orthogonally mounted to form the stable platform. The platform is supported 

 within three gimbals to provide independence of vehicle roll, pitch, and heading. 

 Means are provided to sense spurious precessions instantly and to eliminate 

 them by rotation of the gimbals. Upon the platform the latitude accelerometer 

 measures the north-south component of acceleration, and the longitude acceler- 

 ometer measures the east-west component. Mounting the accelerometers in the 

 level plane makes them insensitive to the influence of the earth's gravitational 

 field (except for a small component resulting from the earth's "out-of- roundness, " 

 which is discussed later). The first integration of acceleration actually occurs 

 within the "accelerometer" itself, so that the signal delivered is a measure of 

 linear velocity. If the vehicle were moving along a fixed, flat surface, these 

 velocities could obviously be integrated to give distances traveled. 



The fact that the earth is rotating and has a rounded surface compli- 

 cates the problem in two ways . First, the system must translate the measured 

 horizontal motions into their corresponding curvilinear equivalents with respect 

 to earth. The computer has two channels, latitude and longitude, for this pur- 

 pose. In the latitude channel north- south velocity is converted from linear to 

 angular terms to determine change of latitude. The longitude channel operates 

 in the same way except that two additional complications are necessary. Be- 

 cause the relationship between longitudinal arc-length and arc-angle is a function 

 of latitude, latitude must be inserted into the conversion from linear to angular 

 velocity. Then the angular velocity must be corrected by adding the angular 

 velocity of the earth, a known constant (for this purpose). 



The second problem caused by the earth's shape and motion is that 

 the platform, which would otherwise remain fixed with relation to space , must 

 be constrained instead to remain fixed with respect to the earth , i.e. , horizontal 

 and indicating the north. Provision of this constraint is another function of the 

 computer. In essence the computed values of ship's latitude and velocity and the 

 known velocity of the earth's surface are used to determine the rate at which the 

 platform should rotate about each of its three axes. These rates are converted 

 to control signals which are sent to three torquing motors, one for each gyro; 

 these motors in turn cause the gyros to precess at the proper rate. The platform 

 is then erected to make its axes correspond to those of the gyros. 



The computer must correct for three other factors: First, the earth 

 is not actually a sphere but has, instead, a greater radius at the equator than at 

 the poles. Because the orientation of the stable platform is controlled on the 

 basis of calculations assuming a spherical earth, the latitude accelerometer 

 tends to incline sli^tly away from a normal to the gravitational axis, i.e., the 

 axis passing through the earth's center of mass, and thus to sense a small com- 

 ponent of the earth's gravitational field. Second, the rotation of the earth about 

 its polar axis produces a centripetal acceleration which has a component lying 



96 



Arthur ai.ll.tttlc.ilnr. 



