Understanding Long Range Bullets Part 1:
Effects of Scaling on Gyroscopic Stability
Now you're in for it! How can I talk about stability without equations?! Well, I promise this section will be lighter on the math than the last section. You're 'over the hump' now.
The gyroscopic stability factor (Sg) is a measure of how well a bullet is stabilized. In theory, Sg only needs to be greater than 1.0 at the muzzle in order to be stable (not tumble) in flight. In practice, bullets should have an Sg of at least 1.4 in standard atmospheric conditions to allow for a margin of error. You control the Sg of your bullets by what twist you choose for your barrel. Faster twist gets you a higher Sg. Other factors affecting Sg are: atmospheric conditions; the denser the air,4 the lower the Sg. Muzzle velocity also affects Sg; faster muzzle velocity increases Sg. Figure 3 shows the gyroscopic stability of our bullets, fired at typical velocities, and how the Sg varies with barrel twist rate.
The one thing that's most apparent about Figure 3 is that the larger caliber bullets require slower twist rates to achieve the same Sg. Why is that? The answer, once again, lies in understanding the nature of scaling.
Two basic things contribute to the gyroscopic stability of spinning bullets:
As long as the inertial stabilizing effects are stronger than the aerodynamic de-stabilizing effects, the bullet flies point first.
The destabilizing aerodynamic effects are related to the area of the bullet and the separation between the center of gravity and the center of pressure. The stabilizing inertial effects are related more to the mass of the bullet. Does this sound familiar at all? It's the same logic involved in scaling the BC. Increasing the size of the bullet generates more stabilizing inertia than destabilizing aerodynamic torque6. The net result is that the larger bullet, fired at the same speed and rate of twist is more stable. Likewise, if you fire a bullet at a higher speed from the same twist barrel, even though the faster bullet has more aerodynamic torque trying to tip it over, the faster bullet is also spinning faster, giving it more stability. The net result is that the bullet is overall more stable when fired at higher velocities.
We've noted that the larger bullets require slower twists to be stable, and explained why. Now for the important question: Is there any practical consequence to a faster or slower twist? Tune in next month to find out!
The last thing I'll cover on stability is how it changes with muzzle velocity, and atmospheric conditions. The numbers in Figure 3 are reported for standard atmospheric conditions and for muzzle velocities typical for each round. I didn't look at atmospheric effects for BC, because it's a more trivial problem; you just multiply the BC by the air density ratio (Ref 4), and presto, you have your new effective BC. Sg is a little less intuitive because it involves inertial effects as well as aerodynamics. Let's take a look at the benchmark and see how the Sg reacts to some non-standard conditions.
In Figure 3, we found that the benchmark requires a 1:8.6 twist to achieve the desired Sg of 1.4 at 2950 fps. Table 1 shows what happens to Sg if we keep the 1:8.6 twist and change other conditions. Notice that for higher speeds and temperatures, the Sg goes up. For lower speeds and temperatures, the Sg goes down. Decreasing barometric pressure and increasing humidity also make the air less dense. These things have the same effect as increasing temperature.
Conclusions
In this first part, I've presented some information about the physical consequences of scaling bullets of similar shape thru a range of calibers.
First we looked at scaling effects on BC. Understanding the nature of scaling empowers you to identify trends and outliers, in spite of the 'smoke and mirrors' stigma associated with BC's.
Then we took a look at scaling effects on stability. We found that larger calibers require less twist to be stable than smaller calibers, provided they share common proportions. We finished with a look at how stability is affected by common variables like muzzle velocity and temperature.
A great deal of the information in this first part was academic. Next month, I'll draw on this material to see what the practical consequences are, and how shooters can use the information to make better decisions about the calibers and bullets they choose for long range target shooting.
4 Cold, dry, high pressure air is the most dense.
5 Minimum twist required for an Sg=1.4. You may get away with slightly lower twist, but it's not recommended. Higher twist rates are generally ok.
6 Because mass increases more than area for a given linear scale factor.
Bryan Litz majored in Aerospace Engineering at Penn State University and worked on air-to-air missile design for 6 years in the US Air Force before taking a job as Berger Bullets Chief Ballistician in November 2008. Bryan has been an avid long range shooter since the age of 15. In particular, Bryan enjoys NRA Long Range Prone Fullbore/Palma competition and is the current National Palma Champion. Bryan is also a husband and proud father of 3.
Now you're in for it! How can I talk about stability without equations?! Well, I promise this section will be lighter on the math than the last section. You're 'over the hump' now.
The gyroscopic stability factor (Sg) is a measure of how well a bullet is stabilized. In theory, Sg only needs to be greater than 1.0 at the muzzle in order to be stable (not tumble) in flight. In practice, bullets should have an Sg of at least 1.4 in standard atmospheric conditions to allow for a margin of error. You control the Sg of your bullets by what twist you choose for your barrel. Faster twist gets you a higher Sg. Other factors affecting Sg are: atmospheric conditions; the denser the air,4 the lower the Sg. Muzzle velocity also affects Sg; faster muzzle velocity increases Sg. Figure 3 shows the gyroscopic stability of our bullets, fired at typical velocities, and how the Sg varies with barrel twist rate.
The one thing that's most apparent about Figure 3 is that the larger caliber bullets require slower twist rates to achieve the same Sg. Why is that? The answer, once again, lies in understanding the nature of scaling.
Two basic things contribute to the gyroscopic stability of spinning bullets:
- Aerodynamic 'overturning' torque acts to de-stabilize the bullet
- Inertial effects of the spinning mass keep it stable.
As long as the inertial stabilizing effects are stronger than the aerodynamic de-stabilizing effects, the bullet flies point first.
The destabilizing aerodynamic effects are related to the area of the bullet and the separation between the center of gravity and the center of pressure. The stabilizing inertial effects are related more to the mass of the bullet. Does this sound familiar at all? It's the same logic involved in scaling the BC. Increasing the size of the bullet generates more stabilizing inertia than destabilizing aerodynamic torque6. The net result is that the larger bullet, fired at the same speed and rate of twist is more stable. Likewise, if you fire a bullet at a higher speed from the same twist barrel, even though the faster bullet has more aerodynamic torque trying to tip it over, the faster bullet is also spinning faster, giving it more stability. The net result is that the bullet is overall more stable when fired at higher velocities.
We've noted that the larger bullets require slower twists to be stable, and explained why. Now for the important question: Is there any practical consequence to a faster or slower twist? Tune in next month to find out!
The last thing I'll cover on stability is how it changes with muzzle velocity, and atmospheric conditions. The numbers in Figure 3 are reported for standard atmospheric conditions and for muzzle velocities typical for each round. I didn't look at atmospheric effects for BC, because it's a more trivial problem; you just multiply the BC by the air density ratio (Ref 4), and presto, you have your new effective BC. Sg is a little less intuitive because it involves inertial effects as well as aerodynamics. Let's take a look at the benchmark and see how the Sg reacts to some non-standard conditions.
In Figure 3, we found that the benchmark requires a 1:8.6 twist to achieve the desired Sg of 1.4 at 2950 fps. Table 1 shows what happens to Sg if we keep the 1:8.6 twist and change other conditions. Notice that for higher speeds and temperatures, the Sg goes up. For lower speeds and temperatures, the Sg goes down. Decreasing barometric pressure and increasing humidity also make the air less dense. These things have the same effect as increasing temperature.
Conclusions
In this first part, I've presented some information about the physical consequences of scaling bullets of similar shape thru a range of calibers.
First we looked at scaling effects on BC. Understanding the nature of scaling empowers you to identify trends and outliers, in spite of the 'smoke and mirrors' stigma associated with BC's.
Then we took a look at scaling effects on stability. We found that larger calibers require less twist to be stable than smaller calibers, provided they share common proportions. We finished with a look at how stability is affected by common variables like muzzle velocity and temperature.
A great deal of the information in this first part was academic. Next month, I'll draw on this material to see what the practical consequences are, and how shooters can use the information to make better decisions about the calibers and bullets they choose for long range target shooting.
4 Cold, dry, high pressure air is the most dense.
5 Minimum twist required for an Sg=1.4. You may get away with slightly lower twist, but it's not recommended. Higher twist rates are generally ok.
6 Because mass increases more than area for a given linear scale factor.
Bryan Litz majored in Aerospace Engineering at Penn State University and worked on air-to-air missile design for 6 years in the US Air Force before taking a job as Berger Bullets Chief Ballistician in November 2008. Bryan has been an avid long range shooter since the age of 15. In particular, Bryan enjoys NRA Long Range Prone Fullbore/Palma competition and is the current National Palma Champion. Bryan is also a husband and proud father of 3.
- Previous page: Understanding Long Range Bullets Part 1
