NAVIGATION — CANOES TO SPACESHIPS — DRAPER 313 



of the local vertical. This direction gives indicated position through 

 its orientation with respect to the artificially established earth co- 

 ordinate reference of the system. On a platform fixed to the earth, 

 the problem of indicating the vertical is easily solved by means of a 

 simple pendulum. On a moving platform subjected to horizontal 

 accelerations, a simple pendulum is no longer satisfactory, because of 

 interfering eilects introduced by these accelerations. This interfer- 

 ence is unavoidable because, by Einstein's principle of equivalence, 

 the mass of any body in its response to a gravitational field is identical 

 with the mass associated with inertia-reaction effects. Thus a pendu- 

 lum bob hanging along the vertical under gravity is deflected when its 

 point of support is given any horizontal acceleration. Under the accel- 

 erations usually experienced by moving vehicles, a simple pendulmn 

 may well have erratic deflections of several degrees. Disturbances of 

 this magnitude are completely unacceptable for the purposes of navi- 

 gation where the required maximum accuracy magnitude is of the 

 order of 1 mile. Wlien it is remembered that on the earth's surface 

 1 minute of arc between local-vertical directions corresponds to a dis- 

 tance of 1 nautical mile, the uselessness of simple pendulum arrange- 

 ments for navigation is apparent. 



Errors in local- vertical indications under conditions of erratic ac- 

 celeration of a moving vehicle may be reduced to satisfactory limits 

 by designing the indicating system so that it has a proper dynamic 

 behavior. The required characteristic is that of responding to a hori- 

 zontal linear acceleration component by an angular acceleration about 

 a horizontal axis at right angles to the linear acceleration. Wlien the 

 angular acceleration has a magnitude equal to the linear horizontal 

 acceleration divided by the radius from the center of the earth to the 

 moving platform, vertical indications change in step with variations 

 in position. A system with perfonnance of this kind is said to have 

 Schuler tuning ; this is in recognition of Professor Schuler, who first 

 published the theory of such arrangements. "When Schuler tuning 

 is used, indications of the vertical remain accurate in the presence of 

 arbitrary horizontal accelerations. On the surface of the earth, 

 Schuler tuning corresponds to a period of about 84 minutes. Any 

 practical system possessing the features suggested in plate 2 would 

 have to use a pendulum with this characteristic. 



Because of the small distance between the pivot and the center of 

 gravity that would be required in a simple physical pendulum with 

 Schuler tuning, a pendulum of this kind is not physically feasible. 

 The practical solution for this problem is to use an equivalent pen- 

 dulum system based on a servodriven gimbal-supported platform 

 carrying sensing elements that respond to gravity and acceleration. 

 Amplifiers in the feedback loops are designed so that electronic cir- 



