[Mathmaticus]

Gentlemen rather than letting you bask in your odd desire to increase complexity may I suggest another solution to your problem.

As I understand it you have a circuit which is imbalanced. You are attempting to use a linear moment arm potentiometer of 90 ohms resistance to propel a 30 ohm gauge linear needle gas gauge.

While your circuits are interesting, without logic, they cannot possibly deliver a linear response only an approximation. This is not the way, in my estimation to solve this problem.

Instead, I propose a mechanical solution. Datcon manufactures 90 ohm sender units. Each degree of moment arm movement represents one ohm. Thus, 90 degrees = 90 ohms. Their float arm is 14 inches long.

Suppose you were to cut off the potentiometer's moment arm from the zero position to 30 degrees. You don't cut it off mechanically, you alter the moment arm distance to achieve the appropriate tank level.

For example if the fuel tank in question was 7 inches deep then one may calculate the required distance of the float through the potentiometer's moment arm quite easily.

In this case the sin of 30 degrees = 0.5. Thus since sin is o/h and o = the tank depth of 7 inches it follows that h = 14 inches [how coincidental!]

Thus, in such a configuration, when the moment arm of 14 inches in length floats from an empty tank to a full tank, its vertical movement is seven inches confined mechanically by the bottom and top of the tank respectively. Further there would be no more approximations. The circuit is now perfectly balanced. The earth as we know it has been restored to its orbit.

This solution is elegant not only because it solves the circuit imbalances with a perfectly linear solution but it matches the aesthetics of engineering in the 1950s. In fact, I had considered calculating the angles on an old slide rule so I could appreciate the moment more fully.

Sometimes mechanical solutions are the perfect solution.

I would like to make one more remark. No matter how you bend your moment arm, into a pretzel if you like, as long as the distance of the moment arm is 14 inch radius and does not encumber the bottom or top of the tank through its empty full arc, it will work perfectly.

And one of the other satisfactions that comes with such a design is the confident knowledge that, though concealed, your's is bigger and oh so much more sensitive, something an intelligent woman can really appreciate... again and again when going for a ride. And you will never have to worry about coming up short [dare I say again] when it really counts.