(Reproduced from "Zero to Eighty" pp.294-297 by EF Northrup)

Let us suppose that we have a projectile held stationary in
a series of coils (as shown in figure 7, page 309) and acted
upon by a travelling magnetic field. We shall now
consider the important question: under stated conditions,
with what force, i.e., with what thrust, will the magnetic field
strive to move the projectile in the direction in which it travels? A
purely mathematical solution is theoretically possible but very
complicated. We shall, therefore, resort to properly devised tests by
which we may determine the value of the so-called thrust constant.
When this constant is experimentally determined for a combination
of coils and a projectile of one size under particular conditions, the
above question becomes comparatively easy to answer for other
dimensions and conditions. Several careful tests have been made
and the thrust constant, K, has been experimentally determined
with a fair precision. In all cases the magnitude of the total thrust
is a function of several variables which the designer has power to
control.

In what follows it is assumed that no magnetic material is used
in the construction of the coils or the projectile.

* * * * *

The starting point for most investigations into electromagnetism
and electromagnetic induction is the ampere turn. The terms
ampere turns or ampere turns per centimeter are convenient ways
of expressing magnetizing force in easily determined and
recognized units. The total magnetizing force, in ampere turns, of
a coil or helix of wire is simply the product of the number of
physically parallel and adjacent
conductors and the current in
amperes flowing in each conductor. For convenience, it is assumed
that the parallel conductors of the helix are one continuous spirally
wound conductor, and that the same quantity of electricity flows
through the conductor from end to end.

It can be shown that the intensity of the magnetizing force in a
closely wound helix is a function of the number of ampere turns per
centimeter of winding length of the helix. Since the expressions for
fundamental units of magnetic force and magnetic intensity
contain terms involving mechanical force, we find that under
certain conditions an ampere turn is capable of producing a certain
mechanical force.

One such condition is that above stated, namely, a conducting
cylinder held stationary in a series of coils carrying high-frequency
polyphase currents.

The experimental procedure for getting the data for calculating
a thrust constant is as follows: Given a certain set of coils and a
cylinder, the thrust in grams on the cylinder, with a certain number
of amperes flowing in each phase, is taken for a number of different
frequencies. If a sufficient number of frequencies are tried it will be
found that one particular frequency gives the highest value of thrust
in proportion to the value of the polyphase current. This peak value
of thrust is used to calculate the peak thrust constant for the type
of polyphase coil used. Other sets of polyphase coils having
different proportions among the factors of coil length, coil spacing,
size of conducting cylinders, etc., would require the same
experimental treatment to find the peak value of thrust.

Having determined the peak value of thrust for the different
sets of coils and cylinders, we first define the thrust constant as the
force in grams which one ampere turn per centimeter of polyphase
current dll impart to one square centimeter of active surface on the
cylinder.
Secondly, the thrust constant as defined is calculated by the
following formula:

where K is the thrust constant in grams per square centimeter of
active cylinder surface, T the total measured thrust in grams on the
cylinder, (in) the average ampere turns per centimeter length of
complete polyphase coil, and A the active area in square
centimeters of the cylinder, i.e., the product of the circumference
of the cylinder and the length covered by the polyphase coil.

Having found the thrust constant, K, for a particularly
proportioned test, we can arrange equation (15) to find any one of the
factors when the others are known or selected. For instance, a
certain type of polyphase coil gave a peak thrust constant of
approximately 13 x 10^{-6} grams. The active area of the test cylinder
was about 4000 square centimeters. What value of ampere turns
per centimeter length would impart a total thrust of one kilogram
to the cylinder?

If the coil winding averaged one turn per centimeter, the polyphase
current per phase would be 139 amperes.

The variable over which the designer has the most control is the
number of ampere turns on the coil. Certain features of practical
construction limit the actual number of conductors on a coil, but
the value of the current in these conductors can be varied over wide
limits. The limiting factors are voltage breakdown and heating, the
effects of which can be greatly modified by suitable choice of
materials and construction.

It may be said that, given a polyphase coil and cylinder, there
is at least a theoretical value of current which will produce any
desired thrust. This last statement has an important bearing other
than its bearing on the question of theoretically producing
unlimited thrust. It has been stated above that with a particular
polyphase coil and cylinder only one frequency will produce the
peak value of the thrust constant. (This assumes that no magnetic
materials were used in the construction of coil or cylinder.) Thus,
under normal conditions — with a projectile in motion under the
influence of a polyphase magnetic field — the thrust constant departs from its maximum value,
and hence an increased value of
current or ampere turns is necessary to produce the desired thrust.

There is no simple accurate formula which will give the thrust
constant for a given set-up at any other than the optimum
frequency. Were the factors of resistance and reactance of the
various current paths simple proportionate quantities, a formula
could be set up. However, alternating current phenomena are
mathematically very complex, and in this case do not lend
themselves to any simple treatment. For design purposes, it is
therefore best to determine experimentally the curve which the
thrust constant takes under varying frequency. Enough
experimental work has been done along this line to fix a number of
points for extrapolating a reasonable curve.