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For example, an ICBM warhead with a CEP of 100 meters will impact within 100 meters of the target point in at least 50% of all attempts.
The impact of munitions near the target tends to be normally distributed around the aim point, with most reasonably close, progressively fewer and fewer further away, and very few indeed at long distance.
A mathematician might characterise this pattern by its standard deviation, but a more intuitive method is to state the radius of a circle within which 50% of rounds will land. That radius is the circular error probable, commonly abbreviated to CEP.
For most weapons, the CEP increases with range, so it should either be stated for a particular range, or as an angleThis article is about angles in geometry. For other articles, see Angle (disambiguation An angle (from the Lat. angulus a corner, a diminutive, of which the primitive form, angus does not occur in Latin; cognate are the Lat. angere, to compress into a ben.
In the case of munitions which strike at a shallow angle to the Earth's surface, the pattern will become elongated into an ellipseThe Ellipse is also an elliptical street immediately in front of the White House. In mathematics, an ellipse is a figure corresponding to a circle which has been stretched in one direction. This is an example of a conic section and can be defined as the l. This can be thought of as the ellipse formed by the planeIn mathematics, a plane is the fundamental two-dimensional object. Intuitively, it may be visualized as a flat infinite piece of paper. Most of the fundamental work in geometry, trigonometry, and graphing is performed in two dimensions, or in other words, of the Earth's surface intersecting a coneA cone is a basic shape in geometry. Several things have also been called cones on account of their shape: A volcanic cone is a mountain formed by material ejected from a volcanic vent. In relativity, the light cone of an event consists of all spacetime e of error. In this case, the CEP is usually given as what it would be if the rounds impacted the surface vertically, and it must be remembered that at shallow trajectoriesIn ordinary language, a trajectory is the path followed by a body moving through space, for instance, the path taken by a falling body or the orbit of a planet. One may either consider just the geometry of the path (i. the set of positions), or also the p it will be elongated.
It should be noted that the concept of CEP is only strictly meaningful if misses are roughly normally distributed. This is generally not true for precision-guided munitionPrecision-guided munitions smart munitions or smart bombs are self-guiding weapons intended to maximize damage to the target while minimizing " collateral damage". Because the damage effects of an explosive weapon scale as a power law with distance, quites.
Another important thing to remember about CEP is that if 50% of rounds land inside the circle, then 50% land outside it! Generally, if CEP is n meters 50% of rounds land within n meters of the target, 43% between n and twice that distance and 7% between two and three times that distance. If misses were exactly normally distributed as in this theory, then the proportion of rounds that land farther than three times the CEP from the target is less than 0.2%.