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Bullet stability is a topic that seems to have many long ranges enthusiasts chasing their tails round and round. There are a number of dynamically interrelating factors that play off of each other in various ways resulting in a bullets overall stability or instability. Whether you are using the Greenhill formula, the Miller formula, or McGryo's mathematical monster - the full story of any bullet's stability characteristics is incredibly difficult to express on paper.
Twist Rates: Determining which twist rate is most appropriate for a given bullet is the big question here. One can get a basic idea as to the predicted stability trends a particular bullet may display when fired through a certain twist, but the only way to know for sure is test it in the field. Often, bullets that should be too long and heavy for a given twist work great while other bullets that should have been easy to tame are going wild. Most manufacturers publish their recommended twist rates for their different bullet tests, so this may be a good way to go. If you don't know what twist would be best, you can try one of the formulas to get a basic estimation.
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In this video we will cover axis of symmetry, principle axis of inertia, statically imbalanced projectiles, and dynamically imbalanced projectiles. We also explore how imbalanced bullets can experience lateral throw off and aerodynamic Jump.
Summary:
1. Spin is required to stabilize bullets in flight.
2. Defects in bullet construction can throw off balance resulting in a statically imbalanced projectile. Also, in-bore tipping can cause the projectile to be dynamically imbalanced, which can cause aerodynamic jump.
3. The faster the twist-rate, the more deviation one can experience due to these factors.
CONCLUSIONS:
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Rifle bullets often spin at over 200,000 RPM! This generates a tremendous 'centrifugal force' which can have some interesting effects on a bullet's external ballistic performance. In this video, Rex explains overstabilization and how it stiffens up a bullet's spin axis to where it experiences a loss in tractability which can lead to increased bullet yaw and spin drift at extreme long ranges.
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Understanding the concepts of gyroscopic stability, overstabilization, dynamic stability the bullet's yaw of repose, tractability and Magnus effect are going to be key if we wish to understand a bullet's Yaw of Repose and correct for spin drift. In this video, Rex shows how a rifle bullet's aerodynamic stability and tractability are mathematically expressed so that we will be better equipped to understand some of the challenges we will encounter when trying to correct for bullets entering the transonic zone. Rex also defines the terms and sets up the knowledge base you will need in order to understand Magnus Effect and spin drift.
In this video, Rex reviews the following concepts in greater detail:
Gyroscopic Stability
Over-Stabilization
Statically Stabile
Dynamically Stable
Dynamic Stability Factor
Yaw of Repose
Tractability
Tractability Factor
Magnus Effect
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All the music in this video was created by TiborasaurusRex, an unsigned artist.
Song Title: Wadi Watir, Under the Ice
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Magnus effect: an effect in which induced pressure differences act upon a spinning projectile deflecting its course by twisting its axis of symmetry off of its axis of flight.
In this video, Rex explains how air flowing around the spinning bullet creates high pressure zones that push on the bullet's center of pressure, causing the bullet to fly crooked through the air. This "yaw" affects the bullets aerodynamic stability which can change the ballistic coefficient as yaw changes as well as affecting its direction of travel as the nose is pointed off center. The Magnus Force is always perpendicular to the sideways vector of the wind acting on the bullet.
Crosswinds Affect Bullet Stability: The Magnus force greatly affects stability because it tries to "twist" the bullet along its flight path.
NOTES: Right Hand wind twist (clockwise)
Wind from Right - Nose shifted Downward into the axis of flight (stabilizing)
Wind from Left - Nose shifted Upward away from axis of flight (destabilizing)
The vertical deflection value tends to be small in comparison with the horizontal wind induced deflection component (10mph starts to make a difference).
NOTES: Yaw caused by Magnus Effect causes Spin Drift
In right hand twist barrels, bullets drift to the right
In left hand twist barrels, bullets drift to the left
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To make your own spin drift tables for your extreme long range precision rifle - watch this video now! This video introduces you to the math behind spin drift calculations as well as the ballistic software that can make your life much easier. The ballistic tables featured in this video are continuously being updated and improved - so be sure to check for updated versions as time goes on. For full context and background on this subject please watch the preceding videos. These Ballistic Excel tables were created by: meccastreisand w/prior contributions from TiborasaurusRex, Arthur Pejsa, Dean Michaelis, Russ Ring, and Jackson Rifles.
Click on below link to download the latest version of these Ballistic Tables:
https://drive.google.com/folderview?id=0B2_BBw2VMf2-VUJZNXVTM0M1akE&usp=sharing
??? If you can't get this to work or figure this out, please watch the end of this video for more detailed instructions.
TECHNICAL QUESTIONS: Please direct your questions to Ballistic_XLR on Twitter or you can contact him via YouTube through private message directed to meccastreisand - he is the ballistic programming ninja you seek :-) Be sure to thank him for his hard work on this project.
ALSO: www.sniper-101.com COMING SOON!!! Log in now for news letter and updates on when it will be fully operational.
Thank you for your donations to the Rex Reviews Project! We hope these videos continue to be a great help to you all.
All the music in this video was created by TiborasaurusRex, an unsigned artist.
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What are you reading stuff way down here for??? Go back up to the top...
Coriolis effects on rifle bullets explained in detail. Yes, the Earth's spin affects the apparent flight path of a rifle bullet when fired at extreme long ranges. How much do you adjust for coriolis? Watch this!
NOTES (to burn into your brain):
Magnitude Depends on Latitude - Poles: Maximum Deflection - Equator: Zero Deflection
Vertical Coriolis Correction
Deflection Changes Respective to Direction of Fire - Shooting Due North - Deflection is ZERO - Shooting Due South - Deflection is ZERO - Shooting East -- Deflects POI HIGH (adjust fire Down) - Shooting West -- Deflects POI LOW (adjust fire Up)
Magnitude Depends on Latitude - Poles: Zero Deflection - Equator: Maximum Deflection
Click on below link to download the latest version of the Excel Ballistic Tables being used in this video:
https://drive.google.com/folderview?id=0B2_BBw2VMf2-VUJZNXVTM0M1akE&usp=sharing
??? If you can't get this to work or can't figure this out, please watch the preceding VIDEO on Spin Drift (SNIPER 101 Part 72) for further instructions...
TECHNICAL QUESTIONS on MS Excel Tables: Please direct your questions to Ballistic_XLR on Twitter or you can contact him via YouTube through private message directed to meccastreisand - he is the ballistic programming ninja you seek :-) Be sure to thank him for his hard work on this project.
ALSO: www.sniper-101.com COMING SOON!!! Log in now for news letter and updates on when it will be fully operational.
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Should horizontal correction be multiplied with the cosine of your heading in relation to a N-S line?
Where is horizontal component when shooting due east and west?
Horizontal correction will NOT be multiplied by the cosine of your heading. At the distances we are shooting, horizontal Coriolis effect is only a function of latitude and time of flight. Out to 2000m, azimuth differences will have no effect on our horizontal correction. It is true that beyond 2000m, you will start to see a small effect on horizontal deflection's magnitude due to azimuth although its direction stays the same. If you look at a TFT for a 105mm gun, the horizontal correction @ 5000m for due North is 0.4 mils L while shooting due East it is still only 0.5 mils L (a very small difference). The reason for this is that a projectile will never travel in a straight line between two points on the surface of a sphere with an unchanging azimuth. If the Earth was a cylinder, this would be much more simple. If you would like to confirm this from other sources to put you mind at rest, please look at the BRL Report No. 1371 The Production of Firing Tables for Cannon Artillery (Nov 1967) page 102. The Kestrel Horus device will also confirm that horizontal Coriolis (inside of 2000 - 2500 meters) is independent of DOF as well.
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How far can a rifle shoot effectively? How does the .408 Chey Tac attain balanced flight? What twist rate is best for extreme long range applications? To answer these questions, there is an outer barrier to be aware of. Your maximum effective range may be limited to your max super-sonic range depending on how well your bullet passes through the transonic zone.
In this video, Rex discussed the behavior of a rifle bullet passing though he transonic zone. The transonic The Transonic zone lies between about Mach 1.2 and 0.8.
The Centre of Pressure (CP) of most bullets shifts around as the angle of attack changes and as velocities decays. The CP experiences a dramatic shift when it crosses the sonic barrier. This shift negatively affects the (dynamic) stability of the bullet. This loss in dynamic stability can cause significant shot dispersion in which coning motion starts, & if it is not damped out it may encounter uncontrollable tumbling. Mathematically correcting for the erratic ballistic behavior of bullets that have passed through the transonic region is extremely difficult. Air density also has a significant effect on dynamic stability during the transonic transition. Thus, thin air poses less of a problem.
Tractability
Tractability factor characterizes the ability of the projectile's longitudinal axis to follow the bending trajectory. The tractability factor is proportional to the inverse of the gyroscopic (static) stability factor. The greater the static stability, the lower the tractability factor -- which can often translate decreased dynamic stability at extreme long ranges.
Balanced Flight
Balanced flight technology utilizes a combination of both projectile profile and special rifling design that ensures the bullet's rotational rate decays proportionally to the decay of its forward velocity. This loosens up the bullets axis of rotation downrange so that its nose can stay on track with the line of trajectory throughout the
In this video Rex will discuss bullet drag, ballistic coefficients, form factor, sectional density, the history of the G1 drag function, G1 VS G7 drag functions, and the effects of dynamic instabilities on bullet drag.
Definitions:
Ballistic Coefficient (B.C.) -- The ratio of The ratio of velocity retardation due to air drag for a particular bullet to that of its larger 'G' Model standard reference projectile due to air drag for a particular bullet to that of its larger 'G' Model standard reference projectile
c=WID^2
c = ballistic coefficient
W = mass of bullet in pounds
I = form factor (determined from a test projectile of the SAME SHAPE)
D = bullet diameter (inches)
Ballistic Coefficient = (Bullet Sectional Density) / (Bullet Form Factor- OF THE SAME SHAPE!!!)
Form Factor: A multiplier which relates the shape of a bullet to the shape of the standard projectile used to prepare the particular ballistic table.
Form Factor (coefficient of retardation) = (C.D. of any bullet) / (C.D. of the Defined 'G' Function Std. Bullet)
Coefficient of Drag (C.D.) = an aerodynamic factor that relates air drag to air density, cross-sectional area, velocity and mass.
Sectional Density: (weight multiplied by its frontal area) can then be used to relate the drag coefficient to different bullet sizes.
Dynamic instability has a tremendous effect on a projectile's trajectory. As the yaw increases, the drag increases, the bullet's velocity is far more retarded. These instabilities are not totally predictable and thus predicting and EXACT firing solution is very difficult.
LIST of Drag Functions and their applications:
G1 Standard model, Flat Based with 2 caliber (blunt) nose ogive
G5 For Moderate (low base) Boat Tails - 7° 30' Tail Taper with 6.19 caliber tangent nose ogive
G6 For flat based "Spire Point" type bullets - 6.09 caliber secant nose ogive
G7 For "VLD" type Boat Tails with long 7.5 degree Tail Taper with 10 caliber tangent
How do you shoot at long range? Depending on the size of your target, the distance to that target and the atmospheric conditions at the time of firing on that target, there are a number of variables you will need to correct for IF you wish to score a clean 1st round hit. There are a number of ways that long range precision shooters use to address all the different variables to make long range shots. So, let us examine the different ways folks use to adjust fire when shooting at long ranges and examine their suitability at the various ranges at which they are most commonly employed.
Corrective techniques discussed in this video:
Point Blank Zero
S.W.A.G.
Calculated Hold-Off
Ballistic Drop Compensation (BDC) techniques
Detailed Ballistic Tables
CALC-FORMS
Handheld Ballistic Computers & phone apps.
Range Categories Discussed in this Video:
Close Range (Point Blank Range) - No holdover need to hit most targets, point blank zero is most common method of engagement. (typically 0 - 300 meters)
Medium Range - Where bullet drop needs to be corrected for, not quite far enough to warrant significant atmospheric corrections. (typically 300 - 600 meters)
Long Range - Where atmospheric corrections need to be applied to the bullet drop in order to hit the target. (typically 600 - 1000 meters)
Extreme Long Range - Where spin drift and Coriolis Effect begin to have a significant impact on POI. (typically 1,000+ meters)
Depending on your cartridge and load, the values of these range categories will vary. In order to have the best results, always adjust fire as precisely as you can.
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All the music in this video was created by TiborasaurusRex, an unsigned artist.
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Calculating a precise firing solution at extreme long ranges can be very difficult. Rex's 3rd generation version of these ballistic calculation forms are designed to be much more intuitive and much more user friendly than other systems that employ the use of poorly understood and difficult to perceive ballistic constants.
In this video, Rex will walk you through the how to use your CALC FORM to adjust your fire for the following ballistic effects:
Ballistic CALC-FORM excel link:
https://drive.google.com/file/d/0Bzvx3RuRX1QTcHZDN2lQYWduZ2c/edit?usp=sharing
Follow these instructions for successful download: Follow the above web address or hyperlink --- "Download the Current Version" (by clicking the button showing a down pointing arrow) --- click "OPEN" on the popup menu --- click "Enable Editing" to use the sheets
Once you have the docs, be sure to save a master copy. There are a number of tabs on the bottom. These tabs include several CALC FORM configurations based on your optical sight configuration. Be sure to select the most appropriate forms for you scope set up. Also included are different PRIMARY FUNCTIONS and SECONDARY FUNCTIONS templates for different optical configurations. The last tab contains a Muzzle Velocity Variation Curve Generator which is very easy to use. If you have not yet confirmed you MVs at various ammunition temperature ranges, you can use this MVV Curve generator to get a ballpark idea of what MV trends you can expect at different ammo temperatures.
Please feel free to modify and customize these forms as needed for your applications.
Calculating a precise firing solution at extreme long ranges can be very difficult. Rex's 3rd generation version of these ballis
In this video, Rex discusses how to set up your primary ballistic functions in an intuitive way so that you can easily digest and comprehend the ballistic character of your projectile. Rex goes through set-up, optics configurations, designated standard conditions, confirming your zeroes, calculating your ballistic correction values, muzzle velocity variation, and much more.
Ballistic CALC-FORM excel link:
https://drive.google.com/file/d/0Bzvx3RuRX1QTcHZDN2lQYWduZ2c/edit?usp=sharing
Follow these instructions for successful download: Follow the above web address or hyperlink --- "Download the Current Version" (by clicking the button showing a down pointing arrow) --click "OPEN" on the popup menu --- click "Enable Editing" to use the sheets. Once you have the docs, be sure to save a master copy. There are a number of tabs on the bottom. These tabs include several CALC FORM configurations based on your optical sight configuration. Be sure to select the most appropriate forms for you scope set up. Also included are different PRIMARY FUNCTIONS and SECONDARY FUNCTIONS templates for different optical configurations. The last tab contains a Muzzle Velocity Variation Curve Generator which is very easy to use. If you have not yet confirmed you MVs at various ammunition temperature ranges, you can use this MVV Curve generator to get a ballpark idea of what MV trends you can expect at different ammo temperatures.
For the Ballistic Excel tables created by: meccastreisand w/prior contributions from TiborasaurusRex, Arthur Pejsa, Dean Michaelis, Russ Ring, and Jackson Rifles. Click on below link to download the latest version of these Ballistic Tables:
https://drive.google.com/folderview?id=0B2_BBw2VMf2-VUJZNXVTM0M1akE&usp=sharing
TECHNICAL QUESTIONS: Please direct your questions concerning these excel tables to Ballistic_XLR on Twitter or you can contact him via YouTube through private message directed to meccastreisand - he is the ballistic progr
In this video, Rex discusses how to set up your secondary ballistic functions.
Ballistic CALC-FORM excel link:
https://drive.google.com/file/d/0Bzvx3RuRX1QTcHZDN2lQYWduZ2c/edit?usp=sharing
Follow these instructions for successful download: Follow the above web address or hyperlink --- "Download the Current Version" (by clicking the button showing a down pointing arrow) ---click "OPEN" on the popup menu --- click "Enable Editing" to use the sheets
Once you have the docs, be sure to save a master copy. There are a number of tabs on the bottom. These tabs include several CALC FORM configurations based on your optical sight configuration. Be sure to select the most appropriate forms for you scope set up. Also included are different PRIMARY FUNCTIONS and SECONDARY FUNCTIONS templates for different optical configurations. The last tab contains a Muzzle Velocity Variation Curve Generator which is very easy to use. If you have not yet confirmed you MVs at various ammunition temperature ranges, you can use this MVV Curve generator to get a ballpark idea of what MV trends you can expect at different ammo temperatures.
For the Ballistic Excel tables created by: meccastreisand w/prior contributions from TiborasaurusRex, Arthur Pejsa, Dean Michaelis, Russ Ring, and Jackson Rifles. Click on below link to download the latest version of these Ballistic Tables:
https://drive.google.com/folderview?id=0B2_BBw2VMf2-VUJZNXVTM0M1akE&usp=sharing
TECHNICAL QUESTIONS: Please direct your questions concerning these excel tables to Ballistic_XLR on Twitter or you can contact him via YouTube through private message directed to meccastreisand - he is the ballistic programming ninja you seek :-) Be sure to thank him for his hard work on this project.
All the music in this video was created by TiborasaurusRex, an unsigned artist.
Song Titles: Wadi Watir, Particle Jam
Music and Lyrics by: TiborasaurusRex
Instrumentation and Vocals by: TiborasaurusRex
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