Measuring Roadway Curve Radius
Using the Compass Method


by John C. Glennon and James R. Loumiet
January 2003

 A very common method used by accident investigators is to calculate roadway curve radii from chord-offset measurements taken in the field. The Chord-Offset Method is taught in most of the major accident reconstruction schools and is described in the Northwestern Traffic Institute's 1990 book, Traffic Accident Reconstruction, by Lynn B. Fricke.

The Chord-Offset Method usually uses a 100-foot tape held on either end at the precise edge of the roadway, while a carpenter's rule is used at the middle of the tape to measure the distance between the edge of the tape and the edge of the roadway. These two measurements, the 100-foot chord length and the measured middle offset, are then used in the following equation to compute the radius:

R = L2 /8m + m/2

Where

R = the roadway curve radius, feet

L = the chord length, feet

m = the measured middle offset, feet
Although the Chord-Offset Method is widely used , it has inherent weaknesses that make it a questionable practice, as follows:
  1. Unless investigators can precisely layout, tie down, and keep taunt a string line for their chord, they will need at least one other person to help with the measurements.
  2. The Chord-Offset Method is dependent on having a clearly definable arc on the roadway. Unpaved roadways have variable edges. Most asphalt pavements or painted edgelines and centerlines do not have a true edge throughout. Concrete pavements with curves have a more definable arc, but are not necessarily true.
  3. The tape or string must be held taunt or will not accurately represent a true chord.
  4. Measuring a chord-offset often puts investigators in harms way on high-speed and/or high-volume roadways.
  5. The Chord-Offset equation is very sensitive to small inaccuracies in measuring the middle offset.
This paper presents a simpler, safer, and more accurate method to measure roadway curve radius in the field. For reference purposes here, this method will be called the Compass Method. The Compass Method involves measuring the length of the roadway curve and its total change in direction. The roadway curve length, L, can be measured around the curve with a measuring wheel. To measure the change in direction involves using a simple compass to measure the compass heading of each tangent approach to the curve, and taking the difference between these headings. The radius of the roadway curve, R, is then calculated using the formula:

R = 57.3L/DC

Where

R = the roadway curve radius, in feet

L = the roadway curve length in feet, and

DC = the change in roadway direction, in degrees.
For circular roadway curves, this method will yield a more accurate estimate of curve radius than the Chord-Offset Method. As discussed earlier, the Chord-Offset Method can be sensitive to common deviations associated with wavy or ragged pavement edges or fluctuations along the centerline or edglines of the highway. In using the Compass Method, however, the only caveat is when the roadway curve is spiraled, multi-centered, or simply laid out without a specific geometric shape. Of course, in these cases, the Chord-Offset method can give very erroneous answers. The Compass Method, on the other hand, will give a reasonably accurate estimate of the average radius around the curve.

From a practical standpoint, a measuring compass and a measuring wheel are easier and safer to handle in the field than a measuring tape. The Compass Method is also a one person task, as opposed to the two or three people needed to accurately make chord-offset measurements.

With the Compass Method, the roadway curve can be safely measured from the shoulder using the measuring compass and measuring wheel. After the radius, R, is calculated, the investigator can then add or subtract the appropriate distance to the calculated radius to determine the radius of any arc on the roadway. For example, if the radius of a curve measured at the inside edgeline is 580 feet, and the normal distance between that edgeline and the centerline is 12 feet, then the radius of the centerline is 592 feet. During this entire operation, the investigator never has to enter the roadway, or stoop on the pavement to make measurements.

In summary, the Compass Method of measuring radii of roadway curves is a safe, accurate, simple, quick, and inexpensive method for determining the radius of roadway curve, and as such is an attractive technique for accident investigators.


About the Author

Dr. John C. Glennon is a traffic engineer with over 45 years experience. He has over 120 publications. He is the author of the book "Roadway Safety and Tort Liability" and is frequently called to testify both about roadway defects and as a crash reconstructionist.

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