Radius of Gyration

The measurements described below were made primarily in 1994 on a number of propellers. A large group of different propellers was assembled and weighed. From this group 21 propellers were chosen as representative of all diameters, shapes, and material in the larger group. A bifilar pendulum was constructed to measure the radius of gyration of each propeller.

The accuracy of each estimate was assessed as well as the error due to factors in the bifilar pendulum. From these measurements data were obtained that permit a fairly accurate estimate of gyro torques. This note presents the results of these measurements and discussed how the resulting data may be used to estimate gyro torques.

The propellers selected for measurement of radius of gyration had both 2 and 3 blades and ranged from 6 to 11 inches in diameter, A substantial amount of time was spent measuring the balance tray by itself because for small propellers it will add significantly to the inertia.

The results, shown on the graph below, show that the radius of gyration is approximated fairly well by 0.225 times the diameter. The single point that is furthest from this approximation was a Top Flight speed propeller with small blade width.

The moment of inertia, I of the propellers in terms of the mass, m and the radius of gyration r_g is:

     I = mr_g²

To keep the units consistent one would use grams and centimeters or slugs and feet.

An engineering paper providig an analysis of the pendulum and the equations equired to compute the radius of gyration can be downloaded in Adobe Acrobat "PDF" format.Bifilar Pendulum Paper