Cam 'K' was very simple - the input was from the control column and the output non-linear. Nothing more than a cleverly shaped pulley and rod system. So small deflexions gave control precision around neutral as the more circular bit of the cam moved, but larger ones gave a much greater output as the more pointy bit moved. The output value was then modified depending on speed - a simple plunger moved in respect to ram air pressure and moved a fucrum in the pitch system to modify the pitch control output accordingly. The output then entered the infamous 'Hobson motor'- an hydraulic motor which moved the slab tail. (Groundschool question 'List the 18 components of the Hobson motor'.......). This device also had a 'scissor restrictor' to stop you moving the control column too fast for Mr Hobson's device to cope with! Because there was no 'natural' control feel in pitch, a 'feel trim' system of a force v. displacement spring tube would take care of that - operated (normally) by electrical stick-top switches, although the position of 'neutral' in pitch moved as IAS increased... Another Gnat system was 'datum shift'; because the Cof G moved forwards as the landing gear extended, a bit of bike chain was wrapped around the gear actuator and as it moved, it added an extra 3(?) deg of pitch input to compensate.....
If the hydraulics failed, you had to act very quickly. First do whatever you needed to do to get the speed below 400KIAS or M0.85. Then move the feel trim so that it was in the 'ideal' sector on the feel trim position indicator, then 'unlock' the little elevators on the trailing edge of the slab tail to assist with pitch control; to make sure that you'd pulled the lever far enough, you counted 2 clicks, checked that a white tell-tale band was visible and that the 'ELEV' caption illuminated. Turn off the hydraulic power supply cock to the tailplane.....now the fun bit. Raise the standby trim switch guards so that you could operate Mr Hobson's device....electrically! But it would only move up from the position at which the hydraulics failed - so you had to exhaust the residual pitch accumulator pressure with the Hobson motor at (I think) 2 1/2 to 3 deg up on the tailplane position indicator or 5 1/2 to 6 with the landing gear down (datum shift didn't work with a hydraulic failure). Then you exhausted the aileron accumulator pressure until a hardening up in roll was noted. Now check that the tailplane will move electrically by moving the standby trim switches - and checking that the 'TRIM' caption illuminated, then check that you had control in roll. The control column only moved the little elevators in this mode, so primary pitch was effected by moving the standby trim switches; pitch trim was effected by....moving the control column - the complete converse to the normal method! The idea was to operate the system to keep the control column 'load-free and central'; to make it even more fun, you could transfer the standby trim switch function to the now-redundant stick-top feel trim switches by opertaing a further pair of switches known as the '399s' as they were fitted post-mod 399.
As you approached for landing - at around 150 kts - you had to preset the slab tail to (I think)51/2 to 6 deg up on the TPI gauge and push the control column to hold the correct attitude; you then relaxed the push and changed to a back pressure to flare.
Fun, eh? But we used to do night manual rollers in the little $od - at Mona!
Don't be put off; it's a wonderful little jet but fiendishly complicated and it MUST be maintained correctly and flown by someone who can cope with its foibles instinctively! It's nearly 30 years since I had my last trip in a Gnat and I'd love to have another chance if I ever had the opportunity!!