Line (angle unit)

Compass rose with graduations

Dash hot in the nautical and the artillery common auxiliary units for specifying flat angles . There are two different angular units that also have different unit symbols and areas of application:

Nautical line : 1/32 full angle , i.e. 360 ° = 32 lines, 1 line = 11.25 °
Artillery line (also mil ; Switzerland: Artilleriepromille A ‰): 1/6400 full angle, i.e. 360 ° = 6400 line

The nautical bar has after the standard DIN 1301 Part 3, the unit symbol "and the artillery line, the unit character ¯. Both are written with no space behind the numerical value, z. B .: 8" or 1600 = 90 °.

The nautical line is related to the earlier customary division of the compass rose and corresponds to a quarter of 45 °, the angle difference between the eight " regions of the world " in ancient nautical science. The artillery line was introduced, among other things, because its sine is almost exactly one thousandth .

The nautical line

Physical unit
Unit name	Nautical line
Unit symbol	"
Physical quantity (s)	Flat angle
Formula symbol	${\ displaystyle \ alpha, \, \ beta, \, \ gamma, \, \ ldots}$
dimension	${\ displaystyle {\ mathsf {{\ frac {L} {L}} = 1}}}$
In SI units	${\ displaystyle \ mathrm {1 '' = {\ frac {\ pi} {16}} \; rad \ approx 0 {,} 196 \, 35 \; rad}}$
Named after	Scale mark on the compass
Derived from	Full angle
See also: angular dimensions

One nautical line corresponds to the 32nd part of a full circle, i.e. 11.25 ° or 200¯.

In shipping , the nautical angle unit dash is still sometimes used for side bearings for rough directional information. The division of lines can also be found in the division of the compass rose . However, compass bearings are usually carried out in degrees , angle measurements with the sextant in degrees with decimal minutes.

"Two lines further aft than abeam" , based on the direction of travel, i.e. 112.5 ° (= 90 ° + 22.5 °) or 247.5 ° (= 270 ° - 22.5 °), is an on in the collision prevention rules dimension related to the transverse axis of the ship. Anyone who is more than two lines further aft than abeam of a vehicle in front will see its white rear light and, if approaching, is considered to be overtaking and is therefore obliged to avoid it.

In shipbuilding, efforts are occasionally made to incorporate this rule into the design of bridges : the control stand protrudes to the front, and the rest of the bridge is sloped backwards up to the cams "two lines astern than abeam" so that the officer on watch has a clear view on the relevant sector.

The name four-line bearing is a special case of seawater bearing .

The artillery line

Physical unit
Unit name	Artillery line; mil
Unit symbol	${\ displaystyle \ mathrm {^ {-}}}$
Physical quantity (s)	Flat angle
Formula symbol	${\ displaystyle \ alpha, \, \ beta, \, \ gamma, \, \ ldots}$
dimension	${\ displaystyle {\ mathsf {{\ frac {L} {L}} = 1}}}$
In SI units	${\ displaystyle \ mathrm {1 \, mil = {\ frac {\ pi} {3200}} \; rad \ approx 0 {,} 001 \, rad}}$
Named after	Scale mark in the rifle scope
Derived from	Full angle
See also: Winkelmeß , Artilleriepromille , Mildot

The artillery line is used in particular in the military for surveying and fire control . A bar corresponding to 1/6400 full angle = 0.05625 degrees , or about 0.98175 milli radian .

advantages

practice

This adaptation results in the following advantages:

This results in "smooth" divisions (64 = 2 ⁶ ), example: 90 ° = 6400 lines / 4 = 1600 lines.
No decimal places are required for “normal” tasks.
Since 1 line covers an arc length of approx. 1 m over a distance of 1 km, simple calculations are possible with the MKS formula (see below).
Military binoculars, surveying and directional optics include reticles that allow an accurate reading of bar values. If a targeted object, for example 2 m high, covers exactly 1 line, it is 2 km away.

MKS formula

The so-called MKS formula is a simplified application of the ray theorem . It stands

M for meters of the target width
K for kilometers to the goal
S for line number of the angle covering the target.

The formula is resolved according to the size to be determined in each case

M = K × S
K = M / S
S = M / K

Application examples:

Determination of the distance from the target: If you see a vehicle with an estimated length of 6 m through binoculars and occupy this vehicle on the reticle with 12 lines, the distance from the vehicle is 0.5 km, because: K = 6 (m) / 12 (line) = 0.5 km.
Determination of the target width: If you see a building 2.5 km away in the binoculars that covers an angle of 10 lines, then this target has a width of 25 m, because: M = 2.5 (km) × 10 (line) = 25 m
Using the thumb jump: A jump of the thumb corresponds roughly to 100 lines: With a target at a distance of 0.1 km, the lateral offset of the jump of the thumb is 10 m. If the deposit is 20 m, then the target is 200 m away.

special cases

Sweden

In Sweden, a different division of a circle into 6300 parts ( stretch ) used to be common. 1 line then corresponded to 0.99733 milliradian, the MKS formula was fulfilled more precisely, but the numbers were inconvenient. The numbering of circles in Swedish directional means ends at 62 (63 = 0), so that such devices can be clearly assigned. The associated angle function tables only apply to these instruments, they cannot be used for the 6400 graduation.

Warsaw Pact states and Finland

In the army of the former USSR and later in the Warsaw Pact states and in Finland, a district division into 6000 lines was used.

armed forces

In the surveying and fire control of artillery and mortars, the angle of direction , direction of fire and partial ring are always given as an angle to the north of the grid in dashes.

Swiss artillery

Full circle with 6400 artillery bullets

In the Swiss Army , artillery promille is used instead of a dash to indicate an absolute direction. The usage differs in that 0 A ‰ (or 6400 A ‰) points to the north (north refers to the north of the grid ), while the indication in a dash is relative to the direction of sight .

Individual evidence

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