Finding pitch in degrees with a rise over run type formula

Someone already suggested it, but here's a good online lesson on Basic Trigonometry.

https://www.khanacademy.org/math/tr...ometry/basic_trig_ratios/v/basic-trigonometry

Everything is explained at the beginners level like it should at least have been taught in every High School math class.

It always makes it easier for one to draw his triangle first in order to have a better visual idea of the relevant dimensions involved in relation to his actual problem at hand.

You'd still get lost in solving a machining problem like a taper degree determination if you couldn't identify which of the triangle sides refer to which in the actual part being machined.


Note: The determination of the correct ratios between triangle sides that would correspond to a certain value in degrees requires a Trigonometry table or a Scientific Calculator.
The actual calculation involved is beyond the basics of trigonometry.
 
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Ray C said:
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?

With a calculator, calculate Tangent (7.125). It equals: 0.125. Now, you just find any two numbers that when multiplied 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 = 0.125/3 which equals: 0.417. This means that if you move in 3" in the horizontal direction, the DI needle should deflect 0.417".

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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I did the work in parentheses first. rise overrun which gives me 0.125. That is the tangent. That is as far as I know how to get. How do I get from rise over run to pitch in degrees? I can get a scientific calculator from the kids. Lord knows I've bought enough of them. I also have 23rd edition M H.
 
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LEEQ said:
I did the work in parentheses first. rise overrun which gives me 0.125. That is the tangent. That is as far as I know how to get. How do I get from rise over run to pitch in degrees? I can get a scientific calculator from the kids. Lord knows I've bought enough of them. I also have 23rd edition M H.
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Refer to my first post. Its all there. Once you have the tan, you use a calculator or tables to find the arctan (which is 7.125 degrees).
 
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Once you get a scientific calculator pryed away from one of the kids, enter 0.125 then, find the arctan button. It may be shown as ATAN, Arctan or TAN[SUP]-1.

[/SUP]As someone else mentioned, Tan[SUP]-1[/SUP] does not mean the reciprocal of the number, it's just a different way of writing arctan. When you press the arctan button, that should give you 7.125. On some calculators, you may need to press a shift key to get the arctan function.


Ray

PS. I accidentally hit the Edit button of your post when I meant to press "Reply with Quote". As a moderator, I'm able to edit other people's posts. It was an accident and I did not change anything in your post.



LEEQ said:
I did the work in parentheses first. rise overrun which gives me 0.125. That is the tangent. That is as far as I know how to get. How do I get from rise over run to pitch in degrees? I can get a scientific calculator from the kids. Lord knows I've bought enough of them. I also have 23rd edition M H.
Click to expand...
 
frank r said:
Refer to my first post. Its all there. Once you have the tan, you use a calculator or tables to find the arctan (which is 7.125 degrees).
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how would I use a calculator instead of tables? how do I do the work?
 
Ray C said:
Once you get a scientific calculator pryed away from one of the kids, enter 0.125 then, find the arctan button. It may be shown as ATAN, Arctan or TAN[SUP]-1.

[/SUP]As someone else mentioned, Tan[SUP]-1[/SUP] does not mean the reciprocal of the number, it's just a different way of writing arctan. When you press the arctan button, that should give you 7.125. On some calculators, you may need to press a shift key to get the arctan function.


Ray

PS. I accidentally hit the Edit button of your post when I meant to press "Reply with Quote". As a moderator, I'm able to edit other people's posts. It was an accident and I did not change anything in your post.
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Ok, just find tangent. rise over run = tan. Then hit arctan to get degrees.
Ok, So if I enter the number 7.125 and hit tangent it will spit out 0.125? Then if I move the table over .500, I need to move it .250 in to be at the7.125 angle?
as you said A x B = tan. A being .500, divide tan .125 by A getting .250 for B. I think that gets me through the problem without charts. I need a good calculator and follow everything lined out right here in this post between the two of us, right?
 
I'm sorry but I made a little error before but, you have the right idea. Here is the correction.

Tan(7.125) is 0.125.

Rise/Run = 0.125 therefore, Rise = 0.125 x Run. If you want the Run to be 0.500 then, Rise will be 0.0625.

Proof:

0.0625/0.500 = 0.125 It works.

Also, on your calculator, if you take Arctan(0.125), you will get 7.125

... I'm sorry, in my earlier post I said the product of two numbers and I meant the quotient which is the result of dividing two numbers. Truth be know, I've had a splitting headache all darn day and my head was not in the right place.

Ray









LEEQ said:
Ok, just find tangent. rise over run = tan. Then hit arctan to get degrees.
Ok, So if I enter the number 7.125 and hit tangent it will spit out 0.125? Then if I move the table over .500, I need to move it .250 in to be at the7.125 angle?
as you said A x B = tan. A being .500, divide tan .125 by A getting .250 for B. I think that gets me through the problem without charts. I need a good calculator and follow everything lined out right here in this post between the two of us, right?
Click to expand...
 
Ray C said:
I'm sorry but I made a little error before but, you have the right idea. Here is the correction.

Tan(7.125) is 0.125.

Rise/Run = 0.125 therefore, Rise = 0.125 x Run. If you want the Run to be 0.500 then, Rise will be 0.0625.

Proof:

0.0625/0.500 = 0.125 It works.

Also, on your calculator, if you take Arctan(0.125), you will get 7.125

... I'm sorry, in my earlier post I said the product of two numbers and I meant the quotient which is the result of dividing two numbers. Truth be know, I've had a splitting headache all darn day and my head was not in the right place.

Ray
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I think you did just awesome. I'm all straightened out with simple useful knowledge I can refer back to without taking college level math. That's just great. I appreciate everyone's help, but you made it simple enough for even me. I hope others get to benefit from the outcome of this thread, thanks.
 
LEEQ said:
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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I wrote a program for calculating solutions to triangles and a few other useful things around the shop.

http://www.dogcreek.ca/shopcalc/WorkshopCalulator.html
 
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