Walther WSR 160 Mechanical Calculator | How To Use

Описание: Watch how basic calculations are performed on a vintage Walther WSR 160 mechanical calculator. Also watch a daring attempt to divide by zero.

A little bit of history
Before the advent of electronic computers in businesses mechanical calculators like these were used, either hand-cranked or driven by an electric motor. The Walther WSR 160 was made some time in the 1950s or 1960s before electronic calculators took over the market because they were faster to operate and more reliable and - eventually - also became much less expensive than mechanical calculators.

The Walther calculators were made by Walther in Germany - yes, the manufacturer behind James Bond's classic firearm. After World War I, the Versailles Treaty imposed restrictions on weapons manufacture, and Walther began using their fine-mechanical skills to build mechanical calculators. The Walther WSR 160 is considered among the finest mechanical calculators of its time and were exported to other countries under different names, including Muldivo Mentor in the UK.

How does it work
Mechanical calculators basically work by applying addition or subtraction using a variable amount of protruding pins on wheels that interact with a counting mechanism. Turning the crank forward (clockwise) adds a chosen number to an accumulation register, and turning the crank in reverse causes the number to be subtracted. Since multiplication basically consists of repeated addition, and since division is simply repeated subtraction and keeping track of a final remainder, these calculators were also capable of multiplication and division, especially because other mechanisms allow adding or subtracting the operand in multiples of 10, 100, 1000, etc., greatly speeding up the computations.

A professional tool
In today's money these calculators were not cheap instruments. They cost approximately the modern equivalent of an office desktop computer and required regular servicing by a technician for smooth and reliable operation of the several hundred mechanical parts inside the calculator. Nowadays you may see them sold in poor condition at bargain prices at fleamarkets, but if you find a good, functional one it can be lots of fun to play with and be reminded of simple mathematical facts that you learned in school but have long-since forgotten.

Mechanical calculators vs Slide rules
Now you might ask: Weren't slide rules the typical tool for doing calculations before the electronic calculators? Good question! And the answer is yes and no .

Yes for engineering applications where small inaccuracies (down to approximately one part in 1000) could be tolerated slide rules were powerful instruments and also allowed more computation of more advanced functions such as logarithms, exponentiation (including exponentiation with an arbitrarily chosen exponent), arbitrary roots, and trigonometric functions.

But no for financial computations. Here accuracy down to the final digit is important, and thus the mechanical calculator which offers extreme precision was the the only option, except from resorting to doing calculations entirely by hand.

How about more advanced mathematical functions?
Running businesses rarely required functions more advanced than addition, subtraction, multiplication and division. But, given the fact that exponentiation is just repeated multiplication, and multiplication is repeated addition, you could do exponentiation with integer exponents on these calculators. Square root extraction is also possible (perhaps surprisingly easily in fact), and with some mechanical calculators the documentation included model-specific tricks to speed up the computation of square roots. However, for advanced financial functions such as computation of compound interest, books with lookup tables where simply used instead. Given that square roots could be computed, logarithms could also be computed using Euler's method, although I wouldn't bother doing it if a table of logarithms was available. I've tried Euler's method for computing logarithms a few times just for fun, and while very educational it's also very, very tedious.

How about trignometric functions? No, not a chance. Well, technically yes, you could turn the trignometric functions into Taylor polynomials and compute those, but now we have moved into territory where advanced slide rules reigned supreme until the electronic scientific calculators took over the scene. Use the right tool for the right job...

Be sure to check out another clip of this calculator doing square roots by subtraction here:    • Computing Square Roots by Subtraction on a...  

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