tag:blogger.com,1999:blog-21972369789112147062024-01-08T18:42:48.147+05:30MahekMody.comYes, I have a lot of spare time.Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.comBlogger16125tag:blogger.com,1999:blog-2197236978911214706.post-48904667990165083692017-11-19T13:49:00.001+05:302018-03-24T18:44:02.615+05:30A Guide to Negative Marking<div dir="ltr" style="text-align: left;" trbidi="on">
<div dir="ltr" style="text-align: left;" trbidi="on">
<div dir="ltr" style="text-align: left;" trbidi="on">
<div dir="ltr" style="text-align: left;" trbidi="on">
<div dir="ltr" style="text-align: left;" trbidi="on">
<div>
<span style="font-family: "arial"; font-size: 11pt; white-space: pre-wrap;">Negative marking in Multiple Choice Answer(MCQ) exams is becoming more mainstream in competitive exams all across India. The intent of negative marking is to prevent students from taking guesses at answers. It is typically quite effective because of <a href="https://en.wikipedia.org/wiki/Loss_aversion" target="_blank">loss aversion</a>.</span></div>
<div>
<span style="font-family: "arial"; font-size: 11pt; white-space: pre-wrap;"><br /></span></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center; width: 90%;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzSV08SaO_kGhRDSFb-0zTKZrbUUM5JkwSQS15OupG9GNkB8Rfbo2Vq7HgEjXrdzYdMF7Ypd8wecCqTred5OeJvkrsaftUyFWoZ8sdVAexTN3_x06dy6gNc35c6492TGdrbpMjzo53pr0/s1600/5843577306_06fd6132f7_z.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="428" data-original-width="640" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzSV08SaO_kGhRDSFb-0zTKZrbUUM5JkwSQS15OupG9GNkB8Rfbo2Vq7HgEjXrdzYdMF7Ypd8wecCqTred5OeJvkrsaftUyFWoZ8sdVAexTN3_x06dy6gNc35c6492TGdrbpMjzo53pr0/s400/5843577306_06fd6132f7_z.jpg" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><a href="https://www.flickr.com/photos/albertogp123/5843577306" target="_blank">CC License</a></td></tr>
</tbody></table>
<div>
Before we move onto the analysis. Some definitions:<br />
<br />
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoTable15Grid4Accent5" style="border-collapse: collapse; border: none; mso-border-alt: solid #9CC2E5 .5pt; mso-border-themecolor: accent5; mso-border-themetint: 153; mso-padding-alt: 2.85pt 5.4pt 2.85pt 5.4pt; mso-yfti-tbllook: 1696;">
<tbody>
<tr>
<td style="background: #5B9BD5; border-right: none; border: solid #5B9BD5 1.0pt; mso-background-themecolor: accent5; mso-border-bottom-alt: solid #5B9BD5 .5pt; mso-border-bottom-themecolor: accent5; mso-border-left-alt: solid #5B9BD5 .5pt; mso-border-left-themecolor: accent5; mso-border-themecolor: accent5; mso-border-top-alt: solid #5B9BD5 .5pt; mso-border-top-themecolor: accent5; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 106.1pt;" valign="top" width="141"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 5; text-align: center;">
<b><span style="color: white; font-family: "times new roman" , serif; font-size: 12.0pt;">Term<o:p></o:p></span></b></div>
</td>
<td style="background: #5B9BD5; border-left: none; border: solid #5B9BD5 1.0pt; mso-background-themecolor: accent5; mso-border-bottom-alt: solid #5B9BD5 .5pt; mso-border-bottom-themecolor: accent5; mso-border-right-alt: solid #5B9BD5 .5pt; mso-border-right-themecolor: accent5; mso-border-themecolor: accent5; mso-border-top-alt: solid #5B9BD5 .5pt; mso-border-top-themecolor: accent5; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 344.7pt;" valign="top" width="460"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 1; text-align: center;">
<b><span style="color: white; font-family: "times new roman" , serif; font-size: 12.0pt;">Definition<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #9CC2E5 1.0pt; mso-border-alt: solid #9CC2E5 .5pt; mso-border-themecolor: accent5; mso-border-themecolor: accent5; mso-border-themetint: 153; mso-border-themetint: 153; mso-border-top-alt: solid #9CC2E5 .5pt; mso-border-top-themecolor: accent5; mso-border-top-themetint: 153; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 106.1pt;" valign="top" width="141"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 4; text-align: center;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">NumChoices<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #9CC2E5 1.0pt; border-left: none; border-right: solid #9CC2E5 1.0pt; border-top: none; mso-border-alt: solid #9CC2E5 .5pt; mso-border-bottom-themecolor: accent5; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #9CC2E5 .5pt; mso-border-left-themecolor: accent5; mso-border-left-themetint: 153; mso-border-right-themecolor: accent5; mso-border-right-themetint: 153; mso-border-themecolor: accent5; mso-border-themetint: 153; mso-border-top-alt: solid #9CC2E5 .5pt; mso-border-top-themecolor: accent5; mso-border-top-themetint: 153; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 344.7pt;" valign="top" width="460"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Number
of Choices of answers in an MCQ<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #9CC2E5 1.0pt; mso-border-alt: solid #9CC2E5 .5pt; mso-border-themecolor: accent5; mso-border-themecolor: accent5; mso-border-themetint: 153; mso-border-themetint: 153; mso-border-top-alt: solid #9CC2E5 .5pt; mso-border-top-themecolor: accent5; mso-border-top-themetint: 153; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 106.1pt;" valign="top" width="141"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 4; text-align: center;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">NegRatio<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #9CC2E5 1.0pt; border-left: none; border-right: solid #9CC2E5 1.0pt; border-top: none; mso-border-alt: solid #9CC2E5 .5pt; mso-border-bottom-themecolor: accent5; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #9CC2E5 .5pt; mso-border-left-themecolor: accent5; mso-border-left-themetint: 153; mso-border-right-themecolor: accent5; mso-border-right-themetint: 153; mso-border-themecolor: accent5; mso-border-themetint: 153; mso-border-top-alt: solid #9CC2E5 .5pt; mso-border-top-themecolor: accent5; mso-border-top-themetint: 153; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 344.7pt;" valign="top" width="460"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">The
ratio of the number of positive marks one gets for a correct answer to the
number of negative marks one gets for an incorrect answer. If it is a +4 and -1
exam, the ratio is 4. If it is a +1 and -2 exam, the ratio is 0.5<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #9CC2E5 1.0pt; mso-border-alt: solid #9CC2E5 .5pt; mso-border-themecolor: accent5; mso-border-themecolor: accent5; mso-border-themetint: 153; mso-border-themetint: 153; mso-border-top-alt: solid #9CC2E5 .5pt; mso-border-top-themecolor: accent5; mso-border-top-themetint: 153; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 106.1pt;" valign="top" width="141"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 4; text-align: center;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Random Strategy<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #9CC2E5 1.0pt; border-left: none; border-right: solid #9CC2E5 1.0pt; border-top: none; mso-border-alt: solid #9CC2E5 .5pt; mso-border-bottom-themecolor: accent5; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #9CC2E5 .5pt; mso-border-left-themecolor: accent5; mso-border-left-themetint: 153; mso-border-right-themecolor: accent5; mso-border-right-themetint: 153; mso-border-themecolor: accent5; mso-border-themetint: 153; mso-border-top-alt: solid #9CC2E5 .5pt; mso-border-top-themecolor: accent5; mso-border-top-themetint: 153; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 344.7pt;" valign="top" width="460"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Strategy
to mark the answers not known, at random<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid #9CC2E5 1.0pt; mso-border-alt: solid #9CC2E5 .5pt; mso-border-themecolor: accent5; mso-border-themecolor: accent5; mso-border-themetint: 153; mso-border-themetint: 153; mso-border-top-alt: solid #9CC2E5 .5pt; mso-border-top-themecolor: accent5; mso-border-top-themetint: 153; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 106.1pt;" valign="top" width="141"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 4; text-align: center;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Refrain Strategy<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid #9CC2E5 1.0pt; border-left: none; border-right: solid #9CC2E5 1.0pt; border-top: none; mso-border-alt: solid #9CC2E5 .5pt; mso-border-bottom-themecolor: accent5; mso-border-bottom-themetint: 153; mso-border-left-alt: solid #9CC2E5 .5pt; mso-border-left-themecolor: accent5; mso-border-left-themetint: 153; mso-border-right-themecolor: accent5; mso-border-right-themetint: 153; mso-border-themecolor: accent5; mso-border-themetint: 153; mso-border-top-alt: solid #9CC2E5 .5pt; mso-border-top-themecolor: accent5; mso-border-top-themetint: 153; padding: 2.85pt 5.4pt 2.85pt 5.4pt; width: 344.7pt;" valign="top" width="460"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
<span style="font-family: "times new roman" , serif; font-size: 12.0pt;">Strategy
to refrain from guessing, if the answer is unknown<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
</div>
</div>
<span style="font-family: "arial"; font-size: 11pt; white-space: pre-wrap;"><br /></span>
<br />
<h2>
<span style="font-family: "arial"; font-size: 11pt; white-space: pre-wrap;">Analysis Level 1:</span></h2>
<div>
On the top level, the probabilities seems simple. For example:</div>
<br />
<div>
If there is an exam with the NumChoices as 4 and NegRatio as 4, the the Math works like this:<br />
<br /></div>
<div>
<div align="center">
<table border="0" cellpadding="0" cellspacing="0" class="MsoTable15Plain5" style="border-collapse: collapse; mso-padding-alt: 0cm 5.4pt 0cm 5.4pt; mso-yfti-tbllook: 1152;">
<tbody>
<tr>
<td style="background: white; border-right: solid #7F7F7F 1.0pt; border: none; mso-background-themecolor: background1; mso-border-right-alt: solid #7F7F7F .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-right-themetint: 128; mso-border-right-themetint: 128; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div align="right" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 68; text-align: right;">
<i><span style="font-size: 13pt;">Probability of getting answer correct
(Pc)</span></i><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></i></div>
</td>
<td style="background: #F2F2F2; mso-background-themecolor: background1; mso-background-themeshade: 242; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 64;">
=<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
<td style="background: #F2F2F2; mso-background-themecolor: background1; mso-background-themeshade: 242; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 64;">
0.25<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="background: white; border-right: solid #7F7F7F 1.0pt; border: none; mso-background-themecolor: background1; mso-border-right-alt: solid #7F7F7F .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-right-themetint: 128; mso-border-right-themetint: 128; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div align="right" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 4; text-align: right;">
<i><span style="font-size: 13pt;">Probability of getting answer
incorrect (Pi)</span></i><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></i></div>
</td>
<td style="padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
=<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
<td style="padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
0.75<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="background: white; border-right: solid #7F7F7F 1.0pt; border: none; mso-background-themecolor: background1; mso-border-right-alt: solid #7F7F7F .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-right-themetint: 128; mso-border-right-themetint: 128; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div align="right" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 68; text-align: right;">
<i><span style="font-size: 13pt;">Marks probabilistically obtained</span></i><i><span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></i></div>
</td>
<td style="background: #F2F2F2; mso-background-themecolor: background1; mso-background-themeshade: 242; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 64;">
=<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
<td style="background: #F2F2F2; mso-background-themecolor: background1; mso-background-themeshade: 242; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 64;">
(Pc * correct answer marks) + <br />
( Pi * incorrect answer marks)<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="background: white; border-right: solid #7F7F7F 1.0pt; border: none; mso-background-themecolor: background1; mso-border-right-alt: solid #7F7F7F .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-right-themetint: 128; mso-border-right-themetint: 128; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"></td>
<td style="padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
=<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
<td style="padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm;">
(0.25 *4) + (0.75*-1)<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="background: white; border-right: solid #7F7F7F 1.0pt; border: none; mso-background-themecolor: background1; mso-border-right-alt: solid #7F7F7F .5pt; mso-border-right-themecolor: text1; mso-border-right-themecolor: text1; mso-border-right-themetint: 128; mso-border-right-themetint: 128; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"></td>
<td style="background: #F2F2F2; mso-background-themecolor: background1; mso-background-themeshade: 242; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 64;">
=<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
<td style="background: #F2F2F2; mso-background-themecolor: background1; mso-background-themeshade: 242; padding: 0cm 5.4pt 0cm 5.4pt;" valign="top"><div class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; mso-yfti-cnfc: 64;">
0.25<span style="font-family: "times new roman" , serif; font-size: 12.0pt;"><o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br /></div>
</div>
<div>
In fact, for different NumChoices and Neg Ratio this table can be used to predict marks obtained by Random Strategy at average, given large number of attempts.<br />
<br />
<div align="center">
<table border="1" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-border-insideh: .5pt solid windowtext; mso-border-insidev: .5pt solid windowtext; mso-padding-alt: 0cm 0cm 0cm 0cm; mso-yfti-tbllook: 1184; width: 70%px;">
<tbody>
<tr style="height: 11.35pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="background: #D5DCE4; border: solid windowtext 1.0pt; height: 11.35pt; mso-background-themecolor: text2; mso-background-themetint: 51; mso-border-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 6.24%;" width="6%"></td>
<td style="background: #CFE2F3; border-left: none; border: solid windowtext 1.0pt; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 19.1%;" width="19%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">NegRatio -><o:p></o:p></span></div>
</td>
<td style="background: #CFE2F3; border-left: none; border: solid windowtext 1.0pt; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.46%;" width="12%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">0.5<o:p></o:p></span></div>
</td>
<td style="background: #CFE2F3; border-left: none; border: solid windowtext 1.0pt; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">1<o:p></o:p></span></div>
</td>
<td style="background: #CFE2F3; border-left: none; border: solid windowtext 1.0pt; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">2<o:p></o:p></span></div>
</td>
<td style="background: #CFE2F3; border-left: none; border: solid windowtext 1.0pt; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">3<o:p></o:p></span></div>
</td>
<td style="background: #CFE2F3; border-left: none; border: solid windowtext 1.0pt; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">4<o:p></o:p></span></div>
</td>
<td style="background: #CFE2F3; border-left: none; border: solid windowtext 1.0pt; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">5<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 11.35pt; mso-yfti-irow: 1;">
<td rowspan="5" style="background: #D5DCE4; border-top: none; border: solid windowtext 1.0pt; height: 11.35pt; mso-background-themecolor: text2; mso-background-themetint: 51; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; mso-rotate: 90; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 6.24%;" width="6%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; margin-left: 5.65pt; margin-right: 5.65pt; margin-top: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">NumChoice<o:p></o:p></span></div>
</td>
<td style="background: #CFE2F3; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 19.1%;" width="19%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">2<o:p></o:p></span></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.46%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.25<o:p></o:p></div>
</td>
<td style="background: #FFE599; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.00<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.50<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
1.00<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
1.50<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
2.00<o:p></o:p></div>
</td>
</tr>
<tr style="height: 11.35pt; mso-yfti-irow: 2;">
<td style="background: #CFE2F3; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 19.1%;" width="19%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">3<o:p></o:p></span></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.46%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.50<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.33<o:p></o:p></div>
</td>
<td style="background: #FFE599; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.00<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.33<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.67<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
1.00<o:p></o:p></div>
</td>
</tr>
<tr style="height: 11.35pt; mso-yfti-irow: 3;">
<td style="background: #CFE2F3; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 19.1%;" width="19%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">4<o:p></o:p></span></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.46%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.63<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.50<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.25<o:p></o:p></div>
</td>
<td style="background: #FFE599; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.00<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.25<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.50<o:p></o:p></div>
</td>
</tr>
<tr style="height: 11.35pt; mso-yfti-irow: 4;">
<td style="background: #CFE2F3; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 19.1%;" width="19%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">5<o:p></o:p></span></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.46%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.70<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.60<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.40<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.20<o:p></o:p></div>
</td>
<td style="background: #FFE599; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.00<o:p></o:p></div>
</td>
<td style="background: #B6D7A8; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.20<o:p></o:p></div>
</td>
</tr>
<tr style="height: 11.35pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes;">
<td style="background: #CFE2F3; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 19.1%;" width="19%"><div align="center" class="MsoNormal" style="line-height: normal; margin-bottom: .0001pt; margin-bottom: 0cm; text-align: center;">
<span style="font-family: "arial" , sans-serif; font-size: 10.0pt;">6<o:p></o:p></span></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.46%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.75<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.67<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.50<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.33<o:p></o:p></div>
</td>
<td style="background: #F4CCCC; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
-0.17<o:p></o:p></div>
</td>
<td style="background: #FFE599; border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 1.5pt 2.25pt 1.5pt 2.25pt; width: 12.44%;" width="12%"><div align="center" class="MsoNormal" style="margin-bottom: 2.0pt; text-align: center;">
0.00</div>
</td></tr>
</tbody></table>
</div>
</div>
<div>
<br />
This analysis however does not tell one too much about what is the right strategy, because it doesn’t tell you how often does the guessing strategy fail you. To better understand we need the Lottery Analogy.<br />
<br /></div>
<table align="center" style="border: 1px solid black; width: 90%;">
<tbody>
<tr><td style="padding: 10px;"><h4>
Lottery Analogy</h4>
Imagine there is a lottery with a 1 in a billion chance to win ₹6 billion. The lottery ticket costs ₹5. By the probability analogy just established, the lottery ticket is worth ₹6 billion / 1 billion = ₹6. So therefore by above practice, it makes sense to always buy the ticket. But for a poor man, whose livelihood depends on the ₹5, it would be stupid to invest in the lottery because there is 99.999999% chance he will starve.</td></tr>
</tbody></table>
<br />
Similarly, if you are in a competitive exam with only one shot, how do you as a student decide, if this one shot is worth the risk. Or what is a probability of getting a zero or greater score by the random strategy?
<br />
<br />
For the analysis so far - only in the unique situation where the probabilistic result is zero, is there clarity over there being 50% chance of the Random Strategy being better than the Refrain Strategy.<br />
<br />
<h2>
<span style="font-family: "arial"; font-size: 11pt; white-space: pre-wrap;">Analysis Level 2:</span></h2>
<div>
This time we will have to move away from direct probability and move to a more brute force solution. For starters, we will simulate someone taking the tests with 100 questions being answered at random from 4 choices with +4 for a correct answer and -1 for an incorrect answer 1,00,000 times.</div>
<br />
<div>
The scores from the simulation look like this -<br />
<div id="Hist4-4-41">
</div>
<br />
The above plot indicates the % of tests in the simulation in which the score was higher than the corresponding number indicated on horizontal axis.<br />
<br />
So, interestingly for this case only 10% of the time does one end up with a net negative score on randomly guessed questions using the Random strategy. On the other hand there is the same 10% chance to get 57 free marks. The average as predicted by the table above is around 25 marks. So Random Strategy could be very beneficial.<br />
<br />
Here is the same plot for +3 and -1 type of exam. The gaps between the columns are because in this scenario there are some score that are not possible.<br />
<div id="Hist4-4-31">
</div>
<br />
As expected from the table above there is close to 50% chance of the Random Strategy doing better than the Refrain Strategy.<br />
<br />
This gets a little bit worse for +2 and -1<br />
<div id="Hist4-4-21">
</div>
<h2>
<span style="font-family: "arial"; font-size: 11pt; white-space: pre-wrap;">Analysis Level 3:</span></h2>
One is not always guessing<br />
<br />
There is the possibility of eliminating at least one answer. For the +4 and -1 case the plot shifts to this<br />
<br />
<div id="Hist4-3-41">
</div>
Significantly, not only has the average moved to 70, but also the chance of random strategy failing you is now down to 0.1% or 1 in a thousand.<br />
<br />
On the test side, there is also the chance that the exam does not have randomised options. That is the options A, B, C and D are in the order the question setter wrote them. Typically, a test has options like "All of the above" or "None of the above" are not randomised. In these situations, the probability of the following option being the correct answer is this:<br />
<br />
<table align="center" style="border-collapse: collapse; text-align: center; width: 350px;">
<tbody>
<tr>
<th style="border: 1px solid black; padding: 5px;">A</th>
<th style="border: 1px solid black; padding: 5px;">B</th>
<th style="border: 1px solid black; padding: 5px;">C</th>
<th style="border: 1px solid black; padding: 5px;">D</th>
</tr>
<tr>
<td style="border: 1px solid black; padding: 5px;">20%</td>
<td style="border: 1px solid black; padding: 5px;">40%</td>
<td style="border: 1px solid black; padding: 5px;">30%</td>
<td style="border: 1px solid black; padding: 5px;">10%</td>
</tr>
</tbody></table>
<br />
If the simulations are run with this in mind and the answer entered is always B, then the distribution for the Random Strategy looks like this-<br />
<br />
<div id="Hist4-4-41b">
</div>
Now no test in the simulation scored < 0. In fact the average positive gain has moves to 127 marks.<br />
<br />
Finally, typically there is a hunch that one might have, let's say that means that the probability of the hunch being correct is 50%. In that situation the distribution shift looks like this -<br />
<br />
<div id="Hist4-2-41">
</div>
No test in the simulations with score < 0 and Average moves upto 152.<br />
<h2>
<span style="font-family: "arial"; font-size: 11pt; white-space: pre-wrap;">Conclusion:</span></h2>
For negative marking exams with NumChoice = 4 and NegRatio > 3, Random Strategy is looking strong. Specifically, in situations where the test is non-randomised, an option is eliminated or there is a strong hunch, there is almost no possible way to be negatively affected by the Random Strategy.<br />
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<script src="https://rawgit.com/MahekMody/Test1/master/negmarkdata.js" type="text/javascript"></script>
<script src="https://rawgit.com/MahekMody/Test1/master/negmarkdata2.js" type="text/javascript"></script>
<script>
function trace1(data1){
this.x = data1;
this.name = 'Cumulative';
this.type = 'histogram';
this.histnorm = 'percent';
this.opacity = 0.8;
this.cumulative = {enabled: true, direction: 'decreasing'};
this.marker = {color: 'Blue', line: {width: 1, color: 'Black'}};
}
function trace2(data1){
this.x = data1;
this.name = 'Absolute';
this.type = 'histogram';
this.histnorm = 'percent';
this.opacity = 0.8;
this.yaxis = 'y2';
this.marker = {color: 'Red', line: {width: 1, color: 'Black'}};
}
function layout() {
this.xaxis = {title: "Score", zeroline: true, zerolinecolor: 'Black', zerolinewidth: 3,};
this.yaxis = {title: "% of Tests Greater than Score",};
<!--this.yaxis2 = {title: "% of Tests at score", side: 'right', overlaying: 'y',};-->
this.barmode = 'overlay';
this.legend = {"orientation": "h"};
}
var layout_single_plot = new layout();
var trace1_4441 = new trace1(x4441);
var trace2_4441 = new trace2(x4441);
var data_4441 = [trace1_4441];
Plotly.newPlot('Hist4-4-41', data_4441, layout_single_plot);
var trace1_4431 = new trace1(x4431);
var trace2_4431 = new trace2(x4431);
var data_4431 = [trace1_4431];
Plotly.newPlot('Hist4-4-31', data_4431, layout_single_plot);
var trace1_4421 = new trace1(x4421);
var trace2_4421 = new trace2(x4421);
var data_4421 = [trace1_4421];
Plotly.newPlot('Hist4-4-21', data_4421, layout_single_plot);
var trace1_4341 = new trace1(x4341);
var trace2_4341 = new trace2(x4341);
trace1_4341.marker.color = 'Orange';
trace1_4341.name = '1 Option Eliminated - Cumulative';
trace2_4341.marker.color = 'Yellow';
trace2_4341.name = '1 Option Eliminated';
var data_4341 = [trace1_4441, trace1_4341];
Plotly.newPlot('Hist4-3-41', data_4341, layout_single_plot);
var trace1_4441b = new trace1(x4441b);
var trace2_4441b = new trace2(x4441b);
trace1_4441b.marker.color = 'Orange';
trace1_4441b.name = 'Non-randomised - Cumulative';
trace2_4441b.marker.color = 'Yellow';
trace2_4441b.name = 'Non-Randomised';
var data_4441b = [trace1_4441, trace1_4441b];
Plotly.newPlot('Hist4-4-41b', data_4441b, layout_single_plot);
var trace1_4241 = new trace1(x4241);
var trace2_4241 = new trace2(x4241);
trace1_4241.marker.color = 'Orange';
trace1_4241.name = 'Strong Hunch - Cumulative';
trace2_4241.marker.color = 'Yellow';
trace2_4241.name = 'Strong Hunch';
var data_4241 = [trace1_4441, trace1_4241];
Plotly.newPlot('Hist4-2-41', data_4241, layout_single_plot);
</script>
</div>
</div>
</div>
</div>
</div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com5tag:blogger.com,1999:blog-2197236978911214706.post-49229932823906081552015-04-06T10:11:00.001+05:302015-04-06T20:09:30.837+05:30Things you must consider before you do the Fast and the Furious jump<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
Fast and the <a href="http://en.wikipedia.org/wiki/Furious_7">Furious
7</a> comes out this week and we are very intrigued by this trailer which has
our heroes jump out of a plane in cars.<o:p></o:p><br />
<div class="separator" style="clear: both; text-align: center;">
<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/RDxQPRnIMdA?rel=0" width="640"></iframe></div>
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
You have to love how the guys in the Fast and Furious 7 find
innovative ways to get their cars to weird locations. Were there other ways?
Yes, but this is cool isn’t it?<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
If you decide to make a similar drop for yourself, may be to
<a href="https://www.youtube.com/watch?v=E94IwD4yQLs">crash a party in style</a>
or <a href="http://youtu.be/1AS-dCdYZbo?t=4m3s">drop straight into a major sporting
event</a> here are the top 5 things you must check for.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div style="text-align: left;">
<h4 style="text-align: left;">
<b>1)<span style="font-size: 7pt; font-stretch: normal;">
</span><!--[endif]-->Get your Parachute pick up point correct</b></h4>
</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKctC5CnN_KwqdaRM7ddeAk0T2_MxXXmqZKDZACfZ1BMvI667-lNSAJrJw3VnLz_q6xLQe8AJfVzc8wH1K0zgihaOSxJS4-Hv0tIAQPqUl-Ry6QF1ev6dvsG0-Zf74R8uUcSjcJh0IXIo/s1600/parachute_pickup.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKctC5CnN_KwqdaRM7ddeAk0T2_MxXXmqZKDZACfZ1BMvI667-lNSAJrJw3VnLz_q6xLQe8AJfVzc8wH1K0zgihaOSxJS4-Hv0tIAQPqUl-Ry6QF1ev6dvsG0-Zf74R8uUcSjcJh0IXIo/s1600/parachute_pickup.png" height="329" width="640" /></a></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: .25in; mso-add-space: auto;">
It
is critical for you to get the place you latch the parachute onto your car
correct. As cars are designed to run on four wheels it important that it lands
on its four wheels so that you can saunter off to do what you want once you
have landed. This can be easily established by <a href="http://www.unece.org/fileadmin/DAM/trans/main/wp29/wp29wgs/wp29grsg/grsginf/79/GRSG79_inf11.pdf">working
out where the Center of Gravity</a> (CG) of the car is, and the chute pick up
point must be directly above it. A convertible will probably not work.<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<div style="text-align: left;">
<h4 style="text-align: left;">
2)<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Get your parachute size correct</h4>
</div>
<div class="MsoListParagraph" style="margin-left: .25in; mso-add-space: auto;">
It is
important you have a soft landing not wrecking your suspension. Road cars can
be modified not too much to continue operation post approximately a <a href="https://www.youtube.com/watch?v=3kntCqeudw0">1 meter jump</a>. This gives
the car a landing speed of 6.26 meter/sec.<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaSG3ZqgKFK-9JTpJ3-S1BSNkIo3M_2V5dpqO_4wLo7OG3RO8lpguJH_UwWW2oZI4Nff7AB1GTuxDwZ9VURgvIpPzG7n4kvI9Ja81svdyh_jhiUOrewrxuUtgKea8s1QYK2mCXIrRbVQo/s1600/parachute_calc.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiaSG3ZqgKFK-9JTpJ3-S1BSNkIo3M_2V5dpqO_4wLo7OG3RO8lpguJH_UwWW2oZI4Nff7AB1GTuxDwZ9VURgvIpPzG7n4kvI9Ja81svdyh_jhiUOrewrxuUtgKea8s1QYK2mCXIrRbVQo/s1600/parachute_calc.png" height="344" width="640" /></a></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: .25in; mso-add-space: auto;">
The
parachute must be at least 550 square meters per ton of the vehicle and driver
weight. The diameter of the chute for a 1000kg (1 ton) vehicle must be at least
26.5 meters.<o:p></o:p></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .25in; mso-add-space: auto;">
<br /></div>
<div style="text-align: left;">
<h4 style="text-align: left;">
3)<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Reinforce your roof pick-up point</h4>
</div>
<h1>
<o:p></o:p></h1>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="MsoListParagraph" style="margin-left: .25in; mso-add-space: auto;">
The roof
of a car is not designed to be connected to a parachute<sup> [citation needed]</sup>.
It would be a good recommendation to add a <a href="https://www.google.co.in/search?q=rally+roll+cage&tbm=isch&tbo=u&source=univ&sa=X&ei=v9z7VPCjK8aSuAT22YGIDw&ved=0CB0QsAQ&biw=1920&bih=965">roll
cage</a> to your car and attach the chute pick up on the top of that to avoid this
situation –<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWqSw7HXHWnQx_nJnxkRq7fhQQTg9YLkRPRhE43Rf_yg1xH4ifo36snAVFJodrXYJcUfz9pZi8XHM5BEoU_6B6-f9vCRL1p2bSjadbvbmc-Cz3hpc9BQ8gR9R6vwbcLFZNIT_QzNf7y7M/s1600/parachute_reinforce.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjWqSw7HXHWnQx_nJnxkRq7fhQQTg9YLkRPRhE43Rf_yg1xH4ifo36snAVFJodrXYJcUfz9pZi8XHM5BEoU_6B6-f9vCRL1p2bSjadbvbmc-Cz3hpc9BQ8gR9R6vwbcLFZNIT_QzNf7y7M/s1600/parachute_reinforce.png" height="422" width="640" /></a></div>
<div style="text-align: left;">
<h4 style="text-align: left;">
4)<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Make sure you have a system to steer the
parachute</h4>
</div>
<h1>
<o:p></o:p></h1>
<div class="separator" style="clear: both;">
</div>
<div class="MsoListParagraph" style="margin-left: .25in; mso-add-space: auto;">
A car is
useless if it lands on the top of a tree or in the middle of a lake. Parachutes
can be steered by <a href="http://www.ehow.com/how_8730364_steer-parachute.html">steering
toggles</a>. Make sure you have them inside the car before you set off from the
plane. Even better if you can connect the toggles to the steering rack.<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMZ8TFAFHtMBovAKBaGzwsHT426pe0arjYs-LmHwfzz9j2H8Py7c-oZluXx_pIr5j15eQke3s9_JceWEmTqQ9ML-oXMj1yiobq6lRa_iZFZAxBxAcaq7HSNBpmlBeccTqxyIcIip513aE/s1600/Steering_teather.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMZ8TFAFHtMBovAKBaGzwsHT426pe0arjYs-LmHwfzz9j2H8Py7c-oZluXx_pIr5j15eQke3s9_JceWEmTqQ9ML-oXMj1yiobq6lRa_iZFZAxBxAcaq7HSNBpmlBeccTqxyIcIip513aE/s1600/Steering_teather.png" height="291" width="400" /></a></div>
<h4 style="text-align: left;">
5)<span style="font-size: 7pt; font-stretch: normal; font-weight: normal;">
</span><!--[endif]-->Make sure you check your oil levels, tire
pressure, coolant level and fuel</h4>
<h1>
<o:p></o:p></h1>
<div class="MsoListParagraphCxSpFirst" style="margin-left: .25in; mso-add-space: auto;">
<!--[if gte vml 1]><v:shapetype id="_x0000_t75"
coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe"
filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="Picture_x0020_2" o:spid="_x0000_i1025" type="#_x0000_t75"
alt="http://carwarninglight.com/im/car_dashboard_indicators_warning_lights.png"
style='width:468pt;height:98.25pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\mahekm\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png"
o:title="car_dashboard_indicators_warning_lights"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><o:p></o:p></div>
<div class="separator" style="clear: both;">
</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .25in; mso-add-space: auto;">
After
you have done all of this, you don’t want your car to break down because you
did not have brake fluid in your cylinders, right? So please check these basic
things before you jump.<o:p></o:p><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDr1p-p_2RNmq6ffhrEXM5gwUS4GbNEtdZmeL3TKK-Z3rAAtkWH4NT4lw39594dM6bkT-bAZLCIOoUGTSIVYBotDx02ePF9iCfsAqOJNXqtt1Hr5mf4a2YuRN4Dgm_RN_Daw3yyflLxkc/s1600/Signals_self.PNG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDr1p-p_2RNmq6ffhrEXM5gwUS4GbNEtdZmeL3TKK-Z3rAAtkWH4NT4lw39594dM6bkT-bAZLCIOoUGTSIVYBotDx02ePF9iCfsAqOJNXqtt1Hr5mf4a2YuRN4Dgm_RN_Daw3yyflLxkc/s1600/Signals_self.PNG" height="162" width="640" /></a></div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .25in; mso-add-space: auto;">
<br /></div>
<div class="MsoListParagraph" style="margin-left: .25in; mso-add-space: auto;">
<br /></div>
<div class="MsoListParagraph" style="margin-left: .25in; mso-add-space: auto;">
<br /></div>
<div class="MsoListParagraph" style="margin-left: .25in; mso-add-space: auto;">
<br /></div>
<h1>
<o:p></o:p></h1>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com5tag:blogger.com,1999:blog-2197236978911214706.post-66797694007673273872015-03-29T19:30:00.000+05:302015-03-29T19:30:11.073+05:30India Vs New Zealand - Second best team at the world cup?<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
The Cricket World Cup 2015 is finally over and Australia are the champions again. They are certainly the best team in this competition.
In fact, knock out tournaments are well designed to find out the best teams in
the competition. In fact, it can be shown that a knockout system is the most
efficient method to find out which team is the best in a given set assuming the
results are transitive.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM3H-OkJkkYENSRXQPeNU63GCVzAF5LLsbzIM_TivH3uPO35Dk57T61PJowyS7b7_jwymcNvKPhsW3sni24oof_zJ2P7QUpWnK3mvj6w4lNLqsPEnwiV8sgYG0eyWVawAwhs9dHU_GW5M/s1600/Transetive.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiM3H-OkJkkYENSRXQPeNU63GCVzAF5LLsbzIM_TivH3uPO35Dk57T61PJowyS7b7_jwymcNvKPhsW3sni24oof_zJ2P7QUpWnK3mvj6w4lNLqsPEnwiV8sgYG0eyWVawAwhs9dHU_GW5M/s1600/Transetive.PNG" height="231" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="MsoNormal">
This format unfortunately is not a good one to find the
second best team in a set of teams. For example Australia beat Pakistan, India
and New Zealand in that order to win the World Cup. Which means that any one of
the 3 teams could have been the second best team after Australia and were just
unfortunate to play Australia early in the tournament. However, there is more
data from this world cup to play with.</div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The elaborate round robin group stage before the knock out
stages provides more results to play with and apply transitivity. For example,
famously India played Pakistan on the second day of the World Cup and India won
that encounter. Which means that one of New Zealand or India is the second best
team. Unfortunately, since the both India and New Zealand were in different
groups and they won all their matches in group stages, data from the group
stages does not sort the problem of which is the second best team.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
In fact if we try and rank the teams in the knock out stages
using world cup data and transitivity this is the only unresolved ranking:<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH62Ohi1n1TV5XPbzdybeydd375DE5LXRzleBfa9zJes5WPK-mTnNIClil1x1ZJf-TazxuYBaaWxQw1MYLCYilLefYVihoif_AUwu7UZXTmHy7APN_9LiMXadaNSPhpeNHoQEb6gQ2I3o/s1600/Ranking.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiH62Ohi1n1TV5XPbzdybeydd375DE5LXRzleBfa9zJes5WPK-mTnNIClil1x1ZJf-TazxuYBaaWxQw1MYLCYilLefYVihoif_AUwu7UZXTmHy7APN_9LiMXadaNSPhpeNHoQEb6gQ2I3o/s1600/Ranking.PNG" height="595" width="640" /></a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: x-small;">Note: The game where New Zealand beat Australia is ignored
because Australia beat them in a game that mattered more.</span><o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
If New Zealand would have beaten Australia in the final then
the transitivity could have accounted for the full ranking. However, now an
India Vs New Zealand match is needed to sort this once it for all. This will
make the world cup more productive.<o:p></o:p></div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com5tag:blogger.com,1999:blog-2197236978911214706.post-34425468830839379022014-11-15T08:48:00.000+05:302014-11-15T12:00:48.622+05:30Why do couples at Marine Drive sit equally spaced from one another?<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
An
interesting observation made by <a href="https://twitter.com/TheToothsayer" target="_blank">@TheToothsayer</a> when we recently visited Marine drive
was that the couples that sit at the sea front, sit equidistant to one another,
quite precisely equidistant that too and over large distances. This nonchalant observation
has more interesting insights than what is prevalent on the first look.</div>
<div class="MsoNormal">
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiD8l_cfwEpxWLk8mk4lo7O_1xAaX-FAquWGOTEJJ_WATZbjXtVfvyyuA7L7D2suDR3A_HvrrkOOXIeGO35NucwcnfDnzefWBCrc6H-CFJIZtoERNxXadGihjjvIgPBeTnuVw1InCJdWw0/s1600/2010-08-30.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiD8l_cfwEpxWLk8mk4lo7O_1xAaX-FAquWGOTEJJ_WATZbjXtVfvyyuA7L7D2suDR3A_HvrrkOOXIeGO35NucwcnfDnzefWBCrc6H-CFJIZtoERNxXadGihjjvIgPBeTnuVw1InCJdWw0/s1600/2010-08-30.jpg" height="266" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><span style="background-color: white; color: #222222; font-family: arial, sans-serif; text-align: start;">Photo courtesy: Kunal Bhatia - </span><a href="http://www.mindlessmumbai.com/" style="background-color: white; color: #1155cc; font-family: arial, sans-serif; text-align: start;" target="_blank">www.mindlessmumbai.com</a></td></tr>
</tbody></table>
Two odd
things – firstly, there is no clear coordinator imposing that they should be
sitting at a certain distance from one another and secondly, there seems to be
no conscious effort to do this coordination. It just happens, it happens every
single day.</div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">How this
formation happens is perhaps not too difficult to imagine if we piece this
together in the chronology of the couples arriving at Marine Drive. Much like the <a href="http://blog.xkcd.com/2009/09/02/urinal-protocol-vulnerability/" target="_blank">XKCD Urinal Protocal Situation</a>, we can
postulate 3 basic rules that a logical couple would follow to find themselves a
spot at the sea front -</span></div>
<div class="MsoListParagraphCxSpFirst" style="margin-left: 38.25pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<br />
<ol style="text-align: left;">
<li>The
couples like privacy<sup> [<strike>citation </strike>experience needed]</sup> and they will optimize their
distance from other couple such that they will maximize the minimum distance
they have from any other couple.</li>
<li>There
is a distance after which increasing the minimum distance from the next
couple has no added value. Simpler way to state this is that a couple once a certain distance away from the next couple will just choose that spot because it’s not
worth walking further.</li>
<li>Similarly,
there is a distance that is the minimum acceptable distance from the next
couple, that a couple can tolerate. This means that if the maximum minimum
distance from any couple is less than this distance, then the couple will
choose to wait for a spot over squeezing themselves awkwardly between the other
couples.</li>
</ol>
</div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 38.25pt; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">Based on these
the situation pans out to be something like this –<o:p></o:p></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_TB6xEd-pywuG6Egayb1H__n6s5yx6-nMoEgmNQuidcLT4Hm3TFG7K5yd4SlnvNBYQ_A3AH3GuaTxb0VqVQtfgobNoFa7PlGUTurfSs9cWcl1vOL5lIyUpiXmJQhhEC5JKUQM5FxkLF0/s1600/Diagram.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_TB6xEd-pywuG6Egayb1H__n6s5yx6-nMoEgmNQuidcLT4Hm3TFG7K5yd4SlnvNBYQ_A3AH3GuaTxb0VqVQtfgobNoFa7PlGUTurfSs9cWcl1vOL5lIyUpiXmJQhhEC5JKUQM5FxkLF0/s1600/Diagram.gif" height="640" width="426" /></a></div>
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
</div>
<br /></div>
<div class="MsoNormal">
What is
remarkable here is that all the 3 rules were for each individual couple and
there was no coordinating agent that ensured that an equidistant pattern was
formed. This is a purely self-organized pattern, which is a social trait of
human beings. In fact, it would be safe to say that if there had been an
established authority that made couples sit equidistant, then there would be
resistance and it would not work with the smoothness it does naturally.</div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">There is
one situation when this logic does break down. When two neighbouring couples leave at the
same time, where would the arriving couple choose their spot?<o:p></o:p></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwSO2JnbRHkSWYjT1CPHHKxDoYLnwuxVOEmxvwyoFnQb4aQFz5apAnPc1EOFijvr3HOTgVl6vwKiFVh9wV286jHGLK2xcaOWD7byRXLaeAgZB4do1v9J6iOnaVn-ATy6YhMtR-MAWrPLI/s1600/Capture.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwSO2JnbRHkSWYjT1CPHHKxDoYLnwuxVOEmxvwyoFnQb4aQFz5apAnPc1EOFijvr3HOTgVl6vwKiFVh9wV286jHGLK2xcaOWD7byRXLaeAgZB4do1v9J6iOnaVn-ATy6YhMtR-MAWrPLI/s1600/Capture.PNG" height="200" width="400" /></a></div>
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">If the 3
logical rules are to be followed, then position A is the logical choice but
Position B and C would keep the couples equidistant. I asked 30 random people on the train I
am on right now, which position they would choose (I told them what I was doing
after they chose). 27 out of the 30 chose position B. </span>I would
have chosen Position A because I would like to think I like logic over symmetry;
however that is probably my frame of mind when writing this. Nature
loves symmetry and it is clearly manifested in the human mind.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-US">And THAT is
why couples at Marine Drive are equidistant to one another.<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">Edit: This
article has resulted in an overnight Phd into co-operative behaviour in the
natural world – Seems like this is not only a human trait; interestingly here
is a picture of ants self-organizing into equidistant pattern around their
food.<o:p></o:p></span><br />
<span lang="EN-US"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhemHiFlVElcjAE18BX16RPJJma_CZDXKFKBXCKlcR8NzQTWCKfcY58CKmrbR_8huJ7drJLkJhUjUIGlJd1ntLdOPnOfTTPGISuBk7Lj_4pOjzdesSxV_zNoJs7A99fkcQ0Dg3FhUHTHhc/s1600/ants-self-organisation.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhemHiFlVElcjAE18BX16RPJJma_CZDXKFKBXCKlcR8NzQTWCKfcY58CKmrbR_8huJ7drJLkJhUjUIGlJd1ntLdOPnOfTTPGISuBk7Lj_4pOjzdesSxV_zNoJs7A99fkcQ0Dg3FhUHTHhc/s1600/ants-self-organisation.png" height="252" width="320" /></a></div>
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">Also surprisingly,
Cognitive Biology is way simpler to make sense of over <a href="http://www.mahekmody.com/2014/08/the-lunar-program-reflection.html" target="_blank">Photometry</a>.<o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
</div>
<br /></div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com7tag:blogger.com,1999:blog-2197236978911214706.post-49399190900036456482014-08-03T17:14:00.000+05:302014-08-04T10:07:33.505+05:30The Lunar Program - A Reflection<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal" style="text-align: justify;">
This is one of the most depressing plots I know -</div>
<div class="MsoNormal" style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm2FEFsqTYGFJ1ge4Z_b2RKHg064J2371xbFxeorQl56ucRr9KcZh9JKL5QJNVhWWaMnoAfQBvSEt43ucKYK2LKYY4f-Qc4qqILB2bU-JJM5rgFa7ox_WFHijGKFCafFxxe3HlEoE3dwQ/s1600/Moon-landing-time-plot-2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm2FEFsqTYGFJ1ge4Z_b2RKHg064J2371xbFxeorQl56ucRr9KcZh9JKL5QJNVhWWaMnoAfQBvSEt43ucKYK2LKYY4f-Qc4qqILB2bU-JJM5rgFa7ox_WFHijGKFCafFxxe3HlEoE3dwQ/s1600/Moon-landing-time-plot-2.png" height="232" width="400" /></a></div>
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="MsoNormal" style="text-align: justify;">
Getting to the moon was significantly difficult to do in the
1960s than it is today, but still for some reason we don't go there. In the
1960s and the 1970s there was a cold war that caused enough motivation for J.F.
Kennedy to pile up the country’s resources outside the NASA headquarters to get
to the moon at any cost. Today, there is no cold war and economics has
dominated the decisions to end the shuttle program. We need economic demand to
go to the moon and we need to do this fast. I am going to do a few blog posts about
a few ideas I have thought of. Consider these as Elon Musk style open patents,
from someone who is significantly more lazier than him. We (humanity) must get some engineers out there to solve our problems.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgg2wNMTRa4dvqqpEN8CANtTmDCCeUePmcgQHJTqmcor3-b2OKd1WL4QrZCBGEET7d4uiQx1PfSWjgCA2eOcX8svgrHaC86L3236NlvRdglidFALf1kSa5X86t7A_eMH2H0sAPaFv5fZK4/s1600/moon-landing-trust-me-im-engineer-flag.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgg2wNMTRa4dvqqpEN8CANtTmDCCeUePmcgQHJTqmcor3-b2OKd1WL4QrZCBGEET7d4uiQx1PfSWjgCA2eOcX8svgrHaC86L3236NlvRdglidFALf1kSa5X86t7A_eMH2H0sAPaFv5fZK4/s1600/moon-landing-trust-me-im-engineer-flag.png" height="303" width="400" /></a></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
What the world needs right now is a solution to the energy crisis.
The Moon probably does not have oil, considering oil was formed from once
fossilised life-forms. The Moon probably does not have coal or natural gas either for the same reason. What the moon has is a lot of barren land. What use is a lot of barren land that is visible from most of the Earth in the night time?</div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Meanwhile, the FIFA world cup has just concluded and there
has been a lot of talk in Brazil, over whether it was worth hosting it. Sports
are good. They are fun, bring the world together in friendly rivalry, boost
local economies, provide great conversation starters and are a welcome
distraction / entertainment source to the daily life. All of this comes at a
cost and it is a good idea to bring these costs down. I am sure the FIFA world
cup is expensive to host, one of the most visual expenses are the stadiums. The
stadiums are large and extravagant. All of them now have flood lights which
turn night to day at the stadium. This obviously is expensive to do, but night
matches are economically worth it. It makes the game happen at prime time, and an
artificial lights game is quite a spectacle.<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal" style="text-align: justify;">
It would be nice if we could play sport in the moon light,
but unfortunately moon light is not enough.<o:p></o:p></div>
<blockquote class="tr_bq" style="text-align: justify;">
<span style="font-size: x-small;">This is an engineering blog so “not enough” is not an
acceptable answer. Illumination can be measured. The SI unit of the Illuminance is ‘lux’. This is what light meters measure. When a cricket umpire
holds out a meter, he is measuring the light per square meter. The SI
unit of light is candela, which is the amount of light provided by one candle
(a definition, a bit like horse power, I am amused by the idea that there is a
standard candle/horse somewhere in the world which was used as <a href="http://www.pgccphy.net/ref/photometry.pdf" target="_blank">reference</a>).
For cricket ‘lights’ is offered to the batsman if the illuminance is less than a
1,000 lux. However, the <a href="http://www.fifa.com/mm/document/tournament/competition/51/54/11/stadium_tech_rec_req_guide_to_lighting_en_7306.pdf" target="_blank">FIFA regulations</a> are tougher, demanding at least an
average of 3,500 lux for an International televised game. Moon light at an
average is 0.4 lux. So moon light is “not enough” by 17,500 times.</span></blockquote>
<div class="MsoNormal">
<o:p></o:p></div>
<div style="text-align: justify;">
Why is the moon light so low? Moon light is essentially
Sunlight that is reflected by the Moon. The moon is at an average equally far
away from the Sun as the Earth is, so the illumination received by the moon is
the same as Earth on a sunny cloudless day, which is 1,20,000 lux. On a full
moon night, the Earth receives a small fraction of light reflected by the moon,
as this diagram will explain (Note the log scale).</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitbHElF_z8SDfjmg56w59INBW9Tv_0O9cmDDufcrPHRoKR57TZyTW3a9ygK4R8TzKmTDvHvs5VtzvDd4Tl9-f8HbrnhVuE_8R0quhcp5YWlxr8lRIQU5bvh-dFplNDnKTLSLQzItmXZog/s1600/moon-reflection-efficiency-2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEitbHElF_z8SDfjmg56w59INBW9Tv_0O9cmDDufcrPHRoKR57TZyTW3a9ygK4R8TzKmTDvHvs5VtzvDd4Tl9-f8HbrnhVuE_8R0quhcp5YWlxr8lRIQU5bvh-dFplNDnKTLSLQzItmXZog/s1600/moon-reflection-efficiency-2.png" height="406" width="640" /></a></div>
<br /></div>
<div style="text-align: justify;">
The reflection co-efficient of the moon is 0.136 which means
that 13.6% of the light incident on the moon is reflected. The fraction of the reflected light that the Earth would
intersect is -<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-85JT-rLRyG9JdRxJxo8HQK3lLlD4gxVKt-VEVBaVgcBI2Yv9A9U5r86ctLqE8N2oJwgq3FQPIdjg3UcGQQcrSuMgELnWt7fC_PsizHf8Vu32LqfFAFWp1cv4llJQeUGsM97Q6aDke0s/s1600/moon-illumination-equation-2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-85JT-rLRyG9JdRxJxo8HQK3lLlD4gxVKt-VEVBaVgcBI2Yv9A9U5r86ctLqE8N2oJwgq3FQPIdjg3UcGQQcrSuMgELnWt7fC_PsizHf8Vu32LqfFAFWp1cv4llJQeUGsM97Q6aDke0s/s1600/moon-illumination-equation-2.PNG" height="50" width="640" /></a></div>
This value is ~.7 lux but the average illumination of the
moon light measured on a clear night is 0.25, which means there is a 35.5%
efficiency factor in there which accounts for light lost in the atmosphere (due
to lack of clear skies) and averaging out of the fact that there is an angle of
incidence involved both on Earth and on the moon.</div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
To have moonlight soccer, we need to start working on making
this more efficient. Let’s start with the reflection co-efficient - place
mirrors on the moon. We clearly need to go to the moon to do this. We have
managed to produce 99.99% reflecting surfaces but let’s cover the moon by 99%
reflecting mirrors. However, even if we cover all of the moon, our new ‘Disco
ball’ moon will only reflect ~7.2 times more light which is still nowhere
enough.<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal" style="text-align: justify;">
Only a fraction of the reflected light actually hits the
Earth, so the rest of the reflected light is wasted. We must have movable
‘sunflower mirrors’ that always point in the direction such that it reflects
light to Earth. These movable mirrors will directly impact the light spread
related efficiency factor. In fact, since all the light reflected by it is
directed towards the Earth this efficiency factor can go up very close to 1. If the entire Moon surface is used to
illuminate the entire Earth's night sky on a full moon day, the average illumination
would be -<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpxPL0dP4s0GNksANcOibla15Ei7Dmei48Dpdw_YgdZWBHHwzm1ZeeyRp5_1-LZDI56v-qm4HhJn2mgEZnOCnLyw4gj_Ee7ihWvm3LkIFX_TzpR5kOHD0ms7B9Jk2Va6sBKJbVELJQzfI/s1600/moon-reflector-equation.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgpxPL0dP4s0GNksANcOibla15Ei7Dmei48Dpdw_YgdZWBHHwzm1ZeeyRp5_1-LZDI56v-qm4HhJn2mgEZnOCnLyw4gj_Ee7ihWvm3LkIFX_TzpR5kOHD0ms7B9Jk2Va6sBKJbVELJQzfI/s1600/moon-reflector-equation.PNG" height="68" width="640" /></a></div>
<div class="MsoNormal" style="text-align: justify;">
Adding the 35.5% efficiency factor accounting for atmosphere
loss and angle of incidences, the average illumination of the Earth at night
would be 3090 lux which is enough to host a cricket match anywhere on Earth any
time of the day.</div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal" style="text-align: justify;">
However, we still have all of the moon covered with
reflectors that illuminate all of the Earth. This is still wasteful and very
<a href="http://en.wikipedia.org/wiki/Ecological_light_pollution" target="_blank">confusing to wild life</a>.
We can consider reducing the effective
reflector size. To illuminate the all of the Earth with 3090 lux we need the
entire moon surface. To illuminate only a specified area on Earth with a
desired illumination, the reflector area on Earth can be calculated by -<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaudVgze4RNLRkP7y4YDDUHfvNdF9FgX6FlzgagEuYkFyrbZIQaU0ELQWDD4iyHoeokjJxvz2J4UHjJk1yViqfHd37BIRARurAOrnUhgIFw38GB-Z8hhunGHVDo9vi47pXFyWkeHYDfks/s1600/moon-reflector-area-equation-2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaudVgze4RNLRkP7y4YDDUHfvNdF9FgX6FlzgagEuYkFyrbZIQaU0ELQWDD4iyHoeokjJxvz2J4UHjJk1yViqfHd37BIRARurAOrnUhgIFw38GB-Z8hhunGHVDo9vi47pXFyWkeHYDfks/s1600/moon-reflector-area-equation-2.PNG" height="54" width="640" /></a></div>
For a cricket field to be illuminated by 1000 lux, we need
reflector area approximately 30 times smaller than a cricket field. For a FIFA match we can
do with the total reflective area of 10 times smaller than a football field.
They seem manageable, don’t they?</div>
<div class="MsoNormal" style="text-align: justify;">
<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
These reflectors can change their angle of incidence, which
means the same reflectors can light up a football match in Australia, Europe
and South America on a single day. Stadiums simply rent the reflectors on a
need basis and pay by the hour. Beyond sport, this gives us the power of shining
light on any part of Earth whenever necessary. Imagine how useful will it be to
literally light up a rescue operation if a train were to have an accident at a
remote location in the middle of the night. To light up 1 km of a 6 lane
highway as per <a href="https://www.ies.org/PDF/100Papers/098.pdf" target="_blank">this, </a>we need only
~35 meter square of reflectors.<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal" style="text-align: justify;">
Anyhow, I'm looking
forward to sporting events scheduled as per the lunar calendar, and a cricket
match being interrupted by a lunar eclipse.<o:p></o:p></div>
<div class="MsoNormal" style="text-align: justify;">
<br /></div>
<div class="MsoNormal">
</div>
<div class="MsoNormal" style="text-align: justify;">
Hash-tag -> <a href="https://twitter.com/hashtag/GoToTheMoonAgain" target="_blank">#GoToTheMoonAgain</a><o:p></o:p><br />
<br />
P.S.: I also learnt that Photometry as a subject has one of the highest (Difficulty to understand / How simple it looks) ratio that I have come across. Also, solid angles are evil.</div>
<div class="MsoListParagraph">
<o:p></o:p></div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com1tag:blogger.com,1999:blog-2197236978911214706.post-33603594713872557342014-07-30T13:48:00.000+05:302014-08-23T14:10:35.533+05:30Suspension Design Kinematics - Degrees of Freedom<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<span lang="EN-US">Suspension
design starts off as a kinematic problem that the designer must solve. There
are very easy methods to evaluate the basic sanity of the solution that one
might have thought of. An independent suspension with its steering locked has
one degree of freedom. This degree of freedom (DOF) is the travel of the
suspension. When a design solution for the suspension is thought of, it is important
to do the degree of freedom analysis.<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">For example,
this double ‘a-arm’ suspension in the figure below has an upper and lower
control arm with a toe rod which has ball joints on either end.</span> </div>
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHZN5JK9GOJ2UUzsVQYgf2QJGAerJwihbEdRhNblmUH_F3__X2WQNrag-FJlI3cetXdfkv6wGg8gltkvkIa6V763IPMnsxbFHgt0lBILVEwXIKNAI_GDllDfQPcxnd1jqjYspYFWfzyPE/s1600/DoubleAArmSuspension.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgHZN5JK9GOJ2UUzsVQYgf2QJGAerJwihbEdRhNblmUH_F3__X2WQNrag-FJlI3cetXdfkv6wGg8gltkvkIa6V763IPMnsxbFHgt0lBILVEwXIKNAI_GDllDfQPcxnd1jqjYspYFWfzyPE/s1600/DoubleAArmSuspension.PNG" height="225" width="400" /></a></div>
<br />
The DOF of
this suspension system can be simply analysed like this –</div>
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHFugIevgPi1qEh5Yn745MnwHotvYib3bDcM-e96asoud5yngxmAdjjTuhQtz1ivZgO7oUDE_09DSZ3IbcKFW9tdKGUyj93LIyIuvcpc57sIsc32t65YHwUJQGl0ZoC9G2IOI87A33w9o/s1600/DoubleAArmDOF.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiHFugIevgPi1qEh5Yn745MnwHotvYib3bDcM-e96asoud5yngxmAdjjTuhQtz1ivZgO7oUDE_09DSZ3IbcKFW9tdKGUyj93LIyIuvcpc57sIsc32t65YHwUJQGl0ZoC9G2IOI87A33w9o/s1600/DoubleAArmDOF.PNG" height="432" width="640" /></a></div>
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US" style="font-size: x-small;">*The A-arms
being joined to the chassis by 2 ball joins is actually an over constrain. The
ideal solution would be to have a ball joint at one of the pick-ups and a ball
joint in a slider on the other pick up. This is however not practical and
usually the kinematic over-constrained is persisted with, to better distribute
loads. Think is this in the same way as a door having multiple hinges when
kinematically a single hinge would do. This is also the ‘a-arm’ must be
manufactured with precision on a jig. Any misalignment will cause compliance in
the structure.<o:p></o:p></span><br />
<span lang="EN-US" style="font-size: x-small;"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US"><span style="font-size: x-small;">** The 2
ball joints are usually rod-ends in a toe rod. The rod-ends are not ideal ball
joints. The limited articulation does not allow the tie rod to spin about its
axis and this constrains another degree of freedom associated with the spinning
of the toe-rod within its place.</span><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">It has one
degree of freedom which means that baring interference the suspension travel is
easily achieved without any of the members flexing.<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">This degree
of freedom analysis is important to determine if a suspension configuration
would work or not. For, example these pictures below illustrate another
solution to toe control in the rear where the tie rod is welded on to the
control arm.<o:p></o:p></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglAkxlgZNLS3RJSicK9ma56Kxrfr7JmRvGuivfFk3_yyCBW1tXNZ_IVdtpIkic0a2bNoDT7EvBHbtzQDPyawxzF_pNHHMg0kgUkLzrxUT3UxvXpnmOkBND6fBccvN9fkqyk6Ghs_XtNKA/s1600/WeldedToeRodBajaFSAE.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglAkxlgZNLS3RJSicK9ma56Kxrfr7JmRvGuivfFk3_yyCBW1tXNZ_IVdtpIkic0a2bNoDT7EvBHbtzQDPyawxzF_pNHHMg0kgUkLzrxUT3UxvXpnmOkBND6fBccvN9fkqyk6Ghs_XtNKA/s1600/WeldedToeRodBajaFSAE.PNG" height="346" width="640" /></a></div>
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
People who
have read <a href="http://www.mahekmody.com/2014/08/toe-compliance-control-toe-base.html" target="_blank">this blog post</a> would be quick to point out that the toe base here is
too small. The <a href="http://www.mahekmody.com/2014/04/load-paths.html" target="_blank">load path</a> is not great because forces apply bending moments on
the control arm. However, this suspension solution also does not fare well with
the DOF analysis.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH2hbjG5rpp40R3Wc9FIf1Xxu5xp1eKGggHBeIVwb3CubeQBjRZFTihpTUWQcVDcSX2AESW-xVCnB74NaOLe07QcSa-wQ5nXPPUXNCH9K5zxO_TGLcI1piToO8n9ItTpmxKS1Z3H1MgOg/s1600/WeldedToeDOF.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgH2hbjG5rpp40R3Wc9FIf1Xxu5xp1eKGggHBeIVwb3CubeQBjRZFTihpTUWQcVDcSX2AESW-xVCnB74NaOLe07QcSa-wQ5nXPPUXNCH9K5zxO_TGLcI1piToO8n9ItTpmxKS1Z3H1MgOg/s1600/WeldedToeDOF.PNG" height="434" width="640" /></a></div>
<br /></div>
<div class="MsoNormal">
<span lang="EN-US">Such suspension
solution might function like a 1 DOF system if the over-constrains are
redundant. However, slight misalignment or manufacturing tolerance error would
cause components to go through high stress cycles and eventually break. For the
sake of completion the correct way to get the DOF correct in the above solution
is to have a control rod, with ball joints at either end as the lower control
arm instead of an ‘a-arm’.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span lang="EN-US">DOF is only
one of the criterions that must be kept in mind. The DOF solution in the
suspension system in the picture below is good. However, there can still be an
issue with the toe compliance here. Even though the toe base is reasonably large
the toe rod pick-up is a cantilever on the upright. It will see a lot of
bending moments and cause compliance due that bit flexing.<o:p></o:p></span><br />
<span lang="EN-US"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2QxGRyx_ahKH5jnEm1aZOsGUXD2UN6SsxN1w4UhyzDlC2y1urn_eVqi4xIsA-TTypgnzqmakV_17fhyphenhyphenAii5QKZ-aGyoc2VFxIN94yrGLGlY6AU28TeWBN8fzXL-aJrpmolrm8rjPXTKM/s1600/CantileverToe.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi2QxGRyx_ahKH5jnEm1aZOsGUXD2UN6SsxN1w4UhyzDlC2y1urn_eVqi4xIsA-TTypgnzqmakV_17fhyphenhyphenAii5QKZ-aGyoc2VFxIN94yrGLGlY6AU28TeWBN8fzXL-aJrpmolrm8rjPXTKM/s1600/CantileverToe.JPG" height="400" width="358" /></a></div>
<span lang="EN-US"><br /></span><span style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;">This blog post is originally written for the </span><a href="http://www.formulastudent.in/" style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;" target="_blank">Formula Student India</a><span style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;"> website and has been cross posted from </span><a href="http://formulastudent.in/designerror/suspension-design-kinematics---degrees-of-freedom" style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;" target="_blank">here</a><span style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;">.</span></div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com0tag:blogger.com,1999:blog-2197236978911214706.post-38246041487906889442014-07-18T20:07:00.000+05:302014-08-22T20:30:39.305+05:30Toe Compliance Control - Toe Base<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<span lang="EN-US">We have a
seen a lot of teams show up with a rear suspension like the one in this picture
–<o:p></o:p></span></div>
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQiKCeKmCTmNXTi99HFcAyWpWBzpP0H8v4JkIw4KH9SvtAaJOVvpfFGES9dpVPb6z_sz28fbxI9dLLn3m-JUonVbqCv0kyuLf8zwPG92manC-akfRcQ4_JtYMW4cSIhz0uEu_sPJ6sbcQ/s1600/No-toearm.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiQiKCeKmCTmNXTi99HFcAyWpWBzpP0H8v4JkIw4KH9SvtAaJOVvpfFGES9dpVPb6z_sz28fbxI9dLLn3m-JUonVbqCv0kyuLf8zwPG92manC-akfRcQ4_JtYMW4cSIhz0uEu_sPJ6sbcQ/s1600/No-toearm.JPG" height="378" width="400" /></a></div>
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">What I am
specifically pointing out is the method of toe control in the rear. There are 2
control arms and the upper one what looks like an implementation of a revolute
joint through a bushing. This works in theory but practically there is bound to
be compliance in the joint. This is not only form the compliance from the
bushing but also from the compliance that arises out of having a tiny toe base.<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">The
definition of the toe base of the vehicle is varied but in general it is the
length of the moment arm of that opposes the re-aligning torque that the tyre
produces. In this above picture it is the length of the cylindrical section at
the outer end of the control arm. This is clearly small as is a definite ‘No No’
for a Formula Student car. The suspension must have a toe link.<o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">In a more
conventional suspension system there is a toe bar that prevents the rear
suspension from steering. Here the toe base can be more clearly defined as the perpendicular
distance of the point where the toe arm meets the upright from the king pin
axis. The diagram clearly demonstrates this –<o:p></o:p></span><br />
<span lang="EN-US"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv47Dys62BZaAHwW5Be__1tYFsvRyfkHCY6uLJFdkYuPGGVAfqIZEXi2ydKgWvRTwenmcKtZe9rKJYmt3VwASIW9EkdxOruLPDgA2xoJf7CeUXnm9aNg1Ck2GLbYa78Bt9WLb9Y6FCv4o/s1600/ToeBaseDefinition.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgv47Dys62BZaAHwW5Be__1tYFsvRyfkHCY6uLJFdkYuPGGVAfqIZEXi2ydKgWvRTwenmcKtZe9rKJYmt3VwASIW9EkdxOruLPDgA2xoJf7CeUXnm9aNg1Ck2GLbYa78Bt9WLb9Y6FCv4o/s1600/ToeBaseDefinition.PNG" height="272" width="400" /></a></div>
<br /></div>
<div class="MsoNormal">
<span lang="EN-US">It is
important for the toe base to be large. The compliance (or the ‘play’) in the
suspension system dramatically reduces as the toe base becomes bigger. This can
be simply illustrated by this simple thought experiment. Support you have a
spherical bearing with 1 mm of compliance in it. Note: 1 mm compliance is chosen
for ease of calculation, if you really have a bearing with 1mm compliance you
must throw it away. This compliance will translate to the wheel being compliant
when turned in the top view of the car. Here is a plot of the compliance in the
wheel in degrees vs the toe base length.<o:p></o:p></span></div>
<div class="MsoNormal">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiNEXINXMqTs9PMq6PQNB4J40lVX44DEo2uAmMYGpOk0T00Q79fdXL7urR1b6kOHnkr8RHi40EpIASTLi9yWWLULYk7c8-12q_cOLjWWQ2otKlU3s8pNbOneSZ03R72hEDD2f74ffha3k/s1600/ToeCompliancePlot.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgiNEXINXMqTs9PMq6PQNB4J40lVX44DEo2uAmMYGpOk0T00Q79fdXL7urR1b6kOHnkr8RHi40EpIASTLi9yWWLULYk7c8-12q_cOLjWWQ2otKlU3s8pNbOneSZ03R72hEDD2f74ffha3k/s1600/ToeCompliancePlot.PNG" height="260" width="400" /></a></div>
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">The graph
clearly illustrates the importance of having a large toe base. Simply having
the toe link will NOT do. The suspension in the next picture will be compliant
of this reason.<o:p></o:p></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQPTCMXi2yqWbr0IP5GaTppqxpAWn1QDzEo49weyM85CsB-QjCI504SMdk8Iqx_hpxbcbAR0DPtstOJR8Akso_2XuYLcwz0MFNLFtL7xWv6jAYGdmCFXDB8FSb1fQREDVL8U8f-I4Oii4/s1600/ToeLengthIssue.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQPTCMXi2yqWbr0IP5GaTppqxpAWn1QDzEo49weyM85CsB-QjCI504SMdk8Iqx_hpxbcbAR0DPtstOJR8Akso_2XuYLcwz0MFNLFtL7xWv6jAYGdmCFXDB8FSb1fQREDVL8U8f-I4Oii4/s1600/ToeLengthIssue.JPG" height="386" width="400" /></a></div>
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">Rear toe
compliance on a Formula Student vehicle will make it handle like a super-market
trolley and will lose points in design. Which is why it finds second place in
Pat’s <a href="https://www.formulastudent.de/academy/pats-corner/advice-details/article/pats-seven-deadly-sins-of-fs-design/" target="_blank">“Seven Deadly Sins of FS Design”</a> <o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US">
</span></div>
<div class="MsoNormal">
<span lang="EN-US">Moral of
the story : Toe compliance is evil. Evil can be fought with larger toe-base.
Hero wins only with a larger toe base, a little like this one -<o:p></o:p></span><br />
<span lang="EN-US"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhyKtPk90xbkf07eiz0eYdXQj7V23_CV6apgWxPdAoRbTMQvIt-CAcId31s5d0X2rm88oOYSK50s9zONkPrlyuFGWq5TUNckWN4biNuxgsCSot28CsgWiJOiwxQimC1jnHorGhdD_s9UU/s1600/ToeBaseCorrect.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhyKtPk90xbkf07eiz0eYdXQj7V23_CV6apgWxPdAoRbTMQvIt-CAcId31s5d0X2rm88oOYSK50s9zONkPrlyuFGWq5TUNckWN4biNuxgsCSot28CsgWiJOiwxQimC1jnHorGhdD_s9UU/s1600/ToeBaseCorrect.PNG" height="386" width="400" /></a></div>
<span lang="EN-US"><br /></span></div>
<div class="MsoNormal">
<span lang="EN-US"><span style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;">This blog post is originally written for the </span><a href="http://www.formulastudent.in/" style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;" target="_blank">Formula Student India</a><span style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;"> website and has been cross posted from </span><a href="http://formulastudent.in/designerror/toe-compliance-control---toe-base-1" style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;" target="_blank">here</a><span style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;">.</span></span></div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com0tag:blogger.com,1999:blog-2197236978911214706.post-57411968059878719642014-06-13T21:28:00.001+05:302014-06-14T11:57:14.589+05:30Bangalore Rain Vs Bombay Rain<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
<blockquote class="tr_bq">
Dear Bangalore,<br />
If you want to be the next Bombay, you HAVE TO figure how to
handle the rain.<br />
Sincerely,<br />
Almost missed the train.</blockquote>
<o:p></o:p></div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal">
<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqgYMcIvvzli3Fj3Eg6kOmAARYrAv8EgkYAqnP8NI9XMwoMvXDQPZ9O_xrtNa4xXGzksdnnP_TwRWVdzyOXYN6syIY21qJDwZLbq0S4YOjHZKTFkUrgmz5HyxZ7uyk_BtdXGO6qXR12F4/s1600/Whats_rain_called_graph.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqgYMcIvvzli3Fj3Eg6kOmAARYrAv8EgkYAqnP8NI9XMwoMvXDQPZ9O_xrtNa4xXGzksdnnP_TwRWVdzyOXYN6syIY21qJDwZLbq0S4YOjHZKTFkUrgmz5HyxZ7uyk_BtdXGO6qXR12F4/s1600/Whats_rain_called_graph.PNG" height="480" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsXAZw_msavKSoq90ZE6D9n4-pli7gI8cVE5k1ZgthhhW7n0JiKHDbmq7iyWMhQJleOPmHlYI3dm_fqOnm0l3KM3fdpwq1Hs8pL9kwD0eY45x1_hDUHNRzmNUClc4SI5WXWMvK2osr37U/s1600/rickshaw_meter_multiplier_graph.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsXAZw_msavKSoq90ZE6D9n4-pli7gI8cVE5k1ZgthhhW7n0JiKHDbmq7iyWMhQJleOPmHlYI3dm_fqOnm0l3KM3fdpwq1Hs8pL9kwD0eY45x1_hDUHNRzmNUClc4SI5WXWMvK2osr37U/s1600/rickshaw_meter_multiplier_graph.PNG" height="480" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieNkS-vHMm_404EruhH4eIalhBakZ66GjyKTMPlOkmT8r-zv1p8hYYovlsTom6FJ9yo8HCzlt_ImcZtoPw-P2WYRybrogvgJyQ09ysJ2e-CXMRCbEeAyZIPRPHWs5Ba_APYL1y9LWoI1Y/s1600/fear_of_drowning_graph.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieNkS-vHMm_404EruhH4eIalhBakZ66GjyKTMPlOkmT8r-zv1p8hYYovlsTom6FJ9yo8HCzlt_ImcZtoPw-P2WYRybrogvgJyQ09ysJ2e-CXMRCbEeAyZIPRPHWs5Ba_APYL1y9LWoI1Y/s1600/fear_of_drowning_graph.PNG" height="480" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_gIxduWkRdq706ieEjCGJVuF01CZAr-ivPSRCcwTYiCKPcxZ8k2ahik6ljxQTL7KkDTtgSJ45Y3Y8f47yMrH_OHSKjYOc5YbQIRPTIORvZDYaCi5QacZZEicd8d6RZPTzUwuNm9W-mjQ/s1600/two_wheelers_under_bridge_graph.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj_gIxduWkRdq706ieEjCGJVuF01CZAr-ivPSRCcwTYiCKPcxZ8k2ahik6ljxQTL7KkDTtgSJ45Y3Y8f47yMrH_OHSKjYOc5YbQIRPTIORvZDYaCi5QacZZEicd8d6RZPTzUwuNm9W-mjQ/s1600/two_wheelers_under_bridge_graph.PNG" height="480" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip-jht6BOL8VV7K4L_3qH-YLGypkSmM9JdiBVPSasGw0u63R8U4J1TORjhnJKWOU6VKx__R7hdXou0wcgM0Wft3dalBEQyj2WXjl3PVpsmjRHPUY2xXS0uFAlh1sHyWwRrzYt9lSTvMII/s1600/time_to_airport_graph.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEip-jht6BOL8VV7K4L_3qH-YLGypkSmM9JdiBVPSasGw0u63R8U4J1TORjhnJKWOU6VKx__R7hdXou0wcgM0Wft3dalBEQyj2WXjl3PVpsmjRHPUY2xXS0uFAlh1sHyWwRrzYt9lSTvMII/s1600/time_to_airport_graph.PNG" height="480" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyTYMOHQSmPDWTRaYMd3BlHNlMol9PenmlEvDonBctkPQsGagrfsVjL1SgmgXnHP4KJUEgu0bwfH0wVLF4nhhKRETeAJeASMzvoLKNhe_XjLeWJgyAhNJNAHbvegM_zWvWNFaHEmPsOi8/s1600/pot_hole_depth_graph.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhyTYMOHQSmPDWTRaYMd3BlHNlMol9PenmlEvDonBctkPQsGagrfsVjL1SgmgXnHP4KJUEgu0bwfH0wVLF4nhhKRETeAJeASMzvoLKNhe_XjLeWJgyAhNJNAHbvegM_zWvWNFaHEmPsOi8/s1600/pot_hole_depth_graph.PNG" height="480" width="640" /></a></div>
<div class="separator" style="clear: both; text-align: left;">
I would have uploaded this earlier if the power did not go away every time it rained.</div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="MsoNormal">
<br /></div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com1tag:blogger.com,1999:blog-2197236978911214706.post-35023467747124412572014-05-26T22:00:00.000+05:302014-05-27T19:49:24.654+05:30Mumbai - Rajasthan NRR situation over-analysed<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal">
Since posts related to the IPL seem to get me a lot of hits on this blog here is another one. Yesterday, while I was watching a rather boring Indy 500 race, I heard shouts and screams from our neighbors who are cricket fans. This quickly distracted me and thankful I was because I witnessed one of the most bizarre cricket match endings I have ever seen.<br />
<br />
The confusion was huge, mathematical and needed some time to get round to. I believe that the teams, even after the scores were level at 14.3 overs had not a true idea of the situation. As this facebook post by Mayur suggests that even if 14.4 where a dot ball, the Mumbai Indians still had a shot at qualifying if they hit 14.5 for a boundary.<br />
<div align="center" id="fb-root">
</div>
<script>(function(d, s, id) { var js, fjs = d.getElementsByTagName(s)[0]; if (d.getElementById(id)) return; js = d.createElement(s); js.id = id; js.src = "//connect.facebook.net/en_US/all.js#xfbml=1"; fjs.parentNode.insertBefore(js, fjs); }(document, 'script', 'facebook-jssdk'));</script>
<br />
<div align="center" class="fb-post" data-href="https://www.facebook.com/photo.php?fbid=10152417730226462&set=a.251015501461.139259.753086461&type=1" data-width="466">
<div align="center" class="fb-xfbml-parse-ignore">
<div align="center" style="text-align: center;">
<a href="https://www.facebook.com/photo.php?fbid=10152417730226462&set=a.251015501461.139259.753086461&type=1">Post</a> by <a href="https://www.facebook.com/srinivasan.mayur">Mayur Srinivasan</a>.</div>
</div>
</div>
<br />
In fact, <a href="http://www.espncricinfo.com/indian-premier-league-2014/content/current/story/747805.html" target="_blank">cricinfo</a> has further gone ahead to explain that even if 14.4, 14.5 and 14.6 were a dot ball, Mumbai could still make it to the play off by hitting a six off the 15.1 delivery. Assuming of course sportsmanship from Rajasthan who would not ball a no-ball post 14.4.<br />
<br />
Further analysis from an over the coffee table debate has spurred an interesting idea. I am going to argue that even if 15.1 were a dot ball - on paper, Mumbai still had a chance to make it to the play offs. All they had to do was a little rain dance.<br />
<br />
No complication in cricket is complete without a discussion on the Duckworth Lewis system<sup><strike>[citation needed]</strike></sup>. In fact with all the confusion that was yesterday, I am surprised it was not mentioned.<br />
<br />
Cricinfo's "net run rate explained" page tells us that -<br />
<blockquote class="tr_bq">
"<span style="font-family: inherit;">[if] <span style="background-color: white; line-height: 18px;">a result is achieved under Duckworth/Lewis, for net run rate purposes Team 1 will be accredited with Team 2's Par Score on abandonment off the same number of overs faced by Team 2.</span><span style="background-color: white; line-height: 18px;">"</span></span></blockquote>
Which means that if it rained when the scores are level at 14.5 and the rest of the game abandoned, then Rajasthan's score would have been reduced. By how much? The D/L system calculation is clearly out of the scope of this blog post, But we do have this handy tool to help us.<br />
<br />
<iframe frameborder="1" height="530px" marginheight="px" marginwidth="0px" name="My iFrame" scrolling="no" src="http://easycalculation.com/sports/embedded_duckworth-lewis-calculator.php" width="650px"></iframe><br />
These calculations suggest that Mumbai would have won by 58 runs if rain poured in at 14.5. Which would make the net run rate look like this -<br />
<br />
<table align="center" border="1" cellpadding="0" cellspacing="0" class="MsoTableLightShading" style="border-collapse: collapse; border: none; mso-border-bottom-alt: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-alt: solid black 1.0pt; mso-border-top-themecolor: text1; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1696; width: 100%px;">
<tbody>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span lang="EN-US">For<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span lang="EN-US">Against<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: none; border-right: none; border-top: solid black 1.0pt; mso-border-bottom-themecolor: text1; mso-border-top-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span lang="EN-US">Net Run Rate<o:p></o:p></span></b></div>
</td>
</tr>
<tr>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span lang="EN-US">Mumbai<o:p></o:p></span></b></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span lang="EN-US">2175/270.8<o:p></o:p></span></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span lang="EN-US">2109/268<o:p></o:p></span></div>
</td>
<td style="border: none; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span lang="EN-US">0.146568<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<b><span lang="EN-US">Rajasthan<o:p></o:p></span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span lang="EN-US">2094/264.2<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span lang="EN-US">2158/272.5<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-border-bottom-themecolor: text1; padding: 0in 5.4pt 0in 5.4pt; width: 25.0%;" valign="top" width="25%"><div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<span lang="EN-US">0.012225<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
This would qualify Mumbai for the play-offs and cause Twitter to accuse the Rain Gods to be Ambani's agents.<br />
<br />
If no wicket falls this can go on till ball 16.4 where Rajasthan would be safe even from the rain Gods. Here is a plot for who would have won given ball when it rained, and Rajasthan did not concede an extra.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiapodDhh-YRqd_hxVnArz67JTS1zCE3pgj9wk98n8QFVPpxWkuBB2GKnXO49N4v93Ej7qfPVtNimoOhpJi4urIpIBQz1sJzJF2w_dEJpJRaOFWu7tTkETuFp2S540wjW4CceY0Q96m65k/s1600/Capture.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiapodDhh-YRqd_hxVnArz67JTS1zCE3pgj9wk98n8QFVPpxWkuBB2GKnXO49N4v93Ej7qfPVtNimoOhpJi4urIpIBQz1sJzJF2w_dEJpJRaOFWu7tTkETuFp2S540wjW4CceY0Q96m65k/s1600/Capture.PNG" height="464" width="640" /></a></div>
<br />
<br />
As the plot shows, Rajasthan could take 2 more wickets to seal the match earlier.</div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com0tag:blogger.com,1999:blog-2197236978911214706.post-61878577464628288342014-05-16T19:34:00.001+05:302014-05-17T19:47:48.983+05:30$2 Undecillion Lawsuit - An alternative solution<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: left;">
<i><span style="font-size: x-small;">XKCD What-ifs are a pleasure to read. This week <a href="http://en.wikipedia.org/wiki/Randall_Munroe" target="_blank">Lord Randall</a> wrote about a <a href="http://www.loweringthebar.net/2014/05/2-undecillion-dollar-demand.html" target="_blank">$2 Undecillion Lawsuit</a>. This what-if got me thinking in an alternative direction, and here is an alternative What-If to the<a href="http://what-if.xkcd.com/96/" target="_blank"> same question</a>.</span></i></div>
<br />
If you have not read the XKCD article - in the <a href="http://www.loweringthebar.net/2014/05/2-undecillion-dollar-demand.html" target="_blank">$2 Undecillion Lawsuit</a> a man called Anton Purisima has filed a lawsuit against Au Bon Pain Store, which if he wins will fetch him 2 Undecillion Dollars which is ($ 2 x 10<sup>36</sup>). Everything in the world can be purchased for $ 7.7 x 10<sup>12</sup> so that is significantly more than all the money in the world.<br />
<br />
As the xkcd article suggests, 2 undecillion dollars is comfortably higher by magnitudes to the sum total of the money that exists in the world. In modern times though, the sum total of money in the world is not such a clear concept. This is because day by day the world is becoming more of a credit based system than a cash based one. When you have a cash based system the sum total of money in the world is a finite. While things are more flexible when it comes to credit -<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLehc3kAkVKdURW7RMRZKUydvK_uhGWMsvKyCb7xE5WNyRx4ISw9WXKoT8G9huUktoT-ALc0ueRkYlHfMtxF1-6uHz0vQD4SZynoyYHcuAKR_fXbzo4XBfrDTZDuORPXnfiwiu8m7NDjk/s1600/economy.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLehc3kAkVKdURW7RMRZKUydvK_uhGWMsvKyCb7xE5WNyRx4ISw9WXKoT8G9huUktoT-ALc0ueRkYlHfMtxF1-6uHz0vQD4SZynoyYHcuAKR_fXbzo4XBfrDTZDuORPXnfiwiu8m7NDjk/s1600/economy.PNG" height="232" width="640" /></a></div>
<br />
In case the Au Bon Pain Store did lose this lawsuit to Anton Purisima - in a cash based system Au Bon Pain simply could not pay. The best they can do is surrender all the cash that they have and everything that they own to Anton. Anton would be rich but not be the undecillionaire which he hopes to be with this lawsuit. However, in the credit based system there is still hope for Anton. All he has to do is convince a bank to loan 2 undecillion dollars to Au Bon Pain so that Au Bon Pain can pay him.<br />
<br />
Why would a bank sanction such a sub-prime loan? For a bank to make such a loan, it must see a profit. The bank takes on risk when it gives out a loan and they like to bundle in the cost associated with this risk into the loan agreement via the interest rate or insurance. To offset the risk associated with a 2 undecillion dollar loan, there needs to be a massive payment as an incentive to make the loan. There is not enough money to make this payment but the bank knows that soon there will be one person who will be rich enough to pay. We are talking about Anton here. Anton is not going to be rich if the bank does not make a loan and the bank is not going to make a loan if Anton is not going to make the bank rich.<br />
<br />
They strike a deal. Bank will make the loan to Au Bon Pain (with everything Au Bon Pain owns as mortgage), the court will send the money to Anton. In return, Anton must become a 'hyper-premiere' customer of the bank for which the bank will charge a modest one-time fee of 1.9 undecillion dollars. Anton will agree because it's better than nothing and still he will have more money than he can possibly spend.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BKIpBxvI-vb7AKD0JaNJf2QFqJuHwUV6SGBaxCo30S-PfTaAK7yY-aMF6CUZvsEEKet30lowtQQmwd1vX7Cc29dDEqcwAlLX8XwwVVe_C5TU4K-WgmWIkYXSZocUEiPV6cgzleE4sd0/s1600/bar_charts.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7BKIpBxvI-vb7AKD0JaNJf2QFqJuHwUV6SGBaxCo30S-PfTaAK7yY-aMF6CUZvsEEKet30lowtQQmwd1vX7Cc29dDEqcwAlLX8XwwVVe_C5TU4K-WgmWIkYXSZocUEiPV6cgzleE4sd0/s1600/bar_charts.PNG" height="234" width="640" /></a></div>
<br />
This leaves 2 ridiculously rich entities in the world - the bank and Anton. They can buy anything and still have almost the same amount of money left over. Anton can do what he pleases with the money. The bank has an agenda though; it still has to make the other 0.1 undecillion dollars to balance its sheets. It made a loan against everything that Au Bon Pain has which is worthless compared to the loaned amount. It must raise the value of everything Au Bon Pain owns in that case, it has more than all the money in the world to do this.<br />
<br />
If Au Bon Pain owned all its stores, then the bank can buy property around the stores at ridiculously high pricing driving the price of the property up. Not only has the price of the property gone up but the neighbours of the store are now suddenly ridiculously rich and Au Bon Pain can start charging astronomical prices because people don't know where to spend. This will not only happen to Au Bon Pain but to everything.<br />
<br />
People will spend because everyone suddenly has a lot of money and the value of this money is falling fast. As more people have access to preposterous sums of money other people want some of it as well and prices will go up. Moreover, the government will be collecting huge taxes on all these transactions which means that the government will get spending and the inflation will spread like wild fire. The bank and Anton will have a gala time for a short while when they can buy anything they want. If they are fast enough, they can be the 'king / corporate entity of the world'. This will not really happen because people can refuse to sell but they can capture a significant portion of the world's stuff.<br />
<br />
Something similar has actually happened before. This is the inflation chart of the Zimbabwean Dollar (If that looks steep then look again and find the logarithmic scale) -<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCOAK9Nt6nIT3ZcFGr8UgS1aJmtxByfo-ZK9384J_RXB-bj_b4kUBcYrZSGoXtQtXqndx1a00mzEqh9Mpr8a0zVoHCyX28tS0uVdVvRUXhukluY6N6OIUEs2HFXv4UeaPMkQlpMDP5jDc/s1600/ZWDvsUSDchart.svg.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCOAK9Nt6nIT3ZcFGr8UgS1aJmtxByfo-ZK9384J_RXB-bj_b4kUBcYrZSGoXtQtXqndx1a00mzEqh9Mpr8a0zVoHCyX28tS0uVdVvRUXhukluY6N6OIUEs2HFXv4UeaPMkQlpMDP5jDc/s1600/ZWDvsUSDchart.svg.png" height="337" width="400" /></a></div>
When the Zimbabwean dollar was introduced, it was arbitrarily valued greater than the American Dollar, which was highly optimistic. The Zimbabwean economy was not in good shape and the exchange rate immediately went into freefall. People lost complete faith in the currency and dumped all the Zimbabwean dollars they had, making the fall worse. What eventually happened was that the country moved to using foreign currencies and <a href="http://www.economist.com/news/finance-and-economics/21569744-use-pre-paid-mobile-phone-minutes-currency-airtime-money" target="_blank">cell phone talk-time</a> as trading units.<br />
<br />
So Anton and the bank will plunge the value of the American Dollar and the country will be forced to move to a foreign currency like the British Pound? Hold on. The banks would have thought of this, they will quickly realise that the USD will fall and will invest in a foreign currency. They will buy out all of it and take the foreign currency down with the dollar. This will go on until a new steady state is reached and the new crazy sum of money is significantly distributed. The world will temporarily move to barter before a new cash based (or limited credit) economy is set up.<br />
<br />
The people who were opportunistic during this turmoil will become the new rich and the people who went on a tech detox vacation in the middle of a desert will be the new poor. There will be a complete <strike>redistribution</strike> reshuffling of the world's wealth. There is a good chance Anton and the bank will end up on the rich side of the new world. If you were a bank would you sanction this loan? I bet some bank would.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0YloyS5D_xs98s9G9JMMc4EoK-fph85e8xJFErYh7L0VSnHDpHyFti8rNTd3WPldbfZlO1kN-WbpjYoRB4Wrnd8jjH9VcKcSv1RPee3zJ_j229NYf3BCxfaSaPB7vyCrtcj0elZHru50/s1600/tec_detox.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi0YloyS5D_xs98s9G9JMMc4EoK-fph85e8xJFErYh7L0VSnHDpHyFti8rNTd3WPldbfZlO1kN-WbpjYoRB4Wrnd8jjH9VcKcSv1RPee3zJ_j229NYf3BCxfaSaPB7vyCrtcj0elZHru50/s1600/tec_detox.PNG" height="233" width="400" /></a></div>
<br />
<span style="font-size: x-small;">Side-note: The bank as per law will have to maintain minimum reserve, but it has to do that only at the end of the day. It can do this in two ways - act so fast that all the turmoil will happen in one day and they own enough barter at the end of it or they can also meet the minimum reserve with a deposit at the central bank, which can make the central bank panic and look for reserve.</span></div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com0tag:blogger.com,1999:blog-2197236978911214706.post-80797922272056443092014-05-03T13:45:00.001+05:302017-12-03T00:45:54.553+05:30G-Train through the Center of the Earth<div dir="ltr" style="text-align: left;" trbidi="on">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.5.0/jquery.min.js"></script>
<script type="text/javascript">
<!--
var epoch_0 = 1399046400;
var epoch_1 = 1399132800;
var d = new Date()
var current_time = d.getTime()/1000;
var dist_0_v1 = 18999119552.2977;
var dist_1_v1 = 18999401692.1622;
function dist_controller()
{
current_dist_km_v1 = ( ( ( current_time - epoch_0 ) / ( epoch_1 - epoch_0 ) ) * ( dist_1_v1 - dist_0_v1 ) ) + dist_0_v1;
document.getElementById('voy1_km').innerHTML = addCommas( Math.round(current_dist_km_v1) + " km" );
//alert("dist_controller.addCommas( Math.round(current_dist_km_v1) ): " + addCommas( Math.round(current_dist_km_v1) ));
current_time += 0.5;
}
function addCommas(nStr)
{
nStr += '';
x = nStr.split('.');
x1 = x[0];
x2 = x.length > 1 ? '.' + x[1] : '';
var rgx = /(\d+)(\d{3})/;
while ( rgx.test(x1) )
{
x1 = x1.replace(rgx, '$1' + ',' + '$2');
}
return x1 + x2;
}
-->
</script>
<script type="text/javascript">
$(window).load(function () {
// Start Voyager distance updates
setInterval('dist_controller()',500);
});
</script>
<br />
<div class="MsoNormal">
Humans have always looked up in the sky, fascinated more by
birds than moles, we built hot air balloons, the Wright brothers flew and
finally NASA took us to the moon (Which is almost 5 decades ago, but that is a
rant for another blog post). Humans have travelled 384,400 kms to the moon and
the voyager is <span id="voy1_km"></span> away from the Earth. What we have not done is
scratched the Earth’s surface.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
An old <a href="http://old.qi.com/talk/viewtopic.php?t=18097&postdays=0&postorder=asc&start=0" target="_blank">QI episode</a> (G for Gravity) talked about drilling a
hole through the center of the Earth and the travel time if the tunnel was
frictionless through it would be 42 minutes and 12 second. This is called a “<a href="http://en.wikipedia.org/wiki/Gravity_train" target="_blank">Gravity Train</a>” and is quite a <a href="https://www.youtube.com/watch?v=wrQjMslFutc" target="_blank">popular concept</a>. The more interesting thing about the “Gravity
train” is that it does not need to pass through the center of the Earth. Even if
we cut a cord across any point of the Earth to another, the train will get from
one end to the other in ~42 minutes in frictionless conditions.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
A
gravity train route that cuts through a chord of Earth looks like this –<o:p></o:p><br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIy2i9asbEXo9lXIG81iCOKJe90TYGPVuqhl5s0ofjf05yUsK9sovQd6SvTPXTo_VyJHXdG8vi6w4XC-NofCUy8sFRcdI27AtFLPxNwbZx82Xvj884C2M0LoPJBu2d0LzDL_wcNzV6jNc/s1600/Capture_1v2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIy2i9asbEXo9lXIG81iCOKJe90TYGPVuqhl5s0ofjf05yUsK9sovQd6SvTPXTo_VyJHXdG8vi6w4XC-NofCUy8sFRcdI27AtFLPxNwbZx82Xvj884C2M0LoPJBu2d0LzDL_wcNzV6jNc/s1600/Capture_1v2.PNG" height="251" width="400" /></a></div>
<br />
If
we move things around such that Gravity always points down then the gravity
train looks like a massive roller coaster –</div>
<div class="MsoNormal">
<o:p></o:p><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI2_8HOfpm1GRpkBhPLbsCMpyZRz4MXDOfJtO1hpIhXT0SE4gNQAc7d4DFbW_Ls-yRtZAPEDb3SvyWdPcAPRf2GK9RsZHPBjuFI-tgPQE5J0R4e7jSL5hkYsyAMIby5tz0WtUzOFudoak/s1600/Capture_2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjI2_8HOfpm1GRpkBhPLbsCMpyZRz4MXDOfJtO1hpIhXT0SE4gNQAc7d4DFbW_Ls-yRtZAPEDb3SvyWdPcAPRf2GK9RsZHPBjuFI-tgPQE5J0R4e7jSL5hkYsyAMIby5tz0WtUzOFudoak/s1600/Capture_2.PNG" height="128" width="400" /></a></div>
<br /></div>
<div class="MsoNormal">
This seems to be a great solution to the world
transportation problem. Get from anywhere to anywhere in less than 43 minutes
and the only energy that is required be used to overcome friction and drag. You
start at the top of the roller coaster, build momentum, go as far as you can up
the other way and top up with some power when steam runs out due to friction.<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
However, it is difficult to drill a hole through the center
of the Earth. It is surprising how quickly we will get to magma if we start
digging downwards, after about 20-30kms of digging and you have almost created
a man-made volcano! (More on this evil plan in a future blog post) Meanwhile,
we will dig sideways. The furthest we have gotten in terms of drilling deep is
the <a href="http://en.wikipedia.org/wiki/Al_Shaheen_oil_field" target="_blank">Al Shaheen Oil Field</a> ~12.5kms which is a surprising 0.19% of the distance to the center of the
Earth, and this was a bore hole and not quite a tunnel. Suppose we could tunnel
this deep – How far can our gravity train travel?<o:p></o:p><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfdF9uujzF2sIOVn4cl4s9OLlDVKQF5PE-X8wIxO-3KDVfOsM98b0CGAYRntYPzPdx58QXpVq_1uFeT3VJxxfCtIV2_Lkr8MiOWMgNGtsMzvXyUSzjbOoMjPQ3ILE3bkTS-FK3eSHjw4U/s1600/Capture_3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjfdF9uujzF2sIOVn4cl4s9OLlDVKQF5PE-X8wIxO-3KDVfOsM98b0CGAYRntYPzPdx58QXpVq_1uFeT3VJxxfCtIV2_Lkr8MiOWMgNGtsMzvXyUSzjbOoMjPQ3ILE3bkTS-FK3eSHjw4U/s1600/Capture_3.PNG" height="460" width="640" /></a></div>
<br /></div>
<div class="MsoNormal">
So from the plot above if we can dig a tunnel that has a max
depth of 12.5 kms which is close to the deepest drilled hole we have today we
can travel ~810 kms on the surface of the Earth. That is Bangalore – Mumbai, New
York – Detroit and London – Zurich in less than an hour. That is an average
speed of ~1000km/hr. What’s more, there is heavy return for development of
technology, for every 1 km we can go deeper, we can travel ~ 30 kms more on the
ground in the same time.<o:p></o:p></div>
<br />
<div class="MsoNormal">
All we need is some <a href="http://www.technologyreview.com/featuredstory/429690/why-we-cant-solve-big-problems/" target="_blank">focused energy</a> to get this done. Half a century
ago people thought going to the moon was a ludicrous idea. It’s difficult to
convince investors why it is worthwhile to go to the moon today, but we can
convince them that this will change the world and be profitable. It’s been
almost 50 years since we were on the moon, come on engineers – Challenge Accepted?<o:p></o:p></div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com2tag:blogger.com,1999:blog-2197236978911214706.post-57652856884127629152014-05-02T23:30:00.000+05:302014-05-03T18:01:34.109+05:30Shank Lengths of Bolts<div dir="ltr" style="text-align: left;" trbidi="on">
Bolts and nuts are the most crucial part of any assembly.
They hold the different components of the vehicle together by providing the structural
strength required. Selection and the usage of bolts, nuts and other fasteners are a very critical aspect of engineering design and should be considered with
high importance at the design phase of the vehicle.<br />
<div class="MsoNormal">
<o:p></o:p></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
A very common mistake on
Formula Student and Baja cars that is seen is the incorrect selection of bolts
in terms of their sizes and shank lengths. Before proceeding here is the
clarification of the shank length and threaded length -<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjT4YCVmy2uQgI_a6vUoseFSoIcFHV4cBanFuU9wmxM09TxhpoaEi1VwRbvzTOd4Ok8cQofWJzlN9wV7jWN7Ve1DYrWy9GpWVNiFh8U_1pCbqZgNqipPhRgM1L8lTlP3_eg0e15GRIHJWA/s1600/Shank_1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjT4YCVmy2uQgI_a6vUoseFSoIcFHV4cBanFuU9wmxM09TxhpoaEi1VwRbvzTOd4Ok8cQofWJzlN9wV7jWN7Ve1DYrWy9GpWVNiFh8U_1pCbqZgNqipPhRgM1L8lTlP3_eg0e15GRIHJWA/s1600/Shank_1.PNG" height="129" width="320" /></a></div>
Bolts are designed to carry
axial loads. It may carry bending loads as well however it is important to
understand which areas of the bolt should see the bending load. To get a better
idea of why this is - consider a rod that needs to be broken. A force is
applied in bending because it is the weakest then (Why? - <a href="http://www.mahekmody.com/2014/04/load-paths.html" target="_blank">Load PathsDesign Error Blog</a>).<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrufAtve3OHeM0enSJGaun4wGv4Bu5Iy_wOsQ6nXselBG-SxQBGLTMgy_7HOu4DEorQlipR9799R4gD_Fmk6ptZi2S4GIEcg99Y9ZEl7s1Z5Y0ycQhvQCtBVa9MKk3fRqjR3YFRttR1mo/s1600/Shank_2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgrufAtve3OHeM0enSJGaun4wGv4Bu5Iy_wOsQ6nXselBG-SxQBGLTMgy_7HOu4DEorQlipR9799R4gD_Fmk6ptZi2S4GIEcg99Y9ZEl7s1Z5Y0ycQhvQCtBVa9MKk3fRqjR3YFRttR1mo/s1600/Shank_2.PNG" height="113" width="320" /></a></div>
If the rod still does not snap
the next best thing to do is create a notch like in the picture below. It
should be easier to break this after that. The notch can be really tiny, but it
has an associated stress concentration factor which will cause it to see higher
stress in that region and break faster. The notch is also a perfect crack
initiation point for the rod to break.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRtDs5JSR8NAazd_olunnVEKHy4dT0S01mMiYcmBMfx6Tb1Km1Wi6IBZjEUE4IZ6_VSBn5xhKESES8Iq_IJtGRTLII5kPH24hI3bqJU7amtDD2wSY9i_yGSjmV9QlnkDm-AAhWTz84XzM/s1600/Shank_3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhRtDs5JSR8NAazd_olunnVEKHy4dT0S01mMiYcmBMfx6Tb1Km1Wi6IBZjEUE4IZ6_VSBn5xhKESES8Iq_IJtGRTLII5kPH24hI3bqJU7amtDD2wSY9i_yGSjmV9QlnkDm-AAhWTz84XzM/s1600/Shank_3.PNG" height="110" width="320" /></a></div>
<br />
<div class="MsoNormal">
The threads on the bolts are
nothing but a series of notches when the bolt comes under bending and the bolt
is much likely to break when loaded in bending at the threaded region. </div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDNRlGNvMVDUx2VYnNBZfEIsVLWkOrunGk3JUHqRVS6Atd3xdjgrMV4zGLjSu48U7riGqoG67EZwN0-HRu2doE4OBDXo4zYNzimBjGbNjBOp80mKC9X6CXOfsbJJHqx8opazfln-b3G_U/s1600/Shank_4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDNRlGNvMVDUx2VYnNBZfEIsVLWkOrunGk3JUHqRVS6Atd3xdjgrMV4zGLjSu48U7riGqoG67EZwN0-HRu2doE4OBDXo4zYNzimBjGbNjBOp80mKC9X6CXOfsbJJHqx8opazfln-b3G_U/s1600/Shank_4.PNG" height="113" width="320" /></a></div>
<div class="MsoNormal">
The
threaded length of the bolt is the section which should be used to fasten the
nut onto the bolt and for that reason only, all the other bending load must be
taken up by the shank region. Which means that a bolt that connects a rod-end
to the chassis mounts must look like this -</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS6zI7Zh05yPS2IDA1AQxf2tPYZ7rZKrg5V16hFXhDSMF4Fc4-FVBwonr5HCAhTfLl9ivsGlHTopfdSYylmgKU1j1WO8EHtAtv5EOOOkXQK62V49ytfoFBilYa6ssmGIc_jDNhhlbiH4o/s1600/Shank_5.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiS6zI7Zh05yPS2IDA1AQxf2tPYZ7rZKrg5V16hFXhDSMF4Fc4-FVBwonr5HCAhTfLl9ivsGlHTopfdSYylmgKU1j1WO8EHtAtv5EOOOkXQK62V49ytfoFBilYa6ssmGIc_jDNhhlbiH4o/s1600/Shank_5.PNG" height="290" width="400" /></a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
The clamps and the spacers and
the rod end see the shanked length of the bolt and the threaded length of the
bolt only starts under the final washer after which the nut is tightened and
torqued up. At least 2 threads should be visible on the other end of the nut to
ensure that the bolt is properly fastened.<o:p></o:p></div>
<div class="MsoNormal">
This not only applies to the
suspension bolts but any critical bolt that might be used in the vehicle. This
mistake is also often seen in brake balance bars there bolts or even studs are
used and the brake forces travel right through the threaded region of the bolt
/ stud. That will break. Custom engine mounts often ignore this as well and we
see these bolts bend and break with time.<o:p></o:p></div>
<div class="MsoNormal">
<br />
<span style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;">This blog post is originally written for the </span><a href="http://www.formulastudent.in/" style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;" target="_blank">Formula Student India</a><span style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;"> website and has been cross posted from </span><a href="http://formulastudent.in/member/designerror/4" style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;" target="_blank">here</a><span style="font-family: Arial, Verdana, sans-serif; font-size: 12px; font-style: italic;">.</span></div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com4tag:blogger.com,1999:blog-2197236978911214706.post-23094038997851283682014-04-27T00:30:00.000+05:302014-04-28T09:05:06.453+05:30On the Boundary Lynn Catch<div dir="ltr" style="text-align: left;" trbidi="on">
I am not big on following the Indian Premier League (IPL), but have noticed this fantastic match winning catch that Chris Lynn took to get AB DeVilliers out. If you have not seen it yet <a href="http://www.starsports.com/cricket/video/vod/videoid=1322060/index.html#the-lynn-sane-move-that-won-kkr-the-match" target="_blank">here</a> it is on the StarSports website. [If you are in America - <a href="https://www.youtube.com/watch?v=joA0yG7s4lQ" target="_blank">here is the YouTube link</a>]<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://www.starsports.com/cricket/video/vod/videoid=1322060/index.html#the-lynn-sane-move-that-won-kkr-the-match" target="_blank"><img border="0" src="http://qph.is.quoracdn.net/main-qimg-afb9194f3d951ab57823f151b562d618?convert_to_webp=true" height="195" width="320" /></a></div>
<br />
This catch is one of the most athletic ones we have seen in cricket and also he seems to pull off a physics defying jump where he catches the ball and still manages to land within the boundary line. There are certain stills of the catch (like the one above) that would convince you that he had to fall over the line and divine intervention or a extra strong draft of wind is the only thing that made him land well within the boundary limits. This obviously prompted <a href="http://www.quora.com/Why-didnt-Chris-Lynn-fall-on-the-boundary-rope-while-making-the-best-catch-in-cricketing-history" target="_blank">this question on Quora</a> - "Why didn't Chris Lynn fall on the boundary rope while making the best catch in cricketing history?" Here's my answer -<br />
<br />
Let's start with a slight detour - There is a very famous (& I think very cool) physics fact about pole vault. When a pole vaulter jumps a high bar, her Center of Gravity (CG) need not go as high as the bar she needs to clear. In other words, at the top of the jump the pole vaulter needs to go over the bar and not her CG. To achieve this the pole vaulter arches her back forwards or backwards to be in a situation where the body is clear of the bar but the CG passes under for the most optimal jump. The idea being that Newton's laws only dictate the trajectories of the CG and not the entire body.<br />
<br />
Lynn's miraculous falling back within the boundary rope is something similar. After the little stumble he has just before he makes his jump, he has his eyes on the ball. Accesses the trajectory of the ball and it looks something like this -<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_XsB9dq9q1DJ-7wOq6QtnAyhc0lypmi8pNXMeyGSu8E5tOxwdOt4MQyKtR0QG-iFfSAO5-9k1VZfXJHgB-VKhXszJaUUueGEwBKxSZbwqD0VfbKvH8OzmrOZRwC-Xiuuh_3xH3Jw5CDQ/s1600/Capture1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_XsB9dq9q1DJ-7wOq6QtnAyhc0lypmi8pNXMeyGSu8E5tOxwdOt4MQyKtR0QG-iFfSAO5-9k1VZfXJHgB-VKhXszJaUUueGEwBKxSZbwqD0VfbKvH8OzmrOZRwC-Xiuuh_3xH3Jw5CDQ/s1600/Capture1.PNG" height="288" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
Now Lynn considers jumping straight up and try get the ball. Is there a chance he can make it? His jumping ability is limited and there is only a limit to which he can raise his CG. He would not have caught the ball.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi32n-ji80vp5xq8ioJ31Ef6h6TCJnhUyeeIj-bSSnVZUgLPJMq21uYpa1OJ-olUgBS2cmHfLSn1XWuX8Q-YIXQel7YC_tpkY-PUxfuDZxURlPgvTIuff0tOVuFCH5S1nYM28bQdE_GsbI/s1600/Capture2.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi32n-ji80vp5xq8ioJ31Ef6h6TCJnhUyeeIj-bSSnVZUgLPJMq21uYpa1OJ-olUgBS2cmHfLSn1XWuX8Q-YIXQel7YC_tpkY-PUxfuDZxURlPgvTIuff0tOVuFCH5S1nYM28bQdE_GsbI/s1600/Capture2.PNG" height="284" width="320" /></a></div>
<br />
However, if he jumped and turned back at the same time things could look very different even if the his jumping ability is considered to be the same. As this diagram illustrates -<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSLLEILN4SbrZPxh9ToJBUXPgB_4nmvzNrsyXxMfyPUI8DUas3ieXaMvhya2YwTE0e_4im21_8lzrMkdKzTZ1nn5S_2M4uouLWcCgGkZ0iTtVeDRmaPLgwl9UaEOnXqfqx5bODY1d38WY/s1600/Capture3.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiSLLEILN4SbrZPxh9ToJBUXPgB_4nmvzNrsyXxMfyPUI8DUas3ieXaMvhya2YwTE0e_4im21_8lzrMkdKzTZ1nn5S_2M4uouLWcCgGkZ0iTtVeDRmaPLgwl9UaEOnXqfqx5bODY1d38WY/s1600/Capture3.PNG" height="286" width="320" /></a></div>
<br />
At this point if a snap was taken it seems as if he would fall on the boundary rope, but he has some angular (spin) momentum on his side which a still would not capture.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5lDBUH4KMTBOMIuc7qVhD42MEE8qYxaXLTNeMsQFMqWyDBTZVTKol0ycPsQpTPPtUeGpQZMMMbcPMQifqtKwgKl3gQ4Jaov4K4FdvKX0PEB8vSugM9EY29Kp6tELgWAFBPrIHQapeVBg/s1600/Capture4.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5lDBUH4KMTBOMIuc7qVhD42MEE8qYxaXLTNeMsQFMqWyDBTZVTKol0ycPsQpTPPtUeGpQZMMMbcPMQifqtKwgKl3gQ4Jaov4K4FdvKX0PEB8vSugM9EY29Kp6tELgWAFBPrIHQapeVBg/s1600/Capture4.PNG" height="285" width="320" /></a></div>
<br />
He does exactly that makes the catch and after which since his CG is still very much inside the boundary region he can easily use his flexible and agile body to bring his hands inside the boundary rope. Eventually using his hands to safely land well within the boundary.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjafNlHCgYifQ1gP6Rz6JhJOIGZGDVJzulF2bZ0JmqsrvAJ1-lVkQqWEkMIogxflWBhmEOhHV2RbWp6S5V4BfGfAciGrKFchyEmPz8CqUglgfFAoiPvx9fOpgp8avhmpYgjMqpwcEIO3YM/s1600/Capture5.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjafNlHCgYifQ1gP6Rz6JhJOIGZGDVJzulF2bZ0JmqsrvAJ1-lVkQqWEkMIogxflWBhmEOhHV2RbWp6S5V4BfGfAciGrKFchyEmPz8CqUglgfFAoiPvx9fOpgp8avhmpYgjMqpwcEIO3YM/s1600/Capture5.PNG" height="283" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<br />
I am sure Lynn did not go through all this physics in his mind before making the catch, but intuition is a powerful physics engine due to the world experience it has.</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com3tag:blogger.com,1999:blog-2197236978911214706.post-18837723711132318032014-04-10T12:14:00.000+05:302014-05-03T18:16:47.991+05:30Bove-torch<div dir="ltr" style="text-align: left;" trbidi="on">
<br />
<div style="border-bottom: solid #4F81BD 1.0pt; border: none; mso-border-bottom-themecolor: accent1; mso-element: para-border-div; padding: 0mm 0mm 4.0pt 0mm;">
<div class="MsoTitle">
Cow fart is essentially a lot of flammable gas (Methane and
Hydrogen Sulphide to be precise) coming out of a small hole (The anus to be
precise). Any engineer in his right mind will think of only one thing about
such a situation. Yes, you are right – Blow torch. So the question is can one
hook up some piping to the correct places to build oneself a Bovine Blow torch
or a Bove-torch?<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht891dbuJ0lI8_9Yw_GZoVdPWMIY41MKmjGXwTj5cKg2qGVx80lh0SWfINBxehcbHmfJn2CeLEOEZsdHos1UAGDTfs9Viyknl_ciyFREDQkgQkWoHA744Jz-JHHiMwdMMaKpD1yQVxqoc/s1600/Moo.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEht891dbuJ0lI8_9Yw_GZoVdPWMIY41MKmjGXwTj5cKg2qGVx80lh0SWfINBxehcbHmfJn2CeLEOEZsdHos1UAGDTfs9Viyknl_ciyFREDQkgQkWoHA744Jz-JHHiMwdMMaKpD1yQVxqoc/s1600/Moo.jpg" height="138" width="320" /></a></div>
First thing is first. We cannot be rude to the cow and set
it’s behind on fire. Apart from facing a lot of scorn from animal activist,
there is a very high probability of being kicked in the face by a cow on
fire. The revenue generated by this
youtube video might make this a good business model, but we will be kind and
attach a pipe with a nozzle at the end of it.</div>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
I’ll start with a
simple assumption which is probably true (Being from India, unfortunately I
have rich experience with being in close proximity to cows) - Cows fart all the
time they are awake, continuously. According to <a href="http://milk.procon.org/view.resource.php?resourceID=001154">this research</a>
13 million cows in USA in 2001 produced 2 million metric tons of Methane which
amounts to 160 kg per cow at an average which is 0.0105g/sec. The Enthapy of
combustion of Methane is 0.891MJ/mole therefore 0.0105g of Methane produce
584.7J/sec (Watt).</div>
<div class="MsoNormal">
</div>
<div class="MsoNormal">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>160</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>kg</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>year</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=0.0105</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>g</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>sec</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=0.000656</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>moles</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>sec</m:r></span></i></m:den></m:f></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id="_x0000_i1025" style="height: 29.25pt; width: 198.75pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\mahekm\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></span><!--[endif]--><o:p></o:p></div>
<div class="MsoNormal">
<!--[if gte msEquation 12]><m:oMathPara><m:oMath><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>Power</m:r><m:r>=</m:r><m:r>Ent</m:r><m:r>h</m:r><m:r>alpy</m:r><m:r>
</m:r><m:r>of</m:r><m:r> </m:r><m:r>combustion</m:r><m:r> ×</m:r><m:r>gas</m:r><m:r>
</m:r><m:r>supply</m:r><m:r>= 891</m:r></span></i><m:f><m:fPr><span
style='font-family:"Cambria Math","serif";mso-ascii-font-family:"Cambria Math";
mso-hansi-font-family:"Cambria Math";font-style:italic;mso-bidi-font-style:
normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i style='mso-bidi-font-style:
normal'><span style='font-family:"Cambria Math","serif"'><m:r>kJ</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>mole</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>
×0.000656</m:r></span></i><m:f><m:fPr><span style='font-family:"Cambria Math","serif";
mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math";
font-style:italic;mso-bidi-font-style:normal'><m:ctrlPr></m:ctrlPr></span></m:fPr><m:num><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>mole</m:r></span></i></m:num><m:den><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>sec</m:r></span></i></m:den></m:f><i
style='mso-bidi-font-style:normal'><span style='font-family:"Cambria Math","serif"'><m:r>=584.7
</m:r><m:r>Watt</m:r></span></i></m:oMath></m:oMathPara><![endif]--><!--[if !msEquation]--><span style="font-family: "Calibri","sans-serif"; font-size: 11.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-bidi; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><v:shape id="_x0000_i1025" style="height: 27pt; width: 452.25pt;" type="#_x0000_t75">
<v:imagedata chromakey="white" o:title="" src="file:///C:\Users\mahekm\AppData\Local\Temp\msohtmlclip1\01\clip_image002.png">
</v:imagedata></v:shape></span><!--[endif]--></div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR7TxwvbSztZr5nj-2ggIuuifAXCHqbFoj2LDBvw5-F7hOQEUxH-H6URryMjmeC96MVt48Vp5fNJqNXvhim5mJOcj-N665e-PCwASPredcwNeokNKvLSYfmuzo6quUQm0RYlxdZA7h9F4/s1600/Capture.PNG" imageanchor="1"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiR7TxwvbSztZr5nj-2ggIuuifAXCHqbFoj2LDBvw5-F7hOQEUxH-H6URryMjmeC96MVt48Vp5fNJqNXvhim5mJOcj-N665e-PCwASPredcwNeokNKvLSYfmuzo6quUQm0RYlxdZA7h9F4/s320/Capture.PNG" height="51" width="320" /></a></div>
<div class="separator" style="clear: both; text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifoObi02wvKtLnJGJT9DwJC5zSqe6J_K9bM3ZmFcOxeAY3b3OSyjq3fjCb-_sYhuq_Kr-T2wxg9Fpyk3oOVeXomuOQkWaZYesq8I-nswELIx3mhE0xn44epRHi6WKizzWVW3oUZpTstc0/s1600/Capture1.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEifoObi02wvKtLnJGJT9DwJC5zSqe6J_K9bM3ZmFcOxeAY3b3OSyjq3fjCb-_sYhuq_Kr-T2wxg9Fpyk3oOVeXomuOQkWaZYesq8I-nswELIx3mhE0xn44epRHi6WKizzWVW3oUZpTstc0/s640/Capture1.PNG" height="40" width="640" /></a></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
This is only half the story we have some (8.6kg/year)
Hydrogen sulphide too being produced which is combustible at 0.519MJ/mole. This
is 0.00055g/sec of Hydrogen Sulphide which is 8.8 Watt of energy. OK so this
half of the story is not that significant.</div>
<div class="MsoNormal">
<br />
Let us assume we are using the blow torch to do some brazing
with copper as filler. Assuming 50% efficiency of the torch, the energy required to melt 1g of copper is 509J, in other words - the bove-torch can melt 0.6g of copper every second. You need about 20g of
copper to braze a 1 inch diameter pipe joint so you might take about 35-40
seconds to do one which is impressive but not quite blow torch.</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
Some simple research (read: <a href="http://www.google.co.in/#hl=en&sclient=psy-ab&q=blow+torch+wattage">google</a>)
shows that a blow torch must be at least 50,000Watts to cause an American to
boast about it. If we hook up say (50000/590 ~= 85) cows to a single tube we
might have a proper blow torch that will operate 12 hours a day! So if you have
80 or more cows then you can run a small scale metal blazing / fitting industry
at zero operating costs.<br />
<br /></div>
<div class="MsoNormal">
More interestingly, these farts also have a LOT of ammonia
in there, which is unfortunately not combustible. But if you remember your 10<sup>th</sup>
grade chemistry lesson well and your mind function is evil by nature you will
realise that ammonia will combust if you add platinum to the mix as this video will
illustrate.</div>
<div style="text-align: center;">
<iframe allowfullscreen="" frameborder="0" height="360" src="//www.youtube.com/embed/FSdBB1vBDKY" width="480"></iframe>
</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
So if we have a platinum nozzle bove-torch (turbove-torch?) things
can get really interesting. We have 54.3kg of ammonia per cow per year which
boils down to 0.00344g/sec burning with 382.81kJ/mole which is an extra
77.5Watt per cow, that’s a full 15% extra!</div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
May I remind you that you are also contributing to saving
the world by doing this as Methane is 50 times more of a green house gas
compared to Carbon dioxide.</div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com1tag:blogger.com,1999:blog-2197236978911214706.post-18499366950035336592014-03-10T14:06:00.000+05:302014-05-03T18:02:05.224+05:30Welded Rotating Components<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;">We see a lot of welding in Formula Student and Baja Cars, which is not surprising. However, design judges always come across a few horror welds that are easy to label as 'GTB' or 'Going to Break'. Here is one example -</span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_j34E9XIsgYEMP1P-0LlT0S-uq9fTY-x_1ZLwWJzH2KjjDxRNw0-sz6QnvjhY1vZUdeiZ9MAvWS2NCs1IFrFtlxfm1yAwtGCXe9v9fVcg64BnVC8NZIs9mTtWKAnsvo82725wkcWBtGM/s1600/Welded_Shaft.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_j34E9XIsgYEMP1P-0LlT0S-uq9fTY-x_1ZLwWJzH2KjjDxRNw0-sz6QnvjhY1vZUdeiZ9MAvWS2NCs1IFrFtlxfm1yAwtGCXe9v9fVcg64BnVC8NZIs9mTtWKAnsvo82725wkcWBtGM/s1600/Welded_Shaft.JPG" height="263" width="400" /></a></div>
<br />
<div style="font-family: Arial, Verdana, sans-serif; font-size: 12px;">
Both the half shaft and the universal joint are off the shelf components which are not designed to be mated with one another. The universal joint on the welded end has an internal spline and a mechanism where one can use a threaded bolt to tighten the grip of the universal joint on the splined shaft. Ideally there was no need for welding, if the shaft could have had splines of the correct size.</div>
<div style="font-family: Arial, Verdana, sans-serif; font-size: 12px;">
<br /></div>
<div style="font-family: Arial, Verdana, sans-serif; font-size: 12px;">
This team for some reason has decided to attempt a "butt-weld" to couple the two. Butt-welded shafts have been a source of debate many a times on technical forums, but they are risky but if done correctly there are championship winning cars out there with butt-welded half-shafts. However, the weld pictured above is probably not going to make it for very long.</div>
<div style="font-family: Arial, Verdana, sans-serif; font-size: 12px;">
<br /></div>
<div style="font-family: Arial, Verdana, sans-serif; font-size: 12px;">
When rotating parts are welded together such that they need to have their individual axis of rotations collinear, extreme care is required to ensure that the components being welded are held together tightly in place via rigid fixtures and jigs. Slight nonlinearity can cause many issues. If for example, the co-linearity is off by half a degree on a meter long half shaft then the other end of the shaft would move around ~9mm either way during rotation causing, compliance in the joints, vibration and high cyclic loading.<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_n01_J_pWmGJY5RMgcxR1nVvQITJnupHKttIqtkA84WkRUxNIynOT9InX7J-v61-4Ofs1zj8IYcnoYtqCa90Gv-Q2ZLSbg3rzNBGwsZrVLVmdAlQ8jXNvrW5_24NKPtwitDEswzMr16I/s1600/Deflection.PNG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_n01_J_pWmGJY5RMgcxR1nVvQITJnupHKttIqtkA84WkRUxNIynOT9InX7J-v61-4Ofs1zj8IYcnoYtqCa90Gv-Q2ZLSbg3rzNBGwsZrVLVmdAlQ8jXNvrW5_24NKPtwitDEswzMr16I/s1600/Deflection.PNG" height="180" width="640" /></a></div>
<br /></div>
<div style="font-family: Arial, Verdana, sans-serif; font-size: 12px;">
<br /></div>
<div style="font-family: Arial, Verdana, sans-serif; font-size: 12px;">
The shaft in the first picture above is clearly misaligned by more than a couple of degrees. In fact even when care is taken when doing such a weld there is invariably going to be some misalignment because of the welding process not being symmetrical (You have to start somewhere). In <a _fcksavedurl="https://www.youtube.com/watch?v=0TqvEXS3f88" href="https://www.youtube.com/watch?v=0TqvEXS3f88" target="_blank">this</a> video a shaft is welded and it is interesting to observe the amount of effort and precision put into making sure the shafts are aligned after the welding is complete.</div>
<div>
<div style="font-family: Arial, Verdana, sans-serif; font-size: 12px;">
This is not only true about half shafts. Any part welded about a rotating axis must take this tolerance into consideration. This includes wheel hubs, steering columns, their connection to joints, brake disk mounts and other rotating components. These welds are many times unavoidable as may have been in this case. here are some ideas to improve the quality of the design -</div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<ul style="text-align: left;">
<li><span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;">Rigid and tight fixtures set up during the welding process. The weld should be completed fully before the components are removed from the fixtures to avoid bending and deformation during the welding process.</span></li>
<li><span style="font-family: Arial, Verdana, sans-serif;"><span style="font-size: 12px;"><span style="background-color: white;">In the case of chrome alloy and there metal being used that require heat treatment after the welding is complete. the component should be heat treated with the fixtures such that the reheating or cooling does not cause any deformation.</span></span></span></li>
<li><span style="font-family: Arial, Verdana, sans-serif;"><span style="background-color: white;"><span style="font-size: 12px;">If possible especially for welded hubs, have some excess material on the welded on bits such that after the welding is complete the entire component can be placed on a turning machine and made radially symmetric. A welded wheel hub like in the picture below is bound to have some misalignment.</span></span></span></li>
</ul>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4En5I2CBBGJ7xY9KvuasQX2-wkldmwVz1tyqX3SQUiTsTm8jwrPSTRNEC8y5AJKk21MJSPAjXHYH5qB4RZDRiB1oubHGdKbFVdzaY5_R99-3nJHa5c58NQfbw89UU1xBpfYkkEEVJlXA/s1600/WeldedHub.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4En5I2CBBGJ7xY9KvuasQX2-wkldmwVz1tyqX3SQUiTsTm8jwrPSTRNEC8y5AJKk21MJSPAjXHYH5qB4RZDRiB1oubHGdKbFVdzaY5_R99-3nJHa5c58NQfbw89UU1xBpfYkkEEVJlXA/s1600/WeldedHub.JPG" height="240" width="320" /></a></div>
<div>
<span style="font-family: Arial, Verdana, sans-serif;"><span style="font-size: 12px;"><br /></span></span></div>
<ul style="text-align: left;">
<li><span style="font-family: Arial, Verdana, sans-serif;"><span style="background-color: white;"><span style="font-size: 12px;">Very small misalignments (not visible without measurement) can still cause vibration and large cyclic loading of the component.</span></span></span></li>
<li><span style="font-family: Arial, Verdana, sans-serif;"><span style="background-color: white;"><span style="font-size: 12px;">It is a good idea to have grooves and steps in the weld areas such that the components fit into one another when on the welding fixture. This drastically reduces the chances of misalignment</span></span></span></li>
</ul>
<span style="background-color: white;"><span style="font-family: Arial, Verdana, sans-serif;"><span style="font-size: 12px;">Apart from misalignment weld strength is also questionable in some of these designs. Specially for rotating parts the weld area see high shear forces, which is not the best place to have them. Special care must be taken to ensure the filler material used during welding is the correct one. Small differences in the material composition in the weld area can cause minute differences in the coefficient of Thermal expansion that can cause tiny cracks to be formed in the area. These cracks will propagate during cyclic loading.</span></span></span><br />
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;"><br /></span>
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;">A couple of ideas to improve the weld strength -</span><br />
<br />
<ul style="text-align: left;">
<li><span style="font-family: Arial, Verdana, sans-serif;"><span style="font-size: 12px;"><span style="background-color: white;">Find a method to increase the weld area. This can be done by having grooves and flanges or have the 2 components to be joined to be cut at an angle. Cutting at an angle not only takes the weld seam out of plane with the shear forces but also increase the weld area significantly.</span></span></span></li>
<li><span style="font-family: Arial, Verdana, sans-serif;"><span style="font-size: 12px;"><span style="background-color: white;">Support the butt-joint with an internal or an external sleeve. This distributes the shear force over multiple welds thereby effectively increasing the welded region and the strength of the component.</span></span></span></li>
</ul>
<div>
<i style="font-family: Arial, Verdana, sans-serif; font-size: 12px;">This blog post is originally written for the <a href="http://www.formulastudent.in/" target="_blank">Formula Student India</a> website and has been cross posted from <a href="http://formulastudent.in/member/designerror/3" target="_blank">here</a>.</i></div>
</div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com8tag:blogger.com,1999:blog-2197236978911214706.post-61841790806416912902014-02-26T09:54:00.000+05:302014-08-03T11:52:45.140+05:30Load Paths<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px; text-align: justify;">Today's article starts with this picture from a Baja competition but still quite valid even for Formula Student vehicles.</span><br />
<div>
<div style="text-align: justify;">
<span style="font-family: Arial, Verdana, sans-serif;"><span style="font-size: 12px;"><br /></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvB0NMrus1O9fNzucJoxOYVYxIz0tgabh7mKRRzVKzN5k-LFb8_gzhZaPajcLxVUrISzemj8ztBI-E8najK9CkeSuLgKhzsd4LWBsS1nwoGfBTM6yUZ0a2Ghyphenhyphen3J84TD6AT0xSiJDAs-Zo/s1600/Image1_upload.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvB0NMrus1O9fNzucJoxOYVYxIz0tgabh7mKRRzVKzN5k-LFb8_gzhZaPajcLxVUrISzemj8ztBI-E8najK9CkeSuLgKhzsd4LWBsS1nwoGfBTM6yUZ0a2Ghyphenhyphen3J84TD6AT0xSiJDAs-Zo/s1600/Image1_upload.jpg" height="285" width="400" /></a></div>
<div>
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px; text-align: justify;"><br /></span></div>
<div>
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px; text-align: justify;">This is a regular double wish-bone front suspension with direct actuation, and there are a few things you can spot here that one can do better. The most striking thing however is the lower mount of the suspension spring on the lower control arm. The spring bears the weight of the vehicle, and also bears greater loads during load transfers associated when driving the vehicle. Since this is a Baja vehicle, shock loads associated with large bumps also would be seen by the suspension spring. These loads are first seen at the wheels and are transferred to the chassis via a path. Note that this path is known as the 'load path' - it is really a visualization of the stress flow. The load is seen at the contact patch, which loads the tyre > the tyre loads the wheel > hub > wheel bearing > upright > lower control arm > spring. Now for this suspension to survive this particular loading, it must be considered while designing all these sub systems. </span></div>
<div>
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px; text-align: justify;"><br /></span></div>
<div>
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px; text-align: justify;">Let's look at the lower control arm in the front view. This control arm is really supported by the ball joint at one end and the chassis pick up points at the other end. The spring loads this control arm right at the center, which as you can probably visualize, causes some (or may be a lot of) bending. [Thought experiment] Give a thin meter long bamboo stick to a 7 year old kid (note she does not have an engineering degree). Ask her to break it, any which way she likes. What is she going to do? She is probably going to hold the 2 ends with her hands and try break it with her legs. Why did she not break it by pulling at its 2 ends? Why did she not compress it until it breaks?</span></div>
<div>
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px; text-align: justify;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvMQprKfJ-LZbn5GDkLPoovC3stbPy_jiq1qU1Ej97GPeNIR1ko7lwMx4VjhKGwIQZIgqzexHtdryHAD2SzdScnnIWqrdYg3dcVLiyW_aPSwfwnVTO52MQfxtTYcpve54hdOOdnSnao-E/s1600/Image2_upload.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgvMQprKfJ-LZbn5GDkLPoovC3stbPy_jiq1qU1Ej97GPeNIR1ko7lwMx4VjhKGwIQZIgqzexHtdryHAD2SzdScnnIWqrdYg3dcVLiyW_aPSwfwnVTO52MQfxtTYcpve54hdOOdnSnao-E/s1600/Image2_upload.png" height="182" width="400" /></a></div>
<div>
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px; text-align: justify;"><br /></span></div>
<div>
<div>
<div style="text-align: justify;">
<span style="font-family: Arial, Verdana, sans-serif;"><span style="font-size: 12px;"><br /></span></span></div>
<div style="text-align: justify;">
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;">Her intuition told her that the stick is most likely going to break in the first way. An engineer would call it bending load. There are probably 10 equations I can write here to prove this using a Solid Mechanics Text book, or a short simulation on a Finite Element analysis to prove this to you. But I am going to assume here that your intuition is in agreement with me.</span><br />
<br style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;" />
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;">Moreover, the bamboo will only break easily if the ends are held and the load is applied at the center. If the load were applied near the either ends, significantly more force will be required to break or even deform the bamboo. So if you want to break the bamboo apply loads to the center and in bending, if you want it not to break or even flex, then apply it near its ends.</span><br />
<br style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;" />
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;">Steel rods are not much different from bamboo [citation needed]. In a Baja car we do not need things to break or flex, specially the important suspension components. The lower control arm in this picture is a steel road in heavy bending load. It is going to flex a lot if not break. In fact this front suspension has 3 significant springs in series. 1) The Tyre 2) The Lower Control Arm 3) The suspension spring. I am willing to bet - the suspension design did not consider this extra spring and compliance in this calculation.</span><br />
<br style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;" />
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;">You should not therefore be surprised to see this picture of the same suspension after the car hit the first bump at the endurance event.</span></div>
<div style="text-align: justify;">
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgt40azZfSa_o3SoqETiIh4oLOrl1WoYAy7lHVzgIQTpDkUtzieS33qujRm0Z835-uZdHitixk5UXgQeRj2JtyI_QR0qGkAwKk8TOOQGgFl6olfliihGBDUQxWlTHzITVzShqqBA5N3hcg/s1600/image3_upload.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgt40azZfSa_o3SoqETiIh4oLOrl1WoYAy7lHVzgIQTpDkUtzieS33qujRm0Z835-uZdHitixk5UXgQeRj2JtyI_QR0qGkAwKk8TOOQGgFl6olfliihGBDUQxWlTHzITVzShqqBA5N3hcg/s1600/image3_upload.jpg" height="140" width="400" /></a></div>
<div style="text-align: justify;">
<i style="font-family: Arial, Verdana, sans-serif; font-size: 12px; text-align: left;"><br /></i>
<i style="font-family: Arial, Verdana, sans-serif; font-size: 12px; text-align: left;">This blog post is originally written for the <a href="http://www.formulastudent.in/" target="_blank">Formula Student India</a> website and has been cross posted from <a href="http://formulastudent.in/designerror/design-errors---load-paths-1" target="_blank">here</a>.</i></div>
<div style="text-align: justify;">
<span style="background-color: white; font-family: Arial, Verdana, sans-serif; font-size: 12px;"><br /></span></div>
<br /></div>
</div>
</div>
</div>
Mahekhttp://www.blogger.com/profile/01961984742300757315noreply@blogger.com1