Sun Angles for Awning Design: Seasonal Sun Height, Sun Paths and How to Use Them

Awning design comes down to one question: how high is the sun, and from which direction, at the hours you want shade? At solar noon the answer is simple arithmetic. Noon sun altitude = 90 degrees minus latitude plus declination, where the declination is about +23.4 degrees at the June solstice, 0 at the March and September equinoxes, and -23.4 degrees at the December solstice. At 40 degrees north (Denver, Philadelphia, Columbus) the noon sun stands about 73 degrees high in June, 50 degrees at the equinoxes and 27 degrees in December. Away from noon you also need the sun's azimuth and the wall's direction, which combine into the profile angle that actually sets an awning's shadow.

This guide gives the tables and the method. If you want the shade result without the trigonometry, the shade calculator does it for any date and time, and the awning shade data page has precomputed results for 14 cities.

The three angles that matter

• Altitude: the sun's height above the horizon, 0 degrees at sunrise to its noon maximum.
• Azimuth: the compass direction of the sun, measured clockwise from true north (90 east, 180 south, 270 west). In the continental US the noon sun is always due south.
• Profile angle: the sun's height seen in a vertical slice taken straight out from your wall. tan(profile angle) = tan(altitude) / cos(sun azimuth minus wall azimuth). When the sun is square to the wall, profile angle equals altitude; when it is off to the side, the profile angle is steeper.

The profile angle is the one an awning cares about. A shadow cast by a front edge at height H lands H / tan(profile angle) feet closer to the wall than the edge itself, so shade depth = horizontal reach minus that offset. The guide to how much shade an awning provides works through that formula in detail.

How the sun's declination changes through the year

Declination is the latitude at which the sun is directly overhead at noon. A standard approximation used in solar engineering is Cooper's equation: declination = 23.45 x sin(360/365 x (284 + n)) degrees, where n is the day of the year (1 for January 1). Values for the 21st of each month, and the noon altitude they give at 40 degrees north:

The last column is the most important design fact in this article. The sun is symmetric around the June solstice, but the weather is not. Outdoor temperatures lag the sun by roughly a month, so late August, often one of the hottest stretches of the year, has the same sun height as a mild late April. A fixed awning cannot tell the two apart: if it shades fully in August it also shades in April, when you might want the warmth. That is the strongest geometric argument for a retractable awning on south glass in mixed climates.

Noon sun altitude by latitude

Computed with the formula above (declination +23.4, 0 and -23.4 degrees). The second figure in each cell is the shadow offset per foot of height at noon on a south wall, 1 / tan(altitude): multiply it by your front edge height to see how far toward the wall the shadow falls.

Read across a row and the design problem is clear. At 40 degrees north a front bar at 7.5 ft throws its noon shadow 7.5 x 0.30 = 2.3 ft toward the wall in June, but 7.5 x 0.84 = 6.3 ft at the equinox. Read down a column and you see why northern patios lose shade so fast in September: the offset per foot more than doubles between 25 and 50 degrees north.

Sun paths: where the sun is through the day

Noon is the high point. Morning and afternoon positions follow a curved path whose shape depends on the season. Altitude and azimuth at 35 degrees north by solar time:

Three things to take from it:

• Summer sun reaches the north side. On June 21 the sun is north of due west (azimuth over 270) after about 4 pm. At the June solstice it rises about 31 degrees north of east at 40 degrees north (about 27 degrees at 30 north, 34 at 45 north) and sets the same amount north of west, so north walls get early and late sun in summer.
• Afternoon sun is low and western. At 4 pm in June the sun is 37 degrees high and nearly due west. For a west wall that is a profile angle of about 37 degrees, so a front bar at 7.5 ft throws its shadow about 10 ft toward the wall: no shade on the ground. See awnings by patio orientation for what to do about it.
• Winter sun stays south. In December the sun never gets far from south and never gets high, which is what lets south overhangs admit winter sun.

A sun path chart plots these curves for your latitude on one diagram. The University of Oregon Solar Radiation Monitoring Laboratory offers a free sun path chart program; draw your wall direction and any obstructions (trees, the neighbor's roof) on it to see which hours actually reach your patio.

Solar time versus clock time

Every table here uses solar time, in which the sun is due south at 12:00. To convert to the clock:

1. Add 1 hour for daylight saving time (most of the US, March to November).
2. Adjust for longitude. Add 4 minutes for each degree you are west of your time zone's reference meridian (75 W Eastern, 90 W Central, 105 W Mountain, 120 W Pacific); subtract if you are east of it.
3. Apply the equation of time, a seasonal correction of up to about 16 minutes. In late July and early August solar noon runs about 6 minutes late; in early November about 16 minutes early.

Example: Chicago sits at 87.6 degrees west, 2.4 degrees east of the Central meridian, so it is about 10 minutes earlier; with the August correction and daylight saving, solar noon is about 12:56 pm. Detroit, at 83 degrees west in the Eastern zone, has solar noon near 1:38 pm in early August. The NOAA Solar Calculator gives exact solar noon for any address.

Applying sun angles to awning design

That trade-off is the core of fixed overhang design: any depth that blocks late-summer sun also blocks some spring sun, and any depth that admits winter sun leaves the equinox partly unshaded. Sloped window awnings with side panels shade more than this horizontal model; window awnings covers the practical sizing rule of about half to two thirds of window height for south glass.

For patio awnings the same angles set projection and pitch. Two rules follow from the tables:

• Design to the latest month you want full shade, not to June. North of about 40 degrees, a patio used through September needs either more projection or a lower front edge than a June calculation suggests. The projection and pitch guide converts a target front bar height into a pitch angle.
• Low sun is solved vertically. When the profile angle is below about 35 degrees (west walls in late afternoon, east walls in early morning, any wall in fall), each foot of lower front edge buys more than a foot of shade, so a valance or drop shade outperforms extra projection.

Who should do this math

• Worth doing: anyone ordering a fixed awning or overhang (it cannot be adjusted afterward), anyone north of about 40 degrees who wants shoulder-season shade, and anyone with a west or angled wall.
• Optional: buyers of a retractable awning on a south wall, where adjustable pitch and the ability to retract cover most mistakes. The awning size planner is enough for most of them.

Frequently asked questions

How do I calculate the sun angle at noon for my location?

Subtract your latitude from 90 degrees and add the solar declination for the date: about +23.4 degrees at the June solstice, 0 at the March and September equinoxes, and -23.4 degrees at the December solstice. At 35 degrees north that gives about 78 degrees in June, 55 at the equinoxes and 32 in December. The result is the sun's height above the horizon at solar noon.

What is the sun angle on the summer solstice?

At solar noon on the June solstice the sun's altitude is about 113.4 degrees minus your latitude: roughly 88 degrees in Miami, 78 at 35 degrees north, 73 at 40 north and 68 at 45 north. It is the highest the sun gets all year, which is why awnings shade most of their footprint in midsummer and less in spring and fall.

What is a profile angle?

It is the sun's height measured in a vertical plane straight out from a wall, and it sets where an awning's shadow falls. Its tangent equals the tangent of the sun's altitude divided by the cosine of the angle between the sun's azimuth and the wall's facing direction. When the sun is off to one side the profile angle is steeper than the altitude.

Should an awning be sized for the summer solstice?

Usually not. The solstice has the highest sun and the easiest shade, but the hottest weather often comes in July and August, when the sun is lower. Size for the latest date you want full shade, typically early to late August, or September in hot southern climates. A retractable awning lets you shade late summer without blocking spring and winter sun.

Why is solar noon not at 12 o'clock?

Clock time is set by time zones and daylight saving, not by the sun. Daylight saving adds an hour, each degree of longitude west of your zone's reference meridian adds about 4 minutes, and a seasonal correction called the equation of time shifts solar noon by up to about 16 minutes. In summer, solar noon in the US usually falls between about 12:30 and 2:00 pm.

Sources and further reading

• NOAA Global Monitoring Laboratory: NOAA Solar Calculator
• Duffie, J. A. and Beckman, W. A.: Solar Engineering of Thermal Processes (Wiley), solar geometry chapter (Cooper's declination equation, hour angle, profile angle)
• University of Oregon Solar Radiation Monitoring Laboratory: Sun Path Chart Program
• U.S. Department of Energy, Energy Saver: Energy Efficient Window Attachments