Development of Maps for the Design of Bioclimatic Housing in Madagascar Based on Mahoney’s Table

The study of climatic conditions and their impact on human habitation is a major focus in bioclimatology and sustainable housing. The Mahoney method, developed in 1967 in “Tables for the Estimation of Indoor Thermal Comfort,” allows for the assessment of thermal comfort requirements in buildings based on local climate data. This approach relies on the analysis of parameters such as temperature, humidity, and precipitation to define appropriate architectural recommendations [1]. Globally, research such as that conducted by Olgyay in 1963 has demonstrated the importance of adapting buildings to specific climatic conditions in order to reduce energy consumption and improve occupants’ well-being [2]. In tropical regions such as Madagascar, where seasonal variations and extreme weather events (cyclones, droughts) are pronounced, this approach is particularly relevant [3]. The design of bioclimatic housing requires a detailed understanding of the interactions between climate, the local environment, and building materials. The Mahoney Table provides a simple yet effective methodological framework for analyzing these interactions by combining decades of meteorological data with planning and design criteria. The study conducted in Madagascar is of major interest given that the island is divided into different climate zones. It aims to compile strategies tailored to each zone in the form of recommendations based on local climate analysis and defined using indicators. The primary objective was to design buildings that provide a significant level of thermal comfort throughout the year, using passive methods. 2. Methods and Materials The sequence of operations is illustrated in the flowchart below (See Figure 1). 2.1. Mahoney’s Method The Mahoney method is a four-step bioclimatic analysis tool that translates meteorological data into architectural recommendations for optimizing thermal comfort. Used primarily for arid and tropical climates, it guides the design of the building envelope, openings, and site layout. Based on basic climate data, it enables the identification of a site’s constraints and potential and the formulation of bioclimatic design recommendations to ensure the thermal comfort of occupants. Diagnostic Tables Diagnostic tables are used to collect and organize essential monthly climate data for the regions under study. They lay the groundwork for comfort analysis and subsequent recommendations. Figure 1. Flowchart of the method for designing housing recommendation maps based on the Mahoney Table. The meteorological data used are based on the centroid of each region (see Figure 1): Monthly average maximum and minimum temperatures. This data is crucial for understanding daily and annual temperature variations. Maximum temperatures indicate the level of daytime heat to which the building will be exposed, influencing solar shading and ventilation strategies. Minimum nighttime temperatures are important for assessing the potential for passive cooling and the risk of cold-related discomfort [4][5]. Monthly average precipitation is critical for water management and protection against moisture. High precipitation levels require effective drainage systems, roofs with adequate slopes, and protective measures for openings and walls. The seasonal pattern of rainfall also influences landscape design and the choice of materials [6][7]. The average monthly relative humidity has a significant impact on the perception of thermal comfort. High humidity intensifies the sensation of heat by limiting the evaporation of sweat. It also promotes mold growth. Effective ventilation strategies are crucial in humid climates to remove moisture-laden air [8][9]. The prevailing wind direction and average monthly wind speed, which are essential for optimizing natural ventilation. The prevailing wind direction helps determine the building’s orientation and the placement of openings to promote air circulation within the spaces. Wind speed influences the efficiency of ventilation [10][11]. For illustrative purposes, consider the example of Alaotra Mangoro region, which falls within climate zone B (very humid, influenced by moderate trade winds, with an average annual temperature of 18°C to 22°C and annual precipitation of 1350 to 2500 mm (see Figure 2). Table 1 of meteorological data for Alaotra Mangoro region is as follows: Table 1. Table of meteorological data for Alaotra Mangoro region. Jan Fev Mar Apr May Jun Jul Aug Sep Oct Nov Dec Temp. Max. 28.1 27.9 27.9 27.3 25.8 23.6 22.5 23.3 25.4 27.3 28.6 28.9 Temp. Min. 18.2 18.2 17.7 16.2 14.4 12.2 11.2 11.5 12.6 14.4 16.2 17.6 Hu. Moy 78.8 80.8 79.4 76.0 74.2 74.3 73.6 70.7 66.4 64.0 64.5 82.4 Precip. 221.2 208.2 132.3 20.5 4.8 0.5 1.8 0.3 1.3 16.8 42.6 146.8 Vit. Vent 0.7 0.8 1.6 2.1 2.0 2.6 2.9 2.7 2.5 2.1 1.8 1.2 Dir. Vent E SE SE SE SE SE SE SE SE E E E Comfort Table [12][13] This table is used to determine the thermal comfort limits for the site under study based on the Annual Mean Temperature (TMA) and the humidity group. TMA= Highest annual maximum temperature+Lowest annual minimum temperature 2 (1) The average temperature in Alaotra Mangoro region is 20.1°C (See Table 2). Table 2. Moisture group table. TMA ≥ 20°C 15 ≤ TMA < 20°C TMA < 15°C Hu. Moy. (%) G.H. Day Night Day Night Day Night [0, 30[ 1 26 - 34 17 - 25 23 - 32 14 - 23 21 - 30 12 - 21 [30, 50[ 2 25 - 31 17 - 24 22 - 30 14 - 22 20 - 27 12 - 20 [50, 70[ 3 23 - 29 17 - 23 21 - 28 14 - 21 19 - 26 12 - 19 ≥70 4 22 - 27 17 - 21 20 - 25 14 - 20 18 - 24 12 - 18 Using the TMA and the humidity group table, we can define the daytime and nighttime comfort zones. These limits are not universal but are tailored to populations acclimated to specific conditions (see Table 3). They take into account the fact that people living in hot climates can tolerate higher temperatures. To fill out this comfort table for each month, let’s take January as an example; first, fill in the humidity group using Table 2. Next, enter the maximum temperature value. Next, find the maximum and minimum TMA values for the day corresponding to the month’s humidity group to fill in the maximum and minimum daytime comfort levels; the same principle applies to filling in the maximum and minimum nighttime comfort levels, but using the TMA for the night. Finally, to fill in the daytime (nighttime) thermal stress, compare the average maximum (minimum) temperature value to the maximum and minimum daytime (nighttime) comfort levels; if the average maximum (minimum) temperature falls between the maximum and minimum daytime (nighttime) comfort levels, we have “comfort ©”; if it is lower, the sensation is “too cold (TF)”; otherwise, the sensation is “too hot (TC)”. Table 3. Comfort table for Alaotra Mangoro region. Jan Fev Mar Apr May Jun Jul Aug Sep Oct Nov Dec G.H. 4 4 4 4 4 4 4 4 3 3 3 4 Temp. Max. 28.1 27.9 27.9 27.3 25.8 23.6 22.5 23.3 25.4 27.3 28.6 28.9 C.D. Max 27 27 27 27 27 27 27 27 29 29 29 27 Min 22 22 22 22 22 22 22 22 23 23 23 22 Temp. Min. 18.2 18.2 17.7 16.2 14.4 12.2 11.2 11.5 12.6 14.4 16.2 17.6 C.N. Max 21 21 21 21 21 21 21 21 23 23 23 21 Min 17 17 17 17 17 17 17 17 17 17 17 17 S.T. Jour TC TC TC TC C C C C C C C TC Nuit C C C TF TF TF TF TF TF TF TF C Tables of indicators [14] - [18] The first indicator table is used to populate the second indicator table. Recall the following definitions of the Koenigsberger indicators: H1 (Essential ventilation): Daytime temperature ≥ 32°C for 4 or more months, consecutive or otherwise. H2 (Ventilation desirable): Daytime temperature 29°C - 32°C for 4 months or more. H3 (Rain protection): Annual rainfall ≥ 1000 mm with a dry season < 3 months. A1 (Thermal inertia desirable): Annual temperature range (Tmax warmest month – Tmin coldest month) ≥ 10°C. A2 (Sleeping outdoors possible): Nighttime temperature ≥ 22°C for 4 months or more. A3 (Cold season issue): Minimum temperature of the coldest month < 10°C. W1 (Strong, disruptive wind (protection)): Wind > 4 m/s for 4 months or more, or gusts > 10 m/s. W2 (Wind useful for ventilation): Moderate wind (2 - 4 m/s) for 4 months or more. In order to preserve seasonal information, temperature ranges and precipitation were analyzed on a monthly rather than an annual basis. This approach is consistent with the principles of bioclimatic design, which require a detailed consideration of seasonal climate variations in order to adapt architectural strategies to local conditions [18]. Therefore, we use the monthly value instead of the annual value for A1 (Monthly Temperature Range or MTR) and H3 (Monthly Precipitation), because the annual range is a single value that smooths out seasonal variations. ATM=Monthly high temperature−Monthly low temperature (2) The first indicator table becomes Table 4. Table 4. First table of indicators. Thermal Stress G.H. ATM (°C) Monthly precipitation (mm) Wind/Additional Conditions H1 C.D. too hot 4 Essential ventilation C.D. too hot 2-3 <10 H2 C.D. Comfort 4 Recommended ventilation H3 >200 Rain protection A1 1-2-3 >10 Thermal inertia A2 C.D. too hot and C.N. Comfort 1-2 > 10 Sleeping outdoors A3 C.D. too cold or C.N. too cold Cold season W1 Inconvenient strong winds (≥1 month) Windbreaks (hedges, walls, rows of trees) W1 + A3 (cold season) Dense windbreaks (solid walls) W1 + H1 (essential ventilation) Permeable windbreaks (hedges, trellises) W2 Moderate prevailing wind (≥1 month) Openings perpendicular to the prevailing wind W2 + H1 (essential ventilation) Wind sensors + opposite outputs W2 + A3 (cold season) Do not face the cold wind; keep the opening on the leeward side W1 + W2 (W2 + H1 or H2) + (A3 = 0 to 5 months) Dual orientation for maximum span (W2 + A3 = 6 to 12 months) Dual-orientation with adjustable openings W1 = 1 to 12 months (strong winds) Double orientation not recommended; single orientation + windbreak The second table of indicators is Table 5. Based on the assessment and indicators, the recommendation tables propose specific bioclimatic design strategies to address the identified thermal stresses and optimize comfort. Columns H1 through A3 indicate the combinations of indicators for which the recommendation in the row applies (See Table 6). Table 5. Second set of indicators for Alaotra Mangoro region. Jan Fev Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTAL H1 0 H2 * * * * 4 H3 * * 2 A1 * * * 3 A2 0 A3 * * * * * * * * 8 W1 0 W2 * * * * * * * 7 Recommendation Tables [19][20]. Table 6. Site plan. Conditions Recommendation Explanation A1 = 0 - 10 Buildings oriented along an east-west axis. If the thermal inertia (A1) is not very high (0 - 10), the orientation is optimized to capture sunlight in the winter and block it in the summer. A3 = 5 - 12 Compact floor plans with courtyards. During the cold season (A3 active), compact layouts reduce heat loss. Interior courtyards provide protection from the cold wind. A1 = 11 - 12 and A3 = 0 - 4 Compact floor plans with courtyards. When thermal inertia is very high (high A1) and the cold season is short (low A3), thermal mass remains useful for stabilizing the temperature. The orientation and compactness of the layout depend primarily on the requirements for thermal mass (A1) and protection against the cold (A3). The spacing is determined almost exclusively by H1 (essential ventilation) (See Table 7). Table 7. Spacing between buildings. Conditions Recommendation Explanation H1 = 11 or 12 Wide spacing to allow for better airflow. When natural ventilation (H1) is required, buildings are spaced apart so as not to block the wind. H1 = 2 - 10 Same as above, but with protection against hot/cold winds. Need for ventilation (H1) but protection from unwanted winds (windbreaks, orientation). H1 = 0 or 1 Compact design. If H1 is not active (0 or 1), ventilation is not a priority → the buildings can be sealed off. The ventilation strategy depends on H1 and H2 (ventilation requirements) and A3 (cold weather may limit the opening) (See Table 8). The size of the openings depends on A1 (inertia) and A3 (cold). The lower the inertia and the less cold there is, the larger the openings can be (See Table 9). Table 8. Airflow. Conditions Recommendation Explanation H1 = 3 - 12 Single-aspect building. Continuous air circulation. Requires essential ventilation (H1) for at least 3 months; the design allows for continuous air circulation (simple cross-ventilation). (H1 = 1 - 2) + (H2 = 2 - 12) + (A3 = 0 - 5) A dual-aspect building designed for intermittent traffic. If H1 is low but H2 is active, and it’s not very cold (A3 is low), intermittent ventilation will suffice, so you can open the vents in either direction as needed. H1 = 0 et (A3 = 0 ou 1) Unnecessary air circulation. No need for ventilation (H1 = 0) and it’s not cold, so we can even close it. Table 9. Opening dimensions. Conditions Recommendation Explanation A1 = 0 - 1 et A3 = 0 Large openings (40% - 80% of north-south facades). Low thermal mass (A1) and no cold (A3) allow for very large openings. A3 = 1 - 12 Moderate openings (25% - 40% of the walls). As soon as cold weather sets in (A3), we close the openings to minimize heat loss. A1 = 2 - 10 Intermediate (20% - 35% of the walls). Moderate inertia, moderate aperture size. A1 = 11 - 12 and A3 = 0 - 3 Small openings (20% - 35% of the walls). High thermal mass and low heat gain, with small openings to regulate heat flow. A3 = 4 - 12 Moderate openings (25% - 40%). If the cold spell lasts longer (A3: 4 to 12 months), we return to the average. The position of the openings is controlled by H1 and H2 (ventilation) and limited by A3 (cooling) (See Table 10). Table 10. Position of the openings. Conditions Recommendation Explanation H1 = 3 - 12 Openings in the north-south walls, at chest height on the windward side. Essential ventilation is required (H1); openings are positioned to capture the prevailing wind. (H1 = 1 - 2) + (H2 = 2 - 12) + (A3 = 0 - 5) As above, with openings in interior walls. Good ventilation is desirable; avoid extreme cold; add interior openings to allow for air circulation. H1 = 0 et A3 = 0 - 1 No ventilation is required; the openings can be positioned as desired. Two distinct needs: protection from the sun (if it’s not cold) or from the rain (if H3 is active) (See Table 11). Table 11. Opening controls. Conditions Recommendation Explanation A3 = 0 - 2 Protect yourself from direct sunlight. When the cold season is short or nonexistent (A3 = 0 - 2), the problem is excessive sunlight, so sun protection measures (sunshades, awnings) are needed. H3 = 2 - 12 Plan for rain protection If it rains (H3) for at least two months, protective measures are needed (awnings, overhanging roofs, waterproof shutters). The thermal mass is directly determined by A1 (See Table 12). Table 12. Walls and floors. Conditions Rec