- Luke M. Snell

# A “Revolutionary” Distance Calculator: the Surveyor’s Wheel

The surveyor's wheel, also called the measuring wheel, goes back to Greek and Roman times. The device was first used to estimate the distance between towns and follows a simple mathematical principle that we learned in grade school.

The circumference of a wheel is defined by the equation C = D, where C is the circumference of the wheel in feet, is constant, or 3.14159, and D is the diameter of the wheel in feet. Thus, if we know the diameter of the wheel and the number of times the wheel completes a revolution, we can calculate the distance between two points.

Alexander the Great used a surveyor’s wheel in 300 BC to estimate the distance between two cities on the Silk Route that were more than 500 miles apart. These measurements had 99.8 percent accuracy when checked with today’s modern equipment.

An auto's odometer uses this method, which measures distance by determining the number of revolutions that the tire turns. Of course, this is assuming that the tires are of specified size, diameter, and do not have appreciable wear.

The surveyor's wheel is a refinement of the "walking wheel" developed by John Metcalf. He used this equipment to build roads and canals throughout England in the 18th century. The wheel had a counter that kept track of the number of times the wheel had completed a revolution to determine the distance.

Today, there are many modifications to the surveyor’s wheel. There are small wheels for flat interior surfaces and bicycle-sized wheels suitable for outside use. These wheels have calibrated counters so that they directly provide the distance between two points.

There are several things to keep in mind when using the surveyor’s wheel:

Make sure the wheel surface is clean.

Set the gage to zero when you are at the starting point.

Walk as straight a line as is possible.

Keep a steady pace.

Take your reading of the distance directly from the equipment at your ending point.

Remember that this is an estimate of the distance.

There are many YouTube videos on how to use the surveyor's wheel including many provided by manufacturers.

Read the instruction manual which should provide detailed instructions.

Try out the surveyor’s wheel on a known distance to develop confidence using it.

So what type of accuracy can you get with a surveyor’s wheel? A research project done while I was a Professor of Construction at Southern Illinois University Edwardsville, examined the accuracy of a surveyor's wheel on various surfaces. The study was conducted utilizing different students using a bicycle-sized surveyor’s wheel measuring a distance determined using a steel tape.

Surface Distance (feet) Surveyor’s Wheel Percent Accuracy

Grass 300 99.72

Sidewalk 300 99.96

Building Interior 300 99.74

Gravel Parking Lot 100 99.74

Roadway 250 99.72

Roadway 1000 99.80

The surveyor’s wheel follows the contours of the ground or surface while conventional surveying measures the distance in a straight line between two points. Thus, the surveyor’s wheel will be expected to be less accurate and will likely slightly overestimate the distance.

From my observations, most of the measurement errors resulted from the users deviating from a straight line, not keeping a uniform pace, and inexact positioning of the surveyor’s wheel at the start and ending points. Our research indicates that individuals with minimal training could still achieve 99 percent accuracy on a variety of surfaces.

So when is it logical to use a surveyor’s wheel? The surveyor’s wheel is lightweight, easy to carry to remote locations, easy to learn how to use, and allows a person to take measurements at a speed of walking. The device has become the preferred measuring equipment for realtors, farmers, police departments (for accident reconstruction surveys), road and pipeline maintenance crews, and field engineers on projects when 99 percent accuracy is sufficient.

There are several types of surveyor’s wheels available; which is best depends on its intended use. For utilization in buildings, the small wheel unit is recommended to get the equipment closer to walls and create better accuracy. For outside use, a bicycle-sized surveyor’s wheel is best.

During our research several inexpensive plastic surveyor’s wheels were used. These provided similar accuracy but didn’t prove durable. They are recommended only for occasional use and must be carefully used and stored.

The surveyor's wheel will never replace the conventional surveying equipment needed on most construction projects. However, when a quick estimate of distance is required, the surveyor's wheel is often the device of choice.