man environment heat exchange equation applied to judo

8/14/2019 man environment heat exchange equation applied to judo

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

VALUTAZIONE

DEL COSTO ENERGETICO DEGLI SPORT DI COMBATTIMENTO IN

I REMOTE SENSING*

PROGRESS REPORT 7

Man environment, heat-exchange equations

a new thermodynamic approach

A. SACRIPANTI .E.N.E.A. - Direzione Centrate Sicurezza e Protezione Sanitaria Roma, Coordinatore Federazione Italiana --Lotta - Pesi - Judo

A. DALMONTE' C.O.N.I.- Istituto Scienze dello Sport

Dipartimento di Fisiologia e biomeccanica Coordinatore Scientifico

M. FABBRI, L. ROCSI ENEA -Area Energia e Innovazione Centro Ricerche Energia Casaccia, Roma

Paper presenteci at the

EIGHTH MEETING OF THE EUROPEAN SOCIETY OF BIOMECHANICS

June 21-24, 1992 Rorne - Italy


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Testo pervenuto nel luglio 1992

Gli autori ringraziano i gruppi sportivi dellaGUARDIA FORESTALE

eGUARDIADI FINANZA

per la gentile e fattiva collaborazione prestata,nel corso della ricerca

I contenuti tecnicclscientifici dei rapporti tecnici dell'ENEArispecchiano l'opinione degli autori e non necessariamente quella dell'ente.


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ABSTRACT* .

Thi s progress report shows a new thermodynamicappro ach to the problem of man-environment heat exchange. The

obtained goal for our studies is a new and more useiul forraof the equation describing the energy output from a man whoperforms a physical exercise.

In appendix, the new energy equation is the basis of acomputer code used to .get quantitative results in theC.O.N.I.- E.N.E.A.- F.I.L.P.J. joint research.

RIASSUNTO .In questo progress report e ' utilizzato un approccio

termodinamico per ottenere unre quazi one che descriva loscambio termico uomo-ambiente in forma piu r utilizzabile perla ricerca congiunta C.O.N.I.-E.N.E.A.- F.I.L.P.J.

In appendice viene presentato il codice di calcolo cheutil izzan do la nuova forma dell'equazione ottenuta, permettela verifica quantitativa delltesperienza.

7


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1.0 - THERNOPHYSIOLOGY: A SH ORT OVERVIEW2.0 - THE EVOLUTION OF HEAT EXCHANGE EQUATIONS2.1 - TH E MICROSCOPIC VISION UPDATE:

THE WEINBAUM AN D J I J I BIDTHERMAL EQUATION.

2.2'- MACROSCOPIC VISION UPDATE: THE CHARMY AND LEVIN MODELr -

3.0 - , m S HEAT ENGINE,

3.1 - CQMPONENTS OF THE INNER AND OUTER HEAT CURRENTS. C

3.2 - PHYSICAL AND CHEMICAL HE AT REGULATION4.0 - HEA T EXCHANGE, .CLASSICAL EQUATION S END NEW

THERXODYNAMIC APPROACH

4.1 - HEAT EXCHANGE BY RADIATION4.2 - HEAT EXCHANGE B Y CONDUCTION

E

4.3 - HEAT EXCHANGE BY RESPIRATORY SYSTEM4.4 - HEAT EXCHANGE BY CONVECTION FROM THE SKIN4.5 - HEAT E X C W G E BY DIFFUSION AtjD MASS TRANSFER5.0 - APPENDIX: A COMPUTER CODE FOR THE ENERGY EQUATION6.0 - BIBLIOGRAPHY


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detriment of the interstitial liquid. The changes stemmingfrom the correspondent vasomotorial changes practicallyconfide themselves to change the features of the "skinradiatorn.

indeed, ince the hlood floow can range from 0.16 toa2.6 litres/min/m the temperature, conductivity and skin heatdispersion ability are substantially altered. The process ofheat dispersion in the external environment has a werely"physicalH chasacter and depens on the temperature humidityand radiant power of the integuments in relation totemperature humidity and speed of the environment air.

The man-environment heat axchange can occur byconvection, radiation, conduction and evaporation. Convectionis the process transferripg heat from the skin to theenvironment by ~d ir ec t adiation associated t& the sta tus ofthermal excita,tion of the air film molecules in contact withthe body .

Radiation is the process tranferring heat from theskin to the environment by direct irradiation linked to therelease of electromagnetic radiation emission in the infraredband by the body.

Conduction is the process tranferring heat from ahigher temperature area to a lower temperature one.Evaporation is the process tranferring heat from the skin tothe environment, linked to the change in the status of a

vaporizing liguid.At the level of the skin two different processes

occur: the former which is generally below 30"., known as"perspiratio insensibilis", caused by the natura1 diffusionof steam through the skin; the latter over 30 C. known as"perspiratio sensibilis", which is. subject to thethermo-regulating contro1 causing perspiration.

A further vaporization occurs dt the level of themucosa of the brething segment. Therefore espiration i s .adethrough a he&t cession to the environment whiEh can be

relevant, durlng bhysical efforts, due to the increase in theventilation frequency.Thus physical activity and the related heat production

trigger a series of physiological meohanisms designed to keephomoiothermy sueh as: variation in the oxygen consumption,lung ventilation, heart beating frequency, peripheralcirculat ion and finally the activation of sweat-glandes.

4-


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9

2.0 - THE EVOLUTION OF HEAT EXCHANGE EQUATIONS5

The study of the methods of regulating the bodytemperature has excited investigative interest since thedawn ing o Biomechanics.

The subsequent developments of tbermodynamic theoryand the related experiments have increased huma nunderstanding of this phenomenbn.

In thermophysiology the key instrument for dissipatingthe interna1 heat surplus is given by the increase of theperipheral blood flow which, by changing the conductivity ofmuscular tissues, consequently alters the emission-dispersionchara cteri stics of the "sknin radiant*.

Even though the procesb for dissipating heat appearsto be well-defined and undestandable in its entirety, indeedthe "local~' icroscopic vision of the heat exchange mechanismand the definition of the tis6ue temperature has so far beendevot e8 no satisfactory analytical description.

The problem of human external body heat exchange isusually tackled determining both the indipendent variables inhuman thermal environment and the physiological "dependent"varia bles and ,at the end, applying an experimental modifiedheat tranfer theo ry (Fan ger 1970, Kerslake 1972,Gagge 1972,Nitchell 1972, Hanson 1974, Gagge and Nishi 1977, etc.).

Due to sport evolution, the need to extend knowledgecalls for an in-depth anal ysis of the equat ions tegulatingman-environment heat exchanges under "free" ( re al ) conditions- with al1 the difficulties we can imagine.

Even though these equations are al1 well-known - witha certain degree of approximation - they were confirmed byextra polat ing them from Zabora tory controlled conditions:

In this respect a joint study by C.O.N.I. - E.N.E.A. -- F.1,L.P.J was star ted at the beginning of 1989 designed toassess the ath let ers energy eost in rea1 competition.

Considering the high complexity of thc issue, it wasrecognized the need to tackle that through an integratedmulti- disciplinary approach, by resorting to knowledge inthe field of physiological biomechanics and the specificequ ipment provid ed by C.O.N.I., to the sophis tic ated methodsand instrument provided by E.N.E.A. and finally to athletesand to the technical and specialized knowledge in the fieldof physical biomechanics provided by F.I.L.P.J.

The "simple" idea is that of viewing athletes as


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complex thermal machines. Therefore the joint applicakion ofboth principles of thermodynamics must allow us tostatiitically assess the average work carried out by athletesduring competitions.

Obviously, from a theoretical point of view, theproblem could be rapidly solved if i t was possible toevaluate the athletesf direct calorimetry during theirperformance. Since this is technically impossible, it isc o m o n practice in sport to assess the ath let efs work bymeans of the "simpleru indirect calorimetry.

This means that through arl appropriate mechanicalequivalent we can trace back - through the fuel kinetics -the work carried out in laboratory which, for many sporti, ismade day by day more similar.to the rea1 competitive load.

In the case of fighting spor ts pertaining toF . I . L . P . J . (wrestling and judo) a e few experimental data are .indeed limited and it is virtually impossible to extrapolatereliable data from these laboratory results which can allowan adequate training based on scientific principles.

The idea is therefore that of retracing directcalorimetry by meqns of improved energy equations of theman-environment heat exchange, which take into account thephenomenon kinetics each point every 15 seconds.


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2.1 - THE MICROSCOPIC VISION UPDATE:ITHE WEINBAUMANDJIJI BIOTHERMAL EQUATION.

.Since 1985 through 1989, on the Journal ofBiomechanical Engineering, a group of researchers from the

New York University seemed to provide a remarkablecontribution t o the evolution of the microthermophysiology bydefining a new biothermal equation.

Weinbaum, Jiji, Zhu and Lemons thus proposed and thengeneralized an equation where the microscopic average tissuetemperature was, for the first time, connected with the bloodflow .and the local microvascular geometry.

A mode1 was made of the basic machanism which allowsthe heat transfer from the tisiue to the blood. This transferis not - as belie3sd so far - the result of the heat exchangewith al1 capillaries, but the result of the heat exchange ofarteriovenous counter-flow of those capillaries having a

analytical exstension of the temperature function enables usto describe - with a good degree of approximation - thetemperature range o-f the close tissue, thereby allowing for

diameter higher that 100 pm, which are considered to be moreimportant from the thermal viewpoint.

This was made on the basis of a theoretical forecastproposed by Chen and Holmes in 1980 who - as for the

the first time to assess the theoretichl results by means ofthe experimental data of the tissue temperatu're.

microcapillary blood flow - made a clear cut distinctionbetween the heat exchange and the mass (oxygen) exchange.

This means that blood vessels under 50 pm are alreadythermally balanced with the local tissue and do notparticipate to the removal of heat which is exchanged andremoved only at the leve1 of those arterioles and venoles

" having a diameter higher than 50 pm.The f rst equation proposed was valid only fr blood

C' vessels of the same diameter, but it is interesting to notethat the last generalization of the equation, to inclu&edifferent diameter blood vesseles and the expression of theeffettive conductivity tensor, has the advantage of keepingthe same analytical form alco in the genera1 case.

. In th is last instance the mathematical device of the


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2.2 - MACROSCOPIC VISION UPDATE:.,THE CHARNY AND LEVIN MODEL

: ,

A good exemplum of macroscopic heat exchangeapplication is the whol e body thermal model of a man, with areafistic circulator y system, made by C. K. Charny and R. L.Levin (1989), used for s imulat ing t h e r a p e u ~ c yperthermiatreatments of non-thermoregulat8d malignant tumours.

Man is lumped into 16 body segments; each body segmentis subdivided into four tissue elements: core, muscle, fat,and skin. In the origina1 model ther e is only one centralblood compartment; this last one is characterized by a singletemperature throughout the,body at a give n time. Ther efor ethere are 64 tissue elements plus one blood compartment inthe origina1 model; each tissue element is characterized byits temp ereture, volume, surface area, density, specificheat, thermal conductivity, basal metabolic rate, basalevaporation rate, basal blood perfusion per unit of mass oftissue, and electrical conductivity.

The blood compartment is characteri zed by a sing letemperature , volume, density, and specific heat. The ne wversion of this model subdivides the central bloodcompartment into one arteria1 element and one venous elementfor each body segment. Also, the abdominal segment is

subdivided into an abdomen and pelvis segment. Each of theseventeen body segment no w consists of six layers: core,muscle, fat, skin, artery, and vein. Thus there are a tota lof 102 elements in the current model of the man: 68 tissueelements plus 34 blood elements. Each blood el em en t- is n owcharacteriz ed by its volume, specific heat, density, andelectrical conductivity. Arter ia1 and veno us blood flowsthrough each segment via a large vessel which exchanges heatwith the surrounding tissue.

This surrounding tissue is the muscle layer in al1 of

the body segfttents except the thorax, abdomen, neck, and head,in whic h the large artery and vein are both assumed to beembedded in the core tissue,

Heat exchange in the pulmonary circu lati on is. modeledseparately by considering th e lungs and heart as part of th elumped thoracic. The effect of temperature on skin blood flowand sweating is modeled based upon the work of Stolwijk.

The ancestor of this model is the thermoregula tionmodel presented by S . J. Stolwijk 'and J. D. Hardy in 1977


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which predicts, with reasonable accuracy,' th-e dynamicthermqregulatory responses to dynamic loads of ambien t -

temperature and interna1 heat produ ctios even during a very

heavy exercise.


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3.0 - MAN AS H EAT ENGINE

The thermodynamic approach to the athlete-environmentheat exchange is a very difficult task which shows us thehigh complexity of the "athl eteN as heat engine and the lackof complete theory of the topic.

Heat production by man depend s upon a large number offactors which are also significant for the core temperatureregulation. Roies of various importance are played by size ofbody, food consumption, age, sex, activity, funct ion ofglands with interna1 secretion, acclimatization, and aboveal1 the varying environmental temperatures and thecontinuously effec'tive elements af heat radiation, of air

humidity, of air displacements, etc.Essentially there are three factors controlling heat

and energy production in the h w a n body:- A ) consumption of food and its combustion by means of

inspired oxygen.- B ) physical activity (work, sport, etc.)- C) incoming heat radiation from natura1 and artifieial

radiators (sun, skin, room, walls, heaters, etc.)They form thg assets in the heat balance which are

necessary for the maintenance of a costant core temperature.,The Losses are those of removal of sensible heat byconduction and convection, and by radiatlon governed by thetemperature of the body and of the surroundings as well as byevaporation. Al1 of them are closely connected with weapherand climhte fluctuations.

Dominating roles in these intricate influences areplayed by the characteristics of the human skin surface withits often greatly varying behaviour, and by the lungsrespiratory sistem. Comprehension of the . changeablecircumstances in the weather courses and climate structuresare facilitated by a review of heat physiological facts.

These dea1 "ith transport methods and the heat fluxes f ombody core towards body sheL1 and beyond to the surroundings.

Accord ing to estimates by Hensel et al. (1 97 3) in ahuman body at rest the greatest heat production(appcoximately 50%) is concentrate in the abdominal organs(parti cularly in the liver); under medium work loads theproduction is naturally taken over by the muscles (7 5 % ) . Thesketch in (fig. 1) shows the processes o f heat transport 'fromthe interior of the body to the skin surface. The body fs heat


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emission and evaporation through the skin surface and therespiratory sistem including the lungs, bes ide s+c ond uct ionand convection are the main mechanisms for heat exchange withthe environment.

Fig. 1 - Heat transport between body and environment(Hensei et ai., 1973)


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3.1 - COPIPONENTS OF THE INNER AND ,OUTER HEAT CURRENTS

Three factors are important in the heat transport fromthe interior to below the skin surface and above al1 withinthe skin system itself, namely : W* = blood stream (progressof arteria1 blood to below the outer. skin); WL = heatconduction stream, conditioned by the drop in temperaturefrom the incide towards the outcide; WA = heat exchange(disorg anized movement of liquid consti tuents of the skin).Thus the sum WB + WL + % constitutes the i n t e r n a l . h ea tstream whic h plays a decisive part in the principal behaviourof physi cal hea t regulation.

Total heat emissiofi Q, the exter nal heat stteam,corresponds to khe sum of t he four factors:

Q P R + K + C + E

whereR is the heat exchange by long wave emission,K is the heat exchange by conduction,C is t he hea t exchange 'by convec tion,E is the heat exchange by evaporation by way of ski n surface

W

/


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4.0 - HEAT EXCHANGE, CLASSICAL EQUBTIONSAN D NEW,THERNODYNAMIC APPROACH

In C.O.N.I. - E.N.E.A. - F.I.L.P.J. experience t0study athlete's performance in rea1 time using "remotesensing" techniques, it is basic to have predictiveequations, as function of indipendent variables of the humanthermal environment related to the "human heat engine" byskin temperature.

If the athleters body is in thermal equilibrium withthe environment, the application of the first principium ofthermodynamics allows us to write the known relation:

b

. I i t C i L - - o

where M is the metabolic. energy.During the kinetic evolution of a performance, a correctionfactor must be introduced and the following equation isapplicable

P t i t E * L - = * S

where the term 6 called "body heat storage" (Winslow, 1939)

would be better renamed "thermal inertia" of the body.As matter of fact this term accounts both for the lagof time present between the start of the performance and thevisible thermal emission related and for the thermal tailpresent at the end of the same. it quantifies therefore thebody trouble (inertia) to change his thermal status. -

For the evaluation of the body "thermal inert ianusually it is applied the following. equation:

6 - (Cb g ATb)/d twhere g represent the body weight, Cb is the specific heat ofthe body assumed to be 3.47 kJ/Kg OR but it may range from2.93 u p t o 3.55 kJ/Kg O R (Hardy, 1970) and ATb is the meanbody temperature determined by a weighted average of AT(skin) and *Tr (rectal) as prpposed by Burton ( 1 9 3 f :(0.65 AT,, + 0.39 bTSk) or by Ctolwijk and Rardy (1966)(0.8 A + 0.2 ATSk)..It is also clear that the therial

- inertia o the-body during an exesercise (in hot environment)cannot be determined from any fixed ratio of inner and skin


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temperature (Wyndham, 1973).The metabolic energy source M represents the free

energy produced by the trasformation of chenical energyduring aerobic and anaero bic-a ctivit ies within the organism.It is impossible to d e s c d b e this process quantitatively, ina usefu l form, therefore usual ly it is assessed by the "moreeasyn measurement o f fuel upkake (oxygen).by the formula:

wherer is the respiratory factor and e

v02 is volume of oxygen uptake,Since the mechanical efficiency of the human body i s

mostly below 2 5 %, the interna1 heat production durin gexercises corresponds to the 75 % of the total energyutilized.

The greater is the exerci se intensity, the greater isth e total amount of heat produced. The heat id excess has tobe removed and dissipated in order to prevent overheating andhyperthermia. j

In heat transfer theory and fluid mechanics conditionsat the bourdary of a finite body in- whi ch heat is flowing areusually described in terms of one or three id ea li za ti ms , ofwhich the last includes the first'two as special cases:

1 ) - the boundary is assumed to be maintained at a fixedpreassigned temperature T, by good thermal.contact with awell-stirred reservoir.

2) - the boundary is assumed to be impervious to heat a o w ,which means that the normal component of the heat current, I,and hence n*grad T vanishes at the boundary ( * &'scalarproduct .

3 ) - transfer of heat across the bound ary is assumed to beproportional to the t emperature of the boundary surface(this means the temperature relative t o the surrounding

cooling mediumj . This is known as "Newtonf law of coolingn.The transfer of heat across the boundary is2

characteri zed by a heat-transfer coefficient h (W/m K ) suchthat at the surface the norma l component of I is hT andtherefore if n is the outward unit normal veotor to thesurface, the boundary condition at the su rf ac e- is


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The nature of the thermal contact is thuscharacterized by a parameter k /h which has the dimensions 0%length. Case 1 corresponds to k/h=O and case 2 corresponds tok/h becoming Infinite.

Mixed cases may arise in which h has different valueson different parts of the bo&ndary surface, as when somesurfaces are in good thermal conctact with a reservoir.

Then the mathematical form of the physical heatregulation equations satisfies this simple relation:

2where Q is the heat rate for unit area in (W/m ) ; (T 2 - TI)is the temperature gradient.from warmer body to qolder region

in (K)'; h is the heat tranfer coefficent in (W/m K).If we confine ourself to study heat exchange producedby physical performance, al1 technical comlexity will befound in defining a right 'Iheat transfer coefficient" foreach process performea -i n the fundamental thermodynamicrelation.


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4.1 - HEAT EXCHANGE BY RADIATION

On this basis the linear radiation exchange satisfies. .the equation:

where Tsk is the skin temperature, calculated directly bythermography or by assigning determined factors to each ofthe thermocouple neasurements (one every 30") proportionallyt6 the fraction of the body total surface area,'representedby each specific area (Hardy and Dubois, 1938):(0.07 head + 0.14 arms + 0.05.hands + 0.07 feet + 0.013 legs+

0.019 thigs + 0.35 trunk).Tr is the mean radiant temperature of the surrounding,and because the physical process is regulated by the Stefan-

4Boltzman law ( A = S T ) the heat transfer coefficent takesthe form:

where a is the Stefan-Boltzman constant and equals 5.67w ~ - ~ K - ~ . he term S(a) is tha 4n radiating arei of the humanbody surface according to Dubois surface, and will vary withposture. The term has been determined with considerableaccuraey by Fanger (1970) by use of optical'methods and wasfound to vary from 0.70 for the sitting position to 0'.725 forstanding within +/- 2 % regardless of height and body weight.When clothing is worn, the radiating area of the body,S(a) isincreased by a factor f. Fanger and Breckenridge & Goldernanhave shown that f increases approximately 15 % for each clounit of clothing insulation worn, i.e., by factor (1 + 0.15Iclo)'

E is called radiation coefficent of the skin; it isthe relation of the emission of a given surface to that of a

black body at'the same temperature. Reliable measurement isby Buettner (1938) and set it for human skin at 0.954, forlong wave emissivities, which is a deviation from the blackbody radiation of only about 5 a . This means that within theenergy range spectrum of human skin (5 - 50y ) only l - e partsare reflected from vertically incoming radition, and thegreatest percentage (approx. 95 % ) is absorbed. The radiationfactor for skin is very close to that for water and othersubstances of importance in the skin structure. Obliquely


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incoming radiation shows an s of 0.893 (Bue ttne r, 1938).Gaertner and Goepfert (19 64) again iqvestigatd the

radiation characteristics of live human skin. For the backthey found E at 0.976, for the forearm at 0.960 and the soleof the foot at 0.941. inci dent ally the average lies veryclose to the value determined by Buettner. Based on thestudies by the above-mentioned authors it must again bestated that liv e human skin' is not a "black radiatorn, but a"gray body* (see tab 1). Other values of s carne from Hardy, .1938 (0.98) and Mitchell, 1967 (0.979).

Radi atio n fig ures $or temper-ature radiation

(After ~ue t tn er, 938)

BLACK BODY 1.000SNOWFROSTWATERHUMANSKIN ( e )BRONZE COLOURFURWOOLPINE NEEDLES

WOODCLOD WITH GRASS

E VARIES FOR DRY AND PERSPIRED SKIN.


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4.3 - HEAT EXCHANGEBY RESPIRATORY SYSTEM

Respiratio n is the exchange of'the gases oxygen and

carbon dioxide between tissue and atmospheri c air. Thesubdivision into approximately 3-4 millions of alveoli at theend of the finest branches 02 the trache causes the lungs-5,to attain an inner sur fac e-o f about 75.m . Noce, pharyngealarea, trachea and bron chi4 do not pafticipate in the gasexchange. They do, however, have the important job of warmingthe inspired air to body temperature and to saturate it withwate vapour .

The surface of these spaces.are covered with ciliatedepithelium, whereby its cjliae move back and fo rth- duri ng therespiratory process. Thanks tho this process foreign bodiescan be removed from the respiratory system. Reflex actionssuch as sneezing, coughing, ect. serve the same purpose.

In the respiratory system the separation of aereosoistakes place in the alveolar area essentially by threeprocesses, i.., diffusign, 'inertial separation (reb oundeffect) and sedimentation. Fig. 2 conveys an idea of thediameter, surface and volume of the respiratory sy st em fs

8 . Trachea2. Mbin bronchii

3 Lobar bronchii

4 . Scgmcntri br.

5. Sucsegmcnla~ bc4. Terminai br.

7. R.spirdtoy br

8. AIveoirr duct'

g. AIvco1.r racc.

~ e n g t i ~ urhc. V Q I U ~ ~ . F":;jC"[cm] [cm-7 Em**]

t 2 60 24 Coneuctivc

G .zone wilh .*O ' Ociih epiih+iivm

3 15 5

1 CJ 100 3

0.5 200 1 0

c insoiration condii;on ca re ci ed te a iung voiumc or 3000cm~)

Fig. 2 - Mode1 of lungs, by Landahl, supplemented by Jacobi,during the inspiration phase (Jacobi, 1965)

indiQidual regions (Landahl, 1966) and is based on therespiratory conditins:


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1minute volume = 15 1. *in-'

respiratory frequency = 15 min -1 .

The main process of heat exchange by respiratory sistem areconvecti on and mass tranfer from the respiratory airwais.

Convective heat exchange by the lyngs depends both onthe pulmo nary ventilat ion and the temperature diff eren cebetween expired and ambient air. Pulmonary ventilati on isrelated to metabolic rate, then usually the followingapproximated formula was used according to Hanson, 1974:

. ~n ma n ~ t h e iass-tranfec from airways i s n o t controlled

by thermore gulatory mechanisms. Heat loss from therespiratory airwais was calculed by formulas proposed byMitchell, 1972:

Eres - 14.9 N ( 5 . 8 8 0 - p,)or by Snellen, 1966:

Eres - VO2 (1.977 XCOZ R - 1.429 XO2)Fram our point of view, for our res6arch, it appa res

more useful treating the problem by .th eo ret ica lthermodynamics.

The theoretical thermodynamical analysis of convectionis greatly simplified by using non dimensional groups tbatcome from similitary theory.

A body imersed in a fluid loses heat through alaminar boundary layer o uniform thickness, then the heatlosses per unit area can be written as

where K is the thermal conductivity of the fluid; 6 is thethicknes s of the boundary layer, is the mean skintemperature and T, in the ambient temperature.

The same equation can be used in a purely forma1 wayto describe the heat loss by forced or free convectio n fromany object with a mean surface temperature of TSk surrounded


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by flwid at Ta even thoug h the boundary layer is neitherlaminar nor uniformly thick. In this case, 6 is the thicknessof an equivalent rather than a rea1 laminar layer. It isdetermined by the size and geometry of the surface and by theway in which fluid circulates over it.

A more useful form of equation can be derived bysubstituting a characteristic dimension of the body d for theequivalent bou nda ry- lay er thickness, which cannot be measureddirectly, The equation then becomes.

The ratio d/6 is called the Nusselt number after its

first exponent and is often written Nu. Just as the Reynolds'number is a convenient way o f comparing the force s associatedwith geometrically similar.bodies immersed in a moving fluid,

athe ~ u s s d t umber provldes a basis for comparing rates ofconvective heat loss from kimilar bodies of different scaleexposed to different wind-speeds.

In forced convection, the Nusselt number depends onthe rate of heat transfer through a boundary layer from asurf ace hotter or cooler than the air passing over it, aproce ss 'ana lo go us to the transfer of momenturn by skinfriction. The Nusselt number is therefore expected to be -afunc tion of the Reyn olds nuxnber (specifyi ng the boundarylayer thicknes s for momentum) and the ratio of boundary layerthicinesses for heat (t ) and for momentum (tM)

This ratio is a Function of the Prandtl number defin ed< b y (v/k), Measurements of heat 'loss by forced conve ction from

planes, cylinders and spheres can be described by the genera1relation

. ' mwhere m and n are exp eri men tal constants and tM/ti - Pr .The convective exchange by the lungs is function offrequency of breathings and of air quantity inspired (s eeTab. 2 ) . Because we have different values of lung ventilationat different levels of activity, the better way to have theconvective stream is to define an "effettive cylindricalsur fac ew of the lungs. Obviously it will depend by the " tidalvolume" of athlete at zest or duriqg exercise. Simple


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-C lculations show that ef ective surface may range from 0.0573 fm at,rest, up to 0.103 m during maximal exercise..

i l . &41-i4lor; p. al . pp. 4 -U104. p. 6J .

Tab. 2 - ~ e l ect s d ung ventilation values at different levelsof activity as a function 6f age

9

:O .Il22

i

The experimental points characterizing heat transferlie on a straight line of the well-known "crit ica1 relat ion"

Thic experimental form of Nusselt nunber gives us the finalrelation:

V I^ in column 2 .rc b d y 4 g h t 1 rkrabk lo iIH d i in r in n quoicd in cilumn 1.f: I m u u y ( br ut hd mi n); V T -6d.11 volumc (ml): 4 -&UU ~ o fu m c ~ m i n ~ ;Aaurlwt aru .

.

.

Nwb o rn

2 C b 1 3 v k4.&h6.6 d

v

2.5-1.33~3.1

34 15 0.5

21 2 1 DJ29 11 0.G

.. .

* I 51l.u*ij.ri-

,

.I ?. p. 351: I l S . 1%.

>M: 430. P. 50:$07. p. l034

116 p 1 3I l . P. 42O, p.220: Il. p.4:


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where- n is the breth frequency value: 3 at rest, 4 for lightexercise, 5 for heavy exercise, 10 ior maximal execise ,- Sp is the effective surface of the lungs,- Lp*is the mean diameter of the lung,- T .is the interna1 temperature of the lung equa1 to thebody core temperature,- Ta is the ambient temperature,- K, is the thermal conductivity of Che fluid.


25/50

flow - fig.3.

Body Region H a d Chs h& U p w i ~ ~rinr ~ a n d r iichs Le*Mun

(h 3

- Rcsting Silling 3.2 25 2.4 4.0 3.3 1.G 2 8 3.7 3.1Trad~rrill 0.9 m r- LI 4.2 3.6

3.2 6.4 6.6 7.2 5.0 10.5 S.3wc&c 1.8 ms-' , 5.4 4.5 4.3 -8.3 10.8 15.4 '7.7 14.4 8.4

Fre* E 7.2 4.8 4.7 G0 11.2 1 l . G 5.7 11.3 5.4walking 3.S 6.7 6.7 17.0 16.3 17.2 12s 17.0 IL0

Bicyclc.. GO rpm 4.4' 3.3 3.2 5.3 5.2 4.7 6.7 l . 6.0- .

Tab.3 - Local convective heat tranfer coefficient ( h e ) , i nW m-2 K-l, dur ing rest and ewer'cisei, in no rma1 air

movement ( 0 .l5 - 0 . 2 r n ~ - ~ )

V E RT I CA L D I RE CT I O N

. WA L K I N G DLRECTION

\ WIP SHOULDER..

Fig . 3 - '~ el at iv e mplitudes of hip and shoulder movement inup-and-down and backwa rd-and-f orward di rection.

Studie s using the Schlieren optical system have shownthe air-flow patterns around moving limbs (Clark et al.,


26/50

1974). Visualization of the air flows around the legs of arunnec have ashown that the "pendulum effectw produces .conpletely different flow patterns to those found in linearflows. The flow around a swinging thigh forms a bow wave and

a trailing wake and these are alternately established andreverscd by each change in direction of the swinging leg(Clark). The flows around the lower legs and forearms aresimilar in %sture, although more complex.

Classica1 fluid dynamics and heat tranfer theories areinappropriate for these condictions, as the movements of the-body during walking and running are far more contplicated thanthose associated with man-made stuctures on which the teory

- is based. Trasla tion of the bbdy through the air producesadditional complications; an. unidirectional air flow issuperiposed on the alternating flows produced by the*pendulum ef fect" ,

Schlieren visualisation shows similar flows aroundswinging and translating heated cylinders, used to simulatethe action of the limbs during the movement.

Measurements of local convective heat loss around thethighs 05 a runner on a treadmill were made in a climaticchamber by Clark. The results show that, both in still airand in the presence of wind, the distibution of a convectiveheat loss around the circumference of the thigh is differentfrom that in an unidirectional airflow.

~ r a ~ h i c a l ntegration was used to obtain a value forthe overall heat tranfer coefficient around the thigh. Thecoefficent was about twice as high as expected i p aunidirectional wind equa1 to the mean velocity of theoscillating leg. A lifi3arq ind, representing the efbect of

. traslation of the body, further increased the convective heatloss.

'1n rea1 condictions, during performance in fightingsports, athle tefs movements are also more complicated, thismeans we do n f t know, how much, heat tranfer coefficient for

convection froin the skin is enhanced in this situation.(Diabatic and irreversible trasformation in complex motion).On the basis of works of A . V. Nesterenko, who

demonstrated that experimental data of many works fa11 on onecurve if the Gukhmann number is used.

A very important improuvement of heat and mass tranfertheory with liquid evaporation into a turbolent air streamwas made by Smolsky et a1.(1962), Katto et al. (1975) andKumada et al. (1986). In these papers for heat tranfer by


27/50

evaporative cooling with heat inputs from surroundigs, it wasobtained and critically analized the following empiricalequation for the treatment of their experimental data.

whsre the number o Reynolds is directly proportional to thefluid air velocity and Gu is the ~ ukh ma nn umber equa1 to(T2 - TI)/ T2 ; the important point is: the "heat transfer ---mcoefficient" which or classlc.al theory of forced convectionwas .-i ndipenden t on temperature, for turbolent convection,with heat inputs, depends not only on air veloclty anddensity but also on skin and air temperature.

Considering this experimental equation the' more useful .

approximation f oqou r conditions, it is possible, making useof a modified Gukhmann number, to write the new convectiveheat exchange equatian as


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4 . 5 - HEAT EXCHANGE BY DIFFUSION AND MASS TRANSFER

Two modes of diffusion are responsible for the

exchange of matter between organisrns and the air surxoundingth'em.

Molecular diffusion operates withig organisms ( e . g . inthe lungs of a man) and in h thin skin of air forming theboundary layer that surrounds the whole organisn.

In the free ' atmosphere, transfer processes areS

dominated by the effects of turbolent diffusion, althoughmolecular diffusion continues to operate and is responsiblefor the degradation of turbolent energy into heat.

Mass transfer to or from objects suspended in a movingairsteam is analogous to hcai tran fer by convection and isconveniently related to a non-dimensional parameter similarto the Nusselt number of heat transfer theory. This is theSherwood number Sh defined by the equation

where- F - rnass fiux of a gas per unit surface area (g m-2 s-l) ,- x,, x = mean concentration of gas at the surface and in theatmoaphere ( g m-2 s - ~ ,

- D - molecular diffusivity of the gas in air ( m2 s-l).As FSh i ----e---------

D ( X , - X) / dthe Sherwood number can be defined as the ratio of actualmass transfer F to the rate of transfer that would occur ifthe same concentration-difference were established across alayer of still air of thickness d.

Just as the Nusselt number or forced convection is afunction of Vd/v (ReynolAs number) and v/k (Prandtl number),the Sherwood number is the same function of Vd/v and .theratio v/D which is known as the Schmidt number, abbreviatedt0 Cc.

Diffusion and mass transfer are the main phenomenarelated to sweating. Sweating glands exist in abundance inthe outer layers of the skin. They are stimulated bycolinergic. sympathetic nerves and secrete a hypotonic watery

i


29/50

solution onto the surfacd of the skin.This represents a large potential source o f cooling if

the sweat can be evaporated*, because each liter of sweatevaporated from the skin surface represents a loss of about2426 kJ of heat to the environment. Large losses of water bysweating can also pdse a potential threat to successfulthermoregulation because a progressive. depletion of bodywater occurs i f the fluid lost is not replaced. Dehydrationaffects thermoregulation significantly and contributes to arise in core temperature.

The difference in water vapor pressure on sweat-wettedskin surface and the air layer next to the skin controls therate of sweat evaporation, as does the speed of air movementover the skin.

As a consequence hot environments with high humiditylimit the amount of sweat that can evaporate. Sweat notevaporated drips or flows from the skin and does not resultin . any heat loss from the body. This can be deleterius,because it still represents a significant loss of watsr andsalt from thecbody.

Sodium chioride and potassium are very importantcostituents of sweat. The efficiency of cooling by sweat

- depends on the rate of evaparation E, which is determined .bythe gradient between the vapor pressure of the wetted skin(es k) and the partial pressure (vap or pressure) of watervapor in the ambient air (e,), mul tip lied by a root functionof effective air velocity at the skin surface ( V ) and thefraction of body surface that is wettsd.

When the heat production of the body is increased byexercise, skin temperature (T sk ) rises above that observedunder less humid conditions at the same air temperature. Whenthis occurs, more sweat glands are activated, therebyincreasing the fraction of wetted body surface.

At higher levels of e, or lower air velocities, thefraction of the body surface that is wetted increases unti1 .

the body'is completely wetted. Any further increase in sweatproduction does not contribute to cooling because the liquidperspiration drips off the body and is wasted as a coolant.

The passage from "insensible perspiration" to the -

"sensible r one may be ipotized between 29 O C and 30 O C asmean skin temperature. In our thermodynarnic equa tion theterm convection, which shares in eva oration, must bemultiplied therefore by a factor a = ( e -38

The well-known analogy between heat and mass tranfer


30/50

allows us writing the corresponding Sherwood number for vaportranfer in turb8lent .air stream as

To calculate the Gukhmann number,.it is convenient toreplace the weighted difference between the skin surface andair temperature (TSI( - Ta) / T, by the difference of virtual'temperagure.

f esk and ea are vapour pres,sure at the skin surfaceand in the air an d ,p is. air pressure, the gradient of virtualtemperature is

The importance of vapor pressure term, when Tsk is close toTa can be illustrated for the case of a man covered withsweat at 3 3 O C, and surrounded by still air at 3 0 C. and 20%relative umidity.

The size of the Gukhmann r&rtber allowing for thedifference in vapor pressure is -2.5 times the number

calculated from the temperature alone; th correspondinger or in calculating the Sherwood number (proportional toGu602) is about 20%.

Now we can write the evaporation cooling equation; onthe basis of experimental relation by Smolsky and Katto.

Considering the mass flow ond substitutjng theatmospheric 'pressure'with the ratio between molecular weightgas constant, and temperature it is possible to write:

This term accounts the corresponding flux of latentheat which comes from evaporation of sensible pe,rspiration,

, But not al1 the sweat produced is evaporated, From studiesperformed by Kobayashi et al. 1980, about percentage of sweatevaporated and dripped, it is possible to introduce a newterm which take in account that the percentage of evaporated'


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sweat from the skin, in uprigth position, may rise from 63 to65%.

On this basis the terms of convective and diffusiveheat loss, which account for evaporative coolinq, should bemultiplied by the factor:

which accounts us not only for the percentage of drops fallendown, but also for the problem that it is not possible tosweat much more that 1/10 of the whole physiological waterwithout rehydration.

At the end, on the basis of prcvio;s thermodynamicapproach, the heat-rate output will take the form of theequation given in the following page:


32/50

m

rI 1 'II Il 2165 DS, A ( esk-ea 1R,

+ I C 3 ---------- - - - - - - - - - - - - - - - - - v - - - 1.2l I

O . 2 ( T v s k- TV,)

Ii 1

ILa Tsik Tva l .

Ll IJ I


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- 5 - 0 APPENDIX: A COMPUTER CODE FOR THE ENERGY EQUATION

A semplified schema of the program for simulation ofenergy consuniption by. an athlete is given in Fig. A. Thevariations of skin .temperature, due to sweat, are alsocomputed. The steps below explain the program.

1) Genera1 variables and constants' are definited in the firs tphase,

M

2) The second step is the read in of the f iles related to themean human body temperature, the environmental temperature,the enetgy consumption ( 5 s computed from oxygen intake) andmean gray leve1 of the body (as a result of the processing o fthe images taken by the IR thermocamera).

3) Section 3 is the setting.o f environmental parameters:opening of the above listed files, opening of output file,copying of input files in the working area and sequence ofperiods (rest, light work, heavy work , maxinal work) with thenumber of samplings or each of them,

4 ) The phace 4 consists in the computing o the external

srface of the body.

For each period of work or rest and for every sampling in theperiod, the skin and environmental temperature (Kelvi ndegree) and atmospheric pressure are evaluated. On these basisthe energies are computed. - i

5) The computing of the radiating energy according to theprevious formula is the fifth phase.

6)Section six computes the energy exchange due to therespiratory system. Into this phase a choosing of pulmonary

surface and equivalent number of b'reaths is done due to thekind of work carried out by athlete; also the interna1temperature of the body is evaluated.

-v

7) The seven th section computes the heat losses due toconvection; it takes into account the threshold temperatureof 30 O C (303.16 O K ) over which the beginnning of sweat isassumed. In this phase the thermic conductivity Q the air on


34/50

DERNITION OFVARIABLES AND

- CONSTANTS

SAMPLINQ ?NOMORESAMPLING

v

2READ IN O FRELATED FILES

v

-

5

COMPUl'iNG OF THERADIATING ENERGY

* I

.COMPUTlNG OFTEMPERATUREVARIATIONS

.

Fig. A

3SETiING OFENVIRONMENTALPARAMETERS

6COMPUTING O F THEENERGY WCHANGEDUE T 0 THERESPIRATORY SYSTEM

8

COMPUTINO OFENERGY ASSOCIATEDT 0 MA SS TRANSFER

r

1 1 12 13COMPUTING OF STEPS EVALUATION OF TOTAL COMPUTING OF7 AN D 8 TAKING INTO 'LOST ENERGY WlTH T H E 4 SWEAT PROOUCEDACCO UNTT HE EVAPORATIVE FACTOR ANO EVAPORATE0

T EVAPORATIVF FACTOR

4

COMPUTING OFEXTERNAL BODYSURFACE

,n IZ

9EVALUATION OFTOTAL LOST ENERGY

'I

-.-).

1 OCOMPUTINO OF THEE VA P O R A ~ ~ V E ACTOR

7

HEAT LDSSES DUE T 0CONVECtlON


35/50

40

the boundary layer of the skin surface is also computed.

8 ) . The computing of the energy associated to the masstransfer occours in the phase 8. At this point the moleculardiffusion coefficient of air and ths saturation vapourpressure on the' boundary layer of the skin surface ' areneeded. The virtual temperature of air and the virtual skinsurface temperature are also computed.

9 ) This step, the nineth, is the evaluation of the totalenergy lost by athlete if the sweat ic not present (sum ofthe preceding losses).

10) The latent heat of.vaporioation of water on the skin

surface permits' the .computing of the evaporative factor astenth step of the program.

11) The section 11 evaluates the energies computed at thesteps 7 and 8 but taking into account tbe evaporation of thesweat from the skin through the evaporative factor.

12) The sum of the radiating energy, the respiratory systemheat exchange and the energies computed at the step 1 1 is thejob of this phase. At this point al1 the obtained data arewtitten on the output file ENERGIE'.DAT.

13) In the section 13 of the program it is computed the massof the sweat produced and evaporated according to the energyexchange by diffusion.

z 1 4 ) The last step of the program consists in the computing ofthe temperature increasing (due to the work of the exercise)and the temperature decreasing (du to the evaporated s&eat)of the skin.

~ e l w s th code of the pragram.


36/50

program ver-enc * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

C Prograrn for checking the energy consumption of an athlete in nonC working conditions.c** * ********************************************** * * * * * * * ************* * * * *

C

C*** 1 ) VAP..TABLES AN D CONS TANTS DEFINITIONSC

hl

char&~re r* l isp,string(l0),termoc*20,tzero*20,ener*2O~tongri*20character *l0 sequeninteger*2 nimvp(lO),flag,ind,index,indt,idx,negatinteger*4 lung,lunglreal*8 vtermc(500),vtzero(500),vener(500),tonog(500)real*8 peso,altez,supcorreal*8 p,ta,tsp,tmb(lO),energt,entevlogica1 e xrea148 neper

data s t r i n g / ~ 0 ~ , ~ l ~ , ~ 2 ~ , ~ 3 ~ t ~ 4 r , ~ 5 ~ , ~ 6 ~ , ~ 7 ~ , ' 8 ~ ~ ~data vtermc/500*0.0/vtzero/500*0.0/data neper/2.71828182845/

real*8 sigma,epsil,irrag,fatfdata sigma/5.6697d-8/epsi1/0.98/fatf/l/

data c1/0.06/lp/0.1.9/re08/4000/pr033/0.89/

data nsp/ 3.000,4.000,5.000,10.000,1 0.057,0.088,0.100, 0.103/

I . da ta ka/lO.O ,15.0 ,20.0, 30.0, 35.0, 40.0, 45.0,1 0.0250~0;0253~0~0260,0,0264,0.0267,0,0270~0.0274/

data c2/0.130/la/O. 34/

real*8 pltp2tp.3tp4tp5real*8 dht,fm,e2,el,tvp,tvatdiffusreal*8 $c033,c3,lambdl

. data sc033/0.86/c3/0.002/fm/lOOOOOO.O/1ambdl/243O/el/O.89/

data dh/10.0,15.0,20.0,30.0,35.0~C0.0145.0,1 22.7,23.4,24.9,25.7,26.$,27.2,28.0/

t

data pvsb/l0.0,ll.0,l2.0~13CO~14.0,15.0,16.0,l7.O,l8.O~l9.O~

1 20.0,21.0,22.0,23.0,24.0,25.0,26.0,27,0,28.0,29.0~1 30.0,31.0,32.0,33.0,34.0,35.0,36.0,37.0,38.0,39.0,1 40.0,41.0,42.0,43.0,44.0,45.0,1 1.227,1.312,1.402,1.497,1.598,1.704,1.817,~.937,~


37/50

real*8 lambda,clvg(7,2)real*8 diffev,convev,sudpr,cudevreal*8 enos(10),con(10,2),dffu(l0,2)real*8 incn(10) incp(10) incctlO) tempm(lO) d iftreal*8' mse, csm

data enos/10*0.0/con/20*0.0/dffu/20*0.0/data mse/99.7/csm/3.47/data clva/ 10.0, 15.0,. 20.0, 30,.0, 35.0, 40.0, 45.0,

1 2477.0,2465.0,2442.0,2430.,2418.0,2406.0,2394.0/

2) READ IN OF FILES (ATHLETErE EAN BODY TEMPERATURE, ENVIRQNMTEMPERAWRE, OXYGEN INTAKE, MEANGRAY LEVEL]

write (6,2)format(/,3xttNome del file della temperatura delltfatleta

1 (senza estensione DAT)r,/,3xft : I , $ )accept 5,1ungrtermocformat (q,a)

inquire (file-termoc(l:lung)//~.dat',exist=ex)if ( &notoex) thenwrite (6, lO) termoc(l:lung)format (/,3xtf11 ile f,a,r.DAT non esistef)goto l .

end ifwrite (6,20)fo rm at (/ ,3 ~, ~N om e el file della temperatura ambiente (senza

1 estensione DAT)',/,3xtt : ' ,$ )accept S,lung,tzeroinquire (file=tzero(l:lung)//'.dat~,exist=ex)if (.not.ex) then

write (6,lO-) tzero(1:lung)goto 19 'end if

write (6,311format(/,3xt 'Nome del file dell' >ener gia (senza estensione

1 D AT ) t t / t 3 ~ , ' : , t $ )accept 5 , lung,enerinquire (file=ener(l:lung)//'.dat',exist=ex)i f (.not.ex) then

write (6 ,lO ) ener(1:lung)goto 30

end ifwrite' (6,41 )fo rm at (/ ,3 xf ~N om e el file dei toni di grigio (senza estensione

1 DAT)' , / ,~X, ~ :accept 5,lungttongriinquire (file=tongri(l:lung)//'.dat',exist-ex)i f (.not.ex) then


38/50

write (6, lO) tongri(1:lung)goto 40

., end if

Cc * * * 3 ) SETTING OF ENVIRONMENTAL P W E T E R S

C - OPENING OF FILESopen (50tfile=termoc(l:lung)//'.dat',ctatus=told~)open (5l,file=tzero(l:l~ng)/J'=dat',ctatus=~old~)open (52,file=ener(l:l~ng)//'.dat~,status=~old~)open (53,file=tongri(l:l~ng)//'.dat',ctatus=~old~)

C - OUTPUT FILE' write (6,100)

100 format(/,3x,'Tutti i risultati totali e parziali sono riassunti1 nel file:tt/,23x,t ENERGIE.DATr)

inquire (fi?.e='energie.datf,existlex)if (.not.ex) goto 150

110 write (6,111)111 fo rm at (/ ,3 ~, ~1 1 ile ENERGIE.DAT esiste giam.t ,/t3x, rSi vuole

1 riscrivere o crearne una nuova versione? (r/n) : ' ,$ )accept 120, risp

120 format(a1if (ri~p.eq.'n*.or,risp.eq.~N~) goto 150i f ( r i~p .eq .~r~ .o r. r i sp .eq .~R~) hen

open (30tfile=tenergie.dat',status=toldt) .

c l o s e ( 3 0 , d i ~ p o s e = ~ d e l e t e ~ )goto 150end ifgoto 110

150 open (30,file=tenergie.dat',ctatus=tnewr)

write (30,241)* 241 for mat (l3 xttV ER1 FIC A EL CONSUMO ENERGETICOr,/,3XttQuando

1 la temperatura corporea a d ambiente ha valore zero ind icat1,/ ,3Xttu n errore .ne lla digitalizzazione dei dati in ingresso1 e quindif,/,3Xt~lrtannullamento i tutti i dati di uscita.',1/,3Xt100(~*r)t/r3x,'Legenda1/,4xftTSP - Temperatura della pelle (gradi Ke lv in Tt r1/,4xttTAMB = Temperatura ambiente (gr adi Kelvin)',1 / ,4xtf1RR = Energia dissipata per irrag giamento (Watt)',1 / ,4xttRESP = Energia dissipa ta con apparato respiratorio (Watt)',1 / ,4xttCONV - Energia dissipata per convezione (Watt)',1/,4xfrDIFF = Energia dissipata per diffusione (Watt)',1/,4x,'TOT = Energia totale = IRR + RES? + CONV + DIFF (Watt)',1/,4xftE-OS = Energia calcolata dal consumo di ossigeno (Watt)',1 / , 4 x t rC E = Energia convettiva con evaporazione (Watt)',~ / , ~ X , ~ D - E Energia diifusiva con evaporazione (Watt)' ,1 / , 4 x t f ~ - ~ E nergia t otale = IRR + RESP + C- + D-E (Watt)',l/tlOO( 1 t / )

C - COPYING OF INPWT FILES INTO THE WORKINGAREAread (50t*,end=250) vtermc(ind),ind=1,500)250 lung = ind-l

read (SI,*) (vtzero(ind),ind=l,lung)
http://tt/,23x,thttp://tt/,23x,t


39/50

C 1 COMPUTING OF ENERGY CONSUMPTIONBY OYGEN INTAKEC THE FACTOR 1 5 TAKES INTO ACCOUNTTHE SAMPLINGRATEC (1 5 SECONDS).

d o ind - 1,lungvener(ind) = vener(ind)*15*4.184*1000.0write(99,*) vener(ind)

end do

C - WORKING[OR REST) PERIOD SEQUENCE (BASAL, LIGHT WORK, HEAVYWORK,C MAXIHALWORK)260 write (6,261)261 , fo rm at (3 xt fI nd ic ar e a 'sequenza dei vari periodi di riposo

1 e/o lav or0 :~~ /,3 x,~ - asale e recupero (B)t ,/,3 x,t- esercizio1 leggero (L) r,/ ,3x ,t- esercizio pesante (P)f ,/,3 x,t- esercizio1 massimale ( M ) ' , / ~ ~ X ~ ' M ~ S S ~ ~ O0 caratteri /(esempio: bPbp) : tl,$)

accept 262,idx,sequen262' formaf(q,a)

do ind = 1,idxif (sequen(ind:ind).eq.'b'.or.seq~en(ind:ind).eq.~B~.or.

1 seq~en(ind:ind).eq.~l~.or.sequen(ind:ind).eq.~L~.or.1 sequen(ind:ind).eq.'p'.or.sequen(ind:ind).eqy1P1.or.1 sequen(ind:ind).eq.tmt.or.sequen(ind:ind).eq.fM) then

continue .,else

write (6,265)265 format(;/,3xftLettera errata nella se qu en za 1)

goto 260end if

en d do. E lungl = idx

wrt e (.6,268) lun g268 format (/ ,3 xf tC i sono ',i4,' dati nei fi le t, y)

C*** 4) COMPUTING OP THE EX T EW AL BODY SURFACEwrite (6,401)401 form at(/ ,3xt tPer il calcolo della superficie corporea (mq )

1 de l lMat le t a ind i~are : ,~, / ,3x ,~- eso ( in k g ) : l , $ )accept *,pesowrite (6,405).

405 format ( 3 x t f - l tezza f in cm) : l , $ ) .accept *,alte2supcor = (peso**0.425)*(a1tez**0.725)*0.007184write (6,410) supcor

410 format(/,3 xttSuperfi cie corporea (m q) : ',f6.3)

flag=O

450 write (6,451)451 format ( / ,3x t tE" presente il judogi ? (s/n) : l , $ )accept 120,rispif (risp.eq.'n'.or.risp.eq.'N') goto C 7 0if (risp.eq.'sf.or.risp.eq.'S') then


40/50

flag 1else

goto 450end ifcontinue

C * * * CO VU TI NG OF THE ENERGIESindt.= O

do ind L 1,lungl

write (30,485) sequen(ind:ind)485 format(3x trPeriodo i lavoro : ' , a , / )

write (30,486)486 . format ( t 4 , r T S P * , t 1 0 , t TA M B t t l 8 , t I R R t r t 2 6 , f R E S P t , t 3 5 , t C O N V f ,

tempo = 0.0negat = O ,sudpr = 0.0sudev = 0.0incn(ind) = 0.0incp(ind) = 0.0incc(ind) = 0.0enos(ind) = 0.0tempm(ind) = 0.0tmb(ind) - 0.0do index = l,nimvp(ind)

i f (vtermc(indt+index).eq.0.0.O.or.vtzero(indt+index).eq.O.O) then

irrag = 0.0respir = 0.0convez = 0.0convev = 0;Odiffus = 0.0,diffev = 0.0energt = 0.0dift = 0.0negat = negat + 1

goto '950end if

C - COMPUTING OF SKIN AN D E~ IR ON ME NT AL EMPERATUREtsp = Ytermc(indt+index) + 273.16ta = vtoero(indt+index) + 273.16

C - COMPUTING OF ATMOSPHERIC PRESSUREpa = 101.325-(ta-273.16)*0,0645

C * * * 5 ) COMPUTING OF RADIATING ENERGY

irrag = 15*supcor*sigma*epsil*fatf*(tsp**4-ta**4)

C * * * 6 ) ENERGY EXCHANGE DUE T0 THE RESPIRATORY SYSTEM


41/50

h

N.Xa-4

ln dN24- +rl--t- -

C C X nQ, @ a r i

C z ..-l -, c , - X

0

m a- A .cc

h C C - -

C rl r l * rdmi Q, . * - X2 5

r( 4-

+ + C - ( -X X - 4F a , x -O - -ri

V

.cc 't3 q4 -..-l f

W - (O a - XE x x x r d a

X ..-la t ; ( * l -u Q, r - i - l u

E n . e c o xU 3 -h - 4 -3 m c s u, e. \El 0'- rl - .+m-

Q,CJ .+l *-*-O e - m + r n c u c sv x e x C I 1 - ,a m a * w a xu 4 . d I - . r 1 0 -

. u (O - (d-.dm O l 4 0 J - J O O + J w - O

- p x O - x a - - V oW d N in- x m3 r A " o 2 % . . - l o w at

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42/50

diffi = diffi/5.diff = diff/5.nvolt = nprec + diffiiindexsp = sppre + diff*index

end ifif (index.eq.nimvp(ind)) thennprec = nvolt

sppre = spend if,

else if (seq~en(ind:ind).eq.~m~.or.sequen(ind:ind),eq.~n~)1 then

if (lind.eq.l).6r.(ind.gt.l.and.index.gt.5))thennvolt = nsp(4,l)sp m nsp(4,2)

elsediffi = nsp(4,l) - nprecdiff = nsp(4,2) - spprediffi = diffi/5.diff = diff/5.nvolt = nprec + diffi*indexsp = sppre + diff*index

end ifif (index.eq.nimvp(ind)) then

nprec = nvoltsppre - sp

end ifend if

C - COMPUTING OF INTERNAL BODY TEMPERATURE. coef = -0.00286*tsp + 1.89164V tint = tsp*coef .

C - COMPUTING OF THE FNERGYrespir = nvolt*cl*(kat/lp)*sp*re08*pr033*(tint-ta)

f

C*** 7) HEAT LOSSES DUE T0 CONVECTION

C - COMPUTING OF THRESHOLD TEMPERATURE 'if (tsp.ge.303.16) then

tdelt = 303.16

elsetdelt = tspend if

C - COMPUTING OF THERMIC CONDUCTIVITY OF AI2 ON SKIN SURFACEdo idx = 1,6

if((tsp-273.16).eq.ka(idxIl)) thenkat = ka(idx,2)goto 520

else if((ksp-273.16).eq.ka(idx+lIl)) thenkat = ka(idx+lt2)goto 520

else if((ttsp-273.16).lt.ka(idx+ltl)) then

kat = (((tsp-273.16)-ka(idx,l))*(ka(idx+l,2)-l ka(idxt2))/(ka(idx+lIl)-ka(idxtl)))+ka(idxb,2)goto 520

end if


43/50

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