(6)
Tx Kye AD . cosB )
T, = Ke AD . sine ) newton-metres, (12)
where Kj, is a proportionality constant that includes Ka of
equation (11). It should be observed that while the torques T, and
T, demanded by Equation (12) can vary over any range, they cannot ever
ih practice exceed the maximum available torque T, of the servomotors.
How can torques obeying Equation (12) be obtained? In Figure 2 the
electronic scanning equipment and electrical resolver allow us to produce
torques of the form specified by equation (12). Let us see how this is
done,
The electronic scanning equipment in an automatic mapping machine
such as Hobrough's” produces as one of its output signels an electrical
voltage e proportional to the x-parallax at the location of the track-
ing point (the centre of symmetry of the scan). X-parallax is proportion-
al to the vertical distance AZ, corresponding to AD, by which the track-
ing point is off the surface of the terrain as shown in Figure 4. Hence
we can write,
e = K,.AZ volts, (13)
where K, is a proportionality constant or conversion gain having the
dimensions volts/metre. K, is a physical constant characteristic of the
scanning equipment and of the photographs being scanned. From Figure 4,
it is clear that,
Z = S.AD metres, (14)
where S is the magnitude of the slope of the terrain in the meighbour-
hood of the tracking point, and AZ is the height error corresponding
to the plotting error AD. From equation (14) it follows that the
electrical signal voltage e in the system of Figure 2 can be expressed
as,
e = K,.S .AD volts. (15)
By passing this signal through an electrical resolver as in Figure 2
and applying the resulting output voltages to the servomotors, it is
possible to obtain motor torques,
x = Kpe€.co80 = KpeKg.S. AD.cos ©
Ty = Kp.e.sin®©
Kp. Ko.8. AD.sin 6
In equation (16), Kp is a physical constant characteristic of
the electrical resolver and of the electric circuits that drive the
servomotor. The torques of equation (16) are of the form required by
equation (12) to accelerate the tracking point back to the contour in
a direction perpendicular to the contour. Equation (12) and equation
(16) are the same if we set the undetermined proportionality constant
(newton-metres). (16)
