(5) 
angular orientation 6. Let the magnitude of this slope be S . The 
effective tracking point has an associated mass M that is to be driven 
by servomotors. 
Suppose the tracking point is initially correctly located on the 
contour as shown in Figure 3(a) and is moving with a linear velocity v 
tangentially to the contour. If no servomotor torques are developed, 
the tracking point continues to move in the direction of its velocity 
vector and hence moves off the contour as in Figure 3(b). At some 
instant the tracking error measured perpendicular to the contour in the 
direction of steepest terrain slope will be AD, The horizontal and 
vertical components of AD are, 
x = AD.cose ) 
2% AD ging 5 metres (8) 
If the control system of Figure 2 is to be useful, it must sense the 
tracking error AD snd produce servomotor torques that will accelerate 
the tracking point back to the contour. To get the tracking point back 
to the contour as quickly as possible, the torques developed by the servo- 
motors should produce a resultant linear acceleration a directed perpen- 
dicular to the contour and hence along the direction of steepest terrain 
slope. This acceleration with its x and y components ay and a 
is shown in Figure 3(c). From Figures 3(b) and 3(c) it is apparent that 
the resultant acceleration is in the correct direction if at any instant 
its resolved components are, 
ay = 8 «C080 ) metres/(second)^, (9) 
ay = a . sine 
where © is the direction of steepest terrain slope. In nulling the 
tracking error AD by means of the acceleration a , it is reasonable 
to make the magnitude of the acceleration a proportional to the mag- 
nitude of the tracking error. Thus let us make, 
a = X, DD metres/(second)*, (10) 
a 
where K, is an as yet undetermined proportionality constent. From 
equation (10), the larger the tracking error the larger the correcting 
acceleration of the tracking point towards the contour. The component 
accelerations ay and ay are then given by Equation (9) as, 
ay = Kg. AD . cose ) 
metres/(second)?^. (11 
m K.AD.sino ) / a 
&y 
Now the accelerstions and in equation (11) are produced 
physically in the control system of Figure 2 by the torques Tx and T 
generatéd by the servomotors. Since these accelerations are proportional 
to the corresponding torques, equation (11) implies that the system of 
Figure 2 should generate torques of the form,