If you want to get the corrected values for torsion and stability factor: Plus or minus. The data Miller used to box the ruler consisted of data from flat projectiles and boat tails. The data for boattail balls match better than that for flat balls, but it`s still a pretty good approximation. As with any calculation, use a reasonable margin of safety, because real life sometimes comes into play. Greenhill`s formula: Introduced in 1879 by Professor George Greenhill, it is still used as a rule of thumb for estimating the torsion rate t in inches per mm using the equation: If we take the Nosler Spitzer .30-06 Springfield shell, which is similar to the one pictured above, we can easily fill in the variables and calculate the estimated torsion rate. [2] Starting with the formula, where PstdP_mathrm{std}Pstd and PTP_mathrm{T} PT are the standard and current atmospheric pressures. TCT_mathrm{C}TC and TFT_mathrm{F}TF are the temperature in the Fahrenheit and Celsius scales, respectively. As with the height correction factor, the square root of the above factor is multiplied by the uncorrected torsion t and the stability factor s to obtain the corrected result. Therefore, the optimal twist rate for this ball should be about 12 inches per revolution. The typical rotation of .30-06 caliber rifle barrels is 10 inches per cartridge, being able to accommodate heavier bullets than in this example. A different turnover rate often helps explain why some bullets perform better in certain rifles when fired under similar conditions.
The above formulas for rifle rotation speed do not take into account conditions such as temperature, atmospheric pressure and altitude. The change of conditions leads to a change in the stability factor and therefore the need to change the barrel with a different torsional speed or the projectile. It is also necessary to make corrections to the formula based on the initial speed. These conditions would have an impact on the stability of the sphere of 20% or even more. Greenhill`s formula is much more complicated in its complete form. The rule of thumb developed by Greenhill based on his formula is actually what can be seen in most writings, including Wikipedia. The rule of thumb is: find the appropriate twist rate with Miller`s rotation rule for a 168 gr ball with a diameter of 0.308 inches and a length of 3.98 inches. Consider the stability factor s as 1.8. Similarly, the equation for the uncorrected torsion t, given in size torsion, is obtained by rearranging the terms: It is of course possible to solve the torsion in inches directly by simply solving Miller`s formula for s {displaystyle s} gives the stability factor for a known enumeration and the torsion rate: With Miller`s formula we can also calculate the stability factor, provided we already know the twist. Easy to solve.
The square root of the above correction factor is multiplied by the torsion t resulting from Miller`s rotation rule to obtain the corrected torsion of the initial velocity. Therefore, Miller essentially took Greenhill`s rule of thumb and expanded it slightly, while the formula remained simple enough to be used by someone with basic math skills. To improve Greenhill, Miller primarily used empirical data and basic geometry. So our rifle should be about 12″ per turn. The rotation, as stated in the Wikipedia article .30-06, is 10 inches per turn as the average .30-06 rifle; Thus, 12 inches per turn is quite accurate. The discrepancy observed here also explains why some bullets in some rifles seem to work best when fired under similar conditions. The distance traveled by a projectile to make a complete revolution along its longitudinal axis is called rotational speed. It is measured in inches or mm per revolution. The square root of the above factor is directly multiplied by the stability factor s and twisted to obtain the corrected values. Miller-Twist rule: The rule uses a semi-empirical relationship to estimate the stability of the projectile. The dimensionless gyro stability factor s for a ball with mass m and dimensional parameters like diameter D and length L is: Initially, the value of s is used as 2.0, which is known as the safety value for the stability factor. The torsion rate in inches per revolution T can be determined by multiplying the torsion t of Miller`s rotation rule by the diameter of the ball.
This calculator gives you the value of T directly. The yaw rate calculator helps you determine the stability of a bullet when fired from a specific fired barrel. It has long been known that a ball must rotate or rotate along the longitudinal axis in order to travel long distances while maintaining stability. This rotation of a ball is induced by the introduction of grooves into the barrel. The stability of the bullet varies between guns and is estimated using Greenhill`s formula or Miller`s rotation rule. Read on to understand what torsion rate is and how to calculate torsion rate. Amazingly. Compared to the more detailed classical methods for determining the stability of the ball, Miller is very suitable. However, there is one caveat. Miller`s rule is based on a library of test data collected by the BRL. The less your sphere resembles the projectiles used in the library, the more likely it is that the rule will not fail.
In other words, Miller works great for reasonable balls. If you start getting into crazy numbers (say, a 200-grain bale .224), it won`t work very well. where T {displaystyle T} = torsion rate in inches per revolution, and Miller`s rotation rule applies to parameters in English units such as: This calculator uses the classic method of calculating gyroscopic stability described by Bob McCoy in his book Modern Exterior Ballistics. Since the classical method requires detailed ball dimensions and aerodynamic coefficients, we apply the simplifications derived by Don Miller in his article A New Rule for Estimating Rifling Twist – An Aid to Choosing Bullets and Rifles and the subsequent article How Good are Simple Rules for Estimating Rifling Twist. The „Miller`s rule,” as it is often called, uses empirical data to simplify mathematics to the point where only the length of the chip is required. The price of the precision of this simplification is surprisingly low. Miller`s torsion rule is a mathematical formula derived from Don Miller to determine the rotational speed that must be applied to a particular ball to ensure optimal stability with a stretched barrel. [1] Miller suggests that while Greenhill`s formula works well, there are better and more accurate methods for determining the correct torsion rate that are no more difficult to calculate.
The result shows an optimal torsion rate of 39.2511937 calibers per revolution. Determine T {displaystyle T} from t {displaystyle t} we have The speed correction ( v {displaystyle v} ) for torsion ( T {displaystyle T} ): f v 1 / 2 = [ v 2800 ] 1 / 6 {displaystyle f_{v}{^{1/2}}=[{frac {v}{2800}}]^{1/6}} Projectile motion Visit the projectile range calculator, time-of-flight calculator and projectile motion calculator to learn the basics of the projectile`s trajectory. The process of having grooves in a single stroke is called rifling. It is given in terms of torsion rate. This twist rate is defined as the distance traveled by a ball to complete a complete turn. A barrel twist rate is measured in 1:x inches, i.e. 1 turn in x inches or alternatively x inches per turn in English units or 1 turn in y mm in SI units. There are two common formulas for calculating the required rifle turnover rate and bullet stability. Using a Nosler Spitzer sphere in a Springfield .30-06 similar to the one shown above, and replacing the variable values, we determine the estimated optimal torsion rate.
[2] Much of this is attributed to various forms of projectiles that match aerodynamics to prevent falls into the air and achieve greater stability. The stability of the projectile was improved by inducing the rotation of the projectile along its longitudinal axis to ensure a higher time of flight and range. The spin is obtained by the torque exerted by the grooves inside the barrel. Velocity correction: For a projectile with a muzzle velocity greater than 2800 ft/s (~853 m/s), the correction factor fvf_mathrm{v} fv can be calculated as follows: Miller notes several correction equations that can be used: To calculate the temperature correction factor on the Fahrenheit scale: Similarly, the correction factor is directly related to the gyro stability factor s as: Yes. The faster you spin a ball, the less accurate it will be. There is no reason to spin a ball faster than necessary to get the desired (S_g). For optimal accuracy, I shoot for 1.3-1.4. For ballistic optimization, 1.5-1.7 is a better number. Everything faster leads to poor accuracy and possibly bullet destruction.
Altitude correction factor: This factor is used to account for high or low height. The correction factor is a function of the altitude or height in feet above sea level:. where L {displaystyle L} = ball length in inches. 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}}}} $$S_g = {{8pi} over {rho_{air}t^2d^5C_{Malpha}}}{{A^2}over{B}} $$.