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<span>History</span> </div> </a> <ul id="toc-History-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Characteristics_and_properties" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Characteristics_and_properties"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Characteristics and properties</span> </div> </a> <button aria-controls="toc-Characteristics_and_properties-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Characteristics and properties subsection</span> </button> <ul id="toc-Characteristics_and_properties-sublist" class="vector-toc-list"> <li id="toc-Mach_stem_formation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Mach_stem_formation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Mach stem formation</span> </div> </a> <ul id="toc-Mach_stem_formation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Constructive_and_destructive_interference" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Constructive_and_destructive_interference"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Constructive and destructive interference</span> </div> </a> <ul id="toc-Constructive_and_destructive_interference-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Damage" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Damage"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Damage</span> </div> </a> <ul id="toc-Damage-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Bombs" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Bombs"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Bombs</span> </div> </a> <ul id="toc-Bombs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Effects_of_blast_loads_on_buildings" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Effects_of_blast_loads_on_buildings"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Effects of blast loads on buildings</span> </div> </a> <ul id="toc-Effects_of_blast_loads_on_buildings-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Astronomy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Astronomy"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Astronomy</span> </div> </a> <ul id="toc-Astronomy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Research" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Research"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Research</span> </div> </a> <ul id="toc-Research-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Increased fluid pressure and flow from an explosion</div> <p> In <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a>, a <b>blast wave</b> is the increased pressure and flow resulting from the deposition of a large amount of energy in a small, very localised volume. The flow field can be approximated as a lead <a href="/wiki/Shock_wave" title="Shock wave">shock wave</a>, followed by a similar subsonic flow field. In simpler terms, a blast wave is an area of pressure expanding supersonically outward from an explosive core. It has a leading shock front of compressed gases. The blast wave is followed by a blast wind of <a href="/wiki/Pressure#Negative_pressures" title="Pressure">negative gauge pressure</a>, which sucks items back in towards the center. The blast wave is harmful especially to objects very close to the center or at a location of constructive interference. High <a href="/wiki/Explosive" title="Explosive">explosives</a> that <a href="/wiki/Detonation" title="Detonation">detonate</a> generate blast waves. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Sources">Sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=1" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>High-order <a href="/wiki/Explosive" title="Explosive">explosives</a> (HE) are more powerful than low-order explosives (LE). HE <a href="/wiki/Detonation" title="Detonation">detonate</a> to produce a defining <a href="/wiki/Supersonic_speed" title="Supersonic speed">supersonic</a> over-pressurization <a href="/wiki/Shock_wave" title="Shock wave">shock wave</a>. Sources of HE include trinitrotoluene (<a href="/wiki/TNT" title="TNT">TNT</a>), <a href="/wiki/C-4_(explosive)" title="C-4 (explosive)">C-4</a>, <a href="/wiki/Semtex" title="Semtex">Semtex</a>, <a href="/wiki/Nitroglycerin" title="Nitroglycerin">nitroglycerin</a>, and ammonium nitrate fuel oil (<a href="/wiki/ANFO" title="ANFO">ANFO</a>). LE <a href="/wiki/Deflagration" title="Deflagration">deflagrate</a> to create a subsonic explosion and lack HE's over-pressurization wave. Sources of LE include <a href="/wiki/Pipe_bomb" title="Pipe bomb">pipe bombs</a>, <a href="/wiki/Gunpowder" title="Gunpowder">gunpowder</a>, and most pure petroleum-based <a href="/wiki/Incendiary_device" title="Incendiary device">incendiary bombs</a> such as <a href="/wiki/Molotov_cocktail" title="Molotov cocktail">Molotov cocktails</a> or aircraft improvised as guided missiles. HE and LE induce different injury patterns. Only HE produce true blast waves.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The classic flow solution—the so-called <a href="/wiki/Taylor%E2%80%93von_Neumann%E2%80%93Sedov_blast_wave" title="Taylor–von Neumann–Sedov blast wave">Taylor–von Neumann–Sedov blast wave</a> solution—was independently devised by <a href="/wiki/John_von_Neumann" title="John von Neumann">John von Neumann</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and British mathematician <a href="/wiki/Geoffrey_Ingram_Taylor" class="mw-redirect" title="Geoffrey Ingram Taylor">Geoffrey Ingram Taylor</a><sup id="cite_ref-taylor_1950_4-0" class="reference"><a href="#cite_note-taylor_1950-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-taylor_1950a_5-0" class="reference"><a href="#cite_note-taylor_1950a-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> during <a href="/wiki/World_War_II" title="World War II">World War II</a>. After the war, the similarity solution was published by three other authors—<a href="/wiki/L._I._Sedov" class="mw-redirect" title="L. I. Sedov">L. I. Sedov</a>,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> R. Latter,<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> and J. Lockwood-Taylor<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>—who had discovered it independently.<sup id="cite_ref-Batchelor_9-0" class="reference"><a href="#cite_note-Batchelor-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Since the early theoretical work, both theoretical and experimental studies of blast waves have been ongoing.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Characteristics_and_properties">Characteristics and properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=3" title="Edit section: Characteristics and properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Friedlander_waveform.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Friedlander_waveform.jpg/300px-Friedlander_waveform.jpg" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Friedlander_waveform.jpg/450px-Friedlander_waveform.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Friedlander_waveform.jpg/600px-Friedlander_waveform.jpg 2x" data-file-width="800" data-file-height="600" /></a><figcaption> A Friedlander waveform is the simplest form of a blast wave.</figcaption></figure> <p>The simplest form of a blast wave has been described and termed the Friedlander waveform.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> It occurs when a high explosive detonates in a free field: that is, with no surfaces nearby with which it can interact. Blast waves have properties predicted by the <a href="/wiki/Wave#Physical_properties" title="Wave">physics of waves</a>. For example, they can <a href="/wiki/Diffraction" title="Diffraction">diffract</a> through a narrow opening and <a href="/wiki/Refraction" title="Refraction">refract</a> as they pass through materials. Like light or sound waves, when a blast wave reaches a boundary between two materials, part of it is transmitted, part of it is absorbed, and part of it is reflected. The <a href="/wiki/Acoustic_impedance" title="Acoustic impedance">impedances</a> of the two materials determine how much of each occurs. </p><p>The equation for a Friedlander waveform describes the pressure of the blast wave as a function of time: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P(t)=P_{s}e^{-{\frac {t}{t^{*}}}}\left(1-{\frac {t}{t^{*}}}\right).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>t</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mfrac> </mrow> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>t</mi> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(t)=P_{s}e^{-{\frac {t}{t^{*}}}}\left(1-{\frac {t}{t^{*}}}\right).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36e891c86e00fbcb1d0eb44a2e6036b89716452f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:26.277ex; height:6.176ex;" alt="{\displaystyle P(t)=P_{s}e^{-{\frac {t}{t^{*}}}}\left(1-{\frac {t}{t^{*}}}\right).}"></span></dd></dl> <p>where P<sub>s</sub> is the peak pressure and t* is the time at which the pressure first crosses the horizontal axis (before the negative phase). </p><p>Blast waves will wrap around objects and buildings.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Therefore, persons or objects behind a large building are not necessarily protected from a blast that starts on the opposite side of the building. Scientists use sophisticated mathematical models to predict how objects will respond to a blast in order to design effective barriers and safer buildings.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Mach_stem_formation">Mach stem formation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=4" title="Edit section: Mach stem formation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Mach_wave" title="Mach wave">Mach wave</a></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Mach_effect_sequence.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Mach_effect_sequence.svg/250px-Mach_effect_sequence.svg.png" decoding="async" width="250" height="320" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Mach_effect_sequence.svg/375px-Mach_effect_sequence.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Mach_effect_sequence.svg/500px-Mach_effect_sequence.svg.png 2x" data-file-width="500" data-file-height="640" /></a><figcaption> A blast wave reflecting from a surface and forming a <a href="/wiki/Mach_stem" class="mw-redirect" title="Mach stem">mach stem</a>. The picture shows a 20 kiloton <a href="/wiki/Air_burst" title="Air burst">air burst</a> at 540 meters, to optimize the area covered by at least 15 <a href="/wiki/Pound_per_square_inch" title="Pound per square inch">psi</a> <a href="/wiki/Effects_of_nuclear_explosions#Blast_damage" title="Effects of nuclear explosions">blast damage</a>.</figcaption></figure> <p><a href="/wiki/Mach_stem" class="mw-redirect" title="Mach stem">Mach stem</a> formation occurs when a blast wave reflects off the ground and the reflection catches up with the original shock front, therefore creating a high pressure zone that extends from the ground up to a certain point called the triple point at the edge of the blast wave. Anything in this area experiences peak pressures that can be several times higher than the peak pressure of the original shock front. </p> <div class="mw-heading mw-heading3"><h3 id="Constructive_and_destructive_interference">Constructive and destructive interference</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=5" title="Edit section: Constructive and destructive interference"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Constructive_interference.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Constructive_interference.svg/250px-Constructive_interference.svg.png" decoding="async" width="250" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Constructive_interference.svg/375px-Constructive_interference.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Constructive_interference.svg/500px-Constructive_interference.svg.png 2x" data-file-width="250" data-file-height="300" /></a><figcaption> An example of constructive interference.</figcaption></figure><p> In physics, <a href="/wiki/Wave_interference" title="Wave interference">interference</a> is the meeting of two correlated waves and either increasing or lowering the net <a href="/wiki/Amplitude" title="Amplitude">amplitude</a>, depending on whether it is constructive or destructive interference. If a crest of a wave meets a crest of another wave at the same point then the crests interfere constructively and the resultant crest wave amplitude is increased, forming a much more powerful wave than either of the beginning waves. Similarly two troughs make a trough of increased amplitude. If a crest of a wave meets a trough of another wave then they interfere destructively, and the overall amplitude is decreased, thus making a wave that is much smaller than either of the parent waves. </p><p>The formation of a mach stem is one example of constructive interference. Whenever a blast wave reflects off of a surface, such as a building wall or the inside of a vehicle, different reflected waves can interact with each other to cause an increase in pressure at a certain point (constructive interference) or a decrease (destructive interference). In this way the interaction of blast waves is similar to that of sound waves or water waves. </p> <div class="mw-heading mw-heading2"><h2 id="Damage">Damage</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=6" title="Edit section: Damage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Blast waves cause damage by a combination of the significant compression of the air in front of the wave (forming a <a href="/wiki/Shock_front" class="mw-redirect" title="Shock front">shock front</a>) and the subsequent wind that follows.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> A blast wave travels faster than the <a href="/wiki/Speed_of_sound" title="Speed of sound">speed of sound</a>, and the passage of the shock wave usually lasts only a few milliseconds. Like other types of explosions, a blast wave can also cause damage to things and people by the blast wind, debris, and fires. The original explosion will send out fragments that travel very fast. Debris and sometimes even people can get swept up into a blast wave, causing more injuries such as penetrating wounds, impalement and broken bones. The blast wind is the area of low pressure that causes debris and fragments to rush back towards the original explosions. The blast wave can also cause fires or secondary explosions by a combination of the high temperatures that result from detonation and the physical destruction of fuel-containing objects. </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=7" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Bombs">Bombs</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=8" title="Edit section: Bombs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In response to an inquiry from the British <a href="/wiki/MAUD_Committee" title="MAUD Committee">MAUD Committee</a>, G. I. Taylor estimated the amount of energy that would be released by the explosion of an atomic bomb in air. He postulated that for an idealized point source of energy, the spatial distributions of the flow variables would have the same form during a given time interval, the variables differing only in scale (thus the name of the "similarity solution.") This hypothesis allows the <a href="/wiki/Partial_differential_equation" title="Partial differential equation">partial differential equations</a> in terms of r (the radius of the blast wave) and t (time) to be transformed into an ordinary <a href="/wiki/Differential_equation" title="Differential equation">differential equation</a> in terms of the similarity variable: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {r^{5}\rho _{o}}{t^{2}E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mrow> <mrow> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>E</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {r^{5}\rho _{o}}{t^{2}E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a2a964d19d831f57ae423e33932075570e7ffbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:5.171ex; height:6.009ex;" alt="{\displaystyle {\frac {r^{5}\rho _{o}}{t^{2}E}}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{o}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{o}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ebd5b4bac2592085bf8525eebc27d5da5f07748a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.232ex; height:2.176ex;" alt="{\displaystyle \rho _{o}}"></span> is the density of the air and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> is the energy released by the explosion.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> This result allowed Taylor to estimate the <a href="/wiki/Nuclear_weapon_yield" title="Nuclear weapon yield">nuclear yield</a> of the <a href="/wiki/Trinity_(nuclear_test)" title="Trinity (nuclear test)">Trinity test</a> in New Mexico in 1945 using only photographs of the blast, which had been published in newspapers and magazines.<sup id="cite_ref-Batchelor_9-1" class="reference"><a href="#cite_note-Batchelor-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The yield of the explosion was determined by using the equation: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E=\left({\frac {\rho _{o}}{t^{2}}}\right)\left({\frac {r}{C}}\right)^{5}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <msup> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>r</mi> <mi>C</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\left({\frac {\rho _{o}}{t^{2}}}\right)\left({\frac {r}{C}}\right)^{5}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab8b005a10d6cbe9ea7728582e85eae24cdcfbdf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.182ex; height:6.176ex;" alt="{\displaystyle E=\left({\frac {\rho _{o}}{t^{2}}}\right)\left({\frac {r}{C}}\right)^{5}}"></span></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span> is a dimensionless constant that is a function of the ratio of the <a href="/wiki/Specific_heat_capacity" title="Specific heat capacity">specific heat</a> of air at constant pressure to the specific heat of air at constant volume. The value of C is also affected by radiative losses, but for air, values of C of 1.00-1.10 generally give reasonable results. In 1950, Taylor published two articles in which he revealed the yield E of the first atomic explosion,<sup id="cite_ref-taylor_1950_4-1" class="reference"><a href="#cite_note-taylor_1950-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-taylor_1950a_5-1" class="reference"><a href="#cite_note-taylor_1950a-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> which had previously been classified and whose publication was therefore a source of controversy.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2015)">citation needed</span></a></i>]</sup> </p><p>While nuclear explosions are among the clearest examples of the destructive power of blast waves, blast waves generated by exploding conventional bombs and other weapons made from high explosives have been used as weapons of war because of their effectiveness at creating polytraumatic injury. During World War II and the <a href="/wiki/Vietnam_War" title="Vietnam War">Vietnam War</a>, <a href="/wiki/Blast_lung" class="mw-redirect" title="Blast lung">blast lung</a> was a common and often deadly injury. Improvements in vehicular and personal protective equipment have helped to reduce the incidence of blast lung. However, as soldiers are better protected from penetrating injury and surviving previously lethal exposures, limb, eye, ear, and brain injuries have become more prevalent. </p> <div class="mw-heading mw-heading3"><h3 id="Effects_of_blast_loads_on_buildings">Effects of blast loads on buildings</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=9" title="Edit section: Effects of blast loads on buildings"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Structural behaviour during an explosion depends on the materials used in the construction of the building. Upon hitting the face of a building, the shock front from an explosion is reflected. This impact with the structure imparts momentum to exterior components of the building. The associated kinetic energy of the moving components must be absorbed or dissipated in order for them to survive. Generally, this is achieved by converting the kinetic energy of the moving component to <a href="/wiki/Strain_energy" title="Strain energy">strain energy</a> in resisting elements.<sup id="cite_ref-Dusenberry_19-0" class="reference"><a href="#cite_note-Dusenberry-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> Typically the resisting elements—such as windows, building facades and support columns—fail, causing partial damage through to progressive collapse of the building. </p> <div class="mw-heading mw-heading3"><h3 id="Astronomy">Astronomy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=10" title="Edit section: Astronomy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The so-called <b>Sedov-Taylor</b> solution <style data-mw-deduplicate="TemplateStyles:r1033199720">.mw-parser-output div.crossreference{padding-left:0}</style><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><span role="note" class="hatnote navigation-not-searchable crossreference selfref">(see <a href="#Bombs">§ Bombs</a>)</span> has become useful in <a href="/wiki/Astrophysics" title="Astrophysics">astrophysics</a>. For example, it can be applied to quantify an estimate for the outcome from <a href="/wiki/Supernova" title="Supernova">supernova</a>-explosions. The Sedov-Taylor expansion is also known as the "blast wave" phase, which is an <a href="/wiki/Adiabatic_process" title="Adiabatic process">adiabatic</a> expansion phase in the life cycle of supernova.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup class="reference nowrap"><span title="Page / location: 96">: 96 </span></sup> The temperature of the material in a supernova shell decreases with time, but the internal energy of the material is always 72% of E<sub>0</sub>, the initial energy released. This is helpful for astrophysicists interested in predicting the behavior of supernova remnants. </p> <div class="mw-heading mw-heading3"><h3 id="Research">Research</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=11" title="Edit section: Research"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Blast waves are generated in research environments using explosive or compressed-gas driven <a href="/wiki/Shock_tube" title="Shock tube">shock tubes</a> in an effort to replicate the environment of a military conflict to better understand the physics of blasts and injuries that may result, and to develop better protection against blast exposure.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> Blast waves are directed against structures (such as vehicles),<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> materials, and biological specimens<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> or surrogates. High-speed <a href="/wiki/Pressure_sensor" class="mw-redirect" title="Pressure sensor">pressure sensors</a> and/or <a href="/wiki/High_speed_camera" class="mw-redirect" title="High speed camera">high speed cameras</a> are often used to quantify the response to blast exposure. Anthropomorphic test devices (ATDs or <a href="/wiki/Crash_test_dummy" title="Crash test dummy">test dummies</a>) initially developed for the automotive industry are being used, sometimes with added instrumentation, to estimate the human response to blast events. For examples, personnel in vehicles and personnel on demining teams have been simulated using these ATDs.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> </p><p>Combined with experiments, complex mathematical models have been made of the interaction of blast waves with inanimate and biological structures.<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> Validated models are useful for "what if" experiments—predictions of outcomes for different scenarios. Depending on the system being modeled, it can be difficult to have accurate input parameters (for example, the material properties of a rate-sensitive material at blast rates of loading). Lack of experimental validation severely limits the usefulness of any numerical model. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Chapman%E2%80%93Jouguet_condition" title="Chapman–Jouguet condition">Chapman–Jouguet condition</a></li> <li><a href="/wiki/Zeldovich%E2%80%93Taylor_flow" title="Zeldovich–Taylor flow">Zeldovich–Taylor flow</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation report cs1"><a rel="nofollow" class="external text" href="https://www.cdc.gov/masstrauma/preparedness/primer.pdf">Explosions and Blast Injuries: A Primer for Clinicians</a> <span class="cs1-format">(PDF)</span> (Report). Centers for Disease Control (CDC). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20220304041203/https://www.cdc.gov/masstrauma/preparedness/primer.pdf">Archived</a> <span class="cs1-format">(PDF)</span> from the original on 4 March 2022<span class="reference-accessdate">. Retrieved <span class="nowrap">7 March</span> 2022</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=report&rft.btitle=Explosions+and+Blast+Injuries%3A+A+Primer+for+Clinicians&rft.pub=Centers+for+Disease+Control+%28CDC%29&rft_id=https%3A%2F%2Fwww.cdc.gov%2Fmasstrauma%2Fpreparedness%2Fprimer.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABlast+wave" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Neumann, John von, "The point source solution," <i>John von Neumann. Collected Works,</i> edited by A. J. Taub, Vol. 6 [Elmsford, N.Y.: Permagon Press, 1963], pages 219 – 237.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">Bethe, H.A., et al, BLAST WAVE, Los Alamos Report LA-2000, Ch. 2, (1947). <a rel="nofollow" class="external text" href="http://www.fas.org/sgp/othergov/doe/lanl/docs1/00320773.pdf">read online</a></span> </li> <li id="cite_note-taylor_1950-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-taylor_1950_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-taylor_1950_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylor1950" class="citation journal cs1"><a href="/wiki/Geoffrey_Ingram_Taylor" class="mw-redirect" title="Geoffrey Ingram Taylor">Taylor, Sir Geoffrey Ingram</a> (1950). "The Formation of a Blast Wave by a Very Intense Explosion. I. Theoretical Discussion". <i><a href="/wiki/Proceedings_of_the_Royal_Society_A" class="mw-redirect" title="Proceedings of the Royal Society A">Proceedings of the Royal Society A</a></i>. <b>201</b> (1065): 159–174. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1950RSPSA.201..159T">1950RSPSA.201..159T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1950.0049">10.1098/rspa.1950.0049</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:54070514">54070514</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+A&rft.atitle=The+Formation+of+a+Blast+Wave+by+a+Very+Intense+Explosion.+I.+Theoretical+Discussion&rft.volume=201&rft.issue=1065&rft.pages=159-174&rft.date=1950&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A54070514%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1098%2Frspa.1950.0049&rft_id=info%3Abibcode%2F1950RSPSA.201..159T&rft.aulast=Taylor&rft.aufirst=Sir+Geoffrey+Ingram&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABlast+wave" class="Z3988"></span></span> </li> <li id="cite_note-taylor_1950a-5"><span class="mw-cite-backlink">^ <a href="#cite_ref-taylor_1950a_5-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-taylor_1950a_5-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTaylor1950" class="citation journal cs1"><a href="/wiki/Geoffrey_Ingram_Taylor" class="mw-redirect" title="Geoffrey Ingram Taylor">Taylor, Sir Geoffrey Ingram</a> (1950). <a rel="nofollow" class="external text" href="http://rspa.royalsocietypublishing.org/content/201/1065/175">"The Formation of a Blast Wave by a Very Intense Explosion. II. The Atomic Explosion of 1945"</a>. <i><a href="/wiki/Proceedings_of_the_Royal_Society_A" class="mw-redirect" title="Proceedings of the Royal Society A">Proceedings of the Royal Society A</a></i>. <b>201</b> (1065): 175–186. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1950RSPSA.201..175T">1950RSPSA.201..175T</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frspa.1950.0050">10.1098/rspa.1950.0050</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+A&rft.atitle=The+Formation+of+a+Blast+Wave+by+a+Very+Intense+Explosion.+II.+The+Atomic+Explosion+of+1945&rft.volume=201&rft.issue=1065&rft.pages=175-186&rft.date=1950&rft_id=info%3Adoi%2F10.1098%2Frspa.1950.0050&rft_id=info%3Abibcode%2F1950RSPSA.201..175T&rft.aulast=Taylor&rft.aufirst=Sir+Geoffrey+Ingram&rft_id=http%3A%2F%2Frspa.royalsocietypublishing.org%2Fcontent%2F201%2F1065%2F175&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABlast+wave" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Sedov, L. I., "Propagation of strong shock waves," <i>Journal of Applied Mathematics and Mechanics</i>, Vol. 10, pages 241 – 250 (1946); in Russian: Седов Л. И. <a rel="nofollow" class="external text" href="http://dictionnaire.narod.ru/Sedov-1946-PMM.djvu">"Распространение сильных взрывных волн</a>," Прикладная математика и механика, т. X, № 2, С. 241-250.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a href="/wiki/Richard_Latter" title="Richard Latter">Latter, R.</a>, "Similarity solution for a spherical shock wave," <i>Journal of Applied Physics</i>, Vol. 26, pages 954 – 960 (1955).</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Lockwood-Taylor, J., "An exact solution of the spherical blast wave problem," <i>Philosophical Magazine</i>, Vol. 46, pages 317 – 320 (1955).</span> </li> <li id="cite_note-Batchelor-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-Batchelor_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Batchelor_9-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Batchelor, George, <i>The Life and Legacy of G. I. Taylor</i>, [Cambridge, England: Cambridge University Press, 1996], pages 202 – 207.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">Dewey JM. 53 years of blast wave research, a personal history. 21st International Symposium on Military and Blast, Israel, 2010</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Rinehart EJ, et al. DTRA weapons effects testing: a thirty year perspective. 21st International Symposium on Military and Blast, Israel, 2010 <a rel="nofollow" class="external text" href="http://www.dtra.mil/dtru/documents/V2_1/DTRA_Weapons_Effects_Testing.pdf">read online</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120313014237/http://www.dtra.mil/dtru/documents/V2_1/DTRA_Weapons_Effects_Testing.pdf">Archived</a> 13 March 2012 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Dewey JM. THE SHAPE OF THE BLAST WAVE: STUDIES OF THE FRIEDLANDER EQUATION. Presented at the 21st International Symposium on Military Aspects of Blast and Shock, Israel 2010 <a rel="nofollow" class="external text" href="http://www.blastanalysis.com/WordDocuments/MABS21/Dewey%20Presentation%20%2323.ppt">read online</a></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">Remmenikov AM. Modelling blast loads on buildings in complex city geometries. Computers and Structures, 2005, 83(27), 2197-2205. <a rel="nofollow" class="external text" href="http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1359&context=engpapers&sei-redir=1#search=%22Analysis%20blast%20loads%20buildings.%22">read online</a></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">for example, Cullis IG. Blast waves and how they interact with structures. J.R. Army Med Corps 147:16-26, 2001</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Neff M. A visual model for blast waves and fracture. Master's Thesis, University of Toronto, Canada, 1998</span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text">Discussion of similarity solutions, including G. I. Taylor's: <a href="/wiki/Buckingham_Pi_theorem" class="mw-redirect" title="Buckingham Pi theorem">Buckingham Pi theorem</a></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">Derivation of G. I. Taylor's similarity solution: <a rel="nofollow" class="external free" href="http://www.atmosp.physics.utoronto.ca/people/codoban/PHY138/Mechanics/dimensional.pdf">http://www.atmosp.physics.utoronto.ca/people/codoban/PHY138/Mechanics/dimensional.pdf</a></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">Discussion of G. I. Taylor's research, including his similarity solution: <a rel="nofollow" class="external free" href="http://www.deas.harvard.edu/brenner/taylor/physic_today/taylor.htm">http://www.deas.harvard.edu/brenner/taylor/physic_today/taylor.htm</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120204152231/http://www.deas.harvard.edu/brenner/taylor/physic_today/taylor.htm">Archived</a> 4 February 2012 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></span> </li> <li id="cite_note-Dusenberry-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-Dusenberry_19-0">^</a></b></span> <span class="reference-text">Dusenberry, Donald. 'Handbook for Blast Resistant Design of Buildings', 2010, pages 8-9.</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFReynolds2008" class="citation journal cs1">Reynolds, Stephen P. (1 September 2008). <a rel="nofollow" class="external text" href="https://www.annualreviews.org/doi/10.1146/annurev.astro.46.060407.145237">"Supernova Remnants at High Energy"</a>. <i>Annual Review of Astronomy and Astrophysics</i>. <b>46</b> (1): 89–126. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2008ARA&A..46...89R">2008ARA&A..46...89R</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1146%2Fannurev.astro.46.060407.145237">10.1146/annurev.astro.46.060407.145237</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0066-4146">0066-4146</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annual+Review+of+Astronomy+and+Astrophysics&rft.atitle=Supernova+Remnants+at+High+Energy&rft.volume=46&rft.issue=1&rft.pages=89-126&rft.date=2008-09-01&rft.issn=0066-4146&rft_id=info%3Adoi%2F10.1146%2Fannurev.astro.46.060407.145237&rft_id=info%3Abibcode%2F2008ARA%26A..46...89R&rft.aulast=Reynolds&rft.aufirst=Stephen+P.&rft_id=https%3A%2F%2Fwww.annualreviews.org%2Fdoi%2F10.1146%2Fannurev.astro.46.060407.145237&rfr_id=info%3Asid%2Fen.wikipedia.org%3ABlast+wave" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text">Rinehart, Dr. E. J., Henny, Dr. R. W., Thomsen, J. M., Duray, J. P. DTRA Weapons Effects Testing: A Thirty Year Perspective. Applied Research and Associates, Shock Physics Division</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text">for example, Bauman, R. A., Ling, G., Tong, L., Januszkiewicz, A., Agoston, D., Delanerolle, N., Kim, Y., Ritzel, D., Bell, R., Ecklund, J., Armonda, R., Bandak, F., Parks, S. An Introductory Characterization of a Combat-Casualty-Care Relevant Swine Model of Closed Head Injury Resulting from Exposure to Explosive Blast. Journal of Neurotrauma, June 2009, Mary Ann Liebert, Inc.</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">Cernak, I. The importance of systematic response in the pathobiology of blast-induced Neurotrauma. Frontiers in Neurology December, 2010.</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text">Makris, A. Nerenberg, J., Dionne, J. P., Bass, C. R., Chichester. Reduction of Blast Induced Head Acceleration in the Field of Anti-Personnel Mine Clearance. Med-Eng Systems Inc.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text">for example, Stuhmiller JH. Mathematical Modeling in Support of Military Operational Medicine Final Report J3150.01-06-306 prepared for the U.S. Army Medical Research and Materiel Command Fort Detrick, Maryland 21702-5012 OMB No. 0704-0188, July, 2006.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Blast_wave&action=edit&section=14" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.deas.harvard.edu/brenner/taylor/handouts/bomb/bomb.html">"The formation of a blast wave by a very intense explosion"</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20060909124752/http://www.deas.harvard.edu/brenner/taylor/handouts/bomb/bomb.html">Archived</a> 9 September 2006 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> G. I. Taylor's solution</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Blast_wave&oldid=1237957478">https://en.wikipedia.org/w/index.php?title=Blast_wave&oldid=1237957478</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Astrophysics" title="Category:Astrophysics">Astrophysics</a></li><li><a href="/wiki/Category:Explosion_protection" title="Category:Explosion protection">Explosion protection</a></li><li><a href="/wiki/Category:Fluid_dynamics" title="Category:Fluid dynamics">Fluid dynamics</a></li><li><a href="/wiki/Category:Shock_waves" title="Category:Shock waves">Shock waves</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Webarchive_template_wayback_links" title="Category:Webarchive template wayback links">Webarchive template wayback links</a></li><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li><li><a href="/wiki/Category:Use_dmy_dates_from_January_2023" title="Category:Use dmy dates from January 2023">Use dmy dates from January 2023</a></li><li><a href="/wiki/Category:All_articles_with_unsourced_statements" title="Category:All articles with unsourced statements">All articles with unsourced statements</a></li><li><a href="/wiki/Category:Articles_with_unsourced_statements_from_July_2015" title="Category:Articles with unsourced statements from July 2015">Articles with unsourced statements from July 2015</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 1 August 2024, at 10:23<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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