A Trifilar Pendulum for the Determination Moments of Inertia

Abstract

A unique trifilar pendulum was constructed at Frankford Arsenal which proved to be an accurate tool for the determination of momen':s of inertia of non-homogeneous objects.The pendulum was used with a calibration curve. The curve was generated by plotting a quantity calculated from the weight and the period squared of a number of homogeneous solids of revolution of increasing size as ordinates, against the calculated (using handbook formulae) moments of inertia of these solids as abscissae.The moment of inertia of an unknown was obtained by weighing the object, establishing its period on the pendulum, locating a quantity calcu]ated from its period squared and its weight as an ordinate on the calibration curve, and finding the moment of inertia as the corresponding abscissa.There are specialized techniques used in operating the pendulum and some unique features in its design for which patents have been applied. The need for such unique features is established, and error analysis shows this trifilar pendulum accurate to 0. 5%.It is concluded that the trif;1ar penLdulum, if properly constructed, has certain advantages over the torsion rod pendulum with no more disadvantages.iii

A study on the mechanism of reaction between refractory materials and aluminium deoxidised molten steel

“…At 1873 K a value of KMgO = 1.99.10-6 is calculated. According to table 2 the partial pressure of magnesium at the refractory interface should be 0.0091 MPa at 1873 K which together with the relation (15) gives a dissolved magnesium content of 28.2·10-4%, that corresponds to a dissolved oxygen of 7·10-4%.…”

Quantifying avian inertial properties using calibrated computed tomography

“…The MoI of the pendulum, I p , was estimated assuming it behaved as a horizontal, single degree of freedom dynamic system with negligible thread mass (1 mm steel cables did not yield accurate results), rotating about its CoM through small angles such that: where m is the mass of the pendulum, g is gravitational acceleration, R is the distance between the threads and the centre of rotation, τ is the period of oscillation and L is the mean length of the threads ( Korr and Hyer, 1962 ). The difference between the pendulum MoI with and without the bird provided an estimate of the bird's MoI about the axis of rotation (without correction for potential misalignment between the bird's CoM and the pendulum CoM).…”

“…where m is the mass of the pendulum, g is gravitational acceleration, R is the distance between the threads and the centre of rotation, τ is the period of oscillation and L is the mean length of the threads (Korr and Hyer, 1962). The difference between the pendulum MoI with and without the bird provided an estimate of the bird's MoI about the axis of rotation (without correction for potential misalignment between the bird's CoM and the pendulum CoM).…”

Methods for accurate measurements of small fixed wing UAV inertial properties

“…These will oscillate freely under the influence of gravity alone, once displaced from rest and released. Pendulum designs have been used with a single suspension wire as the simplest method or using multiple suspension wires to create either a translational or torsional pendulum (5,6) . The latter is more suitable for aircraft applications, because a multi-wire pendulum will hold the test article in a defined attitude.…”