# Evaluating Resilience and Thermal Comfort in Mediterranean Dwellings: A Level(s) Framework Approach
## 2 Materials and Methods
### Assessment of Time Outside of Thermal Comfort Range for Elderly People  
The third phase of our methodology focuses on applying Indicator 4.2, which evaluates the proportion of time throughout the year that occupants experience comfortable indoor thermal conditions. This indicator explicitly measures the percentage of time indoor temperatures fall outside the established comfort range. While the primary emphasis is on ensuring thermal comfort during the summer, assessing how well residents can maintain warmth in their homes during winter is equally important.  
When analysing this indicator, we adhere to the Level(s) framework requirements. For buildings equipped with mechanical HVAC systems, it is crucial to evaluate the performance of the building envelope when the HVAC system is not in operation. This assessment aims to determine the inherent thermal resilience of the building envelope. The performance metrics are derived from dynamic energy simulations, following the methodology outlined in Annex A.2 of EN 16798-1 [26].  
For our thermal comfort calculations, we utilize DesignBuilder Software, version 5.5.2.007 and the CBE Thermal Comfort Tool (an online resource for thermal comfort calculations and visualizations, SoftwareX 12, version 2.4.7). The thermal comfort criteria are based on the standards outlined in EN 16798, which utilize the PMV (Predicted Mean Vote) and PPD (Predicted Percentage Dissatisfied) calculations developed by [PERSON]. His research, grounded in empirical studies of skin temperature, provides a framework for defining comfort levels [27].  
PMV (Predicted Mean Vote): This metric assesses hygrothermal comfort by asking participants to rate their thermal sensation on a seven-point scale, ranging from cold (\(-3\)) to hot (\(+3\)). The Fanger equations are employed to estimate the mean vote of a diverse group of individuals based on various factors, including air temperature, mean radiant temperature, relative humidity, air velocity, metabolic rate, and clothing.  
PPD (Predicted Percentage Dissatisfied): this parameter estimates the percentage of individuals likely to experience discomfort based on the comfort conditions defined by the PMV.  
The _PMV_ is calculated based on the following equation, which predicts the mean thermal sensation vote of a large group of people. It uses several parameters like air temperature, radiant temperature, air velocity, humidity, metabolic rate, and clothing insulation.  
\[PMV=(0.303\,e^{\prime}(-0.036\,M)+0.028)\times((T\_a-T\_r)+(M-W)\times(1-F\_cl))\]  
where:  
* \(M=\) Metabolic rate (in watts per square meter, W/m\({}^{2}\))
* \(W=\) External work (typically assumed to be zero in normal conditions)
* \(T\_a=\) Air temperature (\({}^{\circ}\)C)
* \(T\_r=\) Mean radiant temperature (\({}^{\circ}\)C)
* \(F\_cl=\) Clothing area factor
* \(e=\) Exponential function  
The formula considers both the heat exchange between the body and the environment and the level of comfort that is predicted based on these variables.  
\(PPD\) quantifies the percentage of people dissatisfied with the thermal environment. It is calculated using the following equation:  
\[PPD=100-95\times e^{\prime}(-0.03353\,(PMV)^{\prime}4-0.2179\,(PMV)^{\prime}2)\]  
where:  
* \(PMV\) is the Predicted Mean Vote (from the previous formula).  
The _PPD_ provides a useful metric for gauging the discomfort of building occupants in terms of thermal satisfaction.  
By thoroughly assessing these factors, we aim to ensure that elderly residents can enjoy a comfortable living environment year-round and minimize the time spent outside their thermal comfort range.