Why is mathematics important in building daylight? A bright room is not created by “more glass” alone. The Sun changes altitude and azimuth through the day and year. Sky light reaches windows from many directions. Glass transmits some light, surfaces reflect it, room depth weakens it and shading can block glare as well as useful illumination.
Geometry, ratios and measurement turn those effects into questions we can test. Solar-position equations locate the Sun. A daylight factor compares indoor and outdoor illuminance under a defined sky condition. Window-to-wall ratios, visible transmittance, solid angles and inverse relationships help explain why two rooms with the same window area may feel completely different.
This article uses educational building-daylight models. It does not replace current codes, climate files, glare analysis, simulation, architectural coordination or professional design. Daylight targets depend on task, place, orientation, occupancy and standards; one percentage is never a universal promise of comfort.
- Start with light measurements
- Locate the Sun
- Use window geometry
- Calculate daylight factor
- Work through an example
- Balance daylight and glare
- Study limits
- Build student skills
- Read the FAQs
Illuminance, Luminance and What We Measure
Illuminance on a surface
Illuminance E measures luminous flux arriving per unit area. Its SI unit is lux, equal to lumens per square metre. A desk may receive light from sky, Sun, reflected surfaces and electric luminaires.
Illuminance depends on surface orientation. For a narrow beam with intensity I at distance r and incidence angle theta from the surface normal, a simplified relation is E = I cos theta / r squared. The cosine represents projected area; the inverse square represents spreading.
Daylight through a window is not usually one point source, so complete calculation integrates contributions across the visible sky and surfaces. Still, cosine and distance reasoning explain why orientation and geometry matter.
Luminance and brightness patterns
Luminance describes light leaving or passing through a surface in a particular direction, measured in candelas per square metre. It relates more closely than illuminance to the brightness distribution seen by an observer.
A room can have adequate desk illuminance yet uncomfortable glare if a small window or bright sky region has high luminance relative to its surroundings. Average lux alone cannot describe visual comfort.
Daylight is variable
Outdoor illuminance changes with solar position, clouds, haze and surrounding obstruction. A single noon measurement cannot represent a whole year. Measurements should record date, clock time, location, sky condition, sensor orientation and whether electric lights are on.
In Singapore, clouds and high solar angles can change quickly. The latitude is close to the equator, but that does not mean every façade receives identical sunlight or that day length and solar altitude never vary.
Visible transmittance
Glazing visible transmittance Tv is a fraction of visible light transmitted under stated conditions. If 10,000 lux reaches the outer plane and an idealised pane transmits 60 percent with no frame or angular effects, 6,000 lux would pass through the glass before room reflections and geometry.
Real transmittance depends on wavelength, angle, coatings, dirt, layers and frame. A product value should be taken from current tested data, not guessed from appearance.
Reflectance
Surface reflectance rho is the fraction of incident luminous flux reflected, under a stated model. Pale ceilings often redistribute light deeper into a room; dark surfaces absorb more. A reflectance of 0.8 does not mean the surface looks equally bright from every direction, because directional scattering matters.
Measurement uncertainty
Light meters have calibration, spectral response, cosine response, range and positioning uncertainties. A phone sensor can support relative exploration but is not automatically a calibrated lux meter. Shadows from the observer or sensor can bias readings.
Did You Know? A room can have the same average illuminance in two designs while one has a calm gradient and the other has a glaring window plus a dark back wall. Distribution matters as much as the mean.
Solar Altitude, Azimuth and Time
Coordinate definitions
Solar altitude alpha is the angle of the Sun above the horizon. Zenith angle z is measured down from the vertical, so alpha + z = 90 degrees.
Solar azimuth describes compass direction around the horizon. Conventions differ: some measure clockwise from north, others from south with east or west signs. Every calculation must state its convention.
Latitude phi locates the site north or south of the equator. Solar declination delta is the angular position of the Sun north or south of Earth’s equatorial plane. Hour angle H measures time from solar noon at 15 degrees per solar hour.
Solar altitude equation
For an ideal astronomical model:
sin alpha = sin phi sin delta + cos phi cos delta cos H.
At solar noon, H = 0 and cos H = 1. The zenith angle is approximately the absolute difference between latitude and declination when the Sun is on the local meridian, so noon altitude is 90 degrees minus that difference.
At Singapore latitude about 1.35 degrees north and equinox declination near zero, solar-noon altitude is about 88.65 degrees. Near June solstice delta about +23.44 degrees, noon altitude is about 67.91 degrees to the north of zenith. Near December solstice delta about -23.44 degrees, altitude is about 65.21 degrees to the south.
The Sun can pass north or south of the zenith in the tropics. A fixed assumption that equatorial Sun is always due south is wrong.
Approximate declination
A classroom approximation for day number n is:
delta approximately equals 23.45 degrees times sin[360 degrees times (284 + n)/365].
This supports learning but is not a high-precision ephemeris. Leap years, equation of time, atmospheric refraction and exact orbital geometry need more accurate algorithms.
The National Renewable Energy Laboratory’s Solar Position Algorithm calculates zenith and azimuth from date, time and location with documented high precision over a broad date range. Its revised technical report explains the algorithm and uncertainty.
Clock time versus solar time
Solar noon is when the Sun crosses the local meridian, not necessarily 12:00 on a clock. Time zone longitude, equation of time and daylight-saving rules where used create differences.
Singapore uses one standard time zone across the country and lies west of its time-zone meridian, so solar noon generally occurs later than 12:00 clock time. A shadow study should calculate or observe local solar time rather than assume the clock.
Hour angle
In apparent solar time, H = 15 degrees times (solar time in hours – 12). At 10:00 solar time, H = -30 degrees. At 14:00, H = +30 degrees.
At equinox and latitude 1.35 degrees, use H = 30 degrees. sin alpha is approximately cos 1.35 times cos 30 = 0.8658, so altitude is about 59.97 degrees. The morning and afternoon altitudes are symmetric in the ideal model, though cloud and façade context need not be.
Shadow length
For a vertical object of height h on level ground, horizontal shadow length L = h/tan alpha when the Sun is unobstructed. At alpha = 60 degrees, a 2-metre object casts a shadow about 2/1.732 = 1.155 metres long.
Shadow direction is opposite solar azimuth. This simple triangle helps test sun-angle calculations, but sloping ground and perspective require care.
Sunrise and day length
Ignoring refraction and solar disc size, sunrise hour angle H0 satisfies cos H0 = -tan phi tan delta. Day length is 2H0 divided by 15 degrees per hour.
Near the equator, day length remains close to 12 hours, but exact observed sunrise includes atmospheric refraction, terrain and the Sun’s finite disc. A building receives direct sun only when façade orientation and obstruction also permit it.
For the Earth-science mechanism behind seasonal change, read Why Science? | Seasons, Earth’s Tilt and Reading Daylight. This article keeps ownership of the building-performance intent.
Windows, Solid Angle and Room Depth
Window area is not enough
Window-to-wall ratio WWR = window area divided by gross exterior wall area, often expressed as a percentage. A wall 8 metres wide and 3 metres high has 24 square metres. A 4-by-1.8 metre window has 7.2 square metres, giving WWR = 30 percent.
WWR helps compare façades, but it says nothing by itself about head height, glazing transmittance, external shading, room depth or obstructions. Two façades with 30 percent WWR can deliver very different daylight.
Window head height
Light entering near the top of a wall can reach deeper than the same area placed low because more of the room and ceiling is visible from the aperture. A high window can also admit bright sky while preserving a lower view zone.
Rules of thumb relating daylight depth to window-head height are context-dependent. They should guide early exploration, not certify performance.
Solid angle
From a point in the room, the window subtends a solid angle measured in steradians. A larger apparent window occupies more of the point’s field of view and generally exposes it to more sky luminance.
Move deeper into the room and the same physical window appears smaller. Obstructions and overhangs remove parts of visible sky. This geometric shrinking helps explain the daylight gradient.
For a small aperture of area Aw whose normal points toward the observation point at distance r and angle theta, solid angle is approximately Aw cos theta/r squared. This approximation fails when the aperture is large or close; then integrate or use exact geometry.
Sky component
The sky component of daylight factor is light reaching the point directly from the sky through the window, excluding direct Sun in the standard overcast definition. It depends on the visible sky patch, its luminance distribution, glazing and window geometry.
An overhang may block high sky and direct Sun. A nearby building may block low sky. Their effects differ because sky luminance is not uniform in standard overcast models.
Externally reflected component
Light can reflect from ground and neighbouring surfaces into the window. Bright surroundings may increase this component, while dark walls reduce it. Reflectance, orientation and visible area matter.
Highly reflective façades can create glare or concentrated reflections, so “more reflected light” is not automatically desirable.
Internally reflected component
Once light enters, walls, ceiling and floor redistribute it. Higher ceiling and wall reflectance can lift illuminance deeper in the room. Furniture, occupants and finishes change the result.
The internally reflected component is often more spatially diffuse than the direct sky component. Simple average-reflectance formulas are useful early estimates, but detailed simulation uses surface geometry and optical properties.
Room index
Lighting calculations sometimes use room index K = LW/[Hm(L + W)], where L and W are room dimensions and Hm is the height between luminaires or window reference and working plane, depending on the method. It combines proportions into one dimensionless shape indicator.
One index cannot preserve every geometric detail. A long narrow room and a differently shaped room can share an index yet have different window distribution.
Daylight Factor and Overcast-Sky Reasoning
Definition
At a point, daylight factor DF is indoor illuminance Ei divided by simultaneous unobstructed outdoor horizontal illuminance Eo under a defined overcast sky, times 100 percent:
DF = Ei/Eo times 100 percent.
If indoor illuminance is 300 lux while outdoor diffuse horizontal illuminance is 15,000 lux, DF = 2 percent.
The numerator and denominator must be measured simultaneously or under equivalent stable conditions. Electric lights should be off when measuring daylight contribution. Direct sunlight is generally excluded from the standard daylight-factor framework because it makes the ratio unstable and orientation-specific.
Components
A common conceptual decomposition is DF = sky component + externally reflected component + internally reflected component. These components can be estimated or simulated separately.
The decomposition helps diagnosis. If a point has low sky component because a neighbouring building blocks the window, lighter interior paint can improve internal reflection but cannot restore the missing sky view entirely.
Point, average and uniformity
A point daylight factor describes one location and working-plane orientation. Average daylight factor summarises points or an integrated area under a stated method. Uniformity may be minimum divided by average or minimum divided by maximum, depending on the standard.
Never quote “the room has a daylight factor of 2 percent” without saying whether it is point, minimum or average and under which calculation conditions.
Why the ratio is useful
Outdoor diffuse illumination changes with cloud brightness. Dividing indoor by outdoor value normalises much of that variation under the overcast model. A 2 percent point would have 200 lux indoors when outdoor is 10,000 lux and 400 lux when outdoor is 20,000, assuming linear response and unchanged sky distribution.
The relationship does not predict direct-sun hours, annual autonomy or glare. It is one climate-independent relative metric under a standardised sky.
A simplified transmission estimate
An early estimate might write Ei approximately proportional to Eo times Tv times visible-sky geometry times maintenance factors plus reflections. This is not a complete daylight-factor formula, but it shows multiplicative structure.
If visible transmittance falls from 0.70 to 0.56, transmitted component falls by 20 percent because 0.56/0.70 = 0.8. If the window is also half obstructed in the relevant solid-angle sense, combined direct contribution can fall substantially more.
Annual metrics
Climate-based daylight modelling uses hourly weather data and metrics such as daylight autonomy, useful daylight illuminance or spatial daylight autonomy under specific standards. These account for orientation, direct Sun and climate, unlike the overcast daylight factor.
Metric definitions and thresholds vary. They should be taken from the applicable current standard, not invented or mixed across schemes. The National Renewable Energy Laboratory’s Solar Radiation Data Manual for Buildings shows how building solar and daylight decisions depend on weather and orientation data.
Worked Example: A Singapore Classroom
Consider an illustrative rectangular classroom 8 metres long, 6 metres wide and 3 metres high. One façade has two windows, each 2.4 metres wide and 1.5 metres high. Visible transmittance is assumed 0.60. We calculate geometry and interpret measured daylight, not certify a real classroom.
Window-to-wall ratio
Gross façade area = 8 times 3 = 24 square metres. Total window area = 2 times 2.4 times 1.5 = 7.2 square metres. WWR = 7.2/24 = 0.30, or 30 percent.
The ratio excludes no frame in this simplified definition. If net glazed area is only 6.3 square metres after frames, net glazing ratio is 26.25 percent. State which area is used.
Solar-noon altitude
Take latitude phi = 1.35 degrees north. At equinox delta approximately zero. Solar-noon altitude is 90 – 1.35 = 88.65 degrees.
For a vertical shading calculation, a 1-metre horizontal overhang above the façade creates a vertical shadow projection approximately d tan alpha when Sun is perpendicular to the façade plane. At alpha = 60 degrees, projection is 1.732 metres. Near 88.65 degrees, it becomes extremely large in the simple profile-angle geometry, but façade azimuth and solar azimuth determine whether the Sun is in front of that façade at all.
This is a warning against using altitude alone. Shading uses solar profile angle relative to the façade, not just global altitude.
Shadow test
At an idealised altitude 60 degrees, a vertical 1.2-metre model stick casts L = 1.2/tan 60 = 0.693 metre shadow. Students can compare a safe outdoor observation with a solar-position calculation, avoiding direct viewing of the Sun.
Daylight-factor measurement
Suppose simultaneous overcast readings with electric lights off are:
- Outdoor unobstructed horizontal illuminance: 18,000 lux.
- Point A near window: 1,260 lux.
- Point B mid-room: 540 lux.
- Point C back of room: 180 lux.
DF at A = 1,260/18,000 times 100 = 7.0 percent. At B = 3.0 percent. At C = 1.0 percent.
The gradient is large. An arithmetic average of these three points is 3.67 percent, but three points may not represent the floor area. A grid should use an agreed spacing and area weighting.
Uniformity
Using minimum divided by average for this three-point illustration, uniformity = 1.0/3.67 = 0.273. Using minimum divided by maximum gives 1.0/7.0 = 0.143. The numerical result changes because the definition changes.
This is why every uniformity value must name its formula. Neither ratio alone decides whether the classroom meets a current requirement.
Effect of glazing transmittance
If visible transmittance is reduced from 0.60 to 0.48 with geometry unchanged, a purely transmitted component would scale by 0.48/0.60 = 0.8. Approximate DFs might fall by 20 percent: 7.0 to 5.6, 3.0 to 2.4 and 1.0 to 0.8.
Internal reflections and angular transmittance may make the exact response different. The calculation is a sensitivity estimate, not a simulation.
Interior reflectance change
Painting a dark rear wall lighter could raise the internally reflected component, especially at Point C. It would not necessarily raise Point A proportionally because direct sky component may dominate there.
A measurement before and after should use comparable sky conditions or simultaneous outdoor normalisation. Otherwise a brighter day may be mistaken for an improvement.
Results table
| Location | Indoor illuminance | Outdoor illuminance | Point daylight factor |
|---|---|---|---|
| Near window A | 1,260 lux | 18,000 lux | 7.0% |
| Mid-room B | 540 lux | 18,000 lux | 3.0% |
| Back-room C | 180 lux | 18,000 lux | 1.0% |
The table supports a spatial interpretation. It does not provide annual sunlight, glare or energy performance.
Shading, Glare and Thermal Trade-Offs
Overhang geometry
For a façade, solar profile angle combines altitude and azimuth relative to the façade normal. A horizontal overhang depth d casts a vertical shadow related to d tan(profile angle), under simple geometry.
When the Sun is oblique to the façade, a plan and section are both needed. Vertical fins can block low-angle side Sun that a horizontal overhang misses. Shading design is a three-dimensional angle problem.
Glare
Glare depends on source luminance, apparent size, position in the field of view and background adaptation. A bright window directly ahead can be uncomfortable even if desk illuminance is moderate.
Daylight Glare Probability and related metrics use calibrated formulas and view-based simulation. They are not interchangeable with daylight factor. Blinds, seating direction and screen location can matter as much as window area.
Heat gain
Solar radiation through glazing adds heat. Visible transmittance and solar heat-gain properties are related but not identical. A coating can change spectral transmission.
A design that maximises daylight without considering cooling may increase energy demand or discomfort. Why Mathematics? | Building Insulation, U-Values and Heat Flow explains conductive heat flow; solar gain is a different envelope mechanism.
Electric-light controls
Daylight-responsive dimming can reduce electric lighting when sensors detect sufficient light. Sensor placement, control zones, calibration and occupant acceptance determine savings.
One central sensor may not represent a deep room. A control model needs daylight distribution and occupancy schedule, not only peak outdoor light.
View and wellbeing
Windows provide view, orientation and connection to outdoors as well as light. A high diffuse clerestory and a clear view window serve different purposes. Daylight mathematics should not reduce architecture to one lux number.
Singapore context
Near-equatorial solar paths include high Sun and low east/west Sun. Cloudy-bright skies, heat and glare make external shading and orientation important. Exact design uses current Singapore codes, guidance, climate data and project conditions.
This article does not claim one façade orientation is universally best. Site obstruction, use, neighbouring buildings, ventilation, views and energy systems all matter.
Measurement, Simulation and Uncertainty
Build a measurement grid
Define working-plane height, grid spacing and boundary offsets. Record every point consistently. A denser grid captures gradients near windows better but requires more time.
Area-weight average points if grid cells differ. Do not average a dense window-side cluster with a few rear points as if each represents equal area.
Simultaneous outdoor reference
Outdoor illuminance should be measured in an unobstructed location with the sensor horizontal and appropriately shielded from direct Sun for an overcast test. Indoor and outdoor readings should be simultaneous because sky brightness changes.
If only one meter exists, rapid alternation introduces temporal error. Two calibrated meters or a stable data logger are better.
Sensor uncertainty
If indoor and outdoor measurements have relative standard uncertainties ui and uo and are independent, relative uncertainty of DF is approximately square root(ui squared + uo squared).
For 5 percent indoor and 3 percent outdoor uncertainties, combined relative uncertainty is square root(0.05 squared + 0.03 squared) = 5.83 percent. A DF of 3.0 percent then has about 0.175 percentage-point standard uncertainty from those terms.
Spatial variability and sky mismatch may be larger than instrument calibration. An uncertainty budget should include the dominant effects.
Simulation inputs
Daylight simulation needs geometry, material reflectances, glazing optical data, location, orientation, sky or weather data and analysis grid. A beautiful image is not proof of correct inputs.
Validate the model against measured data where possible. Differences can reveal wrong geometry, dirty glazing, unmodelled obstructions or sensor problems.
False precision
Reporting a daylight factor as 2.734819 percent is rarely justified. Input reflectance, sky and geometry are not known to six decimal places. Round according to uncertainty and decision needs.
What the Simple Model Leaves Out
Direct Sun
Daylight factor is usually defined for diffuse overcast sky and excludes direct Sun. Annual comfort and glare require sun-path and climate-based analysis.
Dynamic façades
Blinds, electrochromic glass and occupant actions change transmission over time. A fixed-state model cannot predict their control behaviour.
Complex glazing
Prismatic, fritted, patterned or light-redirecting systems scatter light directionally. One normal-incidence transmittance is insufficient.
Urban obstruction
Neighbouring façades, trees and balconies alter sky view and reflected light. Trees change with growth and season in some climates. A clear-site model may overestimate performance.
Spectral effects
Daylight has a spectrum. Human photopic illuminance weights wavelengths by visual sensitivity. Circadian and plant responses use different spectral weightings. Lux cannot answer every biological question.
Occupants and tasks
Screens, paper work, art display and laboratories have different visual needs. Seating orientation affects glare. Occupants may close blinds, changing daylight and energy use.
Codes and standards
Current requirements may use minimum illuminance, glare, annual metrics, view or energy performance. They vary by jurisdiction and building type. This article does not set compliance thresholds.
Model table
| Teaching model | Useful insight | Missing reality |
|---|---|---|
| Solar altitude triangle | Shadow length and high/low Sun | Façade-relative azimuth and refraction |
| Window-to-wall ratio | Aperture proportion | Head height, transmittance and obstruction |
| Point daylight factor | Diffuse indoor/outdoor ratio | Direct Sun and annual climate |
| Uniform reflectance | Internal redistribution | Directional materials and furniture |
| Fixed glazing | Sensitivity to transmission | Dynamic shades and angle dependence |
Misconceptions Worth Correcting
“More glass always means better daylight”
More area can admit more light, but glare, heat gain, low-angle Sun and poor distribution may worsen. Window placement and shading matter.
“Daylight factor predicts sunny conditions”
It is normally an overcast-sky ratio excluding direct Sun. Climate-based metrics are needed for annual sunny and cloudy patterns.
“The Sun is always south at noon”
Not in the tropics. In Singapore the Sun can pass north or south of zenith depending on date.
“Lux measures how bright a window looks”
Lux is illuminance on a surface. Luminance and contrast describe viewed brightness and glare more directly.
“Average daylight proves good uniformity”
A high window-side value can raise the mean while the back remains dark. Minimum, distribution and task areas should be examined.
“A phone app is a calibrated light meter”
It may be useful for relative exploration, but sensor spectral and angular response, calibration and device differences limit accuracy.
How Students Can Learn This Mathematics
Track safe shadows
Measure the shadow of a vertical stick from a safe location without looking at the Sun. Calculate altitude from tan alpha = height/shadow length. Compare with an official solar-position algorithm.
Draw a sun path
Calculate noon altitude at equinoxes and solstices for several latitudes. Add hour-angle points. Discuss why Singapore differs from a temperate city.
Make a room section
Draw window head, overhang, working plane and room depth to scale. Use similar triangles for one solar profile angle.
Measure a daylight grid
With appropriate school equipment and electric lights off, record indoor and simultaneous outdoor values under stable overcast conditions. Calculate point DFs and map contours.
Test reflectance
Build two small boxes with the same opening but different interior colours. Measure relative illuminance at several depths. Keep aperture and source condition consistent.
Explore transmittance
Place safe translucent samples over a model opening and calculate transmission ratios. Do not infer building-product performance without calibrated optical data.
Use uncertainty
Repeat measurements, rotate sensors and swap meter positions. Estimate repeatability and systematic differences. Report a plausible range.
Compare related optics
Stage lighting applies inverse-square and colour mixing in a controlled source context. Why Mathematics? | Stage Lighting, Inverse-Square Law and Additive Colour Mixing offers a useful comparison with the extended sky source.
Keep pathways open
Students may explore architecture, building services, environmental engineering, lighting design, physics, geography or simulation. Mathematics supports these pathways but does not guarantee admission or professional status. Verify current official programme requirements.
For Singapore cohorts, consult current MOE and SEAB information for Posting Groups, Full Subject-Based Banding, G1/G2/G3 subjects and the Singapore-Cambridge Secondary Education Certificate. When applicable, use SEC Additional Mathematics Examination for G2/G3 rather than applying older labels automatically.
Guidance for Parents and Teachers
Let students experience the gradient. Walking from a window to the back of a room makes the geometry meaningful before formulas begin.
Ask what the metric excludes. Daylight factor excludes direct Sun; WWR excludes transmittance; average illuminance excludes glare distribution. This habit prevents overclaiming.
Use sketches before trigonometry. Label north, façade normal, solar azimuth, altitude and profile angle. A correct calculator answer with the wrong angle convention is still wrong.
Encourage simultaneous measurement and clear units. Lux, percent, degrees and square metres answer different questions.
Connect comfort and energy without declaring one optimum. Shading can reduce glare and heat but also light. The best choice depends on climate, task and control.
Keep safety simple: never stare at the Sun, do not climb façades or lean from windows, and follow school procedures for outdoor observations.
Celebrate model revision. A simulation that disagrees with measurement is an invitation to check reflectance, obstruction and sensor placement, not to hide the difference.
Frequently Asked Questions
What is daylight factor?
Indoor illuminance divided by simultaneous unobstructed outdoor horizontal illuminance under a defined overcast sky, multiplied by 100 percent.
Does daylight factor include direct sunlight?
Normally no. It is a diffuse overcast-sky metric. Direct-sun hours and annual climate need other analyses.
What is solar altitude?
The Sun’s angle above the horizon. Zenith angle is its complement to 90 degrees.
Why is solar azimuth convention important?
Some systems measure from north, others from south, with different sign directions. Mixing conventions can rotate a result into the wrong façade.
Why is the back of a room darker?
The window subtends a smaller solid angle, direct sky view may be reduced and light undergoes reflection losses. High window heads and bright surfaces can improve distribution.
Is a high window-to-wall ratio always good?
No. It may increase light, view, glare and solar heat together. Geometry, glazing and shading must be coordinated.
Can the cold-looking glass have low visible transmittance?
Appearance alone does not determine tested transmission. Use product optical data for the relevant angle and spectrum.
Why measure outdoors at the same time?
Sky brightness changes. The ratio is meaningful only when indoor and outdoor values represent the same condition.
Can I predict glare from daylight factor?
Not reliably. Glare depends on luminance, source size and view position. A view-based glare metric or assessment is needed.
Can this article certify code compliance?
No. Compliance requires current applicable standards, qualified analysis, project geometry, climate data and documented methods.
Useful Next Reading
- NREL Solar Position Algorithm
- NREL Solar Position Algorithm technical report
- NREL Solar Radiation Data Manual for Buildings
- Why Science? | Seasons, Earth’s Tilt and Reading Daylight
- Why Mathematics? | Building Insulation, U-Values and Heat Flow
- Why Mathematics? | Stage Lighting, Inverse-Square Law and Additive Colour Mixing
Building daylight shows the importance of mathematics as a design conversation. Astronomy tells us where the Sun can be. Geometry tells us what the window can see. Ratios compare indoor and outdoor light. Measurement checks the model, while glare and heat remind us that one metric is never the whole room. The result is not less wonder—it is daylight made understandable.