Critical Root Zone Encroachment Percent
The encroachment check tree-protection-zone's follow-on named: how much of the CRZ a construction limit line cuts off, judged against species tolerance. A limit line at distance d slices a segment R^2 x acos(d/R) - d x sqrt(R^2 - d^2) out of the circle; encroach = segment / (pi x R^2) x 100. A wall 5 ft from a 20-in tree (R = 20 ft) encroaches 34% - fine for a tolerant species (40%), over the line for intermediate (30%) and sensitive (20%): same cut, three verdicts. Move it to 12 ft and it drops to 14%. A planning screen, not a tree-preservation permit.
Formula and source
radius = radius_factor x DBH; segment = radius^2 x acos(d/radius) - d x sqrt(radius^2 - d^2) for a limit line at distance d; encroach_pct = segment / (pi x radius^2) x 100; over when encroach_pct > threshold (tolerant 40 / intermediate 30 / sensitive 20).
Critical root zone encroachment (ANSI A300 Part 5 tree protection; arboriculture practice), by name.
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