Thread dilemma

In order to make tap drill calculations the constant for a given thread needs to be on hand. the constant is just the ratio of the female thread height and the pitch.  While searching for the constant for the Unified thread form (UNC and UNF) I found that the most often cited was 1.299 or 1.3. On one of the on line calculators I found the constant was 1.08254 and now I have a problem only one can be correct, 1.08254 rang a bell from the mid 60s when I was writing tests in my apprenticeship while 1.299 is totally alien to me.
 
I started to search for information on thread forms so that I could verify one or the other constants. During this search I discovered that ISO has an inch thread standard that conforms exactly with unified thread form. I also discovered that ISO metric uses the same thread form as ISO inch threads. This means that the same constant works for unified, ISO inch and ISO metric.
 
The Unified, ISO inch and ISO metric thread form.   (A)NC and (A)NF is identical but without the rounded roots and are mechanically interchangeable. The same constant is required in all cases.
 
Source
http://en.wikipedia.org/wiki/File:ISO_and_UTS_Thread_Dimensions.svg
 
Interchangeability of Unified thread form and American National thread form.
 
Verification
http://www.ring-plug-thread-gages.com/ti-N-vs-UN.htm
 

 
Lets assume a 1/8 inch pitch.
(the height of an equilateral is found by base x 0.866)
 
H = P x 0.866 = 0.125 x 0.866 = 0.10825
Thread height = Height x 5 / 8 = 5 x 0.625 = 0.06765625
Constant = Thread height / Pitch x 2 = 0.06765625

 
(multiply by 2 because we need double depth of thread)
 
constant x 2 = 0.06765625 x 2 = 1.0825

Calculate the tapping size for 1 - 8 threads per inch with 75% thread contact.
One formula is Major Diameter - (Constant x Pitch x percent / 100)
 
1 - (1.0825 x 0.125 x 75 / 100) = 0.898515625   (nearest drill) = 29/32.
 
Calculate the thread contact for a 29/32 tap drill.
percent = ((Major diameter - Drill size) / (Constant x Pitch)) x 100
 
((1 - 0.90625) / (1.0825 x 0.125)) x 100 = 69.28%


Sellers thread (Franklin Institute) for USS, SAE and USF
 
Source
http://www.unionmillwright.com/2879.pdf
 
Verification
http://www.metalwebnews.org/mr-tools/screwthreads-gages.pdf
 
  
 
Again lets assume a 1/ 8 inch pitch.  (the height if an equilateral is found by base x 0.866)
 
Thread depth = Pitch x 0.649519 = 0.125 x 0.649519 = 0.081189875
Constant = Thread height / Pitch x 2 = 0.081189875 / 0.125 x 2 = 1.299038
(multiply by 2 because we need double depth of thread)

 
Calculate the tapping size for 1 - 8 TPI with 75% thread contact.
One formula is Major Diameter - (Constant x P x percent / 100)
 
1 - (1.299 x 0.125 x 75 / 100) = 0.8782151875 (nearest drill) = 7/8.
 
Calculate the thread contact for a 7/8 tap drill.
percent = ((Major diameter - Drill size) / (Constant x Pitch)) x 100
 
((1 - 0.875) / (1.299 x 0.125)) x 100 = 76.98%
 
It is evident that 1.0825 is the correct constant for Unified, ISO inch, ISO metric, (A)NC and (A)NF thread forms.
It is also evident that 1.299 is the correct constant for Sellers thread (Franklin Institute) for USS, SAE and USF thread forms.


The confusion is not just for inch thread, it exists with metric threads as well. Metric threads were mostly unified in 1898 by the International Congress for the standardization of screw threads at Zurich, which defined the new international metric thread standards as having the same profile as the Sellers thread, but with metric sizes. Consequently the constant for the Sellers thread form would apply.
 
Lets assume a 24 x 2 thread with 75% contact.
 
24 - (1.299 x 2 x 75 / 100) = 22.0515 (nearest drill) = 22 mm
 
And the percent contact with a 22mm drill
 
((24 - 22) / (1.299 x 2)) x 100 = 76.98%
 
The metric thread standard currently in use was adopted by ISO in 1947. The profile mirroring the Unified profile and use the same constant as the Unified thread form.

Lets assume a 24 x 2 thread with 75% contact on an ISO thread form.
 
24 - (1.0825 x 2 x 75 / 100) = 22.37625 (nearest drill) = 2.5 mm
 
The percent contact with a 22 mm drill is.
 
((24 - 22.5) / (1.0825 x 2)) x 100 = 69.29%



It appears that tap drill charts have not been updated as standard thread forms have been superseded. A case of ----- "we have always done it that way"? The other thing that comes to mind is that a USS or USF bolt will always fit on a (A)NC - UNC or  (A)NF  -  UNF nut. Also  a USS or USF nut with 75% thread contact will fit an (A)NC - UNC or (A)NF - UNF bolt. The same senario applies to ISO metric and the older international metric thread standard, diameter and pitch being equal.
 
When the Sellers thread form is used major diameter - pitch does give close to 75% thread contact but when the Unified or ISO thread form is used we get 92.38%. This also applies to the international metric thread standard and ISO metric. (France and Germany both used the international metric thread standard but the pitch differed for a given diameter thread. Not interchangable.)


Lathe cutting a Whitworth thread

The Whitworth thread with the rounded thread crest is akward to cut. Once the thread is cut to depth the thread crests must be rounded. If you have a die there is no problem. The correct way to round the thread crests is to use a thread chaser.
 


Toolpost mounted thread chaser, external and internal.
 

External hand chaser.

If you think about it, the rounded thread crests do not do much in the way of thread strength. Consider cutting the major diameter under size enough to eliminate the radiused crest. This is known as modified Whitworth. The crest radius is
 
0.137329 x Pitch.
 
With this in mind, when you select BSW and BSF as the thread the suggested major diameter is sized to give a modified Whitworth flat crested thread.