Target Sports

HANDLOADING PART THREE: TO INFINITY AND BEYOND

Created on 14th May 2009

LAURIE HOLLAND looks at drag-curve-based ballistic coefficients in the final part of his review of Sierra's Infinity V6 programme

I'll finish off my examination of Infinity and the ballistics programme results by looking at problems caused by G1 drag-curve-based BCs, and also at whether it's essential for bullets to remain supersonic, as is widely believed. This problem concerns the BCs held in the programme's bullet database, all based on the G1 drag profile. Without going into what this means in depth, let's note it is based on the comparison of a bullet's performance against a ‘standard' projectile with a BC of 1.0. This projectile goes back to German artillery manufacturer Krupp and mid-19th century breechloading shells. The standard projectile was defined as being around one calibre, weighing around 1lb, with a two calibre radius ogive (ie very blunt) and a length of three calibres (increased to 3.5 calibres when Winchester updated the profile in 1965 to give us what is now called the G1). Does this sound like anything you fire through your rifle? The nearest small-calibre equivalent is early military RN FMJ types with blunt front ends and flat bases, but our long-range HPBT bullets are very different.

The problem with G1-based BCs is that they vary according to velocity, which itself changes considerably over a long-range flight. It may also start off at very different levels depending on the cartridge, load and barrel length. This means that a single BC value cannot be accurate. Sierra partly compensates by quoting three to five values by velocity bracket, but even this can be unsatisfactory when the bullet drops through the 1,400 to 1,500fps transonic zone, which can produce increased turbulence and drag. With Infinity and all other home ballistics programmes being G1-based, we've got problems. I trust the results for .223 and .308 class cartridges at moderate (up to 600yd) ranges and have reasonable faith in our high-performance 6.5-284 Norma results at 1,000yd, but not for any .308W load beyond 800yd.

The starting point for all external ballistics data and predictions is the amount of air resistance or ‘drag' that a projectile encounters during its flight. It has been known since the mid-19th century that drag is not constant - it varies not only according to the shape and weight of the projectile, but also due to its velocity. A typical drag curve is shown below in figure one, illustrating that, counter-intuitively, drag increases as velocity falls, peaks just above the speed of sound (1,122fps), then drops dramatically once the bullet is subsonic. Any BC has such a graph at its heart.

So how do manufacturers and ballisticians produce BC values for bullets? Two design-specific variables are the ‘form factor' and SD or ‘sectional density'. These are compared to those of the standard projectile to produce a lower or higher BC value, which then provides the flight data we're interested in through interaction with the standard drag profile. Form factor is a value given to the projectile's shape, or more precisely the efficiency of that shape. For this, the lower the better, as it's a drag-based measure which is independent of calibre and weight. It's not uncommon for match and VLD bullets from the same maker to have similar forms, a successful design having been applied to other calibre models in the line-up. SD is a measure of projectile weight in relation to calibre, a higher value always producing a higher BC when other factors are equal. This is why the 139gn 6.5mm Scenar has a higher BC than its new 123gn sibling.

However, there are problems if one chooses an inappropriate starting point, such as a drag curve for a standard projectile used over very different velocity ranges or with a very different form factor to that being modelled. That's the situation we face with G1 curve-based BCs. This curve goes back to 19th/early 20th century military research, with all countries using a pretty similar standard in the run-up to WW1. For instance, British ballistics tables introduced in 1909 were based on the drag characteristics of a standard projectile that weighed 1lb (7,000gn) and was 1.0" (25.4mm) calibre with a blunt two calibre ogive, short body and flat base.

Alternative drag profiles

External ballistics is not a modern science. Early work took place 400 years ago, but there were two periods that produced huge advances: the 1860 to 1914 period that gave us the forerunner of the G1 and the 1960s to 1990s, when electronic computers and tracking equipment allowed a new generation of missiles and low-drag artillery shells to be produced. This period also brought far more accurate ballistics data to predict the performance and behaviours of differently-shaped projectiles. Additional drag profiles for individual projectile shapes or ‘forms' were created and eventually published. The one that interests us is the G7 as it is based on low-drag shells with a form factor value of 1.000, close to that of high-performance match bullets, especially VLDs.

So why do manufacturers stick to G1-BCs? The main reason seems to be that shooters are used to the present range of values. Changing to a more appropriate model produces less impressive BC figures and manufacturers are understandably wary of making a switch that could be misinterpreted by customers. Of course, not all bullets are HPBTM designs or VLDs and only a tiny percentage of customers shoot at ultra long-ranges, where differences really show up.

Examples

What does the use of G1-BCs and of ballistics programmes based on them mean in practical terms? If we take 155gn 0.308" HPBTM bullets as an example, Lapua impresses a lot of potential customers with the claimed BC of 0.508 for its Scenar, while Sierra quotes three values from 0.417 to .450 dependent upon velocity for its Palma Match King, an average of 0.436. This is 14% less than the value quoted for the Scenar, so can we assume that it is that much amount less efficient than its competitor? This would mean that if fired at 2,950fps (a typical TR or Palma rifle MV) it would have 14% less remaining velocity at 1,000yd. Run the two combinations through Infinity, and that's almost what is predicted, the Scenar travelling at 1,395fps and the Palma MK at 1,237fps, or 11.3% down. Change the output to wind drift (in a 10mph wind at 90º) and performance differences are magnified, so the Lapua is predicted to move 83.4", the Sierra 100.29" - a significant 20.25% greater, equating to 1.6MOA at 1,000yd.

It's a wonder anybody buys the Sierra with a much more effective competitor available at a similar price.

However, since Palma competitors don't see such a large performance difference on the range, something isn't right. Is Lapua's BC on the optimistic side, exaggerating its bullet's capabilities? We don't know how the company calculates this figure, but the odds are it's computer-generated, based on the shape and weight. We know Sierra undertakes range-testing and measures actual velocity loss over a distance, so its BCs are experimentally derived. (Also, the SMK is a tangent ogive design. Therefore it is easy to get it to shoot well, while the Scenar has a long, secant ogive form, a ‘VLD', and can sometimes be fussy.)

We've noted that G1-BCs are velocity-sensitive, so a single value cannot apply throughout the bullet's flight. Sierra tries to show this with multiple BCs quoted by velocity range. Some Match Kings are now listed with five values, the BC dropping as the bullet slows (table one and figure two, both on the previous page, show the 90gn 0.224" MK). In actual fact, what we should be talking about is the air drag on the bullet increasing, but it's easier to talk about the BC falling. Anyway, stick a single-value bullet like the Lapua, whose BC is computer-generated, and a multiple-value Sierra derived by a different methodology into our ballistics programme, and we're comparing apples and pears to the Palma Match King's disadvantage.

This is why I chose Lapua Scenars throughout for the three 6.5x47 Lapua v .308W v 6.5-284 Norma comparison graphs in last month's issue. The absolute results might not be 100% accurate, but should provide valid comparisons since their BCs have been calculated the same way. Returning to our 155gn Scenar v Match King comparison, Sierra's highest BC value is .450, so what happens if we use this on its own as per the Lapua? It is now calculated to be travelling at 1,281fps at 1,000yd, 45fps or 3.64% faster than before - not a huge amount but closing the gap with the Scenar a bit.

Experimental averages

Ballistician Bryan Litz has done considerable work on 155gn 0.308" bullets' real BCs, calculating them on the basis of flight times between set points over long distances starting at around 3,000fps. This produced an average G1-BC of 0.459 for the Scenar between starting and terminal velocities of 3,030 and 1,370fps. While this is down on the published figure, Bryan says the factory's 0.508 is not unreasonable for velocities above 3,000fps, and manufacturers naturally quote the highest value that reasonably applies. However, note that it is now closer to the Match King's top figure of .450, although Sierra lists that as applicable to 2,600+fps, and the BC will likely be lower in the 2,600-2,999fps range than for 3,000+fps. Bryan calculated an average G1-BC of 0.417 between 3,000fps and 1,500fps for this bullet. This means the Scenar does not have the massive advantage that Infinity predicts. The effective BC is still substantially higher, but it sees a fair reduction from the original 16.5% difference between the published values. Since they are what Infinity works with, we inevitably get skewed results. Why can't manufacturers quote realistic average BCs for their bullets? We're back to the G1 problem again as these BCs vary significantly according to velocity. One person's use of a 155gn bullet may be in a .300 Magnum at targets 300yd away, while another employs it in a .308W TR rifle at a lower velocity, but participates in 1,000 and 1,100yd competitions - the average BCs are very different.

G7 curve

What happens if these experimental results are translated to BCs based on the G7 drag curve with a streamlined low-drag projectile as its standard? The Lapua Scenar is particularly suited to this format, with a form factor of 0.996 against the G7 standard of 1.000. Bryan calculated the Scenar's average G7-BC as 0.234 and the Palma MK's at 0.213. Unlike G1-BCs, there was little variation noted in these values throughout the recorded flights covering 3,000 down to 1,500fps, or still wider in the Lapua's case. This bullet only saw a BC variation of 0.014 over a range of 3,030 to 1,370fps, under 6% of the average, and the Sierra had an even smaller variation of 3.3%. The corresponding variations for conventional G1 curve-based BCs were 18.1% and 15.1% respectively, showing the benefit G7 provides to the long-range shooter who sees large in-flight velocity drops.

Let's cut to the chase - how do our new G7 BCs and their drag curve model affect predicted velocities and wind drift figures? Bryan emailed me a little ballistics programme based on the G7 curve and I re-ran the 1,000yd flights for the two bullets at 2,950fps in standard environmental conditions (59ºF, sea-level altitude, 29.92" Hg pressure, 78% humidity) and with a 10mph crosswind. Table two shows results for the two bullets using Infinity for G1 and Bryan's programme for G7. To make things a little clearer, I also ran Infinity velocity and wind-drift graph plots for the two bullets, adding the G7 results in manually. What we see is that both bullets are now calculated to lose an extra 100+fps at 1,000yd compared to Infinity/G1 - 110fps for the Sierra and 140fps for the Lapua. Wind drift increases too, by 10.6" for the Sierra and a shade over 12" for the Lapua. These are significant amounts, equating to an extra 10% or 1MOA of windage. The Lapua still has a significant edge over its competitor performance-wise. The Sierra is now forecast to be right on the verge of subsonic flight, its terminal velocity reduced to 1,128fps (the speed of sound is 1,122fps under standard environmental conditions). This ties in with the advice usually given to build TR rifles with at least 30" barrels, as 2,950fps is the minimum MV needed to keep a Sierra or the similar 155gn RG FMJBT supersonic to 1,000yd. How about shorter ranges? The two sets of results are not that far apart until 600yd or even 800yd. The G7 programme predicts another half-MOA of wind effect throughout over the G1 results, this growing rapidly at 900yd and 1,000yd as the cartridge runs out of steam.

How about the 155gn v 210gn issue in G1 v G7? I don't have the Berger 210gn VLD's form factor, but do for the company's 155gn model. Bryan quotes it at 1.019 based on measurements taken from 3,000fps down to 1,350fps. Let's assume the heavier bullet is a scaled-up 155gn VLD with the same form factor. So what do we get when we input it into the G7 programme at 2,600fps alongside the 155gn Scenar at 3,100fps? We see in table three (over page) and figures five and six (page 30) that the bullets are forecast to have near-identical 1,000yd retained velocities, comfortably supersonic at 1,350fps. However, the big Berger suffers 9" or just under 1MOA less wind drift. I also ran another bullet on the G7 programme, again making an assumption about its form factor matching a 155gn model from the same stable - the 175gn Sierra MK at 2,640fps. This is the highest MV I can obtain from the 24" barrel FN SPR I use in F/TR without sacrificing accuracy and small velocity spreads. It confirmed what I suspected - that my 1,000yd velocities are likely to be in trouble, the estimate being 1,097fps with a 10mph wind drift of 111", 33" greater than the 210gn/2,600fps VLD load. Throw in higher summer temperatures for our F-Class League fixtures and the 1,000ft elevation of Blair Atholl and Diggle ranges, which reduce air resistance, and bullets are likely to straddle the speed of sound at the far end of their flights - a bad outcome.

Super and subsonic

That takes me onto the final issue that can affect long-range shooters: terminal velocity. The ideal situation is for the bullet to be comfortably supersonic when it reaches the target, preferably a couple of hundred fps or more above the sound barrier to keep it clear of the trans-sonic turbulence zone. However, Target Rifle, Match Rifle and F/TR are limited to 7.62mm/.308 Winchester, a cartridge that runs out of steam ballistically at 1,000yd.

I've often heard it said that bullets must be supersonic at the target, otherwise awful things happen such as elongated shot-holes and huge groups. The reality isn't as straightforward, though. If subsonic bullets don't fly straight, how did four generations of long-range Service Rifle shooters manage with the 0.303" military cartridge, even the ‘high-performance' 174gn Mk VII version with its modest nominal MV of 2,440fps? TR, with the original 7.62mm 144gn FMJBT NATO-spec cartridge, had bullets become subsonic at 900yd and people lived with the situation for nearly 30 years until the 155gn cartridge was introduced. On the other hand, try a 168gn Sierra MK or equivalent from Hornady, Nosler and Speer in .308W at 1,000yd and you'll be lucky to find the target! The answer to this conundrum is that some bullet shapes retain stability as they pass through the trans-sonic zone and sound barrier and only incur a little extra drag. Meanwhile, others become unstable through precession (wandering-nose syndrome) and act as if they've run into the proverbial brick wall. Base shape and boattail length/angle seem to be key factors.

Unfortunately, no ballistics programme tells us how much drag a particular bullet will suffer in the 1,300fps to 1,100fps range, caused by turbulence building up around it. (This is a result of parts of the airflow around its surfaces being supersonic while others slow to subsonic speeds). What we do know is that some designs perform well and the 155gn Sierra Palma MK exceptionally so - hence its enduring popularity with long-range competitors. The 175gn SMK is a big brother to the 155gn Palma specially designed for long-range shooting with short-barrel fast twist military rifles, so why do I have a problem? It is possibly a result of straddling the speed of sound at the 1,000yd target - it's better to have all shots on one side or the other. One solution is to drop my charges and hence MVs, so every shot is guaranteed to be subsonic at the cost of even more wind drift; the other (much better) option is to get a rifle with a longer barrel and restart load development. So while G7 curve-based ballistics give a much-improved picture of what really happens at long range, they don't have all the answers - at least not for cartridges such as .223R and .308W. Yet again, ask successful competitors - whether in longstanding Match Rifle or newfangled F/TR - what they do, then copy it. A common approach for both is very long (31-34") barrels plus stiff loads to maximise MVs. MR has traditionally used heavy (up to 220gn) bullets with success while most top F/TR competitors stick to 155s at higher velocities - both approaches apparently work.

My thanks are due to Bryan Litz who does business as Applied Ballistics in the USA, and who helped me to understand the way BCs are calculated and the differences between the various drag-curve-based formats. Visit http://bryanlitz.bravehost.com or email bsl135@yahoo.com for details. I'll stress that any errors are down to me, not Bryan!