## Roasting Science

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# RS 4.11 Drum Diameter and the Froude Number

The drum speed that will cause beans to stick to the drum wall depends on the inner diameter of the drum. To understand why this is, think back to taking a ride on a Chair-O-Plane at the fairground. Such rides often have multiple rows of chairs attached to a spinning wheel by chains. When the wheel spins, the outermost row of chairs swings out farther than the inner rows because they experience stronger centrifugal forces than the inner rows do. In physics terms, this is because for a given drum speed (in rpm), the velocity at the outer edge of the wheel is greater than the velocity farther in.

Chair-O-Planes demonstrate the effect of diameter on centrifugal forces.

This is why, in general, roasters with larger drums are usually operated at slower drum speeds. Scott Rao, for example, suggests trying drum speeds of 52–56 rpm for a typical 12-kilogram roaster versus 46–50 rpm for a 30-kilogram roaster (Rao 2018). Note that Scott gives these as starting points for experimentation, not as absolute recommendations.

Since different-sized drums need different drum speeds, a more useful way to compare the drum speed of different roasters is the Froude number. The Froude number describes the ratio of centrifugal to gravitational force. When the Froude number is 1, the centrifugal force is equal to the force of gravity and beans will remain pressed to the drum wall through the entire rotation of the drum. As the Froude number decreases, the beans begin to fall from the drum wall earlier, progressing through the flow regimes described earlier.

The Froude number is given by

where ω is the drum speed (in radians per second), R is the drum’s inner radius (in metres) and g is the acceleration due to gravity (9.8 m/s2).

Converting rpm into radians per second and so on is a little cumbersome, so here’s a handy calculator app you can use to work out your own Froude number.