Originally Posted by Private jet
Why do they give different results? Surely the mathematical formulae these devices work to must be the same that ADC's use and they are always spot on.
The answer to your question lies not in mathematics, but in the engineering and manufacture of your whizzwheel.
Interesting (and true) urban legend: Many mathematicians had sought to work out formulae or methods by which to play Roulette and break the bank at a Casino and thereby leave behind the icy garrets of their university chambers and take off to the Mediterranean and enjoy the company of wench(es) of agreeable proportions, etc.
But the first and reputedly only person to do so was not a mathematician, but an engineer.
In 1873 Englishman Joseph Jaggers, an engineer in Yorkshire cotton mills, wondered whether the roulette wheels at Beauz-Arts Monte Carlo Casino were balanced. He found one that was not. His three day stint at the Casino netted him around $325000 (in 1873, when the Colt from Old Regret was worth a thousand pounds!).
I digress. Engineering is the key, you see, not mathematics.
Whizz wheels are circular slide rules and work on the basis of representing numbers as 'distances' or positions on the wheel.
In 1614, John Napier discovered the logarithm which made it possible to perform multiplications and divisions by addition and subtraction.
a*b = 10^(log(a) + log(b))
and
a/b = 10^(log(a) - log(b))
See
http://www.hpmuseum.org/sliderul.htm for full explanation.
Get yourself two sticks in the case of a slide rule, or two concentric wheels for a whizz wheel, and mark them with Logarithmic scales. Slide the scales until the one of the multiplicands is under the index, then the rule 'adds' the scales and the product is adjacent to the other multiplicand. Adding the logarithms in this way by lining up the logarithmic scales on the wheels/sticks gives you multiplication and division without batteries.
The precision (not accuracy) of the device then depends upon how closely your gadget can resolve numbers. This is a function of size of the scale.
So, first up, your 5" Pooleys yields much more accurate results than a 3" pocket Jepp whizz wheel, because it has a circumference 2.77 times the size of the pocket whizz wheel.
This is also why those circular computers on 'pilots watches' are nearly useless, being 1/25th the precision of a 5" and 1/9th the precision of a 3" whizzwheel.
For high precision up to the time of electronic calculators, you might have bought yourself not a straight slide rule,
nor a circular slide rule,
but a cylindrical slide rule with an enormous scale! This one had an outer scale that was 61' long and could still fit in your kitbag:
But even if you had a 5" Jepp to compare to your 5" Pooleys, you would probably still gain different results from the same calculations.
"A badly made slide rule will always give you the same answer for a given calculation ... and it will be just as wrong each time. So it all comes down to how accurately those scales were laid down on the rule in the first place, and how well they have stood up to the ravages of time since then. This is a much harder question to answer, and it can be virtually unique for each rule."
Accuracy of a circular rule may also be affected if the pivot in the centre of the wheel is not exact centre (eccentric movement) or badly worn, printing of the logarithmic scales during manufacture is not accurate, and as said above, accuracy of the logarithmic scales themselves. So better engineered and manufactured circular computers of the same diameter could yield better answers than cheap and cheerful ones.
Therefore if you are taking a Nav or other ATP exam requiring the use of a whizzwheel, use the same make and model that the examiner used!
http://www.sliderule.ca/intro.htm
All a bit rough and off the cuff but there you are.
