Curve Data Conflict in a 1985 Metes-and-Bounds Deed
A 1985 deed conveys a parcel by metes and bounds, beginning at a found iron monument A (assume N 1000.00, E 1000.00) and running N 12°04'18" E, 214.63 ft to point B; thence along a circular curve to the left with radius 350.00 ft and central angle 38°42'00" to point C; thence S 76°18'00" W, 310.00 ft to point D; thence north to A. The deed states the arc length of the curve as 246.43 ft. No original monuments exist at B, C, or D. A field check shows the record traverse nearly closes, but the curve arc length is suspect. You are asked to compute the curve chord and to evaluate whether the deed's arc length is consistent with the radius and central angle.
1. Compute the chord length, chord bearing, and arc length of the curve from B to C.
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Convert the central angle: 38°42'00" = 38.7000°. Arc length = R × Δ in radians = 350.00 × (38.7000 × π/180) = 350.00 × 0.675442 = 236.40 ft. Chord length = 2R sin(Δ/2) = 2 × 350.00 × sin(19.3500°) = 700.00 × 0.33133 = 231.93 ft. The tangent bearing at B is N 12°04'18" E. Because the curve is to the left, the chord bearing is the tangent bearing minus Δ/2: 12°04'18" − 19°21'00" = −7°16'42", which is N 7°16'42" W. The computed arc length is 236.40 ft, not the deed's 246.43 ft; the difference is 10.03 ft. The record arc length is therefore inconsistent with the stated radius and central angle.
2. Which curve element controls if the deed's arc length conflicts with the radius and central angle, and how should the surveyor handle the discrepancy?
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Radius and central angle define the curve geometry; arc length is a derived quantity and serves as a mathematical check. When the deed's arc length conflicts with the radius and central angle by 10 ft, the surveyor should not silently use the erroneous arc length to set point C. The controlling elements are the radius, central angle, and tangent/chord geometry, unless an original monument at C controls-and here no original monument exists at C. The survey should show the record curve data, the computed arc and chord, the computed chord bearing, and a note identifying the 10.03-ft inconsistency. The surveyor should also check whether the 246.43-ft figure is a transcription error or a different curve element, and should not prepare a new description until the conflict is resolved. If the parties need a marketable description, legal review or a corrected deed may be required.