SILENCER SATURDAY #335: Let’s Do The Twist - Bullet Weights (Lengths)

Pete
by Pete

Good evening everyone and welcome back to TFB’s Silencer Saturday brought to you by Yankee Hill Machine, manufacturers of the brand new YHM 338 Bad Larry Suppressor. Last week we discussed holsters for suppressed pistols and a handful of models currently on the market. This week we get out our pocket protectors and nerd caps and talk about the importance of the optimal twist rate for a specific bullet length when shooting a suppressed platform. Fear not, there is no test at the end of today’s lesson. Let’s take a look.


Before we begin, I’d like to add my standard disclaimer: I am not a scientist, but I do play one on the internet. Before modifying any weapon or component from its factory configuration, understand the legal and safety implications. If you are unsure of your knowledge, skills, or abilities, stop what you are doing and seek professional guidance.


SILENCER SATURDAY #335: Let’s Do The Twist - Bullet Weights (Lengths)


Let’s start with the basics, shall we - why is it important that bullets spin in flight?


The dynamics of bullets in flight are significantly influenced by whether or not they spin. A spinning bullet, fired from a rifled barrel, benefits from gyroscopic stability, much like a spinning top. This gyroscopic effect helps the bullet maintain a consistent trajectory, reducing the likelihood of tumbling or veering off course, which greatly enhances its accuracy, especially over long distances. The spin also helps the bullet maintain a streamlined shape, minimizing air resistance and allowing it to travel further with a more predictable flight path. This stability also mitigates the impact of minor imperfections in the bullet or barrel, contributing to a more consistent performance.


On the other hand, a non-spinning musket ball, fired from a smooth bore barrel, lacks this stability and is prone to tumbling or wobbling in flight. This instability results in an unpredictable trajectory, reducing accuracy and making the musket ball more susceptible to external factors such as wind and imperfections. The lack of spin increases air resistance, which slows the musket ball’s velocity more quickly and limits its effective range. This erratic flight path means that musket balls lose kinetic energy more rapidly, diminishing their impact upon reaching the target.


In short, spinning bullets benefit from enhanced precision due to the gyroscopic effect, extended range from improved aerodynamics, and better energy retention leading to greater penetration and impact. These advantages have made rifled barrels and spinning bullets the standard for nearly all modern firearms outside of smooth-bored shotguns.


Rate of Spin:


Contrary to what most of us understand, it is a bullet’s length, not its weight in grains, that determines the best aerodynamic performance. It is because heavier bullets are often longer that the two physical characteristics are often confused.


The relationship between the rate of spin for an object in flight and its length is important in determining the object's stability and accuracy. Generally, longer projectiles require a faster spin rate to maintain stability due to their increased moment of inertia. When a longer projectile spins too slowly, it is more susceptible to destabilizing forces, leading to tumbling in flight. This instability results in an unpredictable trajectory, reducing accuracy and potentially causing the projectile to deviate significantly from its intended path (ie where you are aiming).


On the other hand, when a longer projectile spins at a faster rate, it benefits from greater gyroscopic stability, maintaining a straighter and more predictable flight path. The increased spin rate counteracts any destabilizing forces, ensuring that the projectile remains oriented correctly with its nose forward, enhancing accuracy and effectiveness.


By The Numbers


Determining the optimal rate of spin for a specific length of an object, such as a bullet, involves understanding the relationship between the projectile’s dimensions and the rifling of the barrel. This is typically calculated using the Greenhill Formula, which provides a guideline for the rate of twist necessary to stabilize a bullet. Here’s a short explanation of the calculations involved:


The Greenhill Formula, developed by Sir Alfred George Greenhill, is commonly used to estimate the rifling twist rate required to stabilize a bullet.


The formula is:

Where:

  • C is a constant (usually 150 for bullets traveling at speeds typical of rifle bullets, but it can be adjusted to 180 for higher velocity projectiles).
  • D is the diameter of the bullet in inches.
  • L is the length of the bullet in inches.


Consider a bullet with a diameter of 0.308 inches (7.8 mm) and a length of 1.2 inches (30.5 mm):


Given:

  • Diameter (DD) = 0.308 inches
  • Length (LL) = 1.2 inches
  • Constant (CC) = 150 (for standard rifle velocities)


Let’s apply the Greenhill Formula:

And Calculate:

So, the optimal twist rate for this bullet is approximately 1 turn in 11.86 inches.


Stability Factor (Miller Stability Formula)


In addition to the Greenhill Formula, the Miller Stability Formula can be used to assess the stability factor of a bullet. The formula is:

  • Sg​ is the gyroscopic stability factor.
  • mm is the mass of the bullet in grains.
  • dd is the bullet diameter in inches.
  • ll is the bullet length in calibers (diameter multiples).
  • vv is the muzzle velocity in feet per second.
  • rr is the rifling twist rate in calibers (inches).


A stability factor (Sg) between 1.3 and 2.0 is generally considered optimal for most bullets, indicating stable flight without excessive spin.


What the Heck Does All This Have to Do With Silencers?


I’m glad you finally asked. One important topic that is often overlooked, especially for heavy, subsonic rifle ammunition, is the rate of twist. Many rifle platforms are designed to stabilize very fast bullets that are pushing in excess of 2,500 fps. If that same platform is used to launch longer/heavier bullets at under 1,100 fps, there is a good chance that bullet will not stabilize, dramatically effecting accuracy. A silencer on the end of that barrel risks catastrophic damage because the destabilization could occur as soon as the bullet leaves the muzzle.


I am not suggesting that you should bring a scientific calculator with you evertime you buy ammo. But a proper understanding of your platform’s rate of twist and your bullet’s weight (length) will help keep you out of trouble.


Thanks for reading. Be safe, have fun, and we’ll see you back here next week for another Silencer Saturday.



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Pete
Pete

Silencers - Science Pete@thefirearmblog.com

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