Man Environment Heat Exchange Equation Applied To Judo

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

VALUTAZIONE

DEL COSTO ENERGETICO

DEGLI SPORT

DI COMBATTIMENTO IN

«REMOTE SENSING*

I

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. DAL MONTE'

C.O.N.I. Istituto Scienze dello Sport

Dipartimento di Fisiologia e biomeccanica

Coordinatore Scientifico

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M. FABBRI, L. ROCSI

ENEA Area Energia e Innovazione

Centro Ricerche Energia Casaccia, Roma

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Paper presenteci at the EIGHTH MEETING OF THE EUROPEAN

SOCIETY OF BIOMECHANICS

June 21-24, 1992

Rorne - Italy

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 tecnicclscientifici dei rapporti tecnici dell'ENEA rispecchiano l'opinione degli autori e non necessariamente quella dell'ente.

ABSTRACT

*

.

This progress report shows a new thermodynamic approach to the problem of man-environment heat exchange. The obtained goal for our studies is a new and more useiul forra of the equation describing the energy output from a man who performs a physical exercise. In appendix, the new energy equation is the basis of a computer code used to .get quantitative results in the C.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 unrequazione che descriva lo scambio termico uomo-ambiente in forma piur utilizzabile per la ricerca congiunta C.O.N.I.-E.N.E.A.F.I.L.P.J. In appendice viene presentato il codice di calcolo che utilizzando la nuova forma dell'equazione ottenuta, permette la verifica quantitativa delltesperienza. 7

1.0

-

THERNOPHYSIOLOGY: A SHORT OVERVIEW

2.0

-

THE EVOLUTION OF HEAT EXCHANGE EQUATIONS

2.1

-

THE MICROSCOPIC VISION UPDATE: THE WEINBAUM AND JIJI BIDTHERMAL EQUATION.

2.2'- MACROSCOPIC VISION UPDATE: THE CHARMY AND LEVIN MODEL r3.0

-,mAS

3.1

- CQMPONENTS OF THE INNER AND OUTER HEAT CURRENTS

.

,

C

4.0

-

4.1

-

HEAT EXCHANGE BY RADIATION

4.2

-

HEAT EXCHANGE BY CONDUCTION

3.2

E

HEAT ENGINE

PHYSICAL AND CHEMICAL HEAT REGULATION HEAT EXCHANGE, .CLASSICAL EQUATIONS END NEW THERXODYNAMIC APPROACH

5.0

- HEAT EXCHANGE BY RESPIRATORY SYSTEM - HEAT EXCHANGE BY CONVECTION FROM THE SKIN - HEAT E X C W G E BY DIFFUSION AtjD MASS TRANSFER - APPENDIX: A COMPUTER CODE FOR THE ENERGY EQUATION

6.0

-

4.3 4.4 4.5

BIBLIOGRAPHY

1.0

- THERMOPHYSIOBOGY:

A SHORT OVERVIEW

As is well-known, man is a homoiothermic animal. This means that his idea1 life conditions'are possibles only within a very limited temperature range, without the use of clothing. Both an "internal temperaturen and a "surface extcrnaln temperatura of the body can be identified since, in the case'of the man-environment heat exchange, homoiothermy is guaranteed by the existence of a temperature gradient from insidie to outside. Interna1 tempeqature can usually vary from 36.3O C. and 37.7O C. If it reaches 3g0-39.5O C. the individua1 is on the verge of a heat ,collapse; a 40?S0 C. value entaizs the risk of a complete paralysis of the therdo-regulating mechanisms; whereas values higher that 4 2 O C. cause irreversible brain - damage alongside with enzymic blocks and letal consequences. Tests' on animals showed tiiat the pre-optical hypothalamus is the main seat of thermic regulation contro1 processes. This area is assisted by extra-hypothalamic sensor located in the bone marrow, sensitive to the local temperature variations. In order not to alter the internal heat exchange, the heat produced by the oxydation and fission processes at muscolar level is removed by the body througth the skin. In the case of muscolar activity the heat energy produced by the fission pro-cesses builds up in the muscular mass and causes by the related increase in the local temperature which, ,thermally levelling off in the micr~ca~illaries, warms the blood flow. Hence the blood, after entering the muscle at the internal body temperature, reaches the skin surface at the muscle temperature, thereby dispersing the heat surp1.u~ through ~$11-knownphysical and physiological mechanisms. After al1 the heat energy produced by the physical and metabolic activity is removed from the production area by means of the blood flow and dispersed in the external environment at the skin level. Hence the changes in the skin blood flow play a key role in heat dispersion. The increase in the skin blood flow entails a further drafn on the cardio-circulatory load (the heart capacity can reach values 5-6 times higher than the basa1 ones for naximum loads), even though it is partially made up for by the increase in the plasmatic volume to the . I

detriment of the interstitial liquid. The changes stemming from the correspondent vasomotorial changes . practically confide themselves to change the features of the "skin radiatorn. indeed, ince the hlood floow can range from 0.16 to 2.6 litres/min/m the temperature, conductivity and skin heat dispersion ability are substantially altered. The process of heat dispersion in the external environment has a werely "physicalH chasacter and depens on the temperature humidity and radiant power of the integuments in relation to temperature humidity and speed of the environment air. occur by The man-environment heat axchange can convection, radiation, conduction and evaporation. Convection is the process transferripg heat from the skin to the environment by~direct radiation associated t& the status of thermal excita,tion of the air film molecules in contact with the body Radiation is the process tranferring heat from the skin to the environment by direct irradiation linked to the release of electromagnetic radiation emission in the infrared band by the body. Conduction is the process tranferring heat from a higher temperature area to a lower temperature one. Evaporation is the process tranferring heat from the skin to the 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 diffusion of steam through the skin; the latter over 30° C. known as "perspiratio sensibilis", which is. subject to the thermo-regulating contro1 causing perspiration. A further vaporization occurs dt the level of the mucosa of the brething segment. Therefore espiration is .ade through a he&t cession to the environment whiEh can be relevant, durlng bhysical efforts, due to the increase in the ventilation frequency. Thus physical activity and the related heat production trigger a series of physiological meohanisms designed to keep homoiothermy sueh as: variation in the oxygen consumption, lung ventilation, heart beating frequency, peripheral circulation and finally the activation of sweat-glandes.

a

.

.

4-

9

2.0

- THE

EVOLUTION OF HEAT EXCHANGE EQUATIONS

5

The study of the methods of regulating the body temperature has excited investigative interest since the dawning o£ Biomechanics. The subsequent developments of tbermodynamic theory and the related experiments have increased human understanding of this phenomenbn. In thermophysiology the key instrument for dissipating the interna1 heat surplus is given by the increase of the peripheral blood flow which, by changing the conductivity of muscular tissues, consequently alters the emission-dispersion characteristics of the "sknin radiant*. Even though the procesb for dissipating heat appears to be well-defined and undestandable in its entirety, indeed the "local~'microscopic vision of the heat exchange mechanism and the definition of the tis6ue temperature has so far been devote8 no satisfactory analytical description. The problem of human external body heat exchange is usually tackled determining both the indipendent variables in human thermal environment and the physiological "dependent" variables and ,at the end, applying an experimental modified heat tranfer theory (Fanger 1970, Kerslake 1972,Gagge 1972, Nitchell 1972, Hanson 1974, Gagge and Nishi 1977, etc.). Due to sport evolution, the need to extend knowledge calls for an in-depth analysis of the equations tegulating man-environment heat exchanges under "free" (real) conditions - with al1 the difficulties we can imagine. Even though these equations are al1 well-known - with a certain degree of approximation - they were confirmed by extrapolating them from Zaboratory controlled conditions: In this respect a joint study by C.O.N.I. - E.N.E.A. - F.1,L.P.J was started at the beginning of 1989 designed to assess the athleters energy eost in rea1 competition. Considering the high complexity of thc issue, it was recognized the need to tackle that through an integrated multi- disciplinary approach, by resorting to knowledge in the field of physiological biomechanics and the specific equipment provided by C.O.N.I., to the sophisticated methods and instrument provided by E.N.E.A. and finally to athletes and to the technical and specialized knowledge in the field of physical biomechanics provided by F.I.L.P.J. The "simple" idea is that of viewing athletes as

complex thermal machines. Therefore the joint applicakion of both principles of thermodynamics must allow us to statiitically assess the average work carried out by athletes during competitions. Obviously, 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 comon practice in sport to assess the athletefs work by means of the "simpleru indirect calorimetry. This means that through arl appropriate mechanical equivalent we can trace back - through the fuel kinetics the work carried out in laboratory which, for many sporti, is made day by day more similar.to the rea1 competitive load. In the case of fighting sports pertaining to F.I.L.P.J. (wrestling and judo) a e 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 idea is therefore that of retracing direct calorimetry by meqns of improved energy equations of the man-environment heat exchange, which take into account the phenomenon kinetics each point every 15 seconds.

.

2.1

- THE MICROSCOPIC

VISION UPDATE: ITHE WEINBAUM AND JIJI BIOTHERMAL EQUATION.

.

! ;

l

"

i

C'

I

'1,

!

.

Since 1985 through 1989, on the Journal of Biomechanical Engineering, a group of researchers from the New York University seemed to provide a remarkable contribution to the evolution of the microthermophysiology by defining a new biothermal equation. Weinbaum, Jiji, Zhu and Lemons thus proposed and then generalized an equation where the microscopic average tissue temperature was, for the first time, connected with the blood flow .and the local microvascular geometry. A mode1 was made of the basic machanism which allows the heat transfer from the tisiue to the blood. This transfer is not - as belie3sd so far - the result of the heat exchange with al1 capillaries, but the result of the heat exchange of arteriovenous counter-flow of those capillaries having a diameter higher that 100 pm, which are considered to be more important from the thermal viewpoint. This was made on the basis of a theoretical forecast proposed by Chen and Holmes in 1980 who - as for the microcapillary blood flow - made a clear cut distinction between the heat exchange and the mass (oxygen) exchange. This means that blood vessels under 50 pm are already thermally balanced with the local tissue and do not participate to the removal of heat which is exchanged and removed only at the leve1 of those arterioles and venoles having a diameter higher than 50 pm. The first equation proposed was valid only fÒr blood vessels of the same diameter, but it is interesting to note that the last generalization of the equation, to inclu&e different diameter blood vesseles and the expression of the effettive conductivity tensor, has the advantage of keeping the same analytical form alco in the genera1 case. In this last instance the mathematical device of the analytical exstension of the temperature function enables us to describe - with a good degree of approximation - the temperature range o-f the close tissue, thereby allowing for the first time to assess the theoretichl results by means of the experimental data of the tissue temperatu're.

2.2

-

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

,

A good exemplum of macroscopic heat exchange application is the whole body thermal model of a man, with a reafistic circulatory system, made by C. K. Charny and R. L. Levin (1989), used for simulating t h e r a p e u ~ chyperthermia treatments of non-thermoregulat8d malignant tumours. Man is lumped into 16 body segments; each body segment is subdivided into four tissue elements: core, muscle, fat, and skin. In the origina1 model there is only one central blood compartment; this last one is characterized by a single temperature throughout the,body at a given time. Therefore there are 64 tissue elements plus one blood compartment in the origina1 model; each tissue element is characterized by its tempereture, volume, surface area, density, specific heat, thermal conductivity, basal metabolic rate, basal evaporation rate, basal blood perfusion per unit of mass of tissue, and electrical conductivity. The blood compartment is characterized by a single temperature, volume, density, and specific heat. The new version of this model subdivides the central blood compartment into one arteria1 element and one venous element the abdominal segment is for each body segment. Also, subdivided into an abdomen and pelvis segment. Each of the seventeen body segment now consists of six layers: core, muscle, fat, skin, artery, and vein. Thus there are a total of 102 elements in the current model of the man: 68 tissue elements plus 34 blood elements. Each blood element-is now characterized by its volume, specific heat, density, and electrical conductivity. Arteria1 and venous blood flows through each segment via a large vessel which exchanges heat with the surrounding tissue. This surrounding tissue is the muscle layer in al1 of the body segfttents except the thorax, abdomen, neck, and head, in which the large artery and vein are both assumed to be embedded in the core tissue, Heat exchange in the pulmonary circulation is. modeled separately by considering the lungs and heart as part of the lumped thoracic. The effect of temperature on skin blood flow and sweating is modeled based upon the work of Stolwijk. The ancestor of this model is the thermoregulation model presented by S. J. Stolwijk 'and J. D. Hardy in 1977

which predicts, with reasonable accuracy,' th-e dynamic thermqregulatory responses to dynamic loads of ambient temperature and interna1 heat productios even during a very heavy exercise.

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3.0

-

MAN

AS HEAT ENGINE

The thermodynamic approach to the athlete-environment heat exchange is a very difficult task which shows us the high complexity of the "athleteN as heat engine and the lack of complete theory of the topic. Heat production by man depends upon a large number of factors which are also significant for the core temperature regulation. Roies of various importance are played by size of body, food consumption, age, sex, activity, function of glands with interna1 secretion, acclimatization, and above al1 the varying environmental temperatures and the continuously 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., Losses are those of removal of sensible heat by The conduction and convection, and by radiatlon governed by the temperature of the body and of the surroundings as well as by evaporation. Al1 of them are closely connected with weapher and climhte fluctuations. Dominating roles in these intricate influences are played by the characteristics of the human skin surface with its often greatly varying behaviour, and by the lungs respiratory sistem. Comprehension of the . changeable circumstances in the weather courses and climate structures are facilitated by a review of heat physiological facts. These dea1 "ith transport methods and the heat fluxes f rom body core towards body sheL1 and beyond to the surroundings. According to estimates by Hensel et al. (1973) in a human body at rest the greatest heat production (appcoximately 50%) is concentrate in the abdominal organs (particularly in the liver); under medium work loads the production is naturally taken over by the muscles (75 % ) . The sketch in (fig. 1) shows the processes of heat transport 'from the interior of the body to the skin surface. The bodyfs heat

l

emission and evaporation through the skin surface and the respiratory sistem including the lungs, besides+conduction and convection are the main mechanisms for heat exchange with the environment.

I

Fig. 1

-

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

3.1

-

COPIPONENTS OF THE INNER AND ,OUTER HEAT CURRENTS

Three factors are important in the heat transport from the interior to below the skin surface and above al1 within the skin system itself, namely : W* = blood stream (progress of arteria1 blood to below the outer. skin); WL = heat conduction stream, conditioned by the drop in temperature from the incide towards the outcide; WA = heat exchange (disorganized movement of liquid constituents of the skin). Thus the sum WB + WL + % constitutes the i n t e r n a l . heat stream which plays a decisive part in the principal behaviour of physical heat regulation. Total heat emissiofi Q, the external heat stteam, corresponds to khe sum of the four factors: Q P R + K + C + E

W /

where R is the K is the C is the E is the

heat heat heat heat

exchange exchange exchange exchange

by by 'by by

long wave emission, conduction, convection, evaporation by way of skin surface

4.0

-

HEAT EXCHANGE, CLASSICAL EQUBTIONS AND NEW

,THERNODYNAMICAPPROACH

-

In C.O.N.I. E.N.E.A. - F.I.L.P.J. experience t0 study athlete's performance in rea1 time using "remote sensing" techniques, it is basic to have predictive equations, as function of indipendent variables of the human thermal environment related to the "human heat engine" by skin temperature. If the athleters body is in thermal equilibrium with the environment, the application of the first principium of thermodynamics allows us to write the known relation: b

.IitCiL-È-o where M is the metabolic.energy. During the kinetic evolution of a performance, a correction factor must be introduced and the following equation is applicable:

P t i t E * L - è = * 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 lag of time present between the start of the performance and the visible thermal emission related and for the thermal tail present at the end of the same. it quantifies therefore the body trouble (inertia) to change his thermal status. For the evaluation of the body "thermal inertian usually it is applied the following. equation:

6

-

(Cb g ATb)/d t

where g represent the body weight, Cb is the specific heat of the body assumed to be 3.47 kJ/Kg OR but it may range from 2.93 u p t o 3.55 kJ/Kg O R (Hardy, 1970) and ATb is the mean body 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

temperature (Wyndham, 1973). The metabolic energy source M represents the free energy produced by the trasformation of chenical energy during aerobic and anaerobic-activities within the organism. It is impossible to d e s c d b e this process quantitatively, in a useful form, therefore usually it is assessed by the "more easyn measurement of fuel upkake (oxygen).by the formula:

where e is the respiratory factor and is volume of oxygen uptake, v02 Since the mechanical efficiency of the human body is mostly below 2 5 %, the interna1 heat production during exercises corresponds to the 75 % of the total energy utilized. The greater is the exercise intensity, the greater is the total amount of heat produced. The heat id excess has to be removed and dissipated in order to prevent overheating and hyperthermia. In heat transfer theory and fluid mechanics conditions at the bourdary of a finite body in-which heat is flowing are usually described in terms of one or three idealizatims, of which the last includes the first'two as special cases: 1) - the boundary is assumed to be maintained at a fixed preassigned temperature T, by good thermal.contact with a well-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, n*grad T vanishes at the boundary ( * &'scalar and hence product ) 3) - transfer of heat across the boundary is assumed to be proportional to the temperature of the boundary surface (this means the temperature relative to the surrounding cooling mediumj This is known as "Newtonfs law of coolingn. The transfer of heat across the boundary is characterized by a heat-transfer coefficient h (W/m 2 K ) such that at the surface the normal component of I is hT and therefore if n is the outward unit normal veotor to the surface, the boundary condition at the surface-is

r

j

.

.

The nature of the thermal contact is thus characterized by a parameter k/h which has the dimensions 0% length. Case 1 corresponds to k/h=O and case 2 corresponds to k/h becoming Infinite. Mixed cases may arise in which h has different values on different parts of the bo&ndary surface, as when some surfaces are in good thermal conctact with a reservoir. Then the mathematical form of the physical heat regulation equations satisfies this simple relation:

where Q is the heat rate for unit area in (W/m 2 ); (T2 - 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 produced by physical performance, al1 technical comlexity will be found in defining a right 'Iheat transfer coefficient" for each process performea -in the fundamental thermodynamic relation.

4.1

-

HEAT EXCHANGE BY RADIATION

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

where Tsk is the skin temperature, calculated directly by thermography or by assigning determined factors to each of the thermocouple neasurements (one every 30") proportionally t6 the fraction of the body total surface area,'represented by 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 StefanBoltzman law ( A = S T4 ) the heat transfer coefficent takes the form:

where a is the Stefan-Boltzman constant and equals 5.67 w ~ - ~ K - The ~ . term S(a) is tha 4n radiating arei of the human body surface according to Dubois surface, and will vary with posture. The term has been determined with considerable accuraey by Fanger (1970) by use of optical'methods and was found to vary from 0.70 for the sitting position to 0'.725 for standing within +/- 2 % regardless of height and body weight. When clothing is worn, the radiating area of the body,S(a) is increased by a factor f. Fanger and Breckenridge & Goldernan have shown that f increases approximately 15 % for each clo unit of clothing insulation worn, i.e., by factor (1 + 0.15 Iclo)' E is called radiation coefficent of the skin; it is the relation of the emission of a given surface to that of a black body at'the same temperature. Reliable measurement is by Buettner (1938) and set it for human skin at 0.954, for long wave emissivities, which is a deviation from the black body radiation of only about 5 a . This means that within the energy range spectrum of human skin (5 - 50y ) only l - e parts are reflected from vertically incoming radition, and the greatest percentage (approx. 95 % ) is absorbed. The radiation factor for skin is very close to that for water and other substances of importance in the skin structure. Obliquely

incoming radiation shows an s of 0.893 (Buettner, 1938). Gaertner and Goepfert (1964) again iqvestigatd the radiation characteristics of live human skin. For the back they found E at 0.976, for the forearm at 0.960 and the sole of the foot at 0.941. incidentally the average lies very close to the value determined by Buettner. Based on the studies by the above-mentioned authors it must again be stated that live 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).

Radiation figures $or temper-ature radiation (After ~uettner, 1938) BLACK BODY SNOW FROST WATER HUMAN SKIN ( e ) BRONZE COLOUR FUR WOOL PINE NEEDLES WOOD CLOD WITH GRASS E VARIES

1.000

FOR DRY AND PERSPIRED SKIN.

.

4.3

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HEAT EXCHANGE BY RESPIRATORY SYSTEM

Respiration is the exchange of'the gases oxygen and carbon dioxide between tissue and atmospheric air. The subdivision into approximately 3-4 millions of alveoli at the causes the lungs end of the finest branches 02 the trache to attain an inner surface-of about 75.m Noce, pharyngeal area, trachea and bronchi4 do not pafticipate in the gas exchange. They do, however, have the important job of warming the inspired air to body temperature and to saturate it with wate r vapour The surface of these spaces.are covered with ciliated epithelium, whereby its cjliae move back and forth-during the respiratory process. Thanks tho this process foreign bodies can be removed from the respiratory system. Reflex actions such as sneezing, coughing, ect. serve the same purpose. In the respiratory system the separation of aereosois takes place in the alveolar area essentially by three diffusign, 'inertial separation (rebound processes, i.., effect) and sedimentation. Fig. 2 conveys an idea of the diameter, surface and volume of the respiratory systemfs

-5,.

.

~ e n g t i ~surhc. [cm]

8 . Trachea 2. Mbin bronchii 3 Lobar bronchii

G

5. Sucsegmcnla~bc 4. Terminai br.

0.5

7. R.spirdtoy

.

3 1 .CJ

VQIU~~.

F":;jC"

Em**]

60

t2

Scgmcntri br.

4.

[cm-7

24 'O

*O

5

15 100 200

Coneuctivc zone wilh . ciih epiih+iivm

3 10

br

8. AIveoirr duct'

g. AIvco1.r

racc.

c insoiration condii;on carecied 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, respiratory conditiòns:

1966)

and

is

based

on the

1

minute volume = 15 1. *in-' respiratory frequency = 15 min -1

I

'r

.

The main process of heat exchange by respiratory sistem are convection and mass tranfer from the respiratory airwais. Convective heat exchange by the lyngs depends both on the pulmonary ventilation and the temperature difference between expired and ambient air. Pulmonary ventilation is related to metabolic rate, then usually the following approximated formula was used according to Hanson, 1974:

+-

.

~n m a n ~ t h eniass-tranfec from airways i s n o t controlled thermoregulatory mechanisms. Heat loss from the by respiratory airwais was calculed by formulas proposed by Mitchell, 1972: Eres

-

14.9

N (5.880

-

p,)

or by Snellen, 1966: Eres

-

VO2 (1.977 XCOZ R

-

1.429 XO2)

Fram our point of view, for our res6arch, it appares more useful treating the problem by .theoretical thermodynamics. The theoretical thermodynamical analysis of convection is greatly simplified by using non dimensional groups tbat come from similitary theory. A body imersed in a fluid loses heat through a laminar boundary layer o£ uniform thickness, then the heat losses per unit area can be written as

where K is the thermal conductivity of the fluid; 6 is the thickness of the boundary layer, is the mean skin temperature and T, in the ambient temperature. The same equation can be used in a purely forma1 way to describe the heat loss by forced or free convection from any object with a mean surface temperature of TSk surrounded

by flwid at Ta even though the boundary layer is neither laminar nor uniformly thick. In this case, 6 is the thickness of an equivalent rather than a rea1 laminar layer. It is determined by the size and geometry of the surface and by the way in which fluid circulates over it. A more useful form of equation can be derived by substituting a characteristic dimension of the body d for the equivalent boundary-layer thickness, which cannot be measured directly, 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 forces associated with geometrically similar.bodies immersed in a moving fluid, athe ~ u s s d tnumber provldes a basis for comparing rates of convective heat loss from kimilar bodies of different scale exposed to different wind-speeds. In forced convection, the Nusselt number depends on the rate of heat transfer through a boundary layer from a surface hotter or cooler than the air passing over it, a process 'analogous to the transfer of momenturn by skin friction. The Nusselt number is therefore expected to be -a function of the Reynolds nuxnber (specifying the boundary layer thickness for momentum) and the ratio of boundary layer thicinesses for heat ( t ) and for momentum (tM) This ratio is a Function of the Prandtl number defined < b y (v/k), Measurements of heat 'loss by forced convection from planes, cylinders and spheres can be described by the genera1 relation

.

'

where m and n are experimental constants and

tM/ti

-

Prm

.

The convective exchange by the lungs is function of frequency of breathings and of air quantity inspired (see Tab. 2 ) . Because we have different values of lung ventilation at different levels of activity, the better way to have the convective stream is to define an "effettive cylindrical surfacew of the lungs. Obviously it will depend by the "tidal volume" of athlete at zest or duriqg exercise. Simple

-

lculations show that ef ective surface may range from 3 m at,rest, up to 0.103 mf during maximal exercise.. C

0.057

i l . &41-i4 lor; p. a ll. pp. 4J-U 104. p. 6J .

Nwborn

9 :O Il 22

. 2Cb13vk 4.&h 6.6 d

.

v

34

15

0.5

2.5-1.3 3~

21

21

DJ

3.1

29

11

0.G

*

I

.

VI^ in column 2 .rc b d y 4 g h t 1 rrkrabk lo iIH diinrinn quoicd in cilumn 1.f: .

.

I m u u y (bruthdmin); V T -6d.11

,

volumc (ml):

4

-

&UU

1.16. p. 13 I l . P. 42 O, p.220: Il. p.4: ~ofumc( ~ m i n ~SA ;

Tab. 2 - ~electsdlung ventilation values at different levels of activity as a function 6f age The experimental points characterizing heat transfer lie on a straight line of the well-known "critica1 relation"

Thic experimental form of Nusselt nunìber relation:

.

II?. p. 351: I l S . 1%. >M:430. P. 50: $07. p. l034

51l.u*ij.ri-

i

aurlwt aru.

.

gives us the final

where - n is the breth frequency value: 3 at rest, 4 for light exercise, 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 the body core temperature, - Ta is the ambient temperature, - K, is the thermal conductivity of Che fluid.

flow

-

fig.3.

Body Region

-

Rcsting

H a d Chs h& U arinr p w~ ain d r~ fiichs ~ Le*

Silling

EI :m

Trad~rrill 0.9 m r-L wc&c 1.8 ms-' , Fre* walking

Bicyclc..

GO rpm -

-

Tab.3

..

\

Fig. 3

the

3.2 4.2 5.4

25 3.6

2.4 3.2

4.5

4.3

4.0 6.4 -8.3

7.2 3.S

4.8 6.7

4.4'

3.3

4.7 6.7 3.2

G.0 17.0 5.3

3.3 6.6

7.2

10.8

15.4

11.2 16.3

1l.G 17.2 4.7

5.2

1.G

Mun

(h3

3.7 10.5 14.4

S.3 8.4

5.7

11.3

5.4

12s

17.0

28 5.0 '7.7

6.7

3.1

IL0 l . 6.0

.

Local convective heat tranfer coefficient ( h e ) , in W m-2 K-l, during rest and ewer'cisei, in norma1 air movement ( 0 .l5 - 0 . 2 r n ~ - ~ )

VERTICAL

DIRECTION

.WALKING

DLRECTION

WIP

SHOULDER

- '~elativeamplitudes of hip and shoulder movement in up-and-down and backwa rd-and-f orward di rection.

Studies using the Schlieren optical system have shown air-flow patterns around moving limbs (Clark et al.,

p.

1974). Visualization of the air flows around the legs of a runnec have ashown that the "pendulum effectw produces conpletely different flow patterns to those found in linear flows. The flow around a swinging thigh forms a bow wave and a trailing wake and these are alternately established and reverscd by each change in direction of the swinging leg (Clark). The flows around the lower legs and forearms are similar in %sture, although more complex. Classica1 fluid dynamics and heat tranfer theories are inappropriate for these condictions, as the movements of thebody during walking and running are far more contplicated than those associated with man-made stuctures on which the teory - is based. Traslation of the bbdy through the air produces additional complications; an. unidirectional air flow is superiposed on the alternating flows produced by the *pendulum effect" , Schlieren visualisation shows similar flows around swinging and translating heated cylinders, used to simulate the action of the limbs during the movement. Measurements of local convective heat loss around the thighs 05 a runner on a treadmill were made in a climatic chamber by Clark. The results show that, both in still air and in the presence of wind, the distibution of a convective heat loss around the circumference of the thigh is different from that in an unidirectional airflow. ~ r a ~ h i c a lintegration was used to obtain a value for the overall heat tranfer coefficient around the thigh. The coefficent was about twice as high as expected i p a unidirectional wind equa1 to the mean velocity of the oscillating leg. A lifi3arqwind, representing the efbect of traslation of the body, further increased the convective heat loss. '1n rea1 condictions, during performance in fighting sports, athletefs movements are also more complicated, this means we donft 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 one curve if the Gukhmann number is used. A very important improuvement of heat and mass tranfer theory with liquid evaporation into a turbolent air stream was made by Smolsky et a1.(1962), Katto et al. (1975) and Kumada et al. (1986). In these papers for heat tranfer by

.

evaporative cooling with heat inputs from surroundigs, it was obtained and critically analized the following empirical equation for the treatment of their experimental data.

whsre the number o£ Reynolds is directly proportional to the fluid air velocity and Gu is the ~ukhmannnumber equa1 to (T2 TI)/ T2 ; the important point is: the "heat transfer coefficient" which £or classlc.al theory of forced convection was.-indipendent on temperature, for turbolent convection, with heat inputs, depends not only on air veloclty and density but also on skin and air temperature. Considering this experimental equation the'more useful . approximation foqour conditions, it is possible, making use of a modified Gukhmann number, to write the new convective heat exchange equatian as

-

---m

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 surxounding th'em. Molecular diffusion operates withig organisms ( e . g . in the lungs of a man) and in h thin skin of air forming the boundary layer that surrounds the whole organisn. In the free' atmosphere, transfer processes are dominated by the effects of turbolent diffusion, although molecular diffusion continues to operate and is responsible for the degradation of turbolent energy into heat. Mass transfer to or from objects suspended in a moving airsteam is analogous to hcai tranfer by convection and is conveniently related to a non-dimensional parameter similar to the Nusselt number of heat transfer theory. This is the Sherwood number Sh defined by the equation S

-

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 the atmoaphere ( g m-2 s - 1~, - D molecular diffusivity of the gas in air ( m2 s-l). As F

Sh

i -----e---------

D (X,

-

X) / d

the Sherwood number can be defined as the ratio of actual mass transfer F to the rate of transfer that would occur if the same concentration-difference were established across a layer of still air of thickness d. Just as the Nusselt number £or forced convection is a function of Vd/v (ReynolAs number) and v/k (Prandtl number), ' the Sherwood number is the same function of Vd/v and .the ratio v/D which is known as the Schmidt number, abbreviated t0 Cc. Diffusion and mass transfer are the main phenomena related to sweating. Sweating glands exist in abundance in the outer layers of the skin. They are stimulated by colinergic. sympathetic nerves and secrete a hypotonic watery i

-

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 sweat evaporated from the skin surface represents a loss of about 2426 kJ of heat to the environment. Large losses of water by sweating can also pdse a potential threat to successful thermoregulation because a progressive. depletion of body water occurs if the fluid lost is not replaced. Dehydration affects thermoregulation significantly and contributes to a rise in core temperature. The difference in water vapor pressure on sweat-wetted skin surface and the air layer next to the skin controls the rate of sweat evaporation, as does the speed of air movement over the skin. As a consequence hot environments with high humidity limit the amount of sweat that can evaporate. Sweat not evaporated drips or flows from the skin and does not result in . any heat loss from the body. This can be deleterius, because it still represents a significant loss of watsr and salt from thecbody. Sodium chioride and potassium are very important costituents of sweat. The efficiency of cooling by sweat depends on the rate of evaparation E, which is determined .by the gradient between the vapor pressure of the wetted skin (esk) and the partial pressure (vapor pressure) of water vapor in the ambient air (e,), multiplied by a root function of effective air velocity at the skin surface (V) and the fraction of body surface that is wettsd. When the heat production of the body is increased by exercise, skin temperature (Tsk) rises above that observed under less humid conditions at the same air temperature. When this occurs, more sweat glands are activated, thereby increasing the fraction of wetted body surface. At higher levels of e, or lower air velocities, the fraction of the body surface that is wetted increases unti1 . the body'is completely wetted. Any further increase in sweat production does not contribute to cooling because the liquid perspiration drips off the body and is wasted as a coolant. The passage from "insensible perspiration" to the "sensibler one may be ipotized between 29 O C and 30 O C as mean skin temperature. In our thermodynarnic equation the term convection, which shares in eva oration, must be multiplied therefore by a factor a = ( eT-38 The well-known analogy between heat and mass tranfer

allows u s writing the corresponding Sherwood number for vapor tranfer in turb8lent .air stream as

To

calculate the Gukhmann number,.it is convenient to replace the weighted difference between the skin surface and air temperature (TSI( - Ta) / T, by the difference of virtual' temperagure. Ìf esk and ea are vapour pres,sure at the skin surface and in the air and,p is.air pressure, the gradient of virtual temperature is

The importance of vapor pressure term, when Tsk is close to Ta can be illustrated for the case of a man covered with sweat 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 the difference in vapor pressure is -2.5 times the number calculated from the temperature alone; thè corresponding er or in calculating the Sherwood number (proportional to Gu602) is about 20%. Now we can write the evaporation cooling equation; on the basis of experimental relation by Smolsky and Katto. substitutjng the Considering the mass flow ond atmospheric 'pressure'with the ratio between molecular weight gas constant, and temperature it is possible to write:

,

This term accounts the corresponding flux of latent heat which comes from evaporation of sensible pe,rspiration, But not al1 the sweat produced is evaporated, From studies performed by Kobayashi et al. 1980, about percentage of sweat evaporated and dripped, it is possible to introduce a new term which take in account that the percentage of evaporated'

sweat from the skin, in uprigth position, may rise from 63 to 65%. On this basis the terms of convective and diffusive heat loss, which account for evaporative coolinq, should be multiplied by the factor:

which accounts us not only for the percentage of drops fallen down, but also for the problem that it is not possible to sweat much more that 1/10 of the whole physiological water without rehydration. At the end, on the basis of prcvio;s thermodynamic approach, the heat-rate output will take the form of the equation given in the following page:

m

r

I +

l

IC3

I I L

2165 DS, ---------La

Tsik

A( esk-ea 1R, -----------------v---

O. 2 Tva

(Tvsk

-

1 'I I I l I TV,) 1.2 i 1 l. l l I J I

-

5 - 0 APPENDIX: A COMPUTER CODE FOR THE ENERGY EQUATION semplified schema of the program for simulation of energy consuniption by. an athlete is given in Fig. A. The variations of skin .temperature, due to sweat, are also computed. The steps below explain the program. A

1) Genera1 variables and constants' are definited in the first phase, M' 2) The second step is the read in of the files related to the mean human body temperature, the environmental temperature, the enetgy consumption ( 5 s computed from oxygen intake) and mean gray leve1 of the body (as a result of the processing of the images taken by the IR thermocamera). 3) Section 3 is the setting.of environmental parameters: opening of the above listed files, opening of output file, copying of input files in the working area and sequence of periods (rest, light work, heavy work, maxinal work) with the number of samplings £or each of them,

The phace 4 consists in the sùrface of the body. 4)

computing o£ the external

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

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

6) Section six computes the energy exchange due to the respiratory system. Into this phase a choosing of pulmonary surface and equivalent number of b'reaths is done due to the kind of work carried out by athlete; also the interna1 temperature of the body is evaluated. -v

7) The seventh section computes the heat losses due to convection; it takes into account the threshold temperature of 30 O C (303.16 O K ) over which the beginnning of sweat is assumed. In this phase the thermic conductivity Q £ the air on

v

2 READ IN O F RELATED FILES

-

3

DERNITION OF VARIABLES AND CONSTANTS

4

SETiING OF ENVIRONMENTAL PARAMETERS

COMPUTING OF EXTERNAL BODY SURFACE

SAMPLINQ ?

NO MORE SAMPLING

v

5

6

COMPUl'iNG OF THE RADIATING ENERGY

*

8

7 COMPUTING OF THE ENERGY WCHANGE -.-). HEAT LDSSES DUE T 0 DUE T 0 THE CONVECtlON RESPIRATORY SYSTEM

I 9

EVALUATION OF TOTAL LOST ENERGY

COMPUTINO OF ENERGY ASSOCIATED T 0 MASS TRANSFER

'

1O COMPUTINO OF THE E V A P O R A ~ ~ VFACTOR E

I

,n

Z

r

. T

11 COMPUTING OF STEPS 7 AND 8 TAKING INTO ACCOUNTTHE EVAPORATIVF FACTOR

12

EVALUATION OF TOTAL 'LOST ENERGY WlTH T H E 4 EVAPORATIVE FACTOR

13

COMPUTING OF SWEAT PROOUCED ANO EVAPORATE0 I

.COMPUTlNG OF TEMPERATURE VARIATIONS

Fig. A

40

the boundary layer of the skin surface is also computed. 8 ) . The computing of the energy associated to the mass transfer occours in the phase 8. At this point the molecular diffusion coefficient of air and ths saturation vapour pressure on the' boundary layer of the skin surface ' are needed. The virtual temperature of air and the virtual skin surface temperature are also computed.

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

10) The latent heat of.vaporioation of water on the skin surface permits' the .computing of the evaporative factor as tenth step of the program. 11) The section 11 evaluates the energies computed at the steps 7 and 8 but taking into account tbe evaporation of the sweat from the skin through the evaporative factor. 12) The sum of the radiating energy, the respiratory system heat exchange and the energies computed at the step 11 is the job of this phase. At this point al1 the obtained data are wtitten on the output file ENERGIE'.DAT.

13) In the section 13 of the program it is computed the mass of the sweat produced and evaporated according to the energy exchange by diffusion. z

1 4 ) The last step of the program consists in the computing of

the temperature increasing (due to the work of the exercise) and the temperature decreasing (dué to the evaporated s&eat) of the skin. ~ e l Ò wis thé code of the pragram.

program ver-en

c************************************************************************* C C

Prograrn for checking the energy consumption of an athlete in non working conditions.

c************************************************************************* C

C*** 1 ) VAP..TABLES AND CONSTANTS DEFINITIONS C

h

l

char&~rer*l risp,string(l0),termoc*20,tzero*20,ener*2O~tongri*20 character *l0 sequen integer*2 nimvp(lO),flag,ind,index,indt,idx,negat integer*4 lung,lungl real*8 vtermc(500),vtzero(500),vener(500),tonog(500) real*8 peso,altez,supcor real*8 pà,ta,tsp,tmb(lO),energt,entev logica1 ex rea148 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,fatf data sigma/5.6697d-8/epsi1/0.98/fatf/l/

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

I

.

1

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

1

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

data c2/0.130/la/O.

34/

real*8 pltp2tp.3tp4tp5 real*8 dht,fm,e2,el,tvp,tvatdiffus real*8 $c033,c3,lambdl data sc033/0.86/c3/0.002/fm/lOOOOOO.O/1ambdl/243O/el/O.89/

..

1

data dh/10.0,15.0,20.0,30.0,35.0~C0.0145.0, 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,~

real*8 lambda,clvg(7,2) real*8 diffev,convev,sudpr,cudev real*8 enos(10),con(10,2),dffu(l0,2) real*8 incn(10) ,incp(10),incctlO),tempm(lO) ,dift real*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.Ò,2418.0,2406.0,2394.0/

2) READ IN OF FILES (ATHLETErE MEAN BODY TEMPERATURE, ENVIRQNMENTAL TEMPERAWRE, OXYGEN INTAKE, MEAN GRAY LEVEL] write (6,2) format(/,3xttNome del file della temperatura delltfatleta 1 (senza estensione DAT)r,/,3xft : I,$) accept 5,1ungrtermoc format (q,a) inquire (file-termoc(l:lung)//~.dat',exist=ex) if ( ¬oex) then write (6,lO) termoc(l:lung) format (/,3xtf11 file f,a,r.DAT non esistef) goto l . end if write (6,20) format(/,3~,~Nomedel file della temperatura ambiente (senza : ',$) 1 estensione DAT)',/,3xtt accept S,lung,tzero inquire (file=tzero(l:lung)//'.dat~,exist=ex) if (.not.ex) then write (6,lO-) tzero(1:lung) goto 19 ' end if write (6,311 format(/,3xt 'Nome del file dell' >energia (senza estensione 1 DAT)tt/t3~,' : , t $ ) accept 5 , lung,ener inquire (file=ener(l:lung)//'.dat',exist=ex) if (.not.ex) then write (6,lO) ener(1:lung) goto 30 end if write' (6,41) format(/,3xf~Nomedel file dei toni di grigio (senza estensione 1 DAT)',/,~X,~ : accept 5,lungttongri inquire (file=tongri(l:lung)//'.dat',exist-ex) if (.not.ex) then

write (6,lO) tongri(1:lung) goto 40 ., end if C

c*** C

-

3) SETTING OF ENVIRONMENTAL P W E T E R S OPENING OF FILES open (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~)

-

OUTPUT FILE write (6,100) • 100 format(/,3x,'Tutti i risultati totali e parziali sono riassunti 1 nel file:tt/,23x,t ENERGIE.DATr) C

'

110 111 120

150 *.

241

inquire (fi?.e='energie.datf,existlex) if (.not.ex) goto 150 write (6,111) format(/,3~,~11file ENERGIE.DAT esiste giam.t,/t3x,rSi vuole 1 riscrivere o crearne una nuova versione? (r/n) : ',$) accept 120, risp format(a1 if (ri~p.eq.'n*.or,risp.eq.~N~) goto 150 if (ri~p.eq.~r~.or.risp.eq.~R~) then . open (30tfile=tenergie.dat',status=toldt) close ( 3 0 , d i ~ p o s e = ~ d e l e t e ~ ) goto 150 end if goto 110 open (30,file=tenergie.dat',ctatus=tnewr) write (30,241) format(l3xttVER1FICADEL CONSUMO ENERGETICOr,/,3XttQuando 1 la temperatura corporea ad ambiente ha valore zero indicat 1,/,3Xttun errore.nella digitalizzazione dei dati in ingresso 1 e quindif,/,3Xt~lrtannullamento di tutti i dati di uscita.', 1/,3Xt100(~*r)t/r3x,'Legenda 1/,4xftTSP Temperatura della pelle (gradi KelvinTtr 1/,4xttTAMB = Temperatura ambiente (gradi Kelvin)', 1/,4xtf1RR = Energia dissipata per irraggiamento (Watt)', 1/,4xttRESP = Energia dissipata 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/,4xtrC E = Energia convettiva con evaporazione (Watt)', ~/,~X,~D-= E Energia diifusiva con evaporazione (Watt)', 1 / , 4 x t f ~ - ~ Energia totale = IRR + RESP + C-E + D-E (Watt)', l/tlOO( 1t / )

-

-

COPYING OF INPWT FILES INTO THE WORKING AREA read (50t*,end=250) (vtermc(ind),ind=1,500) 250 lung = ind-l read (SI,*) (vtzero(ind),ind=l,lung) C

C 1 C C

COMPUTING OF ENERGY CONSUMPTION BY OYGEN INTAKE THE FACTOR 15 TAKES INTO ACCOUNT THE SAMPLING RATE (15 SECONDS). do ind 1,lung vener(ind) = vener(ind)*15*4.184*1000.0 write(99,*) vener(ind) end do

-

- WORKING

[OR REST) PERIOD SEQUENCE (BASAL, LIGHT WORK, HEAVY WORK, MAXIHAL WORK) 260 write (6,261) 261 format(3xtfIndicare la 'sequenza dei vari periodi di riposo 1 e/o lavor0:~~/,3x,~-basale e recupero (B)t,/,3x,t- esercizio 1 leggero (L)r,/,3x,t- esercizio pesante (P)f,/,3x,t- esercizio S ~caratteri ~O /(esempio: bPbp) : t 1 massimale ( M ) ' , / ~ ~ X ~ ' M ~ S10 l,$) accept 262,idx,sequen 262' formaf(q,a) C C

,

265

.

E

do ind = 1,idx if (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) format(;/,3xftLettera errata nella sequenza1) goto 260 end if end do lungl = idx

€

268

wrìte (.6,268) lung format (/,3xftCi sono ',i4,' dati nei filet,y)

C*** 4) COMPUTING OP THE E X T E W A L BODY SURFACE write (6,401) format(/,3xttPer il calcolo della superficie corporea (mq) 401 1 dellMatleta indi~are:,~,/,3x,~Peso (in kg) : l , $ ) accept *,peso write (6,405). 405 format ( 3 x t f -Altezza f i n cm) : l , $ ) accept *,alte2 supcor = (peso**0.425)*(a1tez**0.725)*0.007184 write (6,410) supcor format(/,3xttSuperficie corporea (mq) : ',f6.3) 410

.

450 451

flag=O write (6,451) format (/,3xttE" presente il judogi ? (s/n) : accept 120,risp if (risp.eq.'n'.or.risp.eq.'N') goto C70 if (risp.eq.'sf.or.risp.eq.'S') then

l , $ )

flag 1 else goto 450 end if continue C***

COVUTING OF THE ENERGIES indt.= O do ind L 1,lungl

485

486

.

write (30,485) sequen(ind:ind) format(3xtrPeriododi lavoro : ' , a , / ) write (30,486) format (t4,rTSP*,t10,tTAMBttl8,tIRRtrt26,fRESPt,t35,tCONVf,

tempo = 0.0 negat = O , sudpr = 0.0 sudev = 0.0 incn(ind) = 0.0 incp(ind) = 0.0 incc(ind) = 0.0 enos(ind) = 0.0 tempm(ind) = 0.0 tmb(ind) 0.0

-

do index = l,nimvp(ind) i f (vtermc(indt+index).eq.0.0.O.or.vtzero(indt+index)

.eq.O.O) then irrag = 0.0 respir = 0.0 convez = 0.0 convev = 0;O diffus = 0.0, diffev = 0.0 energt = 0.0 dift = 0.0 negat = negat + 1 goto '950 end if C

-

C

-

COMPUTING OF SKIN AND E~IRONMENTALTEMPERATURE tsp = Ytermc(indt+index) + 273.16 ta = vtoero(indt+index) + 273.16 COMPUTING OF ATMOSPHERIC PRESSURE pa = 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

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

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l

end if if (sequen(ind:ind).eq.~bt.or.sequen(ind:ind).q.Bt) then write (30,1510) tempm(ind),tmb(ind) 1510 format(3xt'temperatura media misurata dai toni di 1 grigio : t,f7.2,/,3x,ttemperatura media della pelle : I, l f7.2) end if

indt ='indt + nimvp(ind) end do

!(ind)

C*** 15) THE END do ind = 1,4 close(49+ind) end do

-

1,2 do ind .close(29+ind) end do 3000. continue en&-

BIBLIOGRAPHY

.

m

BEJAN A. "Heat Tranfer-Based,Reconstruction of the Coneepts and Laws of Classica1 Thermodynamicsu Journai of Heat. Tranfer 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 . 'Termoregulatory responses to skin wetting during prolonged treadmill runniqg" Medicine and Science in Sports and Exercise Copyright 1987 by American College of Sports Medicine CAMPBELL G.S., McARTHUR A.J. and MONTEITH J.L. "Windspeed dependence of heat and mass transfer through coats and clothing" Boundary-Layer Meteorology 18 (1980) 485-493 CENA K. and MONTEITH J.L. Transfer~processes in animai c0atS I o Radiative transferu IIO - Conduction and convection" "IIIO - Water vapour diffusion" Proc. R. SOC. Lond. B. 188,413-423 (1975)

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C.K.

CHARNY, M.J. HAGMANN, R.L. LEVIN "A whole body thermal model of man during hyperthemia" IEEE Transactions on Biomedical Engineering ~ ~ ~ (1987) 2 3 4

C.K. CHARNY, R.L. LEVIW "A 'whole' body thermal model of ntan with a realistic circulatory system" IEEE Transactions on Biomedical Engineering HTD-95 BED-7 (1987)'

CLARK R.P. wHuman Skin Temperature and Convective Heat Loss"

ELSGOLC "Calculus of variationsw Pergarnon Pre'ss N.Y.1961

1

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FOWLEIR "Statistical mechanics" Cambridge 1936 J.P. F

~ K "Direct human bodyn

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mear;urement of radiative heat-exchange of the '

NATURE Februa;ry 29,1964 p

GRUCZA R. "Body Heat Baiance inSNan Subjected to Endogenous and Exogenous Heat Loadn Eur 3 Appl Physiol (1983) 51:419-433

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,

HAK-SHING TAM, ROBERT C. DARLING, JOHN A. DOWNEY, and HUK-YUK CHEH "Relationship between evaporation rate of sweat and mean sweating raten Journal of Applied Phisiology No 5 (1976) KHINCHIN "Nathematical fundations of Dover N.Y.1949

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KURT wAxiomatics af Statistica1 Nechanicsw. Pergamon Press N.Y. 1960

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w.L., LEWIS D.A., HYDE D.E.; DIKSTERHOUSE T.s., ARMSTRONG C.G., FOWLER S.R., and WILLIAMS D.A. wPhysiologically derived critica1 evapo rat ive coefficients £or protective clothing ensemles" copyright 1987 the American Physiological Society KENNEY

KATTO Y. and AOKI H. "Peculiarity of Evaporating Liquid-Surface Reference to Rtrbolent Heat Transfer" Bulletin of JSNE, voi. 12 (1969)

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BATTO Y. and KOIZUMI H. 'Turbolent Heat Transfer of a Gas . Flow Evaporation Liquid Surfacen ~ulletinof JSME, ~ 0 1 . ~ 1 (1975) 8

on

an

T. KUMADA, T. HIROTA, N. TAMURA, R. ISBIGURO 'Heat and Xass Transfer With Liquid Evaporation Into a Rirbolent Air Streama Transactions of the ASME vol. 108 (1986)

KANDO KOBAYASHI, STEVEN M. HORVATH, FRANCISCO-J.DIAZ, DONALD R. BRANSFORD, and BARBARA L. DRINKWATER "Thermoregulation during rest and ekercise different postures in a hot humid environmentw Copyright 1980 the herican Physiological Society

in

KHAIR K.R. and BEJAN A. "Hass Transfer to Natura1 Convection Boundary Layer Flow' Driven by Heat Transferm Journal of Heat Transfer voi. 107 (1979) H.E.

LEWIS, A.R. FOSTER, B,J. MULLAN, R. N, COX, R. P. CLARK "Aerodynamics of the human microenvironment' The Lancet Saturday 28.June 1969

A.T. PRATA and E.M. SPARROW *Diffusion-Driven Nonisothermal Evaporation" Journal of Heat Tranfer vol. 107 (1985)

R.S.

RANA, V. CHARAN, and H. K. VARMA 'Heat and Mass Transfer From a Row of ~ u b e s in a Vertical Plane of an Evaporative Heat Dissipator" Transactions of the ASME vol. 111 (1989) SACRIPANTI "Biomeccanica del judow Ed. Mediteranee 1989

_

Valutazione del costo energetico degli sport di combattimento in "REMOTE SmSINGU.

"Screening preliminare" ENEA RT:1989 REPORT s "Intercomparazione orientativan , ENEA RT:1990 REPORT 3 "Teoria biomeccanica della competizione' ENEA RT:1990 REPORT 4/5 Stima dellreffetto.schermo d a Judogi" ENEA RT:1991 REPORT 6 " Valutazione deIlreffetto schermo del Judogi ' ENEA RT:1991

PROGRESS REPORT PROGRESS

PROGRESS PROGRESS PROGRESS

1

S~IAPIROY., PZWDOLF'K.B., and R. F. GOLDMAN* 'Predicting Sweat Loss Response s Environment and Clothingn Eur J Appl Phisiol (1982)

to

Exercise,

STOLWIJK J. A. J. and J.D. HARDY "Partitional calorimetric skudies of responses of man to 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 of ~hysiology-Reactions to Environment Agent. Bethesda, merican Physiological Society 1977 SMOLSKY B.M.,and SERGEYEV G.X. "Heat and Mass Transfer With Liquid Evaporationn Int. J. -Heat and Mass Transfer, vo1.5, 1962 WAX

"Selected papers on Noise and Statictical Processes". Dover N.Y. 1954

WHITTARKER "A Treatise on the Anaiytical Dynamics of and Rigid Bgdiesn . Cambridge Univ. Press 1937

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