Stadiametric rangefinding

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Stadiametric rangefinding, or the stadia method is a technique of measuring distances with a telescopic instrument. The term stadia comes from a Greek unit of length. Stadiametric rangefinding is used for surveying and in the telescopic sights of firearms, artillery pieces, or tank guns, as well as some binoculars and other optics. It is still used in some light equipment, but in many professional applications it has been replaced with microwave, infrared, or laser range-finding methods.

1 Principle
2 Surveying
3 References
4 External links

[edit] Principle

Targeting reticule of the M67 recoilless rifle. Antitank weapons of the 1940–70s used stadiametric range estimation based on the average sizes of armoured fighting vehicles

The stadia method is based upon the principle that in similar triangles homologous sides are proportional. This means that, for a right triangle with a given angle, the ratio of adjacent side length to opposite side length (see sine) is constant. By using a reticle with marks of a known angular spacing then the the principle of similar triangles can be used to either find the distance to objects of known size, or the size of objects at a known distance. In either case, the known parameter is used, in conjunction with the angular measurement, to derive the length of the other side.

Since a radian is defined as the angle formed when the length of a circular arc equals the radius of the circle, a milliradian, or mil, is the angle formed when the length of a circular arc equals 1/1000 of the radius of the circle. An object 5 meters high, for example, will cover one mil at 5000 meters, or five mils at 1000 meters, or 25 mils at 200 meters. Since the radian expresses a ratio, it is independent of the units used; an object 6 feet high covering one mil will be 6000 feet distant.

[edit] Surveying

Stadia readings used in surveying can be taken with modern instruments such as transits, theodolites, plane-table alidades and levels. When using the stadia measuring method, a stadia rod is held so that it appears between two stadia marks visible on the instrument's reticle. The stadia rod has measurements written on it that can be read through the telescope of the instrument, providing a known length for the distance calculations.

An instrument equipped for stadia work has two horizontal stadia marks spaced equidistant from the center crosshair of the reticle. The interval between stadia marks in most stadia instruments gives a stadia interval factor of 100. The distance between the instrument and a stadia rod can be determined simply by multiplying the measurement between the stadia hairs (known as the stadia interval) by 100.

The instrument must be level for this method to work directly. If the instrument line of sight is inclined, the horizontal and vertical distance components must be determined. Some instruments have additional graduations on a vertical circle to assist with these inclined measurements. These graduated circles, known as stadia circles, provide the value of the horizontal and the vertical measurements as a percentage of the direct stadia measurement.

This system is sufficiently precise for locating topographic details such as rivers, bridges, buildings, and roads when an accuracy of 1/400 is acceptable.

The stadia method of distance measurement is primarily historical for surveying purposes, as distance nowadays is invariably measured by electronic or taping methods. Total station instruments do not have stadia lines marked on the reticle. Traditional methods are still used in areas where modern instruments are not common or by practitioners whose primary task is not surveying with sophisticated instruments.