It is, at first sight, easy to pass from one dimension to three. The same 
double integration of acceleration may be performed in a horizontal axis perpen- 
dicular to the first. In addition, we may think it necessary to do this in a verti- 
cal direction. These ideas must be altered, however, when more detailed anal- 
ysis is performed. 
Error analysis shows that since the value of R is so large, the small 
variations in it due to the change in flight altitude are negligible. In addition, 
the length of the natural period of the platform is so long in comparison with the 
expected duration of any vertical accelerations that their effect is also small 
enough to be neglected. The actual analyses are too lengthy and too complicated 
to be profitably discussed in this brief note. 
The system is left with two linear acceleration axes. If these axes are 
fixed to the aircraft (i.e., are mounted on a horizontal platform in the aircraft, 
which rotates with the aircraft about a vertical axis) the azimuth motions of the 
aircraft will cause each axis to measure varying velocities even when the track 
of the system is really unaccelerated. In order to ensure that the system mea- 
sures the true accelerations of the aircraft along two mutually perpendicular 
axes fixed in space, a third degree of freedom is bestowed on the platform. 
This azimuth axis is controlled by an integrating gyro sensitive in that direction 
but having no control applied to its torquer. If its drift rate is low enough, the 
platform may be considered to be fixed in space as far as azimuth is concerned. 
Error analysis shows that commercially available gyros easily have the required 
low drift. 
The result of the above considerations is to produce the Block Diagram