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Old 03-12-2010, 03:29 AM   #1
NYECOGunsmith
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Default Math Tricks for Shooters and Gunsmiths

And a few other applications you can probably think of too.

Math Tricks for Gunsmiths and Shooters.

Iron Sight Correction Formula

Remember the acronym F.O.R.S. Front (Sight) Opposite, Rear (Sight) Same.
You move the front sight the opposite of the way you want the bullet to move, and /or you move the rear sight the same way you want the bullet to shift.
Here’s how to calculate how much to move a sight, or to add to it or subtract from its height.

A = The distance from the rear sight to the front sight measured in inches. For an M1 Garand, this is 27.875 inches if my memory is correct.

B = The distance from the barrel of the rifle to the target in inches. Example: 100 yards is 3600 inches , 200 yards is 7200 inches, 300 yards is 10,800 inches, etc.

C = The CHANGE in height required in the front (or rear) sight to change the elevation, or the windage. The amount (answer) will be in hundredths of an inch in most cases.

D = The height ABOVE or BELOW, or LEFT OR RIGHT of the bull’s-eye of the target that the bullet is off by, again stated in inches. And assuming of course that the bull's eye was your point of aim.


Actual Relationship

A is to B, as C is to D. Therefore, the formula is as follows:

A C
---- = ----
B D

Restated: A x D = B x C or C = (A x D) / B

So if we plug in your numbers, we get:

C = (27.875 X 9) / 3600 OR C= 250.875 / 3600, therefore,

C= 0.0696 inches which is the amount that you need to lengthen / raise the front sight by.

You can build it up with Hard Solder, but for a quick test use JB Weld Epoxy with stiff layers of masking tape forming the "Mold" to fill into with the epoxy.
Once it hardens (20 minutes, tops) you can then shoot it, file it down if needed, build it up more, etc. all right at the range if you want to.

Once you are satisfied that the sight is now the right height, you can then replace the front sight blade, or weld or solder on an extension, whatever you want as a permanent fix, although the JB Weld will last quite a long time if you don't knock anything against it and break it off.

Muzzle Energy

You can calculate muzzle energy (actually the energy at an object’s given velocity) via the following for just about anything. Try it for your 3,200 car at 70 MPH (which is about 105 FPS) and see what you get!

E=Energy in Pounds Feet
V= Velocity
K= Physical Constant = 450240
W=Weight in grains

E=V x V x W / K

Example, for a 230 grain projectile at 800 feet per second we have:

E= 800 x 800 x 230 / 450240

E= 640,000 x 230 / 450240

E= 147200000 /450240

E= 326.9367 Pounds feet.

Free Recoil Energy

Free recoil energy E
Weight of the bullet B (in grains)
Weight of the propellant P (also in grains)
Weight of the gun G in grains
Muzzle velocity V in feet per second

E=(BV+4,700P)^2/64.348 Times G The part of the equation in parenthesis must be squared (multiplied by itself) then divided by the product of 64.348 times the gun's weight in pounds. That's what the ^2 means, is square the proceeding actions.

That number 4,700 could also be 5,200 or 5,600. Why? It's the velocity of the expanding gas produced when the powder is ignited, listed in feet per second.

For most of the smokeless powders used for the .50 BMG and most cannons, it would be the 4,700 figure.

For most shotgun powders, the 5,200 FPS figure is used, and for most rifle and pistol powders, it is the 5,600 fps figure.

For black powder it would be 2,000 fps. Some sources will list 4,000 fps for all smokeless powders, so as you can see, there is some variance in the calculation.


And this gives free recoil energy, not felt recoil, so it gives you an accurate answer that isn't all that particularly useful.

Felt recoil will be perceived differently by persons of different builds, age, fitness level, clothing worn, as well as by the type of firearm being fired. Some types of firearm will spread the recoil impulse over a longer period of time, this results in less perceived recoil than that of a firearm that delivers it in a very short period of time.


Shooting Up Hill or Downhill

Have a range finder but it doesn’t have the inclinator function in it? Want to stop shooting over the top of your target when shooting uphill or down hill?
Measure the line of sight distance to your target, then multiply the distance in yards by the Cosine of the angle and the result is the actual, or horizontal distance to the target. Hold for this distance and hit what you are aiming at.

Memorize (or tape to the side of the stock) the Cosine of a few common angles (10,20,30 degrees) , and if you aren’t quick at math, carry a $1 calculator.
10 seconds work can make the difference between a hit or a miss on that trophy buck. For a few bucks more you can buy a calculator at Wally World that has the Cosine function.

Example:
Line of sight distance up a 30 degree hill to your trophy buck reads as 300 yards. Hold for 300 and shoot over the buck’s back.
Instead, Multiply 300 by the Cosine of 30 degrees, which is .866 (round it off to .87) and you get 261 yards. Hold for that and hit the buck pretty much where you are aiming.

Tap Drill Selection

Need to tap a hole but don’t have a tap/drill chart handy to tell you what size drill to use?
But you do know the size and threads per inch (TPI) of the screw, right?
Divide 1 by the number of threads per inch to find the pitch. Now subtract the pitch from the major (biggest) diameter of the screw, and that’s the drill size to use.

Example, need to drill a hole for a ¼-20 machine screw. The ¼ is the major diameter, and the 20 is the number of Threads Per Inch.
1 / 20 is 0.05. Major diameter is 1/4 inch (.250”)
.250” – 0.05 inch is .0200 inch. Use a Drill that is that size to get a 75% thread engagement. That’s a number 7 drill bit in this example.

How about a drill for a 6-48 thread screw (very common on scope mounts) ?
Well, first we need to know the major diameter of a number 6 screw. We can look it up and find it is 0.1380 inches, but what if you’ve left your screw thread chart in your other pants?
Just remember that the machine screw sizes start at number 1, and its major diameter is 0.0730, and they increase in diameter by 0.013 for each screw size. They go all the way from a number 1 screw to a number 14 screw by the way. After that they are called bolts, not screws.
In other words a number 2 screw is 0.0730 + 0.013 inches or 0.0860 inches in major diameter, a number 3 is 0.0730 + 0.013 + 0.013 for a total of 0.0990 inches in major diameter for a number 3 and so on.
So a Number Six is 0.0730 + (5 x 0.013) inches in major diameter, or 0.1380 inches in major diameter.
And with 48 threads per inch, it has a pitch of 1 / 48 or 0.0208, subtract that from the major diameter of 0.1380 and you have a drill required to be 0.1172 inches in diameter, which is pretty close to a number 32 drill at 0.1160 inches.

Movements Based on Screw Pitch.

Knowing how to calculate the pitch of a screw based on its Threads Per Inch (TPI) has another handy function. If you need to move something precisely a known but very small distance (like, say, the adjustable rear target iron sight on your Colt Python) and you’ve already used the formula under Iron Sight Correction above to figure out how much to move it, if you know the threads per inch of the little tiny screw that moves the rear sight for windage (usually 40 TPI) you can figure out the pitch, which is 0.025” for a 40 TPI screw. The pitch is the linear distance the screw will travel if it is turned one full 360 degree revolution.
If you’ve determined you need to move the rear sight, say, 0.05 inches to the right, you would then know that you could turn the screw in the proper direction two full turns, and be there.
If the amount of movement is an odd number, you can approximate it.
Say you needed to move it 0.067 inches. Well, that would be two full turns ( 0.05) and about 2/3 of another turn. Gets you pretty close, doesn’t it?
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Just because you are paranoid doesn't mean someone ISN'T OUT TO GET YOU!
Just because a complaint was never filed doesn't mean a defective parachute was never made.
I've been to three world's fairs, two rodeos and a goat roping contest, but I've never seen the likes of the stuff that goes on around here before!
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Old 03-12-2010, 11:13 AM   #2
Jim Fuller
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Steve
Seriously
You should write a book on gunsmithing. A lot of the stuff you post about here is unfortunatly becoming a lost art. In these days of modern techology, CNC machines ect.. A lot of what you know will never be discovered by younger gunsmiths who have only know modern convienences.

You are a walking encyclopedia of Gunsmithing tricks and procedures.

Bless you Brother!!
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Old 03-12-2010, 02:02 PM   #3
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Steve, where's that formula to get me from 97's to 100 straight?

Luck - Wind = Straight ??



I'd understand if you didn't want to share that one. I'm sure its cost you lots of cranks on the mec to perfect it! ;)

But like Jim said, you really should do something with all that great info.....glad to have you here as a refrence, thats for sure!
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Old 03-12-2010, 04:05 PM   #4
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Good advice on the high angle shooting! I usually tell people to hold low because the bullet will be arrive at a different point in its trajectory. On high angle shots I us the pythagorean theorem to figure out the actual distance to target, a slope doper helps out a lot too!
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Old 03-12-2010, 09:20 PM   #5
NYECOGunsmith
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Steve
Seriously
You should write a book on gunsmithing. A lot of the stuff you post about here is unfortunatly becoming a lost art. In these days of modern techology, CNC machines ect.. A lot of what you know will never be discovered by younger gunsmiths who have only know modern convienences.

You are a walking encyclopedia of Gunsmithing tricks and procedures.

Bless you Brother!!
Jim, I thank you Sir, you are too kind!
I suspect that most, if not all, the bits and pieces of gunsmithing, mechanical engineering, electronics, machinists and other knowledge I have floating around upstairs could probably be found in a decent public library, used book store, from Barnes and Noble, or via a well thought out Google search.

You are correct in that every day as the older generation, particularly the WWII vintage tradesmen, dies off, a lot of tribal knowledge is lost.
While it might be found in some form or another on the Internet, if the day ever comes where the lights go out and stay out, the Internet will be useless. Better to have the knowledge in hard copy books and in folks minds, particularly if the folks who know it also know how to use it. The two do not always go hand in hand it seems.

That's why I keep dumping it out here, hoping someone will not only remember it, but also put it into practice until they truly understand it, and then, PASS IT ALONG!

I'm not trying to be a know it all, or prove I already am one, or even be long winded (OK, maybe that last one, but only that one, I will give you Top!!) I just hate to see hard acquired information and skill lost.

But write a book on the subjects? I doubt anyone would publish it. I have written a number of books and instructional manuals over the 30 years I worked for Uncle Sam, unfortunately they are all still classified and would be of little or no use to anyone here. And I doubt Uncle would publish anything I wrote on guns or gunsmithing, and the private publishers in the world aren't really interested either it seems.

So I will, for the foreseeable future, just keep burdening you all with my random thoughts on the subject we all have a common interest in.

No, Kyle, not Women! Guns!
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Steve


Just because you are paranoid doesn't mean someone ISN'T OUT TO GET YOU!
Just because a complaint was never filed doesn't mean a defective parachute was never made.
I've been to three world's fairs, two rodeos and a goat roping contest, but I've never seen the likes of the stuff that goes on around here before!
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Old 03-12-2010, 09:22 PM   #6
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Originally Posted by Guido View Post
Steve, where's that formula to get me from 97's to 100 straight?

Luck - Wind = Straight ??



I'd understand if you didn't want to share that one. I'm sure its cost you lots of cranks on the mec to perfect it! ;)

But like Jim said, you really should do something with all that great info.....glad to have you here as a refrence, thats for sure!
Ah Guido, that formula is an easy one. Here it is:

$50K + 50KRF + NSS = 100 straight, where:

$50K = what you spend on birds and ammo
50KR = 50,000 rounds fired
NSS= the above two done non stop until you can't miss anymore!
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Steve


Just because you are paranoid doesn't mean someone ISN'T OUT TO GET YOU!
Just because a complaint was never filed doesn't mean a defective parachute was never made.
I've been to three world's fairs, two rodeos and a goat roping contest, but I've never seen the likes of the stuff that goes on around here before!
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Old 03-12-2010, 10:56 PM   #7
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But write a book on the subjects? I doubt anyone would publish it. I have written a number of books and instructional manuals over the 30 years I worked for Uncle Sam, unfortunately they are all still classified and would be of little or no use to anyone here. And I doubt Uncle would publish anything I wrote on guns or gunsmithing, and the private publishers in the world aren't really interested either it seems.
Steve, self publishing is really awesome nowadays. They can handle the ISBN registration, distribution to booksellers, and can print on demand with no setup costs. I looked into it as a backup plan for a novel that I've been working on for about three years. I'm ready to self publish it if I have to. For a 200 page novel it costs about $5 a book. And you can even order just one copy! If you want nice color photos, it'll probably be a bit more.

Maybe I can help you compile it and get credit as an editor
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Old 03-12-2010, 11:17 PM   #8
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And a few other applications you can probably think of too.

Math Tricks for Gunsmiths and Shooters.


Movements Based on Screw Pitch.

Knowing how to calculate the pitch of a screw based on its Threads Per Inch (TPI) has another handy function. If you need to move something precisely a known but very small distance (like, say, the adjustable rear target iron sight on your Colt Python) and you’ve already used the formula under Iron Sight Correction above to figure out how much to move it, if you know the threads per inch of the little tiny screw that moves the rear sight for windage (usually 40 TPI) you can figure out the pitch, which is 0.025” for a 40 TPI screw. The pitch is the linear distance the screw will travel if it is turned one full 360 degree revolution.
If you’ve determined you need to move the rear sight, say, 0.05 inches to the right, you would then know that you could turn the screw in the proper direction two full turns, and be there.
If the amount of movement is an odd number, you can approximate it.
Say you needed to move it 0.067 inches. Well, that would be two full turns ( 0.05) and about 2/3 of another turn. Gets you pretty close, doesn’t it?
I should have noted in the above section, that this is also how a gunsmith (or a machinist for that matter) goes about figuring out how much to set a barrel back for rechambering or to correct headspace issues.

For example, if you want to set back a Springfield 1903A3 barrel (1.040 inch diameter by 10 Threads Per Inch , and they are square threads, not V threads) you would want to set it back one full turn to keep the barrel clocked in the same plane, if the gun has iron sights for example. You wouldn't want them ending up at 3 o'clock instead of 12!

So if you figure the pitch at 10 TPI is 1 /10 or 0.1 inches, then you need to move the barrel's shoulder , where it will bear against the receiver's face, (which you might want to square up while you have the two apart, and lap the bolt face perpendicular to the receiver face, and lap the locking lugs too, but that's a whole 'nudder story) back by 0.1 inch, right?

Nope. That's where a lot of beginners go wrong in this procedure, because they forget about the "wind up" or "Crush" factor. What you actually want to do is to cut that shoulder back by an amount that will stop the barrel from threading into the receiver about 1/16th of a rotation, (or 22.5 Degrees if you want to think of it that way) short of a full rotation, that is, short of coming home to the co-witness marks you made on the under side of the barrel and receiver before you took the two apart. You did make those marks first, right?

So you calculate that one full turn (360 degrees) yields your 0.10 inch linear travel, which means that each degree is equal to 0.000027 inch of travel (0.10 / 360 = 0.000027 inches per degree of rotation) , and your needed 1/16 rotation or 22.5 degrees is then equal to 0.0062 inches (22.5 X 0.000027").

If you subtract that from your original 0.10 inch set back you get 0.0938 inches (0.10 - 0.0062"), which IS the amount you want to take off the shoulder of that barrel to set it back one full turn. So you set the barrel up in your lathe and steady rest, turn off 0.0938 " from the shoulder and the edn of the threaded shank, and you are ready to move on.
Now, once the barrel is threaded into the receiver finger tight, and you torque it down the proper amount, it will advance under that torque the last 0.0938 inches (approximately, you torque it AND watch the Co-witness marks, stop when they line up!) and now the barrel will not only be properly torqued into place (has the right amount of crush fit at the receiver/shoulder interface) but it will also be back in registration via the co-witness marks.

I should mention that the downside to this method of correcting headspace on this particular rifle is that if you have a contoured barrel, it now is not sitting in the barrel channel in your stock as it was previously, and there may be some unsightly gaps between the barrel and the forearm. If the barrel and action were glass bedded prior to this, that will need to be redone. Make sure you mention that to the customer first!
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Steve


Just because you are paranoid doesn't mean someone ISN'T OUT TO GET YOU!
Just because a complaint was never filed doesn't mean a defective parachute was never made.
I've been to three world's fairs, two rodeos and a goat roping contest, but I've never seen the likes of the stuff that goes on around here before!
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Old 03-12-2010, 11:25 PM   #9
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Steve, self publishing is really awesome nowadays. They can handle the ISBN registration, distribution to booksellers, and can print on demand with no setup costs. I looked into it as a backup plan for a novel that I've been working on for about three years. I'm ready to self publish it if I have to. For a 200 page novel it costs about $5 a book. And you can even order just one copy! If you want nice color photos, it'll probably be a bit more.

Maybe I can help you compile it and get credit as an editor
COOL! Great info, thanks, wasn't aware of any of that. Will have to think about it, if its that easy to get published.

It's been suggested a number of times that I write an autobiography of my 30 years as an intelligence officer and agent.
Not that I had any kind of a James Bond career, because I didn't, just a lot of interesting things happened during those times is all. That one might make me some money if I can get it past Uncle's sensors.

Now if I can learn to write, I'll be on my way to putting dozens, well, maybe 2 or 3 people to sleep with the stuff floating around up there about guns, gunsmithing, machining, etc.! That one I probably could put on the stands without Uncle wanting to redact it.
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Just because you are paranoid doesn't mean someone ISN'T OUT TO GET YOU!
Just because a complaint was never filed doesn't mean a defective parachute was never made.
I've been to three world's fairs, two rodeos and a goat roping contest, but I've never seen the likes of the stuff that goes on around here before!
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Old 03-12-2010, 11:29 PM   #10
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NYECOGunsmith do you think you could teach people willing to pay for your time? My only machining experience was metal shop is high school. I would love to learn how to true and blue print my own actions and chamber and head space my own barrel blanks.
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