A Spreadsheet for Partitional Calorimetry Kerry Atkins MExSpSc and Martin Thompson^{ }PhD School of Exercise and Sport Science, University of Sydney, Sydney, NSW 2141, Australia. Email: kerryatkins@bigpond.com Sportscience 4(3), sportsci.org/jour/0003/ka.html, 2000 (2172 words) Reviewed
by Jim Cotter PhD, Defence Science and Technology Organisation, Melbourne,
Australia 3001

Metabolic heat generated during exercise is transferred to the environment from the skin surface via dry (conduction, convection and radiation) and evaporative heat transfer pathways. Parameters within the environment that influence heat exchange include the ambient temperature and water vapor pressure, radiant heat, air movement, and the properties of clothing (insulation and moisture transfer). Measurement of heat exchanged via dry and evaporative processes is useful to determine how workload, clothing and environmental conditions influence the degree of thermal strain during prolonged exercise. The procedure for calculating heat storage and heat lost or gained via dry and evaporative heat transfer pathways is termed partitional calorimetry. The calculations in partitional calorimetry are necessarily complex. For the benefit of researchers and teachers interested in heat balance during exercise, we present here an Excel spreadsheet to perform the calculations. The spreadsheet automates the calculations with Visual Basic, using an approach similar to that of Egan (1999). A main menu, constructed from a userform, contains command buttons that guide the user to the relevant worksheets to input data and to receive calculated information. View the main menu at any time by typing Ctrl+Shift+R. Instructions are available via the main menu to guide you through the program. Data required to run the program include:
Userforms are provided in the environmental worksheet to calculate mean radiant temperature, the partial water vapor pressure in the ambient air, and the radiative heat transfer coefficient. The user inputs these values into the worksheet. For the intrinsic clothing insulation of garments worn, the user can either enter a measured value or estimate this value by selecting the checkboxes that correspond to the worn clothing items. The data produce the following parameters:
The partitional calorimetry results appear in the worksheet Program Outputs. This worksheet is shown automatically after the program has performed the calculations. If the user is interested in other calculated variables (physiological, environmental and clothing), all the calculated variables are shown in the worksheet Calculation. Formulae that use fabric temperature in their calculations have the term Tcl used within the column. If mean skin temperature is used in a given formula instead of fabric temperature the term Tsk used is shown within the column. Final points:
FORMULAE FOR PARTITIONAL
CALORIMETRY CALCULATIONS Environmental Variables Calculation of mean radiant
temperature, T_{r} T_{r} (^{o}C) = ((1+(0.222 x (v_{a}^{0.5}))) x
(T_{g}  T_{db})) + T_{db} Calculation of convective heat transfer coefficient, h_{c }(from Kerslake, 1972) h_{c} (W.m^{2}.K^{1})
= 8.3 x (v_{a}^{0.6}) Calculation of radiative heat
transfer coefficient, h_{r} h_{r} (W.m^{2}.K^{1})
= 4.E.s.A_{r}A_{d}.((273.2
+ ((T_{cl} + T_{r})/2))^{3}) Calculation of combined heat
transfer coefficient, h h (W.m^{2}.K^{1}) = h_{c}
+ h_{r} Calculation of evaporative heat
transfer coefficient, h_{e} h_{e} (W.m^{2}.kPa^{1}) = 16.5 x h_{c }where h_{c} is the convective heat transfer coefficient (W.m^{2}.K^{1}). Clothing Variables Calculation of the clothing
area factor, f_{cl} f_{cl} = 1 + (0.31 x (I_{cl}/0.155)) Calculation of effective
clothing insulation, I_{cle} I_{cle} (clo units) = I_{cl}  ((f_{cl}1)/(0.155 x f_{cl} x
h)) Calculation of the permeation
efficiency factor of clothing, f_{pcl} f_{pcl} = 1/(1+(0.344 x h_{c}
x I_{cle})) Calculation of the intrinsic thermal resistance of clothing, R_{c }(from Holmer, 1985) R_{c} (m^{2}.K.W^{1})
= (T_{sk}  T_{db})/h_{c} Calculation of the intrinsic
evaporative resistance of clothing, R_{e} R_{e} (m^{2}.kPa.W^{1}) = (P_{s} P_{a})/h_{e }where P_{s} = saturated water vapor pressure at the skin surface (kPa), P_{a} is the partial water vapor pressure (kPa) and h_{e} is the evaporative heat transfer coefficient (W.m^{2}.KPa^{1}). Physiological Variables Calculation of body surface area, A_{D} A_{D} (m^{2}) = 0.00718 x wt^{0.425} x H^{0.725 }where wt = body mass (kg) and H = height (cm). Calculation of mean body
temperature, T_{b} T_{b} (^{o}C) = (0.33 x T_{sk} + 0.67 x T_{c}) Calculation of saturated water
vapor pressure at the skin surface, P_{s} P_{s} (mmHg) = 1.92 x T_{sk}
25.3 (for 27^{o}C < T_{sk }< 37 ^{o}C). Partitional Calorimetry
Equations Calculation of the energy
equivalent of oxygen, EE EE (J.L O_{2}^{1}) = (0.23 x RER + 0.77) x 21 166 Calculation of metabolic free
energy production, M M (W.m^{2}) = (((EE x VO_{2}
x t)/(t x
60))/A_{D}) Calculation of mechanical
efficiency, h h = W/M Calculation of internal heat
production, H H (W.m^{2}) = (M x (1 h
)) x 1/A_{D} Calculation of body heat
storage, S S (W.m^{2}) = ((3474 x wt x
(T_{b} final  T_{b} initial))/t)/A_{D} Calculation of heat transfer
via conduction, K K (W.m^{2}) = A_{D} x
((T_{sk}  T_{cl})/R_{c}) Calculation of heat transfer
via radiation, R R (W.m^{2}) = E.s.f_{cl}.f_{eff}.(T_{s}^{4}
 T_{r}^{4}) Calculation of heat transfer
via convection, C C (W.m^{2}) = (A_{D} x
f_{cl} x h_{c} x (T_{s}
 T_{db}))/ A_{D} Calculation of required
evaporative heat loss, E_{req} E_{req} (W.m^{2}) = H  K  R  C S Calculation of the maximal evaporative
capacity of the environment, E_{max} E_{max} (W.m^{2}) = f_{pcl}
x h_{e}
x (P_{s}
 P_{a}) Calculation of skin wettedness,
w w = E_{req}/ E_{max} Calculation of evaporative heat
transfer via skin diffusion, E_{d} E_{d} (W.m^{2}) = (l
.m.A_{D}.(P_{s}  P_{a}))/A_{D} Calculation of heat transfer by sweat evaporation from the skin surface, E_{sw} E_{sw} (W.m^{2}) = ((((wt_{initial}  wt_{final})(fluid/food intake+urine/feces loss)((0.019 x VO_{2} x (44P_{a}))
x t)))x
2430)/((t x 60) x A_{D}) Calculation of heat transfer via evaporation from the skin surface, E_{sk} E_{sk} (W.m^{2}) = E_{d }+ E_{sw }where E_{d} = heat transfer by skin diffusion (W.m^{2}) and E_{sw }= heat transfer from sweat evaporation from the skin surface (W.m^{2}). Calculation of heat transfer
via the respiratory tract, E_{res}+C_{res} E_{res}+C_{res }(W.m^{2}) = (0.0014 x M x (T_{ex}T_{db}))+(0.0017 x M x (58.7P_{a})) REFERENCES Egan DJ (1999) Analysis
of expired air with GASCALC: an automated spreadsheet. Sportscience 3(3),
sportsci.org/jour/9903/dje.html (1549 words) Fanger PO (1970) Thermal
Comfort. New York: McGrawHill Goldman 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, 290305 Holmer I (1985) Heat
exchange and thermal insulation compared in woollen and nylon garments during
wear trials. Textile Research Journal 55, 511518 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, 474476 Parsons KC (1993) Human Thermal Environments. London: Taylor and Francis ©2000 