perfect strike on the head pin. However, if the
discussions, the functions overlap, and it is not
lane is on latitude 10N, the ball would invariably
accurate for you to consider them separately.
veer south. After a few thousand yards, the ball
would fall into the right-hand gutter if rolled east.
CENTRIPETAL CORRECTION. --Centripetal
It would fall into the left-hand gutter if rolled
errors are false accelerations sensed when the
west. In both cases, the ball would roll into the
platform is torqued to maintain its plane of
south gutter. The reason for this phenomenon is
reference. Centripetal correction differs from that
clear if you consider a lane built on a latitude in
of the Coriolis correction in that it has no
the Arctic only a few yards from the pole. Here,
relationship to earth dynamics. Even if the earth
the curve of the lane is obvious. It is apparent if
were stationary, it would still be necessary to
the ball accelerates due east; it will follow, in
insert centripetal correction voltages to the
inertial space, a straight course intersecting the
accelerometer signal. Correction voltages ensure
outside gutter. For the ball to roll at a uniform
an accurate plot of any course that does not
speed and remain in the alley, a uniform north
coincide with one of the earth's coordinate great
acceleration force must be exerted on the ball in
circle routes; that is, an exact polar or an exact
transit. In this case, the north acceleration force
equatorial orbit.On a great circle route, a route
is exerted on the ball during transit. Also,
that circles the earth's center, every linear
remember that north acceleration is a corrective
acceleration initiates motion. However, unless the
force and does not produce north velocity with
route is due north-south or directly along the
respect to the alley.
equator, the system can't plot the route accurately
As shown in figure 7-45, a north-south
from raw accelerometer signals.
accelerometer aboard an aircraft circling the pole
The orbit resulting from linear acceleration,
finds the same phenomenon. In a steep-banked
and the logic of applying centripetal corrections
turn, the centrifugal force deflects the north-south
to get an accurate plot of track, can be understood
accelerometer. It blindly reports a steady north
if you consider any simple circumstance involving
acceleration. The system will show a growing
a single acceleration and the inertial reaction. For
north velocity when, in fact, only an east velocity
example, assume a perfect bowling lane surrounds
exists.
the earth at the equator. Theoretically, a bowler
The fault is not in the accelerometers but in
could stand behind the pins and roll the ball in
the geographic coordinate system's nonlinear
the lane in the opposite direction (away from the
pattern to which the platform is slaved. The
pins). After a few years time, the bowler gets a
Figure 7-45.-Centripetal correction along latitude.
7-37
