http://ballistipedia.com/index.php?title=Angular_Size&feed=atom&action=history
Angular Size - Revision history
2024-03-28T14:00:24Z
Revision history for this page on the wiki
MediaWiki 1.31.6
http://ballistipedia.com/index.php?title=Angular_Size&diff=1501&oldid=prev
David: /* Conversion between absolute and angular size units */ Updated ShotGroups link
2023-07-22T20:15:42Z
<p><span dir="auto"><span class="autocomment">Conversion between absolute and angular size units: </span> Updated ShotGroups link</span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 20:15, 22 July 2023</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12" >Line 12:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* mil (NATO definition). The unit circle circumference of <math>2 \pi</math> is divided into 6400 mils.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* mil (NATO definition). The unit circle circumference of <math>2 \pi</math> is divided into 6400 mils.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The [http://<del class="diffchange diffchange-inline">dwoll</del>.<del class="diffchange diffchange-inline">shinyapps</del>.<del class="diffchange diffchange-inline">io</del>/<del class="diffchange diffchange-inline">shotGroupsAngular</del>/ shotGroups web app] provides an interactive online tool to convert between absolute and angular size units.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The [http://<ins class="diffchange diffchange-inline">shiny</ins>.<ins class="diffchange diffchange-inline">imbei</ins>.<ins class="diffchange diffchange-inline">uni-mainz.de:3838</ins>/<ins class="diffchange diffchange-inline">shotGroups_AngularSize</ins>/ shotGroups web app] provides an interactive online tool to convert between absolute and angular size units.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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David
http://ballistipedia.com/index.php?title=Angular_Size&diff=1349&oldid=prev
Armadillo at 19:59, 11 January 2016
2016-01-11T19:59:12Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 19:59, 11 January 2016</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12" >Line 12:</td>
<td colspan="2" class="diff-lineno">Line 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* mil (NATO definition). The unit circle circumference of <math>2 \pi</math> is divided into 6400 mils.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* mil (NATO definition). The unit circle circumference of <math>2 \pi</math> is divided into 6400 mils.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The [http://dwoll.shinyapps.io/shotGroupsAngular/ shotGroups web app] provides an online tool to convert between absolute and angular size units.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The [http://dwoll.shinyapps.io/shotGroupsAngular/ shotGroups web app] provides an <ins class="diffchange diffchange-inline">interactive </ins>online tool to convert between absolute and angular size units.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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Armadillo
http://ballistipedia.com/index.php?title=Angular_Size&diff=1348&oldid=prev
Armadillo at 13:13, 11 January 2016
2016-01-11T13:13:48Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 13:13, 11 January 2016</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12" >Line 12:</td>
<td colspan="2" class="diff-lineno">Line 12:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* mil (NATO definition). The unit circle circumference of <math>2 \pi</math> is divided into 6400 mils.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* mil (NATO definition). The unit circle circumference of <math>2 \pi</math> is divided into 6400 mils.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The [http://dwoll.shinyapps.io/<del class="diffchange diffchange-inline">shotGroupsApp</del>/ shotGroups web app] provides an online tool to convert between absolute and angular size units <del class="diffchange diffchange-inline">(choose tab "angular size")</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The [http://dwoll.shinyapps.io/<ins class="diffchange diffchange-inline">shotGroupsAngular</ins>/ shotGroups web app] provides an online tool to convert between absolute and angular size units.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
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Armadillo
http://ballistipedia.com/index.php?title=Angular_Size&diff=396&oldid=prev
Armadillo: /* Calculating the angular diameter of an object */
2014-08-15T09:32:33Z
<p><span dir="auto"><span class="autocomment">Calculating the angular diameter of an object</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 09:32, 15 August 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l27" >Line 27:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Arc length <math>x</math> in NATO mil: <math>x = \frac{6400}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Arc length <math>x</math> in NATO mil: <math>x = \frac{6400}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>(Conversion from MOA to mrad is <math>\frac{21600}{2000 \pi} \approx 3.43775</math>.  Conversion from mrad to MOA is <math>\frac{2000 \pi}{21600} \approx 0.29089</math>. Conversion from MOA to mil is <math>\frac{21600}{6400} = 3.375</math>. Conversion from mil to MOA is <math>\frac{6400}{21600} <del class="diffchange diffchange-inline">= </del>0.2962963</math>.)</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>(Conversion from MOA to mrad is <math>\frac{21600}{2000 \pi} \approx 3.43775</math>.  Conversion from mrad to MOA is <math>\frac{2000 \pi}{21600} \approx 0.29089</math>. Conversion from MOA to mil is <math>\frac{21600}{6400} = 3.375</math>. Conversion from mil to MOA is <math>\frac{6400}{21600} <ins class="diffchange diffchange-inline">\approx </ins>0.2962963</math>.)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We can also give '''formulas for absolute object size <math>s</math> given angle <math>\alpha</math> and distance to target <math>d</math>''':</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We can also give '''formulas for absolute object size <math>s</math> given angle <math>\alpha</math> and distance to target <math>d</math>''':</div></td></tr>
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Armadillo
http://ballistipedia.com/index.php?title=Angular_Size&diff=395&oldid=prev
Armadillo: /* Calculating the angular diameter of an object */
2014-08-14T10:55:50Z
<p><span dir="auto"><span class="autocomment">Calculating the angular diameter of an object</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 10:55, 14 August 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l20" >Line 20:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The angle <math>\alpha</math> subtended by an object of size <math>s</math> at distance <math>d</math> can be calculated from the right triangle with hypotenuse of length <math>d</math> and cathetus of length <math>s/2</math> as <math>\tan\left(\frac{\alpha}{2}\right) = \frac{s}{2} \cdot \frac{1}{d}</math>, therefore <math>\alpha = 2 \cdot \arctan\left(\frac{s}{2 d}\right)</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The angle <math>\alpha</math> subtended by an object of size <math>s</math> at distance <math>d</math> can be calculated from the right triangle with hypotenuse of length <math>d</math> and cathetus of length <math>s/2</math> as <math>\tan\left(\frac{\alpha}{2}\right) = \frac{s}{2} \cdot \frac{1}{d}</math>, therefore <math>\alpha = 2 \cdot \arctan\left(\frac{s}{2 d}\right)</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Assuming that the result from functions <math>\tan(\cdot)</math> and <math>\arctan(\cdot)</math> is in radian, and that distance to target <math>d</math> and object size <math>s</math> are measured in the same unit, this leads to the following '''formulas for calculating <math>\alpha</math> and <math>x</math> in mrad based on <math>d</math> and <math>s</math>''':</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Assuming that the result from functions <math>\tan(\cdot)</math> and <math>\arctan(\cdot)</math> is in radian, and that distance to target <math>d</math> and object size <math>s</math> are measured in the same unit, this leads to the following '''formulas for calculating <math>\alpha</math> and <math>x</math> in mrad <ins class="diffchange diffchange-inline">or mil </ins>based on <math>d</math> and <math>s</math>''':</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Angle <math>\alpha</math> in MOA: <math>\alpha = 60 \cdot \frac{360}{2 \pi} \cdot 2 \cdot \arctan\left(\frac{s}{2 d}\right) = \frac{21600}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Angle <math>\alpha</math> in MOA: <math>\alpha = 60 \cdot \frac{360}{2 \pi} \cdot 2 \cdot \arctan\left(\frac{s}{2 d}\right) = \frac{21600}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Angle <math>\alpha</math> in SMOA: By definition, size <math>s=1</math> inch at <math>d=100</math> yards (<math>= 3600</math> inch) is 1 SMOA. Conversion factors to/from MOA are <math>\frac{21600}{\pi} \cdot \arctan\left(\frac{1}{2 \cdot 3600}\right) \approx 0.95493</math> (fairly close to <math>3/\pi</math>), and <math>\frac{\pi}{21600} \cdot \frac{1}{\arctan(1/7200)} \approx 1.04720</math> (fairly close to <math>\pi/3</math>). Therefore: <math>\alpha = \frac{\pi}{21600} \cdot \frac{1}{\arctan(1/7200)} \cdot \frac{21600}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right) = \frac{1}{\arctan(1/7200)} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Angle <math>\alpha</math> in SMOA: By definition, size <math>s=1</math> inch at <math>d=100</math> yards (<math>= 3600</math> inch) is 1 SMOA. Conversion factors to/from MOA are <math>\frac{21600}{\pi} \cdot \arctan\left(\frac{1}{2 \cdot 3600}\right) \approx 0.95493</math> (fairly close to <math>3/\pi</math>), and <math>\frac{\pi}{21600} \cdot \frac{1}{\arctan(1/7200)} \approx 1.04720</math> (fairly close to <math>\pi/3</math>). Therefore: <math>\alpha = \frac{\pi}{21600} \cdot \frac{1}{\arctan(1/7200)} \cdot \frac{21600}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right) = \frac{1}{\arctan(1/7200)} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Arc length <math>x</math> in mrad: <math>x = <del class="diffchange diffchange-inline">1000 \cdot 2 </del>\cdot \arctan\left(\frac{s}{2 d}\right) = <del class="diffchange diffchange-inline">2000 </del>\cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Arc length <math>x</math> in mrad: <math>x = <ins class="diffchange diffchange-inline">2000 </ins>\cdot \arctan\left(\frac{s}{2 d}\right)<ins class="diffchange diffchange-inline"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* Arc length <math>x</math> in NATO mil: <math>x </ins>= <ins class="diffchange diffchange-inline">\frac{6400}{\pi} </ins>\cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>(Conversion from MOA to <del class="diffchange diffchange-inline">mils </del>is <math>\frac{21600}{2000 \pi} \approx 3.43775</math>.  Conversion from <del class="diffchange diffchange-inline">mils </del>to MOA is <math>\frac{2000 \pi}{21600} \approx 0.29089</math>.)</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>(Conversion from MOA to <ins class="diffchange diffchange-inline">mrad </ins>is <math>\frac{21600}{2000 \pi} \approx 3.43775</math>.  Conversion from <ins class="diffchange diffchange-inline">mrad </ins>to MOA is <math>\frac{2000 \pi}{21600} \approx 0.29089<ins class="diffchange diffchange-inline"></math>. Conversion from MOA to mil is <math>\frac{21600}{6400} = 3.375</math>. Conversion from mil to MOA is <math>\frac{6400}{21600} = 0.2962963</ins></math>.)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We can also give '''formulas for absolute object size <math>s</math> given angle <math>\alpha</math> and distance to target <math>d</math>''':</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>We can also give '''formulas for absolute object size <math>s</math> given angle <math>\alpha</math> and distance to target <math>d</math>''':</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l32" >Line 32:</td>
<td colspan="2" class="diff-lineno">Line 33:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in MOA: <math>s = 2 \cdot d \cdot \tan\left( \frac{(2 \pi/360) (\alpha / 60)}{2} \right) = 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in MOA: <math>s = 2 \cdot d \cdot \tan\left( \frac{(2 \pi/360) (\alpha / 60)}{2} \right) = 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in SMOA: <math>s = \frac{21600}{\pi} \cdot \arctan\left(\frac{1}{7200}\right) \cdot 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in SMOA: <math>s = \frac{21600}{\pi} \cdot \arctan\left(\frac{1}{7200}\right) \cdot 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* From arc length <math>x</math> in mrad: <math>s = 2 \cdot d \cdot \tan<del class="diffchange diffchange-inline">\left</del>(<del class="diffchange diffchange-inline">\frac{</del>x/<del class="diffchange diffchange-inline">1000}{2}\right</del>) = 2 \cdot d \cdot \tan(x \cdot <del class="diffchange diffchange-inline">0.0005</del>)</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* From arc length <math>x</math> in mrad: <math>s = 2 \cdot d \cdot \tan(x / <ins class="diffchange diffchange-inline">2000</ins>)<ins class="diffchange diffchange-inline"></math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* From arc length <math>x</math> in NATO mil: <math>s </ins>= 2 \cdot d \cdot \tan<ins class="diffchange diffchange-inline">\left</ins>(x \cdot <ins class="diffchange diffchange-inline">\frac{\pi}{6400}\right</ins>)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similarly, we obtain the following '''formulas for distance to target <math>d</math> given absolute object size <math>s</math> and angle <math>\alpha</math>''':</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similarly, we obtain the following '''formulas for distance to target <math>d</math> given absolute object size <math>s</math> and angle <math>\alpha</math>''':</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* From angle <del class="diffchange diffchange-inline"> </del><math>\alpha</math> in MOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \pi/21600)}</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in MOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \pi/21600)}</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* From angle <del class="diffchange diffchange-inline"> </del><math>\alpha</math> in SMOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \arctan(1/7200))}</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in SMOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \arctan(1/7200))}</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* From arc length <del class="diffchange diffchange-inline"> </del><math>x</math> in mrad: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(x \cdot <del class="diffchange diffchange-inline">0.0005</del>)}</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* From arc length <math>x</math> in mrad: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(x <ins class="diffchange diffchange-inline">/ 2000)}</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* From arc length <math>x</math> in NATO mil: <math>d = \frac{s}{2} </ins>\cdot <ins class="diffchange diffchange-inline">\frac{1}{\tan(x \cdot \pi/6400</ins>)}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Less accurate calculation of angular size ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Less accurate calculation of angular size ==</div></td></tr>
</table>
Armadillo
http://ballistipedia.com/index.php?title=Angular_Size&diff=394&oldid=prev
Armadillo: /* Conversion between absolute and angular size units */
2014-08-14T10:43:37Z
<p><span dir="auto"><span class="autocomment">Conversion between absolute and angular size units</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 10:43, 14 August 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l9" >Line 9:</td>
<td colspan="2" class="diff-lineno">Line 9:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* MOA = minute of angle = minute of arc = arcmin. The circle is divided into 360 degrees, 1 MOA = 1/60 degree, such that the circle has <math>360 \cdot 60 = 21600</math> MOA.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* MOA = minute of angle = minute of arc = arcmin. The circle is divided into 360 degrees, 1 MOA = 1/60 degree, such that the circle has <math>360 \cdot 60 = 21600</math> MOA.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* SMOA = Shooter's MOA = Inches Per Hundred Yards IPHY. 1 inch at 100 yards = 1 SMOA.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* SMOA = Shooter's MOA = Inches Per Hundred Yards IPHY. 1 inch at 100 yards = 1 SMOA.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* <del class="diffchange diffchange-inline">milrad </del>= milliradian = 1/1000 radian. 1 radian is 1 unit of arc length on the unit circle which has a circumference of <math>2 \pi</math>. The circle is thus divided into <math>2 \pi \cdot 1000 \approx 6283.19</math> <del class="diffchange diffchange-inline">milrad</del>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* <ins class="diffchange diffchange-inline">mrad </ins>= milliradian = 1/1000 radian. 1 radian is 1 unit of arc length on the unit circle which has a circumference of <math>2 \pi</math>. The circle is thus divided into <math>2 \pi \cdot 1000 \approx 6283.19</math> <ins class="diffchange diffchange-inline">mrad.</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* mil (NATO definition). The unit circle circumference of <math>2 \pi</math> is divided into 6400 mils</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The [http://dwoll.shinyapps.io/shotGroupsApp/ shotGroups web app] provides an online tool to convert between absolute and angular size units (choose tab "angular size").</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The [http://dwoll.shinyapps.io/shotGroupsApp/ shotGroups web app] provides an online tool to convert between absolute and angular size units (choose tab "angular size").</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19" >Line 19:</td>
<td colspan="2" class="diff-lineno">Line 20:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The angle <math>\alpha</math> subtended by an object of size <math>s</math> at distance <math>d</math> can be calculated from the right triangle with hypotenuse of length <math>d</math> and cathetus of length <math>s/2</math> as <math>\tan\left(\frac{\alpha}{2}\right) = \frac{s}{2} \cdot \frac{1}{d}</math>, therefore <math>\alpha = 2 \cdot \arctan\left(\frac{s}{2 d}\right)</math>.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The angle <math>\alpha</math> subtended by an object of size <math>s</math> at distance <math>d</math> can be calculated from the right triangle with hypotenuse of length <math>d</math> and cathetus of length <math>s/2</math> as <math>\tan\left(\frac{\alpha}{2}\right) = \frac{s}{2} \cdot \frac{1}{d}</math>, therefore <math>\alpha = 2 \cdot \arctan\left(\frac{s}{2 d}\right)</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Assuming that the result from functions <math>\tan(\cdot)</math> and <math>\arctan(\cdot)</math> is in radian, and that distance to target <math>d</math> and object size <math>s</math> are measured in the same unit, this leads to the following '''formulas for calculating <math>\alpha</math> and <math>x</math> in <del class="diffchange diffchange-inline">milrad </del>based on <math>d</math> and <math>s</math>''':</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Assuming that the result from functions <math>\tan(\cdot)</math> and <math>\arctan(\cdot)</math> is in radian, and that distance to target <math>d</math> and object size <math>s</math> are measured in the same unit, this leads to the following '''formulas for calculating <math>\alpha</math> and <math>x</math> in <ins class="diffchange diffchange-inline">mrad </ins>based on <math>d</math> and <math>s</math>''':</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Angle <math>\alpha</math> in MOA: <math>\alpha = 60 \cdot \frac{360}{2 \pi} \cdot 2 \cdot \arctan\left(\frac{s}{2 d}\right) = \frac{21600}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Angle <math>\alpha</math> in MOA: <math>\alpha = 60 \cdot \frac{360}{2 \pi} \cdot 2 \cdot \arctan\left(\frac{s}{2 d}\right) = \frac{21600}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Angle <math>\alpha</math> in SMOA: By definition, size <math>s=1</math> inch at <math>d=100</math> yards (<math>= 3600</math> inch) is 1 SMOA. Conversion factors to/from MOA are <math>\frac{21600}{\pi} \cdot \arctan\left(\frac{1}{2 \cdot 3600}\right) \approx 0.95493</math> (fairly close to <math>3/\pi</math>), and <math>\frac{\pi}{21600} \cdot \frac{1}{\arctan(1/7200)} \approx 1.04720</math> (fairly close to <math>\pi/3</math>). Therefore: <math>\alpha = \frac{\pi}{21600} \cdot \frac{1}{\arctan(1/7200)} \cdot \frac{21600}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right) = \frac{1}{\arctan(1/7200)} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* Angle <math>\alpha</math> in SMOA: By definition, size <math>s=1</math> inch at <math>d=100</math> yards (<math>= 3600</math> inch) is 1 SMOA. Conversion factors to/from MOA are <math>\frac{21600}{\pi} \cdot \arctan\left(\frac{1}{2 \cdot 3600}\right) \approx 0.95493</math> (fairly close to <math>3/\pi</math>), and <math>\frac{\pi}{21600} \cdot \frac{1}{\arctan(1/7200)} \approx 1.04720</math> (fairly close to <math>\pi/3</math>). Therefore: <math>\alpha = \frac{\pi}{21600} \cdot \frac{1}{\arctan(1/7200)} \cdot \frac{21600}{\pi} \cdot \arctan\left(\frac{s}{2 d}\right) = \frac{1}{\arctan(1/7200)} \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* Arc length <math>x</math> in <del class="diffchange diffchange-inline">milrad</del>: <math>x = 1000 \cdot 2 \cdot \arctan\left(\frac{s}{2 d}\right) = 2000 \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* Arc length <math>x</math> in <ins class="diffchange diffchange-inline">mrad</ins>: <math>x = 1000 \cdot 2 \cdot \arctan\left(\frac{s}{2 d}\right) = 2000 \cdot \arctan\left(\frac{s}{2 d}\right)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(Conversion from MOA to mils is <math>\frac{21600}{2000 \pi} \approx 3.43775</math>.  Conversion from mils to MOA is <math>\frac{2000 \pi}{21600} \approx 0.29089</math>.)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(Conversion from MOA to mils is <math>\frac{21600}{2000 \pi} \approx 3.43775</math>.  Conversion from mils to MOA is <math>\frac{2000 \pi}{21600} \approx 0.29089</math>.)</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l31" >Line 31:</td>
<td colspan="2" class="diff-lineno">Line 32:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in MOA: <math>s = 2 \cdot d \cdot \tan\left( \frac{(2 \pi/360) (\alpha / 60)}{2} \right) = 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in MOA: <math>s = 2 \cdot d \cdot \tan\left( \frac{(2 \pi/360) (\alpha / 60)}{2} \right) = 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in SMOA: <math>s = \frac{21600}{\pi} \cdot \arctan\left(\frac{1}{7200}\right) \cdot 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in SMOA: <math>s = \frac{21600}{\pi} \cdot \arctan\left(\frac{1}{7200}\right) \cdot 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* From arc length <math>x</math> in <del class="diffchange diffchange-inline">milrad</del>: <math>s = 2 \cdot d \cdot \tan\left(\frac{x/1000}{2}\right) = 2 \cdot d \cdot \tan(x \cdot 0.0005)</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* From arc length <math>x</math> in <ins class="diffchange diffchange-inline">mrad</ins>: <math>s = 2 \cdot d \cdot \tan\left(\frac{x/1000}{2}\right) = 2 \cdot d \cdot \tan(x \cdot 0.0005)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similarly, we obtain the following '''formulas for distance to target <math>d</math> given absolute object size <math>s</math> and angle <math>\alpha</math>''':</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similarly, we obtain the following '''formulas for distance to target <math>d</math> given absolute object size <math>s</math> and angle <math>\alpha</math>''':</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle  <math>\alpha</math> in MOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \pi/21600)}</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle  <math>\alpha</math> in MOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \pi/21600)}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle  <math>\alpha</math> in SMOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \arctan(1/7200))}</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle  <math>\alpha</math> in SMOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \arctan(1/7200))}</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* From arc length  <math>x</math> in <del class="diffchange diffchange-inline">milrad</del>: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(x \cdot 0.0005)}</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* From arc length  <math>x</math> in <ins class="diffchange diffchange-inline">mrad</ins>: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(x \cdot 0.0005)}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Less accurate calculation of angular size ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Less accurate calculation of angular size ==</div></td></tr>
</table>
Armadillo
http://ballistipedia.com/index.php?title=Angular_Size&diff=392&oldid=prev
Armadillo at 14:31, 4 August 2014
2014-08-04T14:31:13Z
<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 14:31, 4 August 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l11" >Line 11:</td>
<td colspan="2" class="diff-lineno">Line 11:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* milrad = milliradian = 1/1000 radian. 1 radian is 1 unit of arc length on the unit circle which has a circumference of <math>2 \pi</math>. The circle is thus divided into <math>2 \pi \cdot 1000 \approx 6283.19</math> milrad.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* milrad = milliradian = 1/1000 radian. 1 radian is 1 unit of arc length on the unit circle which has a circumference of <math>2 \pi</math>. The circle is thus divided into <math>2 \pi \cdot 1000 \approx 6283.19</math> milrad.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The [http://dwoll.shinyapps.io/shotGroupsApp/ shotGroups <del class="diffchange diffchange-inline">online </del>app] provides an online tool to convert between absolute and angular size units (choose tab "angular size").</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The [http://dwoll.shinyapps.io/shotGroupsApp/ shotGroups <ins class="diffchange diffchange-inline">web </ins>app] provides an online tool to convert between absolute and angular size units (choose tab "angular size").</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br clear=all></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br clear=all></div></td></tr>
</table>
Armadillo
http://ballistipedia.com/index.php?title=Angular_Size&diff=391&oldid=prev
Armadillo at 14:30, 4 August 2014
2014-08-04T14:30:52Z
<p></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 14:30, 4 August 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l10" >Line 10:</td>
<td colspan="2" class="diff-lineno">Line 10:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* SMOA = Shooter's MOA = Inches Per Hundred Yards IPHY. 1 inch at 100 yards = 1 SMOA.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* SMOA = Shooter's MOA = Inches Per Hundred Yards IPHY. 1 inch at 100 yards = 1 SMOA.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* milrad = milliradian = 1/1000 radian. 1 radian is 1 unit of arc length on the unit circle which has a circumference of <math>2 \pi</math>. The circle is thus divided into <math>2 \pi \cdot 1000 \approx 6283.19</math> milrad.</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* milrad = milliradian = 1/1000 radian. 1 radian is 1 unit of arc length on the unit circle which has a circumference of <math>2 \pi</math>. The circle is thus divided into <math>2 \pi \cdot 1000 \approx 6283.19</math> milrad.</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The [http://dwoll.shinyapps.io/shotGroupsApp/ shotGroups online app] provides an online tool to convert between absolute and angular size units (choose tab "angular size").</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br clear=all></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><br clear=all></div></td></tr>
</table>
Armadillo
http://ballistipedia.com/index.php?title=Angular_Size&diff=308&oldid=prev
David: /* Calculating the angular diameter of an object */
2014-03-18T15:32:59Z
<p><span dir="auto"><span class="autocomment">Calculating the angular diameter of an object</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 15:32, 18 March 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l35" >Line 35:</td>
<td colspan="2" class="diff-lineno">Line 35:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle  <math>\alpha</math> in SMOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \arctan(1/7200))}</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle  <math>\alpha</math> in SMOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \arctan(1/7200))}</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From arc length  <math>x</math> in milrad: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(x \cdot 0.0005)}</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From arc length  <math>x</math> in milrad: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(x \cdot 0.0005)}</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">\end{itemize}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Less accurate calculation of angular size ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Less accurate calculation of angular size ==</div></td></tr>
</table>
David
http://ballistipedia.com/index.php?title=Angular_Size&diff=307&oldid=prev
Armadillo: /* Calculating the angular diameter of an object */
2014-03-07T13:41:48Z
<p><span dir="auto"><span class="autocomment">Calculating the angular diameter of an object</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 13:41, 7 March 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l25" >Line 25:</td>
<td colspan="2" class="diff-lineno">Line 25:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(Conversion from MOA to mils is <math>\frac{21600}{2000 \pi} \approx 3.43775</math>.  Conversion from mils to MOA is <math>\frac{2000 \pi}{21600} \approx 0.29089</math>.)</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>(Conversion from MOA to mils is <math>\frac{21600}{2000 \pi} \approx 3.43775</math>.  Conversion from mils to MOA is <math>\frac{2000 \pi}{21600} \approx 0.29089</math>.)</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>We can also give '''formulas for object size <math>s</math> given angle <math>\alpha</math> and distance to target <math>d</math>''':</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>We can also give '''formulas for <ins class="diffchange diffchange-inline">absolute </ins>object size <math>s</math> given angle <math>\alpha</math> and distance to target <math>d</math>''':</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in MOA: <math>s = 2 \cdot d \cdot \tan\left( \frac{(2 \pi/360) (\alpha / 60)}{2} \right) = 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in MOA: <math>s = 2 \cdot d \cdot \tan\left( \frac{(2 \pi/360) (\alpha / 60)}{2} \right) = 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in SMOA: <math>s = \frac{21600}{\pi} \cdot \arctan\left(\frac{1}{7200}\right) \cdot 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* From angle <math>\alpha</math> in SMOA: <math>s = \frac{21600}{\pi} \cdot \arctan\left(\frac{1}{7200}\right) \cdot 2 \cdot d \cdot \tan\left(\alpha \cdot \frac{\pi}{21600}\right)</math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>* From arc length <math>x</math> in milrad: <math>s = 2 \cdot d \cdot \tan\left(\frac{x/1000}{2}\right) = 2 \cdot d \cdot \tan(0.0005 x)</math></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>* From arc length <math>x</math> in milrad: <math>s = 2 \cdot d \cdot \tan\left(\frac{x/1000}{2}\right) = 2 \cdot d \cdot \tan(<ins class="diffchange diffchange-inline">x \cdot </ins>0.0005<ins class="diffchange diffchange-inline">)</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Similarly, we obtain the following '''formulas for distance to target <math>d</math> given absolute object size <math>s</math> and angle <math>\alpha</math>''':</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* From angle  <math>\alpha</math> in MOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \pi/21600)}</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* From angle  <math>\alpha</math> in SMOA: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(\alpha \cdot \arctan(1/7200))}</math></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">* From arc length  <math>x</math> in milrad: <math>d = \frac{s}{2} \cdot \frac{1}{\tan(</ins>x <ins class="diffchange diffchange-inline">\cdot 0.0005</ins>)<ins class="diffchange diffchange-inline">}</ins></math></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">\end{itemize}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Less accurate calculation of angular size ==</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Less accurate calculation of angular size ==</div></td></tr>
</table>
Armadillo