations. The translational

acceleration indices, SI and HIC, account for this effect and should serve

as guidelines until the state of the art improves. Though analogous

rotational indices have not been suggested, the necessity of reducing

rotational accelerations is obvious.

One approach in the design of protective headgear is to attempt to

reduce the gross head motions by placing deformable material between the

head and the prospective impact surface. Analogous to the simple springmass model of Appendix 1, this is expected to change the inertial response

even if no energy is absorbed by the helmet material. In this analogy,

the percentage increase in the duration of the acceleration response is

the same as the percentage decrease in the average (and maximum) acceleration. According to the injury criteria for which the acceleration is

weighted to the 2.5 power, this changed response is favorable. Any energy

absorbing features of the helmet system would serve to further improve

the response of the head. Another purpose served by these deformable

materials is to spread out the applied load over a large area, thus

reducing the gross head motion of skull bending*.

Several studies have listed some of the general parameters of a helmet

system with qualitative descriptions of their relationship to head protection 1_9 /, 58/-61 / . More recently, simple one dimensional models of head/helmet

systems were used as a guide in optimizing helmet design parameters 62/-65/

.

In these studies the helmets were modelled as Kelvin elements, a spring and

a dashpot in parallel. In Liu's model the helmet element was coupled to

a fluid filled cylinder and the injury criteria was "the averaged time

spent, at contrecoup, beyond the cavitation pressure of the fluid" 63/.

McElhaney et al 65/ coupled the helmet element to the two-mass head model

described earlier 26/ and used the maximum strain criterion for injury.

This paper is not so much concerned with proper design aspects of

protective headgear but rather with methods of evaluating whether or not

a helmet offers suitable protection. In an ideal helmet performance test, one would subject a "head" to a realistic impact load and measure the

response of the head to determine whether this response is within tolerable

limits. The problem of determining which responses to measure has already

*As there are few reports of skull fracture among helmet wearers, it is

assumed that most helmets sufficiently reduce the skull bending mode. Therefore, the question of tolerances for skull fracture has been avoided in

this report, though this particular injury is the most well understood.

For a complete list of references, see Mahajan 3/.
- 9 -

been addressed. While it would be best to measure local deformation

quantities which are related to injury at specific sites, the present

state of the art only suggests guidelines for tolerance of the gross head

motions. Nevertheless, this limitation has not slowed the development of

helmet test methods.

The "head" to be used in a performance test is another source of concern. Ideally the best head-form would incorporate enough essential

features to produce a response similar to the human head. Efforts in the

development of humanoid head-forms have been reported 66/ - 70/ . The

resilient components of these headforms were adjusted so that the response

would fall within a range of static and dynamic (linear acceleration)

responses of cadaver heads 66/ , 67/ . Other comparative tools such as impedance response 69/ and frequency analysis 70/ have also been used.

However, there remain questions as to the reproducibil ity and durability

of these headforms 71/. In most test methods, therefore, a metal headform

is used.

The ability to simulate a realistic impact situation is another

desirable feature of an ideal performance test. In nearly all helmet test

methods, a helmeted headform is dropped onto an impact surface. The rationale for this method is based on two observations 72/ : 1) in laboratory

experiments, cadaver head responses were observed which were nearly independent of the body, and 2) the duration of most impacts is much less than the

neck muscle reaction time. Present test methods incorporate a wide variety

of impact surfaces and drop energies even in evaluating helmets for the same activity. If the purpose of the test is to insure that potentially injurious

head responses are avoided, then it is necessary that the impact conditions

of the test be such as to simulate (or at least be related to) a real life

impact situation. In many activities, one impact mode predominates, but in some (e.g. football) there are several equally important modes.

To illustrate the variety in test methods for protective headgear, a partial list of present methods is shown in table 1. (See references

72/- 81/.) Most methods attempt to account for the time duration effect

Tthat the head can withstand higher accelerations for short times; see Wayne State curve, figure 3) by the "dwell time" concept (where limits are

set for the time duration for which the acceleration exceeds prescribed

values). It is interesting to ask how these criteria compare to a biomechanical injury index like SI. As an example, consider the criteria of

the FMVSS 218 standard. For simple acceleration traces (e.g. curves which

approximate haversines or triangles), a curve representing a barely

safe acceleration response is completely defined by specifying any two of

three rejection criteria (figure 6). The corresponding SI values, also

shown in figure 6, are all extremely high and depend upon which rejection

criteria are specified. Of course, such a comparison may not be relevant

as these methods often do not claim to represent realistic impact situations. Rather they are one means of ranking helmets in one impact

configuration

.

The possibility that this ranking would change if resilient headforms

and/or impact surfaces were substituted for their metal counterparts is

usually not addressed. In one study, for which the same helmets were
10 -

tested by two different methods, there was little or no correlation in

helmet performance as measured by the different methods 82/. In addition

to these differences in test method (headform, impact surface, impact

energy, and rejection criteria), other effects may also influence the

proper ranking of helmets. E.g. would the helmets which perform best in

a typical drop test method also offer the best protection against head

rotations? Does the size of the impacting object make a difference?

IV. Model

Descri ption

In order to address the questions raised in the previous section and

to provide a quantitative framework for comparing one test method with

another, a simple one dimensional, lumped parameter, model is utilized.

The headform, helmet and impact surface are all identifiable elements and

a broad range of test conditions can be studied. The scope of this work

differs from previous modelling attempts 62/ , 67/ , discussed earlier,

in that our purpose is not to identify optimum values of helmet parameters

for preventing a particular injury. The simplistic models for the helmet

and head and the limitations in the available tolerance data would

severely reduce the applicability of such an exercise. Rather we are interested in comparing headform responses (acceleration vs. time) when

test conditions are changed. The model is shown in figure 7, and each of

the elements are explained in turn.

The headform is modelled as either a rigid body, to represent metal

headforms, or as the two-mass resilient system suggested by Stalnaker

et al 83/ (figure 4). The force F H between the masses is given by (see

figure 7):

F h

= K [ L - (X

1 - X

2 )] + C(XZ

- xp (1)

where L is the initial separation of the two masses. The parameters of

this model were evaluated to match the driving point impedance characteristics of cadaver heads (groups 1 and 2 of table 2) 26/. In these studies

the mass M] was subjected to prescribed accelerations, and tolerance curves were developed to correspond to threshold strain levels. However, in

impact simulations, the mass M] makes contact with some foreign object

(possibly the inside of a helmet) and accelerations are recorded for the mass M^ (either by placing an accelerometer at the center of gravity, for

humanoid headforms, or opposite the impact site, in cadaver experiments).

In order to determine whether these parameter values give reasonable

impact accelerations, the acceleration of mass M2 in the model was compared

to the response of cadaver heads in an experimental impact situation.

McElhaney et al 27/ reported the resulting accelerations of cadaver heads

which were impacted by a flat rigid object of known mass (10 kg) and

velocity (11 m/s). Humanoid headforms have been developed to match the

acceleration responses in these cadaver experiments 67/. When the head

model was subjected to the same input conditions (equations of motion and

initial conditions to follow), the maximum acceleration, Amax , was much

greater than in the cadaver experiments, and the time, tma x, at which the
11

maximum occurred, was much sooner. These quantities, a max and tma v, could

be matched when the parameters in group 3 (table 2) were used in trie model*. Slattenschek and Tauffkirchin 23/ using a one degree of freedom

model also chose a similarly low value for the spring constant. Also

static force-displacement curves of laterally loaded cadaver heads (and a representative humanoid headform) suggested that the value of an effective

spring constant would lie in the range 0.7 - 3.5 MN/m 67/. Therefore,

in most of this work, the humanoid headform will be represented by the

parameter values in group 3 of table 2.

Both rigid and resilient impact surfaces were simulated. In the

latter case the deformation of the surface was assumed to be quasi-static**.

Then the relation between the force, F s , and the displacement can be

derived from the contact relations between elastic bodies 85/

,

F

s = B(X3

- d) 3/2

(2)

(see figure 8) where d is the initial thickness of- the helmet liner material

and

„ - 1/2

4 R

B = -

3 ( K-| + K

2

)

R

=

R

1 R

2

R-| + R2

1 - v- K

i — 1 - V. K

2 =

E, v and R are the elastic modulus, poisson's ratio, and radius of

curvature respectively for each body (subscript 1 for impact surface,

subscript 2 for helmet). For an impact surface made of polyurethane,

Ei = 28 - 63 MN/m^ (4000 - 9000 psi) 86/. This is much smaller than the

modulus for typical helmet shell materials like polycarbonate,

E 2 = 6.9 X 10-3 MN/m^ (10° psi) 86/. For a flat pad, R] = =0

, and helmet

radius of order 10 cm, a range of values for the parameter B can be

calculated:

B — 10 - 25 MN/m3/2

Melvin and Roberts 87/ report the results of experiments with typical

helmet liner materials which were loaded at high strain rates. The viscoelastic nature of these materials is evident. To simulate these deformations

we will consider the simplest viscoelastic lumped parameter elements: the

*The masses, Mi and M2 , were arbitrarily chosen to be the averages of the

side and longitudinal cases. K and C were chosen so that a max

and tmax would fall within the range of cadaver responses.

**According to Goldsmith 84/, such approximations are valid if the duration

of contact between the impacting objects is long compared to the time that

it takes for elastic waves to traverse the objects. Wave speeds in typical

impact surface materials like polyurethane are sufficiently large to allow

this approximation.
12 -

Maxwell element, a spring and dashpot in series; and the Kelvin element,

a spring and dashpot in parallel. The equations for the force in these

elements (derived in Appendix 2) are (refer to figure 8 ):

Maxwel 1

Kelvin:

(3a)

(3b)

where E and n are the elastic modulus and viscosity for the helmet liner

material, A is the area over which the load is distributed (see Appendix 2),

d is the initial thickness of the helmet liner material, and a dot above

a symbol indicates differentiation with respect to time. It was found

that the Maxwell model is more capable of reproducing the load-deflection

curves that were reported by Melvin and Roberts 87/ (Appendix 2) and

therefore this model will be used more extensively in this work. This is

in contrast with other previous one dimensional studies 62/, 65/ in which

helmet materials were modelled by Kelvin elements. The range of values

for the parameters E and n were chosen to represent a reasonable range

for helmet materials based on the work of Melvin and Roberts 87/ (see

Appendix 2). Therefore, in this model, the characteristics of a single

helmet are described by a pair of values, (E, n).

The governing system of equations is completed by force balance

relations for each of the masses (figure 7):

¥i - f h

- F

.

< 4 >

For a large rigid impact surface (X 3

= d, X

3

= 0) the system (1), (3a), (4)

and (5) represents four equations for four unknowns X-j , X 2 , F, F^. The

initial conditions are X-|(0) = 0, Xq ( 0 ) = V, X^(0) = -1, MO) = V, F(0) = 0,

where the velocity V is related to the drop height h by V = /2gh*.

If a resilient impact surface is to be included, F = F s (neglecting

helmet mass) and equation ( 2 ) becomes the fifth equation for the now unknown

position X 3

. For the case of a small rigid mass M

3 impacting the head

another equation must be added

«3*3 F

and the initial conditions on velocity must be changed to

^(0) = X

2 (0) = 0, X

3 (0) = -V

Note that the mass of the helmet is neglected in this system.

Preliminary experiments indicate that the response of the headform is

nearly independent of the helmet mass. It is likely that this is the reason that present test methods do not include the mass of the helmet
13

when calculating the input energy. The rationale for neglecting the

helmet mass is as follows: only a small fraction of the helmet mass is

contained within the area of contact; the potential energy associated

with the rest of the helmet mass is not available for compressing the

liner material and instead is dissipated by flexural wave motions of

the helmet material outside of the contact reqion. This latter

behavior was observed in high speed motion pictures 88/.

*' These equations were solved numerically on a Univac 1108 computer

using a modified Runge-Kutta method as outlined by Gill 89/ . The accuracy

was verified by comparision to simple cases for which the exact solution

was easily determined and by computing the same results when time step

was reduced by an order of magnitude. The output variable of most interest

is the acceleration of the headform (the mass M2 when the resilient headform is used in the model) expressed as a multiple of the gravitational

acceleration. Once the acceleration history was obtained, the injury

indicies, SI and HIC (see section on mechanisms) were computed numerically

by fitting the acceleration data with cubic splines 90/. The accuracy of

this latter procedure was verified by comparing the results to that

obtained with simple acceleration curves for which SI and HIC could be

calculated analytically. The computation runs were terminated when the

acceleration dropped below zero.

In the proposed model, a test method is considered to be a combination of headform, impact surface, drop height, and a parameter

for evaluating performance. The simulations for all of these elements

are intentionally simple. It is assumed that enough detail is included

to indicate trends when comparing one test method to another. The

results are expected to be useful in guiding future experiments and are

not to be considered conclusive by themselves.

Results

Variations in each parameter were referred to the following

reference system:

Headform:

Rigid:

Res i 1 ient:

Helmet:

Maxwell model:

M

] = 4.54 kg (10 lb)

M

1 = .23 kg (0.5 lb)

M

2

= 4.31 kg (9.5 lb)

K =1.75 MN/m

C = 7.7 X 10

2 N-sec/m

E =20.7 MN/m2

n

= 2.07 X 10^ poise

d = 2.54 cm
14 -

Impact surface:

Resilient: B = 10 MN/m^

Drop height: h = 1.83 m (6 ft.)

Each parameter was varied through a representati ve range while the others were held fixed at the above values, In addition, the effect of a smaller

impacting mass M

3 was also computed. These results are shown in figures 8 , through 16. In order to examine the effect of different test methods for

a range of helmet parameters, some limited performance measures, a max , SI,

and HIC are listed in tables 3 to 6 .

The effect of variations in the helmet dashpot parameter, n , is shown

in figure 8 for several headform/impact surface combinations. It is seen that the effect of changing n depends upon the test method and becomes less

important as more resiliency is added to the system. Similarly the

effect of changing test method is less important for the smaller values

of n. Generally, it will be seen that the effect of changes in any one parameter decreases in importance as resiliency is added to other parts

of the system. These indications are independent of the parameters

chosen for measuring performance. However, it is seen that HIC is more

sensitive than amax to changes in n (although not shown in the figures,

SI is about 10% higher than HIC and behaves similarly).

Similar results are shown in figure 9 for variations in the helmet

spring parameter, E. The same trends apply as described above for n. Note that changes in this parameter seem to have a smaller effect on the

acceleration response; i.e. percentage changes in E are less noticible

than a similar change in n. Also, for changes in E, HIC is less

sensitive than amax

In figures 10, 11 and 12, the effects of resilient headform parameters,

K, C, M-j and M2 , are shown for both rigid and resilient impact surfaces.

As expected, the effect of variations in each parameter is more noticible

for the rigid impact surface. Of these headform parameters, the acceleration response is most sensitive to changes in the spring constant, K. For

values of K above 3.5 MN/m the response is not very different from that

of the rigid headform.

The effect of the resilient impact surface parameter, B, is shown

In figure 13. Again variations in B are more noticeable for the rigid

headform, and the effect of headform changes is more noticeable for

large values of B.

Figure 14 shows the effect of drop height, h, for several headform/

impact surface combinations. Again the aforementioned trends apply.

Also of note is the very regular dependence of both amax and HIC on h.

It is easily seen that, regardless of test method,

a max (h)oC hV2;
1 '.at is, the maximum acceleration (or maximum force) is proportional to

the impact velocity, all other conditions being equal. Such simple

relationships were not noticed for the other parameters.

In figure 15, the effect of changing the mass of a rigid headform is

shown. Note that both indicies, a ma

„ and HIC decrease with increasing

headform mass. Considering the simple spring-mass analogy of Appendix 1,

this result should not be surprising. However, the compression of the

helmet liner material increases with headform mass, and there may be a greater tendency for the liner material to bottom. Bottoming aside, these

results may indicate a problem for those test methods which only prescribe

a value for the total impact energy, as both higher headform masses and

lower drop heights tend to lower the acceleration response.

As described in the previous section, the governing equations were modified to include the case of a finite-sized missile striking a helmeted head (or headform). Figure 16 shows the effect of varying the mass of this missile while its velocity remains fixed. The response for

M

3

= «= is the same as when the head impacts an infinite rigid mass. Note that as M

3 decreases, the durations of contact are reduced as well as the maximum accelerations.

In table 3, the effect of headform and impact surface are shown for a range of helmet parameters. Here it is seen that the general trends

referred to earlier (figures 8 and 9) are consistent for the entire range

of helmet parameters considered. If the maximum acceleration is used as

a performance measure, there are several examples where the relative

performance (of one "helmet" compared to another) reverses order when the

test method changes. For example consider the helmets represented by the

following pairs of parameters: E = 13.8 MN/m^, n= 3.45 X 10^ poise and

E = 20.7 MN/m^, n = 2.76 X 10^ poise. The former performs better when

tested with a rigid headform and rigid impact surface; as the resiliency

of either test method parameter increases, there is a point at which the

latter helmet performs better. These reversals occur because the quantitative effect of changes in test method is not independent of the helmet

parameters. The occurance of such reversals always involves a change in

both of the helmet parameters (E and n). For the examples where these

reversals occur, the computed accelerations are not very different; however,

it must be emphasized that only a simple helmet model is being utilized

and that an increased likelihood of such reversals should be expected if

real helmets were tested. Experimental evidence of such reversals in the

order of helmet performance have also been reported 82/. Note also that

the occurence of these reversals appears to be far less likely if the HIC

or SI is used as a measure of performance rather than the maximum acceleration. In fact there is only one example of a HIC reversal in table 3.

Probably, this is because these indicies tend to spread out the performance

data for the most sensitive helmet parameter, n .

From table 3, it appears that a rigid headform/resil ient surface

combination can be found such that the performance measure closely

resembles that for a resilient headform for the entire range of helmet

parameters. That is, within the confines of this model, the resiliency
16 -

of the impact surface can be used to compensate for the resiliency of

the headform. As seen from figures 10 and 13, the effect of changing

the impact surface parameter, B, is similar to the effect of changing

the most important headform variable, K. Thus, the response for the rigid

headform/B = 10 MN/m3/2 system is close to that of the resilient

headform/rigid surface, and the response of the rigid headform/B = 5 MN/m3/ 2 system is close to that for the resilient headform/B = 10 MN/m3/2. These

indications are independent of the performance measure, and there are no examples of reversals in these cases.

Similar results are presented in table 4 for a range of spring and

dashpot parameters that are applicable to a Kelvin model (see Appendix 2).

This model gives unreal istical ly large initial accelerations (because the

dashpot is in parallel) for the rigid headform/rigid impact surface and

this case is not presented. The remaining cases show the same trends that were evident for the Maxwell model: 1) the occurence of reversals in the

order of helmet performance when the maximum acceleration is used as a performance measure, 2) the absence of reversals when the HIC is used,

and 3) the indicated suitability of compensating for the resiliency of

the headform by the resiliency of the impact surfaces. It is also of

interest to note the close agreement between the two models when the

values of the parameters are chosen to represent the same helmet liner

material (Maxwell: E = 20.7 MN/m2

, n = 2.07 X 10 5 poise; Kelvin:

E = 2.07 MN/m2

, n

= 1*38 X 10 5 poise; see appendix).

The effect of impact by a smaller object is shown in table 5. In

this table, the velocities are adjusted so that the impact energy in each case is the same (in figure 16, the velocities were constant), and the

same range of Maxwell helmet parameters is considered. From the resilient

headform results, it is seen that the response of the "head" is very

sensitive to these impact conditions. If the HIC is used as a performance

measure, the impact of the head with a large object is much more severe

than if the head is struck by a small object even though the energies are

the same. Again, many examples of reversals are evident if the maximum

acceleration is used as a performance measure.

To further illustrate the results of figure 15, the responses for a range of helmet parameters is shown for two cases of constant energy

impacts in table 6. For both cases a rigid headform/rigid surface

system is used. Large differences in the HIC value are seen for the two

cases, and again reversals in the order of helmet performance are indicated

when the maximum acceleration is used as a performance measure.

V. Discussion

As the preceeding results are derived from a simple one-dimensional

model, they must be regarded with caution until confirmed by suitable

experiments. For now the results should be regarded as reasonable

indications of expected trends when test method parameters are changed.
17

The real life impact situation should be the starting point for test

method development. At the very least the relative velocity at which the

head meets an impacting object and the properties of that object must be

described for one or more modes of impact which pertain to a given

activity. A test method is defined by a choice of headform, drop height,

and impact surface (input parameters) and a measure of performance (output

parameter). There are several approaches:

1. Choose input parameters to simulate the real life impact

situation. The tolerable value of the output parameter is then

based upon the present state of the art on head injury. The

model shows that deviations from reality in the headform and

impact surface are capable of producing reversals (the improper

ranking of helmets)

.

2. Compensate for changes in one input parameter by intentionally

changing another. For example, the model suggests that the

resiliency of the headform can be taken info account by an increased resiliency in the impact surface. In such cases,

the tolerable value of the output parameter would remain fixed

at the appropriate biomechanical value.

3. Compensate for changes in an input parameter by adjusting the

output parameter. For example, if a metal headform is used,

the critical value of the performance measure could be relaxed.

The results of the model suggest likely trends when moving from the real

life situation to the test method situation.

The model also suggests that the ranking may be affected by the

parameter chosen to measure helmet performance. The present state of the

art regarding injury mechanisms strongly suggests that the likelihood of

injury from linear accelerations correlates better with the duration

dependent measures like HIC and SI than with the maximum acceleration.

The results of the parameter studies suggests that the use of these former

parameters is also less likely to introduce errors in the ranking of

helmets that arise from changed test conditions.

With regard to evaluating present test methods the model can be

used to compare present rejection criteria to the biomechanical parameters.

As an example, consider the rejection criteria of the FMVSS 218 motorcycle

standard (table 2). From table 3, the "helmets" that would fail for the

conditions of the test method (rigid headform/rigid impact surface), are characterized by the parameters: E = 27.6 MN/m^; n = 3.45 X 10^ poise;

E = 20.7 MN/m2, n = 3.45 X 10$ poise and E = 13.8 m/m2

, n = 3.45 X 10 5 poise. If the results for the resilient headform/rigid impact surface

are taken as representative of the real life situation, it is seen that

these same three "helmets" are the only ones for which the SI exceeds 1500

(the suggested critical value for distributed impacts). Therefore, the

practice of rejecting helmets when the acceleration exceeds a given value

for a given time duration may be an acceptable alternative to computing the

integral measures, provided that the criteria can be related to the biomechanical measures in the real life situation.
18 -

It remains to discuss some of the limitations of this work. First,

the model was only concerned with the linear acceleration response. If

the headform were allowed to rotate in some realistic manner, the likelihood

of a changed helmet ranking is a distinct possibility and will be the

subject of a future paper. Secondly, all of the conditions considered here were based on an impact mode in which the head is relatively free to

rebound after the impact. Therefore, the results would not be applicable

for a blow to the top of the head (though present test methods do not

make any modifications for this condition). Finally another limitation

is that the helmet model has no provision for bottoming (the increased

rigidity of the helmet liner material with increasing compression) which

is sometimes observed. It is likely that the effect of bottoming would

further contribute to the difficulties in properly ranking helmets.

While this report may raise more questions than it answers, it is hoped

that a quantitative framework is provided which can be used as a guide

in evaluating how well a test method identifies the best helmets for a given activity.

X
PARIETAL REGION

Fiqure 1. Schematic drawinq of skull

and contents (from

Goldsmith 2/)
ROTATIONAL

ACCELERATION

Fiqure 2. Gross notions of skull

followinn impact.
240

220

200

180

160

140

120

100

80

60

40

20

J L_ L I _l_ J 1 1 J 5 10 15 20 25 30 35 40 45

TIME-MILLISECONDS

Fiqure 3. Wayne State Concussion

Tolerance Curve.
AVERAGE

ACCELERATION

C

units

Stiffness of skill

i “1

AA/V

k

3 Viscosity »• Skin, Uncle,! Braio

"2

Parietal Sector

Braie & other Bones

of tie Head

(a)

IOO'

Figure 4. Head model (a) and tolerance

curves (b) for maximum strain

criterion (from Stalnaker,

et. al . 26/).
0.

RAD/

SEC 2

Figure 5. Tolerance curve for rotational

accelerations in monkeys (from

Ommaya, et. al . 30/).
SI VALUES FOR BARELY SAFE ACCELERATION RESPONSES

(AS DETERMINED BY FMVSS 218, W)

CURVE

rejection^<^pe

HAVERSiNE

(SHOWN ABOVE) TRIANGLE

CRITERIA

1 ) a = 400 g and

a>200g for t = 2 msec 4350 3860

2) a = 400g and

a>150g for t = 4msec 7380 5870

3) a>200g fort = 2 msec

and 2700 2800

a>150g for

= 4 msec

Figure 6. Acceptable acceleration

responses (as prescribed by

FMVSS 218 Standard 74/), and

corresponding SI values.
Figure

7.

Lumped-parameter

mathematical

model

used

to

study

effect

of

test

method

parameters.
(b)

RIGID,

RESILIENT

iT+j to

a)O •!-

-*-> <a r—

OJ a-r 4-> E E to »> c

(tj •<- <u a> a»

S.. S- +-><_) •'- (0-0 — C n3 I—

CL E (U 4- ‘r- cn S. t- S- cn

+-> •<- o «—

n a>

O t- 4- *r VI i- CL\ "O 10 \ r E <0 a)4J E

VI

L dJ

L

U

L

Id OC <u o

•a 4- '—. clm- 0 13 O EH 4-> rO 'r— 'r— fQ

(1) Oi Ol » <u E -c •<- dj-or oj r— S_ U •>- O

ai TD fO cn +-> <T3 SZ 'f- -~s 4- *r- C 4- cn jd s- s- aj s_ 4- -r- =3 \-r- D O i- * to E I— to

<D L- •!— 4_> O +J O VI -P a <o <o o 4- cu o

a> 4- (O TO S- <T3 4- S- CL fO CL 4- •• 3 E 0)^E

LUC (/) -r- XI "O -i—

CO

a>

s-3

CD

•r— U_

S.D ‘NOIJLVH31BOOV 8.0 N0I1VM3T399V
RIGID,

RESILIENT X>

r» +J S s_ cd •<- cu cd i

+-> O.T- -M

CD E co - SC E •r- CD CD CD

H3 +-> CD *r- S_ TO \ C cd i

<d •«- E CD 4- -r- CL CD S- •1— S- CO

•iO i— 13 CD CD S- 4— *i— CO L- • C \ -o CO \ i

E CO CD +-> E

i_ S- CD S- CD S- CL O -£C cd O

CO 4-

—- CL 4- o to U E"D

+-> 03 •!— •r- Cd CD CD CD CD • E X -r- (DDr CD

CD •!- CD

CD ~0 cd CD -M cd x • 1— , —

4- -rC 4-

CD XI S- S- CD S- 4- •r“ =3 \-r- 13 O 1- *> CO E r- 00

CD L- -r4-J CD -t-> O 00 +-> CD cd co U 4- CD cd

CD 4— id

D S- cd 4— i_ CL Cd CL

4- • • =3 E CD - • E

UJ LxJ CO •iX T3 •i—

cn

O)

s-3

CD
ACCELERATION,

G’S

ACCELERATION,

G’S

RIGID

TIME, MILLISECONDS

TIME. MILLISECONDS

Figure 10. Effect of resilient headform

spring parameter, K: a) rigid impact surface,

b) resilient impact surface.
ACCELERATION,

G’S

ACCELERATION,

G’S

TIME, MILLISECONDS

Figure 11. Effect of resilient headform

dashpot parameter, C: a) rigid impact surface,

b) resilient impact surface.
300 -

250 - 10

Figure 12. Effect of resilient headform mass parameters, M-i, Mo (where

M] + M2

= 4.54 kgl: a) rigid

impact surface, b) resilient impact

surface.
ACCELERATION,

G’S

ACCELERATION,

G’S

TIME, MILLISECONDS

Figure 13. Effect of resilient impact

surface parameter, B: a) rigid headform, b) resilient headform.
s s

s.o Noiivuaiaoov 8.0 'N0I1VU31333V

8.0 ‘N0I1VM31333V • sw “ <0 • I „ uZ

8.0 N0I1VM31333V

•*“ cn

03 o •>- a)

•1— 03 s- o

S- Q_ \ <a -EE <4- -—. o> •>- s- S_

ID

U

O +->

O

(O -PMC

W

MC TD OJ • • S- 03 03 -p- 4-> _C =3 t- 03 r— O

(/) i— SZ t— «X3

#\ «r— tO CL

4-> 4J (/) 4-> 03 E

jc <_> <u c S_ -r- cn <a s- cu

•i-

— +J

oj E E -a c

_C •<— S- •!— 03 O to — *.—

CLT3 <4- 03 03 O-r-t) S- <_) •!- S_ 03 <o 03 to -a •<- cu —<+- 03

s_ .c o t- i-

<4— 3 \ O E "O - to E

i~ t- 03 S- -M O 03 O 4-3 O

(J <+_ -r- ro

U <4- 03 -O 5- <+- 03 -O

<4— 03 i- Cl 03 4- 03 •>—* O E <U LU _d -Q t/3 •r- JC

<13 S-cn
ACCELERATION,

G’S

ACCELERATION,

G’S

300 -

(b) RESILIENT

TIME, MILLISECONDS

Figure 15. Effect of mass of rigid

headform, M: a) rigid

impact surface, b) resilient impact surface.
ACCELERATION,

G’S

ACCELERATION,

200 -

Figure 16. Effect of mass of a rigid

missile, M3 , striking the

helmeted headform: a) rigid

headform, b) resilient

headform.
Table

1.

Some

Features

of

Selected

Test

Methods

for

Protective

Headgear
9Z* L 2 °L X L’L ZZ*t7 zzz

' (e L 0 P°W

SZ'8

z oi x g*e St7'l7 L9Z' ^DPdulL 1UCUJ (2

/9Z

S5't7

z 0l X Z'P 00*17 8Z L

* laediui apLS ( L ueiunn

(lu/nn )

>1

(U1/D0S-N)

D

(6>l) z w(?>l)

L W

dnojig

[apow pean Sv-oiawejed san^A 'Z 0 Lq<?i
Table 3. Comparison of performance measures for a range of Maxwell

model helmet parameters. E and n . Entries are maximum

acceleration (amax ), severity index (SI), and head injury

criterion (HIC).

Headform Rigid Resi 1 ient

Impact Surface Rigid Resilient Rigid Resi 1 ient

B = 20 MN/m 3/2

10 5 B = 10

n = 1.38

5 amax

= 138 9 124 118 no 123 109

( XI G poise)

SI = 756 s 698 668 625 691 624

HIC = 657 s 625 597 559 626 562

C\J 2.07 165 147 138 127 144 126 \ 1170 1034 969 883 1014 878

2: 1054 930 870 792 922 791

<0 2.76 183 161 151 138 158 137

II 1505 1293 1197 1072 1259 1062

LiJ 1360 1165 1076 963 1145 958

3.45 196 171 160 145 167 144 1773 1498 1371 1214 1448 1199 1604

|

1347 1234 1061 1318 1082

1.38

r 160 139 130 118 134 118 819 753 718 667 730 662

722 668 638 594 657 595

2.07 200 168 155 139 161 138 E 1363 1174 1086 973 1110 957 2: 1222 1051 972 871 1010 852

CO 2.76 228 188 172 153 179 151 1858 1523 1381 1208 1417 1180

Cd II 1672 1365 1238 1082 1292 1064

h- UJ

i.

c£ 3.45 249 202 184 lbJ 1 y 1 lsy

Cd

<x. 2285 1807 1615 1389 1662 1349

Q. 2062 1624 1449 1245 1517 1218

}—

LU

s:

UJ

:c 1.38 173 145 135 122 139 121 840 774 737 683 739 676

730 684 653 607 662 606

C\J£

2.07 221 179 163 145 168 142 \ 1446 1234 1135 1010 1139 987 1287 1102 1012 902 1037 889 O 2.76 256 202 182 160 188 156 2035 1629 1463 1265 1468 1226

UJ 1824 1458 1308 1132 1339 1106

3.45 282 218 196 170 201 166 2569 1959 1728 1464 1736 1421 2308 1757 1549 1311 1584 1273

1.38 181 149 138 124 141 123

851 785 746 691 742 683

727 691 661 613 667 612

CM 2.07 235 185 168 148 172 145 E'

1489 1267 1162 1030 1150 1003 1318 1123 1036 919 1042 903

<0 2.76 275 210 188 164 192 159

CM 2140 1690 1509 1296 1490 1251

II UJ 1908 1512 1349 1159 1360 1128

3.45 306 228 202 175 207 170 2752 2049 1793 1507 1769 1443

2471 1835 1605 1348 1619 1302
HELMET

PARAMETERS

Table 4. Comparison of performance measures for a range of Kelvin

model helmet parameters E and n- Entries are maximum

acceleration (a max ), severity index (SI), and head injury

criterion (HIC)

Headform Rigid

1 Resi 1 ient

Impact Surface Resilient Res i 1 ient Rigid

\ Resi 1 ient'

B=1 0 MN/m3/2

B=5 B= 1 0

*

n = 0.69 a_ . - ill g 106 111

i 105 j

C\J (XI

5 poise) max

SI = 686 s 676 676 674

E HIC = 610 s 603 605 607 \

j 00 1.04 137 125 136 123

00 830 799 802 789 |

II 726 705 706 706

j LU 1.38 158 141 157 138 | 1024 955 972 934 ?

1 900 845 _ 837

0.69 j 122 117 123 116

i 886 865 872 860

C\JE

799 780 792 782

1.04 145 132 143 130

i 989 948 956 935 0 i 874 844 852 841

cvj

1

11 1.38 163 147 162 143

LU 1 1154 1075 1095 1050

1 1018

• 954 - 942

j 0.69 134 128 135 127

1079 1041 1063 1030

cvj

j 978 940 974 938

E

Si 1.04

1 151 139 150 137

CO 1147 1091 1108 1073

1022 976 996 969

CVJ

11 1.38 169 152 167 147

UJ 1285 1192 1219 1162

1136 1062 1092 1046

0.69 146 138 147 136 ! 1263 1202 1245 1185

CVJ 1146 1086 1142 1046

E

1.04 158 146 158 1-43

LO 1300 1226 1255 1202 i 1165 1100 1135 1089

00 i

II 1.38 174 157 172 152

UJ 1413 1305 1341 1268

1257 1165 1205 1145
HELMET

PARAMETERS

Table 5. Effect of mass of impacting object for a range of Maxwell

model helmet parameters E and n. Entries are maximum

acceleration (amax ), severity index (SI), and head injury

criterion (HIC). The case for M 3 = ® is the same as for

headform striking massive surface.

Headform Rigid

1 Resi 1 ient

Mass, M

3

, kg co 4.45 2.22 » 4.45 2 . 22

j

j Impact Velocity, M/S 6.0 6.0 8.5 6.0 6.0 8.5 !

I

n = 1.38c

(X10 poise) w 138 9

SI = 756 s

114 328

143 464123

691

100 290

125]

4051 HIC = 657 s 295 419 626 263 368!

C\JE 2.07 165 132 162 144 113 139! Z 1170 469 633 1014 393 526 j 1054 423 571 922 358 478;

G>

VO 2.76 183 143 173 153 122 147:

II 1505 571 750 1259 464 606 1 UJ 1360 516 678 1145 423 552

3.45 196 151 181 167 127 153! 1773 648 835 1448 516 662 1604 586 755 1318 471 605 J

1.38 160 138 175 134 110 143 819 378 557 730 315 446 1 722 337 500 657 285 400 !

C\J 2.07 200 165 205 161 127

1 161 ; E

1363 585 821 1110 441 599 1 1222 527 739 1010 402 544

'

00

on 2.76 228 183 225 179 139 172 I

' 1858 753 1023 1417 534 705

'

11 UJ 1672 679 924 1292 487 641

3.45 249 196 238 191 145 179 2285 887 1178 1662 603 781 1 2062 800 1065 1517 551 712

1.38 173 151 194 139 114 151 1 840 399 600 739 321 551 ! 730 350 535 662 291 410

j

C\J 2.07 221 186 234 168 132 171 E j 1446 645 928 1139 456 620

1287 579 829 1037 414 562 | 0 2.76 256 209 259 188 144 183 j 00 2035 852 1193 1468 556 735 1

11 UJ 1824 772 1078 1339 506 668

j 3.45 282 226 277 201 152 191 2569 1037 1406 1736 632 819

2308 935 1271 1584 578 746

1.38 181 160 208 141 115 154

851 409 624 742 323 459

727 361 553 667 289 412

C\J 2.07 235 200 254 172 134 176 E

1489 682 997 1150 461 626

2: 1318 603 895 1042 420 562

VO 2.76 275 228 285 192 147 189

C\J 2140 929 1313 1490 565 745

11 UJ 1908 836 1180 1360 517 670

3.45 306 248 307 207 156 198 2/52 1 1 48 15/5 1769 64J 66Z

2471 1031 1415 1619 591 751
Table 6. Effect of rigid headform mass for constant energy

impacts for a range of Maxwell model helmet

parameters, E and n. Entries are maximum acceleration (a ), severity index (SI), and head injury

criterion* (HIC).

LT>

cr.

CDd

«=C

Headform Mass ( kg) 5 6

Drop Height (m) .83 1.53

CNJE\2: 21Or

kO

II LU

n = 1.38

( XI 0° poise)

2.07

2.76

3.45

amax

SI HIC

= 128 g

= 665 s = 594 s

175 1040

936

172 1349 1218

185 1598

1444

102 413

367

124 659

592

139 867

782

150

1039 939

1 1.38 148 117 715 438

629 383

C\J£

2.07 187 148 1200 747 1074 666

00

00 2.76 213 171 1649 1041

UJ 1483 935

3.45 233 188

2041 1303 1840 1174

1.38 159 125

• 732 447

633 383

C\JE

2.07 205 162 Z 1268 781 1126 692 0CXJ 2.76 238 190

11 1796 1122

LU 1606 1001

3.45 264 211 2281 1442 2052 1296

1.38 167 130 740 451 630 379

C\JE

2.07 218 171 1301 799

21 1149 701

<0

r***. 00 2.76 256 203

11 1881 1167

LU 1674 1036

3.45 285 228 2434 1526

1 2186 1369
Appendix 1

Consider the very simplest resilient "head" model with one mass

and one spring. The effect of a "helmet" is modelled by adding a second spring in series.

77777

N\

77777

The governing equation and initial conditions for this system are:

MX = -KX, X(0) = 0, X(0) = V

The acceleration as a function of time is given by

A sketch of the acceleration response is shown below

where T is the time at which the acceleration first vanishes. A severity

index can be computed for this portion of the acceleration curve:

Therefore it is seen that the severity index increases with K. It is

also of note that both the maximum acceleration and the severity index

decrease with increasing mass of the "head."
Appendix 2

In order to evaluate the proposed models for helmet liner materials,

and to determine a realistic range of parameter values, the experimental

results of Melvin and Roberts 87/ were utilized. In this study, cylindrical specimens of representative helmet liner materials were loaded at

constant velocities and the compressive stress was monitored. The

cross-sectional dimensions of the specimens remained constant up to

maximum strain. A typical stress-strain curve is shown below (as the

solid line in the sketch):

D

CO

CO

CL) S-

-l-> CO

CL) >

CO

00

<v

i-CLE

oo

The purpose of this appendix is to fit two simple viscoelastic models,

the Maxwell element and the Kelvin element, to this data and determine the

cooresponding values of the parameters of the models.

Maxwell Kelvin

i±jt\ V

TTTrr- l YT

\TV l v. The relationships between stress and strain for these models are 91/:

Maxwel 1 : a + — a = Ee

n Kelvin: a = Ee + ne For loading at constant strain rate, e = K, the Maxwell equation is easily

solved, and the relationships between stress and strain become:

Maxwell: c = nK [l - exp(- e)]

Kelvin: a = Ee + nK
As Melvin and Roberts 87/ noted, their experiments were conducted at

constant velocity rather than constant strain rate, a difference which is

unimportant for small strains. As our objective is to determine a reasonable range of parameter values rather than an accurate curve fitting,

we use the constant strain rate assumption up to maximum strain as it

simplifies the analysis.

It can be seen from the above equations that the Maxwell model is

much more capable of matching the stress-strain curves. The Kelvin model

is characterized by an instantaneous jump in the stress and by the linear

stress-strain behavior. As shown by the dashed line in the above sketch,

the Kelvin model is only approximately appropriate if the early non-linear

portion of the curve is restricted to sufficiently small strains.

The following quantities were calculated and reported in the Melvin

and Roberts study 87/ : 1) the stress, amax , at maximum strain, e max , and

2) the specific energy absorbed up to maximum strain, defined as

xmax

Fdx

Q

= 0

Initial Volume

where F and x are force and displacement. If A and d are the initial cross sectional area and length of the specimen, Q can also be expressed

as:

ade

For the two viscoelastic models, the expression for <^ ax and Q are

Maxwel 1

°max

= nK l

1 * exp( - nK 'rnax^l

Q

= nK{ E[1 _ 1 max E 1L 1 " exp( ‘^

+ nK max

Kelvin: max

o — r max [y Q

- E — + nK n max

Then if amax , Q, K and e max are known for each model, there are two

equations for the unknown values of the material parameters, E and n.
The data which corresponds to the greatest speed in the Melvin and

Roberts study, 217 in/sec, is used, as this is nearest to the range of

impact velocities considered in this report. The calculated values for

polystyrene, a typical liner material for motorcycle helmets, is shown

below.

Maxwel

1

Kel vi

n

Speci fic

gravi ty

£ max0max MN/m

2

Q

MN/m2

E

MN/m2

n

poise X 10~^

E

MN/m2

n

poise X 10~^

0.0175 .46 .34 .15 4.4 .45 .28 .21

0.0540 .45 1 .21 .50 11.0 1.10 . 97 .69

As both E and n, for both models, appear to vary linearly with density*,

the values for more typical densities (specific gravities of about 0.1 for

motorcycle helmets) can be extrapolated:

Maxwell: E = 20.7 MN/m2

, n = 2.07 X 10^ poise

Kelvin: E = 2.07 MN/m2

, n = 1-38 X 10^ poise

The range of values to be considered in this report are:

Maxwell: E

~ 5 - 30 MN/m2

n

~ 1 - 4 X 10^ poise

Kelvin: E

~ 1 - 4 MN/m2

n

~ 0.5 - 1.5 X 10^ poi se

To derive equations (3a) and (3b) of the text, the strain e is related

to the displacements X-j and X^ (see figure 8) by

d - (X

3

- X-,) e g

and the force is given by

F 0=

A

f assuming that the load is distributed over a constant area**.

*Such linear relationships are not unexpected for polystyrene foams if the

volume fraction of polystyrene is small 91/ as it is for the densities

considered above.

**In a continuum mgdel , the contact area is a function of the force. In this

one dimensional model the area is assumed constant and equal to the somewhat

arbitrary value of .016 m

2

, chosen to give realistic headform responses.
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Acknowl edgements

The author wishes to thank Nicholas J. Calvano for

his interest and advice and Louise Shannon for her

patient typing of the manuscript.

i
NBS-1 1 4 A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR76-1 1 07

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Considerations in Developing Test Methods

For Protective Headgear

5. Publication Date August 1976

6. Performing Organization (-ode 446.03

7. AUTHOR(S)

Robert E. Berger

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4460143

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

National Bureau of Standards

Washington, D.C. 20234

13. Type of Report & Period Covered

Interim

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The purpose of this report is to outline the relationship between test methods

for protective headgear and injury prevention. The state-of-the-art concerning

the mechanisms of head injury and the relationship of these injuries to the

modes of energy input are briefly reviewed. The general guidelines in the

design of protective headgear are discussed, and the difficulties with present

test methods for helmets are summarized.

In order to provide a quantitative framework, a simple model which incorporates

many features of present test methods is defined and executed. The model

predicts the effect of changes in test method parameters (headform, impact

surface, drop height) for a range of helmet parameters. Among the indications

suggested by the model are: 1) the occurrence of reversals in the order of

helmet performance when the maximum acceleration is used as a performance

measure, 2) the absence of reversals when biomechanical measures are used,

and 3) the indicated suitability of compensating for the resiliency of the

headform by the resiliency of the impact surface.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Protective headgear; head injury; helmets; test methods; math model; safety

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