# Surveyor's wheel

Surveyor's wheel

A surveyor's wheel, also called a clickwheel, hodometer, waywiser, trundle wheel, measuring wheel or perambulator is a device for measuring distance.

## Origin

An early surveyors wheel depicted in the hand of late 18th century British road builder John Metcalf.

The origins of the surveyor's wheel are connected to the origins of the odometer. While the latter is derived to measure distances travelled by a vehicle, the former is specialized to measure distances. Much of the material on the earliest stages in the development of the hodometer are adequately covered in odometer.

In the 17th century, the surveyor's wheel was re-introduced and used to measure distances. A single wheel is attached to a handle and the device can be pushed or pulled along by a person walking. Early devices were made of wood and may have an iron rim to provide strength. The wheels themselves would be made in the same manner as wagon wheels and often by the same makers. The measuring devices would be made by makers of scientific instruments and the device and handles would be attached to the wheel by them. The device to read the distance travelled would be mounted either near the hub of the wheel or at the top of the handle.

In some cases, double-wheel hodometers were constructed.

Modern surveyor's wheels are constructed primarily of aluminium, with solid or pneumatic tyres on the wheel. Some can fold for transport or storage.

## How the surveyor's wheel works

A diagram of a surveyor's wheel taking a measurement.

The surveyor's wheel is marked in fractional increments of revolution from a reference position and its current position can be represented as $\frac {a} {b}$ of a revolution from this reference, where a and b are integers. In the figure on the right, the blue line is the reference starting point. As the wheel turned during measurement, it is shown the wheel sweeps out an angle of $\frac{3}{4} \pi$ radians or $\frac{3}{8}$ turns. In this situation, the fraction, $\frac{3}{8}$, would be the relevant $\frac{a}{b}$ ratio. The usefulness of this ratio becomes clear after further consideration of the equation for the arc length of a circle.

This equation is

$s = \theta r$,

where $s$ is the arc length, $\theta$ is the angle, in radians, of the circle swept through and $r$ is the radius of the circle. Now, substitute into the arc length equation the conversion from radians to revolutions to obtain the form,

$s = \frac{a}{b} 2 \pi r$.

The equation for the circumference of a circle, $C=2 \pi r$, can clearly be seen and simplifying gives,

$s = \frac{a}{b} C$.

Thus showing that the base unit of measurement of the surveyor's wheel is determined only by the circumference of the wheel attached.

## Usage of the surveyor's wheel

Each revolution of the wheel measures a specific distance, such as a yard, metre or half-rod. Thus counting revolutions with a mechanical device attached to the wheel measures the distance directly.

Surveyor's wheels will provide a measure of good accuracy on a smooth surface, such as pavement. On rough terrain, wheel slippage and bouncing can reduce the accuracy. Soft sandy or muddy soil can also affect the rolling of the wheel. As well, obstacles in the way of the path may have to be accounted for separately. Good surveyors will keep track of any circumstance on the path that can influence the accuracy of the distance measured and either measure that portion with an alternative, such as a surveyor's tape or measuring tape, or make a reasonable estimate of the correction to apply.

Surveyor's wheels are used primarily for lower accuracy surveys. They are often used by road maintenance or underground utility workers and by farmers for fast measures over distances too inconvenient to measure with a surveyor's tape.

The surveyor's wheel measures the distance along a surface, whereas in normal land surveying, distances between points are usually measured horizontally with vertical measurements indicated in differences in elevation. Thus conventionally surveyed distances will be less than those measured by a surveyor's wheel.