# Independent Study: LRH calibres - 7mm WSM vs 300 RUM vs 338 LM

Discussion in 'Rifles, Bullets, Barrels & Ballistics' started by Haagen Dazs, Mar 24, 2012.

1. ### Haagen DazsWell-Known Member

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Hello,

A friend recently lent me a book I'm sure (and hope) many of you are familiar with. The book is 'Applied Ballistics for Long Range Shooting' by Bryan Litz from Berger Bullets. Wow, what an amazing book, definately going to buy one for myself! His style of writing really appeals to the aeronautical engineer in me. I don't even like reading books but this one is a real page turner; and here I was going into it thinking I knew it all. I was wrong.

Anyway, reading his chapters on bullet lethality and long range hit probability got me goin' on the spreadsheets. Matunas' Optimal Game Weight equation started making me criticize my earlier decision to use a 7mm WSM for a future long range hunting rig. From everything I had read previous to this book, the only good answer I could get for bullet lethality was '1000 ft pounds of force'. Maybe for a female deer but not for serious game as it turns out.

To start putting things into perspective, I plotted a graph of velocity vs OGW for a given calibre/bullet weight and then used the ballistics calculator to match a range to the required velocity to take out a large 1000lb Roosevelt Elk and a 450lb Mule Deer. I picked the 7mm WSM, 300 RUM, and 338 LM because they seem to be some of the most popular precise, non-belted, non-wildcat, 'moderate' barrel burning heavy hitters, all with comparable ballistics.

What I found was rather interesting and honestly, a little disappointing. The 7mm WSM isn't as powerful as I thought; however, it should still be able to take out an oversized Elk at short range (ideally, however, not with a fragile Berger), so not all hope was lost. I also stumbled upon a thread here on LRH spreading the rumor about the new Berger 7mm 195gn bullet. But I digress.

For this study, I used the heaviest, most aerodynamic bullets on the market, all from Berger. I used typical muzzle velocities for a 30" barrel and slow powder. If you can update my numbers based on your real life MVs, I'd be greatful!

As you can see, the OGW method indicates that a heavier calibre requires less energy to take down an animal than the smaller calibre. Can anyone help me explain that one? I guess a larger hole means more hydrostatic shock or something...

After reading about the new 195gn 7mm bullet, I couldn't resist and modified the graph to include this new development. I used one of Bryan's formulas to calculate the new MV for the heavier bullet based on constant pressure. (M1V1^2 = M2V2^2)

As you can see, there is not much of a benefit between the two bullet weights at short ranges on heavy animals. There's only a 20 yard benefit for the big 195gn on large elk. However, at extended ranges on smaller animals, this new bullet should give us an additional 125 yards of effective range on a large deer. Its not hard to assume this based on the higher BC and better retention of velocity, but I thought I'd make that conclusion while I was at it.

Look forward to hearing your thoughts!
Kevin

Last edited: Mar 24, 2012

2. ### sp6x6Well-Known Member

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Dont have the book but of course know of his work. I always watched the energy on bullets at range. That is why over 20 yrs. ago I hung up my 7mm, for a 340wby.Which my son uses.I shoot the lapua's little brother, 338 Norma w/300 pill,getter donegun)

3. ### winmagWell-Known Member

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Very nice work. I see you used 3200 fps as a velocity ceiling. Smart. I've hered conflicting reports on shoving Bergers any harder/faster.
I'm a 30 cal freak, especially for an allround rifle, near to far, gopher to griz, but I will readily admit that the 338 is in a different class, especially for LR work.
Your graph shows what many have preached for years. Bigger is better period in the energy department when comparing optimal to optimal BC's. It's pretty clear where each round gives up to the next.
Many folks here may choose to disagree with it, & I'm sure they'll chime in sooner or later. Be interesting to see what they say.

As a side note, will a 7WSM even shove a bullet that heavy to 3200fps? Not that it matters, cause all the bullets on the graph started at the same 3200fps, thus rendering all the cartriges dead even at the starting line.

This should make for an excellent discussion. Great thread starter.

Last edited: Mar 25, 2012
4. ### ICANHITHIMMANWell-Known Member

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Im sure he will chime in on this discussion

5. ### gritWell-Known Member

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Hmm. I'm looking forward to Brians book myself. That said, I don't buy your numbers. Perhaps "optimal" performance may be achieved at your ranges, whatever that means.

I've killed a small pile of elk with the 180's from 750 to 1200 yards. Maybe they aren't "optimally" dead, I'll ask. Personally, I'd put a 180 in a bulls chest to 1500 yards where I live and hunt.

How do handguns fit into your numbers? Is a 44 mag only fit for three pound jack rabbits at ten yards? How about my bow? Will it bounce of at inches?

I like your idea. It's fun, and food for thought, fur sure.

6. ### winmagWell-Known Member

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Maybe you could make a graph using 1500# for Elk, & 1000# for Deer, since they're "more readily accepted" by most members here. Not that I nesicarily disagree with your current #'s, but obviously some folks will/do.
It may close the gap on the graph & extend the range a bit, but I'd guess the outcome would be the same. 338 on top, 7 on the bottom, & 300 splitting the two.

Grit, what elevation, muzzle velocity, & bullet are you using to get 1500# at 1500yds? Just curious, as I have not personally done the math yet. (oh, & I enjoyed visiting your website. Very nicely done, & easy to navigate).

7. ### Bart BWell-Known Member

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From a retired US Navy Officer and SEAL close to sniper rifle and marksmanship issues:

When the Precision Sniper Rifle (PSR) program compared the AI 338 LM/300 gr Lapua with the Long throat 300 WM/190 & 220 MK (Army, Navy and Marine snipers, including a couple of Palma shooters ) the 300 WM outperformed the 338 Lapua at 1000, 1200, and 1500 yards. The Long throat 300 WM/ 190 MK @ 3100 FPS was the most accurate at 1000 and 1200 yards. The 300 WM/ 220 MK was the most accurate load at 1500 yards, however none of the participants could meet the one MOA PSR requirement. The shooters were unable to keep five shots on the 6'X6' targets in a 5-20 knot gusting wind except with the 300 WM. The Army has continued to pursue the AI 338 LM because it purports to do the job of the 300 WM and the 50 SASR...it does neither job as well.

8. ### gritWell-Known Member

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Re: Independent Study: LRH calibers - 7mm WSM vs 300 RUM vs 338 LM

I'm at 1660 fps and 1140 ft lbs at 1500 yards, under typical hunting conditions here. For the sake of comparison, this equates to a 30-30 at two hundred yards. In fact, the 30-30 barely generates 1500 ft lbs. You could argue the 30-30 is far from ideal for elk, and I'd agree. However, nobody can argue countless have been killed with it. A 180 from a 357 mag leaves the barrel at only 1100 fps with 400 lbs of energy.

I don't personally subscribe to 1500 lbs minimum. I evaluate bullet performance and, most importantly, accuracy. Under good conditions, I can absolutely place a bullet where it needs to go at this range. I shoot constantly. I shoot where I hunt, in all conditions. While I could make an error, I fully understand when I can take such a shot. Point of fact, the appropriate opportunity has not presented itself.

I'm not suggesting my personal choices are appropriate for everyone. They aren't.

Thanks for the compliments and feed back on the website. It is a do it yourself affair. Nothing fancy, and only just begun. I'm pleased to hear you liked it.

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This is a very interesting post, as I shoot the calibers listed.

10. ### Haagen DazsWell-Known Member

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338 Norma Mag? How much is too much?

To answer some questions, I'm not going to compare handguns because it's a big no-no up here in Kanukistan. I'm also just looking at long range chamberings and basing everything of a suggested formula that may or may not be accurate for certain bullet/velocity combos.

Also, I cleared up the original graph to represent the estimate muzzle velocities I had listed in the legend that it may have been hard to see:

Obviously these are not hard and fast numbers to live by; they only take velocity and bullet weight into consideration and not shot placement, expansion, or how armoured the animal is. If you can take out a 1500lb animal at 1500 yards with a 7 WSM that's great, don't stop because of me. I'm just sharing my own detailed ''mathematical analysis' of the predicted merit of a few great LRH calibres.
The formula I'm using estimates that at that remaining velocity, your optimal game weight at that range is about 230lbs or lighter, but then again, this is all speculative/comparative math.

So recently I found the 338 Norma Mag and have been oggeling over that for the past 24 hours. I never saw myself as a 338 guy but this relatively new chambering has got me excited. Punching the numbers into a ballistics calculator yield some interesting trajectories when compared to the 7 WSM 180gn Hybrid:

Basically, the 338 NM will reduce wind drift, increase barrel life (by about 2-3 times), dramatically increase lethality, and, believe it or not, I estimate it should reduce recoil by ~9% assuming the same rifle weight and the addition of a muzzle brake that offers a 30% reduction in felt recoil (je pense un VIAS va suffire). The only 2 cons to this larger calibre I can think of are cost, which I estimate is offset by barrel life (about 60% more \$\$ or ~5:3 shots per same \$\$ compared to the 7WSM), as well as bullet drop, which is a deterministic variable so who cares? My SWFA SS HD 5-20x50 FFP has a true 30 mils of elevation and my calcs suggest the 338 NM needs 24 mils (83 MoA) at 2000 yards in a standard atmosphere.

Anyway, moving on to my new question: I mentioned 'dramatically increased lethality' and am now wondering, how much is too much? To get us started, I plotted the following OGW graph, using the rumored 195gn .284 bullets (G7 BC 0.406) to give the 7mm WSM a bit of a leg up:

Again, we see the real benefits of the larger calibre are for the larger animals. The 338 NM offers the following increases in 'maximum' range for the following animals:

• 200 pound animal: 35% range increase
• 450 pound animal: 59% range increase
• 1000 pound animal: 184% range increase
• 1500 pound animal: ---
I know these results are based of the math used to get the numbers but does anyone have any insight into why Edward Matunas chose this type of relationship for his OGW equation? For anyone who's wondering, the equation is as follows:

OGW = V^3 * M^2 * 1.5*(10^-12); where V is remaining velocity in fps and M is bullet weight in grains.

Anyway, to wrap this up, I'm thinking if I do go 338 NM, I'd need a short range 'through and through' load with very low expansion for small animals at relatively short ranges. Would you say that even this is overkill for a 200 pound animal?

Thanks fo the input gents!

11. ### Bart BWell-Known Member

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Re: 338 Norma Mag? How much is too much?

How many rounds of barrel life do you think the .338 NM will deliver? Especially if you start out with a 5/8 MOA rifle at 1000 yards and want to sustain it over the barrel life. Note the .338 caliber has a bore capacity of about 58 grains of powder. 90 grain powder charges are way overbore and wear out barrels pretty fast.

Long range target rifles with that much overbore capacity powder charges last about 1200 rounds then accuracy drops off. 'Course if you start out with a 2 MOA rifle, then it will last a lot longer at that performance level.

Don't forget, the recoil that's harmful to accurate shooting takes place while the bullet's are going down the barrel. Muzzle brakes don't reduce that. After the bullet's cleared the barrel, recoil's a non-issue except for ones egos.

12. ### Haagen DazsWell-Known Member

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Re: 338 Norma Mag? How much is too much?

7mm WSM 80 gn H2O = 1263 gn/sq in
338 NM 107 gn H2O = 1193 gn/sq in (6% difference)

and for comparison:

338 LM 114 gn H2O = 1271 gn/sq in
308 Win 56 gn H2O = 752 gn/sq in
300 RUM 110 gn H2O = 1479 gn/sq in

I always figured a larger bullet moving slower would mean less barrel wear.

This aritcle seems as good as any in terms of comparing overbore calibres.

Last edited: Mar 25, 2012
13. ### sp6x6Well-Known Member

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The 338 LA has been around since 1989, and military has tested for accuracy to degrade, I have read it and it was 1500+ OR something close. The rifle is used in over 25 countries in LE or military. In 2009 a British snipe set world record for 2707 yrd kill. Next time I see my highschool buddy, SEAL,and Seal intructor, I'll ask him what he thinks of the 338 LA. My other bud that has multiple world records at 1000 bench, has no problem shooting game with his 338 LAI TO 1500 yrds.

14. ### Bart BWell-Known Member

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Re: 338 Norma Mag? How much is too much?

Regarding my barrel life numbers.....
Since the 1960's, I've observed that the most accurate cartridges burn about 1 grain of powder for each square millimeter of the bore's cross sectional area. By that, I mean sub 1/4 MOA at 100 yards, 1/3 at 300, 1/2 at 600 and 3/4 MOA at 1000 yards. Examples are the .222 Rem. and 22 or 6mm PPC benchrest cartridges popular in short range group shooting. Others are the .308 Win. which was popular for 35 years for high power competition. Most notable with these cartridges is they all deliver that accuracy level for about 3000 rounds. So I established a definition of "bore capacity" as one grain of powder for each square millimeter of bore cross sectional area.

Increasing the powder charge by 40% for any successful caliber used in competition tends to cut accurate barrel life by 50%; it drops to 1500 rounds. Doubling the charge weight for a given caliber over its bore capacity ends up with 1/4 the barrel life; 750 rounds. When 30 caliber magnums were popular for long range prone matches, they got about 1200 rounds of accurate barrel life. After my friend set the 1000 yard record at the 1970 Nationals with a borrowed 7mm Rem Mag, it became popular for that course of fire but it got only about 800 rounds of accurate barrel life. My own .264 Win. Mag barrel died at 640 rounds.

Learning what top competitive shooters get for barrel life in all sorts of cartridges showed me my formula is pretty darned accurate. It's been so for all the barrels I wore out shooting matches and testing them for accuracy in. Sierra Bullets' data on barrel life in their test barrels agrees almost exactly with my calculations.

The above aside, rifle barrels whose accuracy is less will have a longer barrel life. One starting out with 1/2 MOA accuracy at 100 yards will have double the life. If the barrel's a 3/4 to 1 MOA tube, it will get 4 times the life. Standard service rifle barrels in 5.56mm and 30 caliber go about 10 to 12 thousand rounds before they need replacing. All this is why most folks claim (and therefore get) longer barrel life. Their barrels plus their abilities don't start out with the accuracy levels I'm referencing so naturally they get longer barrel life because they're using a different standard. Best example is a .22 rimfire barrel life; most folks think they'll last for hundreds of thousands of rounds but those kids on the Olympic teams get only 30,000 or so rounds per barrel before it needs replacing to meet their requirements.

So, with the .338 Lapua Mag, if it starts out shooting no worse than 3/4 MOA at 1000 yards, I think it'll hold that level of accuracy for about 1200 rounds. It's bore capacity is about 59 grains and it uses about 95 grains of powder per charge. If its accuracy is about 1 MOA at 1000 yards, its barrel will go about 1500 rounds according to my calculations.

Last edited: Mar 26, 2012