Effects of Altitude and Temperature on Rifling Twist
By: Daniel Lilja
In an earlier article in NBRSA NEWS, we looked at the effect changing atmospheric conditions had on the ballistic coefficient of a bullet. To summarize briefly we found that the ballistic coefficient of a bullet as published by bullet manufacturers and others is valid only for a standard sea-level atmosphere. This standard atmosphere (has an elevation of sea-level) with the barometer reading either 29.53″ for “Standard Metro” or 29.92″ for the “ICAO” standard atmosphere. The corresponding humidity levels are 78% and 0%. The difference between these two atmospheres means little, about the same as an elevation change of 390 feet. Ballistic coefficients however are usually based on “Standard Metro”.
The overall air density is determined by a combination of these atmospheric measures: temperature; elevation and barometric pressure; and humidity. When the air density increases from standard, the ballistic coefficient decreases, (likewise, when the air density decreases, the ballistic coefficient increases).
In the earlier article we saw that a change in elevation had the most pronounced effect on air density followed by temperature changes. The influence that humidity had on air density was very minor and could be ignored for most practical considerations.
Interestingly, changes in air density also have an effect on the twist rate required to stabilize a bullet. That is, when air density decreases, there is a decrease in the amount of spin required to keep a bullet flying point on. Conversely, when the density of the air increases, more spin is required.
Like air density and ballistic coefficients, bullet stability can be measured. This was originally accomplished by setting up a series of paper cards, referred to as yaw cards, at equally spaced distances. These cards were placed in front of the rifle and a bullet was fired, passing through them. Observing the out-of-roundness of the holes in the cards indicated at what distances the bullet yawed. The stability of the bullet could be determined by applying a complicated mathematical routine, based on the distance of the card from the muzzle and the amount of bullet tipping, along with other factors.
The yaw card system has been replaced with high speed photographs indicating bullet tip, and with computers performing the math functions.
If a bullet is fired from a barrel that has no rifling, the force exerted on the nose of the bullet by the air will cause it to flip over and its trajectory will be wild.
To overcome this tendency, a bullet is spin-stabilized by rotating it about its long axis. The amount of spin required is determined by the specific gravity, shape and construction of the bullet, bullet velocity, and the density of the air it is going to travel through.
It is interesting to note that this force, or overturning moment, acting on the bullet nose is greatest when the bullet first exits the barrel. If a certain bullet-barrel combination will stabilize a bullet at the muzzle, the bullet will remain stable for the rest of its flight. Why is this so? As a bullet flies on toward the target and beyond, it is losing velocity rapidly as any trajectory table will show. For example a 68 grain bullet from a 6PPC leaving the barrel at 3150 fps will be going 2786 fps at 100 yards and 2449 fps at 200 yards (ballistic coefficient of .265 and standard metro conditions). The rotational speed of the bullet or its RPM’s decreases at a much slower rate. The overall result is a lessening force acting on the bullet nose, and that force is being overcome by a proportionately greater spin rate compared to forward velocity. The down-range bullet therefore is more stable than it was at the muzzle. The only exception to this occurs when the bullet passes through the speed of sound. At that velocity, about 1180 fps, it may lose stability.
The ballisticians that perform this work have developed a measure of projectile stability known as the stability factor, or SG. A value of 1.0 describes a bullet that is just barely stable. If the value drops below 1.0 a bullet is unstable; it yaws wildly. Accuracy is nonexistent.
Obviously then, the stability factor must be at some measurable level above the absolute minimum of 1.0. It has been determined that a stability factor of 1.3 is the minimum level for reliable accuracy and performance. As the level of stability goes down, any minor change in the rifle-bullet combination could cause a wild shot. For example, a damaged muzzle or crown could cause a bullet to leave the barrel with enough yaw that it cannot recover in flight. At worst, the bullet will completely lose stability, or it may not hit the target in the intended spot. An excessively fouled bore may also have enough effect to cause these problems, as could a badly imbalanced bullet. Another possibility, as we will see later, has to do with an increase in air density.
Benchrest shooters are without any doubt the most careful bunch of shooters concerning care and cleaning of their rifles. A damaged crown or dirty barrel or other such cause are not very likely to found in a relay of heavy varmint rifles. As a result, benchrest rifles can get by with a very minimum of twist as compared to hunting rifles or military arms.
Some authorities suggest that the stability factor should be no less that 1.5 for any application, including benchrest shooting. Higher levels of stability are suggested for other situations where accuracy may not be the prime consideration. There is evidence that a bullet with a high stability value will shoot through brush better. This is something to consider with a hunting rifle.
Today, bullet stability can be determined with a great deal of accuracy before a bullet has ever been produced using computer modeling techniques. To see what the effects would be on twist when atmospheric conditions change, we will use a computer program and the same range conditions that were used in the earlier article on ballistic coefficient.
The modeling program that was used to determine these values was written by Tioga Engineering and is based on research done by Robert McCoy of the U.S. Army Ballistic Research Laboratory at Aberdeen Proving Ground.
All of the following examples are based on the same bullet used in the ballistic coefficient tests. Namely, a .243″ diameter bullet made on a .825″ long jacket with a seven caliber tangent radius ogive, meplat diameter of .070″ and a flat base. A muzzle velocity of 3150 fps was used, which is typical of a 68 grain bullet in the 6PPC.
It was found that a twist rate of 13.3 inches per turn is required with a Standard Metro atmosphere and this bullet for a stability factor or SG of 1.5. A 14″ twist has an SG of 1.35. This will serve as our base reference point, just as the ballistic coefficient of .265 did in the earlier article.
With our 1990 Phoenix Nationals conditions of 95 degrees F., elevation of 1500 feet and 20 percent humidity an SG of 1.5 is produced with a twist rate of 15.1″. A 14″ twist rate in these conditions has an SG of 1.75. Changing the humidity level here, as we did in the ballistic coefficient tests, has no noticeable effect on stability.
Using the air density conditions at the 1987 Nationals in Charlotte, measured at 100 degrees, 90% humidity, and a range elevation of about 750 feet indicate that a 14″ twist barrel produced a stability factor of 1.74. Again, a twist rate of 15.1″ would create an SG of 1.5.
Going to our simulated wintertime Charlotte conditions of 30 degrees, humidity of 90% and the same elevation of 750 feet, that same 14″ twist barrel generates an SG of just 1.26. It is still stable, but under the suggested minimum stability factor rating of 1.3. A twist of 12.8 inches would be necessary to bring the stability up to 1.5
As would be expected, the summertime air density at the range near Helena, Montana being 5300 feet in elevation and at 70 degrees, humidity at 25%, requires the least twist to stabilize the bullet. With these conditions, a 14″ twist would produce a stability factor of 2.10. To achieve the SG level of 1.5, a twist rate of 16.6″ should be used.
In the cold conditions at the Helena range that produced the equivalent sea-level ballistic coefficient of .265, namely 17 degrees below zero, the twist rate that produces an SG of 1.5 is 13.3″. This is the same twist required in our base Standard Metro conditions for this bullet. A 14″ twist now would produce an SG of 1.35.
At the Tacoma, Washington range, about 200 feet in elevation and at 59 degrees with 78% humidity, a 14″ twist barrel would give the bullet a stability factor of 1.38. To achieve the SG level of 1.5 requires the spin from a 13.4″ twist.
To summarize, we have seen that to produce an equivalent stability factor of 1.5 for the varying atmospheric conditions, the twist rate would change from the fastest, 12.8″ at Charlotte in the winter, to the slowest rate, 16.6″ at Helena in the summer.
Does twist, then, really make any discernable difference in our shooting? You are probably also thinking that most barrel makers only make their barrels in whole inch increments. The answer lies in determining the most dense air conditions in which the shooter expects to fire that bullet-barrel combination.
We have seen that a 14″ twist barrel will offer a stability factor rating of about the minimum suggested 1.3 in most conditions. Cold, winter time, sea level air can bring that factor below the 1.3 level. A 13″ twist rate will, in most cases bring the stability level up to a more comfortable level.
If a barrel will be shot only in warm, higher elevation conditions, a 15″ twist might be the way to go. If colder, lower elevation shooting is to be done, then maybe a 13″ or even a 12″ twist would be the best choice.
The other consideration not taken into account so far, is changing bullet styles. The bullet in the examples is typical of most flat base bullets used in benchrest. A Rorschach die bullet or a Euber bullet fall into this category. Adding a boattail or increasing the bullet length will decrease the stability. Going to a shorter bullet such as a 62 grain bullet made on a .750″ jacket will increase the stability.
In the March 1990 issue of NBRSA NEWS we looked at the effects of twist rate and accuracy. It was found that the faster a bullet is spun the larger the expected group size would be, given a predetermined amount of bullet imbalance. In practical application though, with high quality benchrest bullets, the accuracy decay due to a fast twist is minimal.
A few shooters have had very good success using a 15″ twist barrel. I ran a few calculations to see how this twist looks. At the Tacoma range and 59 degrees the 15″ twist has an SG rating of just 1.20, marginal at best. Dropping the temperature to 18 degrees F. combined with this twist rate, the bullet will not be stable. Bullets, if they hit the target at all, would enter sideways, and accuracy would be measured in feet instead of thousandths of an inch. In the right air density conditions, a 15″ twist should perform very well, and it has.
Specifying the twist rate to the last tenth of an inch is not practical. Only with indoor conditions where the temperature can be controlled would there be any merit to a 13.3″ or a 14.8″ twist, for example. In the real world of benchrest shooting there are too many variables beyond our control. Air density does have a decided influence on the required twist. As can be seen though, it is safer to be conservative when it comes to twist, and err towards the faster rate.