(184) 
erection must be greater than the arbitrary free drift in order to maintain 
positive control of the gyro. If such a pendulously erected gyro is subjected to 
flight conditions, then the pendulum will instantaneously assume the direction 
of the apparent vertical. The apparent vertical is the resultant of gravity and 
any other acceleration caused by the status of flying. Our investigations show 
that accelerations are continuously present during flight. If they were only of 
short periodical nature, integrating to zero, one can easily see that, through 
the slow rate of erection, they could not possibly deflect the gyro an applicable 
amount from the true vertical. But unfortunately there are always some long- 
periodical or non-periodical components of acceleration superimposed. They 
prevent the simple horizon gyro from being used for indicating the vertical 
with static precision under dynamic conditions. 
According to our findings, the first order disturbances of the vertical in 
flight can be safely determined as centripetal accelerations about the longitu 
dinal axis and as fluctuations of speed about the transverse axis of the aircraft. 
Let us assume that an aircraft is just slightly out of trim, which it always 
is. Then according to its own stability, it will tend to perform a turn of a very 
large radius. This turn cannot be detected by the pilot or auto-pilot until it 
has integrated to a change of direction indicated by the control instruments. If 
we assume the rate of change of direction of the aircraft to be l°/min and if 
we assume the accuracy of directional indication to be one half degree, then it 
will take 30 seconds of time until reaction on this very slow turn can be expect 
ed. After the change of direction has been detected we can expect that, by a 
sudden control action, our accumulated error is over-compensated and the 
same procedure is repeated, possibly for a longer period of time, This amounts 
practically to a very slow but continuous turn, periodically interrupted by a 
resetting procedure. The question is: What does such a slow turn do to our 
gyro indication? If we assume the speed of the aircraft to be 600 knots, just 
below Mach No. 1, the radius of such turn is approximately 600 nautical miles, 
and yet, surprisingly enough, it produces a deflection of the apparent vertical 
from true vertical of 30' of arc. At the erection rate of T per sec the gyro will 
need just thirty seconds to assume the full deflection of thirty angular minutes. 
If we want to prevent such errors, we necessarily must measure rates of turn 
of the aircraft very accurately. This particular example shows that it is necessary 
to measure rates of turn down to better than half of earth rate in order to be 
able to achieve verticality about the longitudinal axis within 3 minutes. Once 
the centripetal component of acceleration is determined from rate of turn and 
speed measurements, it can be subtracted from the indication of the gyro pen 
dulum and the gyro can then be forced to erect to the corrected pendulum 
position. 
A rather similar situation exists about the transverse axis of the aircraft, 
although the cause of disturbing accelerations is of a quite different nature. It 
is a well known fact that an aircraft cannot maintain an absolutely horizontal 
flight path. Instability about the transverse axis in connection with trim condi 
tions and control procedures will continuously cause slight altitude variations. 
Any rate of climb or descent must necessarily result in deceleration or accelera 
tion superimposed on gravity. In the first approach, these accelerations will be 
proportional to the rate of climb. Therefore, a rate of climb indicator is the first 
approach for measuring horizontal accelerations in a longitudinal direction.