How are you determining the difference in shaft friction between the FMJ and Axis? I assume you're doing so based on one feeling smoother to the touch than the other. I've never seen any arrow manufacturer publish coefficient of friction or surface roughness values.
Was the point/head geometry exactly the same for both arrows? I'm guessing not since they were different weights. I've anecdotally noticed penetration differences shooting different-shaped field points (tapered, bullet, bulb, etc) into targets, and I'm sure we would all agree that broadhead shape has a major effect on penetration.
Were both arrows the same static spine? If so, their dynamic behavior (bending during the shot) will be different, which is the inherent challenge when trying to isolate the effect of FOC alone. ±50 gr of point weight probably won't majorly alter dynamic behavior, but it's conceivable that a sufficiently large change in point weight (not compensated for by also changing spine and/or re-tuning) could negatively affect arrow flight and possibly reduce penetration.
What was the sample size of your test? What were the min/max/average penetration values? Inconsistency of the target medium is bound to introduce some variation, so I'd want a large sample size if I were trying to test penetration and draw conclusions.
Your claim about friction vs. FOC may well be valid, but I don't think your test is quite as conclusive as you're presenting it to be.
Sample size, roughly 30 shots or so a week with this group over two months.
Friction difference, aluminum vs weaved bare carbon. You can feel the difference both on pulling and by running them through a gripped hand. Its significant enough a scale would read it.
Static spine, they are the same spine from the factory. I shoot through paper at about 8 feet, 12 yards or so. In flight its 125 vs 175 (as well as a third group with 150 up front. for these tests) So in flight is "Paper good"
Penn numbers. I never even bothered to put a ruler on it. It was so consistent there was no need. Outside an arrow hitting the odd soft spot the results were the same every time. FMJ 125, Axis with 175 up front. Axis with 150s and lock washer up front.
Points. In the picture the fmj has a huge 125 kudu field point that stops pen in foam. The axis has a 100g. I also used bullet points.
I actually posted this test elsewhere in greater depth. The results are repeatable to a fault. I got called out on the fmj being a 3 fletch (done to keep the weight even) and built a 4 fletch to repeat the test in case it was an issue with friction in flight or spinning. Made zero difference.
Short version i built three sets of arrows to be the same weight with three different broadheads (Turkey, deer, moose) And did this test while shooting them over a couple months. Then i chewed up one foam target doing broadhead tests for poi.
(pic arrow is a little crusty it was thrown together only for the test)
Again they do not act the same pushing weight in a canvas field bag. It is near impossible to get a fair comparison but pushing folded cloth the 150s seem to have the edge. But again, thats near impossible to say 100% and is prob close to the odds of a coin flip.