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Rifles, Reloading, Optics, Equipment
Rifles, Bullets, Barrels & Ballistics
Light, high BC bullet
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<blockquote data-quote="Warren Jensen" data-source="post: 20901" data-attributes="member: 21"><p>Vince,</p><p></p><p>The explanation you want would be easier to give with the aid of graphics. I may get a little long winded, but bear with me.</p><p></p><p>Using the correct Siacci Function (G1,G5,G6,G7) for the bullet will give a better approximation of the bullet's trajectory than strickly using the G1 curve for all bullets. (Take note of the word approximation, as I will expand on that later.) I am not aware of a popular ballistics program that uses anything other than the G1 function. The G1 is for flat-base bullets with tangential ogives of about 2R. The G5 function is for boattail bullets with tangential ogives of about 6R. The G6 function is for flat base bullets with tangential ogives of about 7R. The G7 function is for boattail bullets with secant ogives of about 10R. All of these functions are mathematical models. All will provide good numbers in two planes of motion, but completely ignore the third plane. For ranges out to 1000 yds for 308 class cartridges and 1300 for the bigger stuff they are good enough. Beyond that the errors start to grow, unless the bullets are balanced, in which case the G functions will be real close. The plane that the Siacci Functions does not account for is the Z axis, drift due to precession, and the axial components of this. When computing the drag coefficient only the side cutaway of the bullet is considered.</p><p></p><p>To get a more accurate trajectory model you have to consider the bullet in three axis and include it's rotational characteristics. When most folks picture a bullet in flight the picture they see is that of the bullet as it was taken out of the box before it was loaded in the case. A bullet in flight does not look like this at all. It has been extruded down a tube, engraved by the rifling, and is slightly longer than it was coming out of the box. It's flight WILL be effected by these changes and more particularly the specific changes that the engraving made to the physical characteristics of the bullet. This is where the word APPROXIMATE that I mentioned above comes in. No ballistics program, none, zero, zip, nada accounts for this. The rate of spin, the rate of decay of that spin, the width and depth of the engraving marks, the density of the projectile, and the surface area of the projectile all have to be accounted for if the trajectory is to be predicted accurately.</p><p></p><p>Let me explain. It is a rule of thumb that rotational (axial) drag is always less than linear (horizontal) drag. (At least it used to be.) This means that with time the bullet will be spinning faster and faster relative to it's forward velocity. It is also a rule of thumb that a bullet is most accurate when it is just stable. Spin is necessary to keep the bullet pointed nose forward, but every bit of spin above what is just necessary starts to cause unwanted things to happen. The more spin above what is necessary the more the unwanted things increase. These include precession, yaw, Magnus moment, and slow and fast mode oscillations. Precession and yaw are the ones that have the most direct effect on the trajectory. As the spin increases the bullets longintudinal axis begins to pivot such the the nose of the bullet is flying a little high and to the right of the oncoming air. It is drawing little cirles in the air. As the precession increases this offset increases and the size of the circles increase. The bullet will begin to yaw and buffet. The effective form factor is decreasing as is the effective BC. This is not really noticeable on round nose or G1 projectiles because there is no real different between the aerodynamic center of the nose and being slightly offset. It really becomes apparent with long, sharp nose bullets, and is the reason that bullets with very fine meplates have been considered inaccurate by many. They simply require a much finer level of tuning than do less sharply pointed bullets. Anyway, this precession, yaw, and increase in drag is completely unaccounted for in the Siacci functions.</p><p></p><p>The rate that the precession occurs is a function of the relationship between the forward drag and the axial drag. The axial drag is effected by the twist rate, the number, width and depth of the lands, the surface area of the bullet, and the effective roughness caused by the engraving. Different twist rates, different land configurations, etc. will impart to the bullet different axial drag numbers which in turn will effect the actual precession that the bullet will have. Therefore, to know exactly what trajectory your bullet will follow, especially past 1000 yds, you have to know these characteristics. </p><p></p><p>OR, you can shoot your bullet from your rifle and plot where it impacts at the various long ranges. This will give you the same effective information, but without all the math. Your trajectory will be slightly to greatly different from the same load and bullet fired from a different rifle with a different twist, and/or, land and groove configuration. It will not match exactly any of the Siacci Functions.</p></blockquote><p></p>
[QUOTE="Warren Jensen, post: 20901, member: 21"] Vince, The explanation you want would be easier to give with the aid of graphics. I may get a little long winded, but bear with me. Using the correct Siacci Function (G1,G5,G6,G7) for the bullet will give a better approximation of the bullet's trajectory than strickly using the G1 curve for all bullets. (Take note of the word approximation, as I will expand on that later.) I am not aware of a popular ballistics program that uses anything other than the G1 function. The G1 is for flat-base bullets with tangential ogives of about 2R. The G5 function is for boattail bullets with tangential ogives of about 6R. The G6 function is for flat base bullets with tangential ogives of about 7R. The G7 function is for boattail bullets with secant ogives of about 10R. All of these functions are mathematical models. All will provide good numbers in two planes of motion, but completely ignore the third plane. For ranges out to 1000 yds for 308 class cartridges and 1300 for the bigger stuff they are good enough. Beyond that the errors start to grow, unless the bullets are balanced, in which case the G functions will be real close. The plane that the Siacci Functions does not account for is the Z axis, drift due to precession, and the axial components of this. When computing the drag coefficient only the side cutaway of the bullet is considered. To get a more accurate trajectory model you have to consider the bullet in three axis and include it's rotational characteristics. When most folks picture a bullet in flight the picture they see is that of the bullet as it was taken out of the box before it was loaded in the case. A bullet in flight does not look like this at all. It has been extruded down a tube, engraved by the rifling, and is slightly longer than it was coming out of the box. It's flight WILL be effected by these changes and more particularly the specific changes that the engraving made to the physical characteristics of the bullet. This is where the word APPROXIMATE that I mentioned above comes in. No ballistics program, none, zero, zip, nada accounts for this. The rate of spin, the rate of decay of that spin, the width and depth of the engraving marks, the density of the projectile, and the surface area of the projectile all have to be accounted for if the trajectory is to be predicted accurately. Let me explain. It is a rule of thumb that rotational (axial) drag is always less than linear (horizontal) drag. (At least it used to be.) This means that with time the bullet will be spinning faster and faster relative to it's forward velocity. It is also a rule of thumb that a bullet is most accurate when it is just stable. Spin is necessary to keep the bullet pointed nose forward, but every bit of spin above what is just necessary starts to cause unwanted things to happen. The more spin above what is necessary the more the unwanted things increase. These include precession, yaw, Magnus moment, and slow and fast mode oscillations. Precession and yaw are the ones that have the most direct effect on the trajectory. As the spin increases the bullets longintudinal axis begins to pivot such the the nose of the bullet is flying a little high and to the right of the oncoming air. It is drawing little cirles in the air. As the precession increases this offset increases and the size of the circles increase. The bullet will begin to yaw and buffet. The effective form factor is decreasing as is the effective BC. This is not really noticeable on round nose or G1 projectiles because there is no real different between the aerodynamic center of the nose and being slightly offset. It really becomes apparent with long, sharp nose bullets, and is the reason that bullets with very fine meplates have been considered inaccurate by many. They simply require a much finer level of tuning than do less sharply pointed bullets. Anyway, this precession, yaw, and increase in drag is completely unaccounted for in the Siacci functions. The rate that the precession occurs is a function of the relationship between the forward drag and the axial drag. The axial drag is effected by the twist rate, the number, width and depth of the lands, the surface area of the bullet, and the effective roughness caused by the engraving. Different twist rates, different land configurations, etc. will impart to the bullet different axial drag numbers which in turn will effect the actual precession that the bullet will have. Therefore, to know exactly what trajectory your bullet will follow, especially past 1000 yds, you have to know these characteristics. OR, you can shoot your bullet from your rifle and plot where it impacts at the various long ranges. This will give you the same effective information, but without all the math. Your trajectory will be slightly to greatly different from the same load and bullet fired from a different rifle with a different twist, and/or, land and groove configuration. It will not match exactly any of the Siacci Functions. [/QUOTE]
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