# POLHODE – A NEW WORD

If an ESG ball were made without the Tantalum inclusions and such a ball was spun up to the normal rotor speed and the ball was maintained at the normal operating temperature, the spinning ball would be round and homogeneous. It would show no evidence of a MUM signal as the surface of the rotating ball would be running “true”.( To use a word taken from the machinist’s lexicon.) The ball would be symmetric around any axis of the ball; the moments of inertia, measured around any axis of the spinning ball ball, would be the same. It would be a very uninteresting spinning ball. If, on the other hand, the Tantalum inclusions were magically inserted into the spinning ball such that the ball spins around what is now the axis of the greatest of the ball’s moments of inertia, and the other conditions under which it is spinning were the same, the surface of the spinning ball would be found to be”running out” by 40 microinches (if my memory is correct) when measured in the plane normal to the spin axis of the ball. If an observer had the patience to monitor the spinning ball for a long time, he, or she, would find the ball appeared to not move relative to an inertial frame of reference. In particular, the “run out” of the surface of the ball would remain at 40 microinches. The observer would be justified in concluding the spinning ball’s position in inertial space is stable, ie, not changing with time. Now spin the ball down until it has stopped spinning. Go to lunch and relax.

After lunch, spin the ball up to the normal speed and bring the temperature of the ball up to the normal temperature. As before, measure the runout of the ball’s surface in the plane normal to the spin axis of the ball. To the great consternation of the observer, the”run out” is less than 40 microinches and, worse, it is slowly changing with time. As time goes on, the observer finds that the runout is slowly increasing and after more time realizes the “runout” has moved up to 40 microinches and is no longer changing. Just to be  sure, the observer waits for more time to pass and, finally, concludes the ball is back to normal, ie, spinning as before the spin down of the ball.

The observer concludes that a pretty fair gyroscope can be made using the asymmetric spinning ball, if some way can be found to shorten up the time it takes the ball to come a stable equilibrium condition. The time to reach this equilibrium “naturally” is not acceptable for any practical navigation system. After some time spent reviewing the relevant theories of the rotation of asymmetric balls, the observer concludes that the observed behavior of the spinning ball can be attributed to these factors:

1.) The asymmetric ball described above has three moments of inertia, each greater in magnitude than the one before it. The three moments of inertia of lie on mutually orthogonal axes. (inertia means “resistance to change”)

2.) The ball, when spinning such that the spin axis lies along the axis of the maximum moment of inertia, is in a stable spin state that will not change over time.

3.) The ball, when spun up to the normal speed, will not, in general, be spinning such that the spin axis lies along the axis of the greatest moment of inertia. It is spinning in an unstable state. Over time the position of the ball will drift toward the stable condition described in 2.).

4.) The path, or motion, of the ball above is called the polhode.

What is needed is an “artificial” scheme to cause the drift of the ball toward the stable position to happen in a much shorter time. This in effect requires that information within the ball “run out” signal must be decoded to determine the magnitude of the difference between where the ball is now and where the ball should be when it is stable, ie, where are we relative to where we want to go. To achieve this, a solid theoretical understanding of the polhodes must be gained and the means by which to move to ball with respect to the spin axis, without moving the spin axis in inertial space, must be developed. The scheme must differentiate between the two possible final orientations of the spin axis with respect to the axis of maximum moment of inertia to enable the control of the polarity of the mass unbalance along the spin axis.

I hope the reader of this has gained a feeling for the process known as “polhode damping”. The process is required to be performed each and every time an ESG rotor is spun up prior to use as a gyroscope. The time allowed to perform polhode damping ranges from “take all the time you need” for test equipment to the astounding 45 second requirement of the N73 system. (the N73 average time was 22 seconds.). I had to learn how to perform polhode damping on test ESGs by what is called “the manual method”. It required the use of old fashioned knobs to control the motor voltage and the recognition of the polhode you were moving on using MUM signals displayed on Bristol Chart Recorders. I was hopelessly lost in the beginning, but with the patient help of Gerry Hardesty, I finally developed a knack for the process.

The development of the N73 polhode damping software was done by Dr. John Wauer. I was very impressed with the software. John was never able to find simple enough explanations of how the software did its thing in such a way as to bring me to a high level of understanding. To this day I still wonder how the motor used for rotor spinup was used to move the rotor without any effect on the rotor spin axis. It must be magic!

I do not recall much discussion on the part of laboratory people about polhode damping and I attribute that to the complex nature of the process. It was not possible to concoct short and sweet answers to questions about polhode damping. As a group, the engineers and technicians of the test laboratories were very proficient in carrying out their assigned tasks and I was, and still am, proud to be counted with them. The labs I worked in all have been leveled but we all have lasting memories of the work we did – at least those of us that are still alive still have memories of those times – when “cost plus” reigned.