Home Forums Hunting & Shooting Hunter's Campfire relative throat erosion, .22 vs 6mm

Classic interior ballistics literature has long pointed out that at any given peak pressure (60,000 lb/sq in. in each barrel, for example), a .224 barrel erodes faster than a 6mm barrel, which in turn erodes faster than a .308 barrel, under the same situation and circumstances � rate of fire, cooling intervals between firings, and such.<P>It's even long-known that the difference lay in a discrete mathematical ratio � expressed in two ways:<BR>� the ratio of the circumference of the bore's cross-section to the area of its cross-section<BR>� the ratio of the surface of the bore to the volume of the bore, with a given length of rifled bore<P>"These ratios" are the same ratio expressed two ways.<P>Now with Mathcad's help, I've just run, in a few minutes, what would've taken me hours and hours to do with a calculator (and days to get for-sure RIGHT).<P>I ran the equations through Mathcad, for a .224 barrel and a 6mm barrel, both with 24 inches of rifled bore. I knew already that the .224 would erode faster but didn't know exactly HOW MUCH faster. Now I know.<P>The surface of 24 inches of a .224 barrel is 16.889 sq in. Its volume is 0.946 cu in., for a surface-to-volume ratio of 17.853-to-1.<P>The surface of 24 inches of a .244 barrel is 18.397 sq in. Its volume is 1.122 cu in., for a surface-to-volume ratio of 16.397-to-1.<P>The .224's ratio is 8.9% greater than the 6mm's, which means that the .224 erodes 8.9% faster than the 6mm at the same peak pressure, with all other conditions the same.<P>Now you know too. (Oh, that's OK � no charge! �o)<P>Mathcad has really opened up and shone light into a passel of dark corners here! Ain't it fun, learning something new 'n' useful? <P>

Ken, This math Cad looks like it could be a lot of fun and quite useful to folks in my line of work. Recently I was in your neighbor hood at a friends alfalfa farm designing a new sprinkler system. He lives a mile or so from a reloading plant and log home manufacturer. Bought the place from some guy who was a welder and local curmudgeon.<BR>Any way looks to me that simply quantifying barrel erosion to a ratio may have some usefulness if you have a baseline to compare your findings too. I envision this formula as being similar to the Hazen Williams formula used to calculate friction loss in pipe.<BR>The problem with these sort of formulas when making comparisons, as you pointed out, is that all factors must be equal. If you try to compare a Sako barrel to a Ruger there are variables that will skew your results such a composition of barrel materials rifling depth and width etc.. If you have a control sample of say several barrels identical in make composition and length in various calibers then comparisons can be made against your baseline to see who makes the best barrel and it can be quantified as a ratio. <BR>Wouldn't that be fun to do? And expensive.<BR>I bet there is not a barrel manufacturer out there that would be willing to fund an independent study that would show who's barrel lasts the longest.<BR>This kind of math is fun and can be useful if applied to real world problems such as barrel erosion. Of course it can lead to statistics that are subject to interpretation and we all know where that<BR>go's.<BR>I want a copy of math cad looks like fun to me.<P>Bullwnkl.

Bull, I'm not sure I should even speak to you, you ol' scoundrel, after you were here in the valley and didn't drop by for a spell. That's nudging awful close to unforgivable sin.<P>The practical value of such notes as the relative erosion rates is much greater than you imply in your post. I'm reminded of something a bit like this from my days as a wildlife biologist � the immense value of knowing the population TREND in a certain elk herd, for example. It isn't necessary or even all that useful to know the actual NUMBERs of the population, down to the last animal, if you can keep a good eye on the trend of that population. You know what the environment is like, how the habitat is doing with approximately x,000 elk. A trend count that indicates about a ten-percent increase, say, is good enough to help you decide other matters relating to the size of that population. It doesn't matter so much whether the base population you started with was x,000, x,050, or even x,100 individual elk. They're not going to be managed or marketed like livestock. They have to be managed as an entity of an approximate size, not as a property asset.<P>The value of this erosion relationship to a designer, or to a shooter comparison-shopping for a cartridge choice, is not so much how much more or less rapidly Chet's barrel erodes than Charlie's barrel, but how much faster or slower A barrel WOULD erode IF IT WERE another caliber, in any lifetime of shooting. There's no point in studying the effects of any factor, in any field, if you don't at least try to isolate it to see what its effects are, apart from the effects of other factors.<P>The value lies in knowing which factors influence erosion, and how. With that nailed down, one can then go on to study another factor by isolating it.<P>One of my next studies, for example, will be to find out whatever I can about how much of a difference the level of maximum pressure affects erosion. I know qualitatively that peak pressures around 60,000 lb/sq in. erode throats faster than peak pressures around 50,000 lb/sq in. But HOW MUCH FASTER, I don't know. To find out, it'll be necessary to look into the matter in terms of how maximum pressure affects erosion when all other factors are identical � in a single given bore size, for example. "When all other factors are identical" is a term of comparative conditions, not what we know or expect typical life situations to be like.<P>It's one thing that makes the task of designing an experiment so tough. And so vital.<BR>

Ken, I agree with your assement of my post to you. How ever you point out the difficulty in setting up expirments. There is also the difficulty in utilizing the data you have developed. One tool in this process is developing a baseline or control inorder to have a comparison of factors for future observation. Comparing the effect of 50,000 psi to 60,000 would show the relative difference and by using your comparitive ratio one could have a basic idea of what effects of the number of shots fired at a given pressure will have on ones barrel. Perhaps this is of greater value to the average shooter than a long and drawn out process that may in fact just varify what you have developed through mathmatics.

Oops' pushed the wrong key and didn't finish.<BR>I would like to meet you in person, it would be an honor. I Plan a trip over to your neighborhood this fall. I usually bring a gallon or so of fresh oysters. Should you be so inclined to join us in an evening of oysters, steak and stimulating Bovine Scatology it would be a pleasure.<P>Jim Tobey<P>Bullwnkl.

Ken, seems the last post I sent your way is gone, didn't make it, lost to the cyber gods.<BR>any way I agree with you as to my assesment of your comparative annylisis. I was trying to point out that this sort of information is a good starting point in developing hypothesis and creating more specific experiments. One must start some place, and have a direction to go when experimenting. You could end up like Leonardo's steam engine, an experiment that proves the power of an expanding gas, but that was all. No practile use (at that time). <BR>For the matter of me being in your back yard I intend to be back over this fall. I would feel it an honer to meet you. I usually bring along a gallon or two of fresh oysters. My buddy needs his sea food fix. It would be a pleasure to get together with you and yours and have a sit down of oysters, steaks and a good modicum of Bovine Scatology.<P>Bullwnkl.<P>Jim Tobey

now it shows up....<P>Bull....

Jim, ol' buddy, you still don't get it. This information is far more useful and practical than you think � but let's let it lie for here and get it clear when you show up here for some Basic Stuff.<P>Cheers!

Ken: Looking at the exhibited numbers, it appears they apply to a smoothbore. Don't have MathCad handy, just a calculator. How far behind the decimal point would rifling affect those numbers? Thanks

This is a matter of ratios. Rifling, absent or present, is practically irrelevant. Throats don't have much rifling anyway.<P>The ratio of (a) the circumference of the cross-section of the bore to (b) the area of the cross-section determines the rate of erosion (as far as the bore dimensions are concerned). Stated another way, it's the ratio of (a) the surface area of the bore to (b) the volume of the bore. Since length is common to both the surface area and the volume of the bore, length cancels itself out of the ratio.<P>Call this ratio C/A for the ratio of circumference to area, or S/V for surface to volume. The C/A for a .224 barrel is larger than the C/A for a .244 barrel, which is larger than the C/A for a .257 barrel, etc. The C/A for a .375 barrel is minute compared to the C/A for a .224 barrel.<P>The larger the C/A, the faster the heat transfer from the powder gas into the steel. <BR>The larger the C/A, the faster the erosion at a given peak pressure. To compare the innate erosion rates of any two calibers of barrel, the ratio is (c/a)/(C/A) when c/a is the ratio for the smaller bore and C/A for the larger.<P>The barrel-makers' rule of thumb for rifling is that the lands occupy 25% of the circumference of the bore, grooves 75%. Grooves are so shallow � lands so low � and their widths are proportional � it's practical to ignore rifling in calculating these ratios.<BR>

Evening Ken, this is just a thought that you may entertain on your computer: with all factors equal the velocity of projectiles of the same weight but of different diameters fired at equal pressures should differ by the ratio of the bore diameters to surface area. Rifling will cancel it self out with all factors equal. of course frontal area and atmospheric resistance comes into play but that too can be factored as a ratio, now see what you have done, my head hurts. <BR>I hope you didn't get the Idea that I was saying your explanation of ratios is incorrect. I was trying to say that using such a program to examine many different barrel materials through comparison would provide useful information the basis of which is the method you explained. This is just a tangent from the original idea.<P>Bullwnkl.<P>Jim

OK I just turned my confuser off when it struck me, BAM... what you are getting at is the number of events, firings, that need to occour to erode a predetermined amount of material from a barrel. So a .224 will erode 8.9% faster than a .244. This means it takes 8.9% less firings to erode an equal amount of material from the smaller bore than it does the larger bore. It's the number of firings that equal time. Wow what a dunderhead I was in not seeing this to begin with. Can I go to bed now?<P><BR>Bullwnkl.

Whwn your head feels better, take note of the fact that x plus 8.9% = y is not the same as y minus 8.9% = x.<P>Now take another Tylenol and go back to bed while I head over east of the Divide to help a bunch of writers shoot prairie dogs. They can't do without me � I'm the designated misser for the crowd (I do all the missing, which enables them to ........ )