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

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

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,

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