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r . c 1\ I ) 7 0 1 3 8 :3 D Y N A M I C M O D E L S O F T H E H U M A N BODY E r n e s t L . S t e c h , e t a 1 F r o s t E n g i n e e r i n g D e v e l o p m e n t C o r p o r a t E n g l e w o o d , C o l o r a d o N o v e m b e r 1 9 6 9 J 0.. e... 0 . 0.. 0.0 a 0. ... 0.. F I L E Distributed ...'to foster, serve a n d p r o m o t e t h e n a t i o n ' s econom Ic de veI op meiit and technblogical advancement.' *** u-s. DEPARTMENT OF COMMERCE/Natlonal Bureau of Standards e . . * e 0. . e.. .. ..e. .*e ....e This document has been approved for public release and sale.

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. L , S I

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Reproduced by the C L E A R I N G H O U S E for Federal Scientific & Technical = -* - 1 - *.I L W I **...l..cr Information Springfield Va 22151 - . ' '- ' I * , ? , I 1 , i A i I / 1 '

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Foreword This study was initiated by the Vibration and Impact Branch, Biodynamics and Bionics Division of the Aerospace Medical Research Laboratory, Wright- Patterson Air Force Base, Ohio, with the support of the Biodynamics Section, Environmental Physiology Branch, Life Systems Division, National Aeronautics and Space Administration-Manned Spacecraft Center, Houston, Texas. The research was conducted by Frost Engineering Development Corporation, 3910 South Kalamath, Englewood, Colorado, under Contract AF 33(657)-9514. Thc work was performed in support of Project No. 6301,“Aerospace Systems Personnel Protection,” and Task No.630102, “Personnel Protection in Acrospacc Systcms,” with Mr. Peter R. Payne as principal investigator. Mr. James Rrinkley o f thc Vibration and Impact Branch was the contract monitor for the Aerospace Mcdical Research Laboratory, while Mr.Harris F. Scherer and Mr. Jack IXityfield wcre the NASA liaison representatives. This report is one of a series of reports generated in the area o f human restraint and supprt system dynamics under Contract No. A F 33(657)-9514. The research in this report was performed from September 1962 to February 1964. This technical report has been reviewed and is approved. C.H. KRATOCHVIL, Colonel, USAF, MC Commander Aerospace Medical Research Laboratory . . . iii

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Table of Contents SectionNo. Page SECTION 1. INTRODUCTION. .................................................................... 1 4 SECTION 11. BASIC BODY DYNAMICS.. ............................................... Theoretical Dynamic System .................................................................... 4 - Validation by Experiment ........................................... APPLICATION OF HUMAN BODY DYNAMICS I I SECTION 111. Inpiit Acceleration Parameters ..................................... 11 Hrimiun Biomechanical Parameters .................. . . . . . . . . . . . I4 Restraint and Support Parameters ......................... 16 SECTION IV. SO‘CJRCESOF DATA ON BODY DYNAMICS 21 Drop Tests .......... ..-................................................................. 21 Sled Tests .................................... ............................ - . . . . . . . 22 y. ............................................................... 22 ibration Tests ........................................................... 22 Structural Tests Animal Tests ............................................................................. 23 Accident Data ............................................................ ___.. 21 Ejection Seat Data . ............................ e.I SECTION v. A DYNAMIC MODEL OF THE HUMAN IODYI N n r E SPINAL DIRECTION 26 Estimates of Mass a n d Spring Stiffness . . . . . . . . . . . . . . 26 Calculation of Natural Frequency . . . . . . . . . . . . . . . . . . . . . . . . 30 The Effect of Age on Spinal Characteristics ........ 31 ~ -. ~~ Estimates of Damping ................................................... . . . . . . . 33 Head Involvement in Spinal Tolerance ............................. ......... 36 Conclusions ~ ~ . . . . . . . . . . . . . . . . . . 39 SECTION 1’1. A DYNAMIC MODEL OF THE BODY IN THE TRANSVlCltSII 1)I 1WXXlON SliCTION 1’11. OTHER DYNAMIC MODELS OF THE HUMAN I 3 0 D Y 47 iV

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Section 1 INTRODUCTION The designers of restraint systems, ejection seats, escape capsules, and space vehicle landing systems are concerned with optimizing the performance of these systems without endangering the human occupant. The immediate design problems must be solved while basic research is still being pursued, requiring the research community to establish interim tolerance limits to minimize the users’ risks aad the designers’ limitations simiiltoneously. Establishment of human tolerance limits has Been a neccssity for cn.ironiiiriits othcr thi1n c x - posure to acceleration and, in virtually every case, a common problcni O C C I I ~ S .I t has Iwcn ciistoinary to set a tolerance limit as a specific and arbitrary value, even though ditfercncc-s i n int1ividii;ils and variations in exposure circumstances will produce gradations of tl;i1nagc~.iiijiiry i i d / o r discusc: on both sides of the tolerance limit unless it is set very low. Similarly, in mnny c ; w s t l l c tolc-raricc: limits must be establislpi prior to gaining a broad enough knowlcdgc of tlw physical, chrriical, and biological factors involved in the situation, with the consequence that ;I largc safety factor should be included in the limit set. The combined effect can be to impose too severe a rostriction on the performance of the system; conversely, ignoring these factors can result in establishmcnt of a tolerance level that is too high. In the case of human tolerance to acceleration, there have been occasions where it has not seemed feasible to incorporate any considerable margin for error. Consider for example, the problem inherent in the design of early ejection seats. To accelerate such escape devices rapidly enough to clear the aircraft tall at high Aight speeds with the short catapult stroke then available, the designer had to impose spinal accelerations close to 20 G. The resulting acceleration environment caused the vertebrae to compressively fracture. Since staying with an airplane after a serious malfunction or making an unaided bailout was known to be lethal in a high percent;igc o f cases, risking some injury fromthe ejection appeared to be the lesser of two evils. Implicit in the above situation are the concepts of risk and probability. Presumably, they w c w regarded only qualitatively, if at all, and for design piirposes a single acceleration limit was set. Such a single limit implies that no one will be injured who is subjected to an acceleration IwIow the limit value. In actual fact, such a situation does not exist, and the prohahility of injiiry iiicrcilscas with increasing accelerations. Had the concept of (and the ability to predict) probability o f injiiry cxistcd at t h tinit. tliv single acceleration tolerance limit was set as a guide for ejection seat ;und catapult clcsijpwrs, ;I lowt’r limit would have been established. Unfortunately, it took thc expcrienw of ;ictii;il iiijrii I(\ lo produce this result. In the interim, ejection seats acquired a repitation that C ~ I I I S ( Y iriaiiy i ~ i l o tc to use them only as a last resort, when the flight conditions were too often lwyond thc p ’ t t o 1 1 1 1 - ‘itice capability of the seat. By applying the analytical techniques described herein to the data availahlc: froin cxpcrirnc-lit, experience, and many other sources, it is possible to predict and/or evaluate. acwlrration tolcrilnces as quantitative risk levels, expressed in terms of probability of injury. The risk or probability approach to tolerance can he a useful tool for thosc who establish and apply acceleration tolerance data. TWOsimple examplcs will serve to illustrate this point. As noted ;lhove, the ejection seat designer is concerned with removing the crew of n disabled aircraft froin ;I Iwtentially lethal situation. This implies that a reasonable risk r!f ij::ryis zcceptiibic in tile c?jcc- 1

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tion sequence, since the alternative is the certainty of much more severe injury and the strong p s - sibility of death. On the other hand, the designer of a space vehicle landing system must virtually eliminate the possibility of injury during the course of normal operational landings. A single parameter should be used to specify injury or damage, since two parameters would involve a large set of combination of numbers to describe the tolerance situation. Fortunately, this limitation to a single injury parameter is not really restrictive. Damage to biological tissue and structure from imposition of accelerations must be assumed to be caused in fundamentally the same manner as damage to mechanical systems, i,e., through the application of forces that result in such deflection or strain that failure of the structure or material being loaded finally ocvurs. Thus, if the characteristics of the structure can be defined, and the maximum force applied to ttic structure can be ascertained, it should be possible to predict whether or not failure will occur. As used in this report, the term “dynamic model” refers to a mathematical analogy to a lumped parameter mechanical system comprised of separate mass,spring, and damping elements. The purpose of the dynamic models is to permit prediction of the peak forces exerted within the body on critical structural items. There is, of course, a relatively wide variation in the characqeristics of these structures and data is not yet adequate in certain areas of interest. Equations can be devcloped that describe the behavior of such a system under the influence of any input acceleration or force. Once developed and proved valid, these models are a useful tool for rapid determination of the effects of variations in the disturbing forces or the components of the system or both. Adequately accurate investigations can be made quickly and economically, for the dynamic models lend themselves well to performance of laborious calculations by analog or digital computers. Despite the complexity of the human body and the variation between individuals,the response of the human body to acceleration environments can be approximately characterized by an analogous dynamic model. Therefore, if body characteristics in these respects can be established, the techniques of dynamic analysis may be applied to the gain the benefits already obtained in the engineering disciplines. One of the major contributions to be expected from this approach is the development o f tolerance data in the form of relative probability of injury curves instead of the single-line graphs or single critical G values used heretofore. The importance of this cannot be over-estimated: although the engineer needs a single value upon which to base his design, he certaioly is not qualified to establish it. Neither is this the province of the experimenter, because he is producing information that is based upon too few sample and too-special situations, in general. Instead, it is u p to the user of the end product to select the limit to be used, and this in turn should be dependent upon knnwledge of the risks involved. Given the relative probabilities of injury for different levels of accelerations exposure, and knowing the many factors involved in the missions that will create these exposures, he can make an intelligent value judgment. Working from the experimental data with analog or digital computation techniques developed as an outcome of the dynamic models, these probabilities of injury can be computed. In addition, irregular and complex acceleration-time histories, impractical to duplicate experimentally, can h. evaluated for their effect gn the human involved. When such calculations show unacceptable probabilities of injury, the parameters involved can be varied singly or in combination to dcrivc knowledge of the modifications necessary to make the acceleration exposure endurablc. I t will always be wise to varify these predictions with tests simulating at least the critical points, h i t tlw savings are still considerable. Since this report is intended as a general treatment of the subject, niirnerical examples of specific acceleration and restraint system design problems are not presented. 2

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The acceleration tolerance pmblems that are of major concern at present involve only seated or recliningsubjects.Tbe head, arms, or legs may or may not be included in the masses that make up a specific dynamic d e l ,dependingon whether they are factors in response of the body to the acceleration situation under study.The models of the human body used in this report generally refer to a whole body response bgsedan a particular failure mode with no special regard to the response characteristicsofeach body segment. 3

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Section II BASIC BODY DYNAMICS THEORETICAL DYNAMIC SYSTEM Human b o d y dynamics has a simple basis: Biological Structures (and the human hocly in particular) respond tu applied loads and accelerations in exactly the same manner a s any othot phvsical systems.Thus the logical starting point in the discussion o f basic I M K I c1ynaritic.s i s tiit, fundamental consideration,of the response characteristics of a mwhanical systeiri. If it rectangular acceleration pulse is applied to a simple spring-inass svstciri, t l i c ~ C . S ~ ) ~ I I S C .01 t l w system is as illustrated in figure 1. Note that the peak acceleration cxpcric*nctxl h y ttit. systc-rll is greater than the peak acceleration of the input pulse. This plienomcnon is tc:rnicd tlrc: dtputnic ocershoot of the system. I- I U L \ 7 \ M E Figure 1. posponn of o Simpk Dynamic S-rn to o Rwbngular Pulse. If the peak force in the spring of the dynamic model is recvr-ded in a series of tests irr which the duration of a rectangular pulse to the system is progressively increased while the acscc:lc:ration level remains constant, the result will be a graph such as that shown in figure 2. At zcro pitlsv duration the peak force in the dynamic system will also be zero since no force can be genc:r;rtctl in zero time. As the pulse duration is gradually increased from this minimum value, thc pcak forcewill continue to increase up to a certain peak value, and then will continue at that valuc for longer and longer pulse durations. The type of curve shown in figure 2 is characteristic of any single degree of freedom systcw The pulse duration at which the force in the system levels out at a cmnstant pcak value owiirs around the natural period of the system. Beyond this critical duration, the peak form in the system reniains constant as pulse duration increases. Both theory and expctirnent show that i i i an tindamped system, the actual value of the force will be twice the input force. ‘That is, the dynamic overshoot will be 100%for pulse durations that exceed the natural period of the system. Relow this critical pulse duration, the peak force in the system will tw a function o f thc arc;t undt?rthe acceleration-time pulse, which is equal to the velocity change incrlrrcd by thc: systcni as a result of this acceleration. 4

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PULSE DUPATlOLJ Two simple rules emerge from the foregoing: The peak force in a dynamic system is relatecl to the oebcity change involved in the acceleration pulse when the pulse duration is less than the natural period of the dynamic system. The peak force in the dynamic system is related to the peak acceleration value of the input acceleration when the pulse duration is greater than the natural period of the dyoamic system. For durations comparable with the natural period, the peak force is a complex function of btb velocity change and acceleration magnitude. NOW if the spring in the system always breaks at a given force level, the system will be damaged any time the force in the spring exceeds this critical value. Knowing the response of a d y - namic system to input acceleration forces, it is then possible to relate thc damage incurred to thc. input pulse parameters.For the rectangular pulse shape, it is necessary to consider only the Iwiik acceleration and the pulse duration. Figure 3 depicts the resultant tolerance graph plotted on a log-log scale. In this figure, the line at the leftof the graph that angles down at 45" represents ttle regime in which velocity change determines the peak f e x ~ilr ihe spring, while the horizontal line extend- - 3

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ing to the right of the graph represents tbe region in which peak acceleration is the governing factor. Figure 3 can be considered typical of tolerance curves for single degree of freedom systems subjected to rectangular acceleration inputs. Such a case is of interest as an illustration of the analytical technique but, for practical problems regarding human body dynamics or restraint system design, it is neceSSary to take into account such factors as damping, statistical variabilities, input pulse irregularities, apd similar factors. Damping exists in all real materials as evidenced by the simple fact that all dynamic systems come to rest after excitation, rather than oscillating indefinitely. The concept that is most useful in human body dynamics is that of viscous damping, which is characterized by a linear proportioilality between the damping force and the velocity of the various parts of the systcin with respect to each other. The effect of damping on a simple dynamic system is illustrated in figure 4, where the amplitude of the system’s oscillation decreases with each cycle until the system comes to rc’st. 111 r e sponse to an acceleration pulse, the damped system exhibits less overshoot than an undampcd system, as illustrated in figure 5. Figuro 4. Damped OlldIIotoq Mation. Rguro 5. E&,of Dampin an Rosponso to a Rutangular lnpvt Aea%mtion Puln. Since a damped system exhibits less overshoot than an undamped system, the effect on ac.cu.1eration tolerance is quite straightforward. A smaller amount of overshoot implies that a 8rcatc.r input acceleration can be applied tothesystem before reaching the critical force level in its “spring” (Thisterm will be used henceforth to express the elasticity characteristic of the hiiinan body.) lhe effect of the reduced ovetshoot on acceleration tolerance is shown in figure 6. 6

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, The addition of a viscous damper to the dynamic model results in the damped single degree of freedom system illustrated scbemoticrlSy in figure7. VAUDATION BY EXPERIMENT All real materials exhibit a marked variability in breaking strength, a fact that is rmwgnizd in most applications by desiping on the basis of allowable strengths which are lower than those which are obtained in tests. Statistical procedures often are used to estimate the lowest strcngth limit, which is then used as a design allowable. The same sort of situation exists, of course, in biological strudwe and must be taken into aocounf when discussing the dynamics of the human body. The point that must be borne in mind at all times is that there is a probability of injury associated with a given input force-timebistoq. Not only do variabilities exist in the breaking strength of materials, but in dealing with the human body the variabilities in bone stii€nesses and body weights must be considered. The variability in these factors result in variations in the response to a given input acceleration and consequently in the peak forceOcCurriDg in tbe human structure. The concept of variability can be illustrated as shown in figure 8 in which statistical distributions are superimposedon the d e d tolerance line that, in this case, is the 50% probability of injury line. Another way of illustrating tbisis presented in figure 9 in which a series of probability of injury lines are draw. (Note that the concept of injury probability is quite similar to that of the Lethal Dose used in any physiological and medical studies.) (II B t o g P t d c8 0.90 0 . 0 1 Figure 9. ProbaMliwof Iniury Lovok on o tokrancr P h . 7

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In the preceding paragraphs, the fundamental nature of physical systems consisting of elements with elasticity and damping were explored. Measurements have been made on various types of mechanical systems to determine sensitivity to impact accelerations, and the results confirm the results just presented. There is, of course, always a question as to whether biological structure in complex arrangements follows simple physical laws, although there is no obvious reason why such laws should not apply. It should be relatively easy to demonstrate that biological specimens exhibit the same diaracteristics as mechanical systems, in terms of impact sensitivity. The only experimental e q i i i p m w t rcquired is a drop test rig with some means of modifying the impact acceleration t o oht;iin varioiis peak accelerations and pvlse durations. Live animal subjects can then bc testccl o n tlic rig to dctvrmine injury or fatality levels. Such experiments have been conducted by K ~ i r n l i ~ ~ i i s ~ ~ r;1ndC : o I J as reported in reference 1. A total of 329 mice were subjected to impacts in two series of tcsts to detcrniine tlw Icvcls at which approximately 5% and 95% of the test subjects died (5%and 95%. Lethal IJose or 1,1> levels). The drops were conducted so that the mice received positive spinal acceleration piilses that varied from slow to moderate rate of onset. The results of these mice impact tests are plotted in figure 10, adapted from reference 1.The points do in fact fall on lines that are either at 45"to the horizontal or are horizontal. This is just as predicted by the dynamic theory. There is an unusual feature in the data that has not previously been discussed. Figure 10 shows two different 45" itngle lines representing two different critical velocities and two different horizontal lines representing two different peak accelerations. Hypothetically such a situation can result from three causes: An artifact may have existed in the test situation; the mice may have constituted a two-degree-of-freedom model; the data may be showing the occurrence of two different failure modes. There is some question as to which of the causes listed results in the shape shown for the mouse impact tests, but as verification of the applicability of dynamic thcwry to biological tissue as well as mechanical materials, the mouse impact test results ;ire prolxibly valitl ;IS an illustration of the basic theory. There remains the basic problem of relating an inpiit accc.lcratioii-tirn(. Iiistory to injury o r some other practical limit. Reflecting for a moment on the load-tlcflc.c.tion ciirvc c+arac.tcristic*so f materials, a force (or its equivalent deflection) is clearly the ineclianisiii o f duiiiagc. i i i ii mat(-rid. Therefore, if interest is centered on tolerance to acceleration, the only pnranwtrr of intc!rc.st is tho peak force developed in the elastic material of the human body. This force is n w s t convcnicwIly described by a parameter called the Dynamic Response Index (DRI). For simplicity and consistency,the DRI is expressed in nondimensional G units by (IividinK thc peak force in pounds by the body weight in pounds. In all subsequent discussion in this report, the peak force in the body will be referred to in terms of DRI. The best example of the DRI in the human body is for the case where the ii~c(lrati011is directed parallel to the spine. In this mode of acceleration of the body, the vertebral column acts ; I S the principal load-bearing member, with the mass of the thorax, thoracic organs, arms, slioiildcrs, ntxk, and head resting 0x1 the column. Actually, these masses are attached along the entire length of the: spinal column, which means that the first analogy that comes to mind is a distribiited paraiiwter dynamic model, i.e., one in which an infinite number of individual masses, springs, and dampers are connected in series. However, there is a lack of data on the precise rnanncr in wliicli thc inasses are distributed, and in addition, it is very difficult to calculate the forces in a complex 8

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Figur. IO. Four Per Cont LD Lirm for Mice Drop Teats. (From Kornhauwr and Gold) 9

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distributed parameter system. This does not mean, however, that useful inforinatioii cannot hc.(I,.. veloped. Instead of a distributed parameter system, the upper body analogy can be simplificxd as ;I lumped parameter system, this means that all the mass is assumed to rest upon the top of the thoracic and lumbar vertebrae which constitute a simple massless spring. In a later section this analogy provides good mrrelation with empirical measurements of body dynamics. Thus, only damage to the vertebral Lolumn need be considered in developing the dynamic model -- at 1c;ist inittally. 10

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Section IIP APPLICATION OF HUMAN BODY DYNAMICS The correct interpretation and use of engineering information is predicated upon presenting it in a manner that enables users to convert and use the data readily. One of the major advantages of using the dynamic model approach to the problem of acceleration tolerance is that it pemiits the use of a standard and well defined vocabulary. Furthermore, the relative effect of various parameters can be evaluatecl, and the relative importance of the parameters investigated quantitatively. This section describes the appropriate parameters that need to be taken into accwunt whrn human tolerance to acceleration is discussed INPUT ACCELERATION PARAMElERS The input acceleration-time history can be characterized by three parameters if it is rectangular or triangular in shape: the time duration involved, the peak value of the acceleration applied, and the time required to get from the initial acceleration condition to the peak value (the r i s e time). In the simplest cases,these parameters are all represented by single values so that linear relationships are assumed. In most real acceleration-timehistories, however, irregularities aTur as a matter of course. The simplest acceleration pulse to evaluate is the rectangular pulse, characterized by a duration and a plateau acceleration value, the rise time being zero. As explained in a preceding section, there are two acceleration tolerance regimes. If the acceleration pulse duration is extremely short, then the peak force in the dynamic system is simply a function of the area under the pulse, which is the velocity change involved in the acceleration. Beyond a certain duration (several times the natural period of the system), the force in the dynamic system becomes a function of the peak acceleration rather than the area under the pulse. As a consequence of this, the curve that represents a given level of damage to the dynamic system can be drawn as in figure 11. The area below and to the left of the lines in the graph represents rectangular acceleration pulses that will cause less damage than the nominal value for the line. Conversely, points aboveand to theright of the lines represent pulses that will cause morc damage. Rgum 11. A Tol.ranco Omph for RectangularPulso Inputs. The curve shown above can be considered a tolerance graph only for ret-tatigrtlar accclcmtiori piilses. When u s e d in such cases, however, the curve should hc lahclcd a darriagc or iiijriry CIII-V~' ii

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rather than a tolerance curve, and the restriction that the curve applies to rectangular pii1sc.s only should always be noted on the graph. Rgum 12. A linear Romp Pulse Showing the R i s e Time (tR). Piilses with a ramp leading up to the peak acceleration, such as that shown in figurc 12,can 1 ~ ; specified in terms of rise time as well as peak acceleration and duration, In general, the longer the rise time the lower the peak force obtained in the dynamic system for a given plateau acceleration. With a rectangular or zero rise time pulse, the dynamic system will experience 100%overshoot it is not damped. If a pulse with a sufficientlylong rise time is applied to the same dynamic system, no overshoot at all will occur. Thus, for a range of rise times, various amounts of overshoot will occur. Since a smaller amount of overshoot occurs as the rise time lengthens, the effect on an injury or damage line is as shown in figure 13.That is to say, the plateau acceleration required to cause damage will be higher than those for the rectangular pulse condition, and an increase in rise time permits the application of larger plateau accelerations. Obviously, rise time cannot affcct tlw a r w where velocity change i s critical, since by definition very long rise titncs wol~ldnot pcrrnit tlw w r y short pulse durations associated with this regime. Figure 13. Effac, of Rise Time on Tolerance. 12

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A tolerance graph should really include all the rise times of interest to the engineer. Such a graph would look approximately as shown in figure 14,where each line represents a different rise time. The uppermost line represents the application of acceleration in a device, such as a centrifuge (very long rise times) while the lowest line represents the rectangular pulse condition. bsG Rgun 14. Illustrationof Problems in PlottingToierancr Cuwes for Various Rise Time Pulses. Even with the addirion of rise time to the problem of assessing acceleration pulse scvcrity, real acceleration pulses will not always look like the trapezoid that will be drawn if only a rise time, peak acceleration, and duration are specified. Most real acceleration pulses involve irregular force-time relationships. In such cases, it is sometimes sufficient to approximate the real aceeleration pulse with a mathematical function, such as a half sine pulse, versed sine pulse, an exponential acceleration onset, and so on. Several mathematical function pulse shapes have been investigated- (ref. 23 and ref. 24) and in figure- 15 the shape of the c mage or injury curve for the half sine pulse is shown. io9 G Figure 15. Tokrancr Curve for a Half-Sine Pulw. \'bile it is posible to approximate real acceleration pulses with an appropriate mathnriatic*:il function to obtain more precise results, no single graph can contain all the lines that wonld hc rcquired to show the damage levels for the various pulse shapes. It would become necessary thcrl to use a number of sequence graphs to represent the potential injury or damage to a dynamic system when dealing with a number of differenttypes of pulses and pulse shapes. Practical acceleration-time histories usually exhibit irregularities that cannot he described I,y i t simple mathematical function. Solutions must then be obtained nilweric~!!j. ::sing d cwilputer. 13

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HUMAN BIOMECHANICAL PARAMETERS As in the first approximation the natural frequency and damping coefficient of the hiiman body, for a given mode of deflection, can be assumed to be invarient. However, the h u m a n h l ) probably has an infinite number of deflection (or injury) modes for any given accolrrati o n 1’(!(.t o r of which the first three to six may be significant in a lumped parameter analysis. For cxanrplv, i i l the application of spinal acceleration to a seated human body, the fundamental mode of f:iiliirc is vertebral damage, but a secondary mode in the form of head injury can occiir for vcry sllort ,is(. times. Similarly, in a transverse direction, the principal type of damage appenrs t o lw hvtiorr11;1g ing in the lungs and damage to the large blood vessels around the heart. E l o \ v c v c ~ ,tralis.c.l.sc~;I<.celeration can also result ip damage to the head, liver, spleen, kidneys. and s o on. . In figure 16 a multiple injury mode situation is illustrated. In the hypotlrctic;il cxscb 11s~’1 0 , this, there are three primary injury modes. Note, however, that a nuinbcr of swonclary iiijilry modes may exist, so that exceeding a given velocity change or peak acceleration can rc:srllt i t r Figure 16. An Example of Multiple Injury Modes. miltipleinjuries. Each injury mode represents the deflection of a piece of tissue or strrlctiirc to a point of passive damage where immediate or subsequent functional or physical failure occurs. WIIIS. each injury mode represents a separate kind of tissue deflection. It is obviously desirable to liavc a dynamic model available for each injury or deflection mode. Unfortunately, insufficientexperimental data are available at present to describe the dynamic characteristics of all the various tissues involved in the injuries sustained by the hriman body whcw it is subjected to large accelerations. Far from precluding the use of the dynamic modcls,this situation emphasizes the use for them, because they furnish the most accurate description availablc of dynamic response to acceleration and a logical basis for extrapolation whcn it is necessary. Just a s aircraft were designed and flown before aerodynamics reached its present level o f sophistication, so the engineer today must design ejection seats, restraint harnesses, and othcx- 1r:irdwarc on thc. most rational basis available, even though he lacks full details as to human injury niodes. The lack of information does indicate, however, that a great deal of biomedic-alexperiiircntation is rcquirctl to extend and refine the data required by engineering personnel. 14

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The multiple injury mode view of the human body can be seen from a review of injury data, such as occurs in accidental free falls. However, particular injury modes tend to occur at different force levels in different individuals and at different times. Statistical variability exists in the mechanical properties of almost all materials. For exarnplp. if a series of samples are cut from 4130 steel ingots and tested in a tensile test machine, a distribiition oi breaking strengths would be found to occur. I n general, the distribution would bv forind to follow the normal Gaussian-type of curve, although other distributions arc: possihlc:.Sirriilar rcstilts can be expected far biological materials. Because of the variability of the meclianical characteristics of biological structilrc.s, i t i.s clc*.sirable to consider the damage to such tissues from a probabilistic stiinctpoint. Instead of ~ S ~ U I I I ~ I I ~ that all the material fails at a given level and none of it fails below that level, it is 11111cliI I I O I ( * i l l keeping with the real world to assume that a larger and larger percentage of samplt.s tcstcd $1i l l fail as the applied load increases. In graphic form, the probability of injury curves for thrcc injury modes might appear as shown in figure 17. Note that the average value where failure occurs, and also the variability in failure loads is different for the three injury modes. Flqlure 17. Probability of Injury Curves for Three Iniury Modes. ‘crsing the statistical approach to the definition of hiinian response to acceleration, a initItiplc: injury mode dynamic system subjected to a rectangular pulse acceleration would have the “to1t:rance lines” as shown in figure 18. One known additional factor should be taken into accoirnt in defining the effect of acceleration on the human body. In Section I11 age has an appreciable effect on the stiffricss and strength of bone. Probably age affectsall biological tissue to some extcnt. Unfortunately, thcrc is very Iittle data available on this effect, other than that on hard bone in compression. This i s an area that warrants further biomedical research, because the effect is sufficient to begin cnrisirig prol)Icws when the age of a person subjected to an acceleration is above 35 Years. Lacking more knowlctlgc ut present, this shodd perhaps be taken into account b y wing conservative factors in cstahlishirig acceptable acceleration levels, when the application is for designs in which older pcoplc will be subjected to the accelerations. 15

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In summary, the three items of principal importance are: (1)a number of injury modes, both primary and secondary, can occur and should be considered; ( 2 ) any given injury mode is best represented by probability of injury curves which have further value as indication of the degrees 1 \oqrrt Figure 18. Probabilityof Injury Tolerance Lines. of risk in operational situations; (3) the effect of age on strength of bone and tissue is of consctqucnce in acceleration exposure conditions, so that the age of the using population should hc considered in selecting acceptable acceleration levels. As the state of the art advances, flirther expwimental and theoretical research will undoubtedly pinpoint other factors worth consideration. RESTRAINT AND SUPPORT PARAMETERS The preceding paragraphs have indicated ~ 1 1 eof the difficulty in describing hriman to1cr;invc. to acceleration as precisely as engineers would like. However, the full picture has not yclt lwtw ( I C , - vclopcd, because thus far the human body has been assumed to be rigidly attachctl to thcb input ;icceleration support surface. Such an assumption would be correct only in those c:isc"; whcrc. :i spinal or transverse acceleration is applied to the human body through a seat strricturc w i t l i o i i t intervening cushions. I n most practical seating systems, cushions or other resilient supports ; ~ r c used to increase comfort and their dynamic characteristics inrlst be taken into account. Furt1it.rnwre, accelerations applied in negative spinal, negative transverse, and laterid directions result in the body impinging upon relatively elastic devices, such as, lap belts and shoultler hiirncsst~\ These devices also act to modify the acceleration transmitted to the humm body. The natural frequency, damping coefficient, and bottoming depth of elastic support devices ran have a major effect in amplifying or attenuating input accelerations. Certain rigid supporting structures such as plastic foam or honeycomb materials used as one-shot energy absorbing clevic(l\ ha\e siniilar effect on the forces felt by the body. A description of these effects is presented in rtyfcrence 2. 16

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In general, the effe@of restraint device characteristics on the ability of the human body to withstand input accelerations is best handled by analog or digital computer techniques. Certain analytical and general reults have been obtained, and such results are usually presented in the format shown in figure 18, in which an amplification-attenuation scale is used. V Rgun 19. A Typical Restraint Effoct Graph Using the kostraint Anaiyrer. One method of assessing an arbitrary acceleration input is to approximate the inpiit acce1cr.ition by using the duration, peak acceleration, and rise time values, or by using a known math(.niatical function such as a half sine pulse. By consulting the appropriate charts and graphs in published reports, the peak force in the dynamic model can be estimated. Then, the appropriatc charts and graphs on restraint characteristics can be used to estimate the modification of this maximum force in the dynamic model as a result of restraint effects. Finally, the maxirniirri forcc. in the dynamic system can be compared to a probability distribution of critical forces t o ohtuin a probability of injury. Is those cases where data is available, the effect of the user population agc' should be included in the analysis to obtain a more nearly realistic probability of injury. In order to use the above procedure intelligently, the engineer must understand the fnc'tors involved in the estimate, and he must be aware of the assumptions involved in the analysis. In gweral, it is recommended that the above procedure be used in preliminary design and similar situations where optimization procedures must be effected rather quickly and on broad scale. A second procedure that can be used to assess an arbitrary acceleration ~)ulscis to use an analog or digital computer. The undamped natural frequency, the damping coefficient or the dainping coefficient ratio, the effect of age on the critical force, and the probability distribution of the force required to cause injury should be known for each injury or deflection mode in the system. 17

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Then, the applicable dynamic parameters of the restraint system, which adds im additional degree of freedom to the model, must be estimated in accordance with the best avai1;ible information. The equations of motion of the resulting two degree of freedom dynamicsystem are then solved. The probability of injury can then be estimated within the computer, or by use of an appropriate distribution graph. In order to simplify the process as much as possible, a fixed circuit analog system using the human body dynamics data presented in this report has been developed for thc sponsoring agencies. This device, called the Frost Restraint Analyzer, is illristratctl it1 fipirc 30.‘ihc tlyn:iriiic* V model circuits in the restraint analyzer are fixed, brit the restraint systcw dynsatic. r.h;irac.tcristics can be varied by means of front panel controls. Selector switches pcrrnitthc opcrator t o se1tu.t 11tc. various body models and restraint models. The readout on the restraint iinnlywr is in tcwirs o f Dynamic Response Index. In addition to analog techniques, a digital computer I)rograin ltas twcn tlcvr-lopcxl for IISV i r i restraint optimization problems. A simplified flow chart for this program is shown iri fig~irc,21. Both the analog and digital approaches are discussed in detail in reference 2. The informationand procedures presented in the preceding paragraphs of thc 1)odyof this report are applicable to the general problem of using dynamic models to describe tlie responsc of the human body to acceleration forces. For the general reader, the presentation was intended its an introduction to the problems, techniques, and solutions involved in protecting humans from acceleration exposures. In the sections that follow, more detailed information is provided, particularly with reference to quantitative estimates of human body dynamic characteristics. Figure 20. Frost RestraintAnalyzer. 18

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h , r1 P I r I

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Section IV SOURCES OF DATA ON BODY DYNAMICS Before describing the dynamic models of the human body that have been developed, it is useful to review the available data on acceleration exposures so that the information used as a basis for the models can be evaluated in proper perspective. This section describes in brief form the types of and usefulness of data that are available. To assess the ability of the human body to withstand acceleration and, subsequently, to establish levels of estimated injury probability, it is necessary to acquire and analyze data on actual exposures to acceleration. In general, there are two sources of data: Controlled experimentation using volunteer subjects and accidentalor involuntary exposures. It is, of cviuse, undersirable to injure volunteer subjects in tests situations.Therefore, the data resulting from tests tcnd to cwnsist of subjective resposses or reports of no injury. Accident data, on the other hand, quitc oftcn include injury levels ranging from mild to lethal, but the circumstances surrounding the exposure are usually illd&ned. Tests have been conducted at various laboratories using live human subjects, human cadavers, and live animals. The tests involving live human beings are of primary interest since they provide the most valid and directly applicable data in terms of assessing human response to acceleration. DROP TESTS By far the simplest kind of test to conduct and evaluate is a drop test. The principal sources of data on drop tests h w e been the Civil Aeromedical Research Institute (CARI) at the FAA Aeronautical Center, Oklahoma City, Oklahoma; the Aerospace Medical Research Laboratory (AMRL) at Wright-Patterson Air Force Base,Ohio; and Stanley Aviation Corporation, Denver, Colorado. Both the CWI and AMRL programs involved the investigation of restraint material effectiveness. Stanley Aviation Corporation conducted a series of drop tests using a prototype B-58 escape capsule, as part ofthe demonstration of operational acceptability of the system, including its shock attenuators and restraint harness. The results of the CARI tests were reported in references 3 and 4. Detailed subjcctive comments on the part of the test subjects were recorded for each drop in the program, and these s ~ h - jective report data have beenused in the development of the spinal model reported in Section VI. As a general rule, subjective comments are known to be extremely variable and often apparently useless. However, if a sufficient number of subjective reports are available, an averaging process can be used tQ reduce the variability to some extent. In the case of the drop tests conducted at CARI, over tests were conducted, which is a sufficient number to permit averaging. Subjective comments were collected in both the A M R L and Stanley Aviation drop test programs. However, in the latter program, the subjectivc comments were not published, nor wcrc the number of drops at each condition sufficient to permit suitable averaging. Also, since the tests involved the use of a prototype! operational escape system, there are the additional cwmplicating factors of illdefined shock attenuator characteristics, unknown impact surface characteristics, and the accelerations imposed were multidirectional. Drop tests conducted at AMRL facilities at Wright-Patterson Air Force Base have tended to consist of evaluations of proposed operational restraint devices. Relatively few drops have hewn 21

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conducted under any one condition, and it is &fEcult to obtain averaged srrhjtu.tivt. c w i u i i c i i t s II! sitch a case. SLED T E S S Major problems exist in assessing the results of short-term acceleration slcd t e s t s . First, tlic’ . I I ? ~ plied acceleration i s usually of a somewhat irregular shape and, in some cases, it is diflicult t o establish the true shape of the pulse because of noise in the record. The second complicating fa(.tor is the presence of viscoelastic restram’t elements in the test. This should not (and does not ) prevent the analysisof the data from the test, but the data reduction process is made much mor(’ complicated since the dynamics of the restraint system must be taken into ammnt in asstssing the forces felt by the subject’s body. The real problem in analyzing sled test data or any other data involving an irregular nntl arbitrary input accleration results from an interesting dilemma. Much of thc sled test t1al;i iirt: i i t - ttrrided for use in establishing human tolerance to a given acmleration cnndition. IIowcvc:I, t l i c data cannot he reduced ta valid usefulnessfor this purpose unless a dynamic mrdcl of t h lwdy i s available. Fortunately, there are ways to get around this difficulty,as will lw shown. ‘fie major effort in testing live human subjects on sleds has h e n conductal a t 1itlw;irds Ail Force Base and Holloman Air Force Base. The results are recvrded in referencws 5, 6, 7, and 8. initial investigations were conducted under the direction of Colonel john 1’. Stapp and involveti considerable risk to the volunteer subjects, including Colonel Stapp. The information resulting from these sled tests has been of great value in preliminary definitions of human tolerance to transverse accelerations, and still remains the only data available on transverse acceleration exposures of d c i e n t duration to be classed as short-term. VIBRATION TESTS If a repetitive input force is applied to the human being, then human tolerance to vibration is the controlling factor. Vibration testing also permits determination of the resonant frequencies and damping of the hum* body. The principal work in ascertaining human response to vibration inputs has been conducted at the Aerospace Medical Research Laboratory, Wright-Patter.wn Air Force Base, Ohio (refs 9, 10, 11, 12). Latham (ref 25) and others have also studied human tolcrance to vibration. One of several summaries of the available information has been given by Colclman and Von Gierke in reference 26. In general, three methods are used in vibration testing. The first is voluntary huinan c*xlwrirc* to vibrations of various frequencies with amplitude increasing up to a subjective limit, tlic scuuml is by measurement of input impedance of the human body; the third is measurement o f ainplitriclt. transmissibility It will be seen later that resonant frequency rncasurements using irnpxkncr ineth ods and subjective reports provide an excellent cross check on other calculations of the frrcp~wt-y of the human body in the spinal direction. In addition, impedance and transmissibility data p:r mit estimates of damping to be made. STRUCTURAL TESTS In addition to tests on live human being, one of the more useful sources of data is thc testing of human cadavers. Tests on the mecbanical characteristics of the body’s hard structure have cvntrihited significantly to arr understanding of the mechanical behavior of the body under curtain cwnditions. The problem of tolerance to accelerations in the spinal direction while seated has I x e n of major importance since the advent of the ejection seat, and as a result a number of studies haw been performed on vextebrae obtained from human cadavers. 22

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_ - The most useful studies of the mechaniml promrties of the vertebra are contained in references 13,14, and 15.Ruff, in reference 13, measur& the strength and deflection of vertebra. Static loading of sections of the vertebral column were used to obtain stress-strain curves. Failure or injury was defined as the first peak in the stress-strain curve, which is the yield point in the curve and corresponds to permanent or irreversible deformation. Subsequently, Perey (ref 14) reported on a series of studies in which end plate fracture was shown to occur at a significantly lower load than the vertebral body deformation reported by Ruff. Perey also reported the proportional limit load for a series of cadaver vertebra. In addition to the strength Characteristics of vertebrae, Perey studies the stiffness of vertebrae for several age groups. Yorra, in reference 15, presents typical stress-strain curves for thc equivalent of one lumbar vertebra plus the intervertebral disc. This information can be u s e d to estimate the natural frequency of the human body, and the effect of age on frequency. Furt1ic.rinore, the degree of noalinearity in the spinal direction can be estimated. The method uscd in alculating the natural frequency and the results of the calculations are presented in Section V for the dynamic model of the human body in the seated position and spinal direction. Aside from the work on the mechanical characteristics of the vertebral column, very little research has been performed to obtain data on st8ness or damping of major body structures. Some studies sponsored by the United States Air Force are under way at present on tissue strength, but because of the inherent difficulties in mechanical measurements on biological tissue and the relatively more complex nature of thoracic and abdominal organs ahd their support systems, it can be anticipated that useful data will not be obtained as readily as was possible with the spinal column. Recent studies at Wayne State University using seated human cadavers (ref 16) are of considerable interest since. they illustxate the capability of predicting dynamic response by use of dynamic models and then obtaining confirmation in an experimental situation. Previous work at Wayne State, particularly in the area of head impact, has resulted in the definition of several important dynamic parameters of the skull-brain system (ref 17). ANIMAL TESTS There are certain sbjections to the use of data from cadavers, particularly since it is possible that storage and preservation techniques can influence the mechanical properties of biological tissue. For certain mecfianical characteristics, it is possible to cross check information obtaincul from cadavers with experiments on live human beings. Another approach, of course, is to usc livc: biological specimens other than humans. A variety of animals have been used in acceleration e x - periments, including hogs, rhesus monkeys, chimpanzees, mice, and bears. The advantage of rising animal subjects is that injurious and even lethal exposures can be attempted providing the experimentation is conducted within the rules for animal experimentation. Thus, the health and wcll being of human subjects need not be risked in severe condition testing. The information obtained fmm animal experimentation must be viewed with sornc skcptirisni if it is to be applied to the problem of assessmg and setting human tolerance limits, however. 'I'hc. forces generated in an animal body will probably not be the same as those generated in the h~imnn Ixdy for an equivalent input acceleration, because of obvious dynamic differences. Also. thc forre required to cause injury in the skeletal structure, organs, or other portions of the animal body may not be the same as the forces required to cause injury in the human body. Before valid extrapdations can be made from animal experimentation to human conditions, the precisc relationship between the dynamics aiid critical force. in the animal's body and those in the human bcdy must l ~ , 23

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known. Unfortunately, this type of definition has not yet been accomplished for any animal subject type. Animal testing does have benefits in certain situations, however. As an example, the experiments conducted by Kornhauser (ref 1)cited earlier in this report resulted in reasonable confirmation of the shape of the tolerance curve predicted by a simple dynamic model. Thus, Kornhauser was able to show thBt a system consisting of biological tissue was equivalent to a mech'mi cal system insofar as tolerance to acceleration was concerned. ACCIDEUT DATA U p to this point, the discussion of acceleration exposure data has been restrictcd to infomiation collected under test conditions in which the investigator presumably is able to control inany of the conditions under which the acceleration is received. Such data is of great valuc since t l i c a parameters affecting the outcome of the exposure are either known or controlltd. IIunian s ~ h - jects cannot be exposed to large acceleration levels in order to determine the magnitude of the forces involved in injury, hpwever. Cadaver or annmal tests can result in a definition of injury levels or modes but exbarnlation of the data to live human beings is fraught with difficuitics. One way in which infwnation can be obtained on injury-producing acceleration cxposures to to obtain data relating to situations in which human beings have been accidentally exposed to very large forces. By far simplest data to collect and analyze is that resulting from situations in which live human beings have fallen from known heights and struck solid surfaces, or wherc the drop height and deceleration distance is known so that the acceleration and duration can tx; estimated. The classic study in this regard is that by DeHaven (ref 18) in which survival of free falls was documented. More recently, an analysis of free falls mcumng in mountain climbing has been performed by one of the authors of this report and the results are presented in Section V. DeHaven collected cases that consisted essentially of miraculous survivals, which results in :I somewhat overly optimistic estimate of tolerance to this kind of acceleration, but perhaps can scrvc to define absolute limits. There exists very little adequately documented accident data other than the vcry qwctac1ilar information on free falls. Ohiously, the many cases in which people slip on icw, fa11 in tlrc homc, and otherwise injure themselves accidentally during the course of everyday living have not twen well documented or recorded, although a program to collect data is now under way at the Civil Aeromedical Research Institute in Oklahoma City (ref 19). EJECTION SEAT DATA There does exist one other major sowce of exposure to large accelerations which can providc: information for assessing acxeleration tolerance. Ejection seats have been in use in military aircraft since World Way 11, and in some cases, the ejections have involved acceleration forccs sufficient to cause an appreciable number of injuries to pilots and crew members who eject from disabled aircraft. An excellent study of ejection injury is contained in ref 20, which summarizes thc medical record involved in the use of ejection seats by the Royal Air Force and Royal Navy. The US Navy and US Air Force also have data relating injury to type of ejection seat. Unfortunately, all of the ejection seat data constitute a very complex data reduction problem. The initial spinal forces generated by an ejection seat are a function of a ballistic cataprdt o r :I rocket catapult that is suhject to the usual statistical vm-ations in propellant performance plus variations caused by temperature. The weight of the eject= also influences the rise tinic and peak accdcration achieved by the seat. Added to these uncertainties are the factors of seat cushion

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thickness, material, and age, restraint harncss configuration and material, restraint harness prvload or slack, and the age and previous loading history of the restraint elements. Since the nominal force-time history of an ejection seat is rarely known with any precision and the dynamic characteristics of the restraint and support devices are totally unknown, the ejection seat data that are currently available do not constitute a very promising source of information, unless suitable data reduction techniques are developed to permit a reasonable assessment of the available information. This could then be used as a crosscheck against data developed from other sotirces, such as tests with live human beings and with cadavers. 25

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Section V A DYNAMIC MODEL OF THE HUMAN BODY IN THE SPINAL DIRECTION A dynamic model for the spinal injury mode of the human body is not complicated, for the ertebralcolumn can be considered the resilent load-bearing member, and the mass of the upper body can be considered to be resting on top of the column. If this simple mechanical analogy to the body is valid, then it ought to be possible to calculate the natural frequency by obtaining information on the stiffnessof the vertebral column and the magnitude of the mass resting on it. Thc latter data should not be difficult to obtain, and since static load-deflection tests have been condircted on vertebrae, it should be possible to obtain stiffnessestimates. ESTIMATES OF M A S S AND SPRING STIFFNESS Yorra (ref 15) obtabed load-deflection curves for several 1uml)ar \xxrtclwac. 'I'hc :wer.igc stiffness obtained for the fourth lumbar ( L4) vertebra was 11,750 pound/inc.li. l'ntortunntc.ly, tlw load-deflection curves for other vertebrae were not obtained. From a knowledge of materials in general the stiffness of any given structriral elcnient may be reasonably assumed to be directly related to the breaking strength of that elcmcwt. Thcrvfore, it is possible to obtain the stiffness of all the vertebrae if their breaking strcmgth is kriowu. The most valid data on vertebral breaking strength in compression is that obtained b y RrifF (ref 13) in Germany during World War 11. He measured the brcaking strength of individual t ertebrae between the fifth lumbar (LS)and eight thoracic (T8) with a minimrim of three samples for each vertebra tested. In addition, Ruff devised a method for estimating the percentage of total body weight carried by each vertebra from T5 through L5. Table I presents the raw data TABLE I RUFF'S VERTEBRAL STRENGTH DATA Raw Data .4oc~r(ig c Vertebra Breaking Strength in. Kg. Aoc.mg!c. it1 111s. T8 840,540,809 T9 610,720 700 593 1315 677 1493 T10 800,660,770,730 740 16.32 T11 750,720,860,755 771 1700 T12 900,690,800,800 797 1757 L1 720,840,900,800,800 812 1790 L2 990,800,830 L3 900,940,1100 Ld 1100,900,950 873 19% 980 2161 983 I! 168 u 1020, 1o00,1200 1073 2366 28

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thrls obtained on the breaking strengths. The percentage of body weight data and the breaking strength in pounds is shown in columns 2 and 4 respectively of table 11. It is possible to extrapolate the percentage of body weight carried from T5 up through T1 if there is a relatively consistent increment of 3%from vertebra to vertebra in the portion of the spinal column actually tested by Ruff. The resulting value of 9740 of body weight for TI is reasonable since this is the approximate weight, in terms of percentage, for the head and neck. Thus. the percentage of body weight camed by each vertebra from T1 through W can be listed. It is then an easy matter to calculate the actual weight in pounds camed by each vertebra for ii 1fXl Ib man as shown in column 3 of table 11. 'The actual weight carried by each vertebra and the compressive breaking strength of each vertebra is known for T8 through W.Therefore, the breaking load (expressed as G-force/static weight) can be calculated quite easily and is shown in column 5 of table 11.If it is aswitned tlliit the breaking load of vertebra from T1 through T7 is relatively constant at 25 G , then the breaking strength in pounds for these vertebra can be calculated since the actual weight carried in pounds is listed in column 3. The results are shown for T1 through Ti'in column 4 of table 11. TABLE I1 CALCULATION OF VERTEBRAL STIFFNESS 70of Body weight Weight Carried Hrraking g,of I,4 Brc-aking Breaking Strength Vertelme Carried 160 lb Man in Ibs. Load in C: Strc:nKth T1 9 14.4 T2 12 19.2 T3 13 24.0 T4 18 28.8 T5 21" 33.6 T6 25" 40.0 TI 29' 4.6.4 T8 33' 52.8 T9 3T0 59.2 T10 40" 64.0 TI1 44" 70.4 T12 47" 75.2 L1 50" 80.0 L2 53' 84.8 L3 w* 89.6 Ld 58" 92.8 L5 60' 96.0 360 25.0 16.0 480 25.0 22.1 600 25.0 27.7 720 25.0 33.2 840 25.0 38.7 lo00 25.0 46.1 1160 25.0 53.5 1315' 24.9 60.7 1493" 25.2 68.9 1632' 25.5 75.3 1700' 24.2 78.4 1757" 23.4 H I .o 1790* 22.4 82.6 1925" 22.7 88.8 2161" 24.1 99.6 2168" 23.4 100.0 2366O 24.6 109.1 "Sin Ir asterisk represents datu collected experimentally by Ruff; i i n i i i d c t l va1iit.s ;ire calciilattd or ;cssillnt.tl , I \ vapY:iined in ;he text. 27

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The procedure outlined above is used simply to obtain the breaking strength in pounds for each vertebra from T1 through L5.Column 6 of table I1 presents the breaking strength of each element in the vertebral column in terms of the percentage of the breaking strength of vertebra LA. Since the stiffness of vertebra J,4 was obtained by Yorra as noted previously, it is then possible to esti- 2 4 J b w Figure 22. Load-Deflection Curve for 14 Vertebra. mate the stiffnesses of the other vertebrae on the basis of the breaking strength percrntagcs. 1l a v - ing established the relative breaking strength of the vertebrae in a spinal column, it is nervssnry t o estimate the stiffnessof vertebra L4 from the Yorra data, reproduced in figure 22. A nonlinear spring has two kinds of equivalent linear stiffness. The first is the tangcmt t o t h * load-deflection curve. This is the apparent stiffnessof the spinal column that would be obscrvcd in small amplitude vibration tests on a shake table. I Figure 23. Estimate of Small Amplitude Equivalent linear Stiffness Using Tangent Method. 28

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The second type of stiffnessis illustrated in figure 24. The straight line approxiination to the nonlinear curve is drawn so that the areas between the straight line and the curved line are eqiial up to the load or deflection value of interest. This estimate of the stiffness is the one that would he observed in a test where large impact forces were applied to the body and it was then permitted to oscillate freely. For this reason, this estimate of stiffness is termed the free oscillation stiffness. Figure 24. Estimate of Free Oscillation Equivalent linear Stiffness Using Equal Area Method. To recapitulate, tlw stiffness of all the vertebra in the, spinal column can he c:stirr);ltrbtl Iroiii the stiffness of vertebra lA, and the relative compressivc brcanking strength of all tltc clt-iric:iits ( ~ : i t i 1)v approximated b y using both the free oscillation and snxlll amplitudc metliods of oI)t:iiiiiiiK cqtiivalent linear stiffnesses. With this data in hand, it is iic.cossary to ohtain a n c o s t i i i i a l c . I J J I II(. \.c.iglit of the body segriicnts resting on the spinal colunin. lhiforcliccs 21 and 22 provitlc. I l t t > cstinintcsfor the weights of various body segments including organs in thc thor;icic ; i r d ; I I K I I ) I I I i r u l cavities. For the purposes of this analysis the mass resting on thc. sljiiial coliimn was assurirclto C X ~ I - sist of tlic neck. head, upper arms, lower arms, hands, and tlw s t i f f strrictiirc o f thr: tliorax. F i - o l i ) a.nilalde data tlic organs in the tliorax were estimated to wcigli al’lroxirti;itc,ly3.41 I w i r i t l s ; I I I ( I t h ) blood circulating throiigh the thorax at any given t i t t l e Mq’ighsapproxirii;rtc-ly4.06 I i o i i t i ( 1 s . ‘ i l t ( ~ t o t a l iipper body wvight, including organs and l~lood,w;is cstimatcd :it 67.52 Imtn(1s ft (1111 t i l t . ; I \ :iilal)le anthropometric data. Subtracting the weight of the orgins and blood iii t l i c , t l t o t x k ( ~ ~ I I ’ i t ? ’ r c w l t e d i n an estimate of 60.5 pounds for the relatively rigid inass o f t l i c i i i q x a r lnitl,. ‘ i l i ~ w ~ cl;rt;t ;we shown in Table I l l . o ~ ~ ~ ~ t ~ I i ~ ~ : u n n(ref9,1 0 ) : i n t i cillicw 11;i.r shown that the filn(laiiic-nt:il li:itiir:il frcv I I ~ * I I C ~( I ( 111c \’isi.cr;i is almlf :i IS. I\‘c slio~ilitt h c w f o r c . c-sptcttlioritcic. org:uIs to I rt.I;tti\q,Iy wisitiic :it till. 1 .y!:b::r ‘ ,.i;;ii.!:. <L.iit.,iitii, Ir c ~ ~ ~ f i i ~ - l i < . ~ 29

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CALCULATION OF NATURAL FREQUENCY The equation for the undamped natural frequency of a simple spring-mass system is f,= - k/m 277dwhere f,, =undamped natural frequency in cps k =stiffness of spring in lbs/ft i n =mass in slugs ( weight/32.2) TABLE 111 BODY SEGMENT WEIGHTS Total Upper Less Body Weight Viscera Head and Neck Trunk Structure Organs Blood Upper Arms Lower Arms Hands (W Obs) 13.20 13.20 67.52 60.05 19.45 19.45 3.41 4.06 18.90 18.90 6.20 6.u) 2.30 2.30 .AS noted, the weight of the upper body for a 50 percentile man was rstimatctl to 1)c 60 11)s. which results in a mass of 1.865 slugs. Using this value of 1.865slugs arid thc varioits stifflwss estiiuatcs froin the load-deflectioncurve shown in figure 22, the effect of vertebral nonlinearity 0 1 1 the free oscillation frequency and small amplitude frequency are obtain. These data are s l ~ illo ~ ~ figure 25. Three resonant frequencies in the range of 1 to 50 cycles per s c ~ o n dhave, lw.cu o b s c n c d 0 1 1 live human subjc-.ctsas indicated in reference 9 for example. Of immc.dintt iiitcmbst is thc r ( w - mince observed in the vicinity of 6 to 7 cps. When corrected to obtain tlw riiidnmpctl iiattiriil f ~ ~ ~ - qrtency, a value of 6.1 cps is obtained. Assuming equivalent coiiditinns for the cadaver d:lta jrtsl :liiiilyzed, the predicted frequency is 5.7 cps. This i s :I rather signific;iiit \wiation. o w r Sy',SO t l ~ l tlw reason for the difference should be investigated. 30

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Figure 25. Effect of Vertebral Nonlinearity on “Free Oscillation” Frequency. The cadaver used by Yorra to obtain the load-deflection curve used in this study was 57.5ycws old at death. The subject used to obtain the estimate of 6.1 cps was 47 years old at the tirric: of tlw test reported. Therefore, one of the variations between the two data points is age, and it is k i p - propriate to investigate its effect on the stifkss of the vertebral column. THE EFFECT OF AGE OM SPINAL CHARACTERISTICS Perey in ref 14 provides a large amount of data on vertebral end plate breaking strength V ( T S I I S ajie as obtained from static tests of wet, fresh cadaver vertebrae. In addition, Perey report.; t l i ( . proportional limit strength for the vertebrae in two different age groups. In figure 26,Perey’s data for end plate fracture is plotted as the end plate 1)rc:akiitgstrciigtlt in psi vs age. Since Perey also measured the area of the end platc upon which loads i ~ t i l ) i ~ i g ( ~ .i t i3 possible to convert these data to ultimate stress. This has been done and the results a r v s l i o w it, figurr 27, together with the proportional limit strength of the vertebra. When both lincs i ~ wctxt i-a. Iiolatcd they meet at the zero breaking strength value, whicli indicates somr d c g r c of cwisistc.:ic.. Ixbtwecn two different sets of data. In addition to the I’crey ctata, a single cstirriatc. o f p w t i : t i i ( * i i t sc’t for the lumbar vertebra is shown in figure 27. As woliltl b c ? c>xpcclctl,this p ( ~ r ~ ~ ~ : i i i ( ~ i isct\ x l i w is al)ove the prop)rtional lirnit value. Not only did Perey obtiiin proportional limit strength v:iIlic.s for Iiinl)arvcrtc,l)rac.I N I ! i t ( %;tiso ( ) l ) t i l i l l c d the stiffiwssfor cichof the vertebra testcd. Iri rcf i.1. tlic datit arc listccl rlnt1c.r t l ~ r c ~ .:igv groups: Less than 50 years, 51-60years, and 61 plus years. A plot of breaking strcvigtli against stiffncw is shown in figiirc 28,where the less than 50 yoars old group and 51 to (iovc’nr old groiip

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n t.03 "J Pigure 26. Variation in Cadaver Vertebral End Plate Breaking Strength with Age. \ L: .I 1 \ b I " Figyre 27. E f f e c t of Age on Vertebral Breoklng Strength. 32

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overlap to some extent. However, the over 60years group is definitely located in the low stiffness and low breaking strength levels. A statistical correlation (known as a Pearson product moment) was calculated on the strengthstiffness data in order to c o h the fact that the two variables were indeed closely related. The result of the calculation was a correlation coefficient of 0.82. A coefficient of 1.00 would indicate c 0 5 I C F h k S 3 L L% / w .IC') Figurn28. RelatiomhipBeatween BreakingStrengthand Stiffness From Fresh Cadaver Vertebrae. a perfect relationship, and a value of 0.00 would indicate pure randomness in the data with no tlisoernible interrelationship between variables. The value of 0.82 obtained in this case can 1 ~ :w n - sidered reasonable validation of the relationship between strength and stiffness. In order to define the exact variation in strffness with breaking strength, a best fit linc was calculated from the data by the least-squares method. The result is a line with the following eqmtion: k -1.672+0.7266@where k is equal to stihess in pounds per inch and 611is equal to thc Imaking strength in pounds. This is the line plotted in figure 28. The surprising aspect of these data is the indication of bones becoming lcss stiff with agv rather than more brittle. Bone consists of a mineral called apatite dispersed through a matrix o f the protein collagen and is termed a two-phase material. Apatite is characterized b y high stiffnass .ind compressive strength and a rather low tensile strength. Collagen has a low stiffncss h i t high triisilc strength. Two two materials combine to form a mmpositc rriaterial having gcxd c h t i c . chracteristics and high compressive and tensile strength, thc combinatioa Iwing sirriilar in s o ~ i i c I cspccts to such materials as prestressed concrete or fihcrglas. Ircsurnatly:I changc in rc-lativc. cwnposition occurs with age and accounts for thc phcnornenon dcscritwxj. Aging, then, apparently results in bones hcwming lcss stiff. Ilic cffcct o n thc natural frcqucncy of thc human b d y can be calculated from the rclationship shown in figurc 28. I t i s only 33

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nccessary to obtain a set of correction factors so that the stiffness values obtained froin the 57.5 year old cadaver reported by Yom can be modified for other ages. Since an approximate relationship between breaking strength and stifmess, and breaking strength and age has been devised, the effect of age on stiffnesscan now be estimated. The result of this evaluation of age on frequency is shown in figure 29. c R ., Rgum29. Variation in Hurnon Spinal Natural Frequency With Age. The predicted frequency for a 47 year old man (fig 2.5) now becvmc-s 6.08 cps c o ~ ~ i p a r ~ ~ it o the 6.1 cps observed in the impedance tests as reported in ref 9. In addition, ;III c>stiin;itcof rcsonant frequency for a group with an average age of 28.5 years is reported in rc-f 11. Tlic c s t i r i i i i t c ~ obtained from subjective comments is 6.6 cps and the value prdictcd from thc mdavc:r c l a t : is 6.75 cps. In both cases, the agreement is good, particularly cvnsidering that the aiialysis of‘ I h c . cadaver data cannot be considered to be extremely precise. At this point, it is necessary to review the implications of the preceding disciissiori. tlsiiig ii very simple dynamic analogy to the human body, the natural frequency of t h c r 1x)dy has I ) c . c w calculated from cadaver data. The agreement between the calculated valws a r i d t l i c : viiIicc: ) I ) tained in vibration tests is very good, particularly when corrcctcd for age and iioiiliric.;\1.ilic.s. 1h n v ever, the undamped natural frequency of the dynamic system is only part o f t l i c ovcrall pic-liirc. It is also necessary to obtain an estimate of the damping in the hurtian body in the. spind d i 1 - c c . t i o 1 \ in order to obtain valid estimates of response to input accelerations. ESTIMATES OF DAMPINO Impedance measrirerylents with the human body repu-ted by Co(iii:iriii i i rc4 $1 ( v i i ~ l ) l c l m - - liniinary estimates of the damping cafficient c‘ tr? 1)c made for rclativc.lv siiiiill aiiipIitii(hosc.ill:\ tions, for frequencies up to 20 cps. The values derived by Coc>rin;mn:ire not ;IS ac.ciiratc;IS t111.y 34

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could be, however, because he used an approximate equation for impedance. In addition, he used only the peak impedance to determine the coefficient c, whereas the ratio of the resonant frequency to the maximum impedance frequency can also be used to obtain a second reading. For one subject, the data can be summarized as shown in Table IV assuming a subject mass of 5.75 slugs. For practical purpses, the variations between sitting erect and relaxed may be neglected. Thus, the fhal figure become~=O.31. TABLE IV Variation of Damping Coefficient and Natural Freqiiency with Body Position - c = 0.31 in the sitting position - c = 0.35 in the standing position f,, = 6.1 cps sitting erect fm = 5.67 cps standing erect Using this value, the effect of the nonlinearities in the spring can be estimated. For practic.aI purposes, the free oscillation case can be considered sinusoidal, although the frcquency natiirally varies with the amplitude achieved. Thus,if we assume linear damping characteristics, on the assumption that the materials involved are essentially viscoelastic, the damping coefficientwill vary directly with the apparent linear frequency. Table V shows the values calculated for various ages and various peak DRI v''11lies in thc spinal column,and the results are shown in figure 30. TABLE V Variation of Natural Frequency and Damping Coefficient with Age and Peak DRI Peak DRZ 1 2 5 Wf/27r 5.15 5.48 6.14 n 5.08 5.38 6.03 n 5.64 6.0 6.71 5.86 6.23 6.99 5.81 6.18 6.91 __ c .374 .352 .314 .336 .315 .282 .323 .3035 .271 3.25 .306 .274 10 15 20 6.9 7.3 7.47 ( cps) ( ;1gc 57.5) 6.78 7.17 7.34 " ( age: 60) 7.55 72% 8.17 " (ag:C..lo) 7.85 8.3 8.5 " (a#' eo) 7.78 8.23 8.42 '* ( ; I # ! 27.9 \ .27Y .m .m (ag" 601 .w)5 2x17 .2715 (agc 4 0 ) 241 .m 22% (age 2 0 ) .243 .a .mFi ( agc 37.9) 35

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In this and all subsequent calculations, thc age of 27.9 years appears since this is thc agc rcported by Hertzberg in ref 23 to be the average age of the Air Force flying population. This value is bascd upon data taken ip 1950, so that this average age may have shifted to some extent in the iiitcrvcning years. \Jsing Ruffs data (ref 13) as a basis for estimating the force at which permanent damagc occurs to the vertehral mlurpn, it is now possible to define the cwmplcte dynamic mcn1c:l o f thc. ~ I J - i i i m h d Y in the spinal direction. Ruffs data indicates that thcrc is a 50%pro1)al)ilityo f Iwririanc:iit damagc at a steady-state value of 20.2 C. and at an age of 32.5 years. Ttic rcsiilts iIr(* Imwvilcul in table VI and in figure 31. TABLE VI DYNAMIC MODEL OF THE HUMAN BODY-I'OSITIVE SPINAL DIRECTION SingleDegreeof Freedom, Linear Model Age (Years) 20 27.9" 40 60 Natural Frequency 8.55 8.45 8.13 7.08 w/2m (cps) .228 230 .237 .264 Damping Ratio (3"" 50%Injury Levels: 23.05 21.30 18.45 13.78 Steady State -Ycrit ( G ) ImpulsiveVelocity ChangePo*-AV 21.00 19.75 18.12 16.78 (fps) 'Average age of USAF flying population. 'At a peak DRI of 15 G . "'Lower AV values may cause injury due to shock wave effect.. in curc1)rospinal lliiicl o r in v i s ( x w HEAD INVOLVEMENT IN SPINAL TOLERANCE In addition to the data already presented, figure 31 shows a somcwliat lowcr to1c.r;tric.c Ic.vc.l below 0.01 seconds due to involvement of the head. This value was obtained from ;I serics of drop tests conducted by Swearingen using live human subjects. Thcsc studies are reportcd in rc:f 3 : ~ r d ref 4, and the subjective comment data from this test series was made availablc to the authors. Of iinmediate interest is the fact that it was possible to use the subjective comments to oblairi an estimate of the average subjective end point in an impact situation. The tests involved human subjects dropped from various heights on a vertical test rig. 130th the seuted and standing positions were investigated, although this review is restricted to the scatcd position. All of the testing involved decelerations parallel to the subject's spine exccpt f o r a f c ~ special cases which are not considered here. Most of the tests were cwnductcd with a hydraulic snubbing dcvicc in the h s c : of t h t c d ri!:. Total :ivailable stroke on the snubber was 1inch. I\ few tests were. Lu)ndiic*ted w i t h ;I rigicl s o a t a r i t l hasr, that is, with the snqbber locked out. Thcsc: arc- of pnrticiilar intcrc.st hc,rc., sinw Iticy ~ r i - sti tlite riltrashort pcrid impacts in which vclocity ~11;irigc:govcrns thc. rcsp)nsc.

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\ Fgum30. Varicltlon of h.nQlcillation Damping Ratio With Age and P w k DRI. Figure 31. Spinal Positive lniury Cune for 50% Probability of a Compressive Fmcture Due to o Rectangular Acceleration Pulse. 37

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The method for using the subjective reports in the drop test situation involved the development of a subjective severity scale. All of the subjective reports were scanned in order to beconic familiar with the terminology used by the subjects, after which the following scale was established Level 1 No subjective report Level 2 Slight jolt or shock or feeling of discomfort Level 3 Definite jolt or shock, mild ache, severe discomfort Level 4 Severe jolt or shock,definite ache, slight and brief pain Level 5 Definite pain Note that the term "shock is used in a lay sense and not in a medical sense. This field of rnultipliers was then established as follows: Multiplier of one -Symptom restricted to one portion of the body (other than the head). Multiplier of two - Symptom was reported for several portions o f the body or for the head alone. Multiplier of three - Symptom reported for entire body or for several portions of the body plus the head. Dy using the multipliers, each level of severity was weighed on two bases, namely, the extent of the subjective feeling and the involvement of the head. Each acceleration exposure was rated using the scales and multipliers just described. However, of major importance is the wnditiori in which a rigid seat was dropped onto a rigid base. The average subjective end point from this test series is eqriivalcnt to an impact vc:lcwity of 1I feet per second and the maximum recorded severity using the siibjectivc s<vc:ritysc:ilc-was eqiiivdent to a velocity change of 14 feet per second. See figlire 32.The age o f the siibjc:c*tsiisc-d in this test series range from 25 to 40 with an average in the 30-35 year range. Using the dynamic- i n c d c 4 previously developed, the critical velocity change in an impact test should have twen lwtwccii JH and 20 feet per second. An explanation for the variation in the two sets of data can he fount1 i n the: sribjwtivc. rt.. ports. In many cases, the impact test results indicated involvernent o f t h c : hcacl or tlic: a t d o r i i i i v i l or thoracic viscera. We hypothesized that very short risc: tiriic accelcration iiipirts m a y rcwll i r k the generation of shock waves in media such as the spinal coliimrr, the! ccrc1)rospiii;iI H i i i d o r - iit the essentially liquid viscera. Unfortunately, the generation of shock waves is principally a matter of input accrkrat ioii rise time so that further tests at various rise times would be required t o dcfine fully thc- mcch:mi m s involved. At any rate, it should always be kept in mind that head and viscera involvcriicwt may occur in such short rise time acceleration pulses. A t prescnt. this does not appcar to 1w ot practical si@lifiance,since most real acceleration pulses havc reasonably Ion&risc times. 1IOWCTC'J, this could prescmt a prohlem in a future application. 38

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, CONCLUSIONS The dynamic model of the human body that has just been described is felt to be applicable to those situations in which the acceleration is applied in such a manner that the body is pushed down into the seat. This is the most common and critical mode of loading the body in that ejection .seats, escape capsules, and landing inpacts apply their principal accelerations in this direction. It is possible, of course,to apply an acceleration in the opposite direction so that the forces tend e I I / I I I / Figure 32. Varioiion in Sub/.ctive Severity with Velocity Change f e r Four lest Conditions in F A A Tests. to lift the body out of the seat. This is frequently called negative acceleration or ncgativc. spinirl acceleration. The model just described for the positive spinal direction is not dircctly applicaldr: t o the negative spinal direction. There are two major differences between the positive spinal and ncgativc spinal ; i c t d c b r i t t i o r l cases. In the first place, the human spinal column is arranged in such a riiaiiner that the str(vtKlli of the individual vertebrae increase for those lower in thc spinal column. This is a sort o f ri;ittir:iI adaptation of the bone niaterial since the lower vertebrae are srihjtutcxl to largvr loads caiirclIy the obvious fact that a seater percentage of the total body is a h v c the lowcr vcrtebrac. TIM,r(' lationship between the load applied to the individual vertebra and position in the spinal coluiiii and breaking strength and position in the spinal column is shown in figure 33. Now, if the loading is reversed, the largest loads will be applied to thc weakcast vertc-hrac- For those vertebrae upon which data is available, the relationship is that as shown in figlirth 3 I lowever, the data is missing for the top thoracic vertebra and cervical vertebra. As a result, t h - v is no precise way to estimate the point at which the first failure would occur. At a n y rat(,, thc. nori-

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symmetrical nature of the spinal column in terms of element breaking strength obviously makes the negative acceleration case a far difFerent situation from the positive spinal case. 111 7 0 79 L4 15 VEQT ri3e4 figure 33. A Com rimof Vertebral Breaking Strength and A& bad.(From Ruff, ref 13). figwre 34. Vertebral Strength if Full Load is R e a d Through Shouldon in a Negative Spinal Acceleration. The second difference between the positive and negative spinal cases is that in the latter thv restraint system effects are of major importance in determining how the load is applied t o 1 1 1 ~ spinal column. If only a bp belt is used, then the spinal column will be pl;i~'(din tension clirririg a negative spinal acceleration. On the other hand, if only a shouldcr harncss is used, then the spinal column will be placed in compression and the situation cited in thc: previous paragraph will occur. Of course the load will probably be divided in some manner between a shorildcI har- 40

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ness and a lap belt, in which case the loading on the spinal column is a function of the relative deflections of the restraint elements. From the preceding discussion, the basic dynamic model of the human body in the spinal direction that has been described is really applicable only to the positive spinal situation. In using this spinal model it must be remembered the restraint harness has an effect on the shape of the vertebral column. The present positive spinal model of the human body assumes good positioning of the vertebral column, so improper positioning must be taken into account in any rcal situation by reducing the load values at which damage occurs. One other factor to be kept in rnincl is the effect of multiple vector acceleration forces. If a spinal accelcration also has a c*orrtponcwt in the transverse direction, the force may tend to bend the vertebral colrinin and C;UISC t . o l l l m r \ 1)ucklingto occur more readily. Since the spine is made up of series of pin-jointed short c w l i m i i i ~ . I t has low resistance to buckling. The prediction of maximum loads that will injure tlie vcvtclmic. intist be expected to be less for such cases. To summarize the situation with respect to the dynamic model of the human lwdy in thc seated position subjected to a positive spinal acceleration, the following information is availahlc:: The natural frequency, damping coefficient, and critical force levels in the spinal direction have been estimated, assuming proper positioning, and agree with data from scvcral different types of experiment. The effect of age on both the natural frequency and critical force has been estimated from cadaver data and appears to be consistent with results from other types of experimcnt. The nonlinearity of the spinal column has been evaluated. The lack of information on negative spinal loadings has prevented development of a suitablc dynamic model although some of the factors involved are presented and no serious handicap to the eventugl development of such a model is foreseen. The degrading effect of arbitrary vector accelerations must he cwnsidercd i r i o1)vr;tIioii;tl situations. 41

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Section VI A DYNAMIC MODEL OF THE BODY IN THE TRANSVERSE DIRECTION In the transverse direction, that is, with the acceleration applied through the chest, either front-to-back or back-to-front, the situation is somewhat more complicated than in thc spinal direction. At least, it is much more difficult to specify precisely the mechanisms involved i n t h c txdy’s response to accelerption. This is because there are a number of organs and stnictiiral ( ~ 1 ~ - rnents involved in the response to transverse accelerations. There are two sources of data concerning the response of the body to triinsvcrsc’ accclcriitioris. In the impact regime, t h q e are a number of recorded accidental free falls i n wliicli thc victirii impacted in the full supine or full prone positions. DeHaven (ref 18) pioneered in the analysis of such data. The second source of data is from experimental sled runs conducted with the sribjcct sitting facing either forward or aft (ref. 5 ) . There is a relatively large amount of the latter ciati1 available but, for the obvious reasons, only a few injury points are available. DeHaven recorded same remarkable cases of survival involving rather enormous frce fall (listances. His data indicated that a human being would be injured, but could survive an impact velocity of 80 feet per second. DeHaven used data involving jumps or falls from buildings, as a general rule, but there is now another source of free fall data that he did not consider; thc accident reports of the American Alpine Club (ref 24, 25,and 26). These data werc analyzed to ohtain an independent estimate of the critical impact velocity. Briefly, the method used by the authors in analyzing the American Alpine Club statistics was to assign an injury severity rating to each reported accident, using the available information in the accident report and rating the severity with the scale developed by Aviation Crash Injury l h - search at the Cornell Aeronautical Laboratories. Figure 35 shows the individual accidcnts plotlcd against the velocity changes involved. From figure 35, note that a few accidents involved head impact and that, in general, thewaccidents resulted in a higher injury severity rating than equivalent accidents where no hcad i i i i - pact was involved. Also note that a few impacts at extreme velocities resulted in dcath, but that death in these cases is a qualitative and not a quantitative measure. In other words, injury scvcbrity rating number 10 represents a fatality resulting from lethal injuries in three or more regions o f t l i ( > body. Obviously, a case could involve just three regions of the body or could involve total r n ~ clianica! demolition of the body. At any rate, the extreme velocity and death points can l)c> igiiorctc! from t h e standpoint of the remainder of this analysis, because of this scaling artifact. A straight best-fit line was calculated using the method of least squares arid i s shourti iri figiti.t% 36. (‘sing this line as representative of the data recorded, the relationship Ixtwcc!ri i r t j i i i ) scvc*rit\ and iinpact velocity could be specified quite precisely. The midpoint of the injury scvc:i-it!, sc.iilc. w a s takcn as the point representing !%% probability of injury in the same sensc as iiscc! i n o t l i c ~ areas o f human l d y dynamics. Using this value, an estimate of 53 fect pcr sccond is f o ~ i i i di o 1 the. 507.probabilitv of injury level. Note that this is 27 feet per second below the vnliic- o l ) t ; i i i l c ~ t l froiii 1)(-Haven’sresults. The disparity is shown in figpre 37 where the 1)c.I Iavcn points arc’ ~ ) l o t t t u l rclati.cB to the 53 feet per second line derived from thc mountaineer frce fall dat;i. The. ohious question that arises is what is the reason for the dislxirity bc:[wcwi t l i c : t w o 1’0stilts? A relatively simple txxplanation is at hand. The lIe~€Iavondata rcprr:st.nts ;I sc-ric.s of iriirii<,- 42

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5 I 0 0 Rpum35. Mountmimeringhfill Data from American Alpino Club Add.nt Ram. K 4 ,'/ /,' / / /

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ulous survivals of free falls from great heights. In other words, DeHaven used aril!. h t C ipoints 111 which the individuals survived the free fall incident, which constitutes a biased sanq)lt~t i o i i i .i statistical standpoint. The American Alpine Club data, on the other hand, represents CAW^ i n which individuals were injured or killed at various impact velocity levels. Thus, the mount.i.i n c i ~ free fall data can be considered more representative in a statistical sense and the estimate o f 5 3 f t v t per second for the probability of injury level is considered to be a reasonably good estirnatcb of the actual capability qf the human body to withstand transverse impact. There is a rehtively large amount of data on the exposure of the human body to short-tciiii transverse accelerations, but very few injuries have been recorded in such tests. Therc.forc., i t I \ somewhat more difficultto specify precisely the probability of injury levels in this rcgiriic.. I%(\ available data points are plotted in figure 38 relative to the 53 feet per second tolcrarrcc. Iiiic. and 4 D A i A 0 0 flgurs 37. D.Hawn F r e e Fall Data Venus Results of AAC Accident Analysis. ;ilso relative to the "minor or no injury" lihe. Using a pdse driratiori of ; i ~ ) ~ ~ r o x i ~ ~ i ~ i ~ ( ~ l ~ ~0.0IS { Y . - oiicts as indicative of the transition point between the iinpaet region and t l l o rcy.$ilic. i i i w l i i c 4 i : I C . cclcration pcak is the governing factor, all of the sled tests data points involving iiijiiry I : ~ l l;il)o,(* the extended minor or fio injury line, and below the 50%proha1)ility of injiiry line. Thtis, ( I N : s1io1-I pried data, although sprtrse, tend to confirm the vclocity chaiigc ctstirnatcs. I h w t l s c - of I I I C . r.c>I;itivc lack of data and mkpown validity of thc cxistirig data, the rcstilts of this aiialysis r i i i i s ~ t J c * viewed in A sonwwhat negative light, that is, the clata is consistcnt within itscblf h i i t t l o c ~i i o t iwo vide a high degrcc of confidence or very m i d l precision. 44

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regime, then the comer duration becomes 0.0411 seconds. If we take the damping ratio value of ;=0.3 from impedance measurements (ref 10) we get the following results for the transverse direction: P A R A M E T E R SMALL A M P L 7 T U D E l M P E N D A N C E IMPACT (Semisupine Position) Subject age Darnping coefficient C o/% 47.0 years 47.0 years 0.3 0.23 7.41 9.68cps Note that, due to nonlinearities of the system, the effective frequency under impact loading is 30%higher than the value from the impedance measurements. This is less than for the spinal case, where an increase of over 40% is indicated in section V of this report. O . D-

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The dynamic model of the human body in the transverse direction can now be suminarized as shown in table VII. TABLE VI1 DYNAMIC MODEL OF THE HUMAN BODY - TRANSVERSE SINGLE DEGREE OF FREEDOM LINEAR MODEL Natural Frequency-w/Pm-cps 9.68 Damping Ratio-; 50% Injury Levels: Steady State-Yc,it-G .23 40 Impulsive Velocity Change-AV-fps 53 Because of the lack qf data, the above transverse body model must be assumed to he invariant with age, although additional data may show a variation with age such as that reported in section V. Similary, the lack of data prevents even a crude estimate of the variation in probability of injury levels. However, the injury severity levels calculated from the mountaineer free fall data can be extrapolated to the short-term region for approximate estimates of injury severity. The investigator muat familiarize himself with the ACIR injury severity scale, which can be found in an appendix to ref eS. 48

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Section VI1 OTHER DYNAMIC MODELS OF THE HUMAN BODY In the preceding sections, dynamic models for the positive spinal direction and for both the positive and negative transverse directions were described. In the transverse dynamic model, the body is assumed to be symmetrical. When more data are available, it may well be that two transverse models will be required, one for the positive direction and one for the negative. The single model developed at the present time may be used for engineering purposes until more refined models can be constructed. There is virtually no data available concerning the response of the human 1 ~ d yto lateral ;it*celerations. One series of tests has been conducted on rhesus monkeys b y the Aerospacc Medical Research Laboratory at Wright-Patterson Air Force Base, in anticipation of further testing WIt h human beings. Such human testing has been conducted, but it was an evaluation of an oIEerationa1 restraint system and did not result in end point data, so it still is not possible to develop other than a hypothetical lateral dynamic model of the human body. For engineering purposes, thc transverse dynamic model of the body may be used since no other information is available. Nowever, the critical loads in the lateral direction may turn out to be significantly less. In addition to the s(x major acceleration vectors applied to the whole body, the response o f the head to acceleration inputs must be taken into account under certain circumstances. Because of the lack of suitable experimental data, the confidence in existing dynamic models of the human head is fairly low. However, the natural frequency and steady-state acceleration tolerance of the head are greater than for the torso, in either the transverse or spinal directions. (This assumes a reasonable amount of cwshioning material between the head and the input acceleration surface provides sufficient attenuation to raise the head injury lwels above those for the torso.) Thus, there is very little head injury data available from operational or accident statistics. 47

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References 1. Kornhauser, Murray, and Arnold Gold, “Application of the Impact Sensitivity Method of Animate Structures,” Presented at the Symposium on Impact Acceleration Stress under the auspices of the National Academy of Sciences - National Research Council, Brooks Air For(e Base, Texas, 27-29 November 1961. 2. Payne, Peter R., “Optimization of Human Restraint Systems for Short-Period Accelerations,” American Society of Mechanical Engineers Paper No. 63-WA-277, Presented at thc \ V i n t c i Annual Meeting,Philadelphia, Pennsylvania, 17-22 November 1963. 3. Swearingen, John J. et al., “Human Voluntary Tolerance to Vertical Iinpact,” Aeroqv?,ci(( Medicine, Vol31, pp 089-998,December 1960. 4. Swearingen, John J., et al., Protection of Shipboard Personnel Against the Effects of Sever(. Short-Lived Upward Forces Resulting from Underwater Explosions, Final report on the Contract NAonr 104-51.Civial Aeromedical Research Institute, Oklahoma City, Oklahoma, January 1960. 5. Stapp, John P., Human Exposure to Linear Decekrution, 11. The Forward Puciry: I’o.sition utul the Development of a Crash Hardness, AFTR-15915, Pt. 2, Wright Air I)evtlopiricnt Centcbr, Wright-Pattarson Air Force Base, Ohio, December 1951. 6. Daisy Tmck Test, 22 A4ay 1958 to 9 ]u&j1959,Air Force Missile Development Center Test k - port No. 59-14, Holloman Air Force Base, New Mexico, December 1959. 7. Ddpy Decelerator TeH, 13 Jury 1959 to 13 April 1960, Air Force Missile Developinent Canter MDW Test Report No. 60-4,Holloman Air Force Base, New Mexico, July 1960. 8. Daisy Track Test 271 to 337,4 February to 19 May 1958, Aeromedical Field l.atmratory, Directorate of Research and Development, Test Report No. 8, Holloman Air Force I3asc, Nvw Mexico, November 1958. 9. Coermann, Rolf R., The Mechanical Impedance of the Human Body in Sitting utul Slaticlitig Positions at Low Frequencies, ASD TR 61-492, Aerospace Medical Lalwratory, Acroii;iiiticxl Systems Divisioo, Wright-Pattenon Air Force Base, Ohio, Septeintwr 1961 ( A l l 113 178). 10. Coermann, Rolf R., “Comparison of the Dynamic Characteristics o f I)iimmics, Anirnals, ;inti Man,” Presented at the Symposium on Impact Acceleration Stress iindcr t h c Aiispicw of t l i c . National Academy of Sciences - National Research Council, Hrcmks Air Forw Ihsc., ‘I‘t-xah, !Z’-29 November 1961. 11. Magid, Edward B., et al., Physiological and Mechanical Reqwonse of the il11nu1r1 10 Lorrgirrtlir~ a1 Whok-Body Vibration as Determined by Subjective Response, MRL-TI)]{-62-66, Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, Ohio, June 1962 ( A I ) 288 877). 12. Mandel, Morris J., One-Minute Tobrlanct: in Man to Vertical Sinusoidul Vihrution i n thc Si/ting Position, AMRL-TR-62-121, Aerospace Medical Research Laboratory. Wright-Patterson Air Force Base, Ohio, October 1962 (AD 292 704). 13. Ruff, Siegfried, “Brief Acceleration: Less Than One Second,” German A i d i o n Mcdicirw in World War Z I , Vol. I, Chapter VI-C, Department of the Air Force, April 1950. 48

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I -- - --.--._ . - ~ . . - . --.. -. I .1” , 21. Hertzberg, H. T.E. (Ed), Annotated Bibliograpb of Applied Physical Anthrgobgy in fluman Engineering, WADC TR 5630, Wright Air Development Center, Wright-Patterson Air Force Base, Ohio, May 1958 ( A D 1%622). 22. Freeman, H. E., W. C. Boyce, and C.F. Gell, Investigation of a Personnel Restraint System for Adwnced Manned Flight Vehicles, AMRGTDR-62-128, Aerospace Medical Rcsmrch Laboratory, Wright-Petterson Air Force Base, Ohio, December 1962 (AD 431 218). 23. Barrett, Stanley, and Peter R. Payne, Resporue of a Linear Damped Dynamic System io SC- &cted AcceIeration Inputs, AMRL-TR45-40, Aerospace Medical Research Lahoriitoricy, Wright-Patterson Air Force Base,Ohio, April 1965 (AD 616 643). 24. Jacobsen, L. S.,and R. S. Ayre (Ed), ETg:;.cering Vibrations, McGraw-Hill R m k CO.,N~:W York, 1958. 25. Latham, F., “A Study in Body Ballistics: Seat Ejection,” Proceedings of the Royal Socict?/ of Lo*, Series B -Biologic Sciences, V O ~147, pp 121-139, 17 December 1957. 26. Goldman, D. E., and H. E. von Gierke, “Effects of Shock and Vibration on Man,” Cyril M. Hams (Ed), Shock aruE Vibmtion Handbook, Vol3, Engineering Design, Chapter 44, pp 44-1 through 4451, McGraw Hill Book Co., New York, 1961. 27. Clarke, N.P., E. B. Weis, Jr., J. W.Brinklcy, and W. E. Templo, LaleraE I r n r M c t To1c.raru.p t Studies in Support of APOLLO, AMRIA Memorandum M-29, Aerospace Medical IIcscarc.Il Laboratories, Wnght-Patterson Air Force Base, Ohio, 1October 1962. i I 49

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UNCLASSIFIED Security Classification DOCWENT CONTROL DATA - R b D Frost Engineering Development Corp. 3910 South Kalamath Englewood, Colorado Dynamic Models of the Human Body . O E S C R I P T I V E N O T E S ( n p * of report and inclusive dates) . AUTHORIS) (First nmmo. mi&* Inltlsl. iaet name) Peter R. Payne R E P O R T D A T E November 1969 m. C O N T R A C T OR G R A N T NO. AF 33(657)-9514 b. PROJECT NO. 6301 Task No. 630102 d. ._ 1 S U P P L E W E N T A R V N O T E S jb FORM I 4 0 Y O ¶ 1473 UNCLASSIFIED Zb. GROUP N / A - 78. T O T A L NO. O F PACES ?b. NO O F R E F S 49 27 9.. ORIGINATOA'S R E P O R T NUMBERIS) Sb. O T H E R R E P O R T NO(5) [Any other numbera I h m l may be sonl&ed thls report) AM RL- TR- 66- 157 12. SPONSORING M I L I T A R Y A C T I V I T Y Aerospace Medical Research Labratow Aerospace Medical Div. A i r Force Systems Command, Wright-Patterson AFB Ufir 343 3 - UNCLASSIFIED - Securihr Classifirn*;--

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UNCLASSIFIED security CIasaification - I 4 K K V W O R D S Acceleration Human Tolerance Dynamic Response Index Mathematical Models Biodynamics Spinal Injury L I N K A L I N K S L I N K C R O L W T R O L l - - UNCLASSIFIED Security Classification