earth's radius is greater at the equator than it is
In view B, the pivot point is closer to the center
at the poles. For this reason the stable element
of gravity than in view A. However, it is farther
uses the process of Schuler tuning. Schuler
away than the one shown in view C, which pivots
tuning torques the platform to a position normal
at the center of gravity.
to the gravity vector by signals received from a
The pivot point of each pendulum in figure
7-42 is given the same acceleration. Therefore,
computing loop.
each pendulum has the same linear motion at its
Frame of Reference
pivot point. Yet, each pendulum has a different
angular motion. As distance d decreases, the
The frame of reference about which the INS
angular motion of the pendulum about the local
defines the instantaneous position of the aircraft
vertical (gravity vector) decreases and distance L
is the conventional latitude-longitude coordinate
increases. Distance L is the distance from pivot
system (fig. 7-43). The local vertical, established
point P to the center of oscillation, point O. Also,
and maintained by the inertial navigation system,
the pivot point and the center of gravity come
is the gravity vertical and is coincident with the
closer together, and equivalent length L of the
geographic vertical. The inertial navigation system
pendulum becomes longer. Figure 7-42, view C,
orients to the true north reference by sensing the
shows the pendulum pivoted at the center of
motion of the earth rotating on the polar axis.
gravity. In this case there is no angular motion
The frame of reference defined is horizontally
of the pendulum and the equivalent length L is
aligned in a plane parallel to the surface of the
infinite. Therefore, it is not a pendulum; it is a
earth and oriented to true north.
perfectly balanced mass that has an infinite period
of oscillation. Thus, it is possible to construct a
ESTABLISHING THE REFERENCE. --Refer
pendulum of infinite equivalent length and period.
to figures 7-36 and 7-43. By establishing the frame
It is also possible to construct one that has an
of reference, three perpendicular axes of the stable
equivalent length of 3,440 nautical miles. Such a
element will align to the horizontal coordinates
pendulum would be pivoted at some distance d
of the latitude-longitude navigational system.
from the center of gravity. This distance would
That is, the stable element z-axis aligns with
be greater than the one in figure 7-42, view C, but
the local vertical and the y-axis aligns north-
less than the one in 7-42, view B. When pivoted
south. Therefore, the z-axis is coincident with
at a point where the period of oscillation is found
to be 84.4 minutes, it becomes a Schuler
lines of longitude, and the x-axis aligns east-
west coincident with lines of latitude. In all
pendulum.
calculations, x-axis is positive east and y-axis is
The stable element is essentially a Schuler
positive north. The z-axis is positive away from
pendulum. However, it is not entirely mechanical
the center of the earth.
because the earth's radius varies with latitude. The
A pair of two-degree-of-freedom gyroscopes
establishes and maintains the stable element to the
frame of reference. Since a two-degree-of-freedom
gyroscope has two sensitive axes, it is necessary
to use two such gyroscopes (fig. 7-36). The
upper gyroscope z-axis is not in use. They
physically mount on the stable element so their
spin axes are exactly perpendicular in the
horizontal plane. With this arrangement, align-
ment of the upper gyroscope spin axis north-south
will automatically align the lower gyroscope spin
axis east-west.
The stable element containing the gyroscopes
is supported by the platform gimbal system. Thus,
the gyroscopes control the stable element.
However, if a free gyroscope initially orients so
the spin axis aligns east-west in a horizontal plane,
s
the gyro will precess. The precession will be about
the earth's surface because of the earth's rotation
on its polar axis. To maintain an earth reference,
Figure 7-43.-Frame of reference.