Misplaced Pages

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21-776: The following formula is one recommended by Miller: t 2 = 30 m s d 3 l ( 1 + l 2 ) {\displaystyle {t}^{2}={\frac {30m}{sd^{3}l(1+l^{2})}}} where Also, since one "caliber" in this context is one bullet diameter, we have: t = T d {\displaystyle {t}={\frac {T}{d}}} where T {\displaystyle T} = twist rate in inches per turn, and l = L d {\displaystyle {l}={\frac {L}{d}}} where L {\displaystyle L} = bullet length in inches. Solving Miller's formula for s {\displaystyle s} gives

42-433: A {\displaystyle a} ) correction under standard conditions: f a = e 3.158 x 10 − 5 ∗ h {\displaystyle f_{a}=e^{3.158x10^{-5}*h}} where h {\displaystyle h} is altitude in feet. Millimetre of mercury A millimetre of mercury is a manometric unit of pressure , formerly defined as

63-1133: A ) ∗ t ∗ d ∗ v 2 {\displaystyle S={\frac {s^{2}*m^{2}}{C_{M_{\alpha }}\div \sin(a)*t*d*v^{2}}}} where Thus, Miller essentially took Greenhill's rule of thumb and expanded it slightly, while keeping the formula simple enough to be used by someone with basic math skills. To improve on Greenhill, Miller used mostly empirical data and basic geometry. Miller notes several corrective equations that can be used: The velocity ( v {\displaystyle v} ) correction for twist ( T {\displaystyle T} ): f v 1 / 2 = [ v 2800 ] 1 / 6 {\displaystyle f_{v}{^{1/2}}=[{\frac {v}{2800}}]^{1/6}} The velocity ( v {\displaystyle v} ) correction for stability factor ( s {\displaystyle s} ): f v = [ v 2800 ] 1 / 3 {\displaystyle f_{v}=[{\frac {v}{2800}}]^{1/3}} The altitude (

84-447: A bowl of mercury and raise the closed end up out of it, keeping the open end submerged. The weight of the mercury would pull it down, leaving a partial vacuum at the far end. This validated his belief that air/gas has mass, creating pressure on things around it. Previously, the more popular conclusion, even for Galileo , was that air was weightless and it is vacuum that provided force, as in a siphon. The discovery helped bring Torricelli to

105-424: A column of mercury 1 millimetre high with a precise density of 13 595.1  kg/m when the acceleration due to gravity is exactly 9.806 65  m/s . The density 13 595.1  kg/m chosen for this definition is the approximate density of mercury at 0 °C (32 °F), and 9.806 65 m/s is standard gravity . The use of an actual column of mercury to measure pressure normally requires correction for

126-419: A gas, and felt that this applied even to solid matter. More condensed air made colder, heavier objects, and expanded air made lighter, hotter objects. This was akin to how gases become less dense when warmer and more dense when cooler. In the 17th century, Evangelista Torricelli conducted experiments with mercury that allowed him to measure the presence of air. He would dip a glass tube, closed at one end, into

147-405: A shape similar to that of an American football. When computing using this formula, Miller suggests several safe values that can be used for some of the more difficult to determine variables. For example, he states that a mach number of M {\displaystyle M} = 2.5 (roughly 2800 ft/sec, assuming standard conditions at sea level where 1 Mach is roughly 1116 ft/sec)

168-1177: Is a safe value to use for velocity. He also states that rough estimates involving temperature should use s {\displaystyle s} = 2.0. Using a Nosler Spitzer bullet in a .30-06 Springfield , which is similar to the one pictured above, and substituting values for the variables, we determine the estimated optimum twist rate. t = 30 m s d 3 l ( 1 + l 2 ) {\displaystyle t={\sqrt {\frac {30m}{sd^{3}l(1+l^{2})}}}} where t = 30 ∗ 180 2.0 ∗ .308 3 ∗ 3.83 ( 1 + 3.83 2 ) = 39.2511937 {\displaystyle t={\sqrt {\frac {30*180}{2.0*.308^{3}*3.83(1+3.83^{2})}}}=39.2511937} The result indicates an optimum twist rate of 39.2511937 calibers per turn. Determining T {\displaystyle T} from t {\displaystyle t} we have T = 39.2511937 ∗ .308 = 12.0893677 {\displaystyle T=39.2511937*.308=12.0893677} Thus

189-484: Is actually what is seen in most writing, including Misplaced Pages . The rule of thumb is: T w i s t = C D 2 L × S G 10.9 {\displaystyle Twist={\frac {CD^{2}}{L}}\times {\sqrt {\frac {SG}{10.9}}}} The actual formula is: S = s 2 ∗ m 2 C M α ÷ sin ⁡ (

210-592: The medical literature indexed in PubMed . For example, the U.S. and European guidelines on hypertension , in using millimeters of mercury for blood pressure , are reflecting the fact (common basic knowledge among health care professionals) that this is the usual unit of blood pressure in clinical medicine. One millimetre of mercury is approximately 1 torr , which is ⁠ 1 / 760 ⁠ of standard atmospheric pressure ( ⁠ 101 325 / 760 ⁠  ≈  133.322 368 421  pascals ). Although

231-512: 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 m {\displaystyle m} through the moment of inertia approximation. Finally, note that the denominator of Miller's formula is based upon the relative shape of a modern bullet. The term l ( 1 + l 2 ) {\displaystyle l(1+l^{2})} roughly indicates

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252-400: The conclusion: We live submerged at the bottom of an ocean of the element air, which by unquestioned experiments is known to have weight. This test, known as Torricelli's experiment , was essentially the first documented pressure gauge. Blaise Pascal went farther, having his brother-in-law try the experiment at different altitudes on a mountain, and finding indeed that the farther down in

273-557: The constant 30 in the formula is Miller's rough approximation of velocity (2800 ft/sec or 853 m/s), standard temperature (59 degrees Fahrenheit or 15 celsius) and pressure (750  mmHg or 1000  hPa , and 78% relative humidity ). Miller states that these values are taken from the 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

294-403: The density of mercury at the actual temperature and the sometimes significant variation of gravity with location, and may be further corrected to take account of the density of the measured air, water or other fluid. Each millimetre of mercury can be divided into 1000 micrometres of mercury, denoted μmHg or simply microns . The precision of modern transducers is often insufficient to show

315-412: The difference between the torr and the millimetre of mercury. The difference between these two units is about one part in seven million or 0.000 015% . By the same factor, a millitorr is slightly less than a micrometre of mercury. In medicine, pressure is still generally measured in millimetres of mercury. These measurements are in general given relative to the current atmospheric pressure: for example,

336-403: The difference in height between two mercury levels by the density of mercury and the local gravitational acceleration. Because the specific weight of mercury depends on temperature and surface gravity , both of which vary with local conditions, specific standard values for these two parameters were adopted. This resulted in defining a "millimetre of mercury" as the pressure exerted at the base of

357-400: The extra pressure generated by a column of mercury one millimetre high, and currently defined as exactly 133.322 387 415 pascals or approximately 133.322 pascals. It is denoted mmHg or mm Hg . Although not an SI unit, the millimetre of mercury is still often encountered in some fields; for example, it is still widely used in medicine , as demonstrated for example in

378-531: The ocean of atmosphere, the higher the pressure. Mercury manometers were the first accurate pressure gauges. They are less used today due to mercury's toxicity , the mercury column's sensitivity to temperature and local gravity, and the greater convenience of other instrumentation. They displayed the pressure difference between two fluids as a vertical difference between the mercury levels in two connected reservoirs. An actual mercury column reading may be converted to more fundamental units of pressure by multiplying

399-466: The optimum rate of twist for this bullet should be approximately 12 inches per turn. The typical twist of .30-06 caliber rifle barrels is 10 inches per turn, accommodating heavier bullets than in this example. A different twist rate often helps explain why some bullets work better in certain rifles when fired under similar conditions. Greenhill's formula is much more complicated in full form. The rule of thumb that Greenhill devised based upon his formula

420-560: The stability factor for a known bullet and twist rate: s = 30 m t 2 d 3 l ( 1 + l 2 ) {\displaystyle {s}={\frac {30m}{t^{2}d^{3}l(1+l^{2})}}} Solving the formula for T {\displaystyle T} gives the twist rate in inches per turn: T = 30 m s d l ( 1 + l 2 ) {\displaystyle {T}={\sqrt {\frac {30m}{sdl(1+l^{2})}}}} Note that

441-444: The two units are not equal, the relative difference (less than 0.000 015% ) is negligible for most practical uses. For much of human history, the pressure of gases like air was ignored, denied, or taken for granted, but as early as the 6th century BC, Greek philosopher Anaximenes of Miletus claimed that all things are made of air that is simply changed by varying levels of pressure. He could observe water evaporating, changing to

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