> W>>>
>>> Very good. Here's a pdf file. I'm a big fan of Wheeler's 1928 IRE
>>> article, and am happy to see this more obscure work of his propagated.
>>> Clearly, 54 years later, he thought it was an important improvement
>>> on his early famous article, and it's good to see that now people can
>>> actually read all about it, just as he wished. Twenty-three years ago
>>> Harold Wheeler paid $190 to have these two pages published, and it's
>>> nice to see his wishes and payment are not dead. Thank you, Phantom.
>>
>> This should be the definitive answer to the question what is a good
>> formula and how accurate is Wheeler's formula. The best of Wheeler's
>> last formulas are good for 0.1%, about 10 times better than the older
>> formula. With the tweaks I showed, we're good for 0.02% for all values
>> of D/L, so there shouldn't be any more doubt about what accuracy we
>> can get with a simple formula. Notice that to get that accuracy one
>> needs physical measurements good to about 4 digits; not easy to do.
>
> With all due respect to your Mathematica ramblings, I question your 0.1%
> and 0.02% assertions. That's because all these Wheeler formulas, good
> as they are, are missing a correction for wire size. So, except for the
> impractical case of a large fine-wire coil, a 0.02% accuracy, etc., won't
> be available to the users of these formulas. It's back to Grover for us.
With all due respect, you are quibbling and missing the larger point. I find it simply astounding what a skilled practitioner is now able to accomplish with today's affordable engineering tools (PC based Mathematica for one).
Can you imagine how long and carefully Grover and Wheeler must have labored to fill out tables and work through algebra? Another poster noted how small mistakes (such as in formulae or tables) would propa- gate from tome to tome because subsequent authors rarely had the time, energy or inclination to redo weeks, months (or sometimes years) of laborious hand calculations.
Now that has all changed. A few hours or maybe a few days to set up the problem, push a button, and the computer spits out a mistake free
*exact* symbolic answer in milliseconds! Who needs tables? (or even numeric solutions?) The paradigm has clearly evolved.
Once he is reasonably well practiced with the tool, the average (well maybe somewhat above average) engineer can now check the heretofore uncheckable. Even though it has been a standard that has passed under the gaze of countless engineers for well over fifty years, The Phantom's "ramblings" have managed to uncover errors in Grover and suggest improvements to Wheeler. Although I certainly admire The Phantom's prowess with Mathematica, what's really wonderful is that almost any reasonably sharp engineer could routinely unravel these knotty old problems - or, better still, do the same sorts of things with new problems. It is a new way of looking at how to get things done.
Don't worry if you don't know how, it's enough to know what "how" could do, and that you could learn how if need be.
I'll get off my soapbox now. :) -- analog