single knob tuning-roller coil geared to tuning cap -questions Like Viking I/II

[Opcom]

These are common in some equipment like the Johnson Viking. One crank knob from 160 to 10 M. It seems like a simple idea but there's likely more to it.

Given there are many combinations of L and C that would tune a specific frequency, are these single knob plate tanks really just a properly calculated PI tank input section, that is, figured for the plate load impedance and Q, such that the Z and Q are met at the highest and lowest frequencies using the inductors min and max value, and same for the tuning capacitor, then gearing them together so the values track?

So if a Pi network is calculated for a tuning cap of 35pF and inductance of 0.7uH at the highest frequency, and for 10uH and 300pF at the lowest frequency, is it just a simple thing to gear the capacitor and inductor together so they each track min to max values arrived at as above?

I ass-u-me they would have to track with the same linearity curve to keep the impedance and Q the same. That's maybe interesting because half the turns isn't guaranteed to be half the inductance acording to some solenoid calculators, but a half meshed capacitor is usually half the capacitance.

Anyone explored this?

[WQ9E]

The coil is variable pitch, at least in the Desk KW.  I expect the loaded Q changes a bit over the range and it also has a switch to remove the variable cap above 13 mhz so only the coil plus "stray" circuit capacitance is used.

I very briefly considered some mechanical ganging schemes when I was designing my homebrew amp and quickly decided that the KISS approach was much more desirable    I calculated the desired L/C combinations during design and checked using my MFJ 259 antenna analyzer and a resistor to simulate plate load.  I have a card next to the amp that shows the dial settings for the roller inductor, vacuum tune, and air variable load capacitors and with turns counter dials I can quickly preset to those values.  This allows very fast band change in a contest and with the available dissipation (2,400 watts from three 4CX800 tetrodes) slight mis-tuning isn't an issue.  A set of G3SEK tetrode boards provides fast shutdown if I really miss the setup at 3:00 A.M. after too many contest hours without sleep

[Opcom]

I have the cards for tuning also, on the Tucker transmitter. It is real handy to get close. Still, the 1-knob is nice if one can get away with it.