TEAM Workshop Problem No. 17
The Jumping Ring
Introduction
This is a bench mark with a difference. Hitherto, the custom has been for
a bench mark to be presented as a set of experimental results, together with
all details to enable calculation to be made by others. Here, we propose a
rather different approach, by describing a simple experimental rig, which
others can build and test. There is a further difference, in that what is
proposed is a set of tests, based on a basic kit of parts. The inspiration
derives from the experiment described by Laithwaite called the "jumping
ring". That experiment can be regarded as the ultimate goal of this bench
mark, in that it requires the solution of a coupled mechanically dynamic
eddy current problem. The set of tests starts with a simple axisymmetric,
linear, magnetostatic problem, and then moves through problems of increasing
levels of difficulty, taking in: magnetic non-linearity; two dimensional
eddy currents, static: three-dimensional eddy currents, static; then finally
two- and three-dimensional eddy currents with transient dynamic
conditions.
The quantities to be measured and calculated include: induced voltages,
inductance self and mutual, impedance self and mutual, forces of attraction
and repulsion abd power flow. These can be in both two and three-dimensions.
Some of the quantities can be determinated analytically. This input would be
most welcome.
The advantages of such an approach are seen as follows:
- The tests are of progressive levels of difficulty, so that
researchers at all levels can contribute and thereby gain experience and
confidence.
- The experimental conditions are completely under the control of those
predicting the results. The experiments, for the static tests, require
only very basic instruments
- The very fact that a number of groups are measuring results on a
variety of rings to the same design, will give useful information on the
statistical spread.
Finally, it should not be overlooked, than most TEAM bench marks so far,
have been of more interest to the physics community rather than the
engineering community. This is an attempt to redress the balance.
The kit of parts
The basic rig compries an exciting coil plus a set of inner cores, various
plates, and conducting rings. This is shown schematically in Fig. 1.

Figure 1. The Basic Jumping Ring Layout.
The Main Coil
The coil was specified 500 turns of a pair of 15 SWG (1.8 mm diameter)
enamelled conductors, wound closely in a parallel. The inner radius was 40
mm, the outer radius was 77.5 mm. This last is a function of the skill of
the winder. The axial length was 100 mm. The coil was wound on a wooden
former, between two side pieces of wood, thickness 12.5 mm. Those side
pieces had a 50+ mm dia hole to take a 50 mm dia plastic pipe, of lenght 434
mm. This was a sliding fit, since the inner core within the pipe to be
removable. The plastic pipe, could contain: air or laminated iron. The two
coils are brought out to two separate pairs of terminals. In most of the
tests, one coil was used to excite the device and the second was to measure
secondary parameters.
The Search Coil
This is wound on a 200 mm dia wooden former, thickness 50 mm. It has 50
turns, of 28 SWG enamelled wire. The coil length is 12 mm axially.
The Inner Core
For the statics experiments, the inner core, within the pipe, is air of
laminated iron. For eddy current experiments, it is proposed that the coe
should be a 25 mm bar, length 150 mm. The core materials of interest are:
solid iron; cooper; and pure aluminium. The small diameter allows for the
fitting of search coils to the bar.
The Plates
For some of the eddy current experiments, a 12 mm pure aluminium plate was
used. This should be of the order 1000 mm square. A refiniment is to cut a
300 mm square from one corner of the plate, to produce a further variation
on the eddy current problem. In addition, a 1000 mm square, 12 mm thick,
iron plate is useful.
The "Jumping Ring"
The original device, as proposed by Lathwaite, [1], had a variety of
rings. By the sudden application of an ac supply, the force on the ring
could produce high levels of acceleration. This aspect should always be
borne in mind from the point of view of safety. The rings used so far were
made out of aluminium alloy and are detailed below.
The Initial Set of Experiments
1. Coil in Air
This is very basic, it serves as a usefull check. The coil has 500 turns,
inner radius 40 mm, outer radius 77.5 mm, length 100 mm. The measured value
of impedance, at 50 Hz, was 5.3 ohms. Voltage, current and power
measurements were made on the main coil. These measurements gave the
following results:
Terminal resistance = 1.29 ohms ± 0.02 ohms
Terminal reactance = 5.15 ohms ± 0.12 ohms
Input impedance = 5.3 ohms.
This is an axisymmetric magnetostatic problem. Measure voltage induced in
the search coil versus vertical distance between the inner edges of the main
and search coils. Determine the mutual inductance as the a function of
distance. Also determine the equivalent circuit parameters. This test also
serves as a useful bench mark for open boundary calculation techniques, [2].
2. Coil with Laminated Iron Core
With the central core vertical, the coil edge is 12 mm above the end of
the iron. The measurements gave the following results:
Terminal resistance = 2.48 ohms ± 0.32 ohms
Terminal reactance = 20.2 ohms ± 0.3 ohms
Input impedance = 20.35 ohms.
This is an axisymmetric magnetostatic problem. Repeat the measurements of
induced search coil voltage.
3. Coil above Large Conducting Plate
The coil was positioned 12.5 mm above the center of the large aluminium
plate, i.e. it was placed directly on the plate so that the wooden end plate
touched the aluminium. The applied voltage, current and input power were
measured at 50 Hz. The measurements gave the following results:
Terminal resistance = 1.53 ohms ± 0.03 ohms
Terminal reactance = 4.48 ohms ± 0.15 ohms
Input impedance = 4.73 ohms.
The power into the plate was measured directly by measuring the "shadow"
coil technique described in [3]. This is an axisymmetric eddy current
problem.
4. Coil with Iron Core and One Ring
Plot the height of the ring above the upper edge of the coil against
current input. This test has to be done quickly to avoid problems with the
rise of temperature of the ring. This is an axisymmetric eddy current
problem.
A ring with the following dimensions was used:
With the bottom of the ring 12.5 mm above the coil, i.e. resting on the
wooden end plate, the following measurements were obtained:
Terminal resistance = 4.87 ohms ± 0.19 ohms
Terminal reactance = 12.04 ohms ± 0.22 ohms
Ring resistance (from shadow coil) = 3.82 ohms ± 0.21 ohms
Ring reactance (from shadow coil) = 12.15 ohms ± 0.24 ohms.
Results in other positions are available from the authors. A complete set
of curves of values against position will be available shortly.
5. Coil with Conducting Inner Core
Measure the impedance and power flow into a conducting bar inside the
coil. Determine the complex mutual impedance between the main coil and a
search coil around the round bar. This is an axusymmetric eddy current
problem, [4].
6a. Coil with the core above Edge of Plate
This is now a three-dimensional eddy current problem. The measurements
were:
Terminal resistance = 3.59 ohms ± 0.18 ohms
Terminal inductance = 18.46 ohms ± 0.25 ohms
Plate resistance (shadow coil) = 2.35 ohms ± 0.09 ohms
Plate reactance (shadow coil) = 18.76 ohms ± 0.06 ohms.
6b. Coil above a Corner of the Plate
Again 3-D. The measurements were:
Terminal resistance = 3.10 ohms ± 0.11 ohms
Terminal reactance = 19.4 ohms ± 0.1 ohms
Plate resistance (shadow coil) = 1.94 ohms ± 0.06 ohms
Plate reactance (shadow coil) = 19.75 ohms ± 0.15 ohms.
6c. Coil above an Inner Corner
Again 3-D. The measurements were:
Terminal resistance = 3.14 ohms ± 0.07 ohms
Terminal reactance = 19.03 ohms ± 0.34 ohms
Plate resistance (shadow coil) = 1.94 ohms ± 0.02 ohms
Plate reactance (shadow coil) = 19.32 ohms ± 0.19 ohms.
7. Coil axis Parallel to Plate
This is more difficult 3-D problem related to shielding losses in
transformers. The coil axis is 200 mm above the plate.
Further Tests
The above are simply an introductory set, to form the basis of discussion
to establish a full working set. Further tests could include: a second main
coil to form an air-cored transformer; upward attraction force to an iron
plate; transient dynamic tests on a conducting ring, this will require
advance data acquisition techniques; and rates of temperature rise.
Variation of values with frequency would be very interesting, since that
opens up the possibility of trying out low and high frequency
approximations. These impedance variations can be plotted as complex
frequency impedance or admitance.
The above is hardly an exhaustive list, but it will serve to start the
bench mark. It should not be overlooked that the tests described could form
the basis of projects for a CAD magnetics course. Indeed, the tests 1 to 5
appear in [5] as standerd problems for CAD magnetics students. The authors
would welcome feedback, by post, phone, fax or email.
Reference
- Laithwaite, E. R., "Propulsion without wheels", London:
English Universities Press, 1966.
- Freeman, E. M. and Lowther, D. A., "An open boundary technique for
axisymmetric and three dimensional magnetic and electric field
problems", IEEE Trans. Mag. V25, 1989, pp. 4135-4137.
- Freeman, E. M., Lowther, D. A., and Laithwaite, E. R., "Scale
model linear induction motors", Proc. IEE, 122, 7, (1975),
pp. 721-726.
- Freeman, E. M. and Bland, T. G., "Equivalent circuit of concentric
cylindrical conductors in an axial alternating magnetic fiels", Ibid,
123, 2, (1976), pp. 149-152.
- Freeman, E. M., "The MagNet User Guide", published by
Infolytica Corp. Montreal, Canada, 1992.