Wet Bulb Calculator

The calculation of wet bulb temperature ($T_w$) combines ambient dry-bulb temperature ($T$) and relative humidity ($RH$) using complex psychrometric approximations. A primary empirical formula frequently utilized is:

$T_w \approx T \cdot \arctan(0.151977(RH + 8.313659)^{1/2}) + \arctan(T + RH) - \arctan(RH - 1.676331) + 0.00391838 \cdot (RH)^{3/2} \cdot \arctan(0.023101 \cdot RH) - 4.686035$

Additionally, the Wet-Bulb Globe Temperature (WBGT) indices factor in globe temperature ($GT$) to quantify heat stress. For outdoor environments with solar radiation, the standard formula is $WBGT = 0.7T_w + 0.2GT + 0.1T$, while indoor or shaded outdoor environments use $WBGTo = 0.7T_w + 0.3T$. Finally, wet bulb depression is simply the difference between dry bulb temperature and wet bulb temperature.

Let us walk through a practical scenario where the ambient dry-bulb temperature is 30°C and the relative humidity is 50% (0.50). We also factor in a globe temperature of 35°C.

Step 1: Calculate Wet Bulb Temperature ($T_w$)
Using the psychrometric formula with $T = 30$ and $RH = 50$, the resulting wet bulb temperature is approximately 21.7°C.

Step 2: Calculate Wet Bulb Depression
Subtract the wet bulb temperature from the dry bulb temperature: $30°C - 21.7°C = 8.3°C$. This indicates significant cooling capacity through evaporation.

Step 3: Calculate Outdoor WBGT
Apply the outdoor WBGT formula: $(0.7 \times 21.7) + (0.2 \times 35) + (0.1 \times 30) = 15.19 + 7.0 + 3.0 = 25.19°C$. This provides safety managers with a clear thermal index to determine appropriate work-rest cycles.

To get the most accurate results from your thermal calculations, always use precision thermometers for dry-bulb and globe measurements. Keep in mind that wind speed also influences actual evaporation rates, though standard relative humidity models offer a reliable baseline. Always cross-reference your calculated WBGT with local occupational safety thresholds before conducting strenuous outdoor activities.