Horizontal Shadow Angle Calculator

The Horizontal Shadow Angle Calculator computes the horizontal shadow angle from solar azimuth and façade orientation to inform vertical shading design.

What Is a Horizontal Shadow Angle Calculator?

A Horizontal Shadow Angle Calculator computes the angle between a facade’s outward normal line and the sun’s bearing on the ground plane. This angle is called the HSA. When the HSA is zero, the sun is hitting the facade squarely. As the absolute HSA grows, the sun is sliding along the facade, and vertical elements gain shading power.

To produce the HSA, the tool needs the site location, date, and time to get the sun’s position. It also needs the facade’s azimuth, which is the direction the facade normal points relative to true north. The Calculator reports the HSA and often the related vertical shadow angle (VSA), which links directly to overhang performance. With these outputs you can check cut-off angles, choose fin projections, and refine construction dimensions.

On actual projects, you may pair HSA results with drawings to size shading devices. That reduces trial-and-error and supports more reliable cost estimate work. The output also serves as a quality check for facade orientation decisions early in design.

How to Use Horizontal Shadow Angle (Step by Step)

Using HSA effectively is about matching site conditions to the facade orientation you are testing. Gather accurate inputs before you start. Then compare the calculated angles to your target cut-off values for shading devices. If you already have the sun azimuth from a weather file, you can compute HSA directly by azimuth difference.

• Confirm your facade azimuth (bearing of the outward normal), measured relative to true north.
• Enter site latitude and longitude, along with time zone and daylight saving status if applicable.
• Select date and clock time or specify local solar time if you prefer sun-time accuracy.
• Optionally, enter wall tilt if the facade is not vertical, and any local magnetic declination corrections.
• Run the Calculator and note HSA and VSA, then compare them to your device cut-off targets.

When testing multiple facades, change the facade azimuth and rerun. For seasons, run solstices and equinoxes. For daily extremes, check morning and late afternoon. This helps you balance shading, daylight, and view.

Formulas for Horizontal Shadow Angle

HSA comes from a small set of solar geometry equations. The sun’s position at a given place and time is defined by solar altitude (angle above the horizon) and solar azimuth (bearing along the horizon from north). Once you know the sun azimuth and the facade azimuth, the HSA is a simple difference wrapped to ±180 degrees.

• Solar declination δ (degrees): δ ≈ 23.45° × sin[360° × (284 + n) / 365], where n is the day of the year.
• Hour angle h (degrees): h = 15° × (LST − 12), where LST is local solar time in hours.
• Solar altitude α: sin α = sin φ sin δ + cos φ cos δ cos h, where φ is latitude (north positive).
• Solar azimuth γ (from true north, clockwise): computed from standard solar position equations using α, φ, δ, h.
• Facade (surface) azimuth β_surf (from true north, clockwise): direction the facade normal points.
• Horizontal Shadow Angle: HSA = wrap_to_±180(γ − β_surf).

Here “wrap_to_±180” converts an angle to the range −180° to +180°. Positive HSA means the sun lies to the right of the facade normal when viewed from the exterior. The VSA relation helps you translate HSA and altitude into device cut-off behavior for overhangs.

Inputs, Assumptions & Parameters

The Calculator needs a small set of inputs to describe the sun and the facade. Accurate values deliver accurate angles. When possible, use survey-based bearings and verified clocks.

• Location: latitude and longitude or a city lookup.
• Date and time: local clock time or local solar time, with time zone and DST flag.
• Facade azimuth: bearing of the outward normal measured from true north, clockwise 0°–360°.
• Wall tilt: 90° for vertical walls; use tilt if the facade leans.
• Optional sun data: direct solar azimuth and altitude from a weather file if you have them.

Edge cases include high latitudes where the sun stays low, and times near sunrise or sunset where refraction affects altitude. Use true north, not magnetic north, or apply magnetic declination to correct field compass bearings. If you use city lookups, remember local terrain and obstructions are not included, so check site photos before finalizing dimensions or material estimate items.

Step-by-Step: Use the Horizontal Shadow Angle Calculator

Here’s a concise overview before we dive into the key points:

1. Enter the project location (latitude and longitude or select a city).
2. Set the date, time, time zone, and whether DST is active.
3. Input the facade azimuth (bearing of the outward normal from true north).
4. Optionally enter wall tilt or paste known solar azimuth/altitude values.
5. Click Calculate to compute HSA and related angles.
6. Compare HSA to your target cut-off angle for vertical fins or side reveals.

These points provide quick orientation—use them alongside the full explanations in this page.

Worked Examples

Case 1: An office facade faces due south (β_surf = 180°). A site weather file for a critical summer hour gives solar azimuth γ = 205° and solar altitude α = 62°. Compute HSA = wrap_to_±180(205° − 180°) = +25°. Then VSA from tan(VSA) = tan(62°)/cos(25°). Numerically: tan(62°) ≈ 1.881; cos(25°) ≈ 0.906; tan(VSA) ≈ 2.075; VSA ≈ 64.6°. What this means: The sun is 25° to the right of the facade normal; a strong overhang must address a 64.6° profile angle to cut sun while keeping views.

Case 2: A residential facade faces due west (β_surf = 270°). For an evening overheating check, the solar azimuth is γ = 260° and solar altitude α = 20°. Compute HSA = wrap_to_±180(260° − 270°) = −10°. For a jamb-mounted vertical fin with glazing setback S = 0.30 m, a simple plan cut-off relation is P ≥ S × tan(|HSA_cut|). For |HSA_cut| = 10°, P ≥ 0.30 × 0.176 = 0.053 m, so a 55 mm projection will block that plan direction. What this means: The sun is 10° to the left of the facade normal; even a modest fin controls late sun without excessive material use.

Limits of the Horizontal Shadow Angle Approach

HSA is powerful but not a complete shading model. It focuses on plan-angle geometry and assumes clear lines of sight to the sun. Real sites have terrain, nearby buildings, and specular reflections that change performance.

• Convention risk: different texts define azimuth from north or south; stay consistent.
• Time errors: clock time is not local solar time; equation of time and longitude shift matter.
• Near-horizon uncertainty: refraction and obstruction make sunrise/sunset less reliable.
• Diffuse light: HSA does not capture sky diffuse, ground-reflected, or internal reflections.
• Magnetic vs true north: field bearings need declination correction for accurate results.

Use HSA for quick sizing and coordination. For final performance claims, verify with full sun-path checks or simulation, then adjust dimensions to control glare and reduce wastage during fabrication.

Units and Symbols

Clear units prevent mistakes when you share results across teams. Angles are in degrees, bearings are clockwise from true north unless noted, and times should reference the local time zone and UTC offsets.

Use the table to align your inputs and outputs. If your field notes use magnetic bearings, convert to true north before entering β_surf. When importing weather file azimuths, confirm they match the same clockwise-from-north convention.

Troubleshooting

If your HSA results look wrong, a few common issues account for most errors. Start by checking conventions and time inputs. Then confirm the facade azimuth came from a true-north reference, not a building grid or a magnetic bearing.

• HSA sign seems flipped: swap your azimuth reference or confirm clockwise-from-north convention.
• Midday results off: verify local solar time vs clock time, and apply the equation of time.
• Strange sunrise/sunset values: the sun altitude near 0° is sensitive to refraction and obstructions.
• Facade azimuth mismatch: correct for magnetic declination or re-survey with a GNSS/compass app set to true north.

Once conventions and times are aligned, rerun the Calculator. Document the inputs in your drawings so procurement and site teams can reproduce results and control dimensions precisely.

FAQ about Horizontal Shadow Angle Calculator

What is the difference between HSA and VSA?

HSA is the plan angle between the sun and the facade normal. VSA is the vertical profile angle that combines sun altitude with HSA to gauge overhang performance.

Can I use HSA for roof shading?

HSA is most useful for vertical surfaces and vertical fins. For roofs or horizontal overhangs, VSA and tilt-based geometry give more relevant cut-off information.

How accurate is the Calculator if I only choose a city?

City lookups are good for early design. For final sizing, use exact latitude and longitude and confirm time zone and daylight saving settings to tighten the estimate.

Does magnetic declination matter?

Yes. Field compass bearings point to magnetic north. Convert to true north using local declination; otherwise, HSA may be biased by several degrees.

Horizontal Shadow Angle Terms & Definitions

Horizontal Shadow Angle

The plan angle between a facade’s outward normal and the sun’s bearing. It indicates how oblique the sun is to the facade.

Solar azimuth angle

The sun’s compass bearing along the horizon measured from true north, clockwise. It describes where the sun is in plan.

Solar altitude angle

The angle of the sun above the horizon. It pairs with azimuth to define the sun’s position in the sky.

Surface (facade) azimuth

The compass bearing of the outward normal to a facade measured from true north, clockwise. It sets the facade’s orientation in plan.

Vertical Shadow Angle (profile angle)

The angle in a plane perpendicular to the facade that combines altitude and HSA. It governs overhang cut-off behavior.

Hour angle

The angular measure of time relative to solar noon. It advances 15° per hour, positive in the afternoon.

Solar declination

The tilt of the sun’s apparent position north or south of the equatorial plane. It varies seasonally between about ±23.45°.

Local solar time

Time referenced to the sun crossing the local meridian at solar noon. It differs from clock time due to longitude and the equation of time.

Sources & Further Reading

Here’s a concise overview before we dive into the key points:

• NREL Solar Position Algorithm (SPA) documentation
• NOAA Solar Calculator: sun position by location and date
• PV Education: Solar zenith and azimuth basics
• Wikipedia: Solar azimuth angle
• CIBSE Knowledge: Solar shading design guidance
• ASHRAE Handbook Fundamentals: Solar geometry and loads

These points provide quick orientation—use them alongside the full explanations in this page.