.223 twist needed for 75gr projectiles

[M.O.A.]

And have fun figuring the BC of the resulting projectile.

Not for shooting.


You can't measure the plastic tip because it has a different density than lead and copper there for the 75gn A-maxs are shorter than the others.

[jhelmuth]

Sure...

I'm using emprical evidence in actual shooting along with full knowledge that the SMK is a totally different design than the AMax. If you agree that angular momentum (the gyroscopic force of rotation - IE RPM) is a critical factor to rotation, then you would need MORE than bullet length to correctly asses the EXACT twist required (again - look at the book I cited - page 142). Look at the 2 bullets cross sectional density. Do you notice that inspite of the actual longer length of the AMax, it has a smaller SD (sectional desity)? Why do you think that is? I think Hornady has something here in this bullet design (and I'm gonna try it in a 1:8 - hopefully with good results out to 600 yds). Again... I'm attempting to point out that there is more than just simple math to all of this "what twist". As little a s 1/4 twist can make the difference in short to medium range stability. I personally believe that these 2 bullets are a possible example of that.

Now.... having said all that - I was somewhat trying to defend my earlier statements about how I did have a more stabil experience with the 75gr AMax vs the 77gr SMK. But I also said I felt neither would work well in a 1:9 barrel (YMMV depending on the actual twist) and I feel BOTH really ougth to be fored out of a 1:8 or 1:7 (which both MFGrs reccommend - another thing I mentioned).

Look.... I'm not defending the AMax or the SMK. I just conceeded (early on) to another post that said they have had good luck with the AMax (and the 77gr SMK - which did NOT meet with my limited experience). The reason I asked you to show the math was to try to get you to see that there IS more to this than simple formulas. I think it foolish to rely on them, but I also think it MORE foolish to go against the manufacturers recommendations. They put way more time and energy (and math I'm sure too) in trying to convey to us what the proper twist is. Why ignore that?


I actually don't think you and I dissagee as much as you might think. I'm happy to have you show me whe I'm wrong - but I need something specific to go on.


All the best,

Jim

[WuzYoungOnceToo]

If you agree that angular momentum (the gyroscopic force of rotation - IE RPM)

You're phrasing this as though those three things are synonyms for one another. They are not.

[MZ5]

I'm using emprical evidence in actual shooting
So was Miller when he came up with the formula we use to calculate stability factors today. Was he using incorrect or insufficient empirical evidence from the Army's actual shooting at their ballistics research lab?


Do you notice that inspite of the actual longer length of the AMax, it has a smaller SD (sectional desity)? Why do you think that is?
Because sectional density is defined as the weight of the bullet in pounds divided by the square of its diameter in inches. SD=w/d^2. Length is not part of the calculation. Accordingly, the lighter amax has a lower SD.

At this point I can't tell whether we disagree on much or not. It seems that we disagree about how to compute centrifugal force, which confuses me given the simplicity of that calculation. It seems to me that we disagree about the relative significance of length, weight, and various other minor forces with respect to gyroscopic stability. We don't disagree (I don't think?) about the existence of these other forces, but to me it seems fairly clear that we disagree as to their significance. I think we agreee that following bullet manufacturers' twist rate recommendations is a fairly 'sure thing,' but I'm not sure we agree as to whether all the bullet manufacturers use the same stability factor for their recommendations. I'm also not sure we agree on how the manufacturers compute the stability factor(s) they use, but I think it's a fairly safe guess that they use Miller's formula.

[jhelmuth]

You're phrasing this as though those three things are synonyms for one another. They are not.
Sorry... I did abuse this. I'll shut up and avoid trying to discuss this further.


So was Miller when he came up with the formula we use to calculate stability factors today. Was he using incorrect or insufficient empirical evidence from the Army's actual shooting at their ballistics research lab?


Because sectional density is defined as the weight of the bullet in pounds divided by the square of its diameter in inches. SD=w/d^2. Length is not part of the calculation. Accordingly, the lighter amax has a lower SD.

At this point I can't tell whether we disagree on much or not. It seems that we disagree about how to compute centrifugal force, which confuses me given the simplicity of that calculation. It seems to me that we disagree about the relative significance of length, weight, and various other minor forces with respect to gyroscopic stability. We don't disagree (I don't think?) about the existence of these other forces, but to me it seems fairly clear that we disagree as to their significance. I think we agreee that following bullet manufacturers' twist rate recommendations is a fairly 'sure thing,' but I'm not sure we agree as to whether all the bullet manufacturers use the same stability factor for their recommendations. I'm also not sure we agree on how the manufacturers compute the stability factor(s) they use, but I think it's a fairly safe guess that they use Miller's formula.


OK... I'm admitting I'm wrong. Feel free to correct me where I'm wrong and I'll try to be better at avoiding these discussions. My intention was to point out how Greenhill was mostly right and that bullet develpoment has come a long way forcing these gerneralized twist calculations to change with them (hey - at least his formula does provide an approximation anyway). Ultimately I think it's MOST prudent to follow the manufactures recommendation on twist rates (at least we can agree on that - maybe we can just leave it there).

BoilerUp made the initial remark that his 1:9 stabilizes both. I did not find that to be true. That is a fact. Either way, those 2 bullets NEED 1:8 or faster twist. That is a fact too.

Regarding the SD.... when the diameter is not constant over the length, which/what diameter would you use to calculate SD? How does Secant ogive vs Tangent ogive (lets not forget hybrids too) and differing radius affect bullet length and SD?


I"m sure I'm in way over my head and all of this is way more simple than I'm thinking. So I'll apologize for whatever misinformation I've provided/stated and try to be better at not commenting on this topic.

[darkker]

BoilerUp made the initial remark that his 1:9 stabilizes both. I did not find that to be true. That is a fact. Either way, those 2 bullets NEED 1:8 or faster twist. That is a fact too.


Well, it seems to be a fact for YOUR set-up. BoilerUp, Myself, and a friend who is not on this board; have the experience that the 8-twist is not NEEDED for us; at least with the 77gr SMK's.
I never saw that you showed, or responded to my velocity question. What were your velocities with BOTH bullets?

[jhelmuth]

Sorry.... did not chrono them (if I had to guess it would have been somewhere around 2800 fps). I never felt that the long range stability would be favorable and just wanted to "see" what other were saying about them shooting in the 1:9. I was actually slightly surprised by the AMax, but that could have been bad information given the small sample. My factory Savage 1:9 has a long throat, so it just made it more attractive to "try" them.

PS - my "understanding" is that velocity will not make a difference in stabilizing a bullet from the muzzle (clearly a bullet can/will become less stabil as it approoaches the 1400 fps (trans-sonic area) mark, but I don't think that applies in the opposite sense at the muzzle).


Did I get that right?

[darkker]

The velocity DOES make a difference for stability, that's why I posted the formula above.
That is why many bullets have a specific twist rating, or velocity rating. TNT's(non-green/high vel) SXSP, Dogtowns, Varmint Nightmares, all say NOT to push them beyond a certain point. Those are all rated between 240-260,000RPM.
If you push them to hard, the RPM skyrockets and they fragment shortly after leaving the bore; often times seen as a *Puff*, sometimes a grey lead vapor trail is seen *tracing* the bullet.

In the case of my 308, I have noticed a rather large difference between the..."Stickiness" of jackets between Hornady and Sierra. Both 168gr HPBT, I can drive the Sierra's much faster than the Hornady's without pressure problems(even the same load shows different velocities).

That is why I asked.
IF, I grant you this is speculation, IF the Amax WAS being pushed at 2800; that is 224,000 RPM, which is closer to it's max RPM limit, than the Sierra is; meaning "well" stabilized.
Whereas, IF the Sierra was pushed (again for arguement based on MAX posted at Hodgdon) 2660fps; That is 212,800 rpm. 212,000 RPM is a fair amount LOWER than what the SMK is rated to withstand, AND significantly less than the amax; which requires more spin.

By way of Apples to Apples, if they were traveling at the SAME velocity; the Amax is closer it's max RPM. The SMK is still NOT as close to it's max rpm, and relatively speaking, not "stabilized" as well as the Amax.

[jhelmuth]

(and I said I wasn't going to continue this 8o( )


... OK - I'll bite (again...)

So the formula you posted was "how" to calculate RPM (velocity - MV - being one factor). How does that create stability over the course of flight? I did not notice stability in the equation (just MV, twist, 720 as a constant, and RPM as the result). Seems to me that while it "might" be margianlly stabil from the muzzle, the reduction in velocity over the course will cause the stability to go to hell pretty quickly (depending upon the delta from the "desired" twist vs actual). Also, RPM from the mfg. is at a rated velocity and that RPM would have to incease as the MV increased due to the added instability introduced from the added spped againt the resistance to the air. I do understand that Stability can be added with faster MV, but only to a point. Am I wrong here (IE - I have gotten bad information from the references I have read)?

[Admin]

When are you guys going to realize that common sense, logic, and the laws of physics have no place in the wonderful world of exterior ballistics?

[jhelmuth]

(from Matthew Mosdell http://www.mamut.net/MarkBrooks/newsdet35.htm) ...



"The Greenhill Formula is a simplified method for determining mathematically the amount of spin necessary to stabilize a bullet. It was worked out in 1879 by Sir Alfred George Greenhill who was a Professor of Mathematics at Woolwich and teaching the Advanced British Artillery Officers Class. It was considered satisfactory for bullets having a density of .392 lbs/cubic inch or greater. (Lead has a density of .409 lbs/ cubic inch, and copper has a density of from .318-.325 lbs/cubic inch, depending on the alloy). The formula is Twist required (in calibers) = 150 divided by the length of the bullet (in calibers). It makes no allowance for nose shape, considering round noses and all spitzers and spire points as the same. It does not work for bullets having a density below .392 lb/ cubic inch. All copper or brass solids and most heavy jacketed bullets have average densities below .392 lbs./cubic inch. Notice I said average, as the formula makes no allowance for bullets of variable construction, linearly. The formula was a shortcut and was useful at the time, as most bullets were roundnoses and were lightly jacketed, if jacketed at all. Because the math is simple, the Greenhill Formula has remained in use to this day. Just a few years ago I had an engineer at a major ammunition manufacturing firm quote me the Greenhill Formula as a method for calculating the spin required to stabilize a long, 10 caliber spitzer, 7mm 175 gr. ,variable density, hunting bullet. Needless to say, he was not even close. The
Greenhill Formula is accurate when used in the context for which it was intended, but many folks who use it today have forgotten, or never learned that context.
The actual formula is much more complicated It is Gyroscopic Stability (GS) = the spin rate (in radians per second, squared) times the polar moment of inertia, squared, divided by the pitching moment coefficient derivative per sine of the angle of attack times the transverse moment of inertia times the air density times the velocity squared. (My keyboard does not have all the correct symbols and that is why I wrote it out). For the bullet to be stable, GS > 1.0. This is actually a short version as the pitching moment coefficient component is a complicated calculation that derives the center of gravity and the center of reverse air pressure. The equation is basically calculating the linear difference between the center of gravity and the center of reverse air pressure on the nose of the bullet. The greater the difference, the greater the spin required to keep the bullet pointed nose forward. It used to take me about three days to calculate one new design by hand. My computer does it in about 20 seconds, now. "

[Westcliffe01]

The velocity is certainly a defining factor for stability. It is the reason why a 22-250 can fire heavier bullets in a stable manner through the same twist rate than the same caliber 223. The MV is just that much higher, so is the bullet RPM. It is also why I mentioned that I had good experience with the Superformance ammo, which is "supposed" to be faster than their regular 75gr match ammo. Since I have not chrono'ed it I do not know if it is true of not, nor have I bought the "regular" match ammo.

[WuzYoungOnceToo]

Regarding the SD.... when the diameter is not constant over the length, which/what diameter would you use to calculate SD?

You use the greatest diameter. ie, the bullet's caliber.


How does Secant ogive vs Tangent ogive (lets not forget hybrids too) and differing radius affect bullet length and SD?

They don't. You don't add form factor into the equation unless you're looking for ballistic coefficient. For projectiles, SD is quite simply...

http://upload.wikimedia.org/wikipedia/en/math/4/f/0/4f0ec0133f8fb70d759d88fca4b2c40a.png

Where M = mass and d = the bullet's greatest diameter. Just remember to use the *real* diameter (not the designated caliber, as the two are often different) and be consistent in your use of measurement systems for both values. If diameter is being expressed in English units (inches) then M is expressed in lbs. If diamter is expressed in metric, convert to meters ("7.62 mm" becomes .00762 meters) and express M in kilograms.

[jhelmuth]

The velocity is certainly a defining factor for stability. It is the reason why a 22-250 can fire heavier bullets in a stable manner through the same twist rate than the same caliber 223. The MV is just that much higher, so is the bullet RPM. It is also why I mentioned that I had good experience with the Superformance ammo, which is "supposed" to be faster than their regular 75gr match ammo. Since I have not chrono'ed it I do not know if it is true of not, nor have I bought the "regular" match ammo.

According to Miller, S (gyroscopic stability) is not defined in terms of velocity....

http://upload.wikimedia.org/wikipedia/en/math/d/9/d/d9d418cdf5ede61f2e114768d74f8f77.png



yet... there ARE other formulas that at least seem to include it.....

Gyroscopic Stability (GS) = the spin rate (in radians per second, squared) times the polar moment of inertia, squared, divided by the pitching moment coefficient derivative per sine of the angle of attack times the transverse moment of inertia times the air density times the velocity squared.

[jhelmuth]

I haven't found any definative answer that agrees with you on "which/what" diameter. Maybe you could help point me to that so I can besure you are correct?


You use the greatest diameter. ie, the bullet's caliber.



They don't. You don't add form factor into the equation unless you're looking for ballistic coefficient. For projectiles, SD is quite simply...

http://upload.wikimedia.org/wikipedia/en/math/4/f/0/4f0ec0133f8fb70d759d88fca4b2c40a.png

Where M = mass and d = the bullet's greatest diameter. Just remember to use the *real* diameter (not the designated caliber, as the two are often different) and be consistent in your use of measurement systems for both values. If diameter is being expressed in English units (inches) then M is expressed in lbs. If diamter is expressed in metric, convert to meters ("7.62 mm" becomes .00762 meters) and express M in kilograms.

[darkker]

So the formula you posted was "how" to calculate RPM (velocity - MV - being one factor). How does that create stability over the course of flight? I did not notice stability in the equation (just MV, twist, 720 as a constant, and RPM as the result). Seems to me that while it "might" be margianlly stabil from the muzzle, the reduction in velocity over the course will cause the stability to go to hell pretty quickly (depending upon the delta from the "desired" twist vs actual). Also, RPM from the mfg. is at a rated velocity and that RPM would have to incease as the MV increased due to the added instability introduced from the added spped againt the resistance to the air. I do understand that Stability can be added with faster MV, but only to a point. Am I wrong here (IE - I have gotten bad information from the references I have read)?

The stability is from the spin, or RPM. The problem is that while the spin is a function of velocity in the barrel(because of the rifling); they aren't connected once the bullet exits the muzzle. The drag function of the air, and the loss of spin all happend at MUCH different rates. Also the bullet(long match type more so) as it exists, "skids" sidways somewhat because of the difference in where the center of pressure Vs. Center of Force is.

[sharpshooter]

You guys are giving me a headache....just use a 1-8" twist and shoot everything.

[WuzYoungOnceToo]

I haven't found any definative answer that agrees with you on "which/what" diameter. Maybe you could help point me to that so I can besure you are correct?

Have you found any authoritative source that DISagrees with me? In the meantime, just for starters...

http://www.chuckhawks.com/sd.htm
http://www.sierrabullets.com/index.cfm?section=techservice&page=xring&volume=7&issue=3

Note that in each case they are using the bullets' max diameter to calculate sectional density. Technically, the measurement of interest is the frontal area. With a bullet, by definition this is going to be determined by the greatest diameter of the bullet perpendicular to its axis.

[jhelmuth]

Good enough...

[helotaxi]

Not for shooting.


You can't measure the plastic tip because it has a different density than lead and copper there for the 75gn A-maxs are shorter than the others.

But you have to include the tip because it is attached to the bullet and the length that it adds affects the spin required for stability. You can't just ignore it because it's a different material.