COMMENTS ON LONG RANGE BALLISTICS

by

Geoffrey Kolbe

Revised and updated in April 2010

SOME HISTORY

In 1907, a great revolution took place in match rifle shooting. For some time the .303 cartridge with a 'Palma' 225 grain bullet had been almost ubiquitous along the firing point. (In those days, any 'military' cartridge was allowed.) Despite its great weight, the bullet had the Metford shape, which was very blunt, and this resulted in a ballistic coefficient of only 0.44 which, combined with a leisurely muzzle velocity of 2350 ft/sec. made for very poor performance beyond 1000 yards.

Meanwhile, the Germans had been experimenting with pointed bullets of the sort which we are familiar with today, and discovered that they had a great deal less drag than the blunt bullets used hitherto. Today, it is difficult to imagine the shock wave that went around the world as the results of these experiments became known. A certain Captain Hardcastle (whose name was to become quite familiar in the shooting world) had access to bullet making plant at the Chilworth Gunpowder Company and, on reading an account of the German results, went straight out and... 'took the heaviest bullet used in .303 and put onto it the best point that I could hear of.'

The result was the 'Swift' bullet. This bullet had a 14 caliber tangent ogive nose whose point had a radius of .020". It was flat based, (the advantages of boat-tails were not discovered until much later), and weighed in at 225 grains. Its ballistic coefficient was 0.67, giving it only two thirds the drag of its 'Palma' counterpart.

History relates that on 29th of May, 1907 Hardcastle shot the English Eight meeting at Bisley as a Tyro, using the 'Swift' bullet. In a strong right hand wind he won the match with 135 out of 150 points - second place scoring 129. In the Scottish meeting, a new world record of 223 out of 225 was scored using the new bullet, (though not by Captain Hardcastle). The Cambridge Match was won without a point being dropped and when the Bisley meeting opened on July 8th, everybody had changed over to ammunition with the 'Swift' bullet!

I relate this little tale because for many years now the ubiquitous bullet seen across the range in MR shooting has been the 190 grain Sierra Match King. Its ballistic coefficient is 0.56, giving it 20 % more drag than the 'Swift' of 90 years ago! Surely, surely we can come up with something better?

Of course we can. But curiously, I find MR shooters very reluctant to move away from the 190 Sierra they know and love, throwing up all sorts of excuses and spurious advantages that the 190 Sierra gives. Anyway, I predict that there will be a revolution of the sort that happened in 1907 and that before long, nobody will be using the 190 grain Sierra.

THE BEST BULLET FOR THE JOB

In long range target shooting, or target shooting at any distance for that matter, what do we look for on a cartridge/bullet combination? We want minimum group size and minimum wind drift. That's it. Muzzle velocity, time of flight, flatness of trajectory are not matters that should concern us - though a lot of MR shooters seem to spend a lot of time worrying about them.

In MR shooting, we are confined to using the .308 Winchester case. While there are a few wrinkles that can stretch performance using this case, which I will talk about later, the main influence on performance over which we have complete control is the choice of bullet. The 190 grain Sierra gives good results up to 1100 yards, where it is still supersonic, but as it goes subsonic on its way to 1200 yards, the group size can increase dramatically. The standard solution to this problem has been to increase the powder charge to primer popping proportions, trying to keep the bullet supersonic at 1200 yards.

Alas, it has all been in vain. John Carmichael has recently masterminded a wonderful set of ballistic measurements in which he and his team have measured the down-range velocities of a variety of bullets at ranges of up to 1200 yards. The results for the 190 grain Sierra are shown in Table I. It can be seen that despite running at chamber pressures of 50,000 psi, (quite stiff!!) velocities at 1200 yards were still subsonic. It is easy to see why people thought they were supersonic at 1200 yards when we look at the predictions using Ingalls tables based on the Mayevski drag curves. In these, predicted 1200 yds terminal velocities, at 1200 ft/sec., are comfortably supersonic and achievable with a 2700 ft/sec. muzzle velocity.

Table l: Measured velocities through the ranges (Courtesy JH Carmichael)
Velocity at range (measured) 0 200 300 400 500 600 800 900 1000 1100 1200
Berger 210 (measured) 2566 2280 2131 1986 1845 1736 1515 1394 1288 1190 1099
Sierra 190 (measured) 2716 2404 2232 2077 1905 1775 1497 1367 1254 1157 1076
Mayevski BC = 0.56 2716 2407 2249 2104 1965 1831 1585 1472 1369 1277 1196
Powley BC = 0.56 2716 2389 2220 2063 1912 1766 1496 1372 1258 1154 1060
Pejsa BC = 0.56 2716 2395 2230 2078 1932 1792 1526 1401 1284 1178 1094

By way of comparison, Table I shows predictions for the 190 grain Sierra using the Powley drag curve and also the those predicted using the Pejsa drag curve. I leave you to decide which is the best fit - but both are a vast improvement on the almost-always-used Mayevski/Ingalls drag curves. So the 190 grain Sierra bullet is not supersonic at 1200 yards out of a .308 Win case and never has been in the history of MR shooting, despite the use of excessive loads to try and make it so. How do we get around this problem? Well, have a look at Table 2.

Table 2. Bullet Weight and 1200 yard Velocity
Bullet Weight 150 155 168 180 190 200 210 220 230 240 250 300
Ballistic Coefficient 0.45 0.46 0.50 0.53 0.56 0.60 0.62 0.65 0.68 0.71 0.74 0.89
Muzzle Velocity 3002 2981 2866 2762 2700 2632 2569 2517 2460 2413 2370 2163
Velocity at 1200 yds 953 978 1017 1040 1061 1083 1099 1114 1123 1136 1149 1167
10 mph wind drift (MOA) 13.7 13.2 12.4 11.9 11.5 11.0 10.7 10.4 10.1 9.8 9.5 8.6

This shows computed muzzle velocities, terminal velocities and wind drifts for a variety of bullet weights fired from .308 Win cases in a 30" barrel. A bullet form factor of i = 0.51 and a chamber pressure of 50,000 psi. is assumed. The Powley drag curve was used to predict 1200 yard velocities. The table was created using a bullet shape which is pretty constant across the Sierra range. Namely an 8 caliber tangent ogive nose with a .050" meplat and a boat-tail. Sierra change the weight (and so ballistic coefficient) of the bullet by essentially just adding more length to the parallel part of the bullet. This is modeled here by keeping the form factor the same at 0.51 and, of course, the diameter the same at .308". The ballistic coefficient then just depends on the bullet weight. Remember;

Ballistic Coefficient equation

where C is the Ballistic Coefficient, i is the form factor, w is the weight(in pounds) and d is the diameter (in inches). The result is quite striking. As the bullet weight goes up the muzzle velocity goes down - as expected, but the terminal velocity goes up and the wind drift goes down as we increase the bullet weight. And there is no apparent turn over where the bullet weight gets so big that the long range ballistics suffer.

Bullet shapes

Bullet Shapes
Examples, rather than the full range. Left to right, the Berger 155 LTB, then a selection of Sierras; the 155, 175, 180, 240 and 250 grain examples. Note the similarities in the noses of the Sierra bullets.

You do not believe me? Look at Table 1 again and see what John Carmichael measured using the 210 grain Berger bullet. Lower muzzle velocity, but higher terminal velocity, just as predicted. You should not be afraid of using big heavy bullets whose muzzle velocities are sauntering rather than stupefying. The .303 British case has a capacity very similar to the .308 Win. and yet, as we have seen, our forefathers were quite happy to use bullets much heavier than anything MR shooters are willing to contemplate today. 250 Grain Sierra bullets are, alas, no longer available. But if you used these you would be 90 ft/ sec. faster than the 190 Sierra at 1200 yards in the same rifle (provided it had an 8" twist barrel) and using the same amount of (somewhat slower) powder to give you the same chamber pressures. But it has long been known that there are much better nose shapes than the 8 caliber tangent ogive. Secant ogive bullets were played with by Hardcastle and it is now known that in general, a bullet with a secant ogive nose will have less drag than one of the same weight but with a tangent ogive nose of the same length. Bullets of this shape have been available for a while as VLD (Very Low Drag) bullets and more are on the way. They offer significant advantages over tangent ogive Sierra type bullets of the same weight.

The lesson to learn here is summed up in this aphorism: 'When choosing a bullet for long range target shooting, find the bullet with the largest ballistic coefficient, and use that. If there are two bullets with the same ballistic coefficient,use the Iighter one' This, of course, is just a restatement of Hardcastle's criterion of 90 years ago.

SQUEEZING THE BEST BALLISTICS FROM YOUR MATCH RIFLE (and staying legal)

The thing to emphasize straight away is that you gain little by increasing the muzzle velocities using the highest-chamber-pressures-the-rifle-will-stand route. The faster a bullet goes, the faster it slows down. Extra velocity gained at the muzzle does not translate to extra terminal velocity of the same amount. For example, take the 190 gr Sierra bullet. When pushed with a moderate load in a 30" barrel you will get about 2600 ft/sec.. At 1200 yards the velocity w ill be around 1010 ft/sec. and the wind drift for a 10 mph would will be 12.3 minutes. Now stuff the powder in until the primers start to pop and you will get about 2700 ft/ sec. for your muzzle velocity - an extra 100 ft/sec. But at 1200 yards your terminal velocity has only gone up by 50 ft/sec. to 1060 ft/sec. and the wind drift for the same wind will be 0.8 minutes less at 11.5 minutes. It is doubtful if you would even notice the difference. Where you will notice the difference is in the life of your cases and your barrel!

It is very important, in Match Rifle shooting, to minimize the instabilities that every bullet suffers in flight. Like a gyroscope, the bullet will yaw and precess as it spins on its way down the range. A certain minimal amount of this precession is required to keep the bullet 'tracking', keeping it pointing along its trajectory. If the bullet did not precess and went completely to sleep' then it would maintain its launch angle throughout its trajectory, which means that on the final part of the flight, when it is descending, it would still be pointing up, thus presenting a much larger cross section and substantially increasing drag. This is the extreme case of what happens when the bullet is spun so fast that the stability factor 'S' is greater than about 3. The gyroscopic forces will prevent the bullet from tracking and the drag goes through the roof for the final part of the trajectory. If the precession is greater than that required to keep the bullet tracking then the result is again an increased effective cross section, giving increased drag and leading to disappointing ballistic performance. To keep precession at the right level, the first thing is to keep the stability factor from around 1.1 to 1.5 for your bullet of choice. Do not use the Greenhill formula to calculate the rate of twist you need, use of this formula is pretty much guaranteed to give you a twist that will stabilize the bullet. But, especially with secant ogive or VLD bullets, Greenhill's formula can suggest twists that will overstabilize the bullet, preventing it tracking well at long range. The computation is not a trivial one, but there are computer programs available which will do this.

The next thing is to minimize in-bore yaw and keep good control of the launch ballistics. What am I talking about? If the bullet assumes some angle inside the barrel then you have in-bore yaw. This is not good because on launch (exiting the muzzle) this yaw translates into precession and so increased drag. Secant ogive VLD bullets seem particularly susceptible to this problem and this may be overcome by loading the bullet out to such a length that the bullet touches the lands in the throat of the barrel. This keeps the bullet well centered on entry into the barrel. It is, of course, also important to load the bullet using an in line seating die or some method that keeps the bullet straight when loaded into the case. You will also reduce your SD's by using some form of bore lubricant, usually molybdenum disulfide in some form. The 'Black Diamond' range of ammunition from Norma uses the NECO process of coating the bullets with a film of molybdenum disulfide, but you can probably do just as well by smearing a little molybdenum disulfide grease around the junction of the bullet and the case neck of your loaded rounds.

Launch ballistics are what happens when the bullet exits the muzzle. A blast of supersonic gas washes over the back end of the bullet and if there is much turbulence or the gas flow is not even over the bullet then it can be upset, inducing yaw and subsequent precession which as we now know, is bad for drag. Boat-tail bullets suffer more from this than flat based bullets, which is why flat based bullets are generally more accurate than boat-tailed ones. The back end of a boat-tailed bullet spends relatively much more time `exiting' the muzzle than a flat based one and so there is more time for the bullet to upset. A good, even crown will ensure that the gas flow over the bullet is even. The 11 degree, so called 'Bench Rest', crown provides a good interface with the boundary of the shock wave from the escaping gases, (so the theory goes), and so minimizes turbulence. Keeping the muzzle pressures down also results in better launch ballistics. Using faster powders gives you lower muzzle pressures, but usually at the expense of muzzle velocity. Or you can use a longer barrel. Longer barrels will give lower muzzle pressures with the benefit of slightly increased muzzle velocity.

Barrels longer than 30" do not result in vast increases in muzzle velocity for the .308 Win. case. For example, a 35" barrel will give you about 50 ft/sec. more than a 30" barrel. The stiffness, (and so inherent accuracy), of the barrel decreases as the fourth power of the length. It does not take many extra inches to give you a barrel with all the stiffness of a piece of spaghetti! But. . . you do get lower muzzle pressures which helps the launch ballistics and, by way of a bonus, the SD of the MV's seems to drop dramatically too. The weight limit (in the rules) for a Match Rifle barrel is the limiting factor on how far one can go in this direction, but stiffness can be maintained to a degree by the use of heavily fluted barrels. Another solution is to bed the rifle on a barrel block situated in the middle of the barrel, instead of on the action as usual. This reduces the effective cantilever length of the barrel substantially and so greatly increases its stiffness. This technique is much favored by 1000 yards bench rest shooters, who look for ten shot group sizes of the order of 3" or better! MR barrels are now being fitted that are over 34" long, early indications are that these barrels give much enhanced performance, at 1200 yards, over a 30" barrel.

REFLECTIONS AFTER 15 YEARS

When I wrote the article, the 190 grain Sierra Matchking was the entreched bullet of choice for the Bisley Match Rifle shooter. The article was an attempt to show firstly, that faith in this bullet was based on faulty data from the misplaced (though general) use of the Mayevski/Ingalls projectile in ballistic models to predict its performance. And secondly, that significant improvements in ballistic performance were easily within reach by the use of heavier bullets which had a higher BC. Did I succeed? Well, there was no spectacular revolution in which the 190 grain Sierra was thrown over for bigger, better bullets. A number of individuals saw the light and using heavier bullets with a higher BC, went on to win the available silverware at Bisley, but most individuals were not prepared to put in the work to develop new loads or invest in the longer barrels necessary to get the heavier bullets moving along at a brisk pace.

But fifteen years later, what goes around comes around. "F" Class shooting has risen in popularity from nothing to a shooting sport of serious significance in that period of time. Any cartridge and any calibre of 8mm or under is allowed. Bench-rest style rests are used. Shooting at 800, 900 and 1000 yards, the 'V' Bull scoring ring is just half a minute in diameter - 5 inches at 1000 yards. After a brief flirtation in the early years with 6.5mm calibre cartriges, The ubiquitious calibre of choice these days is 7mm - usually perched on top of a 7mm WSM case. The 7mm calibre is the best compromise between good ballistic performance and modest recoil. Bigger cartridges with larger calibres undoubtedly give better ballistic performance, but the penalty is punishing recoil, leading to flinching which is the inevitable ruin of a good shoot. The 7mm bullets are usually 190 grain Bergers or the like, the highest BC available. So Hurrah, the lesson has been learnt.

But... a popular sub-class of "F" Class shooting is TR "F" Class shooting, where only the 308 Winchester cartridge may be used. The similarity with the requirements of Match Rifle shooting is obvious - so what has become the popular bullet of choice for TR "F" Class shooters? The 155 grain Sierra! Why...!? I think the reason is that the very small bull has driven up the requirement for accuracy above all else in the face of plain evidence that almost any heavier bullet will give better performance in the wind. Most people do their testing at short range, usually 100 yards, and the big, heavy, 30 calibre bullets do not perform well at 100 yards. At this range, the 155 grain Sierra bullets will all go through the same hole whereas it is a fruitless struggle to better a one inch group with, say, the 210 grain Berger. But get out to 600 yards and beyond and it is a different story. Both are stunning until the flags start to lift - then only the 210 Berger is stunning. It will be interesting to see how long it takes for TR "F" Class shooters to wake up to the possibilities of a heavier bullet.

German Salazer, the noted American Highpower target shooter, seems to have been particularly influenced by reading this article when it first appeared and, switching to heavy bullets for his long range shooting, was rewarded with a string of successes. He published an article, "Heavy Bullets for Long Range" (http://www.6mmbr.com/heavybullets.html) in which he describes how he measured muzzle and 1000 yard terminal velocities for a number of 30 calibre bullets of different weights. His conclusion, "Kolbe was right!"