HuTAS Change log
V1.10 (June 12th, 2019) - Added Strava API integration - Improved mobile user interface - Corrected imst definition - Thanks @ Boris Kingma (NTO) - Auto update activity details when reviewing past thermal audits V1.01 (May 30th, 2019) - Updated date/time selector to be more mobile friendly - Able to fetch historical & 6-days ahead weather data - Added clothing ensembles and estimate Re,cl V1.0 (May 25th, 2019) - Initial Release
Thermal Audit Equation Directory
The equations used for the "Thermal Audit Simulation" are based on the equations found in:
Conceptual Heat Balance Equation:
M - W = ± K ± C ± R ± (Eres + Cres) + Esk ± S [W/m2]
Heat Production (Hprod):
Hprod = M - W [W/m2]
Metabolic Energy Expenditure (M):
(when not provided)
M = (341 * VO2) / BSA [W/m2]
Where VO2 (rate of oxygen consumption) is in L/min, and BSA is body surface area
Rate of oxygen consumption (VO2 in L/min):
VO2 can be provided, or estimated using the 2011 Compendium of Physical Activities normative values (in METs) or through selecting modality and providing a parameter. When the later is selected, ACSM equations are used to estimate VO2.
- VO2 = [(0.1 * SPEED [m/min]) + (1.8 * SPEED [m/min] * GRADE[/1]) + 3.5 ] * MASS [L/min]
- VO2 = [(0.2 * SPEED [m/min]) + (0.9 * SPEED [m/min] * GRADE[/1]) + 3.5 ] * MASS [L/min]
- VO2 = [(10.8 * WATTS / MASS ) + 7] * MASS [L/min]
External Work Rate (W):
(when not provided, i.e. cycling)
If slecting a normative physical activity from the Compendium of Physical Activities
W = M * (0.2 * tanh(0.39 * MET -0.6) ) [W/m2]
Where MET is the metabolic rate; 1 MET = 58.15 W/m2
If selecting the "Walking" or "Running" modality:
W =(103 * (MASS[kg] * SPEED[m/min] * (%GRADE * 100) )) / (6.12 * 60 * 1000) ) / BSA [W/m2]
At present, conduction is assumed negligible.
C = fcl * hc * (Tshell - Tair) * (Pb/760)0.55 [W/m2]
Where fcl is the clothing area factor, hc is the convective heat transfer coefficient, Tshell is the external surface temperature (skin or clothing temperature), Tair is ambient temperature, and Pb is barometric pressure in mmHg
Convective heat transfer coefficient (hc):
The convective heat transfer coefficient is calculated depending on the activity conducted where v is air velocity (m/s) or loc is locomotion speed (m/s);
- Default (rest or normative activities):
- if v < 0.2, hc = 3.1, else hc = 8.3 * v0.6 [W/m2/K]
- Stationary cycling:
- if v < 0.2, hc = 6, else hc = 8.3 * v0.6 [W/m2/K]
- hc = 8.3 * loc0.391 [W/m2/K]
- Outdoor Running:
- hc = 8.3 * loc0.531 [W/m2/K]
- Outdoor Cycling:
- hc = 8.4 * loc0.840 [W/m2/K]
R = fcl * hr * (Tshell - Tair) [W/m2]
Where fcl is the clothing area factor, hr is the radiative heat transfer coefficient, Tshell is the external surface temperature (skin or clothing temperature), and Tair is ambient temperature
Radiative heat transfer coefficient (hr):
hr = 4 * ɛ * σ * Ar [273.2 + (Tshell + Tr / 2)]3 [W/m2/K]
Where σ is the Stefan–Boltzmann constant, 5.67 × 10-8 (W/m2/K4), ɛ is the area-weighted emissivity of the body surface, and Ar is the effective radiative area, Tshell is the external surface temperature (skin or clothing temperature), and Tr is the mean radiant temperature.
Mean Radiant Temperature (Tr):
If the activity is conducted indoors or at night, Tr is assumed to be equal to air temperature.
If air velocity (v) is below 0.15 m/s:
Tr = [ (tg + 273)4 + ( 0.25 * 108 / ɛ ) * [(|tg - ta|)/d]1/4 * ( tg - ta) ]0.25 -273 [°C]
If air velocity (v) is > 0.15 m/s:
Tr = [ (tg + 273)4 + ( 1.1 * 108 * v0.6 / ɛ * d0.4 )* ( tg - ta) ]0.25 -273 [°C]
Where tg is black globe temperature (°C), ɛ is the emissivity of a standard black globe (0.95), and d is the diameter of the globe.
Solar Radiation (Rsolar):
Total clear sky solar radiation, used to estimate black globe temperature (tg) is estimated using equations from Campbell and Norman (1998):
Rsolar,cs = Kb + Kd + Kr [W/m2]
Where Kb (direct beam radiation);
Kb = Kp * cos(ψ) [W/m2]
Where ψ is the solar zenith angle estimated using time of day and day of year using a validated Solar Positioning Algorithm, and Kp is the direct irradiance received on the Earth surface perpendicular to the beam;
Kp = Ko * τm [W/m2]
Where Ko is the solar constant (~1367 W/m2), τ is the atmospheric transmittance which can be given or default to 0.6, and m is the optical mass number derived as:
m = Pb / ( 101.3 * cos(ψ) ) [ND]
Where Pb is the atmospheric pressure in kPa, and ψ is the solar zenith angle.
Kd (diffuse radiation) is calculated as;
Kd = 0.3 * (1 - / τm) * Ko * cos(ψ) [W/m2]
Where τ is the atmospheric transmittance which can be given or default to 0.6, and m is the optical mass number, and ψ is the solar zenith angle.
Kr (reflected solar radiation) is calculated as:
Kr = αgr * Kt [W/m2]
Where αgr is the albedo of the ground surface (default is 0.3) and Kt is the sum of Kb and Kd.
Lastly, cloud cover alters solar radiation and thus is accounted for using the following equation from NASA:
Rsolar = Rsolar,cs *(1 - (0.75*n3.4)) [W/m2]
Where n is the percent (0-1) of cloud coverage.
Black globe temperature (Tg):
When not provided, black globe temperature (Tg) is estimated using the equation from Hajizadeh et al. 2017.
Tg = (0.01498 * $solarrad) + (1.184 * $Tair) - (0.0789 * $relative_humidity) - 2.739;
Respiratory heat loss (Eres + Cres):
Eres + Cres = 0.0014 * (M * (34 - Ta) ) + 0.0173 * (M * (5.87 - Pa) ) [W/m2]
Where M is metabolic rate in W/m2, Ta is ambient temperature in °C, and Pa is the ambient vapour pressure in kPa.
Evaporative requirements for heat balance (Ereq):
Ereq is calculated by rearranging the conceptual heat balance equation:
Ereq = (M - W) ± K ± C ± R ± (Eres + Cres) [W/m2]
Maximum evaporative capacity of the environment (Emax):
Assuming negligible clothing or nude:
Emax = (Psk,s - Pa) / (1/he)[W/m2]
Where the Psk,s - Pa is the ambient vapor pressure difference between skin and air in kPa, and he is the evaporative heat transfer coefficient.
Evaporative heat transfer coefficient (he):
he = 16.5 * hc [W/m2/K]
Where hc is the convective heat transfer coefficient in W/m2/K and 16.5 is the Lewis Relationship (in K/kPa) .
Sweating efficiency (n):
ωreq = Ereq / Emax
if ωreq < 1, n = 1 - (ωreq2 / 2); else n = (2 - ωreq)2 / 2
Evaporation from the skin (Esk):
Where ωmax is the maximum attainable skin wettedness and is assumed to be 0.72 for unacclimated, 0.84 for partially acclimated (Ravanelli et al. 2018), and 1.0 for fully acclimated (Candas et al. 1979);
When Ereq < (Emax * ωmax);
Esk = Ereq [W/m2]
When Ereq > (Emax * ωmax):
Esk = Emax [W/m2]
When Esk > maximum whole body sweat rate:
Esk = maximum whole body sweat rate [W/m2]
Sweat rate required (Sreq):
Sreq = [ ( Ereq / n ) * BSA ] / HLvap,sw * 60 [g/min]
Where BSA is body surface area (calculated using the Dubois & Dubois equation) HLvap,sw is the heat liberated when evaporating one gram of sweat (default: 2426 J).
If Sreq > maximum sweat rate, then Sreq = maximum sweat rate.
Skin Temperature (Tsk):
Skin temperature (Tsk) is estimated using equations from Mehnert et al. (2000) for nude and clothed individuals:
Nude: Tsk = 7.19 + 0.064 * Ta + 0.061 * Tr + 0.198 * Pa - 0.348 * Va + 0.616 * Tre [°C]
Clothed: Tsk = 12.17 + 0.020 * Ta + 0.044 * Tr + 0.194 * Pa - 0.253 * Va + 0.0029 * M + 0.513 * Tre [°C]
Rectal Temperature (Tre):
As rectal temperature (Tre) is required to satisfy the equations for Tsk, it is loosely approximated as:
Tre = 0.0036 * M [W/m2] + 36.6
if Tre > 40°C, Tre = 40°C
Clothing area factor (fcl)
During rest and still air (< 0.2 m/s):
fcl = 1 + [ ( 0.31 * Icl ) / 0.155 ] [ND]
Where Icl is the static clothing insulation in clo units.
Evaporative Resistance of the clothing (Re,cl)
When not provided, and during rest and still air (< 0.2 m/s):
Re,cl = 0.18 * (Icl / 0.155) [m2/K/W]
Where Icl is the static clothing insulation in clo units.
If locomotion or air velocity is > 0.2 m/s, dynamic clothing insulation and evaporative resistance is calculated using equations presented in Chapter 9
Clothing surface temperature (Tcl):
hr = 4 * ɛ * σ * Ar/Ad * (273.2 + ((Tcl + Tr)/2)3
Tcl = (( ( 1/ Icl ) * Tsk ) + (fcl * ((hc * Ta) + (hr * Tr)))) / ((1/$Icl) + (fcl * (hr + hc)))
Where ɛ is emissivity, σ is the Stefan-Boltzmann constant, Ar/Ad is the effective radiative surface area, Tcl is clothing temperature, Tr is radiant temperature, Tr is air temperature, Icl is the clothing thermal insulation, fcl is the clothing area factor, and hc is the convective heat transfer coefficient.
Tcl Is derived using iterative techniques starting at Tcl = 0, until the difference between successive Tcl is < 0.01
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