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#### Cogsy

##### Well-Known Member
Staff member
Global Moderator
Trigonometry - all (most all) hand held calculators have trig functions. Tangent of 41 degrees = .869286. From there basic math. Then touch off the countersink on a suitable shim and plunge the hole for the countersink size needed. Handy for multiple holes for consistency.
Your drawing shows the depth as .0627" which will not result in a .225" dia. countersink.
As has been said, the math here is slightly mixed up. Using Bill's sketch, we do indeed want to find the dimension of 'a' and as it stands we know angle 'B' (41 degrees being 1/2 82 degrees) and side 'b' at 0.1125". Bill is also correct that we need to use tan(B), which is ~0.869. However, remember from SOH CAH TOA that tan is Opposite/Adjacent sides.

So therefore tan(B) = b/a
if we multiply both sides by 'a' we get 'a * tan(B) = b'
then divide both sides by tan(B) and we get 'a = b/tan(B)'
which means 'a = 0.1125/0.869 => a = 0.129'.

So touch off your cutter on the surface then plunge 0.129" and you should have the feature your drawing calls for.

#### willray

##### Well-Known Member
As has been said, the math here is slightly mixed up. Using Bill's sketch, we do indeed want to find the dimension of 'a' and as it stands we know angle 'B' (41 degrees being 1/2 82 degrees) and side 'b' at 0.1125". Bill is also correct that we need to use tan(B), which is ~0.869. However, remember from SOH CAH TOA that tan is Opposite/Adjacent sides.
...
This is mildly an aside, but - you gentlemen do realize that the reason there's an argument going on here, is because that .0627 dimension should never have been provided on a drawing?

There was a recent argument either here, or on PracticalMachinst (can't remember which) where a large portion of the respondents were adamant about how drawings ought not to be properly dimensioned (only those dimensions provided that are necessary to derive all the rest), but rather that every possible redundant dimension should be provided as well. The myriad of problems that are caused by over-dimensioning a print, carried no weight in that discussion.

Well, this argument is one of those problems.

The .0627 dimension is correct - for the depth of the truncated-cone portion of the countersink.

Since the 0.225 dimension, and the 82 degree countersink are the defining features, and all the rest of the dimensions can be calculated from them, none of the rest of the dimensions should have been provided. That the 0.0627 dimension was provided - an absolutely useless dimension[*] to the machinist - served no purpose other than to confuse the issue.

[*] Useless, except for the fact that one could calculate the full depth from it, without needing trig: By similar triangles, the 0.0627 length is the "height" of triangle A, where the "base" of triangle A is 0.225/2.0 minus 0.116/2.0 ( 0.1125 - 0.058 = 0.0545). Triangle B is a similar triangle where its height "d" is your total plunge depth, and its base is 0.1125. Similar triangles are just ratio problems, so d = 0.1125/0.0545 * 0.0627 = 0.1294

Still, if that (0.0627) dimension is provided, the countersink angle is redundant, and it would seem to be the more critical dimension. I'm mostly providing this illustration so the "math challenged" can see there's an answer that they can probably reason their way to, even if trig seems challenging.

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#### easymike29

##### Member
This is mildly an aside, but - you gentlemen do realize that the reason there's an argument going on here, is because that .0627 dimension should never have been provided on a drawing?

View attachment 118424
The .0627 dimension was never on the drawing. It was provided by me in answer to the OP's request for a down and dirty method of fulfilling the requirements of the c'sink specs. I stand by my procedure. Drill the hole to size. Replace the drill with the c'sink. Lower the c'sink untill it just touches the thru hole. Plunge .0627. I purposely did not supply any trig. That is another matter.

Eugene

#### Richard Hed

##### Well-Known Member
This is mildly an aside, but - you gentlemen do realize that the reason there's an argument going on here, is because that .0627 dimension should never have been provided on a drawing?

There was a recent argument either here, or on PracticalMachinst (can't remember which) where a large portion of the respondents were adamant about how drawings ought not to be properly dimensioned (only those dimensions provided that are necessary to derive all the rest), but rather that every possible redundant dimension should be provided as well. The myriad of problems that are caused by over-dimensioning a print, carried no weight in that discussion.

Well, this argument is one of those problems.

The .0627 dimension is correct - for the depth of the truncated-cone portion of the countersink.

Since the 0.225 dimension, and the 82 degree countersink are the defining features, and all the rest of the dimensions can be calculated from them, none of the rest of the dimensions should have been provided. That the 0.0627 dimension was provided - an absolutely useless dimension[*] to the machinist - served no purpose other than to confuse the issue.

[*] Useless, except for the fact that one could calculate the full depth from it, without needing trig: By similar triangles, the 0.0627 length is the "height" of triangle A, where the "base" of triangle A is 0.225/2.0 minus 0.116/2.0 ( 0.1125 - 0.058 = 0.0545). Triangle B is a similar triangle where its height "d" is your total plunge depth, and its base is 0.1125. Similar triangles are just ratio problems, so d = 0.1125/0.0545 * 0.0627 = 0.1294

View attachment 118424

Still, if that (0.0627) dimension is provided, the countersink angle is redundant, and it would seem to be the more critical dimension. I'm mostly providing this illustration so the "math challenged" can see there's an answer that they can probably reason their way to, even if trig seems challenging.
Yes, I would have done it completely different too: I would use the Pythagorean Theorem then finish with what you have done. BTW, the trigonomic identity Sin (x) 2 + Cos(x) 2 = 1, (those twos stand for "squared"), is the same as the Pythagorean Theorem just in a different form. Both work equally well, but somethimes you have an angle and other times you have two lengths of the legs of the triangle.

#### willray

##### Well-Known Member
The .0627 dimension was never on the drawing. It was provided by me in answer to the OP's request for a down and dirty method of fulfilling the requirements of the c'sink specs. I stand by my procedure. Drill the hole to size. Replace the drill with the c'sink. Lower the c'sink untill it just touches the thru hole. Plunge .0627. I purposely did not supply any trig. That is another matter.

Eugene
Ok, I'll soften my "completely useless" assessment. I hadn't thought of touching off on the diameter of the hole with a centered countersink, and then plunging the additional 0.0627. That certainly gets you where you need to be as well.

If I were dimensioning a drawing imagining that the machinist might take that approach, I would have provided the 82 degree countersink, and the 0.0627 additional plunge depth, rather than the .225 diameter.

#### Richard Hed

##### Well-Known Member
Ok, I'll soften my "completely useless" assessment. I hadn't thought of touching off on the diameter of the hole with a centered countersink, and then plunging the additional 0.0627. That certainly gets you where you need to be as well.

If I were dimensioning a drawing imagining that the machinist might take that approach, I would have provided the 82 degree countersink, and the 0.0627 additional plunge depth, rather than the .225 diameter.
I still maintain that the only purpose this whole countersink serves is to put the screw head below the surface of the plate (or what ever). So what does it matter if you go 10thou over? 10 thou isn't even the thickness of a finger nail. If you want perfection on such a thing, then set your drill stop. Occassionally, the screw will be in a place one does indeed wish for it to look nice, and that is where it will be seen prominentlhy on a polished finish or whatever. THen, one might wish for it to be exact.

#### deeferdog

##### Well-Known Member
Project of the Month Winner
For me, put as many dimensions as possible. Plans should be a set of instructions, not a maths exam. Cheers, Peter

#### Richard Hed

##### Well-Known Member
For me, put as many dimensions as possible. Plans should be a set of instructions, not a maths exam. Cheers, Peter
I absolutely agree with that. Put in all the important, necessary dimensions but don't over do it. I have the Ray/Corliss original dwgs. By today's standards they are absolutely KRAP. Over dimensioned up to 4, even 5 times. It made the prints nearly unreadable. This was all hand drawn and could have been so much more readable had he only dimmed each dim once. The dims from one part would overlap the next part and one didn't know what the dim was dimming. Even so, I GREATLY admire the drawings as a work of art.

BTW, I took some photos of the RAY drawings and could not get the lines to darken enough. Recently I managed to darken them. If this forum will accept them, I will put one up and you can examine it.---well krap, I have to find them first.

#### Richard Hed

##### Well-Known Member
OK, if you blow them up a lot, you can read them. Altho' they tend to be rather blurry. Someday, I might be able to afford a camera.

there are 8 more if anyone is intersted.

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#### easymike29

##### Member
...........So touch off your cutter on the surface then plunge 0.129" and you should have the feature your drawing calls for.
Yes and no. For this to be true the c'sink would need to have a dead sharp point. If it had even a .005" radius the mouth diameter would be oversize by .0045. Trivial maybe but needs to be taken into consideration if working within tolerances. It's not a good idea to try to second guess the engineer or designer.

Eugene

#### lennardhme

##### Well-Known Member
Eugene said... It's not a good idea to try to second guess the engineer or designer.
I believe it is; or how can things be improved?
I don't think I've ever built an engine exactly to specs....depends on materials, my mood at the time & a host of other things.....unless of course you are building for someone else [a job]
This is model engine club & I think most of the best models have some innovation & individuality. [IMO of course]
Have fun,
cheers,
Lennard.

#### Peter Twissell

##### Well-Known Member
HMEM Supporter
Yes and no. For this to be true the c'sink would need to have a dead sharp point. If it had even a .005" radius the mouth diameter would be oversize by .0045. Trivial maybe but needs to be taken into consideration if working within tolerances. It's not a good idea to try to second guess the engineer or designer.

Eugene
Mike, the suggestion is not to touch the point of the countersink on the surface, but to touch its cutting edge on the edge of the drilled hole.

#### easymike29

##### Member
Mike, the suggestion is not to touch the point of the countersink on the surface, but to touch its cutting edge on the edge of the drilled hole.
Yes, Peter that is my method but I was replying to a posting by Cogsby. There is also a likelihood that an error would occur if the thru hole is not to size. That also needs to be accounted for if working to tolerances. If you're working for a customer get his/her approval for any variances first.

Eugene

#### easymike29

##### Member
Eugene said... It's not a good idea to try to second guess the engineer or designer.
I believe it is; or how can things be improved?
I don't think I've ever built an engine exactly to specs....depends on materials, my mood at the time & a host of other things.....unless of course you are building for someone else [a job]
This is model engine club & I think most of the best models have some innovation & individuality. [IMO of course]
Have fun,
cheers,
Lennard.
Lennard, of course you're encouraged to be innovative. You can still do that when working for a customer, just don't try it without consulting with whomever is authorized to implement what you are proposing. Your customer will in most cases be appreciative especially if it can improve his bottom line. Engineers/designers do not deliberately try to make parts difficult for the machinist to fabricate. In any case bid on the part as toleranced or pass on it.

Eugene

#### Asm109

##### Active Member
Stepping up onto the soap box...............

The drawing is the embodiment of the designers, wait for it... , design intent. It should completely describe the part and all the tolerances required for the part to function the way the designer intended. The part should also be able to be inspected to the print after fabrication. The how of making the part belongs on Process sheets and other fabrication information, NOT cluttering up the drawing.

#### William May

##### Well-Known Member
HMEM Supporter
In this case, the DESIGNER should have done the trig, and not made the machinist's into designers. HE should have determined what it takes to create the .225 diameter he is calling out, and provided means to do it. Almost every dimension on that crappy drawing could have been skipped, if the designer had done the work he should have done.
The drawing should simply have stated: *82 degree countersink, .129 deep" That is all that is needed to generate the correct hole.
If YOU have to do calculations to figure out what the designer meant, then HE did not do his job.
If HE does it ONCE, then that means that 4000 other people don't have to ALSO DO IT.
Every time you require something to be figured out, you give an excellent opportunity for an error or a misinterpretation.

#### willray

##### Well-Known Member
The drawing should simply have stated: *82 degree countersink, .129 deep" That is all that is needed to generate the correct hole.
Not to be entirely contrary, but, there is a huge difference between instructions, and a design specification.

What you are asking for are instructions. There's nothing wrong with instructions, but, that's not typically the designer's, or draftsman's job. A good designer or draftsman may (should) anticipate the most common approach to machining a feature, and choose a strategy for dimensioning the feature so that the important details for the machining approach can be picked off the print easily, but the _design_specification_ should not rely on a particular machining approach to arrive at correct dimensions, nor obfuscate landmarks necessary to check the part against the print.

How would you propose to use your "82 degree countersink, .129 deep" instruction, to check parts against the print to determine if they are to spec? (The problem being, the missing apex of the countersunk hole, for validation-measurement purposes).

#### William May

##### Well-Known Member
HMEM Supporter
Not to be entirely contrary, but, there is a huge difference between instructions, and a design specification.

What you are asking for are instructions. There's nothing wrong with instructions, but, that's not typically the designer's, or draftsman's job. A good designer or draftsman may (should) anticipate the most common approach to machining a feature, and choose a strategy for dimensioning the feature so that the important details for the machining approach can be picked off the print easily, but the _design_specification_ should not rely on a particular machining approach to arrive at correct dimensions, nor obfuscate landmarks necessary to check the part against the print.

How would you propose to use your "82 degree countersink, .129 deep" instruction, to check parts against the print to determine if they are to spec? (The problem being, the missing apex of the countersunk hole, for validation-measurement purposes).
NO, I'm NOT asking for instructions. I'm asking for the designer to finish his work properly.
If it WAS necessary to check the spec, you don't need the apex. All you need is a go/no-go gauge to drop in the countersink and see if it is correct. In this case, you don't care about the size of the hole. All you care about is making sure the countersink is to spec.
If EVERY person who uses the drawing has to do MORE calculations to determine what the designer really intended, then it's a BAD DRAWING.
I experienced this every day in working on aircraft.
You should CLEARLY state the design in your drawing. If the detail you are presenting needs further calculation and work, then the drawing is NOT FINISHED.
I work a LOT with very early machine drawings, on both locomotives and automobiles, all from before 1920. I can say universally, that these drawings are complete in every detail. People who think CAD drawings are great would tremble after looking at one of them, they are so beautifully done.
Like I said, if every person who uses that drawing has to do calculations to find out where to go, the drawing is NOT finished and useable.

#### willray

##### Well-Known Member
NO, I'm NOT asking for instructions. I'm asking for the designer to finish his work properly.
If it WAS necessary to check the spec, you don't need the apex. All you need is a go/no-go gauge to drop in the countersink and see if it is correct. In this case, you don't care about the size of the hole. All you care about is making sure the countersink is to spec.
And what is the correct go/no-go gauge, if the drawing specifies "82 degree countersink, .129 deep"

If EVERY person who uses the drawing has to do MORE calculations to determine what the designer really intended, then it's a BAD DRAWING.
I don't think we're that far apart on this, however, in any drawing more complicated than a single line, clearly conveying the design intent _requires_ leaving some dimensions for the end-user to calculate. The clever designer minimizes these, but a drawing with 2 or more dimensions either has some omitted dimensions, or, it's over-dimensioned and therefore both prone to a myriad of potential errors, as well as impossible to use to actually determine the design intent.

You should CLEARLY state the design in your drawing. If the detail you are presenting needs further calculation and work, then the drawing is NOT FINISHED.
The drawing should clearly state the feature/product specification. In the case of a countersunk hole, the specification is for a cone coaxial with a hole, the cone having a particular included angle, and either being some width at the surface of the piece, or, sunk to some depth below the surface of the piece. More than those two dimensions (angle, and either width, or depth), and the feature is overspecified, and the design intent can no-longer be interpreted.

Since there are a myriad of ways to produce said feature, a specification of "82 degree countersink, .129 deep" would be a particularly poor specification. That's an instruction, and applies to not just one machining method, but to only one type of countersink. What do you propose to do when the poor schmuck following your proposed "design", has this type of countersink?

How is he going to know what go/no-go gauge to use?

.. and I completely agree with you about the beauty of actually drafted prints. Before the age of "click 'dimension it' in autocad" wizards, there was a lot of thought put into which dimensioning strategy was most helpful to the end user. I lament the passing of this tradition.

#### William May

##### Well-Known Member
HMEM Supporter
If it is a production set-up, a go/no-go gauge would be set up for that inspection operation. On aircraft, the inspectors had the gauges, and checked the holes to make sure they were in conformance with the print. They weren't expected to walk up, do a bunch of calculations, and then determine whether the hole met the specs. To do that with every hole would bring production to a halt.
As far as your example of a countersink. I wouldn't even use the tool illustrated. It's not even a precision tool, since there is no reference point on it, to set it from. It is for farmers and carpenters to make a countersink with. That tool could not be used to produce a precision countersink without trial and error, which is no way to produce a quality part. If you are going to take the time to do a set-up and test with that countersink, then take the setup down to drill the next hole, then set it up again and trial-test it again, you will soon learn why standardized tools exist. You can do it, but it will be MUCH cheaper and faster to use a industry standard tool. That's why they exist.
If you can show me a standard production countersink with a pilot that varies from every other standard production countersink, I would like to see the shop using it.
I have dozens of them, and they are all standard for their size and configuration. I can put the correct size countersink, in the correct spot, and know it will be right the first hole.
You can do things a thousand different, harder, more arduous ways. But why would you do them that way? If you want output, you will work smarter,, not harder.
The spec I gave you is still the easiest and fastest, and best to use. It's the one that should be on the drawing.
Again, making every viewer of the drawing do calculations should not be needed. If calculation is needed, it should be done by the designer, not left to the worker to complete the drawing.