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Old 14th Nov 2017, 4:47 pm   #10
kalee20
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Join Date: Feb 2007
Location: Lynton, N. Devon, UK.
Posts: 7,061
Default Re: Transcendental magic: Schade's peak voltage equation and my discovery!!

Quote:
Originally Posted by astral highway View Post
I wonder under what circumstances it was important to Schade to derive the peak figure, then? It was post-War...
Probably, calculating peak voltage to be sure that insulation, voltage rating of components, conductor spacings, was sufficient to prevent failure or flashover! Schade being nothing if not thorough, worked out the exact formula.

Quote:
Originally Posted by G8HQP Dave View Post
For small values of x, e^(-x) is 1-x. So for high values of Q you are simply calculating 1- (pi/4Q) to whatever accuracy your calculating device can manage. You can easily check this by comparing the two calculations: exp(-x) vs. 1-x. The difference is that you can by hand do 1-x however small x is - you are limited only by the size of your piece of paper.
Good approximation from Dave, which gets more and more accurate the smaller the value of x. And much easier to calculate! In fact it's the approximation behind my % error being 78/Q... as pi/4Q x 100% simplifies to just this!

So, whereas Al's calculator gives up and displays 1 for Q>10,000 we can now do better if we want... so for a Q of 100,000,000 the exponential term would be 0.99999999215.
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