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|
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|
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<div class="usa-overlay"></div>
|
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<header class="usa-header nist-header--www nist-header--minimal" role="banner">
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<div class="usa-navbar">
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<div class="usa-logo flex-fill">
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<a href="/" title="National Institute of Standards and Technology" aria-label="Home">
|
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<img src="/libraries/nist-component-library/dist/img/logo/logo.svg" alt="National Institute of Standards and Technology" width="300px" height="80px" />
|
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|
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</a>
|
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</div>
|
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<div class="usa-header__right grid-row flex-auto">
|
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<div class="grid-col-fill nist-header__search-group">
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<form class="usa-search usa-search--small"
|
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accept-charset="UTF-8"
|
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action="/search"
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id="search_form"
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method="get">
|
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<div role="search">
|
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<label class="usa-sr-only" for="search-form">Search NIST</label>
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<input class="usa-input" id="search-form" type="search" name="s" placeholder="Search NIST" required="" maxlength="128">
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<button class="usa-button" type="submit"><img src="/libraries/nist-component-library/dist/img/usa-icons-bg/search--white.svg" class="usa-search__submit-icon" alt="Search"></button>
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</div>
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</form>
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<div class="grid-col-auto padding-left-1">
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<button class="usa-menu-btn">Menu</button>
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<nav aria-label="Primary navigation" class="usa-nav">
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<ul class="usa-nav__primary usa-accordion">
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<a class="usa-nav__link" href="/publications">Publications</a>
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<button class="usa-accordion__button usa-nav__link" aria-expanded="false" aria-controls="primary_menu-2"><span>What We Do</span></button>
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<a href="/topics" class="usa-nav__link">All Topics</a>
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<a href="/energy" class="usa-nav__link">Energy</a>
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<a href="/fire" class="usa-nav__link">Fire</a>
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<a href="/forensic-science" class="usa-nav__link">Forensic science</a>
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<a href="/health" class="usa-nav__link">Health</a>
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<a href="/information-technology" class="usa-nav__link">Information technology</a>
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<a href="/infrastructure" class="usa-nav__link">Infrastructure</a>
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<a href="/manufacturing" class="usa-nav__link">Manufacturing</a>
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<a href="/materials" class="usa-nav__link">Materials</a>
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<a href="/mathematics-statistics" class="usa-nav__link">Mathematics and statistics</a>
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</ul></div><div class="column-break tablet:grid-col-fill"><ul class="usa-nav__submenu-list">
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<li class="usa-nav__submenu-item">
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<a href="/metrology" class="usa-nav__link">Metrology</a>
|
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</li>
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<li class="usa-nav__submenu-item">
|
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<a href="/nanotechnology" class="usa-nav__link">Nanotechnology</a>
|
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</li>
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<li class="usa-nav__submenu-item">
|
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<a href="/neutron-research" class="usa-nav__link">Neutron research</a>
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<li class="usa-nav__submenu-item">
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<a href="/performance-excellence" class="usa-nav__link">Performance excellence</a>
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<li class="usa-nav__submenu-item">
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<a href="/physics" class="usa-nav__link">Physics</a>
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<li class="usa-nav__submenu-item">
|
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<a href="/public-safety" class="usa-nav__link">Public safety</a>
|
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<li class="usa-nav__submenu-item">
|
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<a href="/quantum-information-science" class="usa-nav__link">Quantum information science</a>
|
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|
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<li class="usa-nav__submenu-item">
|
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<a href="/resilience" class="usa-nav__link">Resilience</a>
|
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|
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</li>
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<li class="usa-nav__submenu-item">
|
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<a href="/standards" class="usa-nav__link">Standards</a>
|
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|
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</li>
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<li class="usa-nav__submenu-item">
|
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<a href="/transportation" class="usa-nav__link">Transportation</a>
|
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</li>
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</ul>
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|
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</div>
|
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</div>
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</div>
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</li>
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<li class="usa-nav__primary-item">
|
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<button class="usa-accordion__button usa-nav__link" aria-expanded="false" aria-controls="primary_menu-3"><span>Labs & Major Programs</span></button>
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<div id="primary_menu-3" class="usa-nav__submenu usa-megamenu">
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<div class="grid-row">
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<div class="tablet:grid-col-fill"><ul class="usa-nav__submenu-list">
|
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<li class="usa-nav__submenu-item">
|
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|
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<a href="/adlp" class="usa-nav__link">Assoc Director of Laboratory Programs</a>
|
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|
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</li>
|
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|
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<li class="usa-nav__submenu-item">
|
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|
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<a href="/laboratories" class="usa-nav__link">Laboratories</a>
|
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|
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<ul class="usa-nav__submenu-list">
|
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|
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<li>
|
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|
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<a href="/ctl" class="usa-nav__link">Communications Technology Laboratory</a>
|
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|
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</li>
|
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|
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<li>
|
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|
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<a href="/el" class="usa-nav__link">Engineering Laboratory</a>
|
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|
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</li>
|
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|
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<li>
|
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|
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<a href="/itl" class="usa-nav__link">Information Technology Laboratory</a>
|
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|
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</li>
|
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|
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<li>
|
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|
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<a href="/mml" class="usa-nav__link">Material Measurement Laboratory</a>
|
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|
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</li>
|
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|
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<li>
|
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|
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<a href="/pml" class="usa-nav__link">Physical Measurement Laboratory</a>
|
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|
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</li>
|
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|
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</ul>
|
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|
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</li>
|
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|
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</ul></div><div class="column-break tablet:grid-col-fill"><ul class="usa-nav__submenu-list">
|
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<li class="usa-nav__submenu-item">
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<a href="/user-facilities" class="usa-nav__link">User Facilities</a>
|
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<ul class="usa-nav__submenu-list">
|
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<li>
|
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|
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<a href="/ncnr" class="usa-nav__link">NIST Center for Neutron Research</a>
|
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|
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|
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|
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<li>
|
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|
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<a href="/cnst" class="usa-nav__link">CNST NanoFab</a>
|
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|
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</ul>
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<li class="usa-nav__submenu-item">
|
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<a href="/labs-major-programs/research-test-beds" class="usa-nav__link">Research Test Beds</a>
|
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|
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</li>
|
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|
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<li class="usa-nav__submenu-item">
|
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|
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<a href="/laboratories/projects-programs" class="usa-nav__link">Research Projects</a>
|
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<li class="usa-nav__submenu-item">
|
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<a href="/laboratories/tools-instruments" class="usa-nav__link">Tools & Instruments</a>
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</li>
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</ul></div><div class="column-break tablet:grid-col-fill"><ul class="usa-nav__submenu-list">
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<li class="usa-nav__submenu-item">
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<a href="/major-programs" class="usa-nav__link">Major Programs</a>
|
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<ul class="usa-nav__submenu-list">
|
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<li>
|
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<a href="/baldrige" class="usa-nav__link">Baldrige Performance Excellence Program</a>
|
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|
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</li>
|
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|
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<li>
|
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<a href="/chips" class="usa-nav__link">CHIPS for America Initiative</a>
|
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|
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</li>
|
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<li>
|
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<a href="/mep" class="usa-nav__link">Manufacturing Extension Partnership (MEP)</a>
|
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|
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</li>
|
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<li>
|
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|
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<a href="/oam" class="usa-nav__link">Office of Advanced Manufacturing</a>
|
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</li>
|
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<li>
|
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<a href="/spo" class="usa-nav__link">Special Programs Office</a>
|
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</li>
|
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|
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<li>
|
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|
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<a href="/tpo" class="usa-nav__link">Technology Partnerships Office</a>
|
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|
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</li>
|
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|
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</ul>
|
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|
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</li>
|
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|
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</ul>
|
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|
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</div>
|
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</div>
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</div>
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</li>
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<li class="usa-nav__primary-item">
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<button class="usa-accordion__button usa-nav__link" aria-expanded="false" aria-controls="primary_menu-4"><span>Services & Resources</span></button>
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<div id="primary_menu-4" class="usa-nav__submenu usa-megamenu">
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<div class="grid-row">
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<div class="tablet:grid-col-fill"><ul class="usa-nav__submenu-list">
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<li class="usa-nav__submenu-item">
|
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<a href="/content/standards-measurements" class="usa-nav__link">Standards and Measurements</a>
|
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<ul class="usa-nav__submenu-list">
|
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<li>
|
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<a href="/calibrations" class="usa-nav__link">Calibration Services</a>
|
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|
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</li>
|
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|
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<li>
|
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|
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<a href="/nvlap" class="usa-nav__link">Laboratory Accreditation (NVLAP)</a>
|
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|
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</li>
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<li>
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|
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<a href="/nist-quality-system" class="usa-nav__link">Quality System</a>
|
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</li>
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<li>
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|
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<a href="/srm" class="usa-nav__link">Standard Reference Materials (SRMs)</a>
|
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|
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</li>
|
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|
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<li>
|
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|
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<a href="/sri" class="usa-nav__link">Standard Reference Instruments (SRIs)</a>
|
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|
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</li>
|
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|
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<li>
|
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|
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<a href="/standardsgov" class="usa-nav__link">Standards.gov</a>
|
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|
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</li>
|
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<li>
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<a href="/pml/time-and-frequency-division/time-services" class="usa-nav__link">Time Services</a>
|
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</li>
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<li>
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<a href="/pml/owm" class="usa-nav__link">Office of Weights and Measures</a>
|
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</li>
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</li>
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</ul></div><div class="column-break tablet:grid-col-fill"><ul class="usa-nav__submenu-list">
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<li class="usa-nav__submenu-item">
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<a href="/services-resources/software" class="usa-nav__link">Software</a>
|
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</li>
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<li class="usa-nav__submenu-item">
|
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<a href="/data" class="usa-nav__link">Data</a>
|
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<ul class="usa-nav__submenu-list">
|
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|
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<li>
|
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|
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<a href="https://webbook.nist.gov/chemistry/" class="usa-nav__link">Chemistry WebBook</a>
|
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|
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</li>
|
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<li>
|
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|
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<a href="https://nvd.nist.gov/" class="usa-nav__link">National Vulnerability Database</a>
|
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|
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</li>
|
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<li>
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<a href="/pml/productsservices/physical-reference-data" class="usa-nav__link">Physical Reference Data</a>
|
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|
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</li>
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<li>
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|
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<a href="/srd" class="usa-nav__link">Standard Reference Data (SRD)</a>
|
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</ul>
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<li class="usa-nav__submenu-item">
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<a href="https://shop.nist.gov/" class="usa-nav__link">Storefront</a>
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<li class="usa-nav__submenu-item">
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<a href="/tpo" class="usa-nav__link">License & Patents</a>
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</li>
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</ul></div><div class="column-break tablet:grid-col-fill"><ul class="usa-nav__submenu-list">
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<li class="usa-nav__submenu-item">
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<a href="https://csrc.nist.gov/" class="usa-nav__link">Computer Security Resource Center (CSRC)</a>
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</li>
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<li class="usa-nav__submenu-item">
|
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<a href="/nist-research-library" class="usa-nav__link">NIST Research Library</a>
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</li>
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</ul>
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</div>
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</div>
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</div>
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</li>
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<li class="usa-nav__primary-item">
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<button class="usa-accordion__button usa-nav__link" aria-expanded="false" aria-controls="primary_menu-5"><span>News & Events</span></button>
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<div id="primary_menu-5" class="usa-nav__submenu usa-megamenu">
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<div class="grid-row">
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<li class="usa-nav__submenu-item">
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<a href="/news-events/news" class="usa-nav__link">News</a>
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<a href="/news-events/events" class="usa-nav__link">Events</a>
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<li class="usa-nav__submenu-item">
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<h1 class="nist-page__title">The Life of (Buckingham) Pi</h1>
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<div class="daterange"><time datetime="2020-03-14T12:00:00Z">March 14, 2020</time>
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<span>By: </span>
|
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<a href="/blogs/taking-measure/authors/cw-clark" hreflang="en">C.W. Clark</a>
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<figure class="nist-image--lightbox nist-image" data-lightbox="https://www.nist.gov/sites/default/files/styles/2800_x_2800_limit/public/images/2020/03/12/Pi%20Day%202020.jpg?itok=5mkYY3rD" data-media-id="575216" data-copyright="Stock Photo">
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<img loading="lazy" src="/sites/default/files/styles/960_x_960_limit/public/images/2020/03/12/Pi%20Day%202020.jpg?itok=SOpXiUPh" width="960" height="600" alt="white pi symbol on a grey field made up of the numbers of pi" typeof="foaf:Image" />
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<span class="nist-image__credit-label">Credit:</span>
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RadenVector/shutterstock.com
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<p>What do the following topics have in common?</p><ul><li>Pricing models for parking reservation systems.</li><li>The mechanics of human walking.</li><li>The die-down of water waves in sea ice.</li><li>The self-hovering of unmanned aerial vehicles right above the ground.</li><li>Bright cosmic infrared arcs that form when stellar dust meets the solar wind.</li><li>The reconnection of whirlpool-like vortices in exotic “superfluids,” which flow without friction.</li></ul><p>They are all subjects of technical papers published in 2019 that cite a remarkable 1914 <a href="https://doi.org/10.1103/PhysRev.4.345">paper</a> published by <span>a physicist at the agency that became the National Institute of Standards and Technology (NIST). Indeed, the Web of Science academic database records that paper as </span><em><span>the</span></em><span> most-cited paper of all that were published in the year 1914: a part of a fervent scientific decade in which Nobel laureates such as Marie Curie, Albert Einstein, Ernest Rutherford, Niels Bohr, J.J. Thomson, and William Lawrence Bragg were active.</span></p><p>Edgar Buckingham, a physicist at the National Bureau of Standards (NBS), was the author of that paper. In it, he laid out what has become known as the "Buckingham pi theorem," which provides a framework for a problem-solving approach called dimensional analysis.</p><p>Isaac Newton knew about dimensional analysis and used it in his masterpiece, the <em>Principia Mathematica</em>. Science students learn about the procedure by their first year of college. NIST researchers use it every day, for it provides a universal structure for solving problems of science and engineering and the design of experiments.</p><p>The basic idea of dimensional analysis is to consider all possible products and ratios of the <em>physical dimensions</em> of the variables in the system under study. Important physical dimensions in many applications involve <em>mass</em>, <em>length</em> and <em>time</em>.</p><p>A simple example is the determination of the area, <em>A</em>, enclosed by a circle of radius, <em>r</em>.</p>
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<div data-lightbox="https://www.nist.gov/sites/default/files/styles/2800_x_2800_limit/public/images/2020/03/13/circle.png?itok=0Xuz9vuZ" data-media-id="575246">
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<img alt="a circle with the diameter, half arc and radius labeled" height="631" loading="lazy" src="/sites/default/files/images/2020/03/13/circle.png" typeof="foaf:Image" width="531">
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<figcaption class="nist-image__caption">A circle of radius of length r, diameter of length d, and half-circumference of length h.<div class="nist-image__credit">
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<span class="nist-image__credit-label">Credit:</span>
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C. Clark/NIST
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<p>There are many choices for describing the size of a circle, such as its radius, <em>r</em>, its diameter, <em>d</em>, or half of its circumference, <em>h</em>. But all of these are proportional to each other — they each have the physical dimensions of length — and quantities such as <em>d</em>/<em>r</em> and <em>h</em>/<em>r</em> are just numbers — without any units or dimensions. There is only one independent<em> physical dimension</em> of length, which we can take to describe by <em>r</em>, measured in meters. The area, <em>A</em>, has dimensions of square meters = meters<sup>2</sup> = meters x meters, and so dimensional analysis requires that <em>A</em>(<em>r</em>) = 𝜋 x <em>r</em><sup>2</sup>, where 𝜋 is a pure number that today we call “pi” (get it — March 14??). This expression is the only way to generate a result in square meters once we have decided on the standard of length, <em>r</em>.</p><p>One more bit of background that will help you follow the rest of the argument:</p><p><em>A</em>(<em>r</em>)= 𝜋 x <em>r</em><sup>2</sup> is something in mathematics called a function. A function, <em>f</em>, is like a machine that takes an input value, <em>x</em>, and produces a unique output value, <em>f</em>(<em>x</em>). Newbies are usually surprised at how much one can milk this very simple idea — see the <a href="http://dlmf.nist.gov/">NIST Digital Library of Mathematical Functions</a> for examples. In this case, <em>A</em>(<em>r</em>) takes the input, <em>r</em>, in units of meters, and outputs the value <em>A</em>(<em>r</em>) = 𝜋 x <em>r</em><sup>2</sup>, in units of meters<sup>2</sup>.</p><p>What if we have <em>multiple </em>independent standards of length in our system? That’s the issue addressed by Buckingham. For example, what is the area of the ellipse inscribed within this rectangle?</p>
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<div data-lightbox="https://www.nist.gov/sites/default/files/styles/2800_x_2800_limit/public/images/2020/03/13/ellipse%20with%20rectangle.png?itok=9Dyu_oTP" data-media-id="575251">
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<img alt="an ellipse inscribed within a rectangle" height="582" loading="lazy" src="/sites/default/files/images/2020/03/13/ellipse%20with%20rectangle.png" typeof="foaf:Image" width="1136">
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<figcaption class="nist-image__caption">An ellipse inscribed inside a rectangle. This becomes a circle when a = b.<div class="nist-image__credit">
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<span class="nist-image__credit-label">Credit:</span>
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C. Clark/NIST
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</div></figcaption>
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<p>We have two independent lengths that describe the rectangle, <em>a</em> and <em>b</em>. Thus, we could choose to write A = <em>a </em>x <em>b </em>x <em>f(a/b</em>), where <em>f</em>(<em>a/b</em>) is some function of the dimensionless ratio <em>a/b</em>, which describes the <em>shape</em> rather than the <em>size</em> of the ellipse. This expression captures the evident fact that if <em>a</em> and <em>b</em> are increased by a common factor of <em>L</em>, the shape of the ellipse stays the same and its area increases by a factor of <em>L</em><sup>2</sup>. In honor of this day, I note that in fact <em>f</em>(<em>a/b</em>) = 𝜋 for any value of <em>a/b</em>.</p><p>In his 1914 paper, Buckingham uses a college-level branch of mathematics known as linear algebra to provide a systematic framework within which such dimensional scaling factors can be determined. Here is an example he gives of its application: to find the thrust of a ship’s propeller that is required to maintain the ship’s speed.</p><p>The thrust depends upon six independent dimensional variables: the diameter and rotation rate of the propeller, the ship's speed, the acceleration of gravity, and the density and viscosity of seawater. How does one even begin to solve such a problem? Buckingham shows that there is a unique set of combinations of the parameters mentioned above that “tells us without any experimentation at all” what the essential relationships must be.</p><p>A testament to the power of this approach is its continued use a century hence, across a wide range of subjects indicated by the examples shown at the beginning of this essay. Those are but a sample of the <strong>131</strong> papers published in 2019 that cite Buckingham's original paper, according to the Web of Science. More than 1,400 citations have been made so far, and at an increasing rate — something quite unusual for a century-old paper.</p><p>Buckingham's achievement derived from a keen understanding of the process of physical measurement, and it put working clothes on Lord Kelvin's dictum: "When you can measure what you are speaking about, and express it in numbers, you know something about it." It is a distinctive contribution to science, and likely one of the most influential.</p>
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<a href="/blogs/taking-measure/categories/249011">Mathematics and statistics</a>,
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<a href="/blogs/taking-measure/categories/249031">Modeling and simulation research</a>,
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<a href="/blogs/taking-measure/categories/249241">Physics</a>,
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<a href="/blogs/taking-measure/categories/249246">Atomic / molecular / quantum</a> and
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<a href="/blogs/taking-measure/categories/249281">Quantum information science</a></div>
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>About the author</h2>
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about="/blogs/taking-measure/authors/cw-clark" class="nist-teaser"
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>
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<div class="entity-reference"> <a href="/blogs/taking-measure/authors/cw-clark" hreflang="en"><img loading="lazy" src="/sites/default/files/styles/thumbnail/public/images/2017/01/27/charles_clark.jpg?itok=sknK1zDN" width="80" height="100" alt="Headshot of Charles Clark" typeof="foaf:Image" />
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<h3 class="nist-teaser__title"><a href="/blogs/taking-measure/authors/cw-clark"><span>C.W. Clark</span>
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<div class="text-with-summary"><p>Charles W. Clark, aka Carbon Tungsten Chlorine Argon Potassium, is among a select group of NIST staff whose surnames can be spelled with the chemical symbols of consecutive elements of the Periodic Table. In addition to this distinction, Charles is a NIST Fellow and Fellow and past co-director of the Joint Quantum Institute (JQI), a research collaboration that includes NIST and the University of Maryland. His research activities are focused on theoretical atomic, molecular and optical physics.</p></div>
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<h2
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class="nist-block__title"
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>Related posts</h2>
|
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<div><div class="js-view-dom-id-e769580a4c4f4b333da59e245a29e28c36f0d65ef6abf30bfb267309137c5b39">
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<article
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about="/blogs/taking-measure/talk-nisty-me-when-everyday-words-take-different-meanings-measurement-science" class="nist-teaser"
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>
|
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<div class="nist-teaser__image">
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<div class="entity-reference"> <a href="/blogs/taking-measure/talk-nisty-me-when-everyday-words-take-different-meanings-measurement-science" hreflang="en"><img loading="lazy" src="/sites/default/files/styles/thumbnail/public/images/2024/07/03/DSC_5319_web.jpg?itok=BmpD3FoJ" width="100" height="67" alt="A researcher wearing a lab coat uses tongs to place a silvery sphere into a large scientific device as another researcher looks on. " typeof="foaf:Image" />
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<header>
|
|||
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<h3 class="nist-teaser__title"><a href="/blogs/taking-measure/talk-nisty-me-when-everyday-words-take-different-meanings-measurement-science"><span>Talk NISTy to Me: When Everyday Words Take On Different Meanings in Measurement Science</span>
|
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</a></h3>
|
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<div class="nist-teaser__date">
|
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<div class="daterange"><time datetime="2024-12-04T12:00:00Z">December 4, 2024</time>
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<div class="text-with-summary"> Words that have common meanings have different definitions in the world of measurement science.
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<article
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about="/blogs/taking-measure/bookmobiles-big-data-how-library-scientists-make-information-accessible-all" class="nist-teaser"
|
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>
|
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|
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<div class="entity-reference"> <a href="/blogs/taking-measure/bookmobiles-big-data-how-library-scientists-make-information-accessible-all" hreflang="en"><img loading="lazy" src="/sites/default/files/styles/thumbnail/public/images/2024/02/22/kathryn_miller_with_book_021324.jpg?itok=p_NY21qb" width="100" height="67" alt="Kathryn Miller sits reading a book at a small table in the NIST library. " typeof="foaf:Image" />
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|
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<header>
|
|||
|
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<h3 class="nist-teaser__title"><a href="/blogs/taking-measure/bookmobiles-big-data-how-library-scientists-make-information-accessible-all"><span>From Bookmobiles to Big Data, How Library Scientists Make Information Accessible to All</span>
|
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|
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</a></h3>
|
|||
|
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<div class="nist-teaser__date">
|
|||
|
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<div class="daterange"><time datetime="2024-03-20T12:00:00Z">March 20, 2024</time>
|
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|
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<div class="nist-teaser__content">
|
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|
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<div class="text-with-summary"> During Women’s History Month, a NIST librarian looks back at the librarian who brought us the bookmobile — back when it brought books by horse and buggy.
|
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|
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<article
|
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about="/blogs/taking-measure/scientific-christmas-tale" class="nist-teaser"
|
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>
|
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|
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<div class="entity-reference"> <a href="/blogs/taking-measure/scientific-christmas-tale" hreflang="en"><img loading="lazy" src="/sites/default/files/images/2023/12/04/NightbeforeXmas_Title_v2_Test-A.gif" width="960" height="600" alt="Title card reads "A Scientific Christmas Tale" with the NIST logo in a wreath and flashing holiday lights. " typeof="foaf:Image" />
|
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|
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|
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<header>
|
|||
|
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<h3 class="nist-teaser__title"><a href="/blogs/taking-measure/scientific-christmas-tale"><span>A Scientific Christmas Tale</span>
|
|||
|
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</a></h3>
|
|||
|
|
<div class="nist-teaser__date">
|
|||
|
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<div class="daterange"><time datetime="2023-12-19T12:00:00Z">December 19, 2023</time>
|
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|
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|
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<div class="nist-teaser__content">
|
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<div class="text-with-summary"> ’Twas the night before Christmas; NIST staff had gone home. Our director was left to reflect all alone. She thought about NIST and the breadth of its work, from
|
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|
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|
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|
|||
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|
|||
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>Comments</h2>
|
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<section>
|
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<article data-comment-user-id="0" id="comment-91326" class="nist-comment js-comment">
|
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|
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="">Jose Hernandez</span></span>
|
|||
|
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on
|
|||
|
|
<span class="nist-comment__date">March 14, 2020 4:10 PM</span>
|
|||
|
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<mark class="hidden nist-comment__new" data-comment-timestamp="1584366486"></mark>
|
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|
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<div class="nist-comment__permalink"><a href="#comment-91326">Permalink</a></div>
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|||
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<div class="text-long"><p>Wonderfull</p>
|
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|
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<ul class="links inline nist-comment__links">
|
|||
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|
|||
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<a href="/comment/reply/node/1613181/comment_node_blog/91326">Reply</a></li></ul>
|
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<article data-comment-user-id="0" id="comment-91336" class="nist-comment js-comment">
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|
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="" content="Bill(aka Bruce)Gadzuk">Bill(aka Bruce)Gadzuk</span></span>
|
|||
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on
|
|||
|
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<span class="nist-comment__date">March 14, 2020 5:43 PM</span>
|
|||
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<mark class="hidden nist-comment__new" data-comment-timestamp="1584366435"></mark>
|
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|
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|
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|
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<div class="text-long"><p>Charles(aka Bruce and/or Carbon Tungsten Chlorine Argon Potassium), you continue to amaze me and the rest of the world with your mastery of interesting obscurities.</p>
|
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|
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<article data-comment-user-id="0" id="comment-91371" class="nist-comment js-comment">
|
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|
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="">Charles Clark</span></span>
|
|||
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on
|
|||
|
|
<span class="nist-comment__date">March 16, 2020 10:29 AM</span>
|
|||
|
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<mark class="hidden nist-comment__new" data-comment-timestamp="1584369491"></mark>
|
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|
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<span class="nist-comment__parent">| Replied to <a href="/comment/91336#comment-91336" class="permalink" rel="bookmark" hreflang="en">Charles(aka Bruce and/or…</a></span>
|
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|
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<div class="nist-comment__permalink"><a href="#comment-91371">Permalink</a></div>
|
|||
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|
|||
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|
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<div class="text-long"><p>If I have not seen as far as others, it is because giants were standing on my shoulders!</p>
|
|||
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|
|||
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<article data-comment-user-id="0" id="comment-91341" class="nist-comment js-comment">
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|
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="">Rick</span></span>
|
|||
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on
|
|||
|
|
<span class="nist-comment__date">March 14, 2020 5:43 PM</span>
|
|||
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<mark class="hidden nist-comment__new" data-comment-timestamp="1584366476"></mark>
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|
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<div class="text-long"><p>I love numbers</p>
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="">Elwood Downey</span></span>
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<span class="nist-comment__date">March 14, 2020 5:56 PM</span>
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<div class="text-long"><p>Good article, thanks. It would be nice to read the paper without paying $35.</p>
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="">Charles Clark</span></span>
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<span class="nist-comment__date">March 16, 2020 4:39 PM</span>
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<span class="nist-comment__parent">| Replied to <a href="/comment/91346#comment-91346" class="permalink" rel="bookmark" hreflang="en">Good article, thanks. It…</a></span>
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<div class="text-long"><p>The American Physical Society will give free access to any Physical Review article to anyone who applies via a U.S. public or high school library. For details, see <a href="https://journals.aps.org/free-access-for-us-public-and-high-school-libraries">https://journals.aps.org/free-access-for-us-public-and-high-school-libr…</a> </p>
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<p>I should also note that the full texts of many classic physics papers can be found via Google Scholar, ResearchGate and other such tools that are widely used in the physical sciences research community.</p>
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="">Robert Wallace</span></span>
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<span class="nist-comment__date">March 15, 2020 5:15 AM</span>
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<div class="text-long"><p>I have always wanted to see the Dimensional Analysis of robot payload motions in terms of inertia and material density. When the CanadaArm 2 on the NASA ISS transports a suited astronaut with their tools to an EVA worksite -- like the site of a battery changeout -- the CanadaArm astronaut operator moves the payload very slowly. It would be very useful to perform the Dimensional Analysis (DA) of the 'envelope' or recommended limits for the elemental motions of all the involved robot joint gearmotors. Is the author aware of any such 'inertia' and 'materialdensity' DA of robot payload motion.</p>
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="">Charles Clark</span></span>
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<span class="nist-comment__date">March 16, 2020 10:14 AM</span>
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<span class="nist-comment__parent">| Replied to <a href="/comment/91351#comment-91351" class="permalink" rel="bookmark" hreflang="en">I have always wanted to see…</a></span>
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<div class="text-long"><p>I don't know of work on this subject, but I am certainly no expert. You might have a look at <a href="https://ntrs.nasa.gov/search.jsp?R=19740008732">https://ntrs.nasa.gov/search.jsp?R=19740008732</a> It uses the approprite language, and Google Scholar indicates that 625 subsequent publications have cited it.</p>
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="">Daniel Lozier</span></span>
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<span class="nist-comment__date">March 15, 2020 10:52 AM</span>
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<div class="text-long"><p>Charles, my hat is off to you. Your ability to explain scientific concepts to a general audience, without dumbing it down, is admirable. And I really appreciate the reference to the DLMF!jBQzo,</p>
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<span class="nist-comment__date">March 16, 2020 10:20 AM</span>
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<span class="nist-comment__parent">| Replied to <a href="/comment/91356#comment-91356" class="permalink" rel="bookmark" hreflang="en">Charles, my hat is off to…</a></span>
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<div class="text-long"><p>Many thanks Dan!</p>
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<span class="nist-comment__author"><span lang="" typeof="schema:Person" property="schema:name" datatype="">Bill/Bruce Gadzuk</span></span>
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<span class="nist-comment__date">March 16, 2020 10:06 PM</span>
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<div class="text-long"><p>You state that "Those are but a sample of the 131 papers published in 2019 that cite Buckingham's original paper, according to the Web of Science. More than 1,400 citations have been made so far, and at an increasing rate". This implies that nearly 10% of the citations over the past century were made in 2019. Surely that cannot be so. The truth is...…..</p>
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