In designing things tapered, I find myself needing to do some
calculations. I thought I'd toss out the formulas I use.

There are four factors...

A = Angle of taper
L = Length of taper
DL = Larger diameter
DS = Smaller diameter

I started with this formula:

L * 2 * Tan(A) = DL - DS


Given any three of the four factors, the fourth is easily calculated
using one of the permutations...

L = (DL - DS) / (2 * Tan(A))

A = Arctan ((DL - DS) / (2 * L))

DL = 2 * L * Tan(A) + DS

DS = DL - (2 * L * Tan(A))


For example, a Morse Taper #2 has a large diameter of .700" and small
diameter of .572" over a distance of 2.500". Therefore, the angle
would be calculated as Arctan(.128/5) or 1.46645 degrees. Now if I
could just figure out how to scale my compound to nail that angle.

-Bruno

Bruno - one more thing to remember: I believe it is United States practice
to measure the angle as "included angle", whereas the European practice
defines the angle as measured from the centerline of turned parts. Thus, if
you use one formula and live in a different geographic region, you might
have an error of 100 percent. I've been there! Dave

"Bruno" wrote in message
...
In designing things tapered, I find myself needing to do some
calculations. I thought I'd toss out the formulas I use.

There are four factors...

A = Angle of taper
L = Length of taper
DL = Larger diameter
DS = Smaller diameter

I started with this formula:

L * 2 * Tan(A) = DL - DS


Given any three of the four factors, the fourth is easily calculated
using one of the permutations...

L = (DL - DS) / (2 * Tan(A))

A = Arctan ((DL - DS) / (2 * L))

DL = 2 * L * Tan(A) + DS

DS = DL - (2 * L * Tan(A))


For example, a Morse Taper #2 has a large diameter of .700" and small
diameter of .572" over a distance of 2.500". Therefore, the angle
would be calculated as Arctan(.128/5) or 1.46645 degrees. Now if I
could just figure out how to scale my compound to nail that angle.

-Bruno

Well, you could always mount a known good part and set up your compound with
a dial gage or even feeler gauges. Then all you have to do is remove it,
set up your stock and go.

Bruno wrote:
Now if I
could just figure out how to scale my compound to nail that angle.

On manual lathes that lack a taper attachment I use the following
procedure to accurately set the angle of the compound rest. First I
chuck up a good straight bar. Verify it is running true. Roughly set
your angle on the compound rest. Mount a dial indicator on the tool post
with the indicator tip resting on the bar. Move the compound rest by
stroking it an inch or two and then checking the deflection on the
indicator. Remember, the stroke of the compound is the hypotenuse.

"Footy" wrote in message
...
Well, you could always mount a known good part and set up your compound
with
a dial gage or even feeler gauges. Then all you have to do is remove it,
set up your stock and go.



Not if the angle is critical. There are too many variables to set angles
by that method, cutting tool height amongst them. One uses a sine plate or
sine bar and inspects the angle being produced and makes the necessary
adjustments to correct the inherent errors made in setup. .

Harold

" Now if I could just figure out how to scale my compound to nail that angle."

I just went thru that with an old live center that the former owner had tried
to turn down to the next morse size lower. I finished the OD by calculating
what the major & minor diameters would be over the total length of the piece,
roughed the od in on the lathe & finished by grinding between centers on the
surface grinder. Very easy to tweek angle between centers with the proper
setup. While doing that job, I realized for the first time that all the
different sizes of morse taper are not of consistant angles. This is also true
of jakobs& jarno. Learn something new everyday.