Cosine error occurs in

measuring instrument A measuring instrument is a device to measure a physical quantity. In the physical sciences, quality assurance, and engineering, measurement is the activity of obtaining and comparing physical quantities of real-world objects and events. Establ ...

readings when the user of an instrument does not realize that the

vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

that an instrument is measuring does not coincide with the vector that the user wishes to measure. Often the lack of coincidence is subtle (with vectors ''almost'' coinciding), which is why the user does not notice it (or notices but fails to appreciate its importance). A simple example is taking a measurement across a

rectangle In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containi ...

but failing to realize that the line of measurement is not quite parallel with the edges, being slightly

diagonal In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word ''diagonal'' derives from the ancient Greek δ ...

. Rather than measuring the desired vector (in this case,

orthogonal In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...

width), the instrument is measuring the

hypotenuse In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equa ...

of a triangle in which the desired vector is in fact one of the legs. The cosine of this triangle correlates to how much error exists in the measurement (hence the name ''cosine error''). Thus the user might measure a block of metal and come away with a width of 208.92 mm when the true width is 208.91 mm, a difference that matters to the subsequent

machining Machining is a process in which a material (often metal) is cut to a desired final shape and size by a controlled material-removal process. The processes that have this common theme are collectively called subtractive manufacturing, which utilizes ...

. Although many workers might not use the term "cosine error" to name this mistake (instead calling it "failing to measure squarely"), the underlying concept is the same. For example, a novice at

carpentry Carpentry is a skilled trade and a craft in which the primary work performed is the cutting, shaping and installation of building materials during the construction of buildings, ships, timber bridges, concrete formwork, etc. Carpenters tr ...

might make this kind of mistake with a

tape measure A tape measure or measuring tape is a flexible ruler used to measure length or distance. It consists of a ribbon of cloth, plastic, fibre glass, or metal strip with linear measurement markings. It is a common measuring tool. Its design all ...

that is slightly

askew Askew is an English surname. Notable people with the surname include: Sports people *B. J. Askew (born 1980), American football player *Billy Askew (born 1959), English footballer *Carl Askew (born 1952), Australian motorcycle speedway and drag bi ...

, whereas a master carpenter would know by ingrained experience to measure squarely. A context in which potential cosine error must often be considered is in the use of an indicator (distance amplifying instrument). Cosine error can also affect laser interferometry. Another context in which potential cosine error draws attention is in

lidar traffic enforcement Lidar has a wide range of applications; one use is in Traffic enforcement camera, traffic enforcement and in particular speed limit enforcement, has been gradually replacing radar gun, radar since 2000. Current devices are designed to automate the ...

and radar traffic enforcement, where drivers assert that the speed measurement was in error because the lidar or radar signal was emitted in a direction not directly along the line of travel. (Cosine error always reduces the measured speed, thus favoring the motorist.) The extent to which it is true that the equipment is prone to this error, , has been argued in traffic courts. It is demonstrably true that missile-guiding radars are capable of accurately measuring the oblique movements of enemy aircraft under a variety of conditions, but to what degree traffic enforcement radar or lidar succeeds at this problem has been challenged by defendants, who speak of the cosine effect or cosine error effect.

Mitigation

The longer the length of the instrument, the easier it is to control cosine error. If the instrument is very small, then optical alignment techniques can be used to reduce cosine error.

References

{{Reflist Error detection and correction