Gallery, Projects and General > How do I??
Math for machinist tapers...
andyf:
Being a bit of a :scratch: duffer when it comes to trig, I find this calculator quite useful: http://www.cleavebooks.co.uk/scol/calrtri.htm (if that offers you options, go for Right Angled Triangles).
Put sides a and b in as 3.5 and 24 (it doesn't matter which is which) and it gives you two angles, the one you want being 8.3 degrees. Then if you have an amazing protractor and even more amazing eyesight, crank it up to (say) 7 significant figures and that becomes 8.297145 degrees. The included angle will be double that, of course.
The same website offers other useful geometry in its index:
http://www.cleavebooks.co.uk/scol/index.htm
Andy
AdeV:
--- Quote from: mklotz on February 07, 2013, 05:48:33 PM ---If the taper is 7" of diameter in 24" then the INCLUDED taper angle is...
arctan (7/24) = 16.2602... deg
and the taper HALF ANGLE is half this value = 8.130... deg.
Note that this is NOT the same as:
arctan (7/48) = 8.297 deg.
Mathematically,
arctan (x/2) is never equal to 0.5*arctan (x)
--- End quote ---
Oops, you're right of course, my bad.
I think I now understand why I have been utterly unable to cut the taper for my lathe headstock... (see posts I made about 3 years ago).
BillTodd:
Do not convert ! (it's much easier)
Tapers that are specified in inches per foot are best set-up using a displacement and length. Converting to angle will always produce an error.
If you are trying to cut the taper with a top-slide, either set the angle with a sine-bar* or dial in on an existing taper.
Bill
BTW - BT40, Int40 , Int30, BT30, BAT50 etc. etc. all use the same 3 1/2" per foot (on diameter), but the drive end will vary (some are designed for auto changers)
* if you are using a 5" sinebar and want a 3.5"/' taper, the spacer block should be 3.5/2 * 5/12 = 0.7292 (OK this produces a tiny error ;))
Pete.:
If I hadn't read any of this I would have assumed that 7/24 was a ratio. To machine it I would use two dial gauges, one to measure compound slide travel and one against and perpendicular to the work. I'd keep adjusting the angle until cranking the compound 24mm moved the dial against the work 3.5mm
RussellT:
This may confuse you - but that's OK because at the moment it's just me that's confused.
If the diameter tapers by 7 units in 24, then the radius must taper by 7 units in 48. So if you're looking to set an angle on a top slide to cut a taper then surely the angle you need is arctan(7/48). I think it's difficult to use trig on the 7/24 as there is a shortage of right angles and for the reasons given by Marv it's not the same as half arctan(7/24)
Russell
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