Centrifuge RPM to RCF Calculator, k-Factor and Pelleting Time

The calculation uses the conventional k-factor method described in Beckman Coulter’s Using k-Factor to Compare Rotor Efficiency (CENT-66APP07.14-B; attached collection pages 155–156), together with the sedimentation definition in the Thermo TH-660 manual, pp. 4-2–4-3 (attached pages 22–23).

For angular speed $\omega$ and radius $r$, $\mathrm{RCF}=\omega^2r/g_0$, with $g_0=9.80665\ \mathrm{m/s^2}$. RPM is converted explicitly to rad/s. The inverse calculation is $\omega=\sqrt{\mathrm{RCF}\,g_0/r}$. Fields are evaluated at the entered minimum and maximum radii and their arithmetic midpoint.

At constant speed, the sedimentation definition gives $dr/dt=s\omega^2r$. Integration yields

One Svedberg is $10^{-13}$ s. The conventional numerical k-factor is the clearing time in hours for a 1 S particle; therefore $t_{\mathrm{hours}}=k/s_{\mathrm{S}}$. The steps first calculate the SI clearing constant, then normalize it using one Svedberg and one hour. This avoids hidden RPM conversion constants.

For a dilute suspension of rigid spheres, buoyant centrifugal force balanced by Stokes drag gives $s=d^2(\rho_p-\rho_m)/(18\mu)$. This is the spherical specialization of the sedimentation/friction relation $s=m_b/f$, with buoyant mass $m_b$ and $f=3\pi\mu d$; it is consistent with Rikkert et al., Eq. 2 (DOI: 10.1002/cyto.a.23641). The outer-radius particle Reynolds number is checked for both operating rotors and every speed-sweep point against a conservative creeping-flow threshold of 0.1. In sphere mode the clearing-time chart omits points above this threshold and reports the cutoff. The centrifugal-field chart remains valid because its kinematics do not depend on particle drag.

For identical particles and medium, equal sedimentation exposure requires $t_2=t_1k_2/k_1$. Both factors use the actual speeds, radii, tubes and fill volumes. Matching maximum RCF alone does not match clearing times. The independently entered protocol time need not equal the ideal particle clearing time.

• Constant operating speed; no acceleration or deceleration exposure is credited.
• A homogeneous Newtonian liquid and a positive, constant sedimentation coefficient at the actual run temperature and medium composition.
• The sphere option assumes rigid, noninteracting spheres in a dilute suspension, negligible wall drag and creeping flow. Diameter is the hydrodynamic diameter.
• The maximum sample radius exceeds the meniscus radius. The reported average radius is the arithmetic midpoint, not a volume average.
• The ideal clearing endpoint is travel from the meniscus to the maximum radius. In fixed-angle tubes, particles first hit the outer wall; later wall sliding and compaction are outside this model.
• The default radii and speed limits are illustrative, not specifications for a named rotor.
• The drawing exaggerates particles and tube proportions. It illustrates radial migration in the rotating frame, not rotor spin or predicted recovery.
• Terrestrial gravity is not included in the radial-settling equations. A separate warning identifies either rotor whose meniscus RCF is below 10 × g.

Use for estimating differential pelleting in homogeneous media and comparing rotor operating conditions. A measured coefficient is preferable for biological particles and nonspherical, porous or aggregating material. A coefficient reported as $s_{20,w}$ must be corrected before applying it to another medium or temperature. Density and viscosity inputs are properties at the actual run temperature; the tool does not estimate them.

The model omits Brownian broadening, hindered settling, density gradients, isopycnic equilibrium, pellet resuspension and recovery or purity. Short predicted runs require particular attention to acceleration and braking. Geometry-based k-factors can differ from manufacturer factors because of actual tube shape and fill volume; check the correct rotor and tube documentation.

Never exceed the rotor’s rated speed. Enter the lowest permissible centrifuge, rotor, bucket, tube and adapter limit, including manufacturer derating for density, temperature, age and condition. The calculator checks entered limits; it does not establish them.

Source discrepancy: the TH-660 manual’s worked example on attached page 23 prints 3.63 hours for 44.4/40. The correct quotient is 1.11 hours. Its radii also differ between the specification table and the later drawing; the reference case explicitly uses Table 1-1’s 64.6 mm and 121.5 mm. The calculation retains the physics rather than reproducing the printed arithmetic error.

In sphere mode, gaps in the clearing-time curve mean its Stokes-predicted particle Reynolds number exceeds 0.1. Use the displayed lower-speed range or a drag model valid at larger Reynolds numbers; a valid operating point does not validate the entire sweep. Low-field warnings identify the affected rotor and apply to its settling and protocol-transfer estimates.