What is Wet-Bulb Temperature?
Wet-bulb temperature is a crucial meteorological and thermodynamic concept that indicates the lowest temperature that can be reached under current ambient conditions by the evaporation of water only. In our daily lives, the standard air temperature (dry-bulb temperature) shown on a typical thermometer doesn't tell the whole story. The amount of moisture in the air—humidity—drastically alters how we feel temperature and how effectively things can cool down. Wet-bulb temperature helps us understand the combined effect of these two variables on the human body and on cooling systems.
Physically, the wet-bulb temperature is measured by wrapping a wet cloth (wick) around the bulb of a thermometer and blowing ambient air over it. As the water from the cloth evaporates, it absorbs heat from the thermometer, causing the reading to drop below the normal dry-bulb temperature. The drier the air (the lower the relative humidity), the faster the evaporation, and the wider the gap between the dry and wet-bulb temperatures. When the air is 100% saturated with moisture, no more evaporation can occur, and the wet-bulb temperature equals the dry-bulb temperature.
The Effects of Dry-Bulb Temperature and Relative Humidity
Air temperature alone isn't enough to describe how oppressive the environment is. Relative humidity tells us how much of the air's moisture-holding capacity is currently filled.
- Low Relative Humidity: In dry climates (like deserts), even if the air temperature is extremely high, the sweat produced by our bodies evaporates very quickly. This rapid evaporation creates a significant cooling effect. In such environments, the wet-bulb temperature is much lower than the actual air temperature.
- High Relative Humidity: In tropical or extremely humid environments, the air is already saturated with moisture, causing sweat evaporation to slow down drastically or stop entirely. The body struggles to cool itself. In these scenarios, the wet-bulb temperature approaches the actual air temperature and can reach dangerous levels.
Understanding this relationship is critical for taking appropriate safety measures. For a quick estimate, you can use our Wet-Bulb Temperature Calculator.
Estimating Wet-Bulb Temperature Using the Stull Formula
To find the exact wet-bulb temperature, complex psychrometric charts or iterative algorithms are typically required. However, in 2011, Roland Stull developed an empirical (data-driven) formula that offers a very practical and acceptably accurate approximation for standard meteorological conditions.
This formula takes the dry-bulb air temperature ($T$) in degrees Celsius and the relative humidity ($RH$) in percentage (ranging from 5 to 99) to estimate the wet-bulb temperature ($T_w$).
The Stull Approximation Formula:
$$T_w = T \cdot \text{atan}\left(0.151977 \cdot \sqrt{RH + 8.313659}\right) + \text{atan}(T + RH) - \text{atan}(RH - 1.676331) + 0.00391838 \cdot (RH)^{1.5} \cdot \text{atan}(0.023101 \cdot RH) - 4.686035$$
This mathematical model is designed to work within:
- Temperatures between $-20\text{ °C}$ and $50\text{ °C}$.
- Relative humidity between $5%$ and $99%$.
Because calculating this manually is tedious, our Wet-Bulb Temperature Calculator runs this Stull approximation in the background to provide instant results.
Practical Examples and Use Cases
Let's look at a few realistic scenarios to see how the formula plays out:
Example 1: A Hot and Dry Summer Day
- Air Temperature (T): $35\text{ °C}$
- Relative Humidity (RH): $20%$
- Estimated Wet-Bulb Temperature: Approximately $19\text{ °C}$.
Context: Even though it is very hot, the low humidity allows your body (and the wet thermometer) to cool down rapidly via evaporation. This environment is relatively tolerable if you stay in the shade.
Example 2: A Sweltering and Humid Evening by the Coast
- Air Temperature (T): $30\text{ °C}$
- Relative Humidity (RH): $80%$
- Estimated Wet-Bulb Temperature: Approximately $27\text{ °C}$.
Context: Although the air temperature is lower than in the first example, the high humidity severely hinders evaporation, making the heat stress much more intense.
Why is it Used?
Wet-bulb temperature is frequently referenced in agriculture, meteorology, HVAC (heating, ventilation, and air conditioning) system design, and workplace safety (heat stress evaluations). By distilling the thermodynamic impact of humidity into a single numerical value, it provides engineers and experts with a practical benchmark.
Limitations and Warnings
While the Stull formula provides a very practical estimate, it is important to be aware of its limitations:
- It is an Empirical Approximation: This formula is not a strict thermodynamic equilibrium equation but a curve-fitted approach derived from a specific dataset. It should not be used for extreme conditions (below -20°C or below 5% humidity).
- It is NOT WBGT (Wet Bulb Globe Temperature): Natural or psychrometric wet-bulb temperature is only one component of the WBGT index. When making workplace safety or heat-stress decisions, other factors like wind speed and solar radiation must also be considered. This tool should not be used as the sole metric for official occupational health and safety criteria.
- Altitude Effects: The formula is optimized for standard atmospheric pressure near sea level. Slight deviations may occur at very high altitudes due to lower air pressure.
In conclusion, wet-bulb temperature is an excellent guide for understanding the combined impact of heat and moisture—the invisible hazard in our environment. For quick assessments, be sure to try our practical calculator.
