Measuring the Vertical Displacements of the Centre of Gravity of a Levitated Superconducting Body

Abstract

Directly comparing the "mechanical" with the "electrical" joule by the levitated mass method implies accurately measuring the vertical displacement of the centre of gravity of a levitated superconducting body. The required accuracy of some parts in 109 over relatively small displacements of a few millimetres when the stability of a standard mass is to be monitored, and the special conditions under which the measurements must be made, pose a number of specific problems. The principles of the D. I. Mendeleyev Institute for Metrology measurements system are discussed. Estimates of the potential of the system, based upon some preliminary results, are presented.

A proposed superconducting magnetic levitation system intended to monitor stability of the unit of mass

“…The effect of linearization depends on the distance between the main and additional coils, and as sets a bound to the space available for levitation a reasonable compromise has to be found. A good result for ␦ , both in the constant-current and constant-magnetic-flux modes, is obtained taking 0,37 1,15: in this case ␦ deviates from zero, as has been calculated with (3), by no more than 10 -2 in the segment from 0,07 to the virtual ceiling. Let us take this element with the two coils as the basis for further discussion and accept the isochronic segment with upper boundary chosen at the point where 0,08 (it is marked in Figure 6 by the solid vertical line) as the working interval of levitated body displacement.…”

“…In a superconducting magnetic levitation system, some of the mechanical energy to be compared is realized as the centre of gravity of the levitated body is made to overcome a gravitational potential difference [1,2]. The main problem in measuring this potential drop precisely, as experience shows, is associated with change of the orientation of the body in its levitation mode [3]. This change in turn is governed by the design of the electromechanical prototype systems.…”

Mass determination with the magnetic levitation method—proposal for a new design of electromechanical system

“…Also a minimum value of the displacement z = z h − z l exists, since the relative uncertainty of displacement measurement should be equal to or better than several parts in 10 8 . Therefore, in practice the required movement of the levitated body should be at least 5 mm [22].…”

Measuring the gravitational acceleration using a superconducting magnetic levitation system

“…The particular problems of measuring the vertical displacements of the centre of gravity of a levitated mass in a superconducting system are described in detail in [12]. In the same paper, estimates of the main contributions to the measurement uncertainty show that, for a system of conical shape, a total relative uncertainty of 1 part in 10 9 over a displacement of a few millimetres is perfectly attainable.…”

“…Then the equation of oscillations for the levitated body becomes isomorphic to that for a simple pendulum of length . The natural, angular frequency of free small-amplitude oscillations, , is thus given by (11) and hence (12) which is the required result. This allows the gravitational acceleration to be determined in terms of (i) the frequency of free small-amplitude oscillations about an arbitrary preset position, and (ii) the effective length of a simple pendulum, which in turn can be found from measurements of the parameters which describe the system configuration.…”