To clarify - do you mean these formulae ?

Here the bit in Brackets is the first resistance that gives the limit current from 230V RMS, the bit subtracted is the wet body worst case lowest resistance ever.

The resulting difference is the lowest permitted reading on test to let us safely assume 'essentially not connected to earth'.

To be honest it is all a bit of a "measured with micrometer, cut with axe" bodge or a measurement anyway, as no real person reads exactly 1000 ohms and a 25mA shock is very similar to a 30mA one, and for paths involving real terra-firma earth or rusty metal , the resistance reading will vary widely with test voltage and with humidity/ soil moisture content from recent weather.

And that is before we get onto the mains not being exactly 230V, ever.

M.

Looking at the answer by mapj, I don't see a "second" 1000 anywhere - it's the same 1000  throughout.  It's assuming that Ztl is 1000.

Each line is of the form: <equation> = <equation with the numbers in> = <simplified version with the bit in brackets calculated> = <result>.

_ quite, and I can't really see what is wrong either, and that's why I put the image up and asked if these were indeed the equations we should be looking at - perhaps the OP has a misprinted older version of the book, or has misread the algebra in some way.

Or indeed there is something else going on and I have not understood the nature of the question at all.

regards Mike.

Maybe I should have made it a Debate rather than a question as I can see what is for me, incorrect. And having put together a Tech Talk for a dozen electricians on the omission of supplementary bonding in a location containing a bath or a shower and the correct determination of potential extraneous-conductive-parts. I realised whilst putting this talk together that after more than 20+ years of staring at this equation that for me I now see it as an incorrectly conceived and lazily written working example of the equation (6.1).

Looking at equation (6.2) as with the others, it's not so clear that everything to the right of the (=) in the middle of the equation is the same equation just with the bracketed part of the equation completed. This surely should have been the symbol for 'equivalent' or 'is equivalent to'? Like an equals symbol but with three lines?

Why is this simplification or staged aproach required?

If followed mathematically then the outcome would be incorrect...

(230 / 0.0005) -1000 = 459 000 - 1000 = 458 000Ω (not 459KΩ)

Surely written correctly it should be:

(230 / 0.0005) - 1000 / 1000 = 459kΩ

It's just messy and if assumes that the person reading it needs help with the bracketed part of the equation, but then goes on to jump from 459 000Ω to 459KΩ without any further guidance for those that required help with the bracketed part of the equation as to how we got from Ω to KΩ.

It's just my opinion of course ;0)

I noted that, in the clip you posted mapj1  the printing of the triple decimal-exponent separator (1000s separator) is not consistent. For example, no space or comma for'1000' and '7667' but space for '23 000' and '460 000'

I can see from a digital copy of the latest re-print of the 5th Edition, that this has been noticed, but it's still inconsistent, but also there are some typesetting problems, so the bottom and right hand side of each expression appear "clipped':

So, in the above, we see a comma separator for '1,000', no separator for '7667' and a space for '460 0000' and '23 000'.

I have also come to understand that we all see things differently for various reasons, so I do get that this inconsistency could prove a 'bar' to grasping what's going on in the maths. Below is how I think it ought to have been set, which may help some people read it more clearly:

It is good that such things are being ironed out - while it's all very well that it iis clear to me in a well lit air conditioned office, (and I already know what the formulae are trying to say, which helps)  I can fully see that for someone in a bit of a hurry who only half remembers the lesson notes from several years ago, perhaps working from a dog eared copy in a badly lit basement or squinting at the online version on a phone screen against the sun, then inconsistent typography is an extra and un-necassary hazard that can lead to k ohms, ohms millohms and so forth being confused.

I must admit to being in 2 minds about the wisdom of  commas though, partly perhaps having worked abroad and with lots of other nationalities, there is the dreaded dot-comma confusion.

Pi= 3,14 ,  1 million is 1.000.000 to the Germans, that kind of thing

Further to those cultural issues, in print or badly rendered computer graphics the comma is not sufficiently different from a stop. It may be age, but to me these  ",  ."   even on this large screen look far too similar.

Perhaps for even more clarity and brevity the use of the international multiplier letter as the decimal marker e.g. 4k7 = 4,700 ohms or 4.7k could be considered  It's what I scrawl over my diagrams already anyway as my writing is too scrappy to be clear otherwise  ;-) 

Anyway thanks for pointing out - funny about the cropping though, I know when I was involved n the 3GPP standards we had a lot of this sort of issue, partly due to submissions using various versions of  MSword, where really a proper publishing program would have been a better choice.

Good that it is being looked at, even if it is not yet quite right in the draft.

Mike

sae70 said:

If followed mathematically then the outcome would be incorrect...

(230 / 0.0005) -1000 = 459 000 - 1000 = 458 000Ω (not 459KΩ)

Surely written correctly it should be:

(230 / 0.0005) - 1000 / 1000 = 459kΩ

That is not correct at all.

Why have you in the first example subtracted 1000 (Ω) twice, and divided by 1000 in the second?

I would prefer to have each = sign starting a new line.

I disagree with your 'correctly written'. I hope from school you will recall

BODMAS

Brackets, operators (sin cos tan etc), division, multiplaction addition, subtraction

For the order of evaluation of nested expressions.

"(230 / 0.0005) - 1000 / 1000 = 459kΩ"

Let us break that down

Brackets

230/0,0005 = 460 000 = 460k  (read all the "=" sign as 'is the same as' with a slight Yorkshire accent.)

no ops,

Division

1000/1000 = 1k/1k = 1

 no addition, but one subtraction

460 000 - 1= 459 999

rather a  long way, well 999 ohms to be exact , from the right answer...
 here 'k' is short for 3 zeros, or multiply bu 1000,  and if we had it M would  be short for 6 zeros = multiply by million etc.

I'm concerned

Mike

mapj1 said:

BODMAS

I usually use "BIDMAS" where "I" stands for "Indices", i.e. powers or roots, but it can be "O" for "orders".