# BA Threads



## J-G (11 Mar 2022)

I know BS 93:1951 is obsolescent but BA threads are still in regular use, particularly in Model Engineering.

I've always known the 'Series' to be the most scientific in that the Pitch of each higher 'Number' is 0.9 of the previous rounded to 2 places. That's fine and causes me no problem but I've also understood (Wiki !!) that the OD is 6 times the pitch. That is certainly true as far as 0BA is concerned - 1mm pitch 6mm OD - but it is not so for any others in the series. 10BA is 0.35mm pitch so ought to be 2.09mm OD but is in fact 1.7mm or 4.87555 times the pitch. 

I don't have the 'Standard' and haven't been able to find a definitive source which details the precise formula to derive the OD from the pitch. 

Can anyone provide such?


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## niemeyjt (11 Mar 2022)

Not sure if it fully answers the question, but for a useful size chart - Convert,compare all Imperial tool,nut,bolt and spanner sizes to metric.


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## J-G (12 Mar 2022)

That link is much more concerned with the automotive industry rather than the British Standards for screw threads. There are numerous size charts like that but they just show a list of the sizes rather than the formulae which determine the Thread Series.

Since posting the question, I have found a site that makes a sideways reference to 'Log base 10' and it's possible that the OD (after 0BA) might be Pitch x 6 + log (Pitch) (which is always negative, being < 1) which looks close but not correct.


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## clogs (12 Mar 2022)

not the answer to ur question but there's quite a big movement in model eng to go metric for ease of supply....
there's even plans available for a new build that have the option of metric threads.....!!!!
mind there's a few rivet counters who will not....


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## Craywater (12 Mar 2022)

J-G said:


> I know BS 93:1951 is obsolescent but BA threads are still in regular use, particularly in Model Engineering.
> 
> I've always known the 'Series' to be the most scientific in that the Pitch of each higher 'Number' is 0.9 of the previous rounded to 2 places. That's fine and causes me no problem but I've also understood (Wiki !!) that the OD is 6 times the pitch. That is certainly true as far as 0BA is concerned - 1mm pitch 6mm OD - but it is not so for any others in the series. 10BA is 0.35mm pitch so ought to be 2.09mm OD but is in fact 1.7mm or 4.87555 times the pitch.
> 
> ...


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## J-G (12 Mar 2022)

That is one of the worst types of BA Data sheets! - It simply lists the imperial aproximations, and does nothing to address the question which is about the formula that equates the OD to the pitch.


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## Sandyn (12 Mar 2022)

J-G said:


> That is one of the worst types of BA Data sheets! - It simply lists the imperial approximations, and does nothing to address the question which is about the formula that equates the OD to the pitch.


I hope you don't mind me saying, I'm sure you didn't intend the reply to be abrupt, but it comes across that way. It is so easily done accidently. Craywater was just trying to be helpful and their information is correct. People just add what information they have in the hope it will be helpful.

BS 93: 2008 defines BA screw thread sizes in Table 1. It also gives the tolerances and defines BA completely so the chart shown by @Craywater is perfectly OK. BS 93:2008 also lists a table of 'approximate' inch equivalents of B.A. Threads. which is where that table probably came from.

Not many people need to know how the threads were derived, so it's not commonly displayed at the bottom of the thread charts.







To answer your question, the standard gives the following informative information






I will delete these images in 24 hours.


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## Fergie 307 (13 Mar 2022)

J-G said:


> I know BS 93:1951 is obsolescent but BA threads are still in regular use, particularly in Model Engineering.
> 
> I've always known the 'Series' to be the most scientific in that the Pitch of each higher 'Number' is 0.9 of the previous rounded to 2 places. That's fine and causes me no problem but I've also understood (Wiki !!) that the OD is 6 times the pitch. That is certainly true as far as 0BA is concerned - 1mm pitch 6mm OD - but it is not so for any others in the series. 10BA is 0.35mm pitch so ought to be 2.09mm OD but is in fact 1.7mm or 4.87555 times the pitch.
> 
> ...


BA not really my thing but surely any measurements would be imperial rather than metric? And I wonder if there is necessarily any formula linking the thread pitch to the diameter. Looking at my BA charts there certainly doesn't appear to be, the pitch appears to be coarser relative to the diameter as they get smaller.


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## niemeyjt (13 Mar 2022)

Any use - Bolt Science - The British Association (BA) Thread Form


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## Sandyn (13 Mar 2022)

Hopefully, this is the information the OP was looking for. "" I don't have the 'Standard' and haven't been able to find a definitive source which details the precise formula to derive the OD from the pitch ""

BA threads are defined in BS 93.
I was going to delete the images in my previous post since they are copyright, but too late to do it


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## Fergie 307 (13 Mar 2022)

Was confused why a Brush thread dating from the 19th century should be metric. According to wiki it was based on the Swiss Thury thread form, so you learn something new every day. Doesn't appear that there is any formula for determining pitch relative to diameter.


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## Sandyn (13 Mar 2022)

The text relating to the basis of the B.A. thread is informative, just there for information and is not required, because all dimensions are defined in the various tables. The formulae are not part of the absolute definition of the B.A thread system any more. 

The Major diameter is derived from the pitch 'P' and the pitch is derived from the BA size. (Designation Number)
6P^6/5 where P = (0.9)^n where n=the BA size

for 0BA, P=(0.9)^0=1
and major diameter =6*(1^6/5)=6


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## J-G (14 Mar 2022)

@Sandyn - You are quite correct on both counts, my reply - on re-reading - does look to be abrupt and aimed at @Craywater - actually it was seeing the Imperial figures which roused my ire ! so appologies to @Craywater  (I can't find a real 'Embarrased' Emoji)

I was coding for 16 hours yesterday and didn't log on the the forum at all (most unusual for me).

Your reply (#10) does seem to provide EXACTLY the detail I am looking for and I'll do a thorough investigation over the next few days (I have some pressing commitments  ).

It was the Wiki article which stated a 'definitive' figure of a simple P x 6 = OD which roused my enquiry, though I am writing a program to determine the dimention over wire used to measure the true effective diameter of threads. For BA I've resorted to 'look-up' which means that it has to be treated as a special case, which is always prone to error. 

@Fergie 307 - No it's the other way round, the OD is determined from the Pitch - though in fact it ought to be possible to reverse the equation.


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## Sandyn (14 Mar 2022)

Thank you J-G 
There is a lot more information in the standard which might be interesting to you. If you want to have a look . It cross refers to BS 6528:1984 for the glossary of terms, One of which is the 'Drunkenness' of a pitch'.
You might have this already, it's the 'NPL Notes on Screw Gauges' which has a lot of info on measuring threads.


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## paul-c (14 Mar 2022)

Craywater said:


> View attachment 131456
> View attachment 131456


zeus charts - always the first place to go to when you need info on threads.


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## Yojevol (14 Mar 2022)

@J-G @Sandyn 
Whilst this discussion has been going on I have been trying to come up with the formula relating diameter to pitch. Having studied BS93 2008 data it seems that there is no such published formula. It is evident that there are clear relationships to pitch which enable the form to be produced but there is no stated relationship to diameter. When the system was designed 0BA was chosen as the basis with a Diameter (actually the OD of the internal thread) of 6mm an a Pitch of 1mm. As stated previously the subsequent pitches are 90% of the previous one, ie, they're in a geometric progression. As J-G has noted the diameters don't follow the same progression, which is a bit peculiar as there is no particular reason why they shouldn't. I've done some analysis of the table in BS93 and it became apparent that all the thread diameters get progressively an relatively smaller than 0BA. I set out all the forms from 0BA to 16BA on common axes and enlarged them so that they were all easily comparable with 0BA. It was immediately apparent that there is a regular 'undersize' compared with 0BA and this undersize is proportional to the BA number. This means that an empirical formula can be produced relating diameter to pitch.

It is (drum role) D=P(6-0.1144N)  

where D= diameter, P= pitch, N = BA number

This all seems very strange.
Why was this undersizing adopted?
Why is it apparently associated with the BA number which is arbitrary?
Why was the major diameter of the internal thread chosen as the base? It's the least accessible of the 4 diameters (internal/external, major/minor)
Why was the numbering system chosen? I imagine the decided that 6mm - 0.25mm would be the range having 26 sizes, 0BA - 25BA

Note: Male/Female references no longer PC

Brian


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## J-G (14 Mar 2022)

Sandyn said:


> You might have this already, it's the 'NPL Notes on Screw Gauges' which has a lot of info on measuring threads.


Thanks Sandyn - very useful - No, I don't (didn't) have such document, I've been working from first principles, plus information remembered since my apprenticship at Coventry Gauge & Tool Co. Ltd. - (1956 - 1962)  - I'm sure you will know CG&T through their 'Matrix' branding - though I did go on to work for Herbert Small Tools Commercial Threading dept.

As you can imaging I have not assimilated the 133 pages of information (yet) but I'm sure that it will be an invaluable reference work - very interesting to see images of some 'Matrix' instruments which I worked on/with.


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## Sandyn (14 Mar 2022)

Yojevol said:


> It is (drum role) D=P(6-0.1144N)


That's really cool, it's frying my brain   but I love a mystery. I don't have any answers. I don't know much about threads, but I do know about Standards. and how they work.
If I ever have the need to derive the Major dimension from the pitch I would use a look-up table based on BS 93. That's what manufacturers will manufacture to. 
Now I am also curious, both methods of calculation seem to give very similar results ( now both 'wrong' according to the Standard, but probably within tolerance) It's too much of a strain on my one brain cell to do the statistics, but I think I managed to calculate the Standard deviation of both sets of results and it's almost identical. Does one formula give a better result? Perhaps Thury was drunk when he devised the thread? There seems no reason why it wouldn't follow the same progression? hence the terminology Thread Drunkenness.


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## ChaiLatte (14 Mar 2022)

J-G said:


> ...I am writing a program to determine the dimension over wire used to measure the true effective diameter of threads.



Start with this link: Dr. Vogel's 3-wire equation

and buy a copy of the Van Keuren handbook (No. 36). It is about the best you will get.

There used to be a pdf copy of the handbook with the equations in on the Internet Archive, but it has been removed, so it is 'out there' somewhere.


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## Sandyn (15 Mar 2022)

J-G said:


> I'm sure you will know CG&T through their 'Matrix' branding


I hadn't heard of CG&T, but have seen Matrix dividing heads. Things of real beauty. I looked up the company. What a great British engineering company. I see the company opened a factory in Brechin Scotland in 1939 to supply the war department. That's just 7 miles from where I was born.


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## J-G (15 Mar 2022)

Being born in Coventry (well physically Leamington Spa due to it being Wartime!) and my father being a Capstan Setter/Operator, the name of the company was very well known to me when growing up. 

Anyone in the midlands area knew that if you wanted to be a toolmaker then getting an apprenticeship at CG&T was a 'top prize' - and I considered myself very fortunate. Once I'd been accepted I still had to wait nearly 6 months for a place to become available - and they paid me! - 17/6 per week - (87½p)  to start.


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## J-G (15 Mar 2022)

Yojevol said:


> This all seems very strange.
> Why was this undersizing adopted?



I'll agree that there were some strange decisions made but it was early days.


Yojevol said:


> Why is it apparently associated with the BA number which is arbitrary?
> 
> Why was the numbering system chosen? I imagine the decided that 6mm - 0.25mm would be the range having 26 sizes, 0BA - 25BA


I don't think the use of numbers as a reference is arbitrary for small diameters - it's so much easier to use a single character as a designation - Can you imagine having to write (say) 

2.8 x 0.53 BA rather than 6BA ? 

and that's without specifying 'mm'...
and since a 'geometric' progression had been determined, the Nº series made even more sense.



Yojevol said:


> Why was the major diameter of the internal thread chosen as the base? It's the least accessible of the 4 diameters (internal/external, major/minor)


I haven't previously seen any reference to the 'Internal' OD being used as the base


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## Sandyn (15 Mar 2022)

J-G said:


> they paid me! - 17/6 per week - (87½p)  to start.


   amazing


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## Yojevol (15 Mar 2022)

@J-G Ref, the numbering system. I wasn't commenting on the numbering system itself, but apparent relationship of the thread diameter 'correction' to it, which, IMO (no H), seems arbitrary.
Brian


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## J-G (15 Mar 2022)

Ah -- That makes sense  

I think the Basic dimensions of the BA 'Standard' was (is?) the most mathematically determined, and yes, the choice of 0.9 as the ratio does seem somewhat arbitrary but I suspect that it was determined very specifically after many hours of calculation.

I haven't considered the US Numbered threads below ¼" but I suspect that may be a similar 'can of worms' 

I must admit that when I posted the original question I didn't anticipate such an interesting discussion !


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## hawkeyefxr (16 Mar 2022)

I have a small TCP tin with BA taps in it, down to about 8BA. Used them when i was in the toolroom, now i cant see them without glasses and as for the threads and drills needed to tap.......forget it.


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## J-G (17 Mar 2022)

I have Taps & Dies down to 12BA - though I seldom use less than 10BA - but when I was an apprentice, I spent some time in the 'Plating' shop where I had to 'wire up' ready to chrome plate the inside threaded portion of 20BA screw ring gauges - the bore on that being ~0.34mm !


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