Trends In Judo Biomechanics Researches

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ENTE PER LE NUOVE TECNOLOGIE L'ENERGIA E L'AMBIENTE

VALUTAZIONE DEL COSTO ENERGETICO DEGLI SPORT DI COMBATTIMENTO IN .REMOTE SENSINGm PROGRESS REPORT 8 New trends in the judo and wrestling Biomechanics research A. SACRIPANTI E.N.E.A. Direzione centrale Sicurezza e Protezione Sanitaria Coordinatore Federazione Italiana Lotta, Pesi, Judo

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M. FAINA, G. GUIDI C.O.N.I. Istituto Scienze dello Sport Dipartimertto di Fisiologia e biomeccanica (Direttore Scientifico A. DAL MONTE)

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M. FABBRI, R. MASO, L. ROSSI ENEA Area Energia e Innovazione Centro Ricerche Energia Casaccia, Roma

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Paper presented at the *%

EIGHTH MEETING OF THE EUROPEAN SOCIETY OF BIOMECHANICS June 21-24, 1992 Rome Italy

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Testo pervenuto nel luglio 1992

Gli autori ringraziano i gruppi sportivi della GUARDIA FORESTALE e GUARDIA DI FINANZA per la gentile e fattiva collaborazione prestata, nel corso della ricerca

I contenuti tecnico-scientifici dei rapporti tecnici dell'ENEA rispecchiano l'opinione degli autori e non necessariamente quella dell'ente.

ABSTRACT In this report the aim of a CONI (Italian Olimpic Commitee) - ENEA (Italian Commitee for Technology Innovation, Energy and Environment) - FILPJ (Italian Federation of Wrestling, Weigthlifting and Judo) joint research is presented. The main goal is to obtain quantitative data on energy consumption of Judo and Wrestling actual competition, by athletesf thernial emission. In the text the first results and the future trends of performed in Italy are this very complex experienke presented. In the appendix it is explained the first mathematical theory for 'both the problems: - analysis of competition on the basis of statistica1 physics interaction between athletes on the basis of variational analysis.

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RIASSUNTO

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In questo rapporto viene presentata una ricerca congiunta fra CONI (Comitato Olimpico Italiano), ENEA (Ente per le Nuove tecnologie, l'Energia e l'Ambiente) ed il FILPJ (Federazione Italiana Lotta, Pesi e Judo). Lo scopo principale della ricerca è quello di ottenere dati quantitativi sul consumo energetico di atleti in competizione tramite rilevamento di emissione termica. Nell'appendice viene ililustrata la prima teorka matematica per entrambi i problemi di analisi della competizione su basi di fisica statistica e di interazioni fra atleti su base di analisi variazionale.

INDEX

1.

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INTRODUCTION

2.

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HISTORICAL BACKGROUND

3.

- DESCRIPTIQN OF EXPERIENCES

4. 5.

- APPENDIX - B.IBLIOGRAPHY

1. INTRODUCTION

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Knowledge remains partial in every field of Science, even thogh it records steady increase thanks to the advanced thecnologies and the theoretical and experimental researchers; thus the advanced thecnologies and the theoretical intuitions enabled us to perfect scientific knowledge in the field o£ macrothermophysiology. A joint research carried out by CONI, ENEA and FILPJ started at the end of 1989 designed to assess the athletefs energy cost in effettive competition. Considering the high complexity of this issue, it was recognized the need to tackle it through an integrated multidisciplinary approach, by resprting to the knowledge in the physiological biomechanics and to the related specific equipment provided by CONI laboratories, to the sophisticated processing methods and instruments provided by ENEA and finally to athletes and to the technical and specialized knowledge in the physical biomechanics by FILPJ. The "simple" idea is td consider athletes as complex thermal machines. The joint application of the principles of thermodynamics must allows us consequently to statistically assess the average work carried out by athletes during competition. Obviosly, from a theoretical point of view, the problem could be rapidly solved if it was possible to evaluate the athletesf direct calorimetry during their performance. Since this is technically impossible, it is common practice in sport to assess the athletefs work by means o,$ the "simpler" indirect calorimetry. This means that through an appropriate mechanical equivalent o£ the oxygen we can trace back - through the fuel kinetics - the work carried out in laboratory which, for many sports, is made day by day more similar to the efiective competitive load. In our time, in the case of fighting sports the few experimental data are indeed limited and it is virtually impossible to extrapolate reliable data from these laboratory results which can allow an adequate training based on scientific principles. The retracing of direct calorimetry by means of the energy equations of the man-environment heat exchange is therefore possible. Doing so the athletefs body superficial average temperature needs to be directly reckoned, because al1 heat transfers are regulated by it.

On the basis of the athletesl heat-energy emission recorded by remote sensing techniques, or retraced by energy exchange equations, more reliable quantitative data can be obtained on the competition without affecting the performace.

1. HISTORICAL BACKGROUND

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The neapolitan Alfonso Borelli was 'one of the first scientists who conceptually associated the oxygen consumption with the muscolar activity. Indeed, in the chapter entitled "De usu respirationis" of his book "De Motu Animalium" (1680), he describes his own individual experience made some years before on the Etna. The following titles of paragraphs. show that such a mechanism was already clear in his mind: "Through breathing, air particles mix with blood", "The mixture of air introduced in blood throug breathing produces and preserves anima1 life", "This is t& reason why breathing is more difficult and rapid during pressing motion and muscolar activity", "That is why muscolar activity in rarefied air causes difficultygin breathing" However, the first scientists who developed laboratory experiments in the fieid of thermophysiology were Lavoisier, Laplace and Sequin between 1775 and 1785. They detected on Guinea pigs at first and then on men that - under confortable temperature conditions - the oxygen consumption was at its lowest before eating; sligthly increased when the environment temperature decreased; sharply increased after food intake and ever more when working. In mid-XIX century the chemical-physical studies by Regnault and Reiset were developed. They sought to de.mostrate that oxydation was the main source of anima1 heat by using the oxygen consumption as the simple measure of heat production. Hoping to relate life processes to the well-known physical laws, Reubner, Helmholtz and other verifed the principle of energy conservation both for biosystems and inanimated systems, defined the basal metabolic temperatu~e and discovered that the hot blood biosystems were basically homoiothermic. Mayer was the first physicist to develop the idea of equating an anima1 with a sort of thermal machine where the breathing hèat is partially turned into muscolar activity. M. Hirn sought to experimentally demonstrate this hypothesis for man by locking an individual in a thermal chamber and placing two rubber pipes in his mouth - the former for air int-ake and the latter for emission gases which' werp thén 'm~rasukea'in te'rms-Q£ oxygen consumed and i1 carbon ' h?bxide produced. The breathing chemical and thermal effects were thus evaluated both under basal and working

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conditions - that is by lifting his own weight on the circumference of a mobile wheel. Indeed the temperature increase in the chamber was measured unti1 when - becoming constant - the radiation emission of the walls was equivalent to the heat produced by the body within it. Afterwards, the individua1 was replaced by a burner (Bunsen jet) regulated in such a way to keep air in the chamber at the same constant temperature. From the volume of the gas burnt it was then possible to infer the heat produced by the combustion and, by way of analogy, the quantity of heat produced by the human body in that given time. This interesting experience led to the result that 30 grams of oxygen consumed corresponded to 150 calories. Considering the time element,'it is appropriate to think over the remarkable accuracy Of the results obtained, since this value of the mechanical equivalent is still used to make rapid calculations in the field of Industria1 Medicine.

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3. DESCRIPTION OF EXPERIENCES

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The aim of the research is to make possible actualcompetition experimental study by means of thermovision cameras. Ti11 now a TV cameia AGA 782 (fig. l ) recorded the athletesf heat emission in the infrared band on a magnetic tape, but it is foreseen a more modern device as the HUGRES PROBEY SYSTEM that display in rea1 time a thermal map in 256 different colours (fig. 2). We can thus obtain quantitative data related to the athletest thermo-energy dispersion which accounts for 75-80 % 'of the overall c~nsumptionof the metabolic energy produced. The data on heat recorded by - 4 photograms a minute are analyzed by a highly specialized system for Image Processing, tha E.D.I. (ENEA ~ I G I T A LI M G E R Y ) system , (fig. 3 ) . This one by means of appropriate programs and procedures is capable of provtding processing-factors as: - the statistica1 survey on the "grey tones" such as maximum, minimum, average and standard deviation, - the construction o£ appropiate histograms, - the cumulative integral of the images in term o£ energy, - the "inverse area" integral of the images, - the "smoothing treatment" of the phenomenon kinetic, - the kinetic trend of the phenomenon, - the electronic "cleaning" of the images, - the electronic "colouringl' of the images. In order to abtain more reliable data, images are subjected to the "electronic" cleaning system, thereby al1 the interferences o£ the environmen-t eliminating background which distorts and downgrades the obtained results. A further possibility of the system, already mentioned, is that o£ providing images trough the electronk pseudo-color technique. This allows to obtain heat maps of the athletesf bodies on high definition screen (fig. 4). These maps enable us to identify the most used muscles in performance, that is "the moast warmed upw one. ThiS knowledge is useful £or technical-related physical preparation, but also £or averting some possible traumatisms in contest situation. In thic field the CONI-ENEA-FILPJ research was awarded the second prize, in the "GRIFO D'ORO" annua1 competition £or the benefits minimizing risks in human activities. The initial stage of the research allowed to-consider the gauged thermal emission as a function of the oxygen

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intake, detected telemetrically by a sophisticated CONI instrument (Cosmed K2 system - fig. 9 ) , by means of an athlete placed on an engine conveyor belt running at costant speed for a given time period (fig. 10.). This was possible through the application of the thermodyfidimic principle of the states,~ for athletes under energy conservation which conditions of vitually neglegible "physicaln work and aerobic "steady-state", that the oxygen uptake and thermal emissiop were roughly equal. Alledgedly, the used technologies allowed, for the first time, to follow the evolution of kinetics of both phenomena (oxygen input and radiation output), thereby enabling us to try to find the functional relation linking them. Considering the biochemical origin of athleters metabolic *energy for the aerobic the "steady-state" conditions - it was possible to associate with a good degree of approximation - the oxygen ineut and the heat output by means of a simple relation; whereas the relation connecting the anaerobic-lactacid energy sources with the heat output is more complex and still unknown. In this respect, the first functional links are being attempted during experiments. A further step was to provide the attempt to measure the kinetics of the "athletets superficial average temperature" by direct methods. For this purpose a set of 16 thermocouples, with special calibration, was used and suitably placed on the athletefs body (fig. 11 ) ; the data mesured in rea1 time were recorded on magnetic tape HP data logger 3497A and the average temperature was computed by HP-9816A computer, with the Hardy, du ~ o i s and Soderstrom formula: Tp = (0.07 T1 + 0.14 T2 + 0.05 T3 + 0.07 T4 + 0.13 T5 + . + 0.19 T6 + 0.35 T7) where T1 trough T7 are head, arms, hands, feet, legs, thigs and trunk average temperatures and the coefficients (which sum is one) are 'the mean weighted surfaces bodyts parts. The knowledge of kinetics of the average superf icial temperature let us intercalibrate them, with oxygen input and thermal infrared output, to obtain the first gross intercomparison of instruments. The next two steps (fig.12) were related first to the rough extimation of Judogi shielding 'ef fect, against thermal long-wave infrared emission (in the CONI laboratories in ROME) and afterwards to the quantitative evaluation of this efect (performing the experiment in a climatic chamber,

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assembled in theSENEA-CASACCIA laboratories fig. 13 ), to have more reliable data from a better controlleà experimental situation. At the same time the theoretical knowled'ge about competition was improved with the first physical-mathemat.ica1 theory of Judo contest to state and carry out the most important physical parameters and to have a first rough extimation of average energy expenditure in competition. For the mean kinetic energy of couple of athletest system, related to-the absolute velocity, changing the Einsteints relation the result was 0.2 of overall oxygen consumption. This problem is discussed in the appendix. The last but one experiment carried out was the fiist of the larger series in pragress and was related to study the oxygen input partition in heat emission and physical work. The physical work, lifting up and down 40 Kg, was separate in two phases: "negativen (pulling down) ,and "positive" (lifting This differentia3ion up) against the gravity force - fig.6 is necessary because, if the total physical work, being cyclic, in conservative field will be zero, 'the athletes' rating perforwnces are different in eaqh of the two paths. last one experiment m s connected to study The different kind of work (a predefined physical work'of 150 J/s using a cycloergometers with two definite numbers of thrusts fig. I - ) and, in the same session by two on pedals thermocameras, to define the work related to some throwing techniques (one technique of couple and one-of physical lever at frequence of 20 throwings a minute - fig.3). The theoretical approch is concerned with equdfions .. describing, in forecasting form, the sweating kinetics of athletes. These thermodynamical equations, not c&npletely known or tested, are very important for studying energy exchanges between athletes and external environment. The problem is to modelize simultaneously heat and mass transier as evaporation by natura1 convection and mass . tranfer by diffusion, throbgh integuments, in transient heat balance during exercise as function of free atmosphere vapor pressure, atmspheric pressur,bodyfs temperature, dimensions and equivalent temperature. At the present time the problem is not completely solved, but some approximative solutions are ready and will be used in the condictions of negligible physical work, during which energy input is equa1 to &nergy output, unless higher rank negligible factors, The use is in an iterative

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Fig. 4 Athlete's Thermografhic Image

Fig. 6 Experience with Phisical Work

Fig. 7 A-B Experience with Cycloergometer

Fig. 8 Judo Throwing Techniques

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4. APPENDIX BIOMECHANICS QF JUDO CONTEST Theoretical-physical-biomechanical analysis is a powerful method of investigation which, when fully used, allows analytically difficult problem to be sqlved with simple and somewhat elegant means. Its basic instruments are differential analysis and structural synthesis. The former consists of dividing the technical performance into severa1 categories (e.9.: holds, posture, unbalance, throw, ect.); if we are to understand in a direct way the problems relating to the correct use of propulsive forces into space, the above division prove to be a useful semplification. The latter consists of the phase through which, the semplified mechanisms or the correlated subsets of technical performance are reinterpreted as a whole. Later, this method will be applied to define contest and interaction in it (throwings). The comparative study through differential analysis carried out on a and structural syntesis will be consecutive-phase basis (fig. 14). In order to obtain analytical proof of the contest as motion and interaction, reference must be made to definitions o£ : "biomechanical athlete" and,@lcoupleof athletes" system, they being the basic preliminary step whereby such a goal may be reached. Therefore, with the due approximation, we shall define the biomechanical athlete as a solid of varying geometry and of cylindrical symmetry, that may assume conditions of different positions, normally placed in unstable equilibrium in the gravitational iield on a plane area with friction, who through the articular joints is abPe to perform only certain rotations. The biomechanical athlete, thus defined, may assume a wide range of positions, called,"postures": each of these will be accomplished by the "fixation" and immobilization of the skeletal segments in a given position expressed as "aptitude" o£ the wole body to maintain through time such a marked state of equilibrium. Whereas the "structure" is able to perform only determined rotations through the articular joints, the execution of translations is made possible only under the condition that the sum. of the angles of the relative articular rotations would be zero. The "couple of athletes" system may be defined in

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physical terms, with' the due approximation, as an articulated system of cylindrical symmetry, placed in the gravitational field in stable equilibrium on a plane area with friction, formed by the semi-rigid union of two biomechanical athletes. The aim of the semplifications introduced in the preceding definitions is to facilitate the mathematical handling of this issue, it falling under the sphere of classica1 mechanics. It is important to note that the ncouple of athletes" may be regarded as a whole system upon which acts only one external force (gravity force) annuled by mat reaction, and that it may shifts or changes its interna1 set-up, under push and pull force only on account of the existence of friction. Very generally, in i~teraction (throwing techiqhes), the analysis as above may be performed under "static conditionsn, that is at zero shifting system velocity or "absolute velocity", since the results obtained will be, with verry good approximation, applicable also to the condition relating to contest, effective average velocity between 0.5-1.2 Km/h. In fact on the basis of Galileots Principle of Relativity, according to which the functional relations in mechanics are equally valid both for an immobile system, and for a system in uniform linear motion with respect to this, the two treatment will be equivalent. Therefore - for rather self-evident convenience-related reasons, it is preferable to treat the mechanical problem of the intraction (throwing techniques) in the condition of greatest semplicity. The mode1 and the characterization of the generic motion of the "couple of athletes" system - developed thanks to the specific techniques of the statical mechanics allowed to affirme that it is ruled by Langevin equation and then that it belongs to the class of *bidimensional Brownian motion. The experimental check could be done from a study of dromodrams made at the Japan Judo CHANPIONSHIP IN 1971. By applying Einstein methods - adequately modified through the second principle of thermodynamics - it has been demonstrated that the average kinetic energy is directly proportional to one fifth of the athletets overall oxygen consumption, and also that the most important parameter in contest are the "absolute velocity" o£ the system, and the "relative velocityn of attack speed. On the other hand, the use of variational'amalysis 9-

applied to the aspect of interaction between athletes in static conditions and extendable to contest on the basis of Galileian relativity - enable us to identify the physical principles on which this ' interaction (throwing techniques) relies and to infer and define the lower energy consumption trajectories of throwing. From a historical point of view, the theory of variations was born thanks to the stydy of the brachistocrone or "smaller transit time" trajectory. This problem was studied by Galileo, Jacobi, Bernoulli, Newton, Leibnitz and and Lagrange are others even though Euler, Bernoulli generally considered to be the founders of this method. It was applied to the problem of identifying the lower transit time*trajectory that a body.can cover between two points when only the gravitational field acts on it. In our case, throwing techniques, since by first approximation, we deem correct the assumption according to which the initial thrust.exerted by the attacking athlete on the attacked one, acts for a neglegible lapse of time, we are once again faced with a formally similar case. The external field of forces to the "couple of athletes" system is conservative and not depending on time (gravitational field). Therefore the principle of minimal action will.be true and we can demonstrate either that the body covers a minimum lenght curve in the space or that its trajectory coincides with a geodesic of a specific simmetry. Considering this study, we may define the two physical principles according to which al1 throwing techniques have been classified:

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Techniques in which the attacker uses a physical lever to throw down his opponent. - Techniques in which the attacker uses a couple of forces to throw down his opponent. For the physical lever techniques, the impulse applied by the attacker at the start ot throw, although its act,ion is limited only to a short time, may be considered sufficient both to obtain unbalance, ?hat is to shift the barycentral projection outside the supporting area, and to simultaneously impart a rotating momemtum on the thrown athletefs body so that, given the mechanics of the techniques (establishment of a stopping point, fulcrum, and rotation around the same.) they strongly depend from the friction between ukefs feet and the

,

mat; the equation of motion is provided by the solution of the classica1 problem of heavy symmetrical ro-tator that starts falling down, in gravitational field. These techniques are less energetically convenient because Ukefs barycentre must be lifted and shifted for a more long trajectory, i.e. as in standing Seoi nage, O goshi, etc. For the couples of forces techniques, the equation of motion proves to be the sum of produced by the couple of forces, parallel to the gravitational field- , called "principal": that is a pure rotative motion independent of the gravitational field, and those ,produced by the composition of the movement of the perpendicular torque to the gravitational field, called ltsecondary", plus the component of the field itself. Such techniques therefore have the property of being pratically non-dependent on the 'friction between ukefs feet and the mat. They are also more energetically convenient, because Uke's body only rotates on its own barycentre and then falls down

.

5. BIBLIOGRAPHY

BEJAN A. "Heat Tranfer-Based Reconstruction of the Concepts and Laws of Classica1 Thermodynaricsn Journal of Heat Transfer vol. 110 (1988) DAVID R. BASSETT JR., FRANCIS J. NAGLE, SWAPAN MOOKERJEE, KEVIN C.DARR, ALEXANDER V.NG, STEPHEN G. VOSS, and JEROME P. NAPP nTermoregulatory responses to skin wetting during prolonged treadmill runningn Medicine and Science in Sports and Exercise Copyright 1987 by American College of Spprts Medicine CAMPBELL G.S.,. McARTHUR A.J. and MONTEITH J.L. "Windspeed dependence of heat and mass transfer .through coats and clothingn Boundary-Layer Meteorology 18 (1980) 485-493 CENA K. a.nd MONTEITH J.L. Transfer processes in animal coats Io - Radiative transfern 11° - Conduction and convection" '111° - Water vapour diffusionn Proc. R. Soc. Lond. B. 188,413-423 (1975) C.K. CHARNY, M.J. HAGMANN, R.L. LEVIN "A whole body thermal model of man during hyperthemian IEEE Transactions on Biomedical Engineering BME-34 (1987) C.K. CHARNY, R.L. LEVIN "A whole body thermal model of man with a realistic circulatory' systemn IEEE Transactions on Biomedical Engineering HTD-95 BED-7 (198.7) CLARK R. P. "Human Skin ~emperatureand Convective Heat Lossn ELSGOLC

"Calculus of variations" Pergarnon Press N.Y.1961

FOWLER "~tatisticalmechanics" Cambridge 1936

J.P. FUNK "Direct human body"

measurement of radiative heat exchange of the

NATURE February 29,1964 GRUCZA R. "Body .Heat Balance in.Han Subjected to Endogenous and Exogenous Heat Load" 51:419-433 HAK-SHING TAM, ROBERT C. DARLING, JOHN A. DOWNEY, and HUK-YUK CHEH "Relationship between avaporation rate of sweat and mean sweating rate" Journal of Applied Phisiology No 5 (1976) a

KHINCHIN "Hathematical

fundations of Statistica1 Dover N.Y.1949

KURT

Hechanics"

.

"Axiomatics of Statkstical H e c h a n i c ~ Pergarnon Press N.Y. 1960

KENNEY W.L., LEWIS D.A., HYDE D.E.,- DIKSTERHOUSE T.S2, ARMSTRONG C.G., FOWLER S.,R., and WILLIAMS D.A. "Physiologically derived critica1 evaporative coefficients for protective clothing ensemles" CopyrigHt 1987 the American Physiological Sodiety KATTO Y. and AOKI H. "Peculiarity of Evaporating Liquid-Surface Reference to Turbolent Heat Transferm Bulletin of JSME, vol. 12 (1969) KATTO Y. and KOIZUMI H.

With

"Turbolent Heat Transfer of a Gas Flow Evaporation Liquid Surfaceu Bulletin of JSME, vol. 18 (1975)

on

an

T. KUMADA, T. HIROTA, N. TAMURA, R. ISHIGURO "Heat and Mass ~ransferWith Liquid Evaporation Into a Turbole'nt Air Stream" Transactions of the ASME vol. 108 (1986) KANDO KOBAYASHI, STEVEN M. HORVATH, FRANCISCO J.DIAZ, DONALD R. BRANSFORD, and BARBARA L. DRINKWATER "The~more~plation during rest and exercise different postures in a hot huniid environment" Copyright 1980 the Amrican Physiological Society

in

KHAIR K.R. and BEJAN A. "Wass Transfer to Natura1 Convection Boundary Layer Flow Driven by Heat Transfer" Journal of Heat Transfer voi. 107 (1979) B.J. MULLAN H.E. LEWJS, A.R. FOSTER, a ~ d "Aerodynamics of the human microenvironmentu The Lancet Saturday 28 June 1969, A.T. PRATA and E.M. SPARROW "Diffusion-Driven Nonisothermal Evaporation" Journal of Heat Transfer vol. 107 (1985)

R.S. RANA, V.CHARAN, and H.K. VA"Heat and Hass Transfer From a Row of hibes in a Vertical Plane of an Evaporative Heat Dissipatorn Transactions of the ASME vol. 111 (1989) V

A. SACRIPANTI "Biomeccanica del judon Ed. Mediteranee 1989 SACRIPANTI, M. FAINA, G. GUIDI, M. FABBRI, G. GALIFI, P.LUPOL1, R. MASO, A. PICCA, L. ROSSI. Valutazione del costo energetico degli sport di combattimento in "REMOTE SENSING"

A.

.

PROGRESS REPORT

1

"Screening preliminare"

ENEA RT:1989 "Intercomparazione Orientativa" ENEA RT:1990 REPORT 3 "Teoria biomeccanica della competizione" ENEA ~ ~ : 1 9 9 0 REPORT 4/5 " Stima dellreffetto schermo del Judogi" ENEA RT:1991 REPORT 6 " Valutazione dellreffetto schermo del Judogi " ENEA RT:1991 REPORT 7 " Han enviroment, heat-excange equations a new thermodynamic approach" ENEA RT:1991

PROGRESS REPORT PROGRESS PROGRESS PROGRESS

PROGRESS

2

SHAPIRO Y., PANDOLF K.B., and GOLDMAN "Predicting . Sweat Loss Response Environment and Clothing" Eur J Appl Phisiol (1982)

to

Exercise,

STOLWIJK,J.A.J., and J.D. HARDY "Partitional calorimetric studies of responses of man thermal transientsn J. Appl. Phisiol 21:967-977 (1966) STOLWIJK,J.A.J., and J.D. HARDY "Contro1 of body temperature" In DHK Lee (Ed.):Handbook o£ ~hysiology-Reactions t0 Environment Agent. Bethesda, American Physiological Society 1977 S?

SMOLSKY B.M.,and SERGEYEV G.T. "Heat and Hass Transfer With Liquid Evaporation" Int. J. Heat and Mass Transfer, vo1.5, 1962 WAX "Selected

papers on Noise and Statistica1 Processes". Dover N.Y. 1954

WHITTARKER "A Treatise on the and.Rigid Bodies"

Anaiytical Dynamics of

Cambridge Univ. Press 1937

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