Shadow Study

Give it a height, a place, and a date, and it computes where the shadow falls. The sun's position is geometry, worked out from formulas and shown step by step. Everything about your site, and everything the jurisdiction demands, is yours to supply.

Workflow

Step 1. Establish place, time, and heights

Ask, in one message:

1. Where is the site? A latitude and longitude, or a city and the latitude you want used. I will state the value I am computing with so you can check it.
2. Which dates and local times? Solstices and equinox at morning, noon, and afternoon are the usual set, but your jurisdiction or your question may name others.
3. The time zone, and whether daylight saving applies on those dates.
4. The massing heights, per option, and the face each height belongs to.
5. Is there a line the shadow must not cross? If so, its distance and direction from the building face.

Confirm the latitude and time zone back before computing. A shadow study run in the wrong time zone is wrong by an hour of sun and looks fine.

Step 2. Compute the sun position, showing the formulas

For each date and time, compute and print, with the formula named on each line:

declination     <formula, then arithmetic>
hour angle      <from local solar time, arithmetic shown>
solar altitude  <formula, then arithmetic>
solar azimuth   <formula, then arithmetic>

These are the published astronomy relations, and they are the one thing this skill supplies itself. State that plainly in the output, and state the approximation: minute-level precision is not the point at massing stage, and anyone needing better runs the model.

If the altitude comes out at or below zero, the sun is down at that time and the row says so instead of printing a shadow length.

Step 3. Compute the shadows

Per option, per time:

shadow length    = height / tan(altitude)     <arithmetic>
shadow direction = azimuth + 180 degrees      <stated as a bearing>
reach            <length compared to the distance you gave, if any>

Flat ground, stated on every run. If the user gave grades, apply them, showing the arithmetic; if the geometry gets beyond a plane and a slope, say so and stop rather than approximating silently.

Step 4. Report

One table, options as rows or columns as fits:

Option	Date, time	Altitude	Shadow length	Direction	Reaches your line?

Then, in prose: which option casts the longest shadow at the times you named, and where the differences between options actually show up. If a jurisdiction criterion was supplied, state each option against it, quoting the criterion as you gave it. If none was supplied, say that reach is geometry, not a verdict, and the rule to hold it against is yours to bring.

Close every run with: flat ground assumed, context not modeled, and a submission-grade study comes from a 3D model with the survey in it.

Step 5. Save, if asked

Ask whether to write the study to a file and where. Write it directly, including the formula lines. There is no template and no script.

Rules

• The solar formulas are the only thing this skill knows. Every height, distance, grade, and criterion comes from you, and each carries its source in the output.
• Print the formula before the arithmetic, every time. A sun angle nobody can re-derive is not checkable.
• Confirm latitude and time zone back to the user before computing.
• A shadow reaching a line is a measurement. Whether that is a problem is the jurisdiction's rule, quoted from what you supplied, or stated as an open question.
• Never convert the user's units. Heights in, shadow lengths out, in the same unit.
• Say on every run that this is a massing-stage study, not a submission.

Anti-patterns

• Recalling a city's shadow ordinance ("Toronto protects parks from 10am to 4pm") instead of asking for the criterion. Named hours and protected places are zoning text and go stale; the user brings them.
• Silently assuming solar noon when the user said noon. Clock noon and solar noon differ, and the difference is part of the arithmetic to show.
• Printing a shadow length for a sun below the horizon.
• Modeling a sloped site as flat without saying so.
• Presenting the table as proof of no impact. It is geometry for a decision, not a finding for a filing.

Resources

None. This skill is one file. Output is written directly at the path you choose.