COMMENTS ON LONG RANGE
BALLISTICS

by Geoffrey Kolbe
Source http://www.border-barrels.com/articles/art1.htm
http://www.border-barrels.com

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 within two years, 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. (So why are the Mayevski drag curves still used? - See my article in the 1995 Spring NRA Journal). 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 throughthe ranges (Courtesy JH Carmichael),

Velocity at	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	150	155	168	180	190	200	210	220	230	240	250	300
Ballistic Coefic't	.45	.46	.50	.53	.56	.60	.62	.65	.68	.71	.74	.89
Muzzle Velocity	3002	2981	2866	2762	2700	2632	2569	2517	2460	2413	2370	2163
Velocity 1200 yds	953	978	1017	1040	1061	1083	1099	1114	1123	1136	1149	1167
10 mph 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. 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.

 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 still available and 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. For instance, a 208 grain .30 cal bullet with a tangent ogive nose and a ballistic coefficient of 0.75 available from Wayne Anderson, an American manufacturer. I know that Berger has a 230 grain bullet on the drawing board with a ballistic coefficient of 0.85. Under Table 2 conditions the 1200 yard velocity for this bullet would be 1331 ft/sec. and the 10 mph wind drift 7.4 minutes. Now there is a bullet you can drool over!

 The lesson to learn here is summed up in my first aphorism:

'When choosing a bullet for long range target shooting, find the bullet with the largest ballistic coefficientand usethat. If there are two bullets with the same ballistic coefficient,usethe 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 will 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. Given that your group, at this range, will be no smaller than a minute of angle (with this bullet), 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. (See the 'Programs' section of this website.)

 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 new '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 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.

 As I write, the Match Rifle committee seems set to introduce a chamber gauge into which your empty case (or loaded round) must fully enter. This is to police the rule which says that you must use a standard .308 Win. or 7.62 x 51 Nato chamber. The gauge is reamed to the maximum dimensional tolerances of the chamber drawings that fall within the rule. By fire-forming cases in such a chamber it is possible to get about 4 % extra volume over a case of standard dimensions. This means you can get two grains more powder into the case, which translates, for a 200 grain bullet, to a muzzle velocity 50 ft/sec. greater Extra case volume can also be created by having the throat of the chamber pushed forward so that the bullet is only minimally held by the neck. By pushing the throat forward 0.1 " over a standard chamber you gain about another 3 % of volume and another 40 ft/sec.

 So what sort of performance can we expect, using fire-formed cases in a 34" barrel with a chamber reamed to the maximum size permitted and the throat pushed forward as far as we dare? We can then shovel in enough powder to give us a stiff 50,000 psi chamber pressure that does not leave us poking about for dropped primers. For a 210 grain bullet, the muzzle velocity would be about 2660 ft/sec. and for a bullet with a ballistic coefficient of 0.75 we should expect a velocity of 1350 ft/sec at 1200 yards, comfortably supersonic. It should be extremely accurate and all without the proof load chamber pressures to which some find it necessary to resort. Wind deflection for a 10 mph wind is just 7.7 minutes. This wind drift is only two thirds of that experienced by the 190 grain Sierra from a 30" barrel, putting this another way, the drift to be expected from a 190 Sierra at 900 yards! All this is possible - Today!

Conclusion

 Technologically speaking, there is a lot more juice to be squeezed out of the Match Rifle rules than most people seem to appreciate. I hope this will have given you a flavor of what is possible within the MR rules. I have not even talked about what you can do with sabotted ammunition, (which, although in fact allowed under the MR rules of combat, would no doubt leave the MR committee scratching their collective heads), but that will have to wait until another time.

What cartridge should I use in my Any Rifle?

 The Any Rifle match allows you to use the cartridge of your choice, within limits, and so exposes one to an agony of choice not experienced by Match Rifle purists. The process of choosing is that of comparing one cartridge case against another, one caliber against another and one bullet against all others in the various cartridge/caliber combinations! To help out, here is a second aphorism.

`Regardless of caliber, bullets of the same ballistic coefficient will have the same muzzle velocity when fired from barrels of the same length - provided the ratio of case capacity to bullet weight is the same. '

 Table 3 shows what I mean. For bullets having a 0.5 ballistic coefficient I show a variety of case and bullet combinations that will give 3000 ft/sec. for a variety of calibres, all with 30" barrels. All these cartridges will have the same ballistic performace. That is the same muzzle velocity, the same terminal velocity and the same wind drift at any range.

 The only assumption made is that all the bullets have the same shape and so the same form factor. But it transpires that this is a pretty good assumption across the range of target type tangent ogive bullets. If in a comparison you find that the case capacity to bullet weight ratio is higher for one combination than the other, then that combination will have the higher muzzle velocity and so a superior ballistic performance.

 Take, for example, the RG Nato 7.62 ammo against a .223 Remington case loaded with a 70 grain .224 caliber Berger bullet. The RG 143 grain bullet has a ballistic coefficient of 0.42, as does the 70 grain .224 Berger bullet. The case capacity of the RG case is 55 grains of water and that of a .223 Remington case is 28.5 grains of water. Which cartridge will have the superior ballistic performance? The ratio of case capacity to bullet weight for the .223 Rem cartridge is .41 while it is .38 for the RG 7.62 ammo. The .223 Rem case with the 70 grain Berger bullet is the better combination. In fact, the muzzle velocity for this cartridge will be about 150 ft/sec. faster than the RG 7.62 ammo and so at all ranges it will have less wind drift - and also be more accurate. There have been those who have written that the .223 Rem somehow hits a brick wall at between 400 and 600 yards (depending on the author) and that there is no point in trying it at long range. On the contrary, this particular cartridge/ bullet combination will outperform the 7.62 RG ammo every day of the week!

Table 3 Comparison of calibres

Calibre	Bullet Weight (BW)	Case Capacity (C)	C/BW	Cartridge
.224	90.0	40	.446	22-250 Rem
.243	105.4	46	.436	No Example
.264	124.4	56	.450	6.5-284 Win
.284	144	64	.444	284 Win
.308	169	75	.444	30-06 Impr'd
.338	203	91	.448	8mm Rem Mag necked down

Ballistic coefficient = 0.5. Form Factor i = 0.51

 Muzzle velocity = 3,000 ft/sec. Barrel Length 30".

 This article was first printed in the Spring 1996 issue of the NRA Journal.

© Geoffrey Kolbe 1998,