I'm going to start handloading for my .223 AR-15. I have a 20" barrel with 1x9 twist. My best factory loads seem to be with 62 gr. bullets, but depending on brand, I can get similar results with 55 grs.
Does anyone know of any tables or formulas that equate bullet weight with rate of twist to produce a specific theoretical "best" bullet. I know there are a lot of other factors involved but that would help to narrow down the loading variables somewhat.

There is a formula, I don't really understand it, but it relates directly to bullet length. That ends up being similar to weight of course, but depending on the bullet composition it will vary, so length is the key. I think it is called the Greenhill formula or something like that.

This is from Brownell's gunsmith supplies.

Calibers and Twists
The information below will help you select the best barrel twist for your specific needs, providing of course there are multiple choices. If you'll be shooting one bullet weight, choose a twist from the chart just fast enough to stabilize it. Too fast a twist simply overspins the bullet and may result in reduced accuracy. So if you're going to be using several bullet weights, be sure to select a twist that will stabilize the heaviest one, since lighter bullets will also be stabilized.
By way of explanation, the numbers in the Twists column indicate how far the bullet must travel through the bore to make one full revolution. This is determined by the rate of rotation of the rifling. For example, a 9" twist barrel spins the bullet one full turn when it travels 9 inches through the bore. In a 16" twist barrel, the bullet makes on revolution in 16 inches. So at the same bullet velocity, the 9" twist is faster (spins the bullet faster) than the 16" twist. Consequently, as the chart reflects in the .224 CF section, the 9" twist is necessary for stabilizing heavier bullet weights.
Again looking at the .224 CF section, if you're planning to shoot 55-grain bullets, the 14" twist is ideal. This twist is also the best choice for 52-and 53-grain match bullets driven at moderate velocities. But if you're also contemplating shooting a 60-grainer, go with the 12" twist, since it will stabilize all the bullets you'll be using. As you can see from the 15" and 16" twists, higher velocities also spin the bullet faster and my enable a slower-than-recommended twist to stabilize a marginally overweight bullet.
As a general rule: The higher the velocity, the slower twist is required.
The lower the velocity, the faster twist is required.
This chart outlines the basic principles
Caliber Twist
.172 10" For all bullets

.22 RF 14"* Twist for pistol barrels
16" Standard twist for rifle barrels
17"* Special twist for rifle barrels

.224 CF 9" For bullets heavier than 63 gr.
12" For bullets up to 63 gr.
14" For bullets up to 55 gr.
15"* For bullets up to 55 gr. driven 4,100 fps or more
16"* For bullets up to 55 gr. driven 4,300 fps or more

6mm/.243 8" Special for VLD bullets
10" For bullets up to 120 gr.
12" For bullets up to 85 gr.
13"* For bullets up to 75 gr.
14"* For bullets up to 70 gr.
15"* Special for bullets up to 70 gr.

.257 9" For bullets heavier than 100 gr.
10" For bullets up to 105 gr.
12" For bullets up to 90 gr.
13"* For bullets up to 80 gr.
14"* For bullets up to 70 gr.

6.5mm/.264 8" For bullets heavier than 120 gr.
9" For bullets up to 120 gr.

.270 10" For all bullets

7mm/.284 9" For bullets heavier than 140 gr.
11" For bullets up to 140 gr.

.307 13"* Special size and twist

.308 8" For bullets heavier than 220 gr.
10" For bullets up to 220 gr.
12" For bullets up to 170 gr.
14"* For bullets up to 168 gr.
15"* For bullets up to 150 gr.

7.65mm/.311 10" For all bullets

.338 10" For all bullets

9mm/.355 14" For low-velocity wadcutters
16" For all other bullets

.38/.357 14" For low-velocity wadcutters
18" For all other bullets

.358 14" For all bullets

.375 12" For all bullets

10mm/.400 16" For all bullets

.411 14" For all bullets

.416 14" For all bullets

.44 20" For all bullets

.451 16" For all bullets

.458 14" For all bullets
*Stainless Steel only
Black Powder Barrels (1.250" x 30")
.32 14" .320" groove

.38 20" .379" groove

.40 20" .403" groove

.457 20" .457" groove

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I'm going to start handloading for my .223 AR-15. I have a 20" barrel with 1x9 twist. My best factory loads seem to be with 62 gr. bullets, but depending on brand, I can get similar results with 55 grs.
Does anyone know of any tables or formulas that equate bullet weight with rate of twist to produce a specific theoretical "best" bullet. I know there are a lot of other factors involved but that would help to narrow down the loading variables somewhat.

The 1/9 twist in your AR will PROBABLY stabilize up to 77 gr bullets adequately, depending upon velocity. The twist rate v stabilization is more dependant upon bullet length than weight; i.e., a longer bullet will require a faster twist than a shorter bullet given similar velocities. Your AR will do fine with up to 75 gr with that twist, and may be fine for the 77 gr SMK, but will be marginal for the 80-90 gr SMK. Those usually require a 1/8 and 1/7 twist to stabilize at the velocities achievable in the 5.56x45 cartridge case. Moving to a .22-250 with a 1/9 twist will probably stabilize up to the 80 gr SMK because of the higher velocities involved. I have a Bushmaster with a 1/9 twist, and it stabilizes the 77 gr SMK, but only just. You can see some yaw present in some of the holes in the targets on loads with lower velocity. If you don't handload, try some of the Blackhills factory with the 77 gr SMK. It's very consistent in velocity, and you can see empirically whether your particular rifle will attain the needed velocity to stabilize the bullet.

I've put this Excel file up before. It helps you select a barrel twist by entering bullet weight and length and muzzle velocity, then barometric pressure (estimator included) and temperature. By entering the bullet information and using the highest and lowest temperatures and adding 2" to the barometric pressure for extreme weather, you can simulate the range of conditions and test that stability remains.

The file hosting service only keeps it for 30 days, so if you have Excel and want to use it, grab it while you can.

Miller Twist Estimator (http://www.savefile.com/files/218126)

My AR has a 1x9 twist and I have have had excellent results with bullet weights from 45 to 75 grs.
75gr. A-Max and other heavy VLD design bullets have to be loaded longer than will fit in the magazine. I use them for 600yd. slow fire.
52 gr. BTHP match bullets are extremely accurate out to 200yd. A 67 or 68 gr. bullet would be a good choice for an across the coarse (200 - 600yd.) load. When called on for ground hog duty the 60gr. V-max produces one hole groups.

Lynn,

Glen Zediker, in his book Handloading for Competition, reports:

I had an 8.2 {inch} twist barrel that "should" shoot 80 grain .224 bullets just fine. It did not often enough. Nothing was wrong with the barrel, just a little slow. A 7.8 from that same maker did just fine. A "straight 8" in other rifles I have does just fine too. That's not the only time a fractional amount makes a difference in a shooting sport, and, no, it never "sounds" like much. My experience with the 8.2 didn't convince me that 8.0 was perfect, but rather that 7.5 sounded even better.

So, it isn't necessary to get fully unstable to be unable to group well under all conditions. Bullets typically become more stable after leaving the muzzle and starting to slow down because a bullet's rotation slows more gradually than its forward motion, causing s to tend to increase a bit. This is why some rifles seem to shoot longer bullets without keyholing occurring than you think they should. That still doesn't mean you are getting the best groups your gun could produce with a little more spin.

I run the 53 grain SMK's at 200 yards and 80 grain Berger VLD's at 600 yards in my 7.5" twist gun. At 300 yards I don't like what the gusting winds on Viale Range at Perry do to the 53's, so I shoot the 77 grain SMK's from there. The 77's are 1.0 inch long with a relatively short ogive that allows you to seat them to NATO OAL for magazine feeding. I gather the Unit Designated Marksmen are finding this bullet very useful in the sandbox.

When I first got my Bushmaster built by Compass Lake, I used the then-new 77's at 600 yards and got good results. The longer 1.1" A-max and Berger bullets cut the wind deflection by about a third, which is significant, but that isn't more important than consistency at that range; just more work to keep on top of wind doping.

My point in describing this is you might want to try the 77's for both 300 and 600 yards with your 9" twist? My 7.5" twist will digest about anything, but the estimator I posted shows that at 2650 fps your 9" twist will let those long bullets destabilize near the muzzle at much below 65°F at sea level, being right at s = 1.00 at the muzzle. At 1000 ft above sea level, that goes up to s = 1.10, which, though stable, is not going to be recovering nose coning motion from muzzle gas deflection well. If you switch to the 77 grain bullet the muzzle stability factor goes up to 1.33, which is much closer to Harold Vaughn's nominal s = 1.4, and should do a better job of ignoring minor bullet imperfections. You may, therefore, discover the 77 grain SMK actually works better for your gun at 600 yards than the long bullets do, despite giving up a third of the wind immunity.

In Winchester cases with deburred flashholes, using Federal 205M primers, seating the 77 grains bullets to the 2.250" OAL NATO spec, my gun likes 23.2 grains of 748. This load is what I run at 300 yards with complete satisfaction.

Good luck with it if you try it out!

Nick

You might want to play with JBM's Bullet Drag and Twist calculator.

http://www.eskimo.com/~jbm/calculations/calculations.html

Bye
Jack

That's an interesting calculator. More conservative than Miller, though less conservative than my RSI Shooting Lab's calculator. More bullet detail, though. It seems to think you need at least 3500 fps to stabilize the 75 grain Hornady from a 9" tube. I'll have to play with it some more. Thanks for the link.

Nick

Hi, Nick:
It looks like there's an error in the altitude correction of your spreadsheet. Pejsa's formula of P0/P = EXP(Altitude/31654) gives a correction of about 1/3 of your's.

Bye
Jack

Hi, Nick:
It looks like there's an error in the altitude correction of your spreadsheet. . .

Jack,

Thanks for the head's up. That is my own formula done by curve fitting to atmospheric data in the CRC Handbook. It's got a better correlation at higher altitude than Pejsa's, but contained just one small beginner's boo-boo: I forgot to convert meters in the CRC table to feet. :D. This is actually a sign of laziness, on my part. I got used to Mathcad keeping track of units for me. However, it doesn't let you carry units into the data tables used for curve fitting, so I actually had to watch what I was doing. Not a good thing, it seems.

You will find the correct file here: http://www.savefile.com/files/224448

Since I was fiddling with it anyway, I went ahead and graphed it against Pejsa’s simpler form, so you can see the difference. I also narrowed the span to fit the real world and tightened it by adding a term. It is now good within a tenth of an inch from the lowest dry point on the earth’s surface (the Dead Sea) to the top of Mt. Everest. If anyone anticipates somehow getting into a rifle-range gunfight at the bottom of an African diamond mine or dueling from high altitude gas balloons, let me know and I’ll see if I can’t get it to project another few miles?

Nick

http://img70.imageshack.us/img70/5734/atmosphericpressurefitgt7.gif

Jack,

Here's a little something more. I played around with the simpler Pejsa equation form, rearranging it to yield standard pressures, and found that as you have it, it does a best fit from -2000 to +2000 feet. The denominator for altitude determines this. If you change it to 25466, you get the following result which tracks the -2000 to + 36000 foot range much better, but not the -2000 to +2000 foot range quite as well. Keeping in mind that weather fronts can alter matters by a couple of inches at sea level, I don't think it is overly important to be more exact. Note that I am using 29.9 inches of mercury for sea level. If you want to, you can add more decimal places (29.9114 being the CRC Handbook standard).

Nick

http://img126.imageshack.us/img126/5786/atmosphericpressurefitpnw5.gif