<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40"><head><meta http-equiv=Content-Type content="text/html; charset=utf-8"><meta name=Generator content="Microsoft Word 15 (filtered medium)"><style><!--
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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple style='word-wrap:break-word'><div class=WordSection1><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b>From:</b> extropy-chat <extropy-chat-bounces@lists.extropy.org> <b>On Behalf Of </b>Adrian Tymes via extropy-chat<br><b>Sent:</b> Monday, 10 June, 2024 5:50 PM<br><b>To:</b> ExI chat list <extropy-chat@lists.extropy.org><br><b>Cc:</b> Adrian Tymes <atymes@gmail.com><br><b>Subject:</b> Re: [ExI] trust the fake science?<o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p><div><div><p class=MsoNormal>On Mon, Jun 10, 2024 at 6:42 PM <<a href="mailto:spike@rainier66.com">spike@rainier66.com</a>> wrote:<o:p></o:p></p></div><div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><div><div><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Now if we imagine the pressure doubling inside the tank, the skin thickness must also double in order to keep the material stress constant. Make sense?<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>Now imagine keeping the pressure constant and doubling the tank radius. The volume of the tank increases by a factor of eight and the surface area of the tank increases by a factor of 4. So we could just square/cube our way to being a hero, ja? <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'> <o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto'>YeeeeeeahNo. With those assumptions, when we double the radius of the tank with constant pressure inside, the thickness of the skin must also double.<o:p></o:p></p></div></div></div></div></div></div></blockquote><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>>…Why so? The pressure did not double. The skin thickness resists pressure per unit area…<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>The hoop stress equation will get you there, but we can do it thought experiment style, which has its advantages for visualization purposes.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Imagine your spherical tank in orbit so no external forces again, now imagine a cutting plane that passes thru the center. Now look at the tensile stress on the material the plane passes thru. It’s area is the circumference of the sphere times the thickness of the tank. The force on that area is (pi*R^2)P where P is the pressure inside the tank.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Now if you double the R, the volume goes up by a factor of 8, the force goes up by a factor of 4 (ja?) The circumference goes up by a factor of 2. To keep the force over area constant, ya hafta double the thickness of the tank.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>With negative pressure tanks (submarines and such) it is more complicated because of stress concentrations with compressive stress. But if we do ideal case, perfectly isotropic material and no stress concentrations anywhere, it works that way for those too.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Adrian, this is a thought experiment only, not a proof your idea can’t work.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>spike<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></div></div></div></body></html>