(3) 
Equation (2) shows that if the mass M if fixed, the maximum 
acceleration a is obtained from the servomotor having the highest 
ratio of torque to square root of inertia. This ratio, 
Tm 
ru 
is an important figure of merit of servomotors and has a characteristic 
order of magnitude for a large class of electrical servomotors. If 
maximum motor torque T, is measured in newton-metres and the motor 
inertia in kilogram -(metres)^, the figure of merit N has the approx- 
imate value, 
Na (3) 
N = 20 (4) 
for many electric servomotors ^. Hence, the maximum linear acceleration 
& in equetion (2) is, 
à. = _10 
- 20 
S pix) EC S X 
where M is in kilograms. 
metres/(second)^ (5) 
The maximum available acceleration given by equation (5) can now 
be equated to the acceleration demanded by the motion of the mass M 
along the topographic turn shown in Figure (1). Thus, from equations (1) 
and (5) we have, 
X 5.10 or v = J/Jor metres/second (6) 
r /M LM 
Suppose a resolution radius of r = 1 mm or 1073 metres is assigned. 
Then the maximum linear plotting speed v obtainable with electric 
servomotors is on order of | 
0.1 10 | 
v = y M metres/second = A/V ems/second (7) 
Equation (7) shows that if M = 1 kilogram, the maximum plotting velocity 
attainable with typical electric servomotors on a circular turn of 1 mm 
radius is on the order of v = 10 cms/second. If the turn radius is 
increased to say 10 mm., equation (6) shows that the allowed velocity 
increases to v = 31.6 cms/second. If the turn radius is 1 mm. and 
the mass M is increased to 10 kilograms, the velocity v = 5.6 
cms/second. 
Since the radius of curvature of topographic paths such as 
contours varies along the path, the maximum linear plotting velocity 
allowed by the maximum available motor torque also varies. The larger 
the radius of curvature the larger the attainable velocity. The linear 
velocity with which an automatic machine traces a contour (or drainage 
path) can readily be controlled, The above analysis shows that if the 
available torque of the servomotors is to be used, the plotting velocity 
should be made a function of the shape of the topographic track in the 
neighbourhood of the tracking point. This is one of several character- 
istics with respect to which the performance of an automatic plotting 
machine should be adaptive.