Every so often a post pops up here about barrel fluting, and there's always a lot of speculation. I am an engineer and I love shooting, so when time allows I try to combine the two. I did a study using what is called Finite Element Analysis, or FEA. I am trying to show a comparison between fluted and unfluted versions of an otherwise identical barrel. I modeled a barrel using Bartlein's MTU specs. I took some modeling liberties that may not be perfect, for example I let the flutes run the full length of the barrel and I only constrained the rear face of the barrel (rather than constraining the threaded length of the barrel). I think for comparison these are decent assumptions.
The first picture is just specifics about the models:
The next picture shows the first natural frequency of the two models. Natural frequency is a function of the stiffness and mass. The fluted barrel is not as stiff, but it's also lighter, so the end result is the first natural frequency is almost identical (1% lower frequency for the fluted barrel):
The last picture shows the bending stiffness of the two barrels under a cantilever load at the tip. The unfluted barrel 21.1% stiffer than the fluted barrel.
I think the second picture is the one that's most important to us from an accuracy standpoint, as we don't often deliberately try and bend our barrels. We are more concerned with the harmonics I think.
These are just a few data points. The results would certainly change if I looked at different contours, lengths, flute depths, etc. When time allows I'd like to do a comparison looking at heat transfer to show the affect of flutes there.
The first picture is just specifics about the models:

The next picture shows the first natural frequency of the two models. Natural frequency is a function of the stiffness and mass. The fluted barrel is not as stiff, but it's also lighter, so the end result is the first natural frequency is almost identical (1% lower frequency for the fluted barrel):

The last picture shows the bending stiffness of the two barrels under a cantilever load at the tip. The unfluted barrel 21.1% stiffer than the fluted barrel.

I think the second picture is the one that's most important to us from an accuracy standpoint, as we don't often deliberately try and bend our barrels. We are more concerned with the harmonics I think.
These are just a few data points. The results would certainly change if I looked at different contours, lengths, flute depths, etc. When time allows I'd like to do a comparison looking at heat transfer to show the affect of flutes there.