DTIC ADA506525: Expanded Prediction Equations of Human Sweat Loss and Water Needs

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2009 Journal Article - Journal of Applied Physiology
4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER
Expanded Prediction Equations of Human Sweat Loss and Water Needs
5b. GRANT NUMBER
5c. PROGRAM ELEMENT NUMBER
6. AUTHOR(S) 5d. PROJECT NUMBER
R.R. Gonzalez, S.N. Cheuvront, S.J. Montain, D.A. Goodman, L.A.
Blanchard, L.G. Berglund, M.N. Sawka
5e. TASK NUMBER
5f. WORK UNIT NUMBER
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
REPORT NUMBER
Thermal and Mountain Medicine Division
M09-20
U.S. Army Research Institute of Environmental Medicine
Natick, MA 01760-5007
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12. DISTRIBUTION/AVAILABILITY STATEMENT
Approved for public release; distribution unlimited
13. SUPPLEMENTARY NOTES
14. ABSTRACT
The Institute of Medicine expressed a need for improved sweating rate (m˙ sw) prediction models that calculate hourly and daily
water needs based on metabolic rate, clothing, and environment. More than 25 years ago, the original Shapiro prediction equation
(OSE) was formulated as m˙sw (g•m-2•h-11) +27.9 (cid:1)Ereq•(Emax-)(cid:1)0.455, where Ereq is required evaporative heat loss and Emax
is maximum evaporative power of the environment; OSE was developed for a limited set of environments, exposures times, and
clothing systems. Recent evidence shows that OSE often overpredicts fluid needs. Our study developed a corrected OSE and a new
m˙sw prediction equation by using independent data sets from a wide range of environmental conditions, metabolic rates
(rest to <450 W/m2), and variable exercise durations. Whole body sweat losses were carefully measured in 101 volunteers (80
males and 21 females; >500 observations) by using a variety of metabolic rates over a range of environmental conditions (ambient
temperature, 15–46°C; water vapor pressure, 0.27– 4.45 kPa; wind speed, 0.4 –2.5 m/s), clothing, and equipment combinations and
durations (2–8 h). Data are expressed as grams per square meter per hour and were analyzed using fuzzy piecewise regression. OSE
15. SUBJECT TERMS
overpredicted sweating rates (P < 0.003) compared with observed m˙sw. Both the correction equation (OSEC), m˙sw =147•exp
t(h0e.0rm01o2r•eOguSlEa)ti,o ann;d m ao ndeewlin pgi;e cfleuwidis bea (lPanWce) ;e hqyudartiaotino,n m; f˙lsuwid = r1e4p7la +ce 1m.5e2n7t•Ereq - 0.87 •Emax were derived, compared with OSE, and
then cross-validated against independent data (21 males and 9 females; >200 observations). OSEC and PW were more accurate
predictors of sweating rate (58 and 65% more accurate, P <0.01) and produced minimal error (standard error estimate (cid:4)
1<61.0 S0E•gCmUR-2IT•Yh -C1L) AfoSrS IcFoICnAdiTtiIOonNs ObFo:t h within an1d7 .o LuIMtsIiTdAe TthIOeN o rOigF inal1 O8.S NEU dMoBmEaRi n1 o9fa .v NalAidMitEy .O TF hReE SnePwON eSqIuBaLtEi oPnEsR SprOoNv ide for more
aca.c uRraEtPeO sRwTe at bp.r AedBiScTtiRoAnCs To vecr. aT HbIrSo aPdAeGr Er ange oAfB cSoTnRdAitCioTn s with applOicFa tions to public health, military, occupational, and sports
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JApplPhysiol107:379–388,2009.
FirstpublishedApril30,2009;doi:10.1152/japplphysiol.00089.2009.
Expanded prediction equations of human sweat loss and water needs
R. R. Gonzalez,1 S. N. Cheuvront,2 S. J. Montain,2 D. A. Goodman,2 L. A. Blanchard,2 L. G. Berglund,2
and M. N. Sawka2
1BiologyDepartment,NewMexicoStateUniversity,LasCruces,NewMexico;and2UnitedStatesArmyResearchInstitute
ofEnvironmentalMedicine,Natick,Massachusetts
Submitted2February2009;acceptedinfinalform28April2009
Gonzalez RR, Cheuvront SN, Montain SJ, Goodman DA, militarypotablewaterplanningreliesonwatertablesgenerated
Blanchard LA, Berglund LG, Sawka MN. Expanded predic- fromexistingpredictionequations(15,25),andsimilarnomo-
tion equations of human sweat loss and water needs. J Appl grams have been generated for public health purposes (11).
Physiol 107: 379–388, 2009. First published April 30, 2009; Although the sports medicine community recognizes the vari-
doi:10.1152/japplphysiol.00089.2009.—The Institute of Medicine
ability of human sweat losses and the need for individualized
expressed a need for improved sweating rate (m˙ ) prediction
sw fluid replacement guidance (23), realistic sweating estimates
models that calculate hourly and daily water needs based on
forsportingscenariosenablethesamewaterplanningcapabil-
metabolicrate,clothing,andenvironment.Morethan25yearsago,
ity as in military logistics and facilitate accuracy of phenom-
theoriginalShapiropredictionequation(OSE)wasformulatedasm˙
sw
(g(cid:1)m(cid:1)2(cid:1)h(cid:1)1)(cid:2)27.9(cid:1)E (cid:1)(E )(cid:1)0.455,whereE isrequiredevap- enological modeling in sport (14). There also are applications
req max req
orative heat loss and E is maximum evaporative power of the for occupational settings (12) and disaster relief efforts.
max
environment; OSE was developed for a limited set of environments, The Institute of Medicine (IOM) recently set U.S. Dietary D
o
exposures times, and clothing systems. Recent evidence shows that Reference Intake (DRI) standards for water and electrolytes w
n
OSEoftenoverpredictsfluidneeds.Ourstudydevelopedacorrected (11). The IOM used the original Shapiro equation (OSE) (28) lo
OSE and a new m˙sw prediction equation by using independent data to estimate sweating rates and calculate daily water needs, as ad
sets from a wide range of environmental conditions, metabolic rates well as daily sodium losses, over a broad range of activity ed
(rest to (cid:1)450 W/m2), and variable exercise durations. Whole body levels and environmental conditions. The OSE was selected fro
sweatlosseswerecarefullymeasuredin101volunteers(80malesand m
because it was the best equation available at the time, but,
21females;(cid:3)500observations)byusingavarietyofmetabolicrates becauseofitslimitations,theIOMpaneldeterminedaneedfor jap
over a range of environmental conditions (ambient temperature, 15– improvements in the “development of capabilities to predict .p
46°C;watervaporpressure,0.27–4.45kPa;windspeed,0.4–2.5m/s), h
clothing,andequipmentcombinationsanddurations(2–8h).Dataare hourly and daily water requirements based on metabolic rate, ys
climatic conditions, and clothing” (11). The OSE (28) is a io
expressed as grams per square meter per hour and were analyzed lo
using fuzzy piecewise regression. OSE overpredicted sweating rates sequel to the Givoni-Goldman model to predict core tempera- gy
(P (cid:4) 0.003) compared with observed m˙ . Both the correction ture(6).Itwasdevelopedfromlaboratoryexperimentsonmen .o
equation (OSEC), m˙sw (cid:2) 147(cid:1)exp (0.0012(cid:1)sOwSE), and a new piece- for energy expenditures ranging from (cid:6)75 W (rest) up to 475 org
wise (PW) equation, m˙ (cid:2) 147 (cid:5) 1.527(cid:1)E (cid:1) 0.87(cid:1)E were W(moderatemetabolicintensity)overarangeofenvironmen- n
sw req max J
derived, compared with OSE, and then cross-validated against inde- tal conditions [20–54°C and 10–94% relative humidity (RH)] u
pendentdata(21malesand9females;(cid:3)200observations).OSECand while wearing shorts and a T-shirt or what is now obsolete ly 3
PacWcuwraetere, mPor(cid:4)ea0cc.0u1r)ateanpdredpircotdoursceodfsmweinaitminaglraetrero(r58(satnadnd6a5r%d merororer militaryclothingandequipment(27,28).Theoriginalderived 1, 2
equation is shown below: 0
estimate (cid:4) 100 g(cid:1)m(cid:1)2(cid:1)h(cid:1)1) for conditions both within and outside 0
9
the original OSE domain of validity. The new equations provide for OSE:sweatingrate(g(cid:1)m(cid:1)2(cid:1)h(cid:1)1)(cid:2)27.9(cid:1)E (cid:1)(cid:7)E (cid:8)(cid:1)0.455 (1)
req max
more accurate sweat predictions over a broader range of conditions
with applications to public health, military, occupational, and sports whereE istheevaporationrequiredtomaintainheatbalance
req
medicinesettings. at any given core temperature and E is the maximal evap-
max
orativecapacityoftheenvironment.Equation1hasbeenused
thermoregulation; modeling; fluid balance; hydration; fluid replace-
widely to predict water needs, assuming the fluid intake (l/h)
ment
replaces the expected water lost by sweating in a heat-accli-
mated person [sweating rate (cid:9) body surface area (BSA) (cid:9)
DAILY WATER NEEDS can be determined from “minimal” water 10(cid:1)2, l/h].
losses and expected increases in different water flux avenues Although E is a final outcome solved by the solution of
req
(11, 22). Metabolic water production and respiratory losses heatbalanceandisadeterminantofthoseparametersinvolved
often offset each other, and fecal losses are usually small (11, in thermoregulation (i.e., skin and core temperature, skin wet-
22). Urinary losses primarily depend on hydration status and tedness,andheatproduction),thisvariableisnotwhollyequal
osmolarload,butsweatrepresentsthelargestpotentialavenue to thermoregulatory sweating. Equivalence is based on the
of body water loss. Knowledge of sweat losses is therefore efficiency of the sweat secreted to cool the skin. For 100%
critical for calculating water needs for active populations, effectiveness,allsweatmustbeevaporatedattheskin,andany
particularlywhenexposedtoheatstress(11,22).Forexample, variance in efficiency or heat storage or imbalances or incon-
sistenciesinheatexchangepropertiescanaffectthesweatrate
equation predictability.
Address for reprint requests and other correspondence: S. N. Cheuvront,
The OSE often overpredicts sweating rates for conditions
Thermal & Mountain Medicine Division, U.S. Army Research Institute of
bothwithinandoutsidetheoriginalexperimentalE andE
EnvironmentalMedicine,KansasSt.,Natick,MA01760-5007(e-mail:samuel. req max
[email protected]). domains of validity (3). Recent tests of its robustness during
http://www.jap.org 379
380 PREDICTIONEQUATIONSOFSWEATLOSS
more prolonged exercise bouts ((cid:3)2 h), higher exercise inten- weredeterminedfrommassbalanceusingthePeters-Passmoreequa-
sities, cooler temperatures, or modern protective clothing in- tion (3) and then time weighted to derive rate. The measurements
dicate poor agreement between predicted and measured sweat assume that 1 ml of sweat is equal to a mass of 1 g. To summarize,
sweatloss(kg)(cid:2)changeinbodymass(cid:5)(solidsin(cid:1)solidsout)(cid:5)
losses (3). Cheuvront et al. (3) found that the overpredictions
(fluidsin(cid:1)fluidsout)(cid:1)(gasesin(cid:1)gasesout),wheregasesreferto
from use of the OSE were also likely associated with compli-
CO -O exchange.
cations attributed directly to non-sweat losses of body mass 2 2
Thesedatasetsaresummarizedbrieflybelow.DatasetsI–IVwere
(NSL).Inaddition,variabilityinestimationsofdryheatlosses
used to develop the new and corrected sweating rate prediction
(radiant,R(cid:5)convective,C)andEmaxfromaclothedindivid- equations,whereasdatasetsVandVIwereusedforcross-validation.
ualcanleadtoincorrectcalculationswheneverimpreciseheat DatasetI.DetailscanbefoundinMontainetal.(15).Datawere
andvaportransfercoefficientsthroughclothing,determinedby obtained from 19 previously heat-acclimatized individuals (13 men
use of static manikins, are subsequently applied to dynamic and6women)whocompletedallexperimentsdressedinhotweather
conditions based on variable wind and walking conditions (1, battle dress uniforms [BDU; with a clo (clothing insulation coeffi-
7,8,10).Itisimperativethatimprovedequationsbedeveloped cient)valueof1.08andaim/clo(evaporativeimpedancecoefficient)
and validated that predict sweating rates over wider thermal value of 0.49]. Volunteers completed 12 randomized exercise-heat
stresstrialsinwhichtheywalkedatthreeexerciseintensitiescharac-
environments, with and without outdoor solar loads, higher
terizedaseasy,moderate,andheavyworkintensitiessetat250,425,
metabolicrates,longerworkdurations,andwithcontemporary
and600Winthreehumidenvironments(T (cid:2)28°C/P (cid:2)2.8kPa,
military clothing including the new combat uniform and other T (cid:2)32°C/P (cid:2)3.57kPa,andT (cid:2)36°C/Paw(cid:2)4.45kwPa,whereT
a w a a
modernprotectiveuniformsandequipment(11,12,15,23,25).
isambienttemperatureandP iswatervaporpressure).Intheother
w
Thepurposesofthisstudywere1)tocomparetheaccuracy three heat stress trials, volunteers walked at 425 W in three dry
ofOSEwithmeasuredsweatingratesduringextendedexercise environments(T (cid:2)36°C/P (cid:2)1.47kPa,T (cid:2)41°C/Pw(cid:2)1.95kPa,
((cid:3)2 h) with higher metabolic rates, contemporary clothing andTa(cid:2)46°C/Paw(cid:2)2.53kwPa).Dryheatstraesstrialswerecompleted Dow
systemsincludingmodernbodyarmor,andabroaderrangeof following a humid test condition. Appropriate work-rest cycles for n
environmental conditions; 2) to develop a new equation that each exercise task were initially determined using a current model lo
a
more accurately predicts sweating rates compared with OSE; (19)forapredicted2-htotalexposure.(cid:1)Intheminorityofheat/e(cid:1)xercise de
trials where mean skin temperature (T ) was not available, T was d
aansdO,SifEp,o,sstihbalte,is3)atpopldiceavbelleopanadcoerarseiclytiomnitgoraOteSdEi,ndtoesivganraioteuds estimatedusingSaltin’s(20)equation:sT(cid:1)ksk(cid:2)0.215Ta(cid:5)26.6(s(cid:10)k 0.5 fro
C SEE),whereSEEisstandarderrorestimate,tocalculatethepertinent m
existing rational and operational thermal prediction models. heatbalanceequationparametersessentialformodelalgorithms. ja
ThefirsthypothesiswasthatOSEoverestimatessweatingrates p
DatasetII.DetailscanbefoundinCheuvrontetal.(3).Thirty-nine .p
over extended periods of exercise and, therefore, leads to healthy volunteers participated in this study specifically designed to hy
excessiveestimatesofwaterneeds.Thesecondhypothesiswas obtaindataforthedevelopmentofanimprovedsweatrateprediction sio
that new and corrected equations, based on a more compre- equation.TheclothingensemblewastheU.S.ArmywoodlandBDU lo
hensivedatabase,wouldprovideamoreaccurateestimationof withfieldcap,sleevesdown[clo(cid:2)1.08,i /clo(cid:2)0.49atwindspeed gy
waterneedstoencompassmostmilitary(15,25),occupational (V)(cid:2)1m/s],andathleticshoes.Testsessmionslastedeither2or8h. .org
(12), and public health scenarios (11), as well as many situa- Twenty-onevolunteers(16menand5women)participatedinthe2-h o
tions within the sports medicine community (23). trials,andphysicalcharacteristicsforthisgroupareshowninTable1. n J
Eighteen different volunteers (17 men and 1 woman) completed the u
ly
METHODS 8-htrials,andtheircharacteristicsareshowninTable2.Tables1and 3
2 also describe the seven different levels of environmental stress, 1
The database consisted of 101 volunteer subjects (80 men and 21 work-rest cycles, metabolic rate at each exercise intensity, and mea- , 2
0
women) with (cid:3)500 observations included in the data set used to suredsweatloss.Inthe2-htrials,volunteerswerenotheatacclimated, 0
9
developthealgorithms.Experimentswereconductedforthepurpose whereasinthe8-htrials,volunteerswereheatacclimated.
of precisely measuring sweating rates over a broad range of condi- DatasetIII.DetailscanbefoundinCheuvrontetal.(2).Thirteen
tions. Each protocol was approved by the appropriate institutional menparticipatedinthisstudyspecificallydesignedtoobtaindatafor
human use review boards, and all volunteers were informed both the development of an improved sweating rate prediction equation.
verbally and in writing of the objectives and procedures of the Each subject completed three trials consisting of 4 h oftreadmill
respective study. No identifications of a given volunteer’s personal walking((cid:6)500W)inahot,dryenvironment(T (cid:2)35°C,P (cid:2)1.7
a w
recordswerepresentinthespreadsheetdatabase. kPa, V (cid:2) 1 m/s). The U.S. Army BDU was worn in all three trials:
Rawdatawereobtainedfromfourseparateenvironmentalchamber alone(trialBDU:clo(cid:2)1.12,i /clo(cid:2)0.44atV(cid:2)1m/s),combined
m
studies and one field study conducted at the U.S. Army Research with interceptor body armor (trial IBA: clo (cid:2) 1.35,i /clo(cid:2)0.27at
m
Institute of Environmental Medicine (USARIEM) and from one V(cid:2)1m/s),orcombinedwithIBAandaspacervest(trialSP:clo(cid:2)1.28,
environmentalchamberstudypreviouslyconductedatDefenceR&D i /clo(cid:2)0.32atV(cid:2)1m/s).IntheBDUtrial,theBDUwaswornwith
m
Canada, Toronto (DRDC) (8). Actual sweat losses were carefully fieldcap,sleevesdown,andathleticshoes.TheIBAvestincludedfront
measured in all studies by weighing volunteers and accounting and andrearballisticprotectiveinserts(throatandgroinprotectionexcluded).
correctingfornon-sweatlossesofmass,food,andfluidintakes(NSL) Thetotalweightofthevestasusedwas7.5kg,anditcovered(cid:6)25%of
(2, 3). In brief, sweat losses were measured by accounting for the thetotalBSA.IntrialSP,thespacerwasa1-cm-thickvestofproprietary
change in individual nude body mass (kg) measured on a electronic knit fabric worn between the IBA and uniform. The spacer vest is
precision balance scale (Toledo 1D; Worthington, OH; accuracy (cid:10) designedtoproduceanairchannelthattheoreticallyincreasesthepoten-
20 g) before and after each experiment. Water from premeasured tialforventilationandevaporativecoolingofthetorso.
bottles was available to drink at will during all experiments, and a Data set IV. Details can be found in Chinevere et al. (4). One
smallmeal((cid:6)500kcal)wasprovidedduringthe8-hexperiments.The womanandfivemendidcontinuoustreadmillexercise((cid:6)400W)for
weights of all food and water consumed and urine voided were 2 h while dressed in BDU plus IBA, as in data set III (IBA: clo (cid:2)
measuredonanelectronicscale(OhausE1M210;Nanikon,Switzer- 1.35,i /clo(cid:2)0.27atV(cid:2)1m/s).EnvironmentalconditionswereT (cid:2)
m a
land;accuracy(cid:10)1g).Theweightofanyfecalmasswasdetermined 30°/P (cid:2)2.1kPa,T (cid:2)35°C/P (cid:2)4.27kPa,andT (cid:2)40°C/P (cid:2)1.47
w a w a w
from body mass changes before and after void. Total sweat losses kPa.AllotherproceduresanddetailswereasoutlinedinDatasetIII.
JApplPhysiol•VOL107•AUGUST2009•www.jap.org
PREDICTIONEQUATIONSOFSWEATLOSS 381
Table 1. Key descriptive and physiological data for 2-h experiments in data set II-B used in developing the present equation
Trial Ta,°C Pw,kPa Work:RestCycles,#(min) n BSA,m2 BodyWeight,kg Tsk,°C V˙O2,l/min SR,l/h
A1 15 0.85 2(cid:9)(50:10) 12M 1.94(cid:10)0.15 77.6(cid:10)8.8 29.3(cid:10)1.0 0.94(cid:10)0.14 0.135(cid:10)0.079
4F 1.70(cid:10)0.03 64.3(cid:10)4.2 28.2(cid:10)0.82 0.79(cid:10)0.17 0.188(cid:10)0.086
A 15 0.85 2(cid:9)(50:10) 13M 1.96(cid:10)0.14 79.7(cid:10)9.3 28.7(cid:10)0.8 1.49(cid:10)0.17 0.305(cid:10)0.136
2F 1.68 60.4 28.7 1.3 0.319
B 15 0.85 2(cid:9)(50:10) 13M 1.96(cid:10)0.14 79.7(cid:10)9.3 29.1(cid:10)1.0 1.99(cid:10)0.21 0.472(cid:10)0.170
2F 1.68 6.4 27.5 1.57 0.424
C 20 1.17 2(cid:9)(50:10) 14M 1.96(cid:10)0.14 80.7 31.1(cid:10)0.8 1.08(cid:10)0.15 0.220(cid:10)0.089
1F 1.63 56.9 31.34 0.81 0.165
D 20 1.17 2(cid:9)(50:10) 15M 1.98(cid:10)0.13 80.9(cid:10)8.9 30.2(cid:10)1.08 1.45(cid:10)0.19 0.410(cid:10)0.177
4F 1.67(cid:10)0.04 62.6(cid:10)5.7 30.4(cid:10)0.47 1.14(cid:10)0.13 0.346(cid:10)0.084
E 20 1.17 2(cid:9)(50:10) 15M 1.97(cid:10)0.14 80.5(cid:10)9.4 30.3(cid:10)1.15 2.03(cid:10)0.26 0.625(cid:10)0.199
2F 1.69 63.5 29.6 1.49 0.498
F 25 1.59 2(cid:9)(50:10) 11M 1.96(cid:10)0.11 80.2(cid:10)8.9 31.8(cid:10)0.55 1.03(cid:10)0.16 0.321(cid:10)0.102
2F 1.68 60.35 31.1 0.84 0.421
G 25 1.59 2(cid:9)(50:10) 9M 1.95(cid:10).12 80.0(cid:10)9.5 31.5(cid:10)0.92 1.47(cid:10)0.20 0.479(cid:10)0.171
1F 1.73 63.8 30.9 1.26 0.515
H 25 1.59 2(cid:9)(50:10) 10M 1.95(cid:10)0.11 80.5(cid:10)8.9 32.1(cid:10)0.62 1.99(cid:10)0.27 0.755(cid:10)0.237
1F 1.63 56.9 31.6 1.54 0.558
I 30 2.12 2(cid:9)(50:10) 10M 1.95(cid:10)0.11 80.5(cid:10)8.9 33.5(cid:10)0.75 1.98(cid:10)0.26 0.935(cid:10)0.317
1F 1.63 56.9 33.1 1.45 0.702
D
Valuesaremeans(cid:10)SDexceptwhenn(cid:4)3;n(cid:2)no.ofsubjects(M,male;F,female)completingtheexperiment.T,airtemperature;P ,ambientwatervapor o
a w w
pressure;Tsk,meanskintemperature;SR,observedsweatingrate.Windspeedforallexperimentswas1m/s.TriallettersareaspresentedinCheuvrontetal.(3). n
lo
a
d
Data set V. An archival raw data set was obtained from a US- BSA(cid:2)1.66(cid:10)0.15m2females.TheambientconditionswereT (cid:2) e
a d
AraRteIsEdMurfiinegldwstaulkdiyngcoenxdeurcctiesdeaintFmt.ilBdlitsos,mToXd,etroatdeesteorlmarinloeasdwceoantidnig- 4(40°eCxearncidseP-wres(cid:2)tc1y.c4l7eskoPfa1a5t:V15(cid:2)m0in.4)omr/us.nStiulbthjeecirtsreecxtearlctiesemdpfeorart2urhe from
tions.DetailscanbefoundinSanteeetal.(21).Inbrief,eightmales reachedapeakvalueof39.5°Corheartratebecameelevatedhigher ja
[averagebodymass(cid:2)80.5(cid:10)15.2kg(SD);BSA(cid:2)1.97(cid:10)0.18m2 than180beats/minfor3min.Averagemetabolicratewas(cid:6)365and p.p
(SD)]walkedat2miles/hfor12miles(24minofcontinuousexercise (cid:6)338Wforthemaleandfemalegroups,respectively.Subjectswere h
y
with a 6-min break) on a calibrated track for 6 h. Subjects carried a dressedintheCanadanuclear,biological,chemical(NBC)protective s
22-kgpack,andaverageheatproductionwasmaintainedat(cid:6)350W. clothingsystempreviouslyevaluatedusingUSARIEMmanikinpro- iolo
Standardchemicalprotectiveclothingdesignatedasmission-oriented ceduresandfoundtohaveheattransfercharacteristicsofclo(cid:2)1.88 gy
psyrostteemctivceonpfiogsuturraetio(MnsOcPoPn)siwstaesdwoforMnOduPrPing0t(hBeDwUa:lkcsl.oT(cid:2)he1c.l3o4thainndg andim/clo(cid:2)0.18atV(cid:2)1m/s(1). .org
iamt/cVlo(cid:2)(cid:2)10.3m1/sa)t,Van(cid:2)d1MmO/s)P,PMO4P(Pclo1((cid:2)clo2(cid:2).441.9an7danid/icmlo/cl(cid:2)o(cid:2)0.01.21)7. balHanecaetetrqaunastfieorna(5n)alwysaess.deEtearcmhienleedmfernotmotfhteherawcomdaptareahnednscivoenchaetea-t on J
m nated together in a unified spreadsheet (Microsoft Excel) for later u
Volunteers walked at night and day in the various MOPP clothing ly
configurations. Daytime ambient conditions were T (cid:2) 23°C/P (cid:2) analysis.ThetechniquesdocumentedbyGaggeandGonzalez(5)and 3
0.2kPa,withamixedsolarload(diffuseanddirect)aestimatedbywthe Breckenridge (1) were applied to the raw spreadsheet values to 1, 2
effective radiant field (ERF) at 500 W/m2, resulting in an operative determinerespectiveheatandmasstransfercoefficientsforcalculat- 0
temperature(To)of49.5°C(1,5,9,27). ingdryheatexchange(R(cid:5)C),Emax,andothervariablesintheheat 09
Data set VI. Raw data from an international cooperative data balanceequation.Clothingheatandevaporativepotentialparameters
sharingprogram(8)wereusedtotestthedevelopedequations.Data weredeterminedonaregionallyheated,articulatedmanikinatvarious
from13malesand9females(thelatterinthefollicularphasesoftheir wind speeds. A heat balance analysis was carried out for each
menstrual cycle) were compiled to compare the various equations. individualresponse.
Physicalcharacteristics((cid:10)SD)werebodymass(cid:2)82.7(cid:10)12.5kgand Ingeneral,heatbalance(inW/m2)ofthehumanbodysurfacearea
BSA(cid:2)2.01(cid:10)0.16m2formalesandbodymass(cid:2)60.4(cid:10)8.9and canbeexpressedby
Table 2. Key descriptive and physiological data for 8-h experiments in data set II-B used in developing the present equation
Trial Ta,°C Pw,kPa Work:RestCycles,#(min) n BSA,m2 BodyWeight,kg Tsk,°C V˙O2,l/min SR,l/h
J 40 2.95 6(cid:9)(60:20) 12M 2.03(cid:10)0.14 84.7(cid:10)12.4 35.9(cid:10)0.61 1.11(cid:10)0.21 0.667(cid:10)0.114
1F 1.63 55.3 36.2 0.775 0.404
K 35 1.69 6(cid:9)(60:20) 15M 1.97(cid:10)0.12 80.2(cid:10)9.8 34.4(cid:10)0.5 1.39(cid:10)0.21 0.569(cid:10)0.062
1F 1.62 54.8 34.12 0.92 0.405
L 35 1.69 6(cid:9)(60:10) 15M 1.99(cid:10)0.15 81.7(cid:10)12.9 33.9(cid:10)0.5 1.05(cid:10)0.15 0.452(cid:10)0.058
M 27 1.43 6(cid:9)(60:20) 14M 1.98(cid:10)0.15 81.7(cid:10)12.9 32.3(cid:10)0.6 1.44(cid:10)0.23 0.406(cid:10)0.096
1F 1.63 55.7 31.83 0.96 0.263
N 27 1.43 6(cid:9)(60:20) 12M 1.98(cid:10)0.16 81.1(cid:10)13.9 32.7(cid:10)0.64 1.05(cid:10)0.14 0.269(cid:10)0.05
1F 1.63 55.6 33.0 0.770 0.153
O 20 1.17 6(cid:9)(60:20) 12M 1.97(cid:10)0.16 80.9(cid:10)14 30.6(cid:10)1.15 1.39(cid:10)0.22 0.229(cid:10)0.087
1F 1.63 55.1 30.3 0.847 0.162
Valuesaremeans(cid:10)SDexceptwhenn(cid:4)3;n(cid:2)no.ofsubjectscompletingtheexperiment.Allsubjectswerepreviouslyheatacclimated.Windspeedfor
allexperimentswas1m/s.TriallettersareaspresentedinCheuvrontetal.(3).
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382 PREDICTIONEQUATIONSOFSWEATLOSS
S(cid:2)netmetabolicheatflux(cid:1)skininsensibleheatflux enthalpic evaporation (7, 10); and relative permeation from skin to
(2) eachsubsequentintrinsicclothinglayer,andultimatelytotheambient
(cid:1)skinsensibleheatloss, temperature important in total latent heat transfer efficiency of mili-
S(cid:2)(cid:7)M(cid:3)Wk(cid:8)(cid:4)E(cid:3)(cid:7)R(cid:5)C(cid:5)K(cid:8) (3) taryclothingpresentinthisstudy.Thesefactorswerenotconsidered
indevelopmentofthelegacyE oftheShapiroetal.(28)studyand
max
where S is the time rate of change of body heat (gain or loss). If willlikelyimprovetheefficacyoftheOSE.
positive, the body is increasing its core and skin temperature, and ValuesforI and(i /I )asafunctionofV werecalculatedfor
T m T eff
thesecanbeestimatedusingM,therateofmetabolicheatproduction; each clothing system in each calculation of E in the heat balance
req
Wk, the rate of accomplished mechanical work; E, the rate of evap- output during each exercise condition or use of body armor and
orative heat loss via regulatory sweating from eccrine sweat glands, transientdynamiceffects.Theseclothingparameterswereascertained
diffusion(E ),respiration(E ),andmetabolicheatloss(m);C,the from the following power curves automatically estimated on the
dif res r
rate of convective heat loss from the total body surface and respira- sweating,articulatedmanikinusedtoevaluateclothingensembles(1):
tion; R, the rate of radiant heat loss (or gain from) the surrounding
I (cid:2)A(cid:1)(cid:7)V (cid:8)B (7)
surfaces, and K, the rate of conductive heat flux to or from the T eff
environment.
and
Radiationexchange.Inanythermalenvironment,alinearradiation
transfercoefficient(hr,inW(cid:1)m(cid:1)2(cid:1)°C(cid:1)1)maybederived(1,5)by (cid:7)im/IT(cid:8)(cid:2)C(cid:1)(cid:7)Veff(cid:8)D (8)
h (cid:2)4(cid:11)(cid:12)(cid:7)A/A (cid:8)(cid:1)f (cid:1)(cid:7)5.67(cid:6)10(cid:1)8(cid:8)(cid:13)(cid:7)T (cid:5)T (cid:8)/2(cid:5)273.15(cid:14)3 (4)
r r D cl o surf wherethecoefficientsAandCarethevaluesforI and(i /I )when
T m T
where(cid:11)istheskinorclothingabsorptancefortheradiationexchange Veff(cid:2)1.0m/s,andthecoefficientsBandDareslopesofplotsofln
totheambient,(cid:12)istheStefan-Boltzmannconstant(5.67(cid:9)10(cid:1)8,in (IT)andln(im/IT)vs.ln(V).
W(cid:1)m(cid:1)2(cid:1)K(cid:1)4), and the factor Ar/AD is the ratio of the effective The intrinsic thermal insulation value, Iint(V), was obtained by D
radiating area of the human body to the total body surface area as subtractingthevalueoftheinsulationoftheairboundarylayer,Iacl, o
fromI : w
measured by the Dubois surface area formula (0.72 for standing T n
individuals). The interior environmental temperature is composed of 1 loa
tfaenmrapeveperrareatsugerenetsos(fTatshufreaf)ctoionprcelrtuahdtaiivtnegintacenrmeyapcseelrosatthutihrneege(sTfuforef)catcpiveluetseAmaplleortfahtetuhreseu(brTfoacdcl)ye; Iint(cid:2) IT (cid:4) (cid:7)facl(cid:8)(cid:1)(cid:7)0.61(cid:5)1.87(cid:1)Veff(cid:8) (9) ded fro
cl r wheref inEq.9istheincreaseinsurfaceareaduetoclothingthat m
asdunerdrCfiavaocenedTv-efbsrcyhotiimrvsteo,Tm(cid:1)Fesxceklcih(cid:2)1na5nt–1hg2eea0.rn%eTdlahTptiiescolrnh(cid:2)sechaloitT(cid:1)pes(k[x1.Tc,oh5a(cid:5))n.gFMecfle(aaT(cid:1)cnstkocr(cid:1)loistThrioen)p]gr.eFssuoernrftasechdeorbityss isestimaactled(1,5)usingfacl(cid:2)1(cid:5)(cid:7)0.2(cid:1)AD(cid:8). (10) jap.phy
s
freeconvectionandforcedconvectionviaincreasedmetabolicactiv- Thealgebraicsumofthetotal(dry)heatlossbyradiantandconvec- io
ity or increased room air movement artificially. Two equations for tiveheatexchange(R(cid:5)C),inwatts(1,9),therefore,is log
ehcsoatvnimeveacbttieinoegnnth(f1eo,rcm5o,un9lva)e:tcetdivebahseeadttorannsafercocomepffiosciiteento(fhcf,rieneWan(cid:1)md(cid:1)f2o(cid:1)r°cCed) Dry(cid:2)(cid:7)R(cid:5)C(cid:8)(cid:2)6.45I(cid:1)ADfacl(cid:2)0.611(cid:7)T(cid:1)sk(cid:4)T(cid:1)r(cid:8)(cid:5)(cid:1)V(cid:1)(cid:7)T(cid:1)sk(cid:1)Ta(cid:8)(cid:3) oy.org
hc(cid:2)1.2(cid:13)(cid:7)M(cid:4)50(cid:8)(cid:7)PB/760(cid:8)(cid:14)0.39 (5) int Iint(cid:5)facl(cid:7)0.61(cid:5)1.87 V(cid:8) n July
where M is metabolic heat production (in W/m2) and P is the (11) 3
B 1
barometric pressure in Torr (1 kPa is equivalent to 7.5 Torr at sea Insensible heat loss (E) was determined by the rate of sweat , 2
laemvebli)e.nAtaltierrmnaotviveemlye,nhtc(Vfo,rmfa/sn)-igsetnheeramteadinfofarccetodrcaofnfevcetcintigonc,oinnvwechtiicvhe fsuelclryetiwoentt(em˙dsws)kianndsuthrfeacmeax(Eimmaaxl)r.atEemoafxeivsapaofruatnicvteiohneaotflotshsefrvoampoar 009
heatexchange,canbeexpressedbyeither pressure gradient between the fully wetted skin surface and the air
h (cid:2)8.6(cid:13)V(cid:1)P /760(cid:14)0.53, (6) (Ps,sk (cid:1) Pw), the evaporative heat transfer coefficient (he), and im,
c B Woodcock’s dimensionless factor for permeability of water vapor
whenpersonsaredressedinshortsandaT-shirt,orby throughclothing(1,5,6).Theevaporativeheattransfercoefficient,h ,
e
isdirectlyrelatedtotheconvectiveheattransfercoefficient,h ,bythe
h (cid:2)12.7(cid:13)V(cid:1)P /760(cid:14)0.50, (6(cid:15)) c
c B Lewisrelationship(LR;2.2°C/Torror16.5K/kPa)(5,7,10).
whenpersonsareclothed(5). Whenevaporationisnotrestrictedbyclothingortheenvironment,
Insensibleheatloss.Proceduresapplicabletoclothingheattransfer then
wereusedtocalculateenvironmentalheatexchangeandappliedtothe E (cid:2)m˙ (cid:1)(cid:16) (12)
respective data for each individual (1, 5, 6, 9). These methods sk sw
considertheskin,clothing,andenvironmentasatotalsystemandthe wherem˙ isingramsperhourand(cid:16)istheheatofvaporizationfor
sw
constantsdefininginsulationandwatervaportransferasfunctionsof sweat at 35°C (0.68 W(cid:1)h(cid:1)g(cid:1)1), as determined by Wenger (31). The
effectiveairmovement(Veff).ThetermVeffisthesumofairmotion expressionforskinevaporativeheatloss(Esk)underconditionswhere
around a stationary object plus the speed at which the object is evaporation of sweat is restricted, particularly during exercise with
moving. IT(Veff) is the total resistance to heat flow by radiation and impermeableclothing(1,5,7,10)andwherethereisfrankdripping
convection (in clo units, 1 clo is equivalent to 0.155 m2(cid:1)K(cid:1)W(cid:1)1 or (E )orwastedsweatduetoskinwettedness((cid:17)(cid:3)1.0)(5,7),is
thermal conductance of 6.45 W(cid:1)m(cid:1)2(cid:1)°C(cid:1)1), and i (V ) is the drip
m eff
relative total resistance to evaporative heat transfer (zero to one, E (cid:2)(cid:7)0.06(cid:5)0.94(cid:17)(cid:8)(cid:1)A E (cid:2)(cid:7)LR(cid:1)6.45(cid:8)A (cid:1)(cid:7)i /I (cid:8)(cid:1)(cid:7)P (cid:1)P (cid:8),
sk D max D m T s,sk w
dimensionless).Inheatbalancecalculations,imisnotusedalonebut (12(cid:15))
asalatentheattransfercoefficient(i /I ),separatelyevaluatedusing
m T
an articulated, moving, sweating manikin; this latter quantity is whenE (cid:1)(cid:1)m (cid:1)(cid:16),whereA istheDuBoissurfacearea(m2)(1,
max sw D
considered as a key dynamic constant incorporating both heat and 5) and P (in Torr) is the vapor pressure of saturated air at skin
s,sk
mass transfer via “pumping” through cuffs, vents, and walking; temperature.P isrelatedtoT bytheAntoineequation(5,7):
s,sk sk
JApplPhysiol•VOL107•AUGUST2009•www.jap.org
PREDICTIONEQUATIONSOFSWEATLOSS 383
(cid:4) (cid:5)
4030.183 banddifferentiationofsome(cid:10)2g/minoveranextendedperiod.The
P (cid:2)exp 18.6686(cid:4) (13) higherlevelrelaxesthepredictionofE thatcanbecalculatedfrom
s,sk T (cid:5)235 req
sk theheatbalanceequation.Thisdecisionisbasedonthefactthatthe
calculation of evaporative heat exchange parameters in clothed indi-
RespiratoryheatlossisalsoapartoftheNSLavenue.C andE
res res
viduals are not exact, and indeed, the latent heat of evaporation is
aredirectlyrelatedtoventilationrateandvaryasafunctionofaerobic
variable, particularly during cold ambient conditions (10), and a
exerciseintensity(M )uptomaximallevels.Thecombinedequation
tot
forestimatingrespiratorylossbyconvectionandevaporation(C (cid:5) model’s accuracy predicting sweating rate is not always tied in with
res evaporativecoolingefficiency(7,9,10),particularlywhen(cid:17)is100%
E , g/min) was taken from Mitchell et al. (18), applicable for high
res
foranextendedperiod.
levelsofexerciseas
Dataareexpressedasmeans(cid:10)SD,means(cid:10)SE,ormeans(cid:10)95%
C (cid:5) E (cid:2)0.019(cid:1)V˙ (cid:7)44(cid:4)P (cid:8) (14) confidence interval (CI). The differences in observed sweating rate,
res res O2 w
heatproduction,andtheoutputfromthevariouspredictionequations
or were analyzed using a factorial ANOVA design to include main
(cid:7)C (cid:5)E (cid:8)(cid:2)A (cid:1)M (cid:13)0.0014(cid:1)(cid:7)34(cid:4)T(cid:8)(cid:5)0.0023(cid:7)44(cid:4)P(cid:8)(cid:14) effectsandinteractionsforcategoricalpredictors(sex,alltrials).Both
res res D tot a a univariate (using a given single continuous dependent variable) and
(14(cid:15))
multivariate designs (multiple continuous dependent variables) were
analyzed. If a significant F value was found for a given dependent
E isalsomodifiedbyaconstant(F)forhighlevelsofexercise(20)
0so.r1es0th6a(Vt˙Oif2V(cid:1)˙O22.6(cid:4))2.2.6 l/min, F (cid:2)1, and if V˙O2 (cid:3) 2.6, F (cid:2) 1 (cid:5) vw0a.a0rs1iaubaslneedd,thacseonamspoidoreesrtcehodoncssetaarptvipasttriiocvaaecllhByotonsiflgeonrcriaofitnceiacnardti;jtuiccsoatmlrrdeeilnfatfteiporrenonscceewdsuitarhetP(a1(cid:4)7P)
Evaporative heat loss corrected for metabolic heat losses by CO
2 value (cid:3)0.01 (including those with P values between 0.01 and 0.05)
andO (m˙ ,g/min)wascalculatedusingthefollowingassumptions
2 res wereconsiderednonsignificant.
(20).Iftherespiratoryexchangeratio(R)isequalto1, D
Wedeterminedthepredictionaccuracyofagivenequation,com- o
m˙ (cid:2)V˙ (cid:7)R(cid:1)(cid:18)CO (cid:4)(cid:18)O(cid:8) (15) pared with observed sweating rates from composite trial data, using w
res O2 2 2 analysesofdifferencesofmeanerrorratesasdescribedbyLimetal. nlo
where(cid:18)CO2,thedensityofCO2,(cid:2)1.96g/lSTPD;(cid:18)O2,thedensity (13). For each trial data set, the algorithm with the lowest error rate ad
ofO2,(cid:2)1.43g/lSTPD,andm˙res(cid:2)0.53(V˙O2).IfR(cid:3)1, compared with the observed sweating rate is assigned rank one, the ed
m˙ (cid:2)V˙ (cid:7)R(cid:1)0.53(cid:8) (15(cid:15)) second lowest rank two, and so on, with average ranks assigned in fro
res O2 caseoftiesasformulatedbyLimetal.(13).TheFriedmanANOVA m
Statistical procedures and quasi-Newton analyses. All concate- nonparametrictest(17)wasthenusedtotestdifferencesinmeanerror ja
p
nateddatafromthespreadsheetwereanalyzedusingfuzzypiecewise rateranksforeachalgorithm. .p
linearandnonlinearregressionanalyses(29,30)withvariousstatis- Finally, an independent cross-validation analysis of the fuzzy hy
ticalmodules(Statistica,version7;Tulsa,OK)toestablishappropri- piecewise equation was executed against two independent archival sio
atechangepointsinsweatlosspertimepointsinthedataset,coded data sets: a field study in which a group of men walked in NBC lo
g
bytrial,sex,andindividualsubjectnumber,andtoobtainintercepts clothing(atMOPPlevels0,1,and4)(19,21)andalaboratorystudy y
for independent parameters derived from the heat balance equation in which men and women walked in NBC protective clothing con- .org
(Ereq, Emax ). A quasi-Newton method was employed to derive ductedatDRDC(8);experimentaldetailsarepresentedabove. o
regression parameters. In this method, the slope of a function at a n J
particular locus is computed as the first-order derivative of the RESULTS u
ly
function(atthatlocus).The“slopeoftheslope”isthesecond-order Table 3 provides the calculated mean heat production (M, 3
derivative, which documents how fast the slope is changing at the 1
respective point and in which direction. The quasi-Newton method W/m2) and observed (measured) sweating rates (g(cid:1)m(cid:1)2(cid:1)h(cid:1)1) , 2
will,ateachstep,evaluatethefunctionatdifferentpointstoestimate (cid:10)SE for data sets I–IV (METHODS) separated by sex. After 00
9
the first-order and second-order derivatives. It will then use this ANOVA tests, a Bonferroni post hoc (17) analysis was per-
informationtofollowapathtowardtheminimumofthelossfunction formed. The only significant difference in measured sweating
(29). The fuzzy piecewise routine is more robust than conventional rates between men and women occurred with the moderate-
methods,isnotsensitivetooutliers,andtrackstransientresponsesor intensity exercise trials in data set I (P (cid:4) 0.01).
irregulardataespeciallyfoundinthisdatasetduetoheavy-intensity Figure 1 plots the individual sweating rates (Fig. 1A) for
exercise and disparate sweating patterns. The technique, as con-
data sets I–IV and the calculated residuals (Fig. 1B) used to
structed for this study, is also suitable for long-term time series
evaluate OSE and develop a new prediction equation. Notice-
predictionsofspecificvariables(29).
ablearethehighpointsanddepressionsinsweatingrates(Fig.
OSE-predicted sweating rates were initially compared against ob-
1A) due to variation in exercise intensity and environmental
served data to obtain residual analyses to ascertain how much OSE
deviatedfromtheobserveddata.Next,thenewfuzzypiecewise(PW) conditions (particularly cooler environments) among data sets
equation (29) was compared with OSE and the observed raw data I–IV. The residual values in Fig. 1B (comparing measured
secured for each separate trial. Corrections to OSE (designated as minus predicted sweating rates for each data point) demon-
OSE, ) were derived by independent piecewise regression analyses stratethatsomepredictedvalueswereoverestimatedby100%
C
incorporating an iterative approach to obtain the most optimum ormore,especiallyduringhigherexerciseintensities(dataset
equation(exponential,logfit)andtestthesignificanceofthederived I),andunderestimatedby80%duringcoolertrials(datasetII).
regressioncoefficients(Waldstatistic)thatfitthedatabase(17).The However,formanyofthedatasets,OSEwaswithin(cid:10)20%of
conditions were that the standard error estimate (SEE) of a new
observed data with residuals distributed symmetrically around
equation (PW) should not deviate from the observed data or the
independentlydeterminedfuzzypiecewiseequationbymorethan(cid:10)125 the zero line, particularly during low exercise intensities and
g(cid:1)m(cid:1)2(cid:1)h(cid:1)1 (roughly less than (cid:10)0.24 l/h for a person with 1.9 m2 mild heat stress conditions.
BSA).Thisisamoreliberalcriterionthantheoneusedpreviouslyby Thedatasetwasnextexaminedtodevelopoptimumregres-
Cheuvrontetal.(3),whichassignedanapriori“zoneofindifference” sion parameters that would satisfy all data sets sufficiently
of(cid:10)0.125l/h(i.e.,(cid:6)65.8g(cid:1)m(cid:1)2(cid:1)h(cid:1)1fora1.9m2BSA)resultingin (withinaSEEof(cid:10)125g(cid:1)m(cid:1)2(cid:1)h(cid:1)1criterionandcoefficientof
JApplPhysiol•VOL107•AUGUST2009•www.jap.org
384 PREDICTIONEQUATIONSOFSWEATLOSS
Table 3. Heat production and observed sweating rate
M,W/m2 OSR,g(cid:1)m(cid:1)2(cid:1)h(cid:1)1
Description DataSet Sex Mean (cid:10)SE Mean (cid:10)SE n
Easywork I-L M 163.04 8.87 295.21 18.35 32
I-L F 148.60 12.18 208.31 25.17 17
Moderatework I-M M 224.00 5.84 407.13 12.06* 74
I-M F 252.24 8.37 332.59 17.29* 36
Heavywork I-H M 329.18 8.25 443.96 17.06 37
I-H F 357.61 11.83 356.88 24.46 18
BDU II-B M 252.42 3.53 224.72 7.30 202
II-B F 231.82 10.04 210.19 20.75 25
Moderatework,BDU III-B M 284.66 13.92 353.21 28.78 13
III-B F NA NA NA NA 1
Moderatework,BDU(cid:5)bodyarmor III-I M 287.79 13.92 407.64 28.78 13
Moderatework,BDU(cid:5)bodyarmor III-I F NA NA NA NA 1
Moderatework,BDU(cid:5)bodyarmorwithvest III-S M 289.52 13.92 420.47 28.78 13
Moderatework,BDU(cid:5)bodyarmorwithvest III-S F NA NA NA NA 1
Easywork,BDU(cid:5)bodyarmorwithvest IV M 213.07 12.96 362.12 26.79 15
Easywork,BDU(cid:5)bodyarmorwithvest IV F 193.80 28.98 483.49 59.91 3
Valuesareleast-squaresmeansbetweenmalesandfemalesforcombineddata,followedbySEvalues;n(cid:2)no.ofobservations.M,heatproduction;OSR,
observedsweatingrate;BDU,battledressuniform;NA,notestimatedduetosmallsampleintrial.*P(cid:4)0.01(Bonferron;posthoctestwithintrialcells).
D
o
w
determination R2 (cid:7) 0.8) as shown in Fig. 2, A–C. Figure 2A small SEE ((cid:10)98.3 g(cid:1)m(cid:1)2(cid:1)h(cid:1)1). Noticeably, the regression nlo
shows that OSE accounted for 74% of the variance but had a coefficient (0.603) is significantly smaller (P (cid:4) 0.01, Wald ad
high SEE (181 g(cid:1)m(cid:1)2(cid:1)h(cid:1)1). Since the data were collected at statistic) than the OSE output equation. ed
differenttimesandcontaineddisparateconditions,anonlinear Figure 3 provides a histogram comparing mean outputs for fro
fuzzypiecewiseregressionemployingaquasi-Newtonsolution OSE, OSE , and PW equations against measured sweating m
provided the best resolution (29, 30). Fuzzy piecewise regres- rates for daCta sets I–IV. The OSE demonstrated the widest ja
p
sion using the E and E values as input parameters pro- variabilitycomparedwiththemeasureddataandwasmarkedly .p
req max h
duced the following equation (PW): elevated for the moderate- and high-intensity exercise experi- y
s
Sweatingrate(cid:7)g(cid:1)m(cid:1)2(cid:1)h(cid:1)1(cid:8)(cid:2)147(cid:5)1.527(cid:1)E (cid:4)0.87(cid:1)E ments. However, OSEC and PW prediction equations tracked iolo
req max measured sweating rates remarkably well. g
y
(16) Cross-validation analyses. To evaluate the prediction equa- .o
tions against averaged responses from independent data sets, rg
Figure2BprovidesthecomparisonofoutputfromPWwith o
we made comparisons with two additional data sets: one an n
respect to observed sweating rates for data sets I–IV. PW J
outdoor field study (data set V) and another conducted in an u
accounted for 78% of the variance for the same data with a ly
muchsmallerSEE(72g(cid:1)m(cid:1)2(cid:1)h(cid:1)1).Forthisanalysis,E and environmental chamber (data set VI). In both studies, volun- 3
tEiomnaxbwyeruesdinegternmeiwnedhefarotmantdheminadsisvidtruaanlsfheeratcboaelfafinccieerneeqtsquaas- tpereortsecwtiovreeaclvoathriientgyo(sfeceloMthEiTnHgODcoS)n.fiFguigruatrieon4s,pinloctlsudtihnegmNeBaCn 1, 200
observed sweating rates and mean predicted values during a 9
explainedinMETHODSandweretransformedtosweatingrateby
division of W(cid:1)m(cid:1)2/(0.68 W(cid:1)h(cid:1)g(cid:1)1) (31). field study test (data set V) (21). In general, PW and OSEC
equationswerenotsignificantlydifferentfromtheexperimen-
Since it was determined that the output from OSE would
tallyobservedsweatingrates.TheOSE,however,consistently
probably not completely unify the data set and predict ade-
predicted responses too high within and between the various
quately because of the imprecise clothing coefficients deter-
trials except for the day with solar load and night trials when
mined from a static manikin and the low wind speeds (10)
subjectsworetheMOPPlevel1clothingconfiguration.Figure5
applied to the heat balance analyses in OSE (28), a similar
plots the mean observed sweating rates and mean predicted
iterative approach was run to correct the OSE by using indi-
values during the environmental chamber study (data set
vidual analysis of E and E using modern analytic ap-
req max VI).TheOSEpredictedsweatingrateshigherthanmeasured
proachestotheclothingcoefficientsinthedatasets(METHODS).
data consistently within the two male and female groups of
An exponential correction to Eq. 1 was successfully obtained
subjects (P (cid:4) 0.01).
after various statistical algorithm solutions were attempted.
Thissolutionproducedthefollowingcorrectionappliedtothe
DISCUSSION
OSE equation to predict sweating rates:
OSE (cid:7)g(cid:1)m(cid:1)2(cid:1)h(cid:1)1)(cid:2)147(cid:1)exp(cid:7)0.0012(cid:1)OSE(cid:8) (17) ThisstudycomparedtheaccuracyofOSEtoanewequation
C (PW) for predicting sweating rate during extended exercise (2
where OSE in Eq. 17 is the uncorrected output from the to8h)withhighermetabolicratesandcontemporaryclothing
original Eq. 1 (28). systems including body armor and developed a correction to
E and E signify the new values obtained with the new OSE(OSE )thatisapplicableandeasilymigratedintovarious
req max C
clothingcoefficients.Figure2Cplotsthecomparisonofoutput existing rational and operational thermal models. The hypoth-
fromOSE, withrespecttoobservedsweatingratesforalldata eses, based on current research and literature results (3, 15),
C
sets. OSE, accounted for (cid:6)64% of the variance but with a werethatOSEoverestimatessweatingratesandthatimproved
C
JApplPhysiol•VOL107•AUGUST2009•www.jap.org
PREDICTIONEQUATIONSOFSWEATLOSS 385
D
o
w
n
lo
a
d
e
d
fro
m
ja
p
.p
h
y
s
io
lo
g
y
.o
rg
o
n
J
u
Fig. 1. A: individual sweating rate measurements from data sets I–IV. ly
B:residualplotoforiginalShapiroequationoutput(OSE)(28)vs.observed 31
dataforeachindividual(n(cid:2)504). , 2
0
0
9
predictionequationscouldbedeveloped.Thenewlydeveloped
OSE and PW equations were better predictors of sweating
C
rates (58 and 65% more accurate, P (cid:4) 0.01) and produced
minimal error (SEE (cid:4) 100 g(cid:1)m(cid:1)2(cid:1)h(cid:1)1) for conditions both
withinandoutsidetheoriginalOSEdomainofvalidity,which
include cooler environments, higher metabolic rates, longer
workdurations,andmodernprotectiveclothingandequipment
ensembles.
The rationale to develop a predictive equation for sweating
rate (and, thereby, water needs) was a unique concept at the
time that OSE was developed and one that had not been
expanded on until this effort. The OSE predicts sweat losses,
and thus water needs, over wide thermal environments by
knowledge of only two key variables, E and E , which
req max
Fig.2. Linearplotsofpredictionequationoutputvs.observedsweatingrates.
A:originalShapiroequation(OSE).B:piecewiseequation(PW).C:corrected
OSE(OSE ).Thecorrelationbetweenmeasuredsweatingratesandpredicted
C
sweatingratesfromeachequationisindicatedineachpanel.FuzzyPWisa
nonlinear transient analysis; linear correlations are shown only for relative
comparisonofaccuracybetweenthevariousoutputalgorithms.SEE,standard
erroroftheestimate.
JApplPhysiol•VOL107•AUGUST2009•www.jap.org
386 PREDICTIONEQUATIONSOFSWEATLOSS
Fig. 3. Sweating rate output (means (cid:10) SD) from the various equations D
comparedwithmeasured(observed,ObsSW)dataplottedfordatasetsI–IV. o
w
Data set designations are the same as in Table 3. Prediction accuracy and n
significancewasdeterminedbyanalysesofmeanerrorrateofeachequation lo
a
vs.observeddata(seeTable4andtext). d
e
d
fro
directlyorindirectlyintegratetheeffectsoftheinternalfactors m
(metabolicrate,skinandcoretemperature)andexternalfactors Fig. 5. Comparison of output from the various prediction equations and ja
(clothing, operative temperature, wind, and humidity). OSE measured(observed)sweatingrateplottedforeachgroup(9femalesand13 p.p
has been shown to often overestimate sweating rates for a mmaelaenss)(cid:10)inSaDn.NexSpedriifmfeerenntaclescrboestsweveanlidgaetnidoenrss;*tu(cid:2)dyP((cid:4)stu0d.y01VwI)i.thVinaglureosupa.re hys
varietyofconditionswithinandoutsidetheoriginalequation’s io
domain of validity (3). lo
g
Theoriginalequationwasnotmeanttopredictresponsesat mate (and invariably Edrip), both of which become limiting y.o
highmetabolicrates.Elevatedheatproductionisaccompanied factors in a person’s ability to achieve steady-state heat bal- rg
by higher levels of core and skin temperatures (20) and ance. Although core temperatures are not shown in this study, on
generally higher sweating rates that can saturate the microcli- this variable is indirectly related to the analysis of the heat J
u
ly
3
1
, 2
0
0
9

Fig. 4. Comparison of output from each of the prediction
equationsandmeasured(observed)sweatingrateplottedfor
each group walking in the outdoor cross-validation study
(datasetV)clothedinvariousNBCclothing.MOPP,mis-
sion-oriented protective posture. Values are means (cid:10) SD.
*P(cid:4)0.01withineachspecifictrial.a(cid:2)P(cid:4)0.01between
nightanddaytrialsinMOPPO.
JApplPhysiol•VOL107•AUGUST2009•www.jap.org
PREDICTIONEQUATIONSOFSWEATLOSS 387
balanceandreflecteddirectlybyanychangesinS.Thelatteris the accuracy it possesses compared with the true (or experi-
affected by core and skin temperature drive so that S/hFcl (cid:2) mentally observed) outcome. Within the scope of this study’s
(dTb/dt)[(0.97mb/A )]/hFcl, where Tb is integrated mean intent,anyequationdevelopedmustexhibitatightassociation
D
body temperature, mb is body mass (kg), A is body surface between the model’s outcome predictions and the group out-
D
area (m2), 0.97 is body specific heat (W(cid:1)h)/(kg(cid:1)°C), and hFcl comes of the test population. The equation serves as a surro-
is the combined heat transfer coefficient times Burton’s cloth- gateofactualobservedsweatresponsesbasedononeormore
ing factor, Fcl (5, 26). independent factors (E , E ) driving the outcome (mea-
req max
Also, steady-state skin temperature levels add errors in sured m˙ ). The analysis of mean error rates for all combined
sw
determining dry heat flux (R (cid:5) C (cid:5) K) through clothing and trialsresultedinarejectionofthenullhypothesisthatallthree
insensible heat loss, and variable latent heat of evaporation equations are equally accurate.
(10) also can introduce errors in E calculations leading to Table 4 shows that PW was almost 65% more accurate in
max
wide discrepancies in prediction accuracy of sweating rates predicting sweating rate compared with the OSE. However,
using OSE. usingOSE wouldstillbe58%moreaccuratethanusingOSE.
C
In this study, OSE consistently overestimated measured Therefore, using either PW or OSE could be considered
C
sweatingrate(Fig.2,A–C),particularlyatthehighermeasured mathematically equivalent over the range of environments,
sweatingrates.AcorrectiontoOSEusingthepresentextensive time domains, or metabolic activities studied. Furthermore,
database (101 subjects, longer work durations from 4 to 8 h, integration with the OSE that resides in many rational and
andavarietyofclothingsystems)extendedaccurateprediction operationalthermalmodelsisnowpossiblebyapplyingOSE :
C
of actual sweating rates from (cid:6)200 to (cid:6)500 g(cid:1)m(cid:1)2(cid:1)h(cid:1)1. The m˙ (g(cid:1)m(cid:1)2(cid:1)h(cid:1)1) (cid:2) 147(cid:1)exp (0.0012(cid:1)OSE), where OSE is
sw
most significant finding of the current study was the develop- output from OSE (28) that leaves the exponential regression
1m4e7Tnht(cid:5)eo1fi.5ma2np7er(cid:1)owEvreeaqdn(cid:1)deiqm0u.pa8rt7ioo(cid:1)vEnemdPaxeW.quaitsiobnaPseWd:om˙nswfu(gzz(cid:1)my(cid:1)p2ie(cid:1)hc(cid:1)ew1)is(cid:2)e cEaonreedqffiaecnvidaepnEotsmraa[txi2v7teo.9ct(cid:1)roEannrefsqof(cid:1)re(mrEmcwaoxie)thf(cid:1)fi0mc.4i5eo5nr]etsirnoatbnaudcsttdbayunntdammmioocddiemfirenasnhiktehianet Downloa
regressionanalysisthatincorporatesthecombinedeffectsofa thermal resistance values. de
d
b(croomadmeronrlayngeempolfoymedetbabyomlicilitraartyesa,nwdelaarwingenfoofrcbeomdeynt)a,rmanodr oriTghineallimErietqsaonfdthEemcaoxrlriemctietsd(p5r0ed(cid:4)icEtirveeq(cid:4)equ3a6t0ioWns/mco2mapnrdis2e0th(cid:4)e from
other aspects of modern military clothing systems. This equa- Emax(cid:4)525W/m2,respectively),buttheselimitsareextended ja
tionisessentiallyapplicableforbothmenandwomenworking so that the equation is applicable for higher metabolic intensi- p.p
fortimeperiodsupto8h.Mostimportantly,thisequationstill ties (M (cid:2) 400 W/m2, (cid:6)700–800 W), lower ambient condi- h
y
incorporates attributes of OSE documenting two essential tions (Ta (cid:2) 15°C), and longer time periods (up to 8 h). sio
physiological mechanisms (5, 26) necessary in thermoregula- PWandOSE werederivedprincipallyfromenvironmental lo
C g
tory function, one coupled with eccrine sweat gland function, chamber experiments. The limited results from the field test y.o
intesceelfssaasrysoicniathteedrewguitlhatiionnteornfahleaatnbdalasnkcine(bEoredqy),atenmdptheeraotuthreesr arepppoeratredvailnidFiing.pr4ed(idcatitnagssewt eVa)tiningdircaatetedtuhraintgPmWildanedffeOcStiEvCe onrg
neededwheneverheattransfermechanismsmustbecharacter- radiantloads.AlthoughsolarloadintermsofERFdidinclude J
u
ized in terms of clothing worn and environmental impact daytimetestsashighas500W/m2,amoreextensivedatabase ly
(Emax). In the latter cases, the factor Ereq/m˙sw is a direct incorporating wider thermal conditions with more intense and 31
correlateofM(metabolicheatproduction),sinceEreqisbased variable solar loads (27) and further testing or modification of , 2
0
on the solution of the comprehensive heat balance equation the equations studied is needed in the future. 0
comprising S (cid:2) (M (cid:10) Wk) (cid:1) E (cid:10) (R (cid:5) C (cid:5) K) (10). Conclusions.Thepresentstudydevelopedbothanew(PW) 9
The relative accuracy of PW and OSEC has only been andacorrected(OSEC)sweatingrate(andfluidneeds)predic-
implied so far in this discussion. The concern is that any tion equation that provides a more accurate estimate of mea-
equation’s output should accurately predict sweating rates sured sweating rates, and therefore also water needs, for a
within a given boundary level because, over an 8-h period, it variety of military, occupational, and sports medicine scenar-
hasanimpactonwaterrequirementsneededbyanindividual. ios. PW and OSE have wide application to public health,
Cheuvront et al. (3) estimated that this should be (cid:10)0.125 l/h military, occupatioCnal and sports medicine communities. Fu-
(some 65.8 g(cid:1)m(cid:1)2(cid:1)h(cid:1)1 for a person 1.9 m2 BSA). Our results ture studies should develop sweating rate databases for other
inthisstudyshowedviatheSEE(Fig.2,A–C)thatthevarious
equations’ domains of accuracy were (cid:10)72.4 g(cid:1)m(cid:1)2(cid:1)h(cid:1)1 for
PW, (cid:10)98.3 g(cid:1)m(cid:1)2(cid:1)h(cid:1)1 for OSE , and (cid:10)181.3 g(cid:1)m(cid:1)2(cid:1)h(cid:1)1
C Table 4. Summary of mean error rate analyses for each
using the original OSE. These translate for the 1.9 m2 BSA
personto(cid:10)0.137l/h(new),0.186l/h(corrected),and0.340l/h equation compared with data over all trials
(original)forthewholedatabaseconsideredinthisstudy.It is
Variable Mean(cid:10)SD
doubtfulthatthe(cid:10)0.137l/hfoundusingthenewequationis
physiologicallymeaningfullycomparedwiththe(cid:10)0.125l/h OSErank 9.75(cid:10)2.31*
criterion, which would result in (cid:6)1,096 ml over 8 h com- OSECrank 5.37(cid:10)3.50†
PWrank 4.12(cid:10)2.16
pared with the 1,000-ml criterion recommended by Cheu-
vront et al. (3). OSE, original shapiro equation; OSEC, corrected OSE; PW, piecewise
equation.RankanalysiswasperformedusingFriedmanANOVA.*P(cid:4)0.01,
Asweatingratepredictivemodelthatisoperationalforwide
PW vs. OSE (64.5% difference). †P (cid:4) 0.01, OSE vs. OSE (57.9% differ-
uses such as determining water requirements over various C
ence). There is no significant difference comparing PW vs. OSE (15.6%
C
environments, activities, and time domains is only as good as difference).
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