# BA and Whitworth thread depth calculations



## bezalel2000 (Dec 9, 2011)

mklotz  said:
			
		

> If you look at a thread diagram, you'll see that the depth of thread (sharp crest to flat root), is given geometrically by:
> 
> D = [[3/8]/tan(30)] / n = K / n
> 
> ...



Simple Question

What is the general formula for thread depth?  :shrug:

Now I know, thanks to Merv's and Rick, that for 60o threads thread depth per pitch can be calculated from a constant k = 0.65 

I can also extrapolate from major/minor diameter charts that for;

 Whitworth k = 0.64         and for,

     BA   k = 0.60  

So how do I calculate it.  ???

I know I could look up the chart, but with advancing years an A4 sheet is just big enough to accommodate the formula where I might previously tabulated the whole chart.  ;D

Thanks

Bez


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## tel (Dec 9, 2011)

Well, I usually just look it up but, as I understand it .....

Whitworth k = 0.64 

means the depth of the thread is the pitch x .64....

so a 1/4" Whit thread has a 20 tpi thread - p = 0.050 ....

so that gives us .050 x .64 = .032

so depth of thread = 0.032"


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## bezalel2000 (Dec 9, 2011)

Thanks Tel

What formula did you use to get 0.64 for 55o thread form?

and what do you use for the K of BA thread?

Bez


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## Maryak (Dec 9, 2011)

Whitworth

d =0.5p x cot 27.50 = 0.64037p (included angle = 550)

BA

p = pitch mm
H = V form height = 1.13634 x p (included angle = 47.50)
r = top and bottom radius = 0.18083 x p
h = depth = 0.60000 x p

Best Regards
Bob


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## bezalel2000 (Dec 10, 2011)

Thanks Bob

I think its coming together now.

though I think there may be a typo in your formular, I can only get the numbers to work out right if I substitute 0.33 in place of 0.5

General formular for thread depth;

d = fp x cot(a) = K/n

where
d = depth
f = form factor  UNC-metric = 3/8 5/16, Whitworth = 1/3, BA = 0.264
p = pitch
a = 1/2 inclued angle
n = Tpi
k = depth x p   UNC-metric = 0.649519,0.5412658 Whitworth = 0.64037, BA = 0.6000

 scratch.gif?


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## Maryak (Dec 10, 2011)

Oops, yes 1/3p is correct Old fingers and even older eyes :

Best Regards
Bob


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## tel (Dec 10, 2011)

I just pulled those out of your original post Bez,



> I can also extrapolate from major/minor diameter charts that for;
> 
> Whitworth k = 0.64         and for,
> 
> ...



Didn't check them against anything.


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## tel (Dec 10, 2011)

The actual numbers are;

Whitworth (and BSF) d = Actual Depth = 0.640327 x P

Metric            d = Actual Depth = 0.541266 x P

UN (coarse and fine) d = Actual Depth = 0.541266 x P

BA             d = Actual Depth = 0.60000 x P

ME             d = Actual Depth = 0.640327 x P

... might be worth getting tattooed on the inside of our eyelids!


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## Maryak (Dec 10, 2011)

tel  said:
			
		

> The actual numbers are;
> UN (coarse and fine) d = Actual Depth = 0.541266 x P



tel, I think the above is for internal threads

external threads are 0.61343p

It has something to do with where the radii, (crests), versus the flats are on internal v external threads.

Makes you wonder who sits down and adds all this, to me, unnecessary complication. I mean at what tolerance do they change/reshape the wheel on a thread grinder or the roller on a thread roller??

Best Regards
Bob


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## tel (Dec 11, 2011)

You could be right mate, but the book I have doesn't distinguish between internal and external, just sez 0.541266 x P

You will notice, however, that this is the same figure given for metric threads and, given that they are both 60° threads that makes sense.

Lets have a look - depth for a 1/4" thread with my figure is 0.0270633

with your figure it's                             0.0306715

... don't figure I"m gonna get in a fist fight over 0.003" on a coarse thread like that!


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## marcel (Dec 11, 2011)

hay

look her http://www.britishfasteners.com/threads/unf.html  :








Marcel


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## bezalel2000 (Dec 11, 2011)

tel  said:
			
		

> The actual numbers are;
> 
> snip/snip
> ... might be worth getting tattooed on the inside of our eyelids!



It would save counting sheep 

0.61344p, and 0.54127P   

Now theres 2 numbers I haven't seen before I thought we were using 0.649519 :wall: which was derived from 3/8*cot(30)

but 0.54127 = 5/16*cot(30) 

 0.61344P is depth of cut for the screw and

0.54127P is depth of cut for the nut 

I think its time to drop the maths and get my Eyelids tatooed  :big:


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