Work-Zone Merging Taper Length and Device Count (MUTCD)
MUTCD merging-taper length for a lane closure and the channelizing devices it takes: for 40 mph or less L = W x S^2 / 60, for 45 mph or more L = W x S; devices = ceil(L / spacing) + 1. Closing a 12 ft lane at 55 mph needs a 660 ft taper and 18 cones at 40 ft spacing; at 30 mph the taper shortens to 180 ft (6 devices) because the low-speed branch uses the speed squared. The low- and high-speed branches are a deliberate step. Shifting, shoulder, and downstream tapers use fractions of L.
Formula and source
taper_length_ft = speed_mph <= 40 ? offset_width_ft x speed_mph^2 / 60 : offset_width_ft x speed_mph; devices = ceil(taper_length_ft / device_spacing_ft) + 1.
MUTCD merging-taper identity by name (L = W S^2/60 for S <= 40, L = W S for S >= 45); first-principles device-count arithmetic.
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