Rules and Guidelines
Want to participate in the discussions? Please read our Community Rules and Guidelines. Need some help? Visit Support and Answers.

  • State Not Answered
  • Locked Locked
  • Replies 15 replies
  • Subscribers 32 subscribers
  • Views 2398 views
  • Users 0 members are here
Options
You may also be interested in
This discussion is locked.
You cannot post a reply to this discussion. If you have a question start a new discussion

kA^2s

Nathaniel
This is not something I need answered: I already have a view - although someone might manage to change it. It's hoped to be a quiz-like stimulus to think about caution with units and prefixes. A comment here a week or two ago prompted me to look again in a standard - this time IEC61008-1 (2010). There I noticed a table of peak currents Ip and 'let through' I2t, that the devices are tested with. Here's a small excerpt,

81e202a88c2cf17c4a84e9cec5efcc52-huge-ka2s.png


The columns give test values for RCDs that have rated currents 16 A and 20 A and with rated withstand of 6 kA 'prospective'. (The low Ip values are reasonable if the RCD is expected to be protected by a current-limiting device rated close to its own rated current In.) 


It seems that the unit they give for I2t is used in a way I've also seen in one manufacturer's specifications for MCBs/fuses.
But is this 'correct'?  

A comparison to mm^2 might be helpful. 



The login process reminded me of another question that often occurs when seeing the IEE building, or logging into a 'thexxx.org' website: nearly 20 years on, is there anyone who sees a benefit of the change from IEE to THEIET? Too late now, in any case. One can hope the name doesn't make too much difference to what happens either way, although I feels the lack of mention of electricity is a bit strange for the institution's current or past work. I wonder if the cynical view I had at the time of the vote was actually unjust. 

  • 0
    If the derived unit is A2s, then 1000 A2s = 1 kA2s
  • 0
    I 2t has a real physical significance - in the same way as the power dissipated in a resistor passing a given current is I2 R the power times time during a fault large enough and fast enough we can ignore slow effects like cooling, is a proxy for the energy absorbed before the power is cut, and so how hot things are at the moment the ADS does its thing.

    As such it allows us to say something about the ultimate temperature reached inside a given bit of equipment, if we know its resistance and the thermal mass that is being heated.  This in turn allows us to decide if something melts, or is vapourized, or indeed is redistributed to the four winds as if a small bomb  had gone off. We can then decide if we should stock a spare fuse,  a spare fuse and holder,  a replacement box, or indeed a replacement transformer and substation roof (some designs being intended to blow off gracefully for the ultimate event.)


    For a thermal fuse in a well controlled thermal environment (sand filled ceramic tube anyone) this works very well.

    The BUT, and it is a big BUT,  is that it is not suitable for mechanical ADS with moving contacts - inertia and saturating iron cores of solenoids conspire to limit the maximum speed, so it stops getting faster at higher current beyond a certain point.

    Hence the 'death or glory' fuse in the basement of all well designed installations, though  it's true function in limiting the total energy that gets downstream, is often misunderstood.

  • 0



       "If the derived unit is A2s, then 1000 A2s = 1 kA2s."



    This interpretation appears to be what the standard intended. For the 1300 A peak value, a let-through of 1600 A2s implies a duration of a few milliseconds, given that the current will be less than the peak during most of the time. This time is consistent with the clear intention that there is current-limiting protection.



    And this interpretation also looks consistent with conventions for multiplied symbols, where RI2 is the same as R(I2) but not (RI)2.

     



    However ... contentious claim coming up ... it's wrong!



    It is, of course, just a convention how we write things. If the IEC wants to define that prefixes are used as above, it can do so. But I don't think the IEC or any other standards organization really would claim that they agree with that use. Two reasons:



    1.   It's not consistent with some other cases, such as mm2. If we followed the above interpretation, then 1 mm2 would be 0.001 m2, which is the area of a circle of about 36 mm diameter. There would be no need to worry about unevenly distributed loading on a 32 A ring-socket circuit with 2.5 mm2 copper conductors, if using that sort of mm2. But terminations would be difficult, as that's nearly the biggest conductor area found in single-core transmission cables: it's 2500 of the real mm2.



    2.  I find it unlikely that IEC/ISO/etc would choose to go against the normal rules of the SI system. The 'custodian' of SI units is BIPM, the Bureau International des Poids et Mesures. Its document "The International System of Units (SI)" has instructions and examples about prefixes, on page 143: "The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or sub-multiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.". It goes on to give examples, including ones similar in principle to the above point about mm2.



    So, having written kA, it is the whole kiloampere that is affected by an exponent such as the squaring. In the style of the quotation above, "the prefix 'kilo' is attached to the unit 'ampere' to form a new inseparable unit symbol 'kiloampere' that can be raised to the power of two and combined with the unit 'second' to form a compound unit symbol".



    That is:    1 kA2s = 106 A2s.



    It's unlikely that the standard's misuse of a prefix will actually cause confusion, as a difference by a factor 1000 is hard not to notice. It's been there for decades, and there must be tens of millions of devices in use that didn't pass the tests prescribed by the standard, even if they passed the tests that were doubtless intended. I only noticed this issue when taking I2t values from several manufacturers' specifications, one of which used 'k' instead of a number. For the future, I'd advise using 103 A2s, in order to be clear and correct.


  • 0
    mapj1:  not suitable for mechanical ADS with moving contacts ....  stops getting faster at higher current beyond a certain point.




    Forgive me if my rather vague initial question made you search for a deeper technical issue in my question. I wanted to leave a bit of puzzle about what the issue could be, requiring some thought about what I2t values made sense in view of the other details about peak and implied duration. But my main point was only the pedantic one about units, now explained in my recent posting.


    Back to your more interesting technical point: yes, although MCBs and larger breakers have become much better at their current limiting over the past few decades, they can't match fuses as the fault currents increase. In case anyone would like quick examples, curves of let-through I2t versus prospective current are good at showing this. Page 24 of Sentron MCB has an example of what looks a good MCB - I've seen cases where the increase of I2t with I_prospective is steeper.  In contrast, page 59 (Fig.4.4.5) of Sentron Fuse, although of miserable graphical quality, shows the classic flat curve for a fuse.


    A few years ago I was at an event where some manufacturers explained the modern world to users of LV switchgear etc. One theme was that fuse backup is no longer needed (provided that ratings aren't exceeded), but is just a folly of dinosaurs (ok, my exaggeration). We could get into the usual issues of statistics, etc, which might so far do little to support a need of fuses.  But I always feel more confident to know there's a good-quality fuse there as well. 

     


  • 0
    Nathaniel:



       "If the derived unit is A2s, then 1000 A2s = 1 kA2s."



    This interpretation appears to be what the standard intended. For the 1300 A peak value, a let-through of 1600 A2s implies a duration of a few milliseconds, given that the current will be less than the peak during most of the time. This time is consistent with the clear intention that there is current-limiting protection.



    And this interpretation also looks consistent with conventions for multiplied symbols, where RI2 is the same as R(I2) but not (RI)2.

     



    However ... contentious claim coming up ... it's wrong!


     



    Well, I'm not sure it is. If you have a look at the SI Specification (currently 9th Edition), you will see that this is correct in terms of derived units.


    For example, keV is 1000's of eV, NOT 1000s of e multiplied by V.


     

    It is, of course, just a convention how we write things. If the IEC wants to define that prefixes are used as above, it can do so. But I don't think the IEC or any other standards organization really would claim that they agree with that use. Two reasons:


    1.   It's not consistent with some other cases, such as mm2. If we followed the above interpretation, then 1 mm2 would be 0.001 m2, which is the area of a circle of about 36 mm diameter. There would be no need to worry about unevenly distributed loading on a 32 A ring-socket circuit with 2.5 mm2 copper conductors, if using that sort of mm2. But terminations would be difficult, as that's nearly the biggest conductor area found in single-core transmission cables: it's 2500 of the real mm2.



    2.  I find it unlikely that IEC/ISO/etc would choose to go against the normal rules of the SI system. The 'custodian' of SI units is BIPM, the Bureau International des Poids et Mesures. Its document "The International System of Units (SI)" has instructions and examples about prefixes, on page 143: "The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or sub-multiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.". It goes on to give examples, including ones similar in principle to the above point about mm2.



    So, having written kA, it is the whole kiloampere that is affected by an exponent such as the squaring. In the style of the quotation above, "the prefix 'kilo' is attached to the unit 'ampere' to form a new inseparable unit symbol 'kiloampere' that can be raised to the power of two and combined with the unit 'second' to form a compound unit symbol".



    That is:    1 kA2s = 106 A2s.



    It's unlikely that the standard's misuse of a prefix will actually cause confusion, as a difference by a factor 1000 is hard not to notice. It's been there for decades, and there must be tens of millions of devices in use that didn't pass the tests prescribed by the standard, even if they passed the tests that were doubtless intended. I only noticed this issue when taking I2t values from several manufacturers' specifications, one of which used 'k' instead of a number. For the future, I'd advise using 103 A2s, in order to be clear and correct.




    Your premise is based on the fact that the SI unit is A. However, we are dealing with an SI derived unit, and therefore you are correct (in one way) that the k does act on the whole unit.


    In fact, in this particular case, you could take one stance or the other and be correct - but in this respect the SI Specification gets things wrong in itself, in that it begins talking about compound units by adding spaces, yet those are removed later in Chapter 5 - which is the real cause of the dilemma.


    If we were to write the units in this case as 1,000 A2s = 1 k A2s with the space before the derived unit which is written as a compound unit, the whole ambiguity would be removed.


    I think I'll stick to my original interpretation, although personally I'd have no objection to writing 1 k(A2s) for 1,000 A2s.



    There are a number of similar cases in which IEC and CENELEC contradict themselves in notational terms, so this isn't really the only example of a debatable transgression of 'the rules'.


    For example, according to the IEV entry for DC, DC as a qualifier should not be used to qualify units - i.e. 24 V DC is strictly INCORRECT, and DC 24 V would be correct - yet many of the standards use 24 V DC as the preferred style. Similarly, the entry for AC says AC should also not be used to qualify units, so 230 V AC is INCORRECT, and AC 230 V would be correct ...


  • 0
    k just means times 1000, and all the multiplier prefices p,n,u,m,k,M,G etc. are one dimensional; that is how SI works, nothing to do with the IET, just a feature of our system of units since 1970 (and the pre 1970 MKS was the same in that regard, but things like sin-1 would have been written as arcsin - a form some of us with grey hair still prefer, but there we go. I do not like to see sulfer with an 'f' either but my kids tell me 'ph' is now wrong for GCSE purposes)

    Units kann be stacked ( uuF) although uncommon, is seen in older texts, micro-micro Farad, or picofarad, and kMHz is 'kilo-mega Herz == gigaherz' so to come back to your example

    1kmm2


    should be spoken as "one thousand square millimetres"

    I assume you would have no problem that 1000 mm2 does not mean a million square millimetres. and yes, the energy of 1keV is the energy required to raise one electron through 1000 volts, or one thousand electrons through one volt - the energy is the same, and multiplication of 1 dimensional quantities is commutative - A times B == B times A (==)is nearest I can get to the three line equals of "equal by definition" not the two line happens to be equal.

  • 0
    I do see the inconsistency:


    kA²s = k(A²s), but


    mm² = (mm)² not m(m²)


    so in general prefix-unit-power could be read either as (prefix-unit)^power or prefix (unit^power) with entirely different results. Not very logical.


        - Andy.
  • 0


    Just seen your post, Andy.  You've again put it more succinctly than I was going to.  


    Yes - the ambiguity will not arise without an exponent (power).


    It's implausible that BIPM or IEC intends ambiguities that are resolved only by an apparently unpublished list of which combinations of units and prefixes get treated one way, and which another.


    I'm confident the IEC intends to follow the SI system, in its modern form.  And I'm confident that kA2 is intended as equivalent to (kA)2 and nothing else, in that system. But - Graham - you've made me realise that the SI document (I assume you refer also the one I linked in the earlier post?) isn't so clear as we'd like. More examples of what can and can't be done would definitely have been helpful, besides some more use of the word "only". 


    As long as we keep to what is explicitly permitted in the SI document, there's not a problem: we get an unambiguous system. 

    * Use a prefix on any of the 28 symbols such as A, Pa, W etc (but not kg), on which prefixing is explicitly permitted: page 138, "Prefixes may be used with any of the 29 SI units with special names with the exception of the base unit kilogram". Ok - this doesn't prohibit other use, and "several" non-SI units can also be prefixed (page 145), but there's nothing explicitly permitting a prefix to apply to a longer construction (compound unit) such as a m2 or m/s2.

    * The symbol with its possible prefix is then a single 'thing' to which one can apply an exponent.

    * Multiple such 'things' (with or without prefix and with or without exponent) can then be combined by multiplying and dividing. 


    For writing, a prefix must attach to its unit without a separator (the examples show no space) and cannot stand alone, and multiplied units must be separated in some way (page 147). This would seem to prevent something like "k A2 s" or even k(A2 s), although I agree that the space after k would be a sufficient way to make it clear in this case. One reason it would not be a good general principle is that milli and metre have the same letter ... there are several messy features to SI, not least the kg.


    Little points: 

    "keV is 1000's of eV, NOT 1000s of e multiplied by V."

    An electronvolt, eV, is regarded as a unit in itself, albeit only a "non-SI unit accepted for use with SI units" - see Table 8 of the document I linked before. So there's no need to consider the letters e and V separately, any more than the letters in a pascal, Pa.  And even if 'e' were a special separate unit, keV and (ke)V etc would be the same anyway, as there's no exponent to complicate things.

    "yet those [spaces] are removed later in Chapter 5"

    I haven't found what was meant here.

    "DC as a qualifier should not be used to qualify units"

    Yes, this is a classic SI strictness, copied into IEC, with the obedience to SI that I would expect. Like the requirement of showing a range "1 V to 3 V" but never "1 - 3 V", it's routinely ignored in practice. The same goes for using a thousands-separator other than a space, as has been done in some examples in this thread (1,000) - not allowed, but many do it. I do wish IEC would follow the SI advice of using a decimal separator that fits the language: decimal commas, while used in many European languages, look strange in English, though I gather they're used in English in South Africa. 

    "Units kann be stacked"

    I know it's an old convention to combine prefixes, such as the μμF. (Ever seen a capacitance given in cm? Try the CGS system.) But in SI nowadays, combined prefixes aren't allowed - page 143 of the document.  So the kmm2 needn't be considered. I assume IEC intends to follow SI (now), not various old conventions.

    "k just means times 1000"

    Indeed, but the issue is how tightly a prefix "binds" to what comes after it: i.e. the order in which exponents and prefixes should be applied. 

    "sulfer with an 'f'":  

    I've felt a bit of a comeback of 'sulphur'. But I remember 25 years ago hearing that chemistry students were docked marks for not using the f.


  • 0
    I still do not see how there can be any misunderstanding with units of k A2s. Perhaps it could be made clearer that it its function is all about thermal damage to contacts and wiring, by re-casting it as joules per ohm? (which is actually the same unit)


    I agree the eV is a slightly special case and perhaps an unwise example in retrospect, I'm sure we both know that e is not a unit but a physical constant for the electronic charge quantum, 1.6 *10 -19 amps.seconds if you like. For anyone working on particle accelerators it is a very handy size, along mit it's relatives the keV, Gev (and just for the big chaps at CERN the TeV). The volt of course could be seen as the joule per coulomb. In some ways the eV is more of a portmanteau unit more like dBm, not like Pa in pascal ,which is just one unit with 2 letters, like Hz. I expect the electron voltlike the Angstrom and the centimetre, to be with us for a while yet..., formal SI units or no. We have inherited an alphabet for units that has left us with m being both a prefix and a unit, which could be perhaps confusing, but I think it is well enough established that we all know what is meant by mm. But all this is meant to clarify not confuse, and I fail to see the original scope for confusion. Have I misread the original question ?

    EDIT light bulb moment thanks to AJ and a decent cup of tea.


    Ok 1mm 2 = 10-6 m2 perhaps 1m m2 could be used to represent 10-3 m2 or or course it could be a cubic measure. perhaps they should have used m and m to distinguish the unit from the prefix.
    The english language version of the SI standard is not helpful

    (my French is not up to the original.)
  • 0
    Yep, we had it drummed into us at school.

    4 sq yards is not the same as 4 yards square etc etc.

    What do we write? 2.5mm2 T & E. Oh dear mm2 when we really mean sq mm.

    Mind you it`s always made me wonder why we say 5 pounds sterling but then write it £5  instead of 5£ (which I admit don`t look right) and countries with dollars write it $5 etc etc. so we get £5 5s 11d instead of 5£ 5s 11d . and yet in Spain where the did have ptas or pts now  they  write 5E (E being Euros, pardon me) instead of us E5. Daft innit?

Join us to get the best from IET EngX.

Joining EngX lets you personalise your experience so you stay up to date on the topics that interest you, plus you’ll be able to make connections who are looking to collaborate, exchange ideas and more.

Join us Not now

Community Rules & Guidelines