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with marks of a known angular spacing, the principle of similar triangles can be used to find either 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
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This system is sufficiently precise for locating topographic details such as rivers, bridges, buildings, and roads when an accuracy of 1/500 (0.2%, 2000ppm) is acceptable. Stadia readings are also used to provide repeated, independent observations for improved accuracy and to provide error checking
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In practice, it can be seen that rough approximations may be made with a right triangle whose base (b) is equal to the distance of the 'rangefinder' from the eye; with the aperture (a) being the hole through which the target is sighted – the apex of this triangle being on the surface of the user's
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greatly simplify the trigonometry, enabling one to scale objects measured in milliradians through a telescope by a factor of 1000 for distance or height. An object 5 meters high, for example, will cover 1 mrad at 5000 meters, or 5 mrad at 1000 meters, or 25 mrad at 200 meters. Since the radian
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methods. Although much easier to use, electronic rangefinders can give away the shooter's position to a well-equipped adversary, and the need for accurate range estimation has existed for much longer than electronic rangefinders small and rugged enough to be suitable for military use.
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The instrument must be level for this method to work directly. If the instrument line of sight is inclined relative to the staff, the horizontal and vertical distance components must be determined. Some instruments have additional
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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 surveying instruments is 10 mrad and gives a
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telescopic sight reticle can be used to determine the distance from a 1.70-meter (5 ft 7 in) tall person or object from 200 m (bracket number 2 to the right) to 1,000 m (bracket number 10 to the
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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 aficionados to antique surveying methods.
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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.
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235:("mil" or "mrad") as the unit of angular measurement. Since a radian is defined as the angle formed when the length of a circular arc equals the radius of the circle, a
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The stadia method of distance measurement is primarily historical for surveying purposes, as distance nowadays is mostly measured by electronic or taping methods.
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is the angle formed when the length of a circular arc equals 1/1000 of the radius of the circle. For telescopic angles, the approximations of
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The approximate range of an object one foot (30.48 cm) in height covering roughly 100 milliradians is 10 feet (3.048 m) or:
189:• When the upper part of the body of a man (≈ 1 m tall) fits under the first line, he stands at approximately 400 meters distance.
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Table for range estimation showing target sizes, distances and corresponding angular measurements. Angular sizes are given in
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expresses a ratio, it is independent of the units used; an object 6 feet high covering 1 mrad will be 6000 feet distant.
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For a standard distance from the eye (b) of 28" (71.12 cm); this being the common length of an archer's draw:
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The above formula functions for any system of linear measure provided r and h are calculated with the same units.
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94:) which was the typical length of a sports stadium of the time. Stadiametric rangefinding is used for
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on a vertical circle to assist with these inclined measurements. These graduated circles, known as
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weapons of the 1940–70s used stadiametric range estimation based on the average sizes of
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Range (r) = approximate height of object (h) × (1000 ÷ aperture in milliradians (a))
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of the instrument, providing a known remote height for the distance calculations.
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Stadia readings used in surveying can be taken with modern instruments such as
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r = h(1000/a) → where r and h are identical units, and a is in milliradians.
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476:— demonstrates stadiametric rangefinding in an anti-tank weapon sight
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and other optics. It is still widely used in long-range military
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r = h/a → where r and h are identical units, and a is in radians
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55:: The stadiametric rangefinder in the bottom-left corner of the
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28" × 1 milliradian ≈ 0.028" (0.071 cm) -- stadia factor 1000
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Technique of measuring distances with a telescopic instrument
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10 milliradians ≈ 0.280" (0.711 cm) -- stadia factor x 100
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100 milliradians ≈ 2.80" (7.112 cm) -- stadia factor x10
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288:{\displaystyle \sin(\alpha )=\tan(\alpha )=\alpha }
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215:The stadia method is based upon the principle of
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355:. When using the stadia measuring method, a
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501:Length, distance, or range measuring devices
474:US Army FM 23-11: 90mm Recoilless Rifle, M67
449:, McGraw-Hill Book Company, 1966 LC 64–66263
204:, correctly ranging a tank at 275 m range.
445:Raymond Davis, Francis Foote, Joe Kelly,
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231:Stadiametric rangefinding often uses the
365:is held so that it appears between two
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480:Mils / MOA and the Range Equations
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78:. The term stadia comes from a
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53:Soldier observed at 400 m
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371:visible on the instrument's
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210:armoured fighting vehicles
88:(equal to 600 Greek feet,
200:Targeting reticle of the
68:Stadiametric rangefinding
385:stadia interval factor
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496:Measuring instruments
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76:telescopic instrument
403:against blunders in
349:plane-table alidades
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202:M67 recoilless rifle
470:"Technique of Fire"
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132:laser rangefinding
114:, as well as some
482:by Robert Simeone
217:similar triangles
171:telescopic sights
100:telescopic sights
16:(Redirected from
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108:artillery pieces
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18:Stadiametric
472:, Ch. 5 of
429:Rangefinder
424:Milliradian
393:graduations
358:level staff
345:theodolites
237:milliradian
233:milliradian
169:as used in
98:and in the
490:Categories
460:The Stadia
440:References
434:Stadimeter
363:stadia rod
116:binoculars
82:of length
80:Greek unit
405:levelling
377:telescope
335:Surveying
283:α
274:α
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256:α
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139:Principle
124:microwave
112:tank guns
96:surveying
70:, or the
418:See also
341:transits
206:Antitank
128:infrared
104:firearms
462:at the
373:reticle
225:reticle
221:tangent
120:sniping
85:Stadion
353:levels
60:left).
300:eye.
130:, or
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57:PSO-1
351:and
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361:or
265:tan
247:sin
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