Converting in/ft taper into degree taper
I have to make several tapered spacers, one with a 2.364 in/ft taper, and the other with a 2.691 in/ft taper. As I do not have a taper attachement, and the holes are only 1" deep, so I plan to use a boring bar in the compound slide. As this is graduated in degrees, I need to convert inch/foot taper measurements to included angle taper measurements.
I googled for a conversion formula, but was unsuccessful. Can anyone assist?
You need Machinery's Handbook
Taper(inches per foot) = 24tan(half angle of taper)
You might benefit from a visual approach to solving your problem (and learn a little trig in the process )
Determine whether your angle is taper per side or taper of the included angle.
Fundamentally you have a right triangle problem to solve.
Let the length be the base and the adjacent side to the angle of interest of a right triangle, that is 1 ft or 12 inches. The opposite side of the right triangle is 1/2 of the diameter change or 2.364/2 = 1.182.
The tangent of an angle B is the ratio of the opposite to adjacent sides. Thus, 1.182/12 = tan B . There is another term called the arctan and this is the inverse of tan. So B = arctan 0.0985 . Using a calculator, or tables you can determine the angle.
From my HP 32S I get 5.63 deg. This is 1/2 half of the included angle of your taper. I believe your compound will be calibrated in degrees of its rotation and not in included angle. Thus, set your compound to 5.63 deg. It might be calibrated such that you need to use 90 - 5.63 .
Double check my calculations.
Taper is .017 per inch for 1 degree. Mach handbook lists constants for 5" sine bar. 1 deg is 0.08725. divide by 5 = .01745. Hope this helps. In the shop we just use .017 for most everything except the nitty gritty. This is taper per side.
And the other one is 90 - 6.398
Half way there
Now, how are you going to set the compound to the desired two decimal accuracy? Some call me Carlos.
Now we go back to not needing the trig, mount a dial indicator on the bed and tram the side of the cross slide until you have it set to .394 in per 2" of saddle movement (.4485 for the second taper). Or what ever ratio of the specified slope you have room to use.
+1 for Shimitup. When I have to set an angle specified in degrees closely, I have to trig it the other way in order to set the compound accurately. With your in/ft spec, it's already done for you.
Take the small dia from the large dia, divide by the length, look up the answer in the tan tables that gives you degrees. Half the answer, that is the setting of the top slide in degrees. If your cutting tool is not at center height it will alter the taper