Stadiametric distance measurement

The stadiametric rangefinding is a method for distance measurement, which is used in optical instruments. It is used, for example, in telescopic sights , but also in binoculars . Although more modern devices such as laser and infrared rangefinders are now available, it is still used. The stadimeter is a nautical and optical measuring instrument in which this method is also used.

Basics

Principle of the stadiametric range finder

The stadiametric distance measurement makes use of the fact that an object appears smaller when it is further away from the observer. An object with the width B appears at the distance E _{1 to} an observer at the point O with an apparent width of . At the distance E ₂ , the object appears to the observer only with an apparent width of . The distance is inversely proportional to the apparent width: ${\displaystyle \beta _{1}}$ ${\displaystyle \beta _{2}}$

${\displaystyle {\begin{aligned}\tan \beta &={\frac {B}{E}}\\E&={\frac {B}{\tan \beta }}\end{aligned}}}$

By measuring the angle , if the distance E is known, the width B of the object or, if the width B is known, the distance E can be determined. To simplify matters, the chord is equated with the arc of a circle . This is acceptable because the error that arises in the angles to be measured is significantly smaller than the reading accuracy. ${\displaystyle \beta }$

Since the calculation with degrees or degrees is difficult to handle for military use and the accuracy achieved is not required, the line angle is used for simplification . In western armed forces, the division of the full circle into 6,400 lines has become common practice, in the Soviet Army and the allied armed forces the division into 6,000 lines was common. A full circle with a diameter of 1000 m has a circumference of 6000 or 6400 m. This means that distances or sizes can be determined approximately using the so-called thousand formula:

${\displaystyle E={\frac {1000*B}{abgeleseneStrichzahl}}}$

This method of determining the distance has some fundamental errors, but the accuracy achieved is quite sufficient for many applications.

Target optics

construction

Representation of the distance measuring scale of the riflescope PSO-1

To measure angles, corresponding markings are made in the target optics or binoculars. Either crosshairs , special distance measuring scales or a combination of both can be inserted. Crosshairs and scales are fixed, so they don't change size when you focus on a distant target.

With a crosshair, a vertical and horizontal graticule with line division is usually reflected. The advantage is that objects of any size can be measured with the help of the graticule. The disadvantage is that the distance cannot be read, but has to be calculated. Under certain circumstances, this can be disadvantageous in combat conditions.

For target optics of military weapons, distance measuring scales have therefore become established which are designed for a typical object of known size. In the Soviet PSO-1 riflescope, for example, the average height of a person is used as the basis for the distance measuring scale. If the target is grasped between the horizontally running baseline and the corresponding measuring mark, the distance can be read off immediately on the scale. In practice, crosshairs and distance measuring scales are usually combined in the target optics. Different manufacturers have different ideas about the shape and arrangement of the target marks.

application

The stadiametric distance measurement is used in binoculars, which in many cases have a reticle. This type of distance measurement is easy to use and works without additional energy sources.

Target optics of hunting weapons often also have a reticle with which distances can be determined.

The main area of ​​application for stadiametric distance measurement is target optics for military weapons. Rifle scopes for rifles often have a reticle, and in some cases also have a distance measuring scale. The accuracy of the distance determination is not very high, so that in the meantime external rangefinders are used in many cases, especially when using precision weapons . Laser rangefinders, however, can give away the position of the shooter through their radiation, so that the stadiametric rangefinder have advantages in certain tactical situations.

For anti-tank guns and tank guns , stadiametric rangefinders are also used. The advantage here is also the simple structure and ease of use. With the increase in the range of these cannons from the end of the 1950s, however, it became apparent that this type of distance measurement was too imprecise. Therefore, from the 1960s onwards, coincidence or spatial distance meters were increasingly used. From the 1980s these were replaced by laser rangefinders. Conventional target optics with distance measuring scales are still used; they serve as a reserve in the event of failure of the electronic distance measuring systems.

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  Marine binoculars with reticle and mirrored compass

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  View through an optic with graticules

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  Looking through a PSO-1. The reticle is used to determine the lead and breakpoint, the distance measuring scale is located under the crosshairs.

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  Rifle scope of the Panzerfaust 44 . The measuring marks correspond to the typical size of a tank at the corresponding distance

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  Depiction of the distance measuring scale of the Panzerfaust M67. The destination is at a distance of 275 m.

Stadimeter

US Navy Stadimeter Mk 5 Mod 0

The stadimeter is a measuring instrument that is mainly used in shipping . It can be used to determine distances to other ships and distances to known landmarks . The way a stadimeter works is also based on measuring an angle. With a known height, the distance to the object can be calculated from the angle between the horizon and the top of the object. More modern stadimeters are similar in structure to sextants . Like these, mirrors are also used in the beam path of the Stadimeter. The main difference is that the height of the object to be tracked must be set on the pointer arm before the bearing is taken. Earlier stadimeters still had a linear scale on which the height had to be set and fixed with the help of a worm gear. The newer design enables the faster direction finding of different objects. Instead of the sextant's degree arc, the stadimeter has a scale on which the determined distance can be read directly.

The first stadimeter was developed by Bradley Allen Fiske, an officer in the US Navy . Originally it was only intended to determine the distance for the ship artillery. It soon turned out, however, that it could also be used to measure the distance between ships during convoy trips or to find landmarks. Compared to coincidence or spatial rangefinders , it was less precise, but cheaper to manufacture and easier and faster to use. In the 1890s, the US Navy procured several types of stadimeters. During the Second World War , the version that is still used today and is similar to the sextant was developed. Such stadimeters are still used today by various naval forces, such as the US Navy or Royal Canadian Navy . They are used when a radiation-free distance measurement is required.

As early as 1919, submarine periscopes were equipped with stadimeters. They were used to determine the distance necessary for calculating the firing solution for torpedoes . Coincidence or spatial rangefinders were too bulky and heavy for use on board submarines. The mast height required to determine the correct distance could be found in manuals. By the Second World War, periscopes with stadimeters had largely gained acceptance.

A type of improvised stadimeter was used by British pilots during Operation Chastise . Since the Dambuster bombs used had to be dropped at a precisely defined distance in front of the dam wall, the problem of continually determining the distance in low flight arose. The problem was solved by using an isosceles triangle to aim for the towers at the ends of the dam and to compare them with the plane. Since the launch angle was calculable, the length of the base was chosen so that at the correct distance for launching the bearing marks covered the towers and the bombs could be released at the correct distance and at the correct height in front of the dam.

Stadimeters have also been used in space. A stadimeter was used next to a sextant on board the Skylab space station . The aim of the experiments was to test whether the ability to work precisely in space is retained even during longer flights.

Web links

• US Army FM 23-11: 90mm Recoilless Rifle, M67 , chapter 5 (English)
• Optical aiming devices (PDF; 291 kB)

literature

• Fred A. Carson: Basic Optics and Optical Instruments. Dover Publications, Mineola, NY 1997, ISBN 0-486-22291-8 . (English)
• Richard M. Ogorkiewicz : Technology of Tanks. Jane's Information Group, 1991, ISBN 0-7106-0595-1 . (English)
• Norman Friedman: US Submarines Through 1945: An Illustrated Design History. US Naval Institute Press, 1995, ISBN 1-55750-263-3 . (English)
• The Naval Institute Guide to World Naval Weapons Systems, 1997-1998. US Naval Institute Press, 1997, ISBN 1-55750-268-4 . (English)
• Bernd Leitenberger: Skylab. America's only space station. Books on Demand , 2011, ISBN 978-3-8423-1864-9 .

Individual evidence

1. ↑ see 1943 Stadimeter (English)
2. ↑ see Friedmann, p. 279.
3. ↑ see Leitenberger, p. 279.