# Effective range

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{{Short description|Operational range in various contexts}}
{{Split|date=January 2026}}
{{Dicdef|date=June 2023}}

'''Effective range''' is a term with several definitions depending upon context.

==Distance==
Effective range may describe a distance between two points where one point is subject to an [energy](/source/energy) release at the other point. The [source](/source/Point_source), receiver, and conditions between the two points must be specified to define an effective range. Effective range may represent the maximum distance at which a measuring device or receiver will predictably respond to an energy release of specified magnitude. Alternatively, effective range may be the maximum distance at which the energy released from a specified device will cause the desired effect on a target receiver. Angular dispersion may be significant to effectiveness for asymmetrical energy [propagation](/source/Wave_propagation) toward small targets.

===Weapons===
The following definition has been attributed to the [United States Department of Defense](/source/United_States_Department_of_Defense): ''The maximum distance at which a weapon may be expected to be accurate and achieve the desired effect.''<ref>{{cite web |url=https://www.militaryfactory.com/dictionary/military-terms-defined.asp?term_id=3284 |title=maximum effective range Definition (US DoD) |website=Military Factory |access-date=12 March 2019 }}</ref> Accuracy is ambiguous in the absence of a specified hit probability per unit of [ammunition](/source/ammunition); and for any given [weapon](/source/weapon), the desired effect could be interpreted differently depending upon the target. Subjective interpretation of these variables has caused endless and heated [debate](/source/debate) for more than a century.<ref>{{cite book |last=Dodd |first=Mead |title =New International Encyclopedia |publisher =Princeton University |volume =19 |date =1916 |pages =542 }}</ref>

{{Off topic|date=May 2024}}

With the addition of [clinometer](/source/clinometer)s fixed [machine gun](/source/machine_gun) squads could set long ranges and deliver [plunging fire](/source/plunging_fire) or [indirect fire](/source/indirect_fire) at more than {{convert|2500|m|yd|abbr=on|-1}}. This indirect firing method exploits the maximal practical range, that is defined by the maximum range of a small-arms projectile while still maintaining the minimum [kinetic energy](/source/kinetic_energy) required to put unprotected personnel out of action, which is generally believed to be 15 kilogram-meters (147&nbsp;J / 108&nbsp;ft⋅lbf).<ref name="krtraining1">{{cite magazine |author1=Kjellgren, G. L. M. |url=http://www.krtraining.com/KRTraining/Archive/PracticalRangeSmallArms.pdf|title=The Practical Range of Small Arms|archive-url=https://web.archive.org/web/20150305142959/http://www.krtraining.com/KRTraining/Archive/PracticalRangeSmallArms.pdf |archive-date=5 March 2015 |magazine=The American Rifleman |pages= 40–44|url-status=live}}</ref>
Advanced planned and unplanned  map and range table predicted support/harassment firing methods developed during [World War I](/source/World_War_I) like plunging fire or indirect fire were not as commonly used by machine gunners during World War II and later as they were during World War I.<ref>{{cite web |title=How The Machine Gun Changed Combat During World War I |website=Norwich University Online |url=https://online.norwich.edu/academic-programs/resources/how-machine-gun-changed-combat-during-world-war-i |access-date=2023-08-05 |archive-date=2023-08-26 |archive-url=https://web.archive.org/web/20230826184131/https://online.norwich.edu/academic-programs/resources/how-machine-gun-changed-combat-during-world-war-i |url-status=dead }}</ref>

===Vehicles===
In a broader context, effective range describes the distance a vehicle (including weapon launch platforms like a [ship](/source/ship) or [aircraft](/source/aircraft)) may be expected to deliver a specified payload from a [base](/source/Military_base) or refueling point.<ref>{{cite web |url=https://www.merriam-webster.com/dictionary/effective%20range |title=effective range |publisher=Merriam-Webster |access-date=17 March 2019 }}</ref>

==Statistics==
In [statistics](/source/statistics), [range](/source/Range_(statistics)) refers to the difference between the largest and smallest value of a set of quantified observations. Some observers consider it appropriate to remove unusually high or low outlying values to narrow the observed range to an effective range of the quantity being observed. Inferences based on effective range are of somewhat doubtful value if subjective judgement is used to determine which observations are discarded.<ref>{{cite web |url=https://stats.oecd.org/glossary/detail.asp?ID=3640 |title=Effective Range |last=Marriott |first=F.H.C. |website=Glossary of Statistical Terms |publisher=Organisation for Economic Co-operation and Development |access-date=17 March 2019 |archive-date=11 January 2021 |archive-url=https://web.archive.org/web/20210111060353/https://stats.oecd.org/glossary/detail.asp?ID=3640 |url-status=dead }}</ref>

==Nuclear physics==
{{confusing|section| date=February 2020|reason=most symbols in the formulae are unexplained. What is the length to do with the potential?}}
In [nuclear physics](/source/nuclear_physics) research, effective range is a physical parameter in the dimension of length to characterize an effective scattering [square well](/source/square_well) potential. It is related to the scattering phase shift by,

<math>k\cot\delta = -\gamma + \frac{1}{2}\left ( \gamma^2+k^2 \right )r_0+O\left(k^4r_o^3\right)</math>.<ref>{{cite journal | last=Bethe | first=H. A. |author-link=Hans Bethe|title=Theory of the Effective Range in Nuclear Scattering | journal=Physical Review | publisher=American Physical Society (APS) | volume=76 | issue=1 | date=1949-07-01 | issn=0031-899X | doi=10.1103/physrev.76.38 | pages=38–50| bibcode=1949PhRv...76...38B }}</ref>

where <math>\gamma</math> is defined by the relation of [deuteron](/source/deuteron) binding energy <math>\epsilon=\hbar^2/M\gamma^2</math>.

In the limit of zero energy (<math>k^2/2m=0</math>), the scattering length can be related to effective length with <math>\alpha=\frac{1}{a}=\gamma\left(1-\frac{1}{2}\gamma r_0\right)</math>.

==References==
{{reflist}}

Category:Scale statistics
Category:Length
Category:Nuclear physics

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Adapted from the Wikipedia article [Effective range](https://en.wikipedia.org/wiki/Effective_range) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Effective_range?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.