OFFICE OF NAVAL RESEARCH

Contract N 000 14-75-c-0486

SCIENTIFIC REPORT

DETERMINATION OF PHYSICAL DATA OF THE HEADSI.CENTER OF GRAVITY AND MOMENTS OF INERTIA OF

HUMAN HEADS

Cu, by

"1") ,:ir Sch', E. Schuliler, and W. S, m

.: •.: ; , -,/,tl i < j• ,

S•-v - ,

THIS DOCUMENT IS BEST

QUALITY AVAILABLE. TflE COPY

FURNISHED TO DTIC CONTAINEDA SIGNIFICANT NUMBER OFFP 'kGES WHICH DO NOT

•.FPRODU7E LEGIBLY.

OFFICE OF NAVAL RESEARCHContract N 000 14-75-c-0486

SCIENTIFIC REPORT

DETERMINATION OF PHYSICAL DATA OF THE HEAD

I. CENTER OF GRAVITY AND MOMENTS OF INERTIA OFV

HUMAN HEADS

by

G. Beler, M. Schuck, E. Schuller, and W. Spann

Institut fOr Rechtsmedizin der Universit1t MOnchen0-8000 Minchen, BRD

Institute of Forensic MedicineUniversity of Munich

D-8000 Munich, West Germany

1 April 1979

Reproduction In whole or in partis permitted for any

purpose of the United States Government.D.istribution of the report is unlimited.

... .... .. , . .. ...

SUMMARY

A study was conducted on fresh, unpreserved human headsof 19 ms.le and 2 female cadavers t o determine thethree-dimensional location of the center of gravity Andthe moments, of Inertia about any axis, related to Finanatomir~allv hased coordinate system F 11owIng theprocedure of Becker (Ref. (3)) the hied~ wera fixed formeasurements within a tetrahedral P-?ame which allowsfthe determi~nation of the center,,O'T gravity f rom the'loads on its, edge midpoints nnqcvthe calculation of theInertial properties from the r ktational oscilantions ofthe trMIn~r suspended frame, Tor X-ray nnthropometryredloqraphs were taken In three positions.,.

I~n the sample the oeas at death range from 19 to 64years, the body lengths from 156 to 185 cm, and thebody weights from 53 to 95 Kg. The weights of thedissected hefids range from 3.656 to 5.757 Kq. Thecenter of gravity is located almost exactly In themid-saglttal plane (+ 0.3 cm), 2,2 to 4.3 cm aoove theFrankfort plane, arnd0.2 to 1.3 cm In front of an nxisconnecting the external aud ito ry meatI. The Inertialellipsoid Is degenerated to a rotational e.Ilipsnid withthe axis pointing to the forehead under an Angle of 45

N ,to 69 degree to the Frankfort plane. The principal'AA moments about this axis range from 110 to 198K g".seft7 the others f rom 136 to 274i and 167 to 298rs!

L I

r TABLE OF CONTENTS

PageI Introduction 1

II Methods and Definitions 2II-I The Coordinate Reference System 2II-2 Preparation of the Specimen 311-2.1 Standard Plane of Division 311-2.2 Method of Dissection and Preparation 4II-3 Radiography 611-4 Physical Measurements 611-4.1 Center of Gravity 811-4.2 Moments of Inertia 8

III Material 9

IV Results 12IV-1 X-Ray Anthropometry 12"IV-2 Head Weigths 19IV-3 Center of nravity 21IV-4 Moments of Inertia 26IV-4.1 Principal Axes 26IV-4.2 Principal Moments 32

V References 35

'p

Determination of Physical Date of the Head:

renter of Gravity and Moments of Inertia of Human Heads

I TNTRnDUeTION

To apply the effects of experimentally produced Impactaccelerations utilizing human volunteers to thecomplete variety of the human beinq with respect tosize, weight attitude etc. as well as to extrapolatetho results up to and even beyond human tolerance,these data have to be acquired on a broad Scale andunder utmost "living" conditions; I. e. fresh cadavericmaterial, since whole body measurements on living humanbeings cannot provide these data, and the values knownfrom measurements on preserved cadaveric specimens askfor validation to this respect. Certainly. the head andneck are among the most exposed elements toacceleration hazards. Therefore the physical dnt a ofthe head were measured In order to determine

-the three-dimensional location of the centerof mass of the head related t.o an anatomicallybased coordinate reference system (ABCRSI,

-the moments of inertia of tho head about anyaxis In this anatomically based coordinatereference system.

w' In addition three-dimensional X-ray anthropometry ofthe head was performed as reference for the appliedABCRS.

1lA .,*,*,.{...

II METHODS AND DFFINITIONS

11-1 THE COORDINATE REFERENCE SYSTEM

The coordinate system to which all locations anddirections of physical head data refer is theanatcmically based coordinate reference system for theHead (ABCRS) as established by NAMRL Detachment,Michoud Station, New Orleans. It is based on fouranatomical landmarks (Fin. II-1-1) and described byThomas (1) as follows,"The points (landmarks) are on the skin over tho leftand right infraorbltal notches and at the superlor edgeof the left and right external auditory meati. Theorigin is at the midpoint of the left and rightexternal auditory meatus markers. The +Z axis Is fromthe origin In a cephalad direction perpendicular to theplane formed by the +X axis and the line between theauditory meatus markers. The +Y axis is from the origintoward the left ear perpendiculAr to the X-Z plane. TheX-Z plane is consldered the mid-saoAttal plane".

*-ANA1OMM&A LAMDUM

rig. IT-1-i: AnatomicAllv based coordinate reference

system (reproduced from Fig,l, Ref. (I1)

-7.

i

IT-? PRFPARATION OF T14F SPELTMF.N

1I..2,| STANDARD PLANE OF DIVISION

The standard plane of division of the head from theneck was that developed by Walker et al. (7) anddefined as follows:The neck is removed from the head by a cut originatingat a point three-fourths of' an inch below the externaloccipital protuberance nnd proceeding anteriorly andInf'eriorly to the etlanto-occipital joint. The tutproceeds to A point anterior to the prevertebral musclemess. At this point, it intersects with a cut whichbegins at a point immediately Interlor to the. hyol•tbone And extends cranially and posteriorly towaro ipecut descrihed above (F•g. 11-2.1-1),

IV.

Fic.I.I-2.1-1: The plane of' separAtion of the head fromthe neck Indicated oni a tracing of nlateral radiograph (reproduced from Fla.2 Ref, (211

TI-2.2 METHOD OF DISSECTION AND PREPARATION

In order to maintain a stanoard distribution of fluidsin the specimen, all specimens were prepared in thefollowinq manner: The cadaver is laid supine upon atable prior to dissection. A torniquet Is appliedcarefully About the neck to close as much as possiblethe large vessels going to the heed. The head Is thenallowed to hang down from the edae of the table, Inthis position the head is removed from the neck with asingle cut through the region of the 2nd and the 3rdcervico-vertebral bodies. Keepinr the separntedspecimen -upside down to avoid fluid loss, the finaldissection is performed according to the standard plane

K of division described in I1-2.1.

.nnce the dissection is completed the dissection planeIs spaled as follows. Thn large vessels are tleo up. Ahot flame is passed quickly over the area of dissectiondrvinn the surface And cauterizing the small vessels.The fornmen magnum Is plunged with ýi small pince oftissue pciper. About 1' to 20 grams of hot parnffin isthen spread over the surface and sealed with a t'innIpass nf the flame.

T The ndvnntaqe of t h - technique Is that tlher weightlosses luring the Course of the measurements are keptwithin I t of the total head weight.

The additional mass due to the parnffin, tissue andsuture material is Iess than ?R arams.

For X-rav Anthronometrv the head is vrepar vd by

post tIon~ng lead markers in the riaht and 1left auditorymeatuses and hv insertinp pins into the zvuomatic hones.

The speciman is now ready for the measurements whichproceed in the following order:

1) Head wetght2) Radlooraphy1) Center of Gravity41 Moment of Inertia5)l Final Head Weioht6) Reference Measurements (empty jig)

u~.s~ .. ......,i..~L,, - - .4 L.

"+CENTRAL BEAM

Fig. 11.3-1: X-Ray svd-up, f.rontal Yew

FILM

24 CM

CENTER OF

TURNTABLE

0 0

Fig. 11-I-) : X-RAy st-up. top view

TI-3 RADIOGRAPHY

For radiography the head rests upside down on threescrews mounted on a turn-table as shown in Figs.ITI-3-1 and 111-3-?. These screws, each e mm indiameter, are set in a triangular array at acenter-to-center distance of 90 mm, Together with twomore screws, 1? mm in diameter, 15 cm apart from eachother and set relative to the triangular array as shownin Fig. 111-3-2, this array serves as a reference forthe radiographic evaluation.

The X-ray film is mounted 24 cm behind the center ofthe turn-table and about 200 cm from the focus of theX-ray tube. The central beam passes the center of theturn-table 9 cm above the heads of the 6 mm referencescrews.

Of each specimen, prepared as outlined in 11-2.2 nndresting upside-down on the suspending set-up threeradiographs are taken In the following positions:

0 degree p-a facing the film45 degree right side turned 45 degree

towards the film90 degree lateral right side turned towards

the film

There are made no provisions or special adjustments toaligne the head on the turn-table to the anatomicalcoordinate system. Thus, the planes of the radloparahsdo not coincide with the Y-Z plane and the X-? planeresp. of the anatomical coordinate system. For eachspecimen this has to be determined separately from thebony structures, the position of the markers ano thereadings taken from thp stereotaxic unit.

11-4 PHYSICAL MEASUREMENTS

The procedures for measuring the center of gravity andthe moments of inertia are described in Reference (3).In these procedures, the head is placed in astereotaxic jig as shown in Fig. 11-4-1. Thisstereotaxic Jig Is designed to facilitate the center ofgravity and moment of Inertia measurements as well asto locate the head anatomical coordinates relatively toits own coordinate system.

-6

Fig. 11-4-1: Stereotaxic unit and tetrahedral frame(Reproduced from Fig. 7 Ref. (3))

Two sets of measurements are made on the head~-jigsystem. The first of these provides the information forthe center of gravity of the totnl system. The secondset then yields the system moments of inertia. The headIs removed from the Jilg and the holding devices resetto their Initial positions. The two sets ofmeasurements for the head-jig system can then becompared to t'lose of the empty JIo t.o extract thecenter of gravity and the moments of inertia.

In add~itinn to these measurements, the settings of thestereotaxic unit are recorded In order to lcocat~e thehead anatomical coordinates relative to the jigha rdwa re.

The data are then forwarded to the NAMRL Dletachment,Michaud Station, New Orleans, for date reduction.

-7-

11-4.1 CENTER OF GRAVITY

The center of gravity measurements are essentially thesame as those In Reference (3). The jig is positionedto rest on three of its edge-midpoint projections andthe load on each projection is measured using a loadcell. Since the jig can be supported on each of fourdifferent sets of these projections, a total of twelvemeasurements is obtained. The use of the load cellyields measurements accurately to within + .005 LBS(+ 2.3 g) and is recommended In Referencle (3) over thebilance employed there.

11-4.2 MOMENTS OF INERTIA

For the determination of the inertial properties thejig is suspended from three wires in the manner of atrifilar pendulum. There are ten different orientationsin which the jig may be suspended, four involvingsuspension by three of the vertexes and six moreinvolving two vertexes and one edge-midpoint projection.

A licht beam reflects from a mirror positioned on thejig in such a manner that slight rotationaloscillations of the pendulum sweep the beam edge hackand forth across a light sensitive device. This lightsensitive device is coupled to an electric counterwhich measures the time for one hundred oscillationswith an accuracy of one millisecond. The measurement ismade twice for each of the ten orientations, and threetimes, if the difference between the first two readingsexceeds one hundred milliseconds,

The suspension of the jig from the wires differsslightly from the technique described in Reference(3),since a cup and cone device was provided whichpermits much closer control of pendulum geometry.

8-

~ ~L~~ju..~.t~zt.L&Mai.

III MATERIAL

Fresh, unpreserved human heads of 19 male and 2 femalecadavers have been investigated. Serial number,registration number, age at death, body length andweight, cause of death and time elapsed between deathand measurements are recorded for all specimens in Tab.111-0-1.

Distributions of age, body length and body weight areshown In Figs. 111-0-I tc 111-0-3. The ages at deathrange from 19 to 64 years with a mean value of 42.4years and a median of 42 years. The body lengthes rangefrom 156 to 185 cm with a mean value of 173 cm and amedian of 175 cm. The body weights range from 53 to 95Kg with a mean value of 74 Kg and a median of 73 Kg.

These specimens were selected from cadavers, deliveredto the Institute of Forensic Medicine (University of

Munich) during the period of 1975 to 1977. Attentionwas paid that the selected cadavers did not show anyevidence of extensive blood loss, head injuries, bodilyabnormalities, wasting desease or significantalterations due to immersion in water where it applies.

Tab. 111-0-1

Ser. Reg. Age at Body Body Cause of Measure-.No. No. death length weight death ment p.m.

(yeare) (cm) (Kg)1 1023/75 21 173 59 Undetermined Id2 1059/75 41 187 88 Coronary trombos. 44h3 50/76 48 175 66 Traum.rupt. heart 86h4 60/76 54 160 53 Coronary trombos. 43h5 107/76 51 156 69 Traum.rupt. aorta 3d6 233/76 40 175 63 undetermined 2d

7 lb764 15 2 Drug overdose 5d

8 455/76 59 179 81 Carbonmonoxilde 3d9 66*/76 - 179 66 Drowning-

10 •712/76 51 10 68 Drug overdose 3d11 753/76 43 169 D5 Myocardian infarc. 2d12 833/76 50 178 99 Carbonmanoxide -13 745/77 52 180 79 Myocardial Infarc. 3d14 392/77 19 .181. 70 Drug overdose 4d15 406/77 64 172' 72 Carbonmonoxide 38h16 448/77 36 177 95 Drug overdose 5d17 564/77 39 185 73 Drowning 12h

18 662/77 35 172 65 Drowning 2d19 667/77 28 177 85 Drowning 2d

20 791/77 28 176 77 Drowning 3d21 820/77 41 172 76 Drug overdose ?d

-9-

--------------------------------------

6.

4

3-

z 2

11 20 30 40 506 9 79AGE <YEARS)

Fig. ITT-0-I: Distribution of age at death

7

5

I -.1*.

3

155 l6e 165 170 175 169 165g in

BODY LENGTH (CM)

Fig. III-0-2: Distribution of body length

- 10

L.....,•

3

41,z

50 SI 70 80 90 logBODY WEIQHT <KG>

Fig. I11-0-3: Distribution of body weight

The dissection and measurements were done at roomtemperature of 20 to 22 degree centigrade. Until theseprocedures could be performed the cadavers were storedat 4 to 6 degree centigrade. Maximum time elapsedbetween death and measurements was 5 days. Priorinvestigation has shown that there is no signtficantchange in brain we!ght of fresh cadavers kept at 4 to 6degree centigrade within at least the first one hundredhours after death (4).

- 11 -

vIII "i• I I

v\ IZA\Y i\N M II 0Iliq MIN,'"

I, v iiihi' I 1, 111 til o f 11 , \II , I ii I' I i w I I ;I I , ii C .I I 1 Jt ii l mill to fu IPlt'olrl' o 111' r .t I I IN

I, 1t r iln 'I t If I i I V Iilt I lit 'l I Ii' t i; t illil i 1-t'w;i' ; i tillIt I I v r I-.

tiIta d I; ,r I I- 1 111) t 1

r' I-•"v '•'• , f ' ttit, o t fit, " r ; I)'o lti llI Ir n! • A; " v!.• , :1 lI I I I I I_._

' ' I I t' ; I" i It ,: ;i l ] ' 1 "1 v I , I I !t ( I 'i I ' I I I v I • t I I' I , '. , l

I •• .i,, ,.t " t it ,

Is"j

No.

.. . .. . .. .... .

N

~I

1 "

No . 10 . I. ...1 1 1

.... ...

No

..........

'521

Fig. IV-1-6: Radilographs oif specimensNo. 18, 19. and 20

-17 -

r

F'1. IV-1-7: Radiographs of specimen No. 21

- 18.-

S.,1 .1

' '. . . . . . .. . . . . . . .. . . . . . . , = ;. . . ..2

k IV-2 HEAD WEIGHTS

The head weight and the position of the center ofgravity in the anatomically based coordinates arerecorded along with body length and weight for each ofthe subjects in Tab. IV-2-1. The head weights listedare those taken before the measurements.

Tab. IV-2-1Ser., Body Body Head WeightNo. Length Weight Weight Loss

(cm) (Kg) (g)1 173 59 4207 1 52 187 88 4120 313 175 66 3949 184 160 53 4028 55 156 69 4025 156 175 61 4190 327 165 82 4544 58 179 81 4652 219 179 66 4319 3710 160 68 3705 1811 169 85 4350 1912 178 99 4335 713 180 79 4627 1314 181 70 4627 4615 172 72 4251 1516 177 95 5257 1017 185 73 4269 518 172 65 3676 919 177 85 3989 2820 176 77 4142 2521 172 76 5069 5

The loss shown Is the difference between these weightsand those taken after completion of the measurements.Since the sealing process described in II-?.? wasdeveloped after the procedures were applied to thefirst specimen, the weight loss for this head is 2.7 %of the total head weight. The weight losses encounteredfor each of the remaining twenty heads are all lessthan I N of the total head weight.

The head weights range from 3 676 to 5 257 q. The meanvalue is 4 305 g, the standard deviation Is 402 g.Their distribution Is shown in Fig. IV-2-1. Thedistribution of the sample investigated by Walker etal. (2) is shown in Fig. IV-2-2. The means and standarddeviations of both samples are compared in Tah. IV-2-2.Applying the T-test, no significant difference is foundbetween these two samples, Direct comparison with thedata of other investigators (5,6,7,8) is not possibledue to differences in the plane of division.

J: - 19 - •

ilA

Tab. IV-7-2

Source Mean head weight (g) StandardDeviation

Walker et a]. (7) 4 376 591Munich 4 305 40?

@

3-33

." 2

2.6 3.2 3.18 4.0 4.4 4.5 5.2 5.8HEAD WEIGHT (KG)

.'.

Fig.IV-7-1: Distribution of head weights (Munich)

•a.-

4.-l]I:

I

2.51 3.2 3.6 4.0 4.4 4.6 5.2 5.0HEAD WEIGHT (KG)

Fig. IV-2-2: Distribution of head weights

(Walker et al. (2))

- 20

TV-3 CENTER OF GRAVITY

SThe center of gravity in the anatomically basedcoordinate reference system is recorded along with

serial number, body length, body weight and head weightIn Tab. IV-3-1.

The distributions of the X, V and Z coordinates areshown in the histograms of Figs. IV-3-1 to Fig. IV-3-3.The values range

for the X-coordinate from 0.2 to 1,3 cmfor the V-coordinate up to +.3 cmfor the Z-coordinate from 2,2 to T.3 cm.

Tab. IV-3-1

Ser. Body Body Head Center of rravitvNo. Length Weight Weight X Y 7

(cm) (Kg) (g) (cm)1 173 59 4207 0.72 -0.17 3.?52 187 88 4120 1.37 -0.05 2.183 175 6 3949 1.05 -0.11 3.314 180 57 4028 0.85 -0.10 3.155 156 67 4025 0.78 -0.05 7.8ý6 175 6. 4190 1.02 .-0.14 3.117 165 82 4544 0.28 0.05 2.968 179 81 4652 0.r9 -0.19 4.249 179 66 4319 0.68 0.00 4.20

10 170 68 3706 0.66 -0.17 2.8719 169 85 4350 0.63 0.30 257012 178 99 4145 0.40 -0.04 2.i713 180 79 4749 1.10 0.00 4.1314 181 70 4627 0.90 0.03 1.31

15 172 72 4251 0.72 0.07 ?3.816 177 95 5257 1.13 -0.15 ".9417 185 73 4269 0.62 -0.09 1.1718 172 65 3676 0.97 -0.26 2.6719 177 85 M S) 1.14 -0.10 ".5320 176 77 4142 0.79 -0.04 2.6723 172 76 •09 0.82 0.15 3.72

The data show that the center of gravity is located

almost exactly in the X-Z plane of the anatomical

coordinates which Is the mid-sa ittal plane of thehead. The maximum deviation from this plane is less

than 3 millimeters.

- 21 -

7

4iS3I;

31.6 6.2 6.4 U.S 6.6 1.3 1.2 1.4.

X.LOCATION (OM>

Fig.IV-3-1: Distribution of the X-coordinates of thecenter of gravity

S 3-!'

2.2 2.63.03.4 3.6 4.0Z-LOCATION (CM)

Fig. IV-3-2: Distribution of the Z-coordinutes of thec-.nter of grevity

-22-

3

G--'-- s1254

12

•ii 11

9

S

3 ,

II 2

--. U-.4,-.2 Ul .2 .4. .8

Y-LOCATION (CM>

Fig. IV-•-3: L~istrtihutlon ot the Y-coordinites of' thocen~ter of' gravilty

- 23 -

The I tient i ons, of' the centers (if cIrav i ty wit hi rn the X -7plano are shown In Fig. IV-3-4. Tho means and standarddev~iations are given In Tab, TV-3-1 A ~a_ men, hece-niler of' gravity of' the head As located within themid-sagi~ttAl plane, CI8 cm In front of' the audi toryMentuse's and 3.1 cm above the Frankf'ort Plane.-

4 A 4A

N 2N 2

0 112 34;CM (CM>

Location of' thr centpr Location' (if the mIPAnof arnvity within the center of' qrnvivtyX-7-plane, within the X-7--p lntit

And Is- 1ipse oifstmndnrd dtevintion

The m@ trtiAx of' the Figerhvectors - wh Ich ti iv e,, theorientatiton of' tho ellipsoid of' vA r i nce -may b tconsidered as n unit matrix and the distrihotitnn of Ih rvnriance on each of' t h ( three ix r 1 a i t metd I ito hn%Independent, thus th a prinripal Ynluers give t hestandard deviAtioin of' each of' the. threne nxn4 In ý`WTV-1-5 the distribution within the X-1 n tie is-revealIed hv t te 2s-eI IIpse about the menn emntisr o fgravi ty.

For comparison, the mean and standard deviationcalculated from the data published by Walker et al. (2)are cumulated In Tab. IV-3.3. Applying the T'-test asignificant difference (p a 0.01 and 0.05 resp.) existsbetween the means of Walker's sample and that of thisstudy. Compared to the emblmed specimens the meancenter of gravity of fresh human heads Is located about1 cm retro-cranimi, I. e. towards the center of thebrain. Besides possible systematical differences due todifferent experimental procedures the reason may be aweight-loss of the soft tissue during fixation or fluidloss during the measurements of the embalmed specimens.

Tab. IV-3-2Analysis of the center of gravity data

(This analysis was done by E. Becker, NAMRL De~tachmenit,New Orleans, LA, USA)

Mean Standard EigenvektorsDeviation

X .3 .3 .90 .136 .054

TAh, IV-3-3Center of gravity from the photo-measurements of

Walker et. al. Ref. (2)

Mean $tandardDeviation

X 1,42 0.76Y not deterininedz 2.41 1.03

No. of specimenn; 17

-25

IV-4 MOMENTS OF INFRTTA

IV-4-I PRINCIPAL AXES

rar each specimen the tensor or the principal axes (X',Y'. Z') of the moments of Inertia are recorded in Tab.IV-4-1. These tensors yield orientations relative tothe planes of the anatomical coordinate system.

Tab.IV-4-1: Tensor of the principal axes of themoments of Inertia

Ser, No. X YI .881 -. 313 .X51

.277 .94Q .148 Y1

-.382 ...n32 ,992 Z'

2 .691 -. W02 .i16 X1

.42 .63 .770 V

-.582 .031 .812 7'

.731 .383 .164 X3,05 .993 -.212 Y

-.610 -. 002 .732 7'

4 ,80 ( .00 580 X-. 16W .983 .075 Yi

.5 4 -. 15A 1810 7'

5 .77 ,26• .621-.184 ,64 -.189 Yi

.765 .250 ,"'X Xi-. 205 ,Q68 -. 14? Yt

-.610 .017 ,7 W??

7 .847 -.0'A ,5?K x.047 .998 -.01? YV

-.528 ,0ý5 .84' 7'

8 .861 -.310 .401 X,.299 ,q4q .092 Y1

-. 410 .040 .911 7'

'4 .514 -. 551 .56 X.579 .787 ,20) Y1

-. 631 .273 .725 I'

10 .763 .298 .%72 X1-2153 Q SA -.159 Y I-,5' .0? .804 70

- 76 -

Tab. IV-4-1: Tensor of the principal nxes of the

moments of inertia (continued)

Ser. No. x V z

11 .536 -.744 .397.659 .664 .352

-.526 .072 .846

12 .801 .160 .576 X

-.098 .985 -.136 Y-.590 .052 .805 7

13 .905 -.114 .409 X

.118 .992 .016 V-.408 .033 .91? 7'

14 .835 -.137 .3

-.080 .986 -.101-.581 -. 2034 .680 71

is .569 -.571 .4837 X

-.415 .828 -.392 y

-.7032 -.002 .71607

19 .912 .0353 .5507-.044 .998 .0162-.506 -.029 .9.14 7'

20 .722 -.045 .6604 X

-.020 .99! -.2090 Y

.6865 .201 .791 7'

213 .850 -.574 .4370 X

-.521 .902 .206 7V

-.479 -.089 .913 7'

21 .8:.0 -.

86 . 440rnv - 1

Tab. IV-A-?.Deviation of the princlpal axes (X' ,y'Y,#Zof the moments of Inertia f(leorees)

Ser, X' from YV from 7' from 7' promNo. X-Z plane X-7 plane 2-Y-plan Z-X-,plane1 -19.5 73.7 -21.0 - ,1.82 -. 5, 9 63,. -30$,6 2.13 27.6 -71.7 -17.6 - 0.14 6.3 -80.5 - 34,8 -1.,19.K -79.1 -40,5 1•818.0 -78.0 -. 0.87 - 2.2 87.3 -31.9 2,.8 -19.8 72.5 - 4.,2 ?,,0 -46.9 53.6 -41.0 20.610 21.ý -75.1 *-36,4 - 1.6

11 -54.? 45,.2 -31.8 4.812 11.2 -84.3 .36.2 .,613 - 7.1 83.2 -24.1 014 - 9,. 84.3 -32.,7 .,Is 44,7 -A3.1 -44.7 - 11IOr -24./4 71.9 -35. 1 3.?17 - 6.4 --85.3 -44..S .16.018 -.9.6 59.? -32.1 0.119 2.1 -87.4 -23. - 1.820 3.4 88.8 -41.9 6.22.1 -18.5 77.1 *.. 7 .

In Tab. IV-4-2 the followinq orientatinn. arp listed.The. devlatton of X' from the X-2 planer the projectton of X' onto the Frankfort plnnr.The deviation of Y' from the X-7 planea the orojectfon of Y' onto the Frankfort plani,The deviation of 7' from the 7-Y planez the proiection of 7' onto the mild-aq1ttal plane.The deviation of ?' from the Z-X planev the proiection of 7' onto the lntern-late.ral plane.The distrihution of the 7' orientation with respcvt tothe ]atero-laterei anrd the mid-sagIttal plane mrP niVpnIn the histograms of Figs, IV-4-1 and IV-.4-2 resp, andthe dtaqrnms of Figs. IV-4-K and IV-4-4 rfsp. . Thpdeviation from the 7-Y plane varies from -21 to .. 49deurees with a mean of .34 degree.The lateral var.ation of P' may exceptior,n]aly amount to. 20 degree, but Is In 85 % of the specimens smallerThan + 10 degree, No side seems to he favored.

- 28 -

.......

!

4

aItII

U

-45 -41 -35 -36 -25 -2I

Fig. IV-A-1: Deviation of Z' from Z-Y-plane

"U "7

4I

3

I" _I

-35 -15I "I • II 15 3(DIM IIV

Fig. IV-4-2: Deviation of Z' from Z-X-planeL 29 -

z

Y

FRig. Iv-4-x: Fig. IV---4

Projection of the Projection of theprincipal axis 21 onto the principal axis Z' onto themid-saqittal (X-Y) plane latero-lateral (Y-Z) plane

Y

x x

Fig. rV-4-5: Fig. rV-4-6:Projection of the Projection of theprincipa] axis X' onto principal axis Y, ontothe Frankfort plane Frankfort plane

The distributions of the X' and Y' deviations from themid-sagIttal plane are shown In the diagrnms of Fiqs,IV-4-5 and IV.-4-6 and the histograms of Figs. IV-4-7and IV-4-8 reap.. They reveal, that these principalmoment orientations are almost Indistinct with respectto the mid-sagittal plane. In the mean, therefore, theX'-Y'-cross-sectlon of the principal inertia ellipsoiddegenerates to a circle rendering calculation of theorientations meaningless.

3 0-

¾ 7

-W -3

F a

tII

[.- -SIl -Si SI 36 66P 63

S•<DEOREK)

riq, IV-4-7: Deviation of X' from mid-saqittal plane

3

S

a

-S.l -SIl -361 I 331 6S SIl(DEGREE)

Fig. IV-A-8: Deviation of' r from mid-sagittal plane

- 31 -

TV-4.? PRINCIPAL MOMENTS

The principal moments are listed along with headweights In Tab. IV-4-3. Their distribution is shown Inthe histograms of Figs. IV-4-9 to IV-4-11.The principalmoments very

from 136 to 274 Kg.cm2 about the X' axis

from 167 to 298 Kgcm2 about the Y' axis

from 110 to 198 Kg'cm2 about the 7' axis

Tab. IV-4-3: Principal moments of Inertia

Ser. Head Principal moments of inertiaNo. Weight X' Y1

S(a) (Kg-cm?)

1 4207 200 238 1432 4120 204 213 1343 3949 191 207 1194 4028 188 202 1295 4025 193 197 1386 4190 204 214 1477 4544 ?27 238 1568 465? 22E 264 1809 4319 197 232 148

10 3705 157 159 116I 4di50 215 225 15312 4335 213 221 14313 4749 247 243 16914 4627 236 258 15615 4251 215 208 142it 5257 274 298 19417 4269 136 223 19818 3676 154 167 11019 3938 175 192 12120 4142 201 207 13121 5069 268 286 189

32

7

04

.4

~3

111111,111311111 131;IND 49 Iw gas v ia s

Fig. IV-4-10: Distribution of principal momentsof inertia about the Y, axis

7 33

7

• ~S

4-

iol 14 I'ml 280 a2go 300

Fig . IV-4-11: Distribution of principal mnmentsof inertia about the 7' axis

34 -

3 I .4. -

i-I

V REFERENCES

(1) THOMAS, D. 3.: Speciallzised AnthropometryRequirements for Protectlve-EquipmentEvaluation. AGARD Conf, Proc. No. 110, Glasgow,Scotland, 1972.

(2) WALKER, L. B.. HPRRIS, E. H. ,and PONTIUS, U.R.: Mass, Volume, Center of Mass and Mass Momentof Inertia of Head and Head and Neck of theHuman Body. Final Report to ONR, March 15, 1973.

(3) BECKER, E. 0,. Measurement of Mass DistributionParameters of Anatomical Segments. Proc. of 16thStepp Car Crash Conf.. p. 160, New York: Societyof Automotive Engineers, Inc., 1973.

(4) BEIER, G., EISENMENGER, W., SPANN, W., andSTEINBERGER., F.: Reziehungen zwlschen Hirndruck,Hirnpewl.cht und Osmolarltdt, I. GOnzburgerfesprhch, Schattauer VerlAg, 1976, p.11.

(5) BRAUNE, W. end FISCHER, 0.: Uber den Schwerpunktdes menschtichen Kbrpers mit ROckslcht auf dieAusrUstung des deutschen InfanterJsten (TheCenter of Gravity of the Human Body as Relatedto the Equipment of the German Infantryman).Abh. d. math. phys. Classe d. k. Sbchs. Ges. d.Wiss. 15 (1889), p. 561.

(6) DEMPSTER, W. T.: Space Requirements of theseated Operator. WADC-TR-159, AeromedicalLaboratory, Wrigth Air Development Center,WrIgth-Patterson Air Force Base, Ohio, 1955,

(7) CLAUSER, C. E., McCONVTLLE, 3. T., and YOUNG. J.W.: Weight, Volume, ana Center of Mass ofSeqments of the Human Body. AMRL-TR-•9-70,Aerospace Medical Research Laboratory,wrigth-Patterson Air Force Base, Ohio, 1969

(8) LIU, Y. K., LABORDE, J. M., and VAN BUSKIRK, W,C,: Inertial Properties of a Segmented CadaverTrunk: Their Implications in AccelerationInjuries. Aerospace Med, 42. (1971), p. 50.

I,3 -{

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Anthroposetryl DiomechanicsX Human Sngineerinqu Head - mass, center of gravity,

Moments of Inertiat Human Body Modoels Anatomy

Ast'u4was coneere uua ed f1male und 2 female cadavers to dulwiuimne the tji. dimensionallocation of the center of gravity and the moments of inertia aboutany axis related to an anatomuically based coordinate system.

The ages at death range from 19 to 64 years, the body lengthsfrom 156 to 1815 amp and the body weights from 53 to 95 kg. Theweights of the dissected heads range from 3,656 to 5,257 kg. The

DD 1473 avilIwOF 1 Nov s i IOvsoLsi a

IRCUNITY OLMSIPIATON 60 T141 PAGE (Men D... b5ee0i)

.tI.wittITY~ CL Ati VIPCAT iON OF Tm IS P A O(WIh, ee 0 081"

2o. (Continued)center of gravity is located almost exactly in the mid-sagittalplane (+ 0,3 am), 2.2 to 4.3 cm above the Frankfort plans, and0.2 to T.3 cm in front of an axis connecting the external auditormeati. The inertial ellipsoid 'is degoherated to a rotationale*lipsoid 'with the axis painting to the forehead under an angleof 45 to 69 degree to the FrankfOrt plane. The psnoipa monmentsabout this axis range from I1l to 194 kg.oi, the others from135 to 274 and 167 to 298 resp.,

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