**V: 1.1**)

**The information provided is at the risk of the user.**

##### 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:
*

- The Biophysics of Human Heat Exchange (in Heat Stress in Sport and Exercise, 2019); and
- Human Thermal Environments: The Effects of Hot, Moderate, and Cold Environments on Human Health, Comfort, and Performance, Third Edition

**Conceptual Heat Balance Equation:**

M - W = ± K ± C ± R ± (E_{res} + C_{res}) + E_{sk} ± S [W/m^{2}]

**Heat Production (H _{prod}):**

H_{prod} = M - W [W/m^{2}]

**Metabolic Energy Expenditure (M):**

(when not provided)

M = (341 * VO_{2}) / BSA [W/m^{2}]

Where VO_{2} (rate of oxygen consumption) is in L/min, and BSA is body surface area

**Rate of oxygen consumption (VO _{2} in L/min):**

VO

_{2}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 VO

_{2}.

- Walking:
- VO
_{2}= [(0.1 * SPEED [m/min]) + (1.8 * SPEED [m/min] * GRADE[/1]) + 3.5 ] * MASS [L/min]

- VO
- Running:
- VO
_{2}= [(0.2 * SPEED [m/min]) + (0.9 * SPEED [m/min] * GRADE[/1]) + 3.5 ] * MASS [L/min]

- VO
- Cycling:
- VO
_{2}= [(10.8 * WATTS / MASS ) + 7] * MASS [L/min]

- VO

**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/m^{2}]

Where MET is the metabolic rate; 1 MET = 58.15 W/m^{2}

If selecting the "Walking" or "Running" modality:

W =(10^{3} * (MASS[kg] * SPEED[m/min] * (%GRADE * 100) )) / (6.12 * 60 * 1000) ) / BSA [W/m^{2}]

**Conduction (K):**

At present, conduction is assumed negligible.

**Convection (C):**

C = f_{cl} * h_{c} * (T_{shell} - T_{air}) * (P_{b}/760)^{0.55} [W/m^{2}]

Where f_{cl} is the clothing area factor, h_{c} is the convective heat transfer coefficient, T_{shell} is the external surface temperature (skin or clothing temperature), T_{air} is ambient temperature, and P_{b} is barometric pressure in mmHg

**Convective heat transfer coefficient (h _{c}):**

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, h
_{c}= 3.1, else h_{c}= 8.3 * v^{0.6}[W/m^{2}/K]

- if v < 0.2, h
- Stationary cycling:
- if v < 0.2, h
_{c}= 6, else h_{c}= 8.3 * v^{0.6}[W/m^{2}/K]

- if v < 0.2, h
- Treadmill:
- h
_{c}= 8.3 * loc^{0.391}[W/m^{2}/K]

- h
- Outdoor Running:
- h
_{c}= 8.3 * loc^{0.531}[W/m^{2}/K]

- h
- Outdoor Cycling:
- h
_{c}= 8.4 * loc^{0.840}[W/m^{2}/K]

- h

**Radiation (R):**

R = f_{cl} * h_{r} * (T_{shell} - T_{air}) [W/m^{2}]

Where f_{cl} is the clothing area factor, h_{r} is the radiative heat transfer coefficient, T_{shell} is the external surface temperature (skin or clothing temperature), and T_{air} is ambient temperature

**Radiative heat transfer coefficient (h _{r}):**

h_{r} = 4 * ɛ * σ * Ar [273.2 + (T_{shell} + T_{r} / 2)]^{3} [W/m^{2}/K]

Where σ is the Stefan–Boltzmann constant, 5.67 × 10^{-8} (W/m^{2}/K^{4}), ɛ is the area-weighted emissivity of the body surface, and Ar is the effective radiative area, T_{shell} is the external surface temperature (skin or clothing temperature), and T_{r} is the mean radiant temperature.

**Mean Radiant Temperature (T _{r}):**

If the activity is conducted indoors or at night, T_{r} is assumed to be equal to air temperature.

If air velocity (*v*) is below 0.15 m/s:

T_{r} = [ (t_{g} + 273)^{4} + ( 0.25 * 10^{8} / ɛ ) * [(|t_{g} - t_{a}|)/d]^{1/4} * ( t_{g} - t_{a}) ]^{0.25} -273 [°C]

If air velocity (*v*) is > 0.15 m/s:

T_{r} = [ (t_{g} + 273)^{4} + ( 1.1 * 10^{8} * v^{0.6} / ɛ * d^{0.4} )* ( t_{g} - t_{a}) ]^{0.25} -273 [°C]

Where t_{g} 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 (R _{solar}):**

Total clear sky solar radiation, used to estimate black globe temperature (t_{g}) is estimated using equations from Campbell and Norman (1998):

R_{solar,cs} = K_{b} + K_{d} + K_{r} [W/m^{2}]

Where K_{b} (direct beam radiation);

K_{b} = K_{p} * cos(ψ) [W/m^{2}]

Where ψ is the solar zenith angle estimated using time of day and day of year using a validated Solar Positioning Algorithm, and K_{p} is the direct irradiance received on the Earth surface perpendicular to the beam;

K_{p} = K_{o} * τ^{m} [W/m^{2}]

Where K_{o} is the solar constant (~1367 W/m^{2}), *τ* is the atmospheric transmittance which can be given or default to 0.6, and *m* is the optical mass number derived as:

m = P_{b} / ( 101.3 * cos(ψ) ) [ND]

Where P_{b} is the atmospheric pressure in kPa, and ψ is the solar zenith angle.

K_{d} (diffuse radiation) is calculated as;

K_{d} = 0.3 * (1 - / τ^{m}) * K_{o} * cos(ψ) [W/m^{2}]

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.

*K _{r}* (reflected solar radiation) is calculated as:

K_{r} = α_{gr} * K_{t} [W/m^{2}]

Where *α _{gr}* is the albedo of the ground surface (default is 0.3) and K

_{t}is the sum of K

_{b}and K

_{d}.

Lastly, cloud cover alters solar radiation and thus is accounted for using the following equation from NASA:

R_{solar} = R_{solar,cs} *(1 - (0.75*n^{3.4})) [W/m^{2}]

Where *n* is the percent (0-1) of cloud coverage.

**Black globe temperature (T _{g}):**

When not provided, black globe temperature (T_{g}) is estimated using the equation from Hajizadeh et al. 2017.

T_{g} = (0.01498 * $solarrad) + (1.184 * $Tair) - (0.0789 * $relative_humidity) - 2.739;

**Respiratory heat loss (E _{res} + C_{res}):**

E_{res} + C_{res} = 0.0014 * (M * (34 - T_{a}) ) + 0.0173 * (M * (5.87 - P_{a}) ) [W/m^{2}]

Where *M* is metabolic rate in W/m^{2}, T_{a} is ambient temperature in °C, and P_{a} is the ambient vapour pressure in kPa.

**Evaporative requirements for heat balance (E _{req}):**

E_{req} is calculated by rearranging the conceptual heat balance equation:

E_{req} = (M - W) ± K ± C ± R ± (E_{res} + C_{res}) [W/m^{2}]

**Maximum evaporative capacity of the environment (E _{max}):**

Assuming negligible clothing or nude:

E_{max} = (P_{sk,s} - P_{a}) / (1/h_{e})[W/m^{2}]

Where the P_{sk,s} - P_{a} is the ambient vapor pressure difference between skin and air in kPa, and h_{e} is the evaporative heat transfer coefficient.

If clothing is worn and locomotion or air velocity exceed 0.2 m/s, E_{max} is derived using dynamic evaporative resistance clothing equations found in Chapter 9 which are also used in the PHS model.

**Evaporative heat transfer coefficient (h _{e}):**

h_{e} = 16.5 * h_{c} [W/m^{2}/K]

Where h_{c} is the convective heat transfer coefficient in W/m^{2}/K and 16.5 is the Lewis Relationship (in K/kPa) .

**Sweating efficiency ( n):**

ω_{req} = E_{req} / E_{max}

if ω_{req} < 1, *n* = 1 - (ω_{req}^{2} / 2); else *n* = (2 - ω_{req})^{2} / 2

**Evaporation from the skin (E _{sk}):**

Where *ω _{max}* 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 E_{req} < (E_{max} * ω_{max});

E_{sk} = E_{req} [W/m^{2}]

When E_{req} > (E_{max} * ω_{max}):

E_{sk} = E_{max} [W/m^{2}]

When E_{sk} > maximum whole body sweat rate:

E_{sk} = maximum whole body sweat rate [W/m^{2}]

**Sweat rate required (S _{req}):**

S_{req} = [ ( E_{req} / *n* ) * BSA ] / HL_{vap,sw} * 60 [g/min]

Where BSA is body surface area (calculated using the Dubois & Dubois equation) HL_{vap,sw} is the heat liberated when evaporating one gram of sweat (default: 2426 J).

If S_{req} > maximum sweat rate, then S_{req} = maximum sweat rate.

**Skin Temperature (T _{sk}):**

Skin temperature (T_{sk}) is estimated using equations from Mehnert et al. (2000) for nude and clothed individuals:

Nude: T_{sk} = 7.19 + 0.064 * T_{a} + 0.061 * T_{r} + 0.198 * P_{a} - 0.348 * V_{a} + 0.616 * T_{re} [°C]

Clothed: T_{sk} = 12.17 + 0.020 * T_{a} + 0.044 * T_{r} + 0.194 * P_{a} - 0.253 * V_{a} + 0.0029 * M + 0.513 * T_{re} [°C]

**Rectal Temperature (T _{re}):**

As rectal temperature (T_{re}) is required to satisfy the equations for T_{sk}, it is loosely approximated as:

T_{re} = 0.0036 * M [W/m^{2}] + 36.6

if T_{re} > 40°C, T_{re} = 40°C

**Clothing area factor (f _{cl})**

During rest and still air (< 0.2 m/s):

f_{cl} = 1 + [ ( 0.31 * I_{cl} ) / 0.155 ] [ND]

Where I_{cl} is the static clothing insulation in clo units.

**Evaporative Resistance of the clothing (R _{e,cl})**

When not provided, and during rest and still air (< 0.2 m/s):

R_{e,cl} = 0.18 * (I_{cl} / 0.155) [m^{2}/K/W]

Where I_{cl} 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 (T _{cl}):**

h_{r} = 4 * ɛ * σ * Ar/Ad * (273.2 + ((T_{cl} + T_{r})/2)^{3}

And;

T_{cl} = (( ( 1/ I_{cl} ) * T_{sk} ) + (f_{cl} * ((h_{c} * T_{a}) + (h_{r} * T_{r})))) / ((1/$I_{cl}) + (f_{cl} * (h_{r} + h_{c})))

Where ɛ is emissivity, σ is the Stefan-Boltzmann constant, Ar/Ad is the effective radiative surface area, T_{cl} is clothing temperature, T_{r} is radiant temperature, T_{r} is air temperature, I_{cl} is the clothing thermal insulation, f_{cl} is the clothing area factor, and h_{c} is the convective heat transfer coefficient.

T_{cl} Is derived using iterative techniques starting at T_{cl} = 0, until the difference between successive T_{cl} is < 0.01

**Fetching Strava Data...**

**Activity Data Retrieved.**

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