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🎂 Wedding Cake Zoning Architect
This is not a floor-area-ratio problem. Before 1961, New York City controlled skyscraper massing with a "sky exposure plane": build straight up to a base height for free, then every metre you step back from the street buys you several more metres of height — on a smaller floor plate. Push the setback too far and you're adding height to almost no floor area. Don't set back at all and you get no bonus height either. Somewhere in between is the real optimum.
Zoning
Street width: 20 m, district ratio K=1.5 → base height 30 m
Sky exposure plane slope: 2.5 m height per 1 m setback
Site: 25 m wide × 30 m deep, floor-to-floor 3.5 m
Your Setback
Live Result
—
Total Floor Area (m²)
—
Total Height (m)
🎯 Goal: find the setback distance that maximizes total buildable floor area — not the tallest building, the most floor area.
Powered by the exact quadratic footprint/height
trade-off (
engine/setback-zoning.js) — the optimum (d=15m, half
the site depth) is verified before publishing two independent ways: by
calculus (dA/dd=0) and by a brute-force numerical scan across the whole
range, which agree to within scan resolution.Method
NYC 1916 ZoningSky exposure plane — base height + setback-proportional height bonus; the historical origin of "wedding cake" skyscraper massing.
ResultA(d) = (H0/hf)WsiteDsite + (Rd/hf)Wsite(Dsite−d) — maximized at d=Dsite/2, independent of R, H0, or Wsite.