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    Re: Coriolis and gyros (second attempt)(typos corrected)
    From: Gary LaPook
    Date: 2009 Aug 23, 16:10 +0200
    I am attaching an excerpt from AFPAM 11-216, Air Navigation, which may help explain the behavior of gyros and the Foucault Pendulum. These both exhibit the "apparent precession" due to "earth rate" which make them appear to change direction at a rate of 15.04º per hour times the sine of the latitude. The Foucault Pendulum, hanging in the Pantheon in Paris, is located at 48º 50' 47" north latitude, the sine of which is  .7529 multiplied by 15.04º per hour  produces a rate of apparent precession of the pendulum of 11.32º per hour. The information plaque near the pendulum states that it changes 11º per hour, obviously rounded to the nearest whole degree for the tourists. Coriolis is not involved since the Pantheon has not moved across the surface of the earth since its foundations were laid in 1758 so its ground speed is zero.


    Section 14D— Gyro Precession

    14.13. Basics. To eliminate the difficulties imposed by magnetic compass unreliability in polar areas,
    you disregard the magnetic compass in favor of a free-running gyro. Gyro steering is used because it is
    stable and independent of magnetic influence. When used as a steering instrument, the gyro is restricted
    so its spin axis always remains horizontal to the surface of the earth and is free to turn only in this
    horizontal plane. Any movement of a gyro spin axis from its initial horizontal alignment is called
    precession. The two types of precession are real and apparent, with apparent broken into earth rate,
    transport, and grid transport precession. Total precession is the cumulative effect of real and apparent

    14.14. Real Precession. Real precession, illustrated in Figure 14.9, is the actual movement of a gyro
    spin axis from its initial alignment in space. It is caused by such imperfections as power fluctuation,
    imbalance of the gyro, friction in gyro gimbal bearings, and acceleration forces. As a result of the
    improved quality of equipment now being used, real precession is considered to be negligible. Some
    compass systems have a real precession rate of less than 1o per hour. Electrical or mechanical forces are
    intentionally applied by erection or compensation devices to align the gyro spin axis in relation to the
    earth's surface. In this manner, the effects of apparent precession are eliminated and the gyro can then be
    used as a reliable reference.

    304 AFPAM11-216 1 MARCH 2001

    Figure 14.9. Real Precession.

    14.15. Apparent Precession. The spin axis of a gyro remains aligned with a fixed point in space, while
    your plane of reference changes, making it appear that the spin axis has moved. Apparent precession is
    this apparent movement of the gyro spin axis from its initial alignment.

    14.15.1. Earth Rate Precession. Earth rate precession is caused by the rotation of the earth while the
    spin axis of the gyro remains aligned with a fixed point in space. Earth rate precession is divided into
    two components. The tendency of the spin axis to tilt up or down from the horizontal plane of the
    observer is called the vertical component. The tendency of the spin axis to drift around laterally; that is,
    to change in azimuth, is called the horizontal component. Generally, when earth rate is mentioned, it is
    the horizontal component which is referred to, since the vertical component is of little concern.
    14.15.2. Figure 14.10. A gyro located at the North Pole, with its spin axis initially aligned with a
    meridian, appears to turn 15.04o per hour in the horizontal plane because the earth turns 15.04o per hour.
    As shown in A of Figure 14.10, the apparent relationship between the Greenwich meridian and the gyro
    spin axis will change by 90o in 6 hours, though the spin axis is still oriented to the same point in space.
    Thus, apparent precession at the pole equals the rate of earth rotation. At the equator, as shown in B of
    Figure 14.10, no earth rate precession occurs in the horizontal plane if the gyro spin axis is still aligned
    with a meridian and is parallel to the earth's spin axis.

    14.15.3. Vertical Component. When the gyro spin axis is turned perpendicular to the meridian (Figure
    14.11), maximum earth rate precession occurs in the vertical component. But the directional gyro does
    not precess vertically because of the internal restriction of the gyro movement in any but the horizontal
    plane. Thus, for practical purposes, earth rate precession is only that precession which occurs in the
    horizontal plane. Figure 14.11 illustrates earth rate precession at the equator for 6 hours of time.

    14.15.4. Precession Variation. Earth rate precession varies between 15.04o/hr at the poles and 0o/hr at
    the equator. It is computed for any latitude by multiplying 15.04o times the sine of the latitude. For
    example, at 30o N, the sine of latitude is 0.5. The horizontal component of earth rate is, therefore,
    15o/hour right x 0.5 or 7.5o/hour right at 30o N as shown in Figure 14.12.

    AFPAM11-216 1 MARCH 2001 305

    Figure 14.10. Initial Location of Gyro Affects Earth Rate Precession.

    306 AFPAM11-216 1 MARCH 2001

    Figure 14.11. Direction of Spin Axis Affects Earth Rate Precession.

    Figure 14.12. Earth Precession Varies According to Latitude.





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