A surveyor's wheel, also called a clickwheel, hodometer, waywiser, trundle wheel

Trundle wheel

The trundle wheel is a measuring device, a simplified form of a surveyor's wheel. It is commonly used by school children who need an easy way to find the rough distance from one place to another...

, measuring wheel, or perambulator is a device for measuring distance.

Origin

The origins of the surveyor's wheel are connected to the origins of the odometer

Odometer

An odometer or odograph is an instrument that indicates distance traveled by a vehicle, such as a bicycle or automobile. The device may be electronic, mechanical, or a combination of the two. The word derives from the Greek words hodós and métron...

. 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

Odometer

An odometer or odograph is an instrument that indicates distance traveled by a vehicle, such as a bicycle or automobile. The device may be electronic, mechanical, or a combination of the two. The word derives from the Greek words hodós and métron...

.

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

Aluminium

Aluminium or aluminum is a silvery white member of the boron group of chemical elements. It has the symbol Al, and its atomic number is 13. It is not soluble in water under normal circumstances....

, with solid or pneumatic tire

Tire

A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...

s on the wheel. Some can fold for transport or storage.

How the surveyor's wheel works

The surveyor's wheel is marked in fractional increments of revolution from a reference position and its current position can be represented as 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 radians or turns

Turn (geometry)

A turn is an angle equal to a 360° or 2 radians or \tau radians. A turn is also referred to as a revolution or complete rotation or full circle or cycle or rev or rot....

. In this situation, the fraction, , would be the relevant ratio. The usefulness of this ratio becomes clear after further consideration of the equation for the arc length of a circle.

This equation is

,

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

.

The equation for the circumference of a circle, , can clearly be seen and simplifying gives,

.

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

Yard

A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...

, metre

Metre

The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

 or half-rod

Rod (unit)

The rod is a unit of length equal to 5.5 yards, 5.0292 metres, 16.5 feet, or of a statute mile. A rod is the same length as a perch or a pole. In old English, the term lug is also used.-History:...

. 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.

External links

• Perambulator Information on the use of perambulators in surveying in Queensland, Australia in the 19th century.
• Waywisers at the Smithsonian National Museum of American History
• Example of 16th century German hodometer