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Effective range
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<h2 id="distance">Distance</h2> <p>Effective range may describe a distance between two points where one point is subject to an <a href="/facts/Energy/wd8PrQM7">energy</a> release at the other point. The <a href="/facts/Point_source/AHmNlt03">source</a>, 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 <a href="/facts/Wave_propagation/PXhWIt7k">propagation</a> toward small targets. </p> <h3>Weapons</h3> <p>The following definition has been attributed to the <a href="/facts/United_States_Department_of_Defense/dWAvf7e3">United States Department of Defense</a>: <i>The maximum distance at which a weapon may be expected to be accurate and achieve the desired effect.</i><a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> Accuracy is ambiguous in the absence of a specified hit probability per unit of <a href="/facts/Ammunition/ajd1wm1I">ammunition</a>; and for any given <a href="/facts/Weapon/fV9QfoBh">weapon</a>, the desired effect could be interpreted differently depending upon the target. Subjective interpretation of these variables has caused endless and heated <a href="/facts/Debate/B76DJtj3">debate</a> for more than a century.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> </p> <p>With the addition of <a href="/facts/Clinometer/NB4nFvg5">clinometers</a> fixed machine gun squads could set long ranges and deliver <a href="/facts/Plunging_fire/MAtBGP2a">plunging fire</a> or <a href="/facts/Indirect_fire/g86Xc8b6">indirect fire</a> at more than 2,500 m (2,730 yd). 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 required to put unprotected personnel out of action, which is generally believed to be 15 kilogram-meters (147 J / 108 ft⋅lbf).<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> Advanced planned and unplanned map and range table predicted support/harassment firing methods developed during 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.<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a> </p> <h3>Vehicles</h3> <p>In a broader context, effective range describes the distance a vehicle (including weapon launch platforms like a <a href="/facts/Ship/418ptx1L">ship</a> or <a href="/facts/Aircraft/EhC4mBep">aircraft</a>) may be expected to deliver a specified payload from a <a href="/facts/Military_base/uzTGn8ul">base</a> or refueling point.<a class="footnote-ref" id="fnref:5" href="#fn:5"><sup>5</sup></a> </p> <h2 id="statistics">Statistics</h2> <p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, <a href="/facts/Range_(statistics)/Yu0HgeRj">range</a> 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.<a class="footnote-ref" id="fnref:6" href="#fn:6"><sup>6</sup></a> </p> <h2 id="nuclear-physics">Nuclear physics</h2> <p>In <a href="/facts/Nuclear_physics/fzQbt1aF">nuclear physics</a> research, effective range is a physical parameter in the dimension of length to characterize an effective scattering <a href="/facts/Square_well/rezR97ky">square well</a> potential. It is related to the scattering phase shift by, </p><p> k cot δ = − γ + 1 2 ( γ 2 + k 2 ) r 0 + O ( k 4 r o 3 ) {\displaystyle k\cot \delta =-\gamma +{\frac {1}{2}}\left(\gamma ^{2}+k^{2}\right)r_{0}+O\left(k^{4}r_{o}^{3}\right)} .<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> </p><p>where γ {\displaystyle \gamma } is defined by the relation of <a href="/facts/Deuteron/Bv4wfCkw">deuteron</a> binding energy ϵ = ℏ 2 / M γ 2 {\displaystyle \epsilon =\hbar ^{2}/M\gamma ^{2}} . </p><p>In the limit of zero energy ( k 2 / 2 m = 0 {\displaystyle k^{2}/2m=0} ), the scattering length can be related to effective length with α = 1 a = γ ( 1 − 1 2 γ r 0 ) {\displaystyle \alpha ={\frac {1}{a}}=\gamma \left(1-{\frac {1}{2}}\gamma r_{0}\right)} . </p> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>"maximum effective range Definition (US DoD)". Military Factory. Retrieved 12 March 2019. <a href="https://www.militaryfactory.com/dictionary/military-terms-defined.asp?term_id=3284" target="_blank">https://www.militaryfactory.com/dictionary/military-terms-defined.asp?term_id=3284</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Dodd, Mead (1916). New International Encyclopedia. Vol. 19. Princeton University. p. 542. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Kjellgren, G. L. M. "The Practical Range of Small Arms" (PDF). The American Rifleman. pp. 40–44. Archived (PDF) from the original on 5 March 2015. <a href="http://www.krtraining.com/KRTraining/Archive/PracticalRangeSmallArms.pdf" target="_blank">http://www.krtraining.com/KRTraining/Archive/PracticalRangeSmallArms.pdf</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>"How The Machine Gun Changed Combat During World War I". Norwich University Online. <a href="https://online.norwich.edu/academic-programs/resources/how-machine-gun-changed-combat-during-world-war-i" target="_blank">https://online.norwich.edu/academic-programs/resources/how-machine-gun-changed-combat-during-world-war-i</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>"effective range". Merriam-Webster. Retrieved 17 March 2019. <a href="https://www.merriam-webster.com/dictionary/effective%20range" target="_blank">https://www.merriam-webster.com/dictionary/effective%20range</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Marriott, F.H.C. "Effective Range". Glossary of Statistical Terms. Organisation for Economic Co-operation and Development. Retrieved 17 March 2019. <a href="https://stats.oecd.org/glossary/detail.asp?ID=3640" target="_blank">https://stats.oecd.org/glossary/detail.asp?ID=3640</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Bethe, H. A. (1949-07-01). "Theory of the Effective Range in Nuclear Scattering". Physical Review. 76 (1). American Physical Society (APS): 38–50. Bibcode:1949PhRv...76...38B. doi:10.1103/physrev.76.38. ISSN 0031-899X. <a href="/wiki/Hans_Bethe" target="_blank">/wiki/Hans_Bethe</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> </ol>