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Twist Rates & Bullet Stability

Why are barrels rifled?

Why not use a smooth bore? It would certainly simplify things for the barrel manufacturer and lower costs for everyone.

The answer is that bullets will not fly straight unless you spin them. The rifling grips the bullet by the jacket and forces it to spin at a high rate as it is pushed down the bore by propellant gasses. Rifling ensures bullets will be stable.

The spin applied to a bullet by the rifling is called the twist rate. This is expressed as one complete turn (revolution) in a given number of inches or millimetres. The longer a projectile is the faster it must be spun to stabilize or remain point first in flight.

SAAMI has established standard twist rates for most cartridges which are chambered by firearms manufactures. These standard twist rates will stabilize standard-for-caliber bullet weights. Military and long range target shooters have gone to heavy-for-caliber bullets to increase ballistic coefficient for extreme long range shooting. The same applies to monolithic bullets as due to the lower specific gravity (SG) these bullets are long for caliber. These long bullets require faster twist rates in order to properly stabilize. If these heavy-for-caliber or long-for-caliber bullets are shot in standard twist-rate barrels, they will wobble or tumble going through the target sideways—known as “key-holing”.

As shooters we are interested in two types of bullet stability—gyroscopic stability and dynamic stability. For a bullet to be stable you need to meet both of these conditions:

A bullet that is gyroscopically stable but dynamically unstable is not stable – it will tumble.

Bullet Flight

At this point I would like to touch on External Ballistics, and the three stages that a centre fire rifle bullet goes through.

SUPERSONIC FLIGHT: the bullet leaves the barrel at a supersonic speed which allows the bullet to force away the air in its path—creating a shock wave that travels in front of the bullet. At this point you have two factors on the bullet, the centre of gravity and in front of that you have the centre of pressure.

TRANSONIC FLIGHT: as the bullet flies and slows down closer to the sound barrier it enters what is known as the TRANSONIC ZONE. This occurs around the 1340fps mark and disappears as the bullet crosses over into SUBSONIC FLIGHT. Generally the TRANSONIC ZONE is where all the bad things that can happen to a bullet can happen to it.

SUBSONIC FLIGHT: as the name implies this is where the bullet flies at under the speed of sound. This is a very good place for a bullet to be as external forces are at their minimum and the bullet’s drag reduces by around 70%.

Gyroscopic Stability

Gyroscopic stability is the easier of the two to understand. It’s usually referred to as a variable called Sg. In theory, if a Sg is greater than 1.0 the bullet can be said to be gyroscopically sable. Sg goes up if you spin the bullet faster.  If a bullet starts out gyroscopically stable, it tends to stay that way because velocity drops faster than the bullet’s spin rate. However, this can change when a bullet enters the transonic stage of its flight. If a bullet is gyroscopically unstable at the muzzle it will never be stable. This is why bullet manufacturers aim for a Sg of1.5 which allows for a safety factor to overcome most conditions.

Factors That Increase Gyroscopic Stability

  • Higher spin rate
  • Shorter/fatter bullet geometry
  • Lower air density
  • Higher temperatures
  • Lower air density

Dynamic Stability (Sd)

Dynamic Stability is extremely complicated to calculate.

It depends on coefficients that are difficult to identify, making it exhausting to predict and is dependant on subtle features of the bullet’s design. Bullets can lose dynamic stability as they lose velocity. Unlike the case with gyroscopic stability, just because a bullet is stable at the muzzle does not mean that it will be stabile down range.

A bullet with an Sd equal to 1.0 will be perfectly stable. A Sd greater than 1.0, or less than 1.0 may cause the bullet to become unstable. The safety margin for Sd is dependent on Sg. A bullet with a high Sg has a better chance of going through the transonic zone without becoming unstable.

Further down range some bullets will experience a dramatic shift in Sd, which can cause the bullet to leave the stable region and begin to tumble. The infamous .30 caliber 168 grain Sierra Match King suffers from this problem and are prone to losing stability at transonic velocities. This is one reason that long range shooters like to keep velocities over 1,300 feet per second at the target. Bullets that tend to lose stability do so in the transonic region.

Over Spin

As the saying goes, too much of a good thing is bad for you.

The same can be said about bullet spin. As mentioned above a bullet needs a certain amount of spin to be gyroscopically stable and a bullet that has higher spin stability will handle the transonic zone more effectively, and therefore less chance of becoming dynamically unstable.

Why not aim for the fastest spins that you can get for that particular calibre?

In the worst case scenario the buffeting air onto the larger exposed surface area will cause the bullet to lose dynamic stability, reaching its overturning moment and start tumbling.

Cross winds play a big part in the over-stabilised bullet problem. In a right hand twist barrel a wind from the right will force the bullet point down, assisting the bullet with its tracking. A wind from the left will lift the bullet and worsen the bullet tracking.  

 For long range shooting it is recommended to stick to a bullet barrel combination of a SG between SG1.4 and SG2.0. If the SG is below 1.4 go to a lighter bullet. If it is above SG2.0 go to a heavier bullet.

A bullet that has lost its ability to track due to over-stabilising

Atmospheric Effects

Further complicating matters is that everything covered so far depends on air density, which is in turn dependant on things like altitude, temperature and humidity. Lower air density means greater stability. A helpful way to think of it is there is less air to cause the bullet to tumble. So it’s possible to have a bullet shoot well at high altitude, but tumble at sea level.

Bullet revolutions per minute is a function of two factors, barrel twist rate and velocity through the bore. With a given rifling twist rate, the quicker the bullet passes through the rifling the faster it will be spinning when it leaves the muzzle. To a certain extent then, if you speed up the bulletyou can use a slower twist rate and still end up with enough RPM to stabilize the bullet. But you have to know how to calculate RPM so you can maintain sufficient revs.

MV X 720/Twist Rate = RPM

Example:

In a 1:12″ twist barrel the bullet will make one complete revolution for every 12″ (or 1 foot) it travels through the bore. This makes the RPM calculation very easy. With a velocity of 3000FPS in a 1:12″ twist barrel the bullet will spin 3000 revolutions per SECOND (because it is traveling exactly one foot, and thereby making one complete revolution, in 1/3000 of a second). To convert to RPM simply multiply by 60 since there are 60 seconds in a minute. Thus, at 3000 FPS, a bullet will be spinning at 3000 x 60, or 180,000 RPM, when it leaves the barrel.

What about a faster twist rate. Say a 1:8″ twist?

We know the bullet will be spinning faster than in the example, but how much faster? Using the formula, this is simple to calculate. Assuming the same MV of 3000 FPS, the bullet makes 12/8 or 1.5 revolutions for each 12″ or one foot it travels in the bore. Accordingly, the RPM is 3000 x (12/8) x 60, or 270,000 RPM.

Calculating the RPM based on twist rate and MV gives us some very important information.

Firstly we can tailor a load to decrease velocity just enough to avoid jacket failure and bullet blow-up at excessive RPMs. Secondly, knowing how to find bullet RPM helps us compare barrels of different twist rates. Once we find that a bullet is stable at a given RPM it gives us a “target” to meet or exceed in other barrels with a different twist rate. There are other important factors to consider.

If you speed up the bullet (i.e. increase MV), you may be able to run a slower twist-rate barrel so long as you maintain the requisite RPM for stabilization and other factors contributing to gyroscopic stability are present. In fact, you may need somewhat more RPM as you increase velocity because more speed puts more pressure, a destabilizing force, on the nose of the bullet. You need to compensate for that destabilising force with more RPM. But as a general rule, if you increase velocity you can decrease twist rate. What’s the benefit? The slower twist-rate barrel may, potentially, be more accurate.

Just remember that as you reduce twist rate you need to increase velocity, and you may need more RPM than before. (As velocities climb, destabilizing forces increase, RPM being equal.) There is a formula by Don Miller that can help you calculate how much you can slow down the twist rate as you increase velocity.This is the “safe bet” to achieve stabilization with that bullet, and it may also indicate the twist rate at which the bullet shoots best. An RPM calculation does not ensure stability but it can be useful.  An 8-twist barrel at 2800 FPS MV, would stabilize in a 9-twist barrel at 3200 FPS MV.

MV = 2800 FPS
8-Twist RPM = 2800 x (12/8) x 60 = 252,000 RPM

MV = 3200 FPS
9-Twist RPM = 3200 x (12/9) x 60 = 256,000 RPM

BC that is theoretical rather than actual could become inaccurate as the bullet enters into the transonic flight zone due to increased pitching and yawing

Below are a number of graphs of bullet flight paths for three different bullet profiles. As can be seen the flat based bullets survive the transonic zone far better than a boat tail and remain stable virtually until they fall out of the sky.

If you look at the left leg or X axis of the graph you will see the Sg factor. Remember going under 1.0 the bullet will become unstable. The trick is to keep the Spitzer shaped bullets above 1.0 at its lowest point and under SG2.0 at the higher point.

180gr Bush Supreme 1:10 twist at 2650fps (flat base)
180gr Plain’s Supreme 1:10 twist 2650fps (boat tail)
180gr Bush Supreme 1:10 tiwst at 2650fpt (flat base)

For long range shooting the high BC Spitzer shaped bullets their increases in BC outweigh their problems making them the only viable choice.

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