Most "efficient" cartridge for each caliber?

[Newtosavage]

Macchina, I like your choices. I have a scout-scoped pre-65 Winchester in 30-30 for my thick woods gun. That rifle has put down literally hundreds of pigs and deer for me over the past 35 years. I really like that Marlin .44 mag lever gun and have always wanted one, but just can't really justify it with my old Winchester in the safe. Pretty guns though.

In these calculations, Recoil as a function of rifle weight is always a consideration for me for a couple reasons. First, I like to shoot a lot and tinker with handloads as a winter hobby. Second, none of my rifles weigh more than 7 lbs. scoped. My first deer rifle was that pre-64 Winchester 30-30, and I got used to short and light and handy hunting rifles and just can't get used to longer heavier ones. Plus, the hunts I plan most for these days are high elevation western hunts where a 6.5 lb. rifle is really all you want to carry all day long. So, that affects felt recoil which affects cartridge selection and to some degree, cartridge shape - since all my rifles are also short actions.

 

[redneck2]

223 in a 224 bore. Feel free to disagree

I can shoot a .22 Hornet 90% of the velocity of a .223 with less than 1/2 the powder. (Lighter bullet).

 

[wombat13]

Here's something I've been fooling around with and I think the results are interesting. Drag increases with the square of velocity, so there should be significant diminishing returns with respect to gains in trajectory (flatter = better) and wind drift (less = better) as velocity increases (and consequently recoil). So, I took a look at my metric "Max effective range/Recoil Energy" (units are yards per ft-lb). Recall that the "Max ethical range" is the maximum range at which the bullet should be traveling 2,200 fps (my reasoning for that velocity is upthread - basically to ensure good expansion). I used the same data set as my prior graphs.

Each dot represents a different cartridge shooting that bullet weight. The cartridges for .308 caliber are: .300 savage, .308win, .30-06, .300RCM, .308 Norma Mag, .300 H&H, .300WSM, .300WM, 30 Nosler, .300 wby, .30-378 wby, and .300 RUM. .300 Savage and .308 win are not included for 200 gr as Nosler doesn't publish load data for those cartridges in that weight. The cartridge that excels by this metric (with these weights in Nosler Accubonds) is .300WSM. The next best is .300WM.

Note that for all three bullet weights, the predicted most efficient velocity (i.e., the velocity that offers the best tradeoff between range and recoil) is between 2,900 fps and about 3,000 fps. Also note that the predicted most efficient velocity decreases as bullet weight increases. This makes sense because heavier bullets have higher BCs and produce more recoil.




The cartridges used for 7mm are: 7mm BR (120 gr only), 7-30 Waters (120 only), 7x57 mauser, 7mm-08, .280rem, 7mm WSM, .280ai, 7mm RM, 7mm wby, 7mm STW, 7mm RUM, 28 Nosler. In 7mm, the cartridges that consistently perform well are 7mm-08, .280ai, and 7mm RM (i.e., they do better than the predicted max effective range / recoil energy; they are above the line).

The predicted most efficient velocity for all four bullet weights is between about 3,000 fps and about 3,100 fps. Again the predicted most efficient velocity decreases as bullet weight increases.



The cartridges used for 6.5mm are: 6.5 Grendel, 6.5x55, 6.5 Creedmoor, .260 rem, 6.5-284, 6.5-06, .264WM, 6.5 PRC (not in 100 gr), 6.5 RM, 26 Nosler. In 6.5 mm cartridges, the standouts are 6.5 creed, .260 rem, and 6.5-06 in the light to medium weight bullets (up to and including 130 gr) and the 6.5 PRC in 130 gr and 140 gr.

Here we have a little wrinkle - 6.5mm 120 gr is the only case where the predicted most efficient velocity is higher than that of the lighter bullet weight (3140 fps for 120 and 3067 for 100 gr). Excluding the 120 gr we have the same relationship as in 7mm and .308 where the predicted most efficient velocity decreases as bullet weight increases. This suggests that I have a data problem with the 6.5mm 120 grain cartridges.

 

[wombat13]

Looking at these results and the consistency with which the predicted "most efficient velocity" decreases with bullet weight (except for the anomaly with 6.5mm 120 gr), I wondered if it would be possible to predict the "most efficient velocity" for a given bullet. So I did a multi-variate regression using each bullet's BC and SD and the predicted most efficient velocity based on the data set (excluding 6.5 mm 120 gr). Here are the results of the regression:



I haven't had a chance to test this on a different set of data. It would be interesting to try it on 6mm and .338 (both have several cartridges listed in Nosler's data). Note the "Actual" in the table is the predicted most efficient velocity based on the data set and the maximum of the polynomial best fit line (on the graph). The column to the left is the predicted most efficient velocity calculated using the results of the multi-variate regression and the BC and SD for each bullet. They match pretty closely with the difference between the two being 1.2% or less.

 

[d2wing]

I am happy that this post makes me more smug about shooting a 7-08. That said , the best shot I ever saw with my buddy with a .284 Winchester,

 

[Newtosavage]

I am happy that this post makes me more smug about shooting a 7-08. That said , the best shot I ever saw with my buddy with a .284 Winchester,

Yea, me too. And those are my two main rifles. A 7mm-08 and a .284 Win.

 

[redneck2]

Drag increases with the square of velocity, so there should be significant diminishing returns with respect to gains in trajectory (flatter = better) and wind drift (less = better) as velocity increases (and consequently recoil)

It takes more and more to get less and less. Again, those pesky laws of physics

 

[wombat13]

One of the things I find interesting is how this confirms much of what we see in reality. The cartridges that come out on top are some of the most popular. Also, I noticed that the most common velocity for factory 180 gr .300WM loads is very close to the predicted most efficient velocity. Many such factory loads are a nominal 2,960 fps which is about halfway between the two predicted values. I haven’t checked any others, I’m just very familiar with .300wm.

 

[wombat13]

Yea, me too. And those are my two main rifles. A 7mm-08 and a .284 Win.

I'll add .284 win when I have a chance. I'd like to add .300PRC, but Nosler doesn't publish data for that cartridge and Hodgdon's data is spotty. For example, the only 180 grain .300 PRC load on Hodgdon is the Nosler E-tip which is monometal. Monometal muzzle velocities tend to be very different.

 

[wombat13]

I suspect that the most efficient velocity will vary a bit by bullet since each will have different bearing surface and different BCs. I also suspect that the most efficient velocity will be significantly different for monometals since they are so much longer for the same weight. I mostly shoot Nosler ballistic tips and Barnes TTSX, so eventually I will repeat this for TTSX. It's a big undertaking, so the TTSX analysis won't be for a while.

 

[Varminterror]

Not so surprising to see a velocity dependence when the graphical representation is f(MV)/f(MV) vs MV.

Have you considered - as I mentioned above - how much your subjective choice for variable limit in your max range parameter (a function of MV) would skew this particular measure of “efficiency”? You’re assigning that the common velocities should be the efficient velocities…

 

[Newtosavage]

Yea, me too. And those are my two main rifles. A 7mm-08 and a .284 Win.

Looking again at the numbers (didn't have time last night) the velocities for the 7mm 120, 140 and 150's are very close to what I get from my 7mm-08 and .284 Win.

I don't have nearly as much reloading experience as some here, but from what I've played with, the .284 Win certainly seems like the "sweet spot" for efficiency with the 7mm-08 very close behind.

My .284 Win is giving me 3k fps with NBT 140's and my 7mm-08 gives me 3100+ with 120 TTSX's. Neither have enough recoil to distract me from shooting even my sub-7 lb. mountain rifles from a bench. And of course, offhand it's even less noticeable.

 

[wombat13]

Not so surprising to see a velocity dependence when the graphical representation is f(MV)/f(MV) vs MV.

Have you considered - as I mentioned above - how much your subjective choice for variable limit in your max range parameter (a function of MV) would skew this particular measure of “efficiency”? You’re assigning that the common velocities should be the efficient velocities…

Agreed, I am not surprised that the graphs show a relationship. I expected there to be a relationship, that's why I spent the time to make them. It's more accurate to say the graph is f(MV)/g(MV) vs. MV in that the two functions are different. I wanted to see how those two functions change relative to each other and I expected that there would be significant diminishing returns to velocity, which is exactly what they show.

Regarding my "subjective" choice: there is nothing opinion based about certain cartridges shooting bullets faster than others. I did choose to use the metric "distance at which the bullet velocity is 2,200 fps," but that is not a subjective measure (it's not my opinion that a bullet fired from a .300WM will be farther down range when it drops to 2,200 fps than a bullet fired from a .308 win).

In any case, let's consider how these graphs would change if I chose a different velocity metric, for example, distance at which the bullet velocity is 2,000 fps. The position of the data points on the X-axis will not change since MV would remain the same. The denominator of the y-axis metric is recoil energy, so that number will remain the same. The numerator will increase for all of the data points, so all of the points will move up. The predicted "most efficient velocity" is the peak of the curve. It is very likely that the exact velocity that is the peak will change, but I doubt it would change that much. I'll go on record and predict 3% or less change in the predicted most efficient velocity if I re-analyze using 2,000 fps. I will also predict that the peak of the curve will be found between the same cartridges and that the same cartridges perform better than expected. In other words, I predict that there will be no meaningful difference in the conclusions one would draw. Should I do it for 7mm or .308?

 

[Varminterror]

What happens when your choices of rifle weight per cartridge are skewed by using a long action vs short action, Winchester vs. Remington, etc etc?

As I said dozens of posts ago, you’re putting a lot of your own choices into variable limits, over defining the system, and then dividing your way into velocity divided by velocity divided by velocity…

 

[wombat13]

I used the same weight rifle for all of the recoil calculations. You're arguing that some makes of rifle are lighter than others? So what? The denominator will be larger for lighter rifles and will affect all cartridges. I doubt that will significantly change the shape of the curve.

Your objection regarding short action vs. long action would have some impact. To the extent that short action rifles (and cartridges that are typically offered in rifles with shorter barrels) are lighter, they will look worse. Given that short action/short barrel cartridges are mostly to the left of the peak of the curve and most of long action/long barrel cartridges are to the right, the peak will shift to the right a bit.

You keep saying this is overdetermined, but refuse to explain the objection. To calculate recoil, one must estimate rifle weight, charge weight, bullet weight and bullet muzzle velocity. Explain what is wrong with the way I did it. To estimate range, one must pick a metric for range and then estimate bullet weight, BC, and muzzle velocity. Please explain what is wrong with the way I did it.

Do you reject the idea that there is tradeoff between performance at range and recoil? It is patently obvious that there is. Do you disagree that greater recoil than is necessary is objectionable?

I still don't understand your objection.

Edited to add: There is no "velocity divided by velocity divided by velocity."

 

[Varminterror]

Can you define the metric of “efficiency” which you’ve calculated for comparison here?

If you can’t acknowledge f(mv)/g(mv)/mv as broken, acknowledge your choice to use equal rifle weights for long action magnum and short action cartridges as undermining of the analysis, as well as ignoring the relevance of bullet weight and cartridge capability in this extremely odd choice of analysis, AND the subjectivism which lead the development of the calculus you’ve written here, I can’t help you…

As I stated in my first, this kind of thread has been done OVER AND OVER, and they all end up in the same twisted pseudoscience as guys try to advance their analysis, with overdefined systems and subjective biases hidden in the “algorithm.” This isn’t unique, it’s just your flavor of the same thread.

 

[wombat13]

My metric of efficiency rationale: I want to shoot bullets as far as the hunting bullet will reliably expand as expected. This is a function of the velocity at impact. Therefore, cartridges that send a bullet farther down range while maintaining a minimum velocity are better. I don't like recoil. Cartridges that higher recoil are worse. The metric of efficiency is range per unit of recoil or yards/ft-lb. There is nothing wrong with this as a metric of efficiency.

I just re-ran my calculations with differing rifle weights. Don't have time to post the details (will do so later today), but the predicted most efficient velocities shifted higher (as I expected) and the new values are within 3% of the original values.

 

[Varminterror]

Range per recoil is a metric which makes sense - assuming we ignore the subjective choices for rifle weight and impact velocity minima. But then you’ve proposed the subsequent analysis of “range per recoil per velocity” - what’s the premise for this new divisor?

 

[Newtosavage]

Wombat, these are brilliant calculations and I find them fascinating. You have put to "paper" exactly the question I had in my mind, and have in fact answered it.

A searchable "app" that used these calculations to tell the shooter what options they have, depending on where their priorities lie, would be a fascinating tool.

 

[wombat13]

Too busy last night, but here is the updated graph for .308 using differing rifle weights. My first step to estimate rifle weights was to check weights of Savage 110 rifles, but as I did so, I noticed there was little variation which made me think that perhaps they were using the same receiver for short actions and long (standard) actions. I looked at Winchester but they're website is a PITA to pull info. So then I went to Ruger and checked Hawkeye weights. Here is the data I based my estimates on: .308 win (short action) 20" barrel - 7.0 lbs; 6.5 creed (short action) 22" barrel 7.2 lbs; .30-06 (long action) 22" barrel 7.4 lbs; .300WM (long action) 24" barrel (8.1 lbs). Most of the rifles in the list fit into one of these categories, but a few didn't. .300 WSM is a short action COAL but uses about the same powder charge as .30-06, so I assumed it would be offered with same barrel length as .30-06. So I estimated 7.2 lbs (same as 6.5 creed). .300 WSM is short action, but the powder charge now is approaching .300WM so I assumed 24" barrel. 2" of barrel appears to increase weight by 0.2 lbs, so I assumed 7.4 lbs. Finally, .30-378 and .300 RUM rifles and other magnum action length cartridges are rarely offered, so I went with 8.3 lbs, i.e., the .300WM weight plus 0.2 lbs (the difference between short action and long action weights).

Before nit-picking the rifle weights, look at the graph and the estimated most effcient velocity. Changing the rifle weights had barely any impact on the results:



All of the predicted MEVs are within 3% of the prediction when I used 8 lbs for all rifle weights. 168 gr increased from 3,013 fps to 3105 (+3%). 180 gr increased from 2,949 to 3,033 (+2.8%) and 200 gr increase from 2,934 to 2,983 (+1.6%). So using reasonable variation in rifle weights barely changes the results. The peak shift to the right (higher velocity) because the short action/barrel rifles are lighter than the original analysis so they look worse on the y-axis while the magnum action rifles are heavier so they look better.

Now, I still maintain that it is more appropriate to perform this analysis using same weight rifles. The whole point of this exercise is to evaluate the tradeoffs when shooting a bullet farther. A heavier rifle reduces recoil but now the shooter has to hump that heavier rifle around. The heavier rifle is just reducing the "recoil cost" and increasing "carrying cost."

 

[wombat13]

Range per recoil is a metric which makes sense - assuming we ignore the subjective choices for rifle weight and impact velocity minima. But then you’ve proposed the subsequent analysis of “range per recoil per velocity” - what’s the premise for this new divisor?

So if range per recoil makes sense and we know that it will vary with muzzle velocity, why would it not make sense to look at how it varies with muzzle velocity?

 

[wombat13]

I'm going to do .338 cal next. Based on the BCs and SD of the Accubonds, the multi-variate regression predicts that the most efficient velocities should range from about 2,800 fps for the 300 gr bullet to a little over 3,000 fps for the 180 gr bullet. This should be interesting (to me at least).

 

[wombat13]

So here's the chart for .338 cal. I used the same process above with 8 lb rifles.



The cartridges included are: 338 Fed (up to 225 gr), 338-06 (up to 250 gr), 338WM, 340 wby, 338 lapua, 33 nosler, 338 rum, 338-378 wby. First, a couple caveats: the 33 Nosler velocities seem high when compared to Hodgdon data. Since that is a Nosler round and I[m using Nosler load data, I wouldn't be surprised if those velocities are optimistic. I did notice that Fed, -06, and WM were 24" barrels while 33 Nosler and the rest were 26" barrels. I could knock 50 fps off the 33 Nosler and run this again.

Second, notice that the curves for 250 gr and 300 gr are cut off on the right. 300 gr in particular, there aren't any common .338 cartridges that shoot that bullet fast enough.

So how did the multi-variate regression do predicting the most efficient velocity based solely on the bullets' BCs and SDs? Pretty darn good, except for the 300 gr. Here is the data:

180 gr: MV regression - 3022 fps; Graph curve - 3038 fps (-0.5% difference)
200 gr: MV regression - 2970 fps; Graph curve - 2956 fps (+0.5% difference)
225 gr: MV regression - 2985 fps; Graph curve - 2974fps (+0.4% difference)
250 gr: MV regression - 2891 fps; Graph curve - 2931 fps (-1.4% difference)
300 gr: MV regression - 2802 fps; Graph curve - 2693fps (+4.0% difference)

That looks very good to me. I think the larger delta for 300 gr bullet (4% difference) is likely the result of the curve being cut off. We don't really know where the efficiency begins to drop.

.338-06 performs well up to 200 grain bullets. 33 nosler does well up to 225 grain bullets (with the caveat that maybe the velocities are a bit optimistic; I still think it will perform well even if I knocked 50 fps off). 338 RUM shines with 225 gr and 250 grain bullets, and 338 lapua is best with 250 and 300 grain bullets. 340 wby makes a surprise excellent showing with the 300 gr bullet.

 

[Varminterror]

So if range per recoil makes sense and we know that it will vary with muzzle velocity, why would it not make sense to look at how it varies with muzzle velocity?

I don’t believe it does - because what is the point of punishing fast flying cartridges which would otherwise have satisfactory YIELDS (not efficiency) in the Y axis metric?

Again, we’re talking (f(x)/g(x))/x - if you want to evaluate d(f(x)/g(x))/dx, then the incremental slopes of the curves should have meaning. So what’s the meaning here?

Say we have a 22-250 which has a short effective range because of its low BC and low recoil, and a 300win mag, with a long effective range and a lot of recoil. The proportionality of range/recoil yield might be very similar. But the much higher velocity 22-250 will have a different position on the chart, and significantly different slopes as the proportionate change for various bullet weights, shifting, say, 300fps, is much more significant in a 2900fps cartridge than a 3500fps cartridge… we’d kind of reverted back to the problem in which we don’t really have great relevance for field application in the Y axis - because a 22-250 could be very similar to a 300win mag in Y value, but then naturally there’s a difference in proportionate change of velocity per bullet weight change…

When we compare those two curves, the integrated slopes of each, what do we know that we didn’t before? What does the differential analysis of range per recoil per velocity actually show?

Feels a lot like plotting scatters of a group of people, based on shoe size / pant size / height.

 

[wombat13]

I don’t believe it does - because what is the point of punishing fast flying cartridges which would otherwise have satisfactory YIELDS (not efficiency) in the Y axis metric?

Again, we’re talking (f(x)/g(x))/x - if you want to evaluate d(f(x)/g(x))/dx, then the incremental slopes of the curves should have meaning. So what’s the meaning here?

Say we have a 22-250 which has a short effective range because of its low BC and low recoil, and a 300win mag, with a long effective range and a lot of recoil. The proportionality of range/recoil yield might be very similar. But the much higher velocity 22-250 will have a different position on the chart, and significantly different slopes as the proportionate change for various bullet weights, shifting, say, 300fps, is much more significant in a 2900fps cartridge than a 3500fps cartridge… we’d kind of reverted back to the problem in which we don’t really have great relevance for field application in the Y axis - because a 22-250 could be very similar to a 300win mag in Y value, but then naturally there’s a difference in proportionate change of velocity per bullet weight change…

When we compare those two curves, the integrated slopes of each, what do we know that we didn’t before? What does the differential analysis of range per recoil per velocity actually show?

Feels a lot like plotting scatters of a group of people, based on shoe size / pant size / height.

I wasn't ignoring your post (I'm sure you've been waiting anxiously for my response /sarc); Just got very busy with work and family. First off, the analysis I've been doing is completely irrelevant to a cartridge like .22-250. The whole point of the analysis is to recognize the tradeoff between range and recoil. A .22-250 maxes out at about 7 ft-lbs of recoil so most adults aren't going to be concerned about the recoil. This analysis is most relevant for 6.5mm and larger because that is where recoil starts to become objectionable for the typical shooter using an average weight rifle. The analysis also is less relevant for big bore cartridges meant to stop dangerous game. Performance required to prevent hunter fatality/injury far outweighs concerns with recoil.

Now, what is the point of punishing fast flying cartridges? The point is that those cartridges are themselves punishing to the shooter. Within a given performance window, why not identify the cartridge that is likely to generate the least recoil?

I think the way to use this analysis would be as follows. Determine what bullet weight and diameter you think is required for the game you plan to hunt. Next, evaluate cartridges that will launch that bullet between 2,900 - 3,100 fps (this is the relevant window for Nosler Accubonds and Ballistic Tips; it may be slightly different for a different bullet). We actually can narrow the range down based on the bullet's BC and SD. Will any of those cartridges meet your minimum range requirements? If yes, you're done because anything launching the bullet faster will offer a bad trade-off in range/recoil because the recoil is increasing faster than the range. There is no reason to look at cartridges that launch the bullet slower than 2,900 fps because they always offer a bad trade-off in recoil/range (because the range decreases faster than the recoil). If there is no cartridge that launches your chosen bullet in the "efficient" velocity window AND meets your minimum range requirement, then you will have to consider a cartridge that launches it faster than the "efficient" window, knowing that you will be dealing with rapidly increasing recoil as you increase velocity.

The table below offers an example using cartridges that lie on the curve in the graph of 180 grain 30 cal bullet. The .300 savage fires the bullet at 2,360 fps generating 14.8 ft-lbs of recoil, but the bullet will drop below 2,200 fps at only 98 yards. By moving up to .30-06,the shooter will deal with 10 ft-lbs more recoil, but the "effective" range increases by 236 yards! In percentage terms, the .30-06 increases the effective range by 241% but the recoil only increases by 66%. Moving up from .30-06 to .300RCM increases range by 16% but recoil by only 9%; still a favorable trade-off. Moving from .300RCM to .300 H&H is about break-even; recoil and range increase about the same in percentagoe terms. Moving up from .300 H&H to 30 Nosler increases range by 18% but recoil by 27%; not a favorable trade-off and only worth it if you really need the extra range.