Climate, Sun and Comfort: Zones, Solar Geometry, Shading and Thermal Comfort
2. Macro, meso and micro climate in design
Climate is read at three scales. The macro-climate is that of the region or zone, the data a weather station gives. The meso (local) climate is that of a city, valley or coast, where the urban area, a hill range or a sea breeze modifies the regional picture. The micro-climate is that of the site and the few metres around the building. The designer cannot change the macro-climate but can change the micro-climate, and a well-handled site can move conditions a long way toward comfort before any building element is drawn.
- Topography: in the northern hemisphere slopes facing the equator receive more sun; cold air is dense and drains downhill at night, so valley floors and hollows are cold pools and frost pockets, hilltops are windy, and the mid-slope “thermal belt” is mildest. In a cold climate, avoid the hollow and the cold-wind crest.
- Vegetation: shades, cools by evapotranspiration, and breaks the wind. Deciduous trees on the sun-facing and west sides shade in summer and let winter sun through; a windbreak shelters the leeward side for a distance of many times its height.
- Water bodies: water has a high specific heat, so it narrows the diurnal range and cools by evaporation; coasts have land and sea breezes. In the warm-humid zone the extra moisture they add is a cost, in the hot-dry zone a gain.
- Ground surfaces: paving and dark surfaces absorb and re-radiate heat; grass and light, high-albedo surfaces stay cooler. Neighbouring buildings shade, create wind shadow or channel the wind.
At the meso scale the main phenomenon is the urban heat island: a dense city stays several degrees warmer than its surroundings, most visibly at night. The causes are sealed surfaces and little evapotranspiration, heavy dark materials that store heat, street-canyon geometry (a low sky view factor traps long-wave radiation and slows night cooling), waste heat from vehicles and air-conditioning, and reduced wind. The remedies are trees and open space, cool (high-albedo) roofs and paving, water, and street orientation and breeze corridors.
| Aspect | Hot-dry | Warm-humid |
|---|---|---|
| Building grouping | Compact, mutual shading, courtyards | Spread out with gaps for the breeze |
| Streets | Narrow, deep, shaded; high height-to-width ratio | Wider, aligned to the prevailing wind |
| Open space | Shaded, with water and planting | Planted but never blocking the breeze |
3. The sun's path and solar angles
The earth's axis is tilted 23.45° (about 23°27′) to its orbit, which gives the seasons. The declination δ is the angle between the sun's rays and the equatorial plane: about +23.45° at the June solstice (21 June), 0° at the equinoxes (about 21 March and 23 September) and about −23.45° at the December solstice (22 December). Cooper's approximation is δ = 23.45° × sin[360° × (284 + n) / 365], with n the day of the year. The sun is overhead at noon on the Tropic of Cancer on 21 June, and at the equator at the equinoxes.
| Quantity | Meaning and standard result |
|---|---|
| Hour angle h | h = 15° × (solar time − 12 h); zero at solar noon, negative in the morning, positive in the afternoon |
| Altitude α | Angle of the sun above the horizon; zenith angle = 90° − α. sin α = sin φ sin δ + cos φ cos δ cos h |
| Noon altitude | α = 90° − φ + δ when the sun is south of the zenith (φ is the latitude) |
| Azimuth A | Compass direction of the sun's vertical plane; sin A = cos δ sin h / cos α. Say which datum (north or south) a problem uses |
| Sunrise hour angle | cos h_s = −tan φ tan δ; day length = 2 h_s / 15 hours. At an equinox the day is 12 h everywhere |
Worked example at latitude 28° N: the noon altitude is 90° − 28° + 0° = 62° at an equinox, 90° − 28° + 23.5° = 85.5° on 21 June and 90° − 28° − 23.5° = 38.5° on 21 December. On the equinoxes the sun rises due east and sets due west; in summer it rises and sets north of those points, in winter south of them. Near the equator the day length hardly varies and the sun is high all year, which is why the tropical sun is a roof and east-west problem rather than a south-wall one.
Solar time is the time by the sun, so solar noon is when the sun is on the local meridian. Solar time = standard time + 4 minutes × (local longitude − standard meridian) + equation of time, where the equation of time is a correction of at most about 16 minutes through the year. Indian Standard Time is set on the 82.5° E meridian, so a place at 72.5° E is 10° west and has solar noon 40 minutes after 12:00 IST (ignoring the equation of time). A sun-path diagram plots the sun's course for a latitude: concentric circles of altitude, radial lines of azimuth, one arc for the 21st of each month and cross-lines for the hours. A shadow-angle protractor laid over it shows at once which hours a device shades.
4. Shadow angles, shading devices, orientation and solar gain
Two shadow angles turn the sun's position into a device size. The horizontal shadow angle (HSA, γ) is the difference in azimuth between the sun and the normal to the wall (the direction the facade faces). The vertical shadow angle (VSA) is the sun's elevation measured in the vertical plane normal to the wall, given by tan VSA = tan α / cos γ. For a facade facing the sun directly (γ = 0) the VSA equals the altitude. For γ = 60° and α = 45°, tan VSA = 1 / 0.5 = 2, so VSA = 63.4°.
- Horizontal overhang (chhajja) of projection P casts a shadow of depth P tan VSA on the wall below its edge. To shade a window of height H whose head touches the overhang, P = H / tan VSA. At latitude 28° N, a 1.2 m window facing south at noon on an equinox (α = 62°) needs P = 1.2 / tan 62° = 0.64 m.
- Vertical fin of projection P casts a shadow of width P tan HSA along the wall; fins at spacing S shade fully when P = S / tan HSA.
- Egg-crate (horizontal plus vertical) and angled louvres serve where the sun is both low and oblique, as on west and south-west facades.
| Face | Sun and what it needs |
|---|---|
| Roof | Receives the most radiation in summer; shade, insulate and finish it light |
| East and west walls | Low, strong sun, hard to shade; keep glazing small or buffer them with service rooms, trees or vertical and egg-crate devices |
| South wall | High noon sun, easy to shade with an overhang; admits low winter sun |
| North wall | Little direct sun (a little at sunrise and sunset in summer); steady, glare-free daylight |
Solar gain enters two ways. Through glass the beam, diffuse and reflected radiation passes directly (glass transmits short-wave sun and blocks the long-wave heat re-radiated by the room, the greenhouse effect); glazing is rated by its solar heat gain coefficient (SHGC, the fraction of incident solar energy that becomes heat inside) and visible light transmittance. Through opaque walls and roofs the sun acts as if the outside air were hotter, expressed by the sol-air temperature T_sa = T_o + α·I / h_o (ignoring the long-wave term), where α is the surface absorptivity, I the incident radiation and h_o the outer surface coefficient. With α = 0.6, I = 700 W/m² and h_o = 20 W/m²K, the sun adds 0.6 × 700 / 20 = 21 K to the air temperature in the heat-flow calculation.
5. Thermal comfort: the heat balance and the indices
Thermal comfort is the condition of mind that expresses satisfaction with the thermal environment, and it is physically a heat balance. The body makes metabolic heat M, does external work W (small), and must lose the rest by convection C, radiation R, evaporation E (sweat and breath) and a minor conduction K, with the core held near 37 °C and the skin near 33 to 34 °C. If loss falls short the body stores heat and feels warm; if it exceeds M − W the body feels cool.
| Factor | Kind | What it governs |
|---|---|---|
| Air (dry-bulb) temperature | Environmental | Convective loss C |
| Mean radiant temperature (MRT) | Environmental | Radiant exchange R with walls, roof, sun |
| Air velocity | Environmental | Raises both convection and evaporation |
| Humidity (vapour pressure) | Environmental | Evaporative loss E; weak at mild temperature, strong when hot |
| Metabolic rate (met; 1 met = 58.2 W/m²) | Personal | Heat produced: seated rest is about 1 met |
| Clothing insulation (clo; 1 clo = 0.155 m²K/W) | Personal | Resistance to heat loss from the skin |
No single temperature captures comfort, so indices combine the factors. The operative temperature is roughly the mean of air temperature and MRT at low air speed (28 °C air and 34 °C MRT give 31 °C); the globe thermometer measures MRT. Effective temperature (ET, Houghton and Yaglou) is the temperature of still, saturated air that gives the same sensation as the actual dry-bulb, humidity and air movement, read from a nomogram; corrected ET adds radiation through the globe temperature. The tropical summer index (TSI), developed in India for Indian subjects, is the temperature of calm air at 50% relative humidity that would feel the same. Bioclimatic charts (Olgyay; Givoni) plot dry-bulb against humidity with the comfort zone and the strategy (shade, wind, evaporative cooling, mass, heating) that moves a point back into it, and the Mahoney tables convert tabulated climate data into design recommendations.
6. PMV and PPD, adaptive comfort and psychrometric reasoning
Fanger's PMV (predicted mean vote, the basis of ISO 7730 and ASHRAE 55) feeds the six factors into the heat-balance equation and predicts the mean vote of a large group on a seven-point scale: −3 cold, −2 cool, −1 slightly cool, 0 neutral, +1 slightly warm, +2 warm, +3 hot. PPD (predicted percentage dissatisfied) follows from it: PPD = 100 − 95 exp(−0.03353 PMV⁴ − 0.2179 PMV²). It has a minimum of 5% at PMV = 0, because people differ and some are dissatisfied even at neutrality; PMV = ±0.5 gives about 10% and PMV = +1 about 26%. The model rests on steady, uniform conditions and climate-chamber trials, so it suits mechanically conditioned rooms.
Field surveys in real buildings show that occupants of naturally ventilated (free-running) buildings accept warmer conditions than PMV allows, because they adapt: behaviourally (clothing, windows, fans, posture), physiologically (acclimatisation) and psychologically (expectation and control). Adaptive comfort therefore makes the comfort temperature move with the prevailing outdoor temperature. The ASHRAE 55 adaptive model is T_comf = 0.31 T_out + 17.8 (°C, T_out the prevailing mean outdoor temperature), with an acceptable band of ±3.5 K for 80% and ±2.5 K for 90% acceptability; at T_out = 30 °C, T_comf = 27.1 °C. Indian field studies give their own adaptive models, and a ceiling fan lifts the upper limit by several kelvin.
| Feature | PMV–PPD (heat balance) | Adaptive model |
|---|---|---|
| Basis | Physics of the body plus chamber trials | Field surveys of real occupants |
| Best suited to | Air-conditioned, controlled rooms | Naturally ventilated, occupant-controlled buildings |
| Comfort temperature | Fixed by the six factors | Moves with the outdoor mean temperature |
Psychrometric reasoning uses the chart whose horizontal axis is dry-bulb temperature and vertical axis the humidity ratio, with curves of relative humidity and sloping wet-bulb (nearly constant-enthalpy) lines; the dew point is read horizontally to the saturation curve. For still air and light indoor clothing the comfort zone sits at moderate temperature in the mid-twenties °C, between roughly 30% and 60% relative humidity. Sensible heating or cooling moves a point horizontally; direct evaporative cooling moves it down a constant wet-bulb line (the dry-bulb falls, the humidity rises); cooling below the dew point dehumidifies. A surface colder than the dew point of the air touching it collects condensation, which is how mould forms on cold walls.
Key takeaways
- The five zones are hot-dry, warm-humid, composite, temperate and cold; humidity (not temperature) separates hot-dry from warm-humid, and composite means no season lasts half the year.
- Macro-climate is given, micro-climate is designed: topography, vegetation, water, ground surface and neighbours; the urban heat island comes from sealed surfaces, stored heat, canyon geometry and waste heat.
- Noon altitude = 90° − φ + δ (sun south of the zenith); declination runs +23.45° to −23.45°; h = 15° per hour from solar noon; solar time shifts 4 minutes per degree from the 82.5° E meridian.
- tan VSA = tan α / cos γ; an overhang shades P = H / tan VSA; overhangs suit sun-facing faces, while low east and west sun needs minimised glazing, fins or egg-crate devices; long axis east-west in hot zones.
- Comfort is a heat balance of six factors: air temperature, MRT, air velocity, humidity, metabolic rate and clothing; ET, TSI and operative temperature are equivalent temperatures, not readings.
- PMV runs −3 to +3 and PPD never falls below 5%; the adaptive model (T_comf = 0.31 T_out + 17.8) suits free-running buildings; on the psychrometric chart evaporative cooling follows a wet-bulb line and works only where the wet-bulb depression is large.
Practice questions (18)
Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.
A housing cluster is planned in a warm-humid coastal city. Which set of decisions best fits the climate?
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Answer: B — An open, elongated plan facing the prevailing breeze, with large shaded openings, a light low-mass envelope and wide eaves on a sloping roof
Warm-humid air offers no wet-bulb depression to exploit and no cool night to flush mass, so the only effective relief is air movement: an open, breeze-facing plan with shaded openings and a light envelope. The compact, high-mass courtyard scheme is the hot-dry answer, and its mass would hold the day's heat through a night that never cools; the insulated sun-trap is the cold-zone answer.In the five-zone classification of Indian climates, the hot-dry and warm-humid zones are separated mainly by:
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Answer: C — The relative humidity, because both zones are hot and humidity decides the design response
Both zones have mean monthly maxima above about 30 °C, so temperature cannot separate them; relative humidity does (the usual dividing line is about 55%). The tempting answer, a higher temperature in the hot-dry zone, is wrong because the warm-humid zone is just as hot but feels more oppressive for lack of evaporative cooling.Which of the following contribute to the urban heat island effect?
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Answer: A — Sealed, impervious surfaces that suppress evapotranspiration; B — Waste heat released by vehicles and air-conditioning equipment; C — A narrow street canyon with a low sky view factor that slows night-time long-wave cooling
Impervious surfaces remove evaporative cooling, waste heat adds to the load, and a deep canyon with little sky view traps long-wave radiation at night. A tree canopy and high-albedo roofs are heat island remedies: they cut absorbed sunshine and add evapotranspiration, so they reduce the effect.A house is to be sited on a hillside in a cold, sunny region of the northern hemisphere. Which location gives the mildest conditions?
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Answer: D — The mid-slope of a south-facing hillside, above the night-time cold-air pool and sheltered from the cold wind
Cold air is dense and drains downhill at night, so the valley floor becomes a cold, frosty pool even though it is sheltered; the crest takes the full wind chill. A south-facing mid-slope gains the sun and lies in the milder thermal belt above the pool. The valley floor is the tempting choice because it is sheltered, but its cold-air collection outweighs that.At a latitude of 28° N, the noon altitude of the sun on 21 December, taking the declination as −23.5°, is ____ degrees (correct to one decimal place).
Numerical answer — type the value.
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Answer: 38.5
Noon altitude = 90° − latitude + declination = 90 − 28 + (−23.5) = 38.5°. Check by the zenith angle: it equals |φ − δ| = 28 + 23.5 = 51.5°, so the altitude is 90 − 51.5 = 38.5°.At a place at 13° N a vertical pole 10 m tall is observed at solar noon on 21 June (declination +23.5°). The length of its shadow, in metres correct to two decimal places, is ____.
Numerical answer — type the value.
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Answer: 1.85
Here δ exceeds φ, so the noon sun is north of the zenith: zenith angle = δ − φ = 23.5 − 13 = 10.5°, altitude = 79.5° (the formula 90 − φ + δ would give 100.5°, which is not an altitude). Shadow = 10 / tan 79.5° = 10 × tan 10.5° = 10 × 0.1853 = 1.85 m, falling to the south.A south-facing window 1.2 m high at 28° N has an overhang whose underside is flush with the window head. To shade the whole window exactly at solar noon on an equinox, the overhang must project ____ m (correct to two decimal places).
Numerical answer — type the value.
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Answer: 0.64
At an equinox δ = 0, so the noon altitude is 90 − 28 = 62°. The wall faces the sun (γ = 0), so VSA = α = 62°. Projection P = H / tan VSA = 1.2 / 1.8807 = 0.638, or 0.64 m. Check: the shadow depth P tan 62° = 0.64 × 1.8807 = 1.20 m, the window height.Ignoring the equation of time, solar noon at a place on 72.5° E occurs ____ minutes after 12:00 Indian Standard Time (IST is based on the 82.5° E meridian).
Numerical answer — type the value.
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Answer: 40
The place is 82.5 − 72.5 = 10° west of the standard meridian. The sun crosses each degree of longitude in 4 minutes, and it reaches a western place later, so solar noon = 12:00 + 10 × 4 = 12:40 IST, which is 40 minutes after 12:00.Which shading approach is most effective for a west-facing window in the late afternoon in the tropics?
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Answer: A — Vertical fins or an egg-crate device with a small window, because the sun is low and nearly square to the wall
A low sun almost normal to the wall passes under any practical overhang, so shading must act in the plane of the facade: vertical or egg-crate devices, with glazing kept small. Overhangs are the south-face device. A curtain inside the glass lets the heat in first (the radiation is already inside the building), so it is the weakest option.The sol-air temperature of a roof surface is best described as:
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Answer: C — A fictitious outdoor air temperature that would give the same heat flow into the surface as the real air temperature plus absorbed sunshine
Sol-air temperature is the fictitious outside air temperature that, with the outer film coefficient, reproduces the combined effect of air temperature, absorbed solar radiation (T_sa = T_o + α I / h_o) and long-wave exchange on heat flow into the surface. It is not the measured surface temperature, which is the tempting reading; the surface temperature depends on the building's own response.Which statements about solar geometry and orientation at Indian latitudes are correct?
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Answer: A — At solar noon on an equinox the sun's altitude equals 90° minus the latitude; B — The hour angle changes by 15° every hour and is negative before solar noon; C — At a place south of the Tropic of Cancer the noon sun can be north of the zenith in summer
At an equinox δ = 0 so the noon altitude is 90° − φ; the hour angle is 15° per hour, negative in the morning; and when the declination exceeds the latitude the noon sun lies north of the zenith. The sun rises due east only at the equinoxes, north of east in the northern summer and south of east in winter, so that statement is false.A window faces due south. At a certain hour the sun's altitude is 40° and its azimuth is 60° away from the wall normal. The vertical shadow angle (tan VSA = tan α / cos γ) is nearest to:
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Answer: B — 59°, since tan VSA = tan 40° / cos 60° = 0.839 / 0.5 = 1.68
tan VSA = tan 40° / cos 60° = 0.8391 / 0.5 = 1.678, so VSA = 59.2°. The VSA exceeds the altitude whenever the sun is off the wall normal, because the shadow is measured in the vertical plane normal to the wall; it equals the altitude (40°) only for γ = 0. Dividing the angle (not its tangent) by cos γ is a common slip.Which of the following are personal factors, rather than environmental factors, in the PMV comfort model?
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Answer: A — Metabolic rate of the occupant; B — Thermal insulation of the clothing worn
The PMV model has six inputs: four environmental (air temperature, mean radiant temperature, air velocity, humidity) and two personal (metabolic rate in met and clothing insulation in clo). Mean radiant temperature and air velocity describe the room, not the person.In the PMV–PPD model the lowest value that the predicted percentage dissatisfied can reach is:
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Answer: D — 5%, reached at PMV = 0 because individual preferences differ
PPD = 100 − 95 exp(−0.03353 PMV⁴ − 0.2179 PMV²) equals 5% at PMV = 0 and rises on both sides; PMV = ±0.5 gives about 10%. It never reaches zero because people differ in preference, so some are dissatisfied even at thermal neutrality.In a naturally ventilated office where staff open windows and use fans, the PMV model predicts more discomfort than occupants report. The best explanation is that:
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Answer: A — Occupants adapt, so their neutral temperature rises with the outdoor temperature, which a steady-state heat balance does not capture
PMV was derived from steady-state chamber trials and holds the comfort temperature fixed by the six factors. Field studies show free-running occupants adapt, and the comfort temperature drifts with the prevailing outdoor mean, so PMV overpredicts warm discomfort there. The model does use air temperature, so the claim that it ignores it is false; the issue is adaptation, not a missing input.On a day with a dry-bulb temperature of 33 °C and 90% relative humidity, which measure gives the occupants of a house the most relief?
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Answer: D — Increased air movement over the occupants through well-placed openings and fans
With the air near saturation the wet-bulb depression is tiny, so evaporation of water or sweat is weak and a cooler would only add moisture; and a cool night to recharge mass does not exist. Moving air over the skin raises convective and evaporative loss directly, and it is the one measure that works. Sealing the house traps the humidity and removes the only breeze.Air at 30 °C dry-bulb has a dew-point temperature of 20 °C. A chilled-water pipe in the room has an outer surface temperature of 18 °C. What happens at the pipe surface?
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Answer: A — Condensation forms, because the surface temperature is below the dew-point temperature of the air touching it
Air chilled to its dew point can hold no more vapour, so a surface at 18 °C, below the 20 °C dew point of the adjoining air, collects condensation. Relative humidity of the room need not reach 100% overall: it is the thin layer next to the cold surface that saturates. Freezing is irrelevant to condensation.Which design features suit a cold-sunny climate such as that of Ladakh?
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Answer: A — A compact form with a low surface-to-volume ratio; B — Sun-facing glazing with thermal mass behind it to store the heat; C — Insulated walls and roof together with double glazing
A cold-sunny climate calls for both capturing and conserving heat: a compact form loses less, sun-facing glazing with mass collects and stores sunshine, and insulation with double glazing holds it. Large openings on every side would lose heat to the cold wind, which is the opposite of what is needed.