An overhang that projects P over a window of height H shades the whole window whenever the sun’s altitude is at least arctan(H/P), so the depth you need depends on the latitude and on the date you want shading to start. At 40 degrees north the carrier’s factor of 0.50 gives a 0.75 m overhang over a 1.5 m window, which shades the window completely at solar noon from late April to mid-August.
Part of Passive Solar Building Design
Sizing a fixed overhang so it blocks the high summer sun and admits the low winter sun, including windows that do not face due south.
Why a Bare Number Fails
An overhang does one geometric job. The sun is a point of light at altitude a; the overhang casts a shadow down the wall of depth P x tan(a), where P is the projection and the overhang sits at the top of the window. The window is fully shaded when P x tan(a) is at least H, the window height, that is when tan(a) is at least H/P. The ratio f = P/H is the carrier’s “overhang factor”. Which altitude you shade at, and therefore which factor, is a design choice about dates, and the dates move with latitude. This page uses Northern Hemisphere wording with the glass facing south; in the Southern Hemisphere put the glass and overhang on the north wall and use the same equations.
The Carrier’s Factors, Read as Shading Seasons
The carrier gives projection = H x factor, with factors of about 0.55 at 36 N, 0.50 at 40 N, 0.45 at 44 N and 0.40 at 48 N, and says the overhang starts at the top of the window or slightly above, with a gap between wall and overhang of about one third the projection so hot air can escape.
Take each factor and ask: at what noon altitude does it shade the whole window? That is arctan(1/f). Noon altitude at latitude L on a day with declination d is 90 - L + d, so the declination at which shading begins is d = arctan(1/f) - (90 - L).
| Latitude | Factor | Full-shade altitude | Declination needed | Full shade at noon |
|---|---|---|---|---|
| 36 N | 0.55 | 61.2 degrees | 7.2 degrees | about 10 April to 2 September |
| 40 N | 0.50 | 63.4 degrees | 13.4 degrees | about 27 April to 16 August |
| 44 N | 0.45 | 65.8 degrees | 19.8 degrees | about 20 May to 24 July |
| 48 N | 0.40 | 68.2 degrees | 26.2 degrees | never |
The dates use Cooper’s declination equation (see Seasonal Sun Angle Calculation) and are approximate. At 48 N the maximum noon altitude is 65.4 degrees, so a factor of 0.40 never shades the whole window at noon, even on 21 June. The factor needed for full shade at the summer solstice, 1 / tan(90 - L + 23.44), is 0.22 at 36 N, 0.30 at 40 N, 0.38 at 44 N and 0.46 at 48 N: it rises with latitude, because the summer sun is lower at higher latitude. The carrier’s factors fall with latitude, so they must be read as describing a shorter and shorter shading season, not full shade at the solstice. If your climate needs full shade through midsummer at high latitude, use the larger factor from this calculation.
What You Need
- Window height H — clear glass height.
- Your latitude — and the dates you want shade from and to.
- True south — see Finding True South.
Method: Size the Overhang
Step 1: Choose the design altitude Pick the altitude at which the window must be fully shaded, a, from your latitude and the date you want shading to begin.
Step 2: Compute the projection P = H / tan(a). For the carrier’s 40 N case a = 63.4 degrees, tan = 2.0, P = H x 0.50.
Step 3: Place it Start the overhang at the top of the window or slightly above, and leave a gap of about one third of P between the overhang and wall so that hot air escapes.
Step 4: Check the winter Compute the shadow the overhang casts at winter noon: P x tan(winter altitude). The sunlit part of the glass is H minus that.
Worked Example: 40 N, Window 1.5 m High
P = 1.5 x 0.50 = 0.75 m. Gap = 0.75 / 3 = 0.25 m.
| Day (noon) | Sun altitude | Shadow on glass | Sunlit glass |
|---|---|---|---|
| 21 June | 73.4 degrees | 0.75 x tan 73.4 = 2.52 m | none |
| Equinox | 50.0 degrees | 0.75 x tan 50 = 0.89 m | 0.61 m |
| 21 December | 26.6 degrees | 0.75 x tan 26.6 = 0.37 m | 1.13 m |
On 21 December 1.13 m of the 1.5 m window is sunlit at noon, about three quarters. At the equinox only 0.61 m is, 41%. The equinoxes are symmetrical for the sun but not for the house: in March the house is still cold, in September it carries the summer’s heat. A fixed overhang treats them alike. Movable shading, a deciduous vine or trellis, or shutters correct it.
Windows Not Facing South: Use the Profile Angle
An overhang shades according to the sun’s profile angle p, the altitude as seen in a plane at right angles to the wall: tan p = tan(a) / cos(g), where g is the difference between the sun’s azimuth and the direction the wall faces. A window turned 30 degrees east of south (wall facing azimuth 150 degrees) at 40 N, at 10:00 solar time:
- 21 June: altitude 59.8 degrees, azimuth 114.2 degrees, g = 35.8 degrees, tan p = 1.7197 / 0.8110 = 2.12, p = 64.7 degrees. Shadow = 0.75 x 2.12 = 1.59 m, more than 1.5 m, so the window is fully shaded.
- 21 December: altitude 20.7 degrees, azimuth about 151 degrees, g is under 1 degree, p = 20.7 degrees. Shadow = 0.75 x tan 20.7 = 0.28 m, leaving 1.22 m sunlit.
A due-south wall at the same hour has a much higher profile angle in summer (76.6 degrees), so it is shaded easily. An east or west wall takes the sun nearly head-on at low angle; its profile angle stays near the sun’s altitude (37 degrees at 4 p.m. on 21 June at 40 N, on a west wall), which a horizontal overhang barely helps. That is the carrier’s reason for minimizing east and west windows.
Common Mistakes
- Copying the factor from another latitude — recompute for yours.
- Overhang flush with the wall — leave the gap so hot air can escape.
- Forgetting snow and wind loads — a deep overhang is a lever on the wall.
- Assuming equinox sun is harmless — in September it is a heat source on a hot house.
Safety
Overhangs carry loads and work is at height
A projecting beam collects snow and wind load that the wall must carry back; size and brace it like a roof eave. Build from scaffolding or a secure ladder with a second person present, and keep clear below when lifting beams into place.
What’s Next
- Learn next: Window Placement & Sizing — how much glass the overhang is protecting
- Combine with: Trigonometry Basics — the tangent used throughout