[HELP] Cutting A Taper On Lathe

[Cross Slide]

I need some help. 
I’m attempting to cut a taper on my lathe by swiveling the compound. 
The math has me confused at what angle to set my compound at. 
D=0.693
d=0.663
Angle is 0.30
1/2 of A=0.15
L=1.000
Can someone help me figure this out?
I have the Engineers Black Book. BUT.
I’m lost trying to figure out Tangents

Who knew my high school math teacher was going to be right!!!

Thanks
Cross Slide
Trevor

[EdK]

Those dimensions don't give you a .30 degree angle. More like .86 degrees.

Ed

[Hawkeye]

Just guessing, but it looks like a total included angle of 1.719 degrees, or a setting of 0.8596 degrees off axis.

[Vinny]

Have you seen this video? https://www.youtube.com/watch?v=YCllVu4K738

[Hopefuldave]

Tangent is pretty simple, it's how far you need to move the cross-slide for every inch of carriage travel, for the *half angle* (you're cutting the same amount off front and back of the workpiece). That 0.3 degree taper is *very* fine, I'll run through how to measure your setup to get the topslide set to the right angle BUT I think you may have confused taper/inch with angle - the D/d and L you give suggest another angle entirely, 1.78 degrees included / 0.859 per side?

So for your 0.30 degrees Included Angle (what you would measure with e.g. a vernier protractor, if you could hold it all in place accurately for long enough to read it) you need the tangent of 0.15 look it up and it says "0.002618" - your tool needs to move this much in every inch of carriage travel, now this is awkward to set up as you can't use the topslide (compound) dial measurements as it's no longer moving along the lathe axis (you swivelled it, remember?) so either you need two indicators mounted to the topslide (gets crowded), one against the work (which needs to be very accurately cylindrical, on centre and finely-finished to make the following steps accurate - but doesn't need to be the actual workpiece, if you're a Scrounger like me you use one of the guide rods found in the bigger inkjet printers - they meet all the requirements and once dead (or empty, you seen the ripoff prices for a few cc of ink????) the printers are free on freecycle etc. :) ) to measure the tool travel towards the work, one from the topslide to a stop or the chuck face to measure travel towards the headstock - the desired tangent of the angle will be the change on the work indicator divided by the travel towards the headstock (an inch is good, easy calculation dividing by 1 :) BUT more travel and multiplying the tangent by it will be more accurate - see above, for your angle a very small number of thou" inward/outward movement with lots of digits you'll end up guessing).

OR, probably better if you're using the topslide anyway, just one indicator topslide to workpiece and use the *sine* of the angle - this is the movement of the topslide towards/away from the work for each inch of topslide travel: for your half-angle of 0.15 degrees, the sine is the same value, 0.002618 !!only true for very small angles!! so wind the topslide an inch and you're looking for 0.002618" indicator movement - hard to get that accurately, so again you can scale up, e.g. move the topslide 3" and look for 0.0078" on the dial.

If I was right earlier, and you confused taper with angle, use the second method, and adjust the compound for 0.015" (technically 0.01499 but that would be very hard to get accurately with tools we mere mortals can afford!) inward/outward movement per inch of topslide travel - getting easier to measure now :)

I hope this helps, rather than confuses!

Dave H. (the other one)