MEW 253: Workshop Techniques; Darren Conway

[Kiwi BlokeParticipant @kiwibloke62605]

Interesting stuff, but I think the lack of proof-reading &/or printer's errors have let the author down. It's good to see this sort of article in the mag, rather than the all-too-common picture-heavy 'Wot I did on me 'olidays wiv a welder/angle-grinder/'eavy 'ammer' type of article that is not very enlightening.

An explanation of the maths in Table 1 would be appreciated – there are undefined variables, and the formulae are truncated. I suspect there should have been a diagram to accompany the table. Also, I'm sure it's just a slip: RMS calculation (as used for the total error calc'n) requires the root is taken of the mean of the squares, not their total.

[Kiwi BlokeParticipant @kiwibloke62605]

[Russell EberhardtParticipant @russelleberhardt48058]

Posted by Kiwi Bloke 1 on 10/04/2017 10:44:50:Also, I'm sure it's just a slip: RMS calculation (as used for the total error calc'n) requires the root is taken of the mean of the squares, not their total.

Well, he could have divided the answer by the square root of the number of measurements but he seems to have forgoten to do that.

Russell

[Neil WyattModerator @neilwyatt]

Ouch!

I hadn't picked up on the table columns getting cropped.

You will appreciate I generally don't have the capacity to work through the maths when I get articles, but I should have noticed the cropping.

Neil

[John FlackParticipant @johnflack59079]

Neil…..with respect Kiwi Bloke is suggesting a little more than truncating/cropping. If an article is complex

1 do not print the article

2 have the article checked by a competent third party

Given that there was no great clamour as to errors by subscribers,perhaps the article was too complex for the average reader. And there's me thinking computers solved the worlds logic problems!! But then Kiwi Bloke could be wrong?

[John Stevenson 1Participant @johnstevenson1]

Why do you need it checking by a competent 3rd party ?

This forum is full of them.

[John FlackParticipant @johnflack59079]

Mr Stevenson…… There are those on this forum who THINK they know everything much to the annoyance of those that DO. My only concern is presenting the truth in a manner that is decipherable to those willing to learn

[Michael GilliganParticipant @michaelgilligan61133]

Posted by John Stevenson on 10/04/2017 14:23:38:
Why do you need it checking by a competent 3rd party ?

This forum is full of them.

.

… But they only see the text after publication.

Admittedly, it does seem that some of the tool suppliers let the customer do the quality control; but it's not really an approach to be encouraged.

MichaelG.

[Russell EberhardtParticipant @russelleberhardt48058]

To be fair, it's not a learned journal that needs peer revue.

Russell

[Tim StevensParticipant @timstevens64731]

Learned Journals need peer revue, Russell, because readers are going to rely on the information. If we are not able to rely on the information in MEW (or ME – just as wobbly) then what is the point of it?

Regards, Tim

[Enough!Participant @enough]

Posted by Kiwi Bloke 1 on 10/04/2017 10:44:50:

Also, I'm sure it's just a slip: RMS calculation (as used for the total error calc'n) requires the root is taken of the mean of the squares, not their total.

I haven't read the article but it sounds like confusion between RMS and RSS …. e.g. here.

[Neil WyattModerator @neilwyatt]

There is no simple answer.

I don't have the budget to get someone to check every article that has a formula in it. Indeed we don't even have proof readers these days. Publishing is a very 'skinny' operation these days.

Sometimes I do get things checked, but only in extremis. The main reason for this is that there are usually only a few days available for such checking.

The other alternative is simply not to publish any article that I am not able to 100% check myself or that I don't agree with 100%. This would make MEW a very thin and boring magazine…

I must admit, I put a lot more effort into trying to get my head around the calculations for the Jacob's Hobber – I failed to get past grasping the basic principles; I saw Darren's article as largely about technique and his 'error budget' was just incidental to the whole so I gave it less attention.

Neil

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Neil Wyatt on 10/04/2017 19:33:35:

There is no simple answer.

.

You have my sympathy, Neil

… and I think Russell's comment sums-up the situation nicely.

MichaelG.

[SillyOldDufferModerator @sillyoldduffer]

My sympathies are with Neil too. Proof reading is difficult and time consuming. As it's also hard work I don't think I'll be volunteering.

I find much of interest in MEW and ME and quite enjoy spotting the boobs. Safety issues apart, the mistakes rarely matter much. After all, only God is perfect.

Dave

 

Edited By SillyOldDuffer on 10/04/2017 20:09:44

[BazyleParticipant @bazyle]

I haven't read the article yet as I get put off by too much maths, except as Neil says for the occasional thing that intrigues me like hobbing and dividing calculations. However picking up on an earlier post about RMS if errors are being analysed then RSS (Root Sum of Squares) may be the correct technique not RMS. I used to use it a lot in the days before we had computers ie by long hand for understanding errors in microwave equipment design. Sometimes took an hour to run a calculation that is now done in seconds in excel.

RSS is used for variables that are vectors – effectively it is equivalent to calculating the hypotenuse of a triangle formed by two vectors. Apart from electrical power of pure sine waves I'm not sure when RMS is appropriate.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Bazyle on 10/04/2017 23:38:01:

… Apart from electrical power of pure sine waves I'm not sure when RMS is appropriate.

.

Maybe worth noting that RMS is essentially the same thing as Standard Deviation … which broadens the field of relevance a little.

MichaelG.

[time for bed now]

[Kiwi BlokeParticipant @kiwibloke62605]

Oh, wonderful! This is why this forum is solid gold. There's so much knowledge and wisdom around. Thank you Bandersnatch and Bazyle! It has to be RSS, doesn't it? I found physics, pure and applied maths fine, but statistics and probability calculations caused cerebral meltdown. Why are they so counter-intuitive?

Neil, just getting the mag out regularly must be a nightmare. Well done! Unfortunately, as editor, you get to be the focus of all criticism, discontent, etc., whether deserved or not. Perhaps the occasional praise, if you're lucky, makes it all worthwhile. Proof-reading must be a dying/dead art – or just too expensive. Spell-checkers are no substitute. I have the unfortunate ability (disability?) to spot typos and similar errors almost as soon as I turn a page – except in my own writing, of course… It was useful, professionally, but it's a pain. I also wince when I see misplaced apostrophes. I'm glad to see that MEW is better in this regard, under your stewardship.

Whilst MEW is not a learned journal, it aims to be instructive. Let's hope it retains that aim, and doesn't degenerate into a colour-glossy entertainment rag. It has a responsibility to print correct information (wherever possible). That's a big ask.

[Neil WyattModerator @neilwyatt]

I think RSS applied in this situation.

My understanding is that it applies when the cumulative effect of several uncorrelated errors is being estimated, rather than multiple instances of the same error.

Neil

[Neil WyattModerator @neilwyatt]

Posted by Kiwi Bloke 1 on 11/04/2017 05:03:23:

I also wince when I see misplaced apostrophes. I'm glad to see that MEW is better in this regard, under your stewardship.

Whilst MEW is not a learned journal, it aims to be instructive. Let's hope it retains that aim, and doesn't degenerate into a colour-glossy entertainment rag. It has a responsibility to print correct information (wherever possible). That's a big ask.

MEW is written almost entirely by its readers, rather than by 'experts'; this has pros and cons!

Apostrophe's? One doe's ones best.

Neil

[Anonymous]

Posted by Bazyle on 10/04/2017 23:38:01:

Apart from electrical power of pure sine waves I'm not sure when RMS is appropriate.

The rms value is applicable, and useful, for any electrical waveform, not just sine waves.

Andrew

[SillyOldDufferModerator @sillyoldduffer]

So what should the formula mangled in Table 1 have been?

Ta,

Dave

[Roger Williams 2Participant @rogerwilliams2]

Bloody hell, Im lost

[Benny AvelinParticipant @bennyavelin86238]

Ok, I tried to write something below but it gets technical very quickly and its not very well written (too lazy). So if you cannot handle wrong-prints please don't read the text below as it will only be an offense.

With that said let me see if I can shed some light on this issue. Normally when we are dealing with measurement uncertainty the error reported on a manufacturer sheet is a 95% confidence interval of the error. We are here assuming that the error is normally distributed and the error is 2 standard deviations from the mean.

Let us consider measurement X with uncertainty U i.e. we are seeing X+U in our instrument, where U is N(0,s), where s is the reported error of the instrument halved. Let f denote the function transforming our measurement to an angle, i.e. we are interested in f(X+U)-f(X). But notice that f is not linear and f(X+U)-f(X) is not normally distributed anymore, the author mentions "the linear part of the error" which I guess is referring to the fact that f is linearized as a function F and we can proceed in assuming that F(X+U)-F(X) is normally distributed (linearity). The author transforms the 2*Std(U) to 2*Std(F(X+U)-F(X)), i.e. two times the standard deviation.

Another important point here is that although the presence of one error affects the effect of another error so their transformed error (angle) are not independent anymore (they where independent to begin with). This can essentially be disregarded since the influence on angle is so small that considering them as independent is not a great error.

Now we come to the conclusion of this. Consider the four angular errors which according to the above can be regarded as independent, we wish to compute the standard deviation of this total error, so that we can compute a 95% confidence interval. Due to independence the sum of the variance is the variance of the sum, i.e. we can just add the squares together to get the variance of the sum.

To make this clearer we are considering measurements X1,X2,X3,X4 with uncertainties U1,U2,U3,U4, and denote Std(U1)=s1,…,Std(U4)=s4. We are also considering four functions f1,f2,f3,f4 that transforms a measurement to the angle (given the other values), to be clear f1(X1+U1,X2+U2,X3+U3,X4+U4), but we approximated this with F1(X1+U1,X2,X3,X4), (where F1 is a linear approximation of f1 around the point (X1,X2,X3,X4), in the following we will suppress the X2,X3,X4 depencence). Now what the author calculated was F1(X1+2*s1) which due to linearity is 2*Std(F1(X1+U1)), the same goes for F2,F3,F4. Now what we want to calculate is

2*Std(F1(X1+U1)+F2(X2+U2)+F3(X3+U3)+F4(X4+U4)) = 2*sqrt(Var(F1(X1+U1)+F2(X2+U2)+F3(X3+U3)+F4(X4+U4))

where Var indicates Variance (square of standard deviation). Now using independence we get

2*sqrt(Var(F1(X1+U1)+F2(X2+U2)+F3(X3+U3)+F4(X4+U4)) = 2*sqrt(Var(F1(X1+U1))+Var(F2(X2+U2))+Var(F3(X3+U3))+Var(F4(X4+U4)))

Which is then equivalent to what the author performed. So this means that a 95% confidence interval for the angle error is roughly 0.006 degrees when rounded off.

Quite sure somewhere is an error but the overall idea is sound, we are considering the calculated angular errors as standard deviations of independent random variables and thus squaring, summing and then taking the root gives the standard deviation of the sum.

[Neil WyattModerator @neilwyatt]

Error Source	Error (mm)	Formula	Error (Deg)	Error squared
D diameter	0.001	asin(d/D) -asin((d+e)/D)	-0.0060	3.6E-05
d diameter	0.001	asin(d/D) -asin((d+e)/D)	-0.0016	2.5E-06
Taper Length	0.008	asin(d/D) -asin(d/(D+e))	0.0003	1.1E-07
DTI error	0.0001	asin(d/D)-asin((d+e)/D)	-0.0002	2.5E-08
Mean square error (Deg)				0.006

Edited By Neil Wyatt on 12/04/2017 14:41:05

[Michael GilliganParticipant @michaelgilligan61133]

Neil,

Thanks for posting the table … but is there any chance you could provide a link to it ?

… it currently runs under the Adverts.

MichaelG.

[Author]

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