How to calculate machining angle 20 MOA taper

J

J. Valentine

Guest
How do I calculate the machining angle for a 20 moa taper.
Over a 6 inch long rail .
Using a sinebar program I get .035 stack height over 6 inch .
Angle of .33 degrees
Does this sound right?
 
Using small angle shortcut method

I think you have it right.

20 MOA is 1/3 degree.

For 1/3 degree rise at 6"----(1/3) X (pi/180) X 6 = .034907" = .035"

A. Weldy
 
Thanks Boyd and Lucky Shooter for the quick replies.
.035 seemed like a lot but I guess not.
Lucky shooter could you explain that math a bit more as I am weak on understanding math.
 
John, do it as a proportion:

1 MOA is 1.047" at 100 yards, 20 MOA is 20.94".

6 inches is 1/6 of a yard, so the rise for a 6" rail is 20.94/600".

Sound any better worked out that way?

John
 
A good reference is the sine tables in machinerys handbook.

Chuck
 
J. Valentine said:
How do I calculate the machining angle for a 20 moa taper.
Over a 6 inch long rail .
Using a sinebar program I get .035 stack height over 6 inch .
Angle of .33 degrees
Does this sound right?
Click to expand...

These new digital angle finders are really useful for setting angles like this, once you have determined the degree setting you want to use. I have one I got for about $40 that's accurate to 1/10 degree. I had to match a very tapered section of barrel to a scope mount I was making out of Picatinny blank. I used my angle finder to level the barrel, measure the taper and then set up the blank in my milling machine. It came out perfect, both with my collimator and later on paper.
 
Because the ratios of the sides of right triangles can be used in many useful ways, we have named them. The ratio, expressed as a decimal fraction, of the length of the side opposite an angle, divided by the length of the hypotenuse (the longest side of a right triangle) is called the sine of the the angle.

Before scientific calculators, we used printed trig. (trigonometry) tables to determine what the sine of a particular angle was. Now all we have to do is enter the angle in a scientific calculator and push the "sin" button.

Once we have the sine of a particular angle, we can use what we do know to calculate what we do not.

Since we do know that your sine bar, that takes the position of the hypotenuse in a right triangle ( a triangle that has a 90 degree angle) is 6", we can say that X (the number that we are solving the equation for) divided by 6 equals the sine of the angle.

There are 60 minutes in a degree; 20 minutes may be expressed as a third of a degree, or .33 degree (rounded).

Going back to our scientific calculator and entering .33 and hitting the sin key gives us the sine of the angle as .0058 (rounded).

If we then multiply both sides of the equation by 6, we get x on one side and six times .0058 on the other. six times .0058 equals .0348, which rounds to .035.

I wish that I could use a white board to explain this. It is harder to understand as a narrative.
 
Last edited:
John Kielly said:
John, do it as a proportion:

1 MOA is 1.047" at 100 yards, 20 MOA is 20.94".

6 inches is 1/6 of a yard, so the rise for a 6" rail is 20.94/600".

Sound any better worked out that way?

John
Click to expand...

No I can't work that out I get 579.96 which means nothing to me.
I have worked out the math from Lucky Shooter OK and it is making sense after a bit of head scratching. Thanks anyway.
 
Boyd Allen said:
Because the ratios of the sides of right triangles can be used in many useful ways, we have named them. The ratio, expressed as a decimal fraction, of the length of the side opposite an angle, divided by the length of the hypotenuse (the longest side of a right triangle) is called the sine of the the angle.

Before scientific calculators, we used printed trig. (trigonometry) tables to determine what the sine of a particular angle was. Now all we have to do is enter the angle in a scientific calculator and push the "sin" button.

Once we have the sine of a particular angle, we can use what we do know to calculate what we do not.

Since we do know that your sine bar, that takes the position of the hypotenuse in a right triangle ( a triangle that has a 90 degree angle) is 6", we can say that X (the number that we are solving the equation for) divided by 6 equals the sine of the angle.

There are 60 minutes in a degree; 20 minutes may be expressed as a third of a degree, or .33 degree (rounded).

Going back to our scientific calculator and entering .33 and hitting the sin key gives us the sine of the angle as .0058 (rounded).

If we then multiply both sides of the equation by 6, we get x on one side and six times .0058 on the other. six times .0058 equals .0348, which rounds to .035.

I wish that I could use a white board to explain this. It is harder to understand as a narrative.
Click to expand...

I understand how to use my sinebar with a taper and stack height calculating program . However outside of that I am very dumb on math in general.
I am a powerful observer and have rock crushing logic but math has always been difficult.
I sort of understand some of what you are saying .
I will have to study it for some time to understand it better.
Thanks Boyd for the kind effort .
 
Boyd Allen said:
20.94/600 means 20.95 divided by 600. If you do that, you will arive at the same place that he did.
Click to expand...

I must have been hitting the wrong button or something because it is right now as you say. Ok that looks like a good short cut.
 
Last edited by a moderator:
John Kielly said:
John, do it as a proportion:

1 MOA is 1.047" at 100 yards, 20 MOA is 20.94".

6 inches is 1/6 of a yard, so the rise for a 6" rail is 20.94/600".

Sound any better worked out that way?

John
Click to expand...

Thanks John I get it now , Thats a good short cut way , I was having some finger ( brain ) malfunctions or something .
 
Last edited by a moderator:
RCE1 said:
These new digital angle finders are really useful for setting angles like this, once you have determined the degree setting you want to use. I have one I got for about $40 that's accurate to 1/10 degree. I had to match a very tapered section of barrel to a scope mount I was making out of Picatinny blank. I used my angle finder to level the barrel, measure the taper and then set up the blank in my milling machine. It came out perfect, both with my collimator and later on paper.
Click to expand...

That is another good idea for me to have on hand . I have built a sine bar device for setting short tapers on the lathe and have one for the surface plate and understand the way they are used but not the math principles very well.
What brand and model angle finder do you have?
 
Last edited by a moderator:
OK I have played with the math and studied the whole thread quite a bit.
I want to say that the response to my question has been excellent for several reasons.
I/ Lucky Shooter gave me that math answer.
2/ John Kielly rearranged it in a way that let me understand Lucky Shooters math better.
3/ Boyd explained the principles of the sine function so I can see why the math works.
4/ Chuck and RCE1 gave me alternatives.
Just excellent . I am very greatful as I really suffer in this area at times.
Although since the internet I am getting better at math .
If I had a high school teacher as good as you blokes are , I would not be so dumb now . My math teacher for 3 consecutive years was so out of it all the time that he put his head through a closed window by mistake . He was so lucky he never cut his throat.
90% in his class failed math every year but it took three years to sack him.
The poor students got forgotten about and just put down as dummies untill he put his head through the window and the headmaster had to explain why.
He was drunk and or high all the time.
Hope that bast*rd died a slow painful death.
 
Last edited by a moderator:
J. Valentine----late reply

Sorry to take so long to get back to you.

Thanks to Boyd for his explanation of the math.

You claim a weakness in math so I’ll skip that part and give you a short cut formula to use under the conditions of small angles.

To calculate the build-up:

Build-up = angle X pi / 180 X bar length
Your angle = 20 MOA or 1/3 degree.
Pi = 3.14159. Your bar lengh = 6”.

Build up = 1/3 X 3.14159 /180 X 6 = .034907” = .035”

Your calculated build-up----using your 6” bar----will be within .0005” of a true calculation for angles under about 2 degrees and will be within .001” for angles under about 2.5 degrees. The smaller the angle, the closer the calculation. Note that you don’t need a scientific calculator----a cheap 4-function job will work, again, for small angles only.

There are a lot of ways to skin this cat and this is only one of them. Don’t forget-----small angles only.

Let me know if you need more.

A. Weldy
 
J. Valentine said:
That is another good idea for me to have on hand . I have built a sine bar device for setting short tapers on the lathe and have one for the surface plate and understand the way they are used but not the math principles very well.
What brand and model angle finder do you have?
Click to expand...

The one I bought is marked Wixey. I bought it from a Woodcraft. They sell them for setting saw angles, which I imagine they are quite useful for. I have also seem them in some metalworking sites as well, although under a different brand.
 
RCE1 said:
The one I bought is marked Wixey. I bought it from a Woodcraft. They sell them for setting saw angles, which I imagine they are quite useful for. I have also seem them in some metalworking sites as well, although under a different brand.
Click to expand...

OK thanks for that . I found the Wixey digital angle gauge and I now see what kind of tool it is.
 
Lucky Shooter said:
Sorry to take so long to get back to you.

Thanks to Boyd for his explanation of the math.

You claim a weakness in math so I’ll skip that part and give you a short cut formula to use under the conditions of small angles.

To calculate the build-up:

Build-up = angle X pi / 180 X bar length
Your angle = 20 MOA or 1/3 degree.
Pi = 3.14159. Your bar lengh = 6”.

Build up = 1/3 X 3.14159 /180 X 6 = .034907” = .035”

Your calculated build-up----using your 6” bar----will be within .0005” of a true calculation for angles under about 2 degrees and will be within .001” for angles under about 2.5 degrees. The smaller the angle, the closer the calculation. Note that you don’t need a scientific calculator----a cheap 4-function job will work, again, for small angles only.

There are a lot of ways to skin this cat and this is only one of them. Don’t forget-----small angles only.

Let me know if you need more.

A. Weldy
Click to expand...

I have broken the equasion down and layed it out in a word document so I don't forget how to do it. Because sure as shoot'n I will forget how to do it in 6 months time. Also added John Keillys method and Boyds explanation .
I am quite pleased with the information in this thread every single post was of value. Thankyou everyone .
 
You are quite welcome. The fact that you have taken the step of studying the various responses and summarizing them in your own words, so that you can refresh your memory at a later date, speaks well of your thoroughness and attention to detail. Helping someone who "listens" so carefully is a real pleasure.
 
You must log in or register to reply here.
Back
Top