The analog calculator
How it works
The schematic I propose is inspired by the article "Archimede, calcolatore elettronico" (Sperimentare, July 1968), without the addition and subtraction circuit, which requires a complicated voltage stabilization. At the time it was necessary to grade the scales by hand according to the characteristics of each potentio-meter, but now they can be purchased with ready-made and precise pot-knobs.
The circuit diagram: just three potentiometers and an ammeter
Let's have a look at the diagram: the battery and the central zero ammeter are connected in one side through the potentiometers P1 and P2, on the other through P3, all graduated with scales from 1 to 10. When all are settled to the same value the instrument will read zero.
To perform 8x5 we set P1 on 8 (20% of the resistance) and at the output we will have 80% of the input current which will feed P2 positioned on 5 (50% of the resistance). At its output the original current will be 50% of 80% (40%) and will move the instrument's needle from the central zero.
Now we rotate P3 until the instrument reads zero: this will happen when the potentiometer is at 40% of the scale, 4, and its output perfectly balances the 40% of P1 and P: 40 is just the result of 5x8! All the operations are settled like in a classic slide rule, decimals and commas being calculated by mind as usual.
To perform a multiplication we need just to set multiplicand and multiplier on P1 and P2, turning after P3 until the instrument reads zero and then read the result on its scale.
Because we treat percentages the results will always be correct, whatever the input voltage. All the operations can be done, but it's difficult to made addition and subtraction because in this case the voltage must always be accurate and stable: 1.5 volt + 1.5 volt will read 3 volts on the voltmeter.
The error in the calculations (ca. 2.5%) is higher than on standard slide rules, despite today we have economic and precise potentiometers which instead in the 60s were expensive and with a poor linearity (the relationship between angle of rotation and resistance). Due to the unreliability of these components the analog calculators met very little success.
In the '60 large scales were needed due the imprecision of the pots
What you need to build one
Different models of precision pot knobs
How to use it
Elevation to the square:
To properly center the needle on zero press S2 (ZERO) to sharpen the reading.
Turn the knobs with care to not overloading the instrument. When possible avoid to use the lower end of the scale (eg. to perform 5x5 set 500x500, not 005x005. Remember that, as in the slide rules, commas and decimals are relative and must be positioned by mind.
If the ammeter reads zero but the result read on the knob is wrong, you must account for this error or adjust the P3's knob.
The calculator mounted in photo frame
Back of the calculator with the simple wiring
Nicola Marras 2008
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