Taper lengths, buffer spaces and device spacing

A taper that is too short forces drivers to swerve. A buffer that is too short leaves no room for a driver who misjudges the taper. Devices spaced too far apart look like a scattering of cones rather than a line. These three numbers, taper length, buffer length and device spacing, are the arithmetic of a work zone, and a supervisor who can work them out, or at least check them, can spot a dangerous layout before anyone is hurt. This lesson shows where the numbers come from and works through examples on Larch Avenue and the state highway.

Why taper length depends on width and speed

A merging taper asks drivers to move sideways by the width of a lane while they keep moving forward. The wider the lane, the further they must move. The faster they are going, the more forward distance they cover while making that move, and the harder it is to find a gap in the next lane. So taper length grows with lane width and grows faster than speed.

The US manual expresses this with two formulas, one for lower speeds and one for higher speeds, and many Canadian manuals use the same relationships in their taper tables. In US units, with L the taper length in feet, W the width of the offset in feet and S the speed in miles per hour:

In metric units, with L in meters, W in meters and S in kilometers per hour:

The speed used is normally the posted speed limit before the work started, the 85th-percentile operating speed, or the expected operating speed, whichever the road authority specifies. Using a reduced work zone speed limit to shorten the taper is not allowed unless the road authority's rules say so, because many drivers do not slow down.

the Texas Manual on Uniform Traffic Control Devices (TMUTCD) uses the same formulas and gives them in tables. TxDOT's standard plan sheets also show taper lengths for common speeds and widths. The supervisor follows the road authority's requirements, using the formulas to check or to handle unusual widths.

Different tapers, different lengths

Once L, the merging taper length, is known, the other tapers are worked out from it.

Worked example: the curb lane on Larch Avenue

Buffer space: room to stop

The longitudinal buffer space gives a driver who enters the closed lane by mistake, or who loses control, room to stop before reaching workers. Its length is usually based on stopping sight distance: the distance a driver travels while seeing a hazard and reacting, plus the distance needed to brake to a stop.

Here d is the stopping distance, v the speed, t the perception-reaction time (2.5 seconds is commonly used in design) and a the deceleration rate (about 3.4 m/s², or 11.2 ft/s², a comfortable hard stop for most drivers on dry pavement). The program below computes stopping sight distance and compares it with the rounded values commonly used for buffers.

# Stopping sight distance for buffer lengths (t = 2.5 s, a = 3.4 m/s^2).
def ssd_m(kmh, t=2.5, a=3.4):
    v = kmh / 3.6
    return v * t + v * v / (2 * a)
def ssd_ft(mph, t=2.5, a=11.2):
    v = mph * 5280 / 3600
    return v * t + v * v / (2 * a)
print("km/h   SSD (m)")
for kmh in (40, 50, 60, 70, 80, 100):
    print(f"{kmh:>4}   {ssd_m(kmh):6.0f}")
print("mph    SSD (ft)")
for mph in (25, 35, 45, 55, 65):
    print(f"{mph:>4}   {ssd_ft(mph):6.0f}")

km/h   SSD (m)
  40       46
  50       63
  60       83
  70      104
  80      128
 100      183
mph    SSD (ft)
  25      152
  35      246
  45      359
  55      492
  65      644

At 35 mph the stopping sight distance is about 246 ft, close to the 250 ft value in the MUTCD's buffer table, and at 65 mph it is about 644 ft. Where the work space is short or the buffer cannot fit, the solution is to change the layout, close more of the road or protect the work space with a truck-mounted attenuator, not to shrink the buffer.

A lateral buffer, between the open lane and the edge of the work space, matters too. Even a meter (about 3 ft) of empty space between passing traffic and workers lowers the risk of being clipped by mirrors, trailers or a vehicle that drifts. Where a lateral buffer is not possible, a speed reduction, a closure of the next lane or positive protection should be considered.

Device spacing

Devices must look like a line, not a scatter. The closer the spacing, the clearer the line, especially at night and in rain. On the US side, the MUTCD's guidance is simple: in a taper, the maximum spacing in feet is about the speed in miles per hour; along the work space, about twice that. In metric terms, that works out to roughly a fifth of the speed in km/h, in meters, in the taper, and two fifths along the work space. Road authorities' tables may specify closer spacing in urban areas and at intersections.

import math
# Devices needed for a taper and a tangent, using the spacing rule of thumb.
def devices(length, spacing):
    return math.floor(length / spacing) + 1
# Metric: spacing in taper ~ 0.19 x km/h (m); tangent ~ 0.38 x km/h
for name, kmh, taper, tangent in (("Larch Ave", 50, 60, 140), ("Highway tie-in", 100, 231, 400)):
    st, sg = round(0.19 * kmh), round(0.38 * kmh)
    print(f"{name}: taper {taper} m at {st} m -> {devices(taper, st)} devices; "
          f"tangent {tangent} m at {sg} m -> {devices(tangent, sg)} devices")

Larch Ave: taper 60 m at 10 m -> 7 devices; tangent 140 m at 19 m -> 8 devices
Highway tie-in: taper 231 m at 19 m -> 13 devices; tangent 400 m at 38 m -> 11 devices

Putting the numbers together

The full length of a lane closure is the advance warning area, plus the taper, plus the buffer, plus the work space, plus the termination area. On a highway, that can easily exceed 1.5 km (about a mile). On a city street, it may not fit in one block, which is why advance warning signs are often placed on the approach block and why some city jobs close a whole block to traffic rather than one lane. When the numbers will not fit, the answer is a different layout, not a shorter taper or buffer.

Checking a layout in the field

Supervisors rarely carry a tape long enough to measure a highway taper, so they pace it, count devices or use the lane line markings, which are painted at a regular pattern on most roads, to estimate distance. On Larch Avenue, Nadia's crew knew that their cone spacing in the taper was 30 ft (about 9 m), so a taper of seven cones gave about 54 m from first cone to last, close enough to the planned 60 m with the first cone placed at the edge line. On the highway job, the crew measured the taper with a wheel at set-up and marked the start and end with paint on the shoulder, so later crews could set up in exactly the same place each morning.

Rounding and judgment

Formulas give a minimum, and in the field the numbers are rounded up, never down. Where a curve, a hill crest or a busy driveway sits near the start of the taper, supervisors move the taper or lengthen it so drivers can see it well in advance.