View Full Version : How to calculate machining angle 20 MOA taper

J. Valentine

02-14-2010, 12:06 AM

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?

Boyd Allen

02-14-2010, 12:51 AM

yes

Lucky Shooter

02-14-2010, 01:09 AM

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

J. Valentine

02-14-2010, 02:31 AM

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 Kielly

02-14-2010, 03:15 AM

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

chuck furniss

02-14-2010, 08:48 AM

A good reference is the sine tables in machinerys handbook.

Chuck

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?

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.

Boyd Allen

02-14-2010, 12:36 PM

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.

J. Valentine

02-14-2010, 04:15 PM

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

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

02-14-2010, 04:23 PM

20.94/600 means 20.95 divided by 600. If you do that, you will arive at the same place that he did.

J. Valentine

02-14-2010, 04:25 PM

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.

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 .

J. Valentine

02-14-2010, 04:28 PM

20.94/600 means 20.95 divided by 600. If you do that, you will arive at the same place that he did.

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.

J. Valentine

02-14-2010, 04:37 PM

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

Thanks John I get it now , Thats a good short cut way , I was having some finger ( brain ) malfunctions or something .

J. Valentine

02-14-2010, 04:43 PM

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.

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?

J. Valentine

02-14-2010, 08:49 PM

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.

Lucky Shooter

02-14-2010, 09:00 PM

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

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?

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.

J. Valentine

02-15-2010, 12:52 AM

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.

OK thanks for that . I found the Wixey digital angle gauge and I now see what kind of tool it is.

J. Valentine

02-15-2010, 01:01 AM

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

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 .

Boyd Allen

02-15-2010, 01:11 AM

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.

J. Valentine

02-15-2010, 03:57 AM

Thankyou for making it very easy to listen . I tend to freeze up when confronted by complicated math . It is a hang over from my very bad experiences at school. I think it happened again right here when I tried to work out John Kiellys simple easy method and I got that stupid result .

Something dislexic is happening and I think I see the wrong numbers or something . I can't explain it really. When I tried it again very slowly it was perfect. I actually tried many times to recreate that wrong answer and could not get anything like it.

How the F*ck could I screw up 20.94 / 600 but I did totally , the first time.

I know it happens because I used to see it on math exams that I got back after marking. Later when the stress is gone and I sit down and look at the mistakes I can do the sum correctly. It has ruined my life really because math is so important.

John Kielly

02-15-2010, 05:50 AM

Hey, you published that elegant method of adjusting the Lee collet die. The rest is floss.

Boyd Allen

02-15-2010, 10:30 AM

Math anxiety is fairly common. That is why it is so important that beginning students get as much help and practice as is needed to feel confident in the subject, early on. There is a wide range in the amount of work it takes for students to master the subject, and schools can't customize their curriculum to the degree needed to overcome the problem. The trick is extra work early on.

In the case of older students who have issues at a level above the basics, even though they know their math facts well, spending time on how problems are approached and viewed can be productive. Developing a sound plan before beginning calculations is the key.

phantom496

02-15-2010, 04:17 PM

Anyone that can multiply and divide can do Trig. at least that is what a Tool Design Teacher once told me. The one thing that opened the trig door to me was so/sa= Tan. The Side Opposite and the Side Adjacent will move and that is the confusing part to most people starting out doing Trig. . . depending on which angle you are looking for. If you hit the wrong angle and get some really oversize numbers - hit the inverse function and you will most likely have the correct answer.

I used to pick up a bunch of Trig Tables at Machine Shows and give them to the guys in the shop for references, to double check their calculators with - :eek:. If you look in a trig function book and want 20' of angle it will show you .00582 under the Sine of the angle, and if you use a 6" sine bar . . just multiply that by 6.00 and you will come up with the .03492, put that under a 6" sine bar and you have your 20' of angle, or a #65 (.035) drill blank.

My HP15 does it a little different than most calculators, RPN gives a different aspect to working the problem. If I want 20' of a degree, I push the 0.2 and hit the f-degree and get .33333 hit the SIN and get .005818 multiply that by 6. and get the .034906 . . and with the JOB Blocks that is what goes under the 6" sine bar. . .

But the easy way to do trig is to start out with the SO/SA=TAN and all will come together if you practice with it. Being a Mold maker for years you get really handy with TRIG. . everything is an angle . . there is nothing straight in molds . . :o

I had the same problem with math teachers, they were more interested in flirting with the girls in the class than they were in teaching the subject. Some people don't catch on to math as well as others, and I was one of them that had a hard time with it. It took me years of night school and lunch times working with the numbers to get a good grasp on it. One of my teachers had a great way of simplifying it - that equation above was the answer for me, once I had that the SO & SA were movable - Trig was easy from there on out . . And I still keep a Trig Function book handy. . just to unwind the mind with at times. . .:rolleyes:

MColeman

02-15-2010, 07:11 PM

I am a powerful observer and have rock crushing logic but math has always been difficult.

You and me both! When it comes to math I am a total idiot.

brian roberts

02-15-2010, 08:25 PM

24 others in this class, if you don't 'get it', you'll just have to sit there, because I don't have the time to hold up the class for YOU!" :o:confused: And, another one bites the dust...... Amazing how this post after alllll those years, still brings back those painful memories.

J. Valentine

02-16-2010, 02:42 AM

Yes I agree something that affects you forever is hard to forget.

So I now understand the small angle calculation and can switch it around for different amounts of MOA .

My next logical question is .

What do you use for larger angles over 2 degrees?

I think I am going to regret this but what the hell.

John Kielly

02-16-2010, 03:36 AM

Financial incentive to a competent practicioner?

Boyd Allen

02-16-2010, 10:31 AM

Sine of the angle times sine bar length equals stack height for that angle.

Convert the angle to degrees and/or decimal degrees. For example 31 2/3 is 31.667, 40 MOA becomes .667.

Enter the number into a scientific calculator

Push the SIN key

Push the X key (for multiplication)

Enter the length of your sine bar, in inches(not the OAL, but the specified length, from where the round under one end touches the surface you are working on to where the one at the other end touches.). In the previous example, the length was 6"

Push the = button.

The answer is your stack height in inches.

This is for angles less than 90 degrees.

J. Valentine

02-16-2010, 09:05 PM

Ok thanks Boyd. It's the normal sine function that I have in my stack height program anyway.

However programs break down so I would like to understand it manualy also.

How do I work out this part . I have difficulty with fractions.

" Convert the angle to degrees and/or decimal degrees. For example 31 2/3 is 31.667, 40 MOA becomes .667. "

pbike

02-16-2010, 11:36 PM

If you're using a 6" Kurt Vise as I am, and your stacking your shim stock under the one side of the vise at the bolt down ears you'll notice that the ears aren't 6 inches apart. You may want to refigure to get a closer value to the actual spacing of the bolts.

Paul

AJ300MAG

02-17-2010, 12:17 AM

Why would you want to abuse a vise like that??? :eek:

I've got a fixture mock-up of a Remington long action. There's two dowel pins precisionally located sticking out the side spaced exactly 6" apart. I machine the bottom of the rail, bolt it to the fixture. I place shim between the dowel pins and the vise jaw to give me the correct MOA angle and then machine the top of the rail.

That's why we don't let millwrongs play with our precision equipment...

:D

J. Valentine

02-17-2010, 02:51 AM

I new it could not last . It was only a matter of time before insults started to fly.

If you can respond Boyd please email or PM me as I am out of here.

chuck furniss

02-17-2010, 08:03 AM

Check your e-mail.

Chuck.

AJ300MAG

02-17-2010, 10:18 AM

I new it could not last . It was only a matter of time before insults started to fly.

Insults???? NO.

I've known Paul and have shot with him once or twice. Good natured ribbing. ;)

zp3design

02-17-2010, 04:21 PM

J. Valentine,

In this article (link below) I attempt to show how to not only determine just how much correction you need in your scope base but how to set up and do the math for those not trigonometry inclined.

http://www.longrangehunting.com/articles/scope-base-angle-1.php

Hope you find this helpful.

Bob T.

Lucky Shooter

02-17-2010, 06:57 PM

You have a PM.

A. Weldy

pbike

02-17-2010, 09:12 PM

Why would you want to abuse a vise like that??? :eek:

I've got a fixture mock-up of a Remington long action. There's two dowel pins precisionally located sticking out the side spaced exactly 6" apart. I machine the bottom of the rail, bolt it to the fixture. I place shim between the dowel pins and the vise jaw to give me the correct MOA angle and then machine the top of the rail.

That's why we don't let millwrongs play with our precision equipment...

:D

Great Al,

Ok Smartiepants. What do you do if you're starting with a blank section of Rail like brownells sell and machining the bottom of the rail to fit the top of your action with 20 or 15 moa as needed? I have cut my soft jaws to hold the rail upside down and cut across the top (bottom)... but this method would require seperate jaws for each moa offset.

Paul

AJ300MAG

02-18-2010, 09:08 AM

Paul they make a sine plate that has "T" slots for bolting a vise on, or you can make a fixture to hold the rail to machine the bottom.

Last thing I'd do (meaning NEVER) is try warping the bottom of one of my vises OR putting divits into to top of a mill table by bolting something to it that isn't clean and flat. Thats why we stone off the table and vise bottom before bolting down a vise... every time.

Bob Kingsbury

02-18-2010, 10:21 AM

A jig can be made to hold damn near anything. Machine the angle

into the jig. Its completely repeatable and simple to set up at

a moments notice. You can make a fixture/ jig as ornate as you want,

just think it thru ahead of time. No shims under the vise please

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