Calculating Gravitational Acceleration

Calculation of Gravitational Acceleration on a Centrifuge

            To calculate the gravitational acceleration experienced by specimens on a centrifuge, you must know a little algebra and trigonometry. There is a formula for determining how much gravity is experienced due to the rotation of a centrifuge (centripetal acceleration). The centripetal acceleration is the outward force on any organism or object rotating around the centrifuge. It is centripetal force that causes cars to skid around corners and people to fall off merry-go-rounds if they let go. For the centrifuge, it depends on the rotation speed of the wheel and the distance from the center of the wheel to the object or organism.

            The formula you can use to calculate centripetal acceleration is:

            a          is the centripetal acceleration in meters per second squared (m^.s^-2)

            p          is Pi = 3.14159

            r          is the distance from the center of the wheel to the organism in meters (m)

            T         is the period of rotation, which is the number of seconds per rotation (s)

Figure 1: Adding Centripetal and Gravitational Acceleration

           This is the acceleration the organism "feels" due to spinning on the wheel. The centripetal acceleration is perpendicular to gravity (horizontal). So, while the organism sits on the rotating centrifuge, it feels the normal downward acceleration due to gravity plus the outward centripetal acceleration. The downward acceleration due to gravity (g) is a constant 9.81 m.s-2. The centripetal acceleration (a) is horizontal, pointing outward away from the center of the turntable. The magnitude and direction of the two put together is the total gravitational acceleration (A) the organism "feels." This is related through geometry using the Pythagorean Theorem. The two accelerations, a and g, make the sides of a triangle. The total acceleration, A, is represented by the hypotenuse of the triangle (See Figure 1)

            Total acceleration on the centrifuge is calculated using the Pythagorean Theorem, which relates the three sides of the triangle:

            A         is the total gravitational acceleration in meters per second squared (m^.s^-2)

            g          is the acceleration due to gravity = 9.81 m^.s^-2

            a          is the centripetal acceleration in m^.s^-2

           For example, if the distance from the center of rotation is 25 inches (this is the exact distance from the center of rotation to the center of the object or organism) and the wheel is spinning at 45 revolutions per minute (rpm), let’s calculate the g force felt by the organism. Converting the radius to meters and the period to seconds we have:

            r = 25 inches x 0.0254 meters/inch = 0.635 meters

            T = 60 seconds per minute / 45 rpm = 1.33 seconds per rotation

Now, substituting into equation 1:

Substituting into equation 2:

Dividing by the normal Earthly gravitational acceleration: 9.81 m.s-2 yields the total gravitational “force” felt by the organism: