Don,

If you read the articles on our club web page, you would have encountered this one that I wrote on that very subject.

Like most folks who thread on the lathe, I have a fishtail gauge (also called a

center gauge) which I use to ensure that the thread cutting tool is

perpendicular to the work.

On said gauge (and most others that I've seen) is a set of numbers labeled

"double depth of sharp thread". Specifically, the numbers on mine are those

given in columns A (tpi) and B (double depth of sharp thread) in the chart

below. I've always guessed that these numbers were somehow useful in deciding

how much to feed in when cutting a thread but I never took the time to sort out

how to use them. (For me, it's always been easier to draw a picture of the

thread and derive the depth I need using mathematics.)

A couple of questions at the meeting made me decide to puzzle out, once and for

all, what those numbers really are and how to make use of them.

Mathematically, the height of a thread, measured perpendicular to the thread

axis from sharp root to sharp crest is given by the following equation.

h = .5*pitch/tan(30)

where:

h = height of thread

pitch = 1/tpi

The little program I wrote prints out two times 'h' in column C in the table

below. As you can see, 2*h agrees perfectly with the numbers printed on the

fishtail gauge.

So the numbers on the gauge are indeed as described - the "double depth of

sharp thread".

So now the question becomes, "Why are those numbers on the fishtail gauge?"

Those numbers aren't particularly useful when cutting the thread. Most of the

time the question is, "How much do I need to feed in the compound when it is

set to angle 'ca' (compound angle)?" Mathematically, the answer to that

question is:

cin = h/cos(ca)

where:

cin = compound infeed

I've printed out cin for ca=30 deg in column D. For this case, we have:

cin = .5*pitch/[tan(30)*cos(30)] = .5*pitch/sin(30) = .5*pitch/.5 = pitch

and you'll note that the numbers in column D are exactly equal to the pitch of

the thread with tpi as given in column A.

So, the bottom line here is that I still don't know why those numbers are

there. Perhaps an old school machinist can explain how to use them but I

don't see any immediate value to them. (I can't imagine a machinist

multiplying the number in column B by .5/cos(ca) to get the compound feed

depth he needs.) If you didn't angle the compound at all when cutting threads

(i.e., feed straight in with the cross feed) and your crossfeed was calibrated

in diameter reduction (a .001 feed reduces diameter by .001), then the numbers

in column B would be your infeed to cut that thread. But what competent

machinist wouldn't angle the compound?

I don't know the answer but I do know this...I'm going to continue to ignore

the numbers on my fishtail gauge and base my calculations on what I understand.

A B C D

4 0.433 0.433 0.250

5 0.346 0.346 0.200

6 0.289 0.289 0.167

7 0.247 0.247 0.143

8 0.217 0.217 0.125

9 0.192 0.192 0.111

10 0.173 0.173 0.100

11 0.157 0.157 0.091

12 0.144 0.144 0.083

14 0.124 0.124 0.071

16 0.108 0.108 0.062

18 0.096 0.096 0.056

20 0.087 0.087 0.050

22 0.079 0.079 0.045

24 0.072 0.072 0.042

26 0.067 0.067 0.038