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'''Miller twist rule''' is a mathematical formula created by Don Miller to calculate the optimum rate of twist for a given bullet traveling through a [[Rifling|rifled]] barrel.<ref name=c1>Miller, Don. ''[http://www.jbmballistics.com/bibliography/articles/miller_stability_2.pdf How Good Are Simple Rules For Estimating Rifling Twist]'', Precision Shooting - June 2009</ref> Miller suggests that while [[Alfred George Greenhill|Greenhill]]'s formula works well there are better and more precise ways to calculate what the proper twist rate for a bullet should be that are not much more difficult to calculate.
A civil rights organization on Thursday demanded a meeting with the CEO of Barneys New York and threatened to picket the luxury department store in Manhattan after two black customers said they were stopped by police after making expensive purchases.<br><br>Trayon Christian, 19, of Queens said after he bought a $349 Ferragamo belt on April 29 he was handcuffed and [http://Www.google.co.uk/search?hl=en&gl=us&tbm=nws&q=detained&gs_l=news detained] for two hours before being released with no charges. He filed a discrimination lawsuit against Barneys and the New York City Police Department on Monday.<br><br>Undercover police swarmed Kayla Phillips, 21, of Brooklyn at a subway station and demanded to see her credit card after she left Barneys with her purchase of a $2,500 [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine Bag Online] purse on Feb. 28, said her lawyer Kareem Vessup.<br>Phillips, a nursing student, had received a tax return and decided to splurge on the designer purse, Vessup said.<br><br>She filed notice of an upcoming lawsuit against the NYPD and plans to sue Barneys, he said.<br>In his lawsuit, Christian, a mechanical engineering student, said when he bought the belt, Barneys telephoned police to report a criminal act. When he stepped out of the store with his shopping bag, he was handcuffed on the sidewalk and brought to the 19th Precinct, the lawsuit said.<br><br>Police interrogated him "as to how a young black man such as himself could afford to purchase such an expensive belt and that the debit card he had in his possession had to be fake," the lawsuit said.<br>Michael Palillo, a lawyer representing Christian, said his client had saved up earnings from a work-study program at New York City College of Technology and was excited to treat himself to a trendy belt he'd admired on some of the rappers he follows on television.<br><br>"He enjoys fashion," Palillo said.<br>The racial profiling incident violated his civil rights, said the lawsuit, which was filed in state Supreme Court in Manhattan and seeks unspecified damages.<br>Barneys on its Facebook page said "no employee of Barneys" was involved and it "has zero tolerance for any form of discrimination and we stand by our long history in support of all human rights."<br><br>The NYPD did not immediately respond to a request for comment.<br>National Action Network, a civil rights group led by Reverend Al Sharpton, said it was mobilizing activists to take direct action against the store and the NYPD.<br>"National Action Network will immediately demand a meeting with the Barneys New York CEO," NAN spokeswoman Rachel Noerdlinger said in a statement.<br><br>The group is "planning to picket the store if the pattern of racial profiling is not immediately rectified after numerous incidents of discrimination have come to light," Noerdlinger said.<br>The incidents came to light little more than two months after a judge ruled the NYPD discriminated against black and Hispanic youths in its controversial stop-and-frisk crime fighting tactic.<br><br>On its website, Barneys describes itself as "... a mecca for discerning fashionistas and clothing connoisseurs since 1923" and quotes "Sex and the City" actress Sarah Jessica Parker as telling Vanity Fair, "If you're a nice person and you work hard, you get to go shopping at Barneys. It's the decadent reward."<br><br>(Additional reporting by Luke Swiderski; editing by Gunna Dickson)
 
==Formula==
[[File:.30-06 Springfield.svg|thumb|400px|A diagram of a [[.30-06 Springfield]] showing the bullet diameter (7.85 mm) and length (31.28 mm).]]
The following formula is one recommended by Miller.<ref name="c1" />
 
<math>{t}^2 = \frac{30m}{sd^3l(1+l^2)}</math>
 
where:
* m = bullet mass in grains
* s = gyroscopic stability factor (dimensionless)
* d = bullet diameter in inches
* l = bullet length in calibers
* t = twist in calibers per turn
 
Given those definitions we can expand:
 
<math>{t} = \frac{T}{d}</math>
 
where <math>T</math> = twist in inches per turn, and
 
<math>{l} = \frac{L}{d}</math>
 
where <math>L</math> = bullet length in inches.
 
===Stability factor===
Using Miller's formula we can also calculate the stability factor assuming we already know the twist. Simply solve for <math>s</math>.
 
<math>{s} = \frac{30m}{t^2d^3l(1+l^2)}</math>
 
===Twist in inches===
It is, of course, possible to solve for twist in inches directly by simply solving for <math>T</math>
 
<math>{T} = \frac{30m}{sdl(1+l^2)}</math>
 
===Notes===
Note that the constant 30 is Miller roughly approximating the velocity as 2800&nbsp;ft/sec, standard temperature (59 degrees Fahrenheit), and pressure (750&nbsp;mm Hg and 78% humidity) in the equation. Miller states that these values are taken from the [[Standard conditions for temperature and pressure|Army Standard Metro]] but does note that his values are slightly off. He goes on to point out that the difference should be small enough that it can be ignored.
 
It should also be noted that the bullet density is missing from Miller's formula despite the fact that Miller himself states his formula expands upon Greenhill's. The bullet density in the equation above is implicit in <math>m</math> through the [[moment of inertia]] approximation.
 
Finally, note that the denominator in Miller's equation is based upon the relative shape of a modern bullet. <math>l(1+l^2)</math> is roughly the formula for the shape of an American football.
 
===Safe values===
When computing this formula Miller states several ''safe'' values that can be used in place of some of the more difficult to determine variables. For example he states that assuming a [[Mach number|mach]] number of <math>M</math> = 2.5 (or roughly 2800&nbsp;ft/sec assuming standard conditions at sea level where 1 Mach is roughly 1116&nbsp;ft/sec) is a safe value to use in regards to velocity. He also states that when making rough estimates that involve temperature that using <math>s</math> = 2.0.
 
==Example==
If we take the [[Nosler]] [[Spitzer (bullet)|Spitzer]] [[.30-06 Springfield]] round which is similar to the one pictured above we can easily fill in the variables and calculate the estimated twist rate.<ref>''[http://www.nosler.com/Reloading-Data/30-06-Springfield-180-Grains.aspx Nosler - Up Front]'', Accessed February 2012</ref> Starting with the formula
 
<math>t = \sqrt{\frac{30m}{sd^3l(1+l^2)}}</math>
 
We then fill in:
* m = 180 grains
* s = 2.0 (the safe value noted above)
* d = .308 inches
* l = 1.180" /.308" = 3.83 calibers
 
<math>t = \sqrt{\frac{30 * 180}{2.0 * .308^3 * 3.83(1+3.83^2)}} = 39.2511937</math>
 
Which tells us we have 39.2511937 calibers per turn. We calculate <math>T</math> using <math>t</math> and see that
 
<math>T = 39.2511937 * .308 = 12.0893677</math>
 
So our rifling should be roughly 12" per turn. The twist, as listed on [[Wikipedia]]'s [[.30-06]] article is 10" inches per turn as an average of .30-06 caliber rifles; thus 12" inches per turn is fairly accurate. The discrepancy seen here also helps explain why certain bullets seem to work better in certain rifles when fired under similar conditions.
 
==Comparison to Greenhill's formula==
Greenhill's formula is actually much more complicated in full form. The [[rule of thumb]] that Greenhill devised based upon his formula is actually what is seen in most places, including [[rifling|Wikipedia]]. That rule was:
 
<math>Twist = \frac{C D^2}{L} \times \sqrt{\frac{SG}{10.9}}</math>
 
The actual formula was:<ref>Mosdell, Matthew. ''The Greenhill Formula''. http://www.mamut.net/MarkBrooks/newsdet35.htm (Accessed 2009 AUG 19)</ref>
 
<math>S = \frac{s^2 * m^2}{C_M\alpha \div \sin(a) * t * d * v^2}</math>
 
where:
* S = gyroscopic stability
* s = spin rate in radians per second squared
* m = polar moment of inertia
* C<sub>M<sub>α</sub></sub> = [[Stability derivatives|pitching moment coefficient]]
* a = angle of attack
* t = transverse moment of inertia
* d = air density
* v = velocity
 
Thus, Miller, in essence, took Greenhill's rule of thumb and expanded it slightly while, at the same time, keeping the formula simple enough to calculate without advanced training in mathematics. In order to improve on Greenhill, Miller used mostly empirical data and some basic geometry.
 
==Corrective equations==
Miller, in his work, notes several corrective equations that can be used:
 
The velocity (<math>v</math>) correction for twist (<math>T</math>): <math>f_v{^{1/2}} = [\frac{v}{2800}]^{1/6}</math>
 
The velocity (<math>v</math>) correction for stability factor (<math>s</math>): <math>f_v = [\frac{v}{2800}]^{1/3}</math>
 
The altitude (<math>a</math>) correction under standard conditions: <math>f_a = e^{3.158x10^{-5} * h}</math> where <math>h</math> is altitude in feet.
 
==See also==
*[[Rifling]]
 
==References==
{{Reflist}}
 
==External links==
 
=== Calculators for stability and twist ===
*[http://kwk.us/twist.html Bowman-Howell Twist Rate Calculator]
*[http://www.jbmballistics.com/~jbm/cgi-bin/jbmstab-5.0.cgi Miller Formula Calculator]
*[http://www.jbmballistics.com/~jbm/cgi-bin/jbmdrag-5.0.cgi Drag/Twist Calculator based on Bob McCoy's "McGyro" algorithm]
 
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[[Category:Articles created via the Article Wizard]]
[[Category:Firearm terminology]]

Latest revision as of 19:34, 16 September 2014

A civil rights organization on Thursday demanded a meeting with the CEO of Barneys New York and threatened to picket the luxury department store in Manhattan after two black customers said they were stopped by police after making expensive purchases.

Trayon Christian, 19, of Queens said after he bought a $349 Ferragamo belt on April 29 he was handcuffed and detained for two hours before being released with no charges. He filed a discrimination lawsuit against Barneys and the New York City Police Department on Monday.

Undercover police swarmed Kayla Phillips, 21, of Brooklyn at a subway station and demanded to see her credit card after she left Barneys with her purchase of a $2,500 Celine Bag Online purse on Feb. 28, said her lawyer Kareem Vessup.
Phillips, a nursing student, had received a tax return and decided to splurge on the designer purse, Vessup said.

She filed notice of an upcoming lawsuit against the NYPD and plans to sue Barneys, he said.
In his lawsuit, Christian, a mechanical engineering student, said when he bought the belt, Barneys telephoned police to report a criminal act. When he stepped out of the store with his shopping bag, he was handcuffed on the sidewalk and brought to the 19th Precinct, the lawsuit said.

Police interrogated him "as to how a young black man such as himself could afford to purchase such an expensive belt and that the debit card he had in his possession had to be fake," the lawsuit said.
Michael Palillo, a lawyer representing Christian, said his client had saved up earnings from a work-study program at New York City College of Technology and was excited to treat himself to a trendy belt he'd admired on some of the rappers he follows on television.

"He enjoys fashion," Palillo said.
The racial profiling incident violated his civil rights, said the lawsuit, which was filed in state Supreme Court in Manhattan and seeks unspecified damages.
Barneys on its Facebook page said "no employee of Barneys" was involved and it "has zero tolerance for any form of discrimination and we stand by our long history in support of all human rights."

The NYPD did not immediately respond to a request for comment.
National Action Network, a civil rights group led by Reverend Al Sharpton, said it was mobilizing activists to take direct action against the store and the NYPD.
"National Action Network will immediately demand a meeting with the Barneys New York CEO," NAN spokeswoman Rachel Noerdlinger said in a statement.

The group is "planning to picket the store if the pattern of racial profiling is not immediately rectified after numerous incidents of discrimination have come to light," Noerdlinger said.
The incidents came to light little more than two months after a judge ruled the NYPD discriminated against black and Hispanic youths in its controversial stop-and-frisk crime fighting tactic.

On its website, Barneys describes itself as "... a mecca for discerning fashionistas and clothing connoisseurs since 1923" and quotes "Sex and the City" actress Sarah Jessica Parker as telling Vanity Fair, "If you're a nice person and you work hard, you get to go shopping at Barneys. It's the decadent reward."

(Additional reporting by Luke Swiderski; editing by Gunna Dickson)

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