I saw a posting by Ray C with mention of finding pitch using rise over run . In this method you need to measure over a distance (run) and measuring the difference in pitch(rise) at that point. Having these numbers to input, what do I input them into to work towards an answer in degrees? Can I rearrange the formula to use desired pitch and one other input (rise or run) to give me the other figure? Thanks for any help. I would love to explore this further.
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Finding pitch in degrees with a rise over run type formula
- Thread starter LEEQ
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Machinery's Handbook 23rd Edition has two charts. One is " Rules for figuring tapers" The second table is "Tapers per foot and corresponding angles" Or you could use a section titled "Solutions for triangles" which uses trigonometry. Google found this-http://www.practicalmachinist.com/vb/general-archive/converting-ft-taper-into-degree-taper-156106/ or this from Starrett http://www.unionmillwright.com/2885.pdf
Hope this helps.
Hope this helps.
I'll have to check out that right triangle solution section. I am often overwhelmed with the vast amount of dry reading it takes me to figure if I'm even in the right place with the handbook. I also forgot to mention that rise and run have a friend named Arctan also at this party.
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A "rise" with "run" amount to find the degree of elevation is a simple Tangent formula relationship.
Tangent of an Angle = rise / run
1 unit of rise for every 1 unit of run is equivalent to the tangent of 45° (or 100% grade in road construction)
If two of the three unknowns are given you can solve for the third.
Tangent of an Angle = rise / run
1 unit of rise for every 1 unit of run is equivalent to the tangent of 45° (or 100% grade in road construction)
If two of the three unknowns are given you can solve for the third.
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The rise divided by the run is the tangent of the angle. You want to find the inverse tangent (or arctangent) of rise/run. Thus "angle = arctangent(rise/run)" and "rise/run = tangent(angle)". Your calculator can figure this for you. A machinist should know basic trigonometry. Khan Academy has a course, and there's lots of other stuff on the Web on the subject.
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Or if you want to cheat, or work some compound angles, there are online calculators, of course.
http://www.pdxtex.com/canoe/compound.htm
http://www.pdxtex.com/canoe/compound.htm
Divide rise by the run (=the tangent value). Then find that number under the TAN heading on this table:
http://www.industrialpress.com/ext/StaticPages/Handbook/TrigPages/mh_trig.asp#30
Once you find it, the equivalent degrees will be in the left column under Angle.
Notice the source of this table is the Machinery's Handbook.
http://www.industrialpress.com/ext/StaticPages/Handbook/TrigPages/mh_trig.asp#30
Once you find it, the equivalent degrees will be in the left column under Angle.
Notice the source of this table is the Machinery's Handbook.
So, no less confused. It seems as if some are saying I want tan and some arctan. I might need both. What I am hoping to accomplish is to learn how Ray C ran the calculations. I'm dreaming I can learn the formula and not need to use charts. I prefer to be able to scratch math out with pencil and paper. I then leave myself the process and examples in my notes. I can refer to these and remember how to figure things such as how to set up my rotary table for dividing. If I can get this process down, I can use it to do different angle set ups. I learn best through interaction and was hoping someone could lead me through this in terms vastly more simple than proper technical math terms. Explaining the proper terms so a simpleton( ie me) gets it would be great too. " the spindle DI gave me 0.025" the carriage moved 0.200". Arctan (0.025/0.200) = 7.125*." This shows the Problem as Ray layed it out.
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If there's some other example you'd like to review, let me know. If you were measuring the angle of the lip on the D1 spindle, it seems you got it right. The edge of the lip is not very wide so that's probably how much the needle deflected downward or upward when you moved the DI 0.2" horizontally. Therefore the rise (or drop depending on which way you were moving) was 0.025 and run was 0.200". Arctan (0.025/0.200) = 7.125*. That by the way, is the one-side angle. The included angle (the angle from the centerline) is 14.25* which takes into account both angles.
Now, lets turn it around... What happens if you only know the one-side angle and someone tells you it's 7.125*. What would be the rise over run?
EDIT: In the original post here, I mis-wrote something. What follows has been edited/corrected as not to cause anyone confusion. -ray
With a calculator, calculate Tangent (7.125). It equals: 0.125. Now, you just find any two numbers whose quotient equals 0.125. That is A / B = 0.125. Pick a number, any number... Let's say 3. Now substitute 3 for either A or B; I'll use A.
3 / B = 0.125". or, B = 3 x 0.125 which equals: 0.375. This means that if you move in 3" in the horizontal direction, the DI needle should deflect 0.375".
The trick of course, is to pick the first number in a range corresponding to the distances you're working with.
Does that help?
Ray
Now, lets turn it around... What happens if you only know the one-side angle and someone tells you it's 7.125*. What would be the rise over run?
EDIT: In the original post here, I mis-wrote something. What follows has been edited/corrected as not to cause anyone confusion. -ray
With a calculator, calculate Tangent (7.125). It equals: 0.125. Now, you just find any two numbers whose quotient equals 0.125. That is A / B = 0.125. Pick a number, any number... Let's say 3. Now substitute 3 for either A or B; I'll use A.
3 / B = 0.125". or, B = 3 x 0.125 which equals: 0.375. This means that if you move in 3" in the horizontal direction, the DI needle should deflect 0.375".
The trick of course, is to pick the first number in a range corresponding to the distances you're working with.
Does that help?
Ray
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You need both. It is not easy to do by hand. John Hasler's response above is correct. You need to use a calculator with an arctan (AKA: inverse tan) function to calculate them.
I just finished a pre-calculus course and we studied this topic. We also had to use a graphing calculator (about $100) to figure out our answers. If you don't have the calculator you can use the table.
tan 45 degrees = 1 (that is a rise of 1 divided by a run of 1) [the tangent will result in a number]
The arctan of 1 = 45 degrees [the arctan will result in a degree]
Note that inverse tan does not mean the reciprocal of tan (you can't just flip the rise over run and get the correct answer).
I just finished a pre-calculus course and we studied this topic. We also had to use a graphing calculator (about $100) to figure out our answers. If you don't have the calculator you can use the table.
tan 45 degrees = 1 (that is a rise of 1 divided by a run of 1) [the tangent will result in a number]
The arctan of 1 = 45 degrees [the arctan will result in a degree]
Note that inverse tan does not mean the reciprocal of tan (you can't just flip the rise over run and get the correct answer).