Inspired by Varmint AL great pages I have used finite element method for couple of gun projects. FEA is actually what I do for a living so I'm familiar with these powerful calculation tools.

First I was a bit skeptical with accuracy of transient FEM if one were to use it in real design analysis. So initially I made some analyzes just to study general phenomena. That's of course area where FE-analysis works fine in any case.

Then something happened that changed my mind. About a year ago I ordered combination gun from my gunsmith and when I got it the rifle barrel was shooting like a shotgun. Vertical spread of 8 MOA or so! It was custom design; rifle barrel on top and shotgun below. Rifle barrel was totally free floating. I used FEA to model the gun and it pretty much explained what the problem was. We redesigned it and the problem disappeared. However at the same time there was another problem as well. Since rifle barrel was free floating there was no mechanical way to zero these two barrels relative to each other. As you you might expect when gun was zeroed for rifle it was not for shotgun. Then I used FEA (for internal ballistics) to estimate point of impacts for both barrels. External ballistics side I calculated with bfx. It turned out that my calculations were pretty much perfect match with range results! That was quite a surprise for me since this FEA analysis for barrel vibrations and gun launch dynamics is really pretty complicated. We had to make drastic changes to gun design anyway to solve the accuracy issues explained earlier so I thought, what the hell, I could actually calculate how these barrels should be installed (angled relative to each other) and rifle barrel could still be free floating. And so I did. And once again the calculations were perfect match with range testing, and this time I could use same scope zero settings for both barrels. All this can of course be just luck but at least it looks promising for these calculations.

Okay, but how this all is related to "barrel profile optimization with FEM" mentioned in the title. We are getting there. My long range rifle barrel's life is coming to an end. So in a year or so it's time to rebarrel. I thought I could use FEA to optimize barrel profile and see how it compares to real range testing this time. I don't know if you are familiar with ladder test but in short idea is to find load where vertical spread due to muzzle velocity variation is minimized. Traditionally ladder test is done by load testing. At least in theory it could be done by calculations as well. I have attached below couple of pictures which should explain it.

There is same kind of charts on Varmint AL's pages. It is result of barrel vibration calculation of my long range gun with old or current barrel profile. It shows where barrel swings the bullet (blue and green balls) with two different shots within my normal load's muzzle velocity variation. Both bullets start pretty much same angle so barrel vibration does not increase or compensate vertical spread which is due to muzzle velocity variation. This is in line with my range diary which tells me that vertical spread is always in line with measured muzzle velocity variation for various ranges (800 - 1100 m) where most part of vertical spread comes from MV variation. This is not enough to validate model but at least it doesn't disprove it.

This is picture from optimized barrel profile. Slower bullet leaves later from muzzle and also jumps higher. This should compensate MV variation. Same phenomenon happens when long range accuracy load is found with ladder test. New barrel is going to be somewhat longer and that's why muzzle velocities are higher and barrel times longer. As you can see I tried to find a profile that places exit times in the middle of upward slope which is the compensation area. This should give some margin for varying loads and accuracy of analysis itself. By the way these barrel times are defined with quick load, targeting OBT window (

http://www.the-long-family.com/OBT_paper.htm).

Okay what's the gain? This picture shows that with new profile MV variation spread is fully compensated on 420 meters. It's not possible to get full compensation for all ranges but for only one. For same reason ladder test should be done for the same range you are competing with the rifle. Anyways in this case the compensation is only good for longer ranges. New barrel could actually shoot higher groups for ranges shorter than 200m than the old barrel. Not a problem because this rifle is mainly for long range use. But for example in 800 meters vertical spread could be about half of the old profile. Okay we'll see how these calculations hold against real life testing...