You sit in an office on the sunny side of the building. By two in the afternoon the blinds are down, the lights are on, the air conditioning is roaring and you are still too warm. Three machines are fighting the building. Down the corridor, in an old stone church, nothing is running and it is cool in August and not freezing in March. The difference is not technology. The church was designed around the sun, the air and the thermal mass of its walls, and the office was designed to look good and then fixed.
This course is where architects learn the order of attack: first shape the building to use sun, light and air; then, if you must, add machines for what is left. A graduate walks into a room and sees where the sun will be at four o'clock, why one corner is dim, why the window seat is cold, and why the echo is so long.
The sun's path is the most predictable thing a designer has. The Earth's axis is tilted 23.44°, so the sun's declination swings between +23.44° in June and −23.44° in December. The sun's height at solar noon is then 90° minus your latitude plus the declination. At 52°N (London) that is about 62° in June and 15° in December. In Lagos or Quito it is almost overhead twice a year.
Once you know the sun's position, shading is trigonometry. For a window facing the equator, the overhang above it casts a shadow downward by (overhang depth) × tan(profile angle). A fixed overhang can be sized to block the high summer sun and let in the low winter sun.
Real solar geometry (declination 23.44°·sin(360°·(284+n)/365)), solar time, no atmosphere or equation-of-time correction. The window is 1.4 m high, starts 0.2 m below the overhang, and faces the equator. Latitudes are rounded.
At 52°N on 21 June at noon, a 0.6 m overhang shades about two-thirds of the glass. On 21 December the same overhang shades none, so the low sun reaches deep into the room. Move to Quito at an equinox: the sun is directly overhead at noon and even a shallow overhang shades the whole glass. A west-facing window is different: the afternoon sun is low and shines straight in, so a horizontal overhang casts only a short shadow, and vertical fins or shutters work better.
A window lets in light, but also heat and glare, so the question is how much is enough. Designers use the daylight factor: the share of the light outdoors under an overcast sky that arrives at a point in the room. A simple rule from the UK Building Research Establishment gives the room average:
The BRE's rule of thumb: an average of 5% or more and the room looks daylit; between 2% and 5% daylight is noticeable but you will use electric lamps; below 2% it looks gloomy. Two quick lessons come out of the formula. First, a bigger window helps only in proportion. Second, the room's own surfaces matter: bright walls raise R, and a deep room dilutes the same window over more surface.
Average daylight factor with T = 0.7, M = 0.9. The depth check is the BRE limiting-depth rule (depth/width + depth/window-head height ≤ 2/(1 − back-half reflectance)); I use the same R and a 2.2 m head height. A rule-of-thumb estimate: modern practice uses annual simulation (daylight autonomy; the European standard EN 17037).
The default room, a 2 m window in a 5 m deep room with open sky, scores 1.8%: gloomy by the rule. Widen the window to 4 m, the full wall, and the average doubles to 3.7%. Deepen the room to 8 m and the depth check fails while the average falls to 1.3%. A cheaper fix than a bigger window is often a lighter wall, or a window higher in the wall, since light from high up reaches deeper.
The thermostat measures air temperature. Your body does not. Thermal comfort depends on six things: air temperature, radiant temperature, air speed, humidity, and two properties of you, clothing and activity. The model behind most comfort standards is P. O. Fanger's predicted mean vote (1970), used in ISO 7730 and ASHRAE Standard 55. Researchers who survey people in real buildings (the adaptive school, associated with de Dear and Brager) find that people in naturally ventilated buildings accept a wider range, because they can open windows and change clothes. Standards now include both.
The one you can feel is radiant temperature. Your skin exchanges heat with every surface you can see. A cold window radiates the cold at you, even when the air is 20 °C. To a first approximation, comfort follows the operative temperature: the average of air temperature and mean radiant temperature.
Window 2 × 1.5 m, you facing it, all other surfaces at 20 °C, indoor air 20 °C and 50% humidity. Glass surface temperature = 20 − 0.13 · U · (20 − outdoor); the view factor is integrated numerically. U-values are rounded typical figures.
With single glass at −5 °C the pane's inside surface is about 1.5 °C. A person 1 m away has a mean radiant temperature of about 11 °C, so the operative temperature is about 15.6 °C while the thermostat says 20. That is the cold draught you feel (it is radiation, not air). Swap to triple glazing and the glass is at 17.4 °C and the effect nearly vanishes. The same cold pane is also below the dew point, 9.3 °C at 20 °C and 50% humidity, which is why single glass drips. This is the wet window of Building Technology (34/93).
A room with heavy walls warms slowly and cools slowly. In physics terms it has a large thermal capacity C and is connected to the outside through a conductance H, and the ratio τ = C ÷ H is its time constant. A room is then a low-pass filter on the weather: the outdoor temperature swings every day, the indoor temperature follows a smoothed, delayed version.
One lumped zone, no sun or internal gains, heat capacity per m² of floor (light 40, medium 110, heavy 300 kJ/m²K: illustrative), integrated numerically over four days; the last day is shown. A real thick wall is distributed, not lumped, and can delay the peak by 8 to 12 hours.
With the medium building (τ about 20 hours) and a 20 K swing outside, the inside swings only about 3.7 K, and its peak comes some 5 hours late. The light timber building (τ about 7 hours) swings 9 K. The heavy one swings 1.4 K, which is the logic of adobe and stone houses in hot dry climates. The Great Mosque of Djenné in Mali is made of mud, and the thick earth walls hold the cool of the night through the day. Mass helps only if you can get rid of the heat at night, with open windows or night ventilation. In a climate where nights stay hot, mass hurts as much as it helps.
People exhale carbon dioxide at about 0.3 litres a minute while seated. In a sealed room it builds up; ventilation washes it out. The steady level depends only on how much fresh air each person gets: outdoor concentration plus generation divided by airflow. Carbon dioxide is not itself the problem at these levels, but it is a good marker for body odours and other pollutants, and it is easy to measure.
Well-mixed single zone; 0.0052 L/s CO₂ per seated person (a typical figure); outdoor air 420 ppm. The 1,000 ppm line is a common rule of thumb for "stuffy", not a health limit. Standards set ventilation by person and by floor area, with values that differ by country and use.
Two people in a 50 m³ bedroom with half an air change an hour settle toward about 1,900 ppm. At three changes an hour, about 670 ppm. This is why tight, well-insulated houses need deliberate ventilation: with the infiltration cut to a tenth, the air stops being renewed by accident. A balanced system with heat recovery brings fresh air in while returning most of the heat, and is standard in Passivhaus-style buildings. Natural alternatives use the same physics as the stack effect of Building Technology: the badgir wind catchers of Yazd, Iran, and tall light wells draw air through a building with no fan.
Two different problems hide under "acoustics". Room acoustics is how a room sounds inside: how long a sound lingers after the source stops. Sound insulation is how much sound passes through a wall. Wallace Sabine, at Harvard around 1900, found the first, and it is still the first formula an acoustician learns.
The second is the mass law: a heavy wall is hard to shake, so it passes little sound. Each doubling of mass, or of frequency, adds about 6 dB. And, crucially, sound goes through holes. A wall with a small opening transmits through it nearly everything, so the opening sets the limit.
Surface area is taken as 6·V^(2/3), a cube. Sabine's formula is accurate when absorption is low; the Eyring formula is shown when it is high. Wall masses are rounded from typical densities. The reverberation targets (about 0.6 s for a small classroom, about 2 s for a concert hall) are common design aims, not legal requirements.
A bare concrete box of 240 m³ with an average absorption of 0.05 rings for 3.3 seconds, which is unintelligible for speech. Add ceiling tiles and carpet to reach 0.25 and it falls to 0.67 s. Meanwhile a 215 mm brick wall gives about 59 dB at 500 Hz, and a single sheet of plasterboard only 27 dB. Open 1% of the area and the brick wall drops to 20 dB. That is why acoustic detailing is about gaps: sockets, ducts, doors that do not seal, a gap under a partition. "Mass, seal and decouple" is the short form.
The order of attack across all these sections is the same. First shape and orient the building: sun on the equator side in the cold season, shade in the hot, rooms that need light along the window wall, narrow plans for cross-ventilation. Second make the envelope good: insulation, airtight, shaded windows, mass where it helps. Last add the machines, sized for what remains. Done in this order, the machines are small. Done backwards, they are large and run all day.
Vernacular building shows this without a drawing board: the thick shaded courtyards of Cairo and Seville, the wind catchers of Yazd, the high ceilings and verandas of the humid tropics, the mud walls of the Sahel. The Passivhaus standard formalises it with measured targets (about 15 kWh/m² a year for heating, or a 10 W/m² peak, and no more than 0.6 air changes an hour at 50 Pa). Nothing here is a law of architecture: the right answer depends on the climate, and each place has different priorities.
Comfort is mostly decided by shape, orientation and the skin: the sun's geometry sets shading, glass area and room depth set daylight, radiant temperature and mass set how warm you feel, ventilation sets the air, and mass and gaps set sound. Do those first and the machines are small.
Try this: in one room of your home, at three times of day, note where the sun is on the floor and which spot is warm, dim or noisy. Then clap once and listen for how long the echo lasts.
Sources. Solar geometry: standard formulas (Duffie & Beckman; Brown & DeKay); axial tilt 23.44°. Daylight factor formula and the 2% and 5% thresholds: BRE, Site Layout Planning for Daylight and Sunlight and BS 8206-2, as commonly cited. EN 17037 (Daylight in buildings, 2018). Thermal comfort: Fanger (1970), ISO 7730, ASHRAE 55; adaptive comfort: de Dear and Brager (late 1990s). Dew point by the Magnus formula. Sabine's RT60 formula, 0.161 V ÷ A, from his work at Harvard around 1900, and the Eyring correction; mass law TL = 20 log10(f·m) − 47 dB (field incidence); composite transmission loss from the area-weighted sound transmission coefficient (standard acoustics texts: Egan, Architectural Acoustics). Passivhaus criteria (15 kWh/m²a heating or 10 W/m² peak, 0.6 air changes per hour at 50 Pa): Passive House Institute criteria as summarised by Building Science Corporation and others. Djenné mud mosque and the wind catchers of Yazd: general architectural history. Every number in the interactives was computed in node: London, 21 June noon: altitude 61.9°, shade 66% with a 0.6 m overhang; 21 December noon: 15.1°, 0%; default daylight factor 1.85%, 3.70% with a 4 m window, 1.27% at 8 m depth (fails the depth check); single glass at −5 °C: 1.5 °C surface, view factor 0.48, operative 15.6 °C; triple: 17.4 °C surface; dew point 9.26 °C; thermal mass at 10 K amplitude: swing ratio 0.46, 0.18, 0.07 with lags 4.2, 5.3, 5.8 h; CO₂ 1,918 ppm at 0.5 air changes per hour, 670 ppm at 3; RT60 3.34 s at α = 0.05 and 0.67 s at α = 0.25; mass law 27 dB (10 kg/m²) and 58.8 dB (390 kg/m²) at 500 Hz, 20.0 dB for 390 kg/m² with 1% open.