| Package: |
| heatex |
| Type: |
| Package |
| Version: |
| 1.0 |
| Date: |
| 2013-01-28 |
| License: |
| GPL (version 2 or later) |
Following is the list of data variables that are needed to run the heatex function in the required order of the arguments: 1. time = Total time for physical activity in minutes. 2. workrate = The work rate (power output) of the activity in watts. 3. ht = Subject height in centimetres. 4. wt = Subject body mass in kilograms (to calculate the body surface area, usual body mass). 5. bmi = Subject body mass before commencing physical activity in kilograms. 6. bmf = Subject body mass after physical activity in kilograms. 7. fluidfood = Fluid and food consumption during the physical activity. 8. urinefaeces = Urine and faeces loss during the physical activity. 9. sweat = Dripped sweat in grams. 10.tci = Initial body core temperature in degrees celsius. 11.tcf = Final body core temperature in degrees celsius. 12.tski = Initial skin temperature in degrees celsius. 13.tskf = Final skin temperature in degrees celsius. 14.vo2 = Oxygen consumption in litres per minute. 15.rer = Respiratory exchange ratio. 16.tdb = Dry bulb temperature of the environment in degrees celsius. 17.tg = Black globe temperature in degrees celsius. 18.va = Air velocity in metres per second. 19.pa = Ambient water vapour pressure in mmHg. 20.icl = Intrinsic clothing insulation in m2.oC.W-1. 21.tcl = Temperature of the outer body surface, including clothing temperature if relevant, in degrees celsius.
Following is a description of the formulae and outputs for the calculations.
1. Environmental Variables
1.1 Calculation of mean radiant temperature, Tr (from Goldman, 1978) Tr (oC) = ((1+(0.222 x (va0.5))) x (Tg - Tdb)) + Tdb where va = air velocity (m.s-1), Tg = black globe temperature (oC) and Tdb = dry bulb temperature (oC).
1.2 Calculation of convective heat transfer coefficient, hc (from Kerslake, 1972) hc (W.m-2.K-1) = 8.3 x (va0.6) where va = air velocity (m.s-1).
1.3 Calculation of radiative heat transfer coefficient, hr (from Parsons, 1993) hr (W.m-2.K-1) = 4.E.sigma.ArAd.((273.2 + ((Tcl + Tr)/2))3) where E = emissivity of the skin surface (0.98: Gonzalez, 1995, p.299), sigma = Stefan-Boltzmann constant (5.67 x 10-8 W.m-2.K-4), ArAd = ratio of the area of the body exposed to radiation versus the total body surface area (0.70 for seated postures, 0.73 for standing postures), Tcl = mean surface temperature of the body (oC), and Tr = mean radiant temperature (oC).
1.4 Calculation of combined heat transfer coefficient, h (from Parsons, 1993) h (W.m-2.K-1) = hc + hr where hc is the convective heat transfer coefficient (W.m-2.K-1) and hr is the convective heat transfer coefficient (W.m-2.K-1).
1.5 Calculation of evaporative heat transfer coefficient, he (from Kerslake, 1972) he (W.m-2.kPa-1) = 16.5 x hc where hc is the convective heat transfer coefficient (W.m-2.K-1).
2. Clothing Variables
2.1 Calculation of the clothing area factor, fcl (adapted from Parsons, 1993) fcl = 1 + (0.31 x (Icl/0.155)) where Icl = intrinsic clothing insulation (m2.oC.W-1).
2.2 Calculation of effective clothing insulation, Icle (from McIntyre, 1980) Icle (clo units) = Icl - ((fcl-1)/(0.155 x fcl x h)) where Icl = intrinsic clothing insulation (m2.oC.W-1), fcl = clothing area factor (ND), h = combined heat transfer coefficient (W.m-2.K-1).
2.3 Calculation of the permeation efficiency factor of clothing, fpcl (adapted from Parsons, 1993) fpcl = 1/(1+(0.344 x hc x Icle)) where hc is the convective heat transfer coefficient (W.m-2.K-1) and Icle is the effective clothing insulation (clo units).
2.4 Calculation of the intrinsic thermal resistance of clothing, Rc (from Holmer, 1985) Rc (m2.K.W-1) = (Tsk - Tdb)/hc where Tsk = mean skin temperature (K), Tdb = dry bulb temperature (K) and hc is the convective heat transfer coefficient (W.m-2.K-1).
2.5 Calculation of the intrinsic evaporative resistance of clothing, Re (from Holmer, 1985) Re (m2.kPa.W-1) = (Ps- Pa)/he where Ps = saturated water vapor pressure at the skin surface (kPa), Pa is the partial water vapor pressure (kPa) and he is the evaporative heat transfer coefficient (W.m-2.KPa-1).
3. Physiological Variables
3.1 Calculation of body surface area, AD AD (m2) = 0.00718 x wt0.425 x H0.725 where wt = body mass (kg) and H = height (cm).
3.2 Calculation of mean body temperature, Tb (from Kerslake, 1972) Tb (oC) = (0.33 x Tsk + 0.67 x Tc) where Tsk = skin temperature (oC) and Tc = body core temperature (oC).
3.3 Calculation of saturated water vapor pressure at the skin surface, Ps (from Fanger, 1970) Ps (mmHg) = 1.92 x Tsk -25.3 (for 27oC < Tsk < 37 oC). where Tsk = skin temperature (oC).
4. Partitional Calorimetry Equations
4.1 Calculation of the energy equivalent of oxygen, EE (modified from Parsons, 1993) EE (J.L O2-1) = (0.23 x RER + 0.77) x 21 166 where RER = respiratory exchange ratio (ND), 21 166 is the energy equivalent of oxygen (J.LO2-1).
4.2 Calculation of metabolic free energy production, M (modified from Parsons,1993) M (W.m-2) = (((EE x VO2 x t)/(t x 60))/AD) where EE = energy equivalent (J.L O2-1), VO2 = oxygen consumption (L.min-1), t = exercise time (min) and AD = body surface area (m2).
4.3 Calculation of mechanical efficiency, n (from Parsons, 1993) n = W/M where W = work rate (W.m-2) and M = metabolic free energy production (W.m-2).
4.4 Calculation of internal heat production, H (from McIntyre, 1980) H (W.m-2) = (M x (1- n)) x 1/AD where M = metabolic free production (W.m-2), n= mechanical efficiency and AD is the body surface area (m2).
4.5 Calculation of body heat storage, S S (W.m-2) = ((3474 x wt x (Tb final - Tb initial))/t)/AD where 3474= average specific heat of body tissue (J.kg-1.oC-1), wt= body mass (kg), Tb = mean body temperature (oC), t = exercise time (s) and AD = body surface area (m2).
4.6 Calculation of heat transfer via conduction, K K (W.m-2) = AD x ((Tsk - Tcl)/Rc) where AD = body surface area (m2), Tsk = mean skin temperature (K), Tcl = mean fabric temperature (K), and Rc = intrinsic thermal resistance of clothing (m2.K.W-1).
4.7 Calculation of heat transfer via radiation, R (adapted from McIntyre, 1980) R (W.m-2) = E.sigma.fcl.feff.(Ts4 - Tr4) where E = emittance from the outer surface of a clothed body (0.97), sigma = Stefan-Boltzmann constant (5.67 x 10-8 W.m-2.K-4), fcl = clothing area factor (ND), feff = effective radiation areaof a clothed body (0.71), and Ts = surface temperature of the body (oC) and Tr = mean radiant temperature (oC).
4.8 Calculation of heat transfer via convection, C (from Fanger, 1970) C (W.m-2) = (AD x fcl x hc x (Ts - Tdb))/ AD where AD = body surface area (m2), fcl = clothing area factor (ND), hc = convective heat transfer coefficient (W.m-2.K-1), Ts = surface temperature of the body (oC) and Tdb = dry bulb temperature (oC).
4.9 Calculation of required evaporative heat loss, Ereq (from Gonzalez, 1995) Ereq (W.m-2) = H - K - R - C -S where H = internal heat production (W.m-2), K = heat exchange via conduction (W.m-2), R= heat exchange via radiation (W.m-2), C = heat exchange via convection (W.m-2), and S = body heat storage (W.m-2).
4.10 Calculation of the maximal evaporative capacity of the environment, Emax (from McIntyre, 1980) Emax (W.m-2) = fpcl x he x (Ps - Pa) where fpcl = permeation efficiency factor of clothing, he = evaporative heat transfer coefficient (W.m-2.kPa-1), Ps = partial water vapor pressure at the skin surface (kPa), and Pa = partial water vapor pressure of ambient air (kPa).
4.11 Calculation of skin wettedness, w w = Ereq/ Emax where Ereq = required evaporative heat loss (W.m-2) and Emax= maximal evaporative capacity of the environment (W.m-2).
4.12 Calculation of evaporative heat transfer via skin diffusion, Ed (modified from Fanger, 1970) Ed (W.m-2) = (l.m.(Ps - Pa)) where l = latent heat of evaporation of sweat (2430 J.g-1), m = permeance coefficient of the skin (1.694 x 10-4 g.s-1.m-2.mmHg-1), Ps = partial water vapor pressure at the skin surface (mmHg) and Pa= partial water vapor pressure in ambient air (mmHg)
4.13 Calculation of heat transfer by sweat evaporation from the skin surface, Esw Esw (W.m-2) = ((((wtinitial - wtfinal)-(fluid/food intake+urine/faeces loss)-((0.019 x VO2 x (44-Pa)) x t)))x 2430)/((t x 60) x AD) where wt = body mass (g), fluid/food intake and urine/faeces loss are in grams, the expression 0.019 x VO2 x (44-Pa) accounts for respiratory weight loss in g.min-1 (Mitchell et al., 1972), VO2= oxygen uptake in L.min-1, t = observation time (min), and AD = body surface area (m2).
4.14 Calculation of heat transfer via evaporation from the skin surface, Esk Esk (W.m-2) = Ed + Esw where Ed = heat transfer by skin diffusion (W.m-2) and Esw = heat transfer from sweat evaporation from the skin surface (W.m-2).
4.15 Calculation of heat transfer via the respiratory tract, Eres+Cres (from McIntyre, 1980) Eres+Cres (W.m-2) = (0.0014 x M x (Tex-Tdb))+(0.0017 x M x (58.7-Pa)) where M = metabolic heat production (W.m-2), Tex= expired air temperature (assumed to be 34oC if Tex is not measured directly), Tdb = dry bulb temperature (oC), and Pa= partial water vapor pressure of ambient air (mmHg).
Fanger PO (1970) Thermal Comfort. New York: McGraw-HillGoldman RF (1978) Prediction of human heat tolerance. In: Folinsbee LJ, Wagner JA, Borgia JF, Drinkwater BL, Gliner JA, Bedi JF (editors). Environmental Stress: Individual Human Adaptations. New York: Academic Press.
Gonzalez RR (1995) Biophysics of heat exchange and clothing: applications to sports physiology. Medicine Exercise Nutrition and Health 4, 290-305.
Holmer I (1985) Heat exchange and thermal insulation compared in woolen and nylon garments during wear trials. Textile Research Journal 55, 511-518.
Kerslake DM (1972) The Stress of Hot Environments. Cambridge: University Press.
McIntyre DA (1980) Indoor Climate. London: Applied Science.
Mitchell JW, Nadel ER, Stolwijk JAJ (1972) Respiratory weight losses during exercise. Journal of Applied Physiology 32, 474-476. Parsons KC (1993) Human Thermal Environments. London: Taylor and Francis.
# The following example demonstrates the use of the heatex function with the supplied example data:
data(df)
example<-heatex(df)
#view results
example
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