Editing Centrifugation (section)

==Mathematical formula==
In a liquid suspension, many [[particles]] or [[Cell (biology)|cell]]s will gradually fall to the bottom of the container due to [[gravity]]; however, the amount of time taken for such separations is not feasible. Other particles, which are very small, can not be isolated at all in solution until they are exposed to a high [[centrifugal force]]. As the suspension is rotated at a certain speed or [[revolutions per minute]] (RPM), the centrifugal force allows the particles to travel radially away from the rotation axis. The general formula for calculating the revolutions per minute (RPM) of a centrifuge is:

<math>RPM= \sqrt{g \over r}</math>,

where ''g'' represents the relative centrifugal force (RCF) and ''r'' the radius from the center of the rotor to a point in the sample.<ref name="Ballou"/>

However, depending on the centrifuge model used, the respective angle of the rotor and the radius may vary, thus the formula gets modified. For example, the Sorvall #SS-34 rotor has a maximum radius of 10.8&nbsp;cm, so the formula becomes <math display="inline">RPM= 299\sqrt{g \over r}</math>, which can further simplify to <math display="inline">RPM = 91\sqrt{g}</math>.<ref name="Ballou">{{cite book|last1=Ballou|first1=David P.|last2=Benore|first2=Marilee|last3=Ninfa|first3=Alexander J.|title=Fundamental laboratory approaches for biochemistry and biotechnology|date=2008|publisher=Wiley|location=Hoboken, N.J.|isbn=9780470087664|pages=43|edition=2nd}}</ref>

When compared to gravity, the particle force is called the 'Relative Centrifugal Force' (RCF). It is the perpendicular force exerted on the contents of the rotor as a result of the rotation, always relative to the gravity of the Earth, which measures the strength of rotors of different types and sizes. For instance, the RCF of 1000 x g means that the centrifugal force is 1000 times stronger than the Earth's gravitational force. RCF is dependent on the speed of rotation in rpm and the distance of the particles from the center of rotation. The most common formula used for calculating RCF is:<ref name="Burtis">{{cite book |last1=Burtis |first1=Carl A. |last2=Ashwood |first2=Edward R. |last3=Bruns |first3=David E. |title=Tietz Textbook of Clinical Chemistry and Molecular Diagnostics - E-Book |date=14 October 2012 |publisher=Elsevier Health Sciences |isbn=978-1-4557-5942-2 |url=https://books.google.com/books?id=BBLRUI4aHhkC&pg=PA217 |language=en}}</ref>

<math>RCF = 1.118 \times 10^{-5} \times r \times (rpm)^2</math>,

where <math display="inline">1.118 \times 10^{-5}</math> is a constant; ''r'' is the radius, expressed in [[centimeters|centimetres]], between the axis of rotation and a point in the sample; and ''rpm'' is the speed in revolutions per minute.<ref name="Burtis"/>

Historically, many separations have been carried out at the speed of 3000 rpm; a rough guide to the ‘g’ force exerted at this speed is to multiply the centrifugation radius by a factor of 10, so a radius of 160&nbsp;mm gives approximately 1600 x g.<ref>{{cite web |title=NÜVE {{!}} Centrifugation Tips |url=https://www.nuve.com.tr/Useful-Tips/Centrifugation-Tips |website=www.nuve.com.tr |access-date=24 November 2020 |archive-date=11 July 2021 |archive-url=https://web.archive.org/web/20210711064124/https://www.nuve.com.tr/Useful-Tips/Centrifugation-Tips |url-status=dead }}</ref> This is a rather arbitrary approach, since the RCF applied is linearly dependent on the radius, so a 10% larger radius means that a 10% higher RCF is applied at the same speed. Roughly, the above formula can be simplified to <math display="inline">RCF = 10 \times r</math>, with an error of only 0.62%.